[ { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Bettina chooses five points $A, B, C, D$ and $E$ on a circle and draws the tangent to the circle at point $A$. She realizes that the five angles marked $x$ are all equally big. (Note that the diagram is not drawn to scale!) How big is the angle $\\angle A B D$?\n\\n Options: A. $66^{\\circ}$, B. $70.5^{\\circ}$, C. $72^{\\circ}$, D. $75^{\\circ}$, E. $77.5^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/290.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows two squares: one has a side with a length of 2 and the other (abut on the first square) has a side with a length of 1. What is the area of the shaded zone?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/166.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Monika wants to find a path through the labyrinth from 'Start' to 'Ziel'. She has to stick to the following rules: She is only allowed to move horizontally and vertically respectively. She has to enter every white circle exactly once but is not allowed to enter a black circle. In which direction does Monika have to move forwards when she reaches the circle marked with $x$ ? \\n Options: A. $\\downarrow$, B. $\\uparrow$, C. $\\rightarrow$, D. $\\leftarrow$, E. there are several possibilities", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/997.png" }, { "solution": "\\boxed{54}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of $\\triangle ABC$ is 6 square centimeters. $\\overline{AB}\\|\\overline{DE}$. $BD=4BC$. What is the number of square centimeters in the area of $\\triangle CDE$? ", "completion": "\\boxed{54}", "image_path": "dataset/math_vision/images/3037.png" }, { "solution": "\\boxed{33}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An artist has $14$ cubes, each with an edge of $1$ meter. She stands them on the ground to form a sculpture as shown. She then paints the exposed surface of the sculpture. How many square meters does she paint?\n", "completion": "\\boxed{33}", "image_path": "dataset/math_vision/images/2533.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many routes are possible for the king to travel from the top left square to the bottom right square of the grid with the minimum number of moves. (The king can move to any adjacent square, including that adjacent diagonally.)\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1301.png" }, { "solution": "\\boxed{84}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Quadrilateral $QABO$ is constructed as shown. Determine the area of $QABO$. ", "completion": "\\boxed{84}", "image_path": "dataset/math_vision/images/2958.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Circle $C_1$ and $C_2$ each have radius $1$, and the distance between their centers is $\\frac{1}{2}$. Circle $C_3$ is the largest circle internally tangent to both $C_1$ and $C_2$. Circle $C_4$ is internally tangent to both $C_1$ and $C_2$ and externally tangent to $C_3$. What is the radius of $C_4$?\n\n\\n Options: A. $\\frac{1}{14}$, B. $\\frac{1}{12}$, C. $\\frac{1}{10}$, D. $\\frac{3}{28}$, E. $\\frac{1}{9}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2254.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle of radius $4 \\mathrm{~cm}$ is divided, as shown, by four semicircles with radius $2 \\mathrm{~cm}$ into four congruent parts. What is the perimeter of one of these parts?\n\\n Options: A. $2 \\pi$, B. $4 \\pi$, C. $6 \\pi$, D. $8 \\pi$, E. $12 \\pi$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1336.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A river goes through a city and there are two islands. There are also six bridges how it is shown in the attached image. How many paths there are going out of a shore of the river (point $A$ ) and come back (to point $B$ ) after having spent one and only one time for each bridge?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/740.png" }, { "solution": "\\boxed{64}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: This figure is made of squares. What is the side of the biggest square?\n", "completion": "\\boxed{64}", "image_path": "dataset/math_vision/images/411.png" }, { "solution": "\\boxed{81}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Toninho wants to write strictly positive and consecutive whole numbers, in the nine places of the figure, so that the sum of the three numbers in each diameter is equal to 24. What is the largest possible sum for all the nine numbers?\n", "completion": "\\boxed{81}", "image_path": "dataset/math_vision/images/1442.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An isosceles triangle is a triangle with two sides of equal length. How many of the five triangles on the square grid below are isosceles?\n\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/2523.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Inside a unit square a certain area has been coloured in black. In which square is the black area biggest?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1428.png" }, { "solution": "\\boxed{792}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a game of Chomp, two players alternately take bites from a 5-by-7 grid of unit squares. To take a bite, a player chooses one of the remaining squares, then removes (\"eats'') all squares in the quadrant defined by the left edge (extended upward) and the lower edge (extended rightward) of the chosen square. For example, the bite determined by the shaded square in the diagram would remove the shaded square and the four squares marked by $\\times$. (The squares with two or more dotted edges have been removed form the original board in previous moves.)\n\n\nThe object of the game is to make one's opponent take the last bite. The diagram shows one of the many subsets of the set of 35 unit squares that can occur during the game of Chomp. How many different subsets are there in all? Include the full board and empty board in your count.", "completion": "\\boxed{792}", "image_path": "dataset/math_vision/images/2054.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In which picture are there more black Kangaroos than white ones?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/499.png" }, { "solution": "\\boxed{770}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One commercially available ten-button lock may be opened by depressing -- in any order -- the correct five buttons. The sample shown below has $\\{1, 2, 3, 6, 9\\}$ as its combination. Suppose that these locks are redesigned so that sets of as many as nine buttons or as few as one button could serve as combinations. How many additional combinations would this allow?\n\n", "completion": "\\boxed{770}", "image_path": "dataset/math_vision/images/2046.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Simon runs along the edge round a $50 \\mathrm{~m}$ long rectangular swimming pool, while at the same time Jan swims lengths in the pool. Simon runs three times as fast as Jan swims. While Jan swims 6 lengths, Simon manages 5 rounds around the pool. How wide is the swimming pool?\n\\n Options: A. $25 \\mathrm{~m}$, B. $40 \\mathrm{~m}$, C. $50 \\mathrm{~m}$, D. $80 \\mathrm{~m}$, E. $180 \\mathrm{~m}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1172.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shows a map with some islands and how they are connected by bridges. A navigator wants to pass through each of the islands exactly once. He started at Cang Island and wants to finish at Uru Island. He has just arrived at the black island in the center of the map. In which direction must he go now to be able to complete his route?\n\\n Options: A. North., B. East., C. South., D. West., E. There is more than one possible choice", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/937.png" }, { "solution": "\\boxed{4+\\sqrt{2}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each triangle in this figure is an isosceles right triangle. The length of $\\overline{BC}$ is 2 units. What is the number of units in the perimeter of quadrilateral $ABCD$? Express your answer in simplest radical form.\n\n", "completion": "\\boxed{4+\\sqrt{2}}", "image_path": "dataset/math_vision/images/2921.png" }, { "solution": "\\boxed{46}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture you can see a number flower. Mary pulled out all the leaves with numbers which give remainder 2 when divided by 6. What is the sum of the numbers on the leaves that Mary pulled out?\n", "completion": "\\boxed{46}", "image_path": "dataset/math_vision/images/433.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four cogs are connected to each other as shown in the picture. The first has 30 teeth, the second 15, the third 60 and the fourth 10 . How many turns will the last cog make for each full turn of the first cog?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/812.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jilly makes up a multiplication magic square using the numbers $1,2,4,5,10,20,25,50$ and 100. The products of the numbers in each row, column and diagonal should be equal. In the diagram it can be seen how she has started. Which number goes into the cell with the question mark?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1397.png" }, { "solution": "\\boxed{62.8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure below consists of four semicircles and the 16-cm diameter of the largest semicircle. What is the total number of square cm in the area of the two shaded regions? Use 3.14 as an approximation for $\\pi$, and express your answer as a decimal to the nearest tenth.\n\n", "completion": "\\boxed{62.8}", "image_path": "dataset/math_vision/images/2907.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which two building blocks can be joined together so that the object shown is created?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/375.png" }, { "solution": "\\boxed{44}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anna uses 32 small grey squares to frame a $7 \\mathrm{~cm}$ by $7 \\mathrm{~cm}$ big picture. How many small grey squares does she have to use to frame a $10 \\mathrm{~cm}$ by $10 \\mathrm{~cm}$ big picture?\n", "completion": "\\boxed{44}", "image_path": "dataset/math_vision/images/616.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows two rectangles whose corresponding sides are parallel as shown. What is the difference between the lengths of the perimeters of the two rectangles? \\n Options: A. $12 \\mathrm{~m}$, B. $16 \\mathrm{~m}$, C. $20 \\mathrm{~m}$, D. $22 \\mathrm{~m}$, E. $24 \\mathrm{~m}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1639.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram we see a cube and four marked angles. How big is the sum of those angles?\n\\n Options: A. $315^{\\circ}$, B. $330^{\\circ}$, C. $345^{\\circ}$, D. $360^{\\circ}$, E. $375^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1400.png" }, { "solution": "\\boxed{33}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $ABC$ has right angle at $B$, and contains a point $P$ for which $PA = 10$, $PB = 6$, and $\\angle APB = \\angle BPC = \\angle CPA$. Find $PC$.\n\n", "completion": "\\boxed{33}", "image_path": "dataset/math_vision/images/2044.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consider the two touching semicircles with radius 1 and their diameters $A B$ and $C D$ respectively that are parallel to each other. The extensions of the two diameters are also tangents to the respective other semicircle (see diagram). How big is the square of the length $A D$ ? \\n Options: A. 16, B. $8+4 \\sqrt{3}$, C. 12, D. 9, E. $5+2 \\sqrt{3}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1497.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shows graphs of functions $f$ and $g$ defined on real numbers. Each graph consists of two perpendicular halflines. Which equality is satisfied for every real number $x$?\n\\n Options: A. $f(x)=-g(x)+2$, B. $f(x)=-g(x)-2$, C. $f(x)=-g(x+2)$, D. $f(x+2)=-g(x)$, E. $f(x+1)=-g(x-1)$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/175.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The ratio of the radii of two concentric circles is $1: 3$. The line $A C$ a diameter of the biggest circle. A chord $B C$ of the big circle touches the small circle (see diagram). The line $A B$ has length 12. How big is the radius of the big circle?\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/265.png" }, { "solution": "\\boxed{12.6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The big wheel of this penny-farthing bicycle has perimeter 4.2 metres. The small wheel has perimeter 0.9 metres. At a certain moment, the valves of both wheels are at their lowest points. The bicycle begins to roll.\nHow many metres will the bicycle have rolled forward when both valves are next at their lowest points at the same time?\n", "completion": "\\boxed{12.6}", "image_path": "dataset/math_vision/images/1898.png" }, { "solution": "\\boxed{500}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square corners, $5$ units on a side, are removed from a $20$ unit by $30$ unit rectangular sheet of cardboard. The sides are then folded to form an open box. The surface area, in square units, of the interior of the box is\n\n", "completion": "\\boxed{500}", "image_path": "dataset/math_vision/images/2568.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the cube $ABCDEFGH$ with opposite vertices $C$ and $E,$ $J$ and $I$ are the midpoints of edges $\\overline{FB}$ and $\\overline{HD},$ respectively. Let $R$ be the ratio of the area of the cross-section $EJCI$ to the area of one of the faces of the cube. What is $R^2?$\n\n\\n Options: A. $\\frac{5}{4}$, B. $\\frac{4}{3}$, C. $\\frac{3}{2}$, D. $\\frac{25}{16}$, E. $\\frac{9}{4}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2754.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In his garden Tony made a pathway using 10 paving stones. Each paver was $4 \\mathrm{dm}$ wide and 6 dm long. He then drew a black line connecting the middle points of each paving stone. How long is the black line?\n\\n Options: A. $24 \\mathrm{dm}$, B. $40 \\mathrm{dm}$, C. $46 \\mathrm{dm}$, D. $50 \\mathrm{dm}$, E. $56 \\mathrm{dm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/460.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: These children are standing in a line. Some are facing forwards and others are facing backwards. How many children are holding another child's hand with their right hand?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/124.png" }, { "solution": "\\boxed{27000-4500\\pi}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The length of the diameter of this spherical ball is equal to the height of the box in which it is placed. The box is a cube and has an edge length of 30 cm. How many cubic centimeters of the box are not occupied by the solid sphere? Express your answer in terms of $\\pi$. ", "completion": "\\boxed{27000-4500\\pi}", "image_path": "dataset/math_vision/images/2942.png" }, { "solution": "\\boxed{400}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square fits snugly between the horizontal line and two touching circles of radius 1000, as shown. The line is tangent to the circles.\nWhat is the side-length of the square?\n", "completion": "\\boxed{400}", "image_path": "dataset/math_vision/images/2023.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four ribbons $\\mathrm{M}, \\mathrm{N}, \\mathrm{P}$ and $\\mathrm{Q}$ are wrapped around a box. In which order were they wrapped around the box?\\n Options: A. M, B. N, C. Q, D. P, E. N, F. M, G. P, H. Q, I. N, J. Q, M, P, N, M, Q, P, $Q, N, M, P$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/982.png" }, { "solution": "\\boxed{96\\pi+120}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The solid shown was formed by cutting a right circular cylinder in half. If the base has a radius of 6 cm and the height is 10 cm, what is the total surface area, in terms of $\\pi$, of the solid? ", "completion": "\\boxed{96\\pi+120}", "image_path": "dataset/math_vision/images/2965.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Where is the Kangaroo?\n\\n Options: A. In the circle and in the triangle but not in the square., B. In the circle and in the square but not in the triangle., C. In the triangle and in the square but not in the circle., D. In the circle but in neither the square or the triangle., E. In the square but in neither the circle or the triangle.", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/458.png" }, { "solution": "\\boxed{144}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the area in square inches of the pentagon shown?\n\n", "completion": "\\boxed{144}", "image_path": "dataset/math_vision/images/2962.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Erwin has got the following paper pieces:\n\nWith these four pieces he must exactly cover a special shape. In which drawing will he manage this, if the piece is placed as shown?\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/518.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square $ ABCD$ with sides of length 1 is divided into two congruent trapezoids and a pentagon, which have equal areas, by joining the center of the square with points $ E,F,G$ where $ E$ is the midpoint of $ BC$, $ F,G$ are on $ AB$ and $ CD$, respectively, and they're positioned that $ AF < FB, DG < GC$ and $ F$ is the directly opposite of $ G$. If $ FB = x$, the length of the longer parallel side of each trapezoid, find the value of $ x$.\n\\n Options: A. $\\frac{3}{5}$, B. $\\frac{2}{3}$, C. $\\frac{3}{4}$, D. $\\frac{5}{6}$, E. $\\frac{7}{8}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2435.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A sandwich and a juice cost 12 Euros together. A sandwich and two juices cost 14 Euros together. How many Euros does one juice cost?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/138.png" }, { "solution": "\\boxed{625}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shows a quadrilateral $A B C D$ in which $A D=D C$ and $\\angle A D C=\\angle A B C=90^{\\circ}$. The point $E$ is the foot of the perpendicular from $D$ to $A B$. The length $D E$ is 25 . What is the area of quadrilateral $A B C D$ ?\n", "completion": "\\boxed{625}", "image_path": "dataset/math_vision/images/2008.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four cars enter a roundabout at the same time, each one from a different direction, as shown in the diagram. Each car drives in a clockwise direction and leaves the roundabout before making a complete circuit. No two cars leave the roundabout by the same exit. How many different ways are there for the cars to leave the roundabout? ", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1606.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sam paints the 9 small squares in the shape either white, grey or black. What is the minimum number he must paint over so that no two squares sharing a side have the same colour?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/841.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The shortest path from Atown to Cetown runs through Betown. The two signposts shown are set up at different places along this path. What distance is written on the broken sign? \\n Options: A. $1 \\mathrm{~km}$, B. $3 \\mathrm{~km}$, C. $4 \\mathrm{~km}$, D. $5 \\mathrm{~km}$, E. $9 \\mathrm{~km}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1677.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows three squares of side-length $3 \\mathrm{~cm}, 5 \\mathrm{~cm}$ and $8 \\mathrm{~cm}$. What is the area, in $\\mathrm{cm}^{2}$, of the shaded trapezium? \\n Options: A. $13$, B. $\\frac{55}{4}$, C. $\\frac{61}{4}$, D. $\\frac{65}{4}$, E. $\\frac{69}{4}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1982.png" }, { "solution": "\\boxed{60}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows three triangles which are formed by the five line segments $A C D F, B C G, G D E, A B$ and $E F$ so that $A C=B C=C D=G D=D F=E F$. Also $\\angle C A B=\\angle E F D$. What is the size, in degrees, of $\\angle C A B$ ? ", "completion": "\\boxed{60}", "image_path": "dataset/math_vision/images/1775.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: North of Straße A (street A) there are 7 houses. East of Straße B (street B) there are 8 houses. South of Straße A (street A) there are 5 houses. How many houses are there West of Straße B (street B)?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/690.png" }, { "solution": "\\boxed{7.2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In parallelogram $ABCD$, $\\overline{DE}$ is the altitude to the base $\\overline{AB}$ and $\\overline{DF}$ is the altitude to the base $\\overline{BC}$. If $DC=12$, $EB=4$, and $DE=6$, then $DF=$\n\n", "completion": "\\boxed{7.2}", "image_path": "dataset/math_vision/images/2584.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The cells of the $4 \\times 4$-table on the right should be coloured either in black or white. The numbers determine how many cells in each row/column should be black. How many ways are there to do the colouring in?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1349.png" }, { "solution": "\\boxed{158}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the calculations shown, each letter stands for a digit. They are used to make some two-digit numbers. The two numbers on the left have a total of 79. What is the total of the four numbers on the right? ", "completion": "\\boxed{158}", "image_path": "dataset/math_vision/images/1948.png" }, { "solution": "\\boxed{27}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If circular arcs $ AC$ and $ BC$ have centers at $ B$ and $ A$, respectively, then there exists a circle tangent to both $ \\stackrel{\\frown}{AC}$ and $ \\stackrel{\\frown}{BC}$, and to $ \\overline{AB}$. If the length of $ \\stackrel{\\frown}{BC}$ is $ 12$, then the circumference of the circle is\n", "completion": "\\boxed{27}", "image_path": "dataset/math_vision/images/2442.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On a pond 16 lilly pads are arranged in a $4 \\times 4$ grid as can be seen in the diagram. A frog sits on a lilly pad in one of the corners of the grid (see picture). The frog jumps from one lilly pad to another horizontally or vertically. In doing so he always jumps over at least one lilly pad. He never lands on the same lilly pad twice. What is the maximum number of lilly pads, including the one he is sitting on, on which he can land?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1117.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shows a semicircle with center $O$. Two of the angles are given. What is the size, in degrees, of the angle $\\alpha$?\n\\n Options: A. $9^{\\circ}$, B. $11^{\\circ}$, C. $16^{\\circ}$, D. $17.5^{\\circ}$, E. $18^{\\circ}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1458.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $5 \\times 5$ square is made from $1 \\times 1$ tiles, all with the same pattern, as shown. Any two adjacent tiles have the same colour along the shared edge. The perimeter of the $5 \\times 5$ square consists of black and white segments of length 1 . What is the smallest possible number of black segments on the perimeter of the\n\n$5 \\times 5$ square?", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1616.png" }, { "solution": "\\boxed{$5+\\sqrt{19}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $\\vartriangle ABC$ be equilateral. Two points $D$ and $E$ are on side $BC$ (with order $B, D, E, C$), and satisfy $\\angle DAE = 30^o$ . If $BD = 2$ and $CE = 3$, what is $BC$?\\n", "completion": "\\boxed{$5+\\sqrt{19}$}", "image_path": "dataset/math_vision/images/2865.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram the circles represent light bulbs which are connected to some other light bulbs. Initially all light bulbs are switched off. If you touch a light bulb then that light bulb and all directly adjacent light bulbs switch themselves on. What is the minimum number of light bulbs you have to touch in order to switch on all the light bulbs?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/890.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Tom throws two darts at the target shown in the diagram. Both his darts hit the target. For each dart, he scores the number of points shown in the region he hits. How many different totals could he score?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1753.png" }, { "solution": "\\boxed{\\frac{\\sqrt{130}}{13}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below, $ABCDEFGH$ is a rectangular prism, $\\angle BAF = 30^o$ and $\\angle DAH = 60^o$. What is the cosine of $\\angle CEG$?\\n", "completion": "\\boxed{\\frac{\\sqrt{130}}{13}}", "image_path": "dataset/math_vision/images/2850.png" }, { "solution": "\\boxed{58}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On a standard dice, the sum of the numbers of pips on opposite faces is always 7. Four standard dice are glued together as shown. What is the minimum number of pips that could lie on the whole surface? ", "completion": "\\boxed{58}", "image_path": "dataset/math_vision/images/1697.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four identical small rectangles are put together to form a large rectangle as shown. The length of a shorter side of each small rectangle is $10 \\mathrm{~cm}$. What is the length of a longer side of the large rectangle? \\n Options: A. $50 \\mathrm{~cm}$, B. $40 \\mathrm{~cm}$, C. $30 \\mathrm{~cm}$, D. $20 \\mathrm{~cm}$, E. $10 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1619.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $ ABCD$ be a rhombus with $ AC=16$ and $ BD=30$. Let $ N$ be a point on $ \\overline{AB}$, and let $ P$ and $ Q$ be the feet of the perpendiculars from $ N$ to $ \\overline{AC}$ and $ \\overline{BD}$, respectively. Which of the following is closest to the minimum possible value of $ PQ$?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/2455.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: By shooting two arrows at the shown target on the wall, how many different scores can we obtain?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/764.png" }, { "solution": "\\boxed{84}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $\\triangle$ or $\\bigcirc$ is placed in each of the nine squares in a 3-by-3 grid. Shown below is a sample configuration with three $\\triangle$s in a line.\n\n\nHow many configurations will have three $\\triangle$s in a line and three $\\bigcirc$s in a line?", "completion": "\\boxed{84}", "image_path": "dataset/math_vision/images/2780.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Wendy wants to write a number in every cell on the border of a table.\nIn each cell, the number she writes is equal to the sum of the two numbers in the cells with which this cell shares an edge. Two of the numbers are given in the diagram.\nWhat number should she write in the cell marked $x$ ?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/1661.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shown is called a trefoil and is constructed by drawing circular sectors about sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length $ 2$?\n\\n Options: A. $\\frac{1}{3}\\pi+\\frac{\\sqrt{3}}{2}$, B. $\\frac{2}{3}\\pi$, C. $\\frac{2}{3}\\pi+\\frac{\\sqrt{3}}{4}$, D. $\\frac{2}{3}\\pi+\\frac{\\sqrt{3}}{3}$, E. $\\frac{2}{3}\\pi+\\frac{\\sqrt{3}}{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2144.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the unit circle shown in the figure, chords $PQ$ and $MN$ are parallel to the unit radius $OR$ of the circle with center at $O$. Chords $MP$, $PQ$, and $NR$ are each $s$ units long and chord $MN$ is $d$ units long.\n\nOf the three equations\n\\[ \\textbf{I.}\\ d-s=1, \\qquad \\textbf{II.}\\ ds=1, \\qquad \\textbf{III.}\\ d^2-s^2=\\sqrt{5} \\]those which are necessarily true are\\n Options: A. $\\textbf{I} \\text{only}$, B. $\\textbf{II} \\text{only}$, C. $\\textbf{III} \\text{only}$, D. $\\textbf{I} \\text{and} \\textbf{II} \\text{only}$, E. $\\textbf{I, II} \\text{and} \\textbf{III}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2306.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Points $A, B, C$ and $D$ are on a circle of diameter $1$, and $X$ is on diameter $\\overline{AD}$. If $BX=CX$ and $3 \\angle BAC=\\angle BXC=36^{\\circ}$, then $AX=$\n\\n Options: A. $\\cos 6^{\\circ}\\cos 12^{\\circ} \\sec 18^{\\circ}$, B. $\\cos 6^{\\circ}\\sin 12^{\\circ} \\csc 18^{\\circ}$, C. $\\cos 6^{\\circ}\\sin 12^{\\circ} \\sec 18^{\\circ} \\$, D. $\\sin 6^{\\circ}\\sin 12^{\\circ} \\csc 18^{\\circ}$, E. $\\sin 6^{\\circ} \\sin 12^{\\circ} \\sec 18^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2404.png" }, { "solution": "\\boxed{121}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The pattern shown in the diagram is constructed using semicircles. Each semicircle has a diameter that lies on the horizontal axis shown and has one of the black dots at either end. The distance between each pair of adjacent black dots is $1 \\mathrm{~cm}$. The area, in $\\mathrm{cm}^{2}$, of the pattern that is shaded in grey is $\\frac{1}{8} k \\pi$. What is the value of $k$ ?\n", "completion": "\\boxed{121}", "image_path": "dataset/math_vision/images/2012.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The letter M in the figure below is first reflected over the line $q$ and then reflected over the line $p$. What is the resulting image?\n\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2773.png" }, { "solution": "\\boxed{30}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $ABCD$ and equilateral triangle $AED$ are coplanar and share $\\overline{AD}$, as shown. What is the measure, in degrees, of angle $BAE$? ", "completion": "\\boxed{30}", "image_path": "dataset/math_vision/images/3029.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The sides of a triangle have lengths $6.5$, $10$, and $s$, where $s$ is a whole number. What is the smallest possible value of $s$?\n\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2559.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture $A B C D$ is a square of side 1 and the semicircles have centers on $A, B, C$ and $D$. What is the length of $P Q$?\n\\n Options: A. $2-\\sqrt{2}$, B. $\\frac{3}{4}$, C. $\\sqrt{5}-\\sqrt{2}$, D. $\\frac{\\sqrt{3}}{3}$, E. $\\sqrt{3}-1$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1321.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A naughty pup grabs the end of a roll of toilet paper and walks away at a constant speed. Which of the functions below best describes the thickness $y$ of the roll as a function of the unrolled part $x$?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/358.png" }, { "solution": "\\boxed{28}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are $n$ different prime numbers $p_{1}, p_{2}, \\ldots, p_{n}$ written from left to right on the last line below the table shown beside. The product of two neighboring numbers in the same line is written in the upper two boxes. The number $K=p_{1}^{\\alpha_{1}} \\cdot p_{2}^{\\alpha_{2}} \\ldots p_{n}^{\\alpha_{n}}$ is written in the last house above. In a table like this, in which $\\propto_{2}=9$, how many numbers are divisible by number $p_{4}$?\n", "completion": "\\boxed{28}", "image_path": "dataset/math_vision/images/349.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maddie has a paper ribbon of length $36 \\mathrm{~cm}$. She divides it into four rectangles of different lengths. She draws two lines joining the centres of two adjacent rectangles as shown.\n\nWhat is the sum of the lengths of the lines that she draws?\\n Options: A. $18 \\mathrm{~cm}$, B. $17 \\mathrm{~cm}$, C. $20 \\mathrm{~cm}$, D. $19 \\mathrm{~cm}$, E. It depends upon the sizes of the rectangles", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1740.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If this path is to continue in the same pattern:\n\n\nthen which sequence of arrows goes from point $425$ to point $427$?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2573.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square $P Q R S$ with sides of length 10 is rolled without slipping along a line. Initially $P$ and $Q$ are on the line and the first roll is around point $Q$ as shown in the diagram. The rolling stops when $P$ first returns to the line. What is the length of the curve that $P$ has travelled?\n\\n Options: A. $10 \\pi$, B. $5 \\pi+5 \\pi \\sqrt{2}$, C. $10 \\pi+5 \\pi \\sqrt{2}$, D. $5 \\pi+10 \\pi \\sqrt{2}$, E. $10 \\pi+10 \\pi \\sqrt{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1832.png" }, { "solution": "\\boxed{22}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The measure of one of the smaller base angles of an isosceles trapezoid is $60^\\circ$. The shorter base is 5 inches long and the altitude is $2 \\sqrt{3}$ inches long. What is the number of inches in the perimeter of the trapezoid? ", "completion": "\\boxed{22}", "image_path": "dataset/math_vision/images/2893.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The shape in the diagram is made up of a rectangle, a square and an equilateral triangle, all of which have the same perimeter. The length of the side of the square is $9 \\mathrm{~cm}$. What is the length of the shorter sides of the rectangle? \\n Options: A. $4 \\mathrm{~cm}$, B. $5 \\mathrm{~cm}$, C. $6 \\mathrm{~cm}$, D. $7 \\mathrm{~cm}$, E. $8 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1765.png" }, { "solution": "\\boxed{30}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangle $W X Y Z$ is cut into four smaller rectangles as shown. The lengths of the perimeters of three of the smaller rectangles are 11, 16 and 19 . The length of the perimeter of the fourth smaller rectangle lies between 11 and 19. What is the length of the perimeter of $W X Y Z$ ? ", "completion": "\\boxed{30}", "image_path": "dataset/math_vision/images/1785.png" }, { "solution": "\\boxed{65}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two rectangles with measurements $8 \\times 10$ and $9 \\times 12$ overlap to some extend. The dark grey area is 37. What is the area of the light grey part?\n", "completion": "\\boxed{65}", "image_path": "dataset/math_vision/images/776.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture above rotated. The picture below shows the new position after the rotation. Which footprints are missing after the rotation?\n\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/565.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows two tangential circles with radii in the ratio 1:2. The smaller circle rolls around the inside of the large circle. Which of the following is the path traced out by the point $P$ of the smaller circle?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1279.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A triangle $A B C$ is divided into four parts by two straight lines, as shown. The areas of the smaller triangles are 1,3 and 3. What is the area of the original triangle?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/364.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube is being rolled on a plane so it turns around its edges. Its bottom face passes through the positions $1,2,3,4,5,6$ and 7 in that order, as shown. Which of these two positions were occupied by the same face of the cube? \\n Options: A. 1 and 7, B. 1 and 6, C. 1 and 5, D. 2 and 7, E. 2 and 6", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1594.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram on the right shows a square with side $3 \\mathrm{~cm}$ inside a square with side $7 \\mathrm{~cm}$ and another square with side $5 \\mathrm{~cm}$ which intersects the first two squares. What is the difference between the area of the black region and the total area of the grey regions? \\n Options: A. $0 \\mathrm{~cm}^{2}$, B. $10 \\mathrm{~cm}^{2}$, C. $11 \\mathrm{~cm}^{2}$, D. $15 \\mathrm{~cm}^{2}$, E. more information needed", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1585.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six coins build a triangle (see picture). What is the smallest number of coins that must be moved to create the circle?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/469.png" }, { "solution": "\\boxed{23}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a special die. Each pair of numbers on opposite faces has the same sum. The numbers on the hidden faces are all prime numbers. Which number is opposite to the 14 shown?\n", "completion": "\\boxed{23}", "image_path": "dataset/math_vision/images/1900.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a shaded quadrilateral $P Q R S$ drawn on a grid. Each cell of the grid has sides of length $2 \\mathrm{~cm}$. What is the area of quadrilateral $P Q R S$ ? \\n Options: A. $96 \\mathrm{~cm}^{2}$, B. $84 \\mathrm{~cm}^{2}$, C. $76 \\mathrm{~cm}^{2}$, D. $88 \\mathrm{~cm}^{2}$, E. $104 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1604.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $ABCD$ is a square 4 inches on a side, and each of the inside squares is formed by joining the midpoints of the outer square's sides. What is the area of the shaded region in square inches?\n\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2936.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The graph relates the distance traveled [in miles] to the time elapsed [in hours] on a trip taken by an experimental airplane. During which hour was the average speed of this airplane the largest?\n\n\\n Options: A. $\\text{first (0-1)}$, B. $\\text{second (1-2)}$, C. $\\text{third (2-3)}$, D. $\\text{ninth (8-9)}$, E. $\\text{last (11-12)}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2542.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture, the three strips labelled 1,2,3 have the same horizontal width $a$. These three strips connect two parallel lines. Which of these statements is true? \\n Options: A. All three strips have the same area., B. Strip 1 has the largest area., C. Strip 2 has the largest area., D. Strip 3 has the largest area., E. It is impossible to say which has the largest area without knowing $a$.", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1801.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Equilateral triangle $ T$ is inscribed in circle $ A$, which has radius $ 10$. Circle $ B$ with radius $ 3$ is internally tangent to circle $ A$ at one vertex of $ T$. Circles $ C$ and $ D$, both with radius $ 2$, are internally tangent to circle $ A$ at the other two vertices of $ T$. Circles $ B$, $ C$, and $ D$ are all externally tangent to circle $ E$, which has radius $ \\frac{m}{n}$, where $ m$ and $ n$ are relatively prime positive integers. Find $ m + n$.\n", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/2075.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the figures below will cover the most dots when laid on the square shown on the right.\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/825.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four tangent congruent circles of radius $6 \\mathrm{~cm}$ are inscribed in a rectangle.\n\nIf $P$ is a vertex and $Q$ and $R$ are the points of tangency, what is the area of triangle $P Q R$?\\n Options: A. $27 \\mathrm{~cm}^{2}$, B. $45 \\mathrm{~cm}^{2}$, C. $54 \\mathrm{~cm}^{2}$, D. $108 \\mathrm{~cm}^{2}$, E. $180 \\mathrm{~cm}^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1043.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle is divided into 4 triangles as shown in the figure. Of the following possibilities for the areas of the triangles at most one can be true. Which one is it?\n\\n Options: A. $4,5,8,9$, B. $3,5,6,7$, C. $5,6,7,12$, D. $10,11,12,19$, E. $5,6,8,10$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1282.png" }, { "solution": "\\boxed{2\\sqrt{3}-2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, square $ABCD$ has sides of length 4, and $\\triangle ABE$ is equilateral. Line segments $BE$ and $AC$ intersect at $P$. Point $Q$ is on $BC$ so that $PQ$ is perpendicular to $BC$ and $PQ=x$. \n\nFind the value of $x$ in simplest radical form.", "completion": "\\boxed{2\\sqrt{3}-2}", "image_path": "dataset/math_vision/images/2988.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a solid with six triangular faces and five vertices. Andrew wants to write an integer at each of the vertices so that the sum of the numbers at the three vertices of each face is the same. He has already written the numbers 1 and 5 as shown.\n\nWhat is the sum of the other three numbers he will write?", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/1993.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The shaded area is equal to $\\sqrt{3}$. What is the area of the triangle $A B C$?\n\\n Options: A. $2 \\sqrt{3}$, B. 2, C. 5, D. 6, E. $4 \\sqrt{3}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/197.png" }, { "solution": "\\boxed{96}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, each of the squares touches adjacent squares at its corners and the line $G H$ along one of its edges. The line $G H$ is $24 \\mathrm{~cm}$ long. What is the total perimeter, in centimetres, of all the squares? ", "completion": "\\boxed{96}", "image_path": "dataset/math_vision/images/1544.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the road signs has the most axes of symmetry?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1131.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Amelia built a crown using 10 copies of this piece . The parts were joined together so that the sides in contact had the same number, as shown in the picture, where four parts are visible. What is the number that appears in the colored triangle?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/631.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a game one is allowed to take (some or all) building blocks from the top of a stack of building blocks, turn them upside down and place them back in the same position within one move. Goran starts with this stack of building blocks: In the end all building blocks should be ordered according to size. What is the minimum number of moves Goran needs to make?", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/991.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two identical cylindrical glasses contain the same amount of water. The left glass is upright, while the right one rests against the other one at a slant. The water level in both glasses is at the same height. The water level in the leaning glass touches its bottom in exactly one point (see diagram). The bases of both glasses have an area of $3 \\pi \\mathrm{cm}^{2}$. How much water is in each glass? \\n Options: A. $9 \\pi \\mathrm{cm}^{3}$, B. $6 \\pi \\mathrm{cm}^{3}$, C. $3 \\sqrt{3} \\pi \\mathrm{cm}^{3}$, D. $\\frac{3 \\pi}{4} \\mathrm{~cm}^{3}$, E. It cannot be uniquely determined from this information.", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/395.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How big is the angle indicated with a question mark?\n\\n Options: A. $10^{\\circ}$, B. $20^{\\circ}$, C. $30^{\\circ}$, D. $40^{\\circ}$, E. $50^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1334.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each area in the picture on the right should be coloured using one of the colours, red (R), green (G), blue (B) or orange (O). Areas which touch must be different colours. Which colour is the area marked $X$?\n\\n Options: A. red, B. blue, C. green, D. orange, E. The colour cannot definitely be determined.", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1075.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Susi makes this pattern using ice-lolly sticks. Each stick is $5 \\mathrm{~cm}$ long and $1 \\mathrm{~cm}$ wide. How long is Susi's pattern?\n\\n Options: A. $20 \\mathrm{~cm}$, B. $21 \\mathrm{~cm}$, C. $22 \\mathrm{~cm}$, D. $23 \\mathrm{~cm}$, E. $25 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/83.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many different patterns can be made by shading exactly two of the nine squares? Patterns that can be matched by flips and/or turns are not considered different. For example, the patterns shown below are not considered different.\n\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/2544.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following represents the result when the figure shown below is rotated clockwise $120^\\circ$ about its center?\n\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2570.png" }, { "solution": "\\boxed{4.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In trapezoid $ABCD$, $AD$ is perpendicular to $DC$, $AD=AB=3$, and $DC=6$. In addition, E is on $DC$, and $BE$ is parallel to $AD$. Find the area of $\\Delta BEC$.\n\n", "completion": "\\boxed{4.5}", "image_path": "dataset/math_vision/images/2679.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Numbers 2, 3, 4 and one more unknown number are written in the cells of $2 \\times 2$ table. It is known that the sum of the numbers in the first row is equal to 9 , and the sum of the numbers in the second row is equal to 6 . The unknown number is\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/757.png" }, { "solution": "\\boxed{2.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Costa is building a new fence in his garden. He uses 25 planks of wood, each of which is $30 \\mathrm{~cm}$ long. He arranges these planks so that there is the same slight overlap between any two adjacent planks, as shown in the diagram. The total length of Costa's new fence is 6.9 metres. What is the length in centimetres of the overlap between any pair of adjacent planks? ", "completion": "\\boxed{2.5}", "image_path": "dataset/math_vision/images/1688.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In each of the cells, a number is to be written so that the sum of the 4 numbers in each row and in each column are the same.\n\nWhat number must be written in the shaded cell?", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/1954.png" }, { "solution": "\\boxed{$\\frac{\\sqrt{6}}{6}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $\\vartriangle ABC$ be an equilateral triangle with side length $M$ such that points $E_1$ and $E_2$ lie on side $AB$, $F_1$ and $F_2$ lie on side $BC$, and $G1$ and $G2$ lie on side $AC$, such that $$m = \\overline{AE_1} = \\overline{BE_2} = \\overline{BF_1} = \\overline{CF_2} = \\overline{CG_1} = \\overline{AG_2}$$and the area of polygon $E_1E_2F_1F_2G_1G_2$ equals the combined areas of $\\vartriangle AE_1G_2$, $\\vartriangle BF_1E_2$, and $\\vartriangle CG_1F_2$. Find the ratio $\\frac{m}{M}$.\\n", "completion": "\\boxed{$\\frac{\\sqrt{6}}{6}$}", "image_path": "dataset/math_vision/images/2796.png" }, { "solution": "\\boxed{96}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Cleo builds a pyramid with identical metal spheres. Its square base is a $4 \\times 4$ array of spheres, as shown in the diagram. The upper layers are a $3 \\times 3$ array of spheres, a $2 \\times 2$ array of spheres and a single sphere at the top. At each point of contact between two spheres, a blob of glue is placed. How many blobs of glue will Cleo place?\n", "completion": "\\boxed{96}", "image_path": "dataset/math_vision/images/1683.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nFive cards are lying on a table as shown. Each card has a letter on one side and a whole number on the other side. Jane said, \"If a vowel is on one side of any card, then an even number is on the other side.\" Mary showed Jane was wrong by turning over one card. Which card did Mary turn over?\\n Options: A. $3$, B. $4$, C. $6$, D. $\\text{P}$, E. $\\text{Q}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2509.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are five gaps in the following calculation. Adriana wants to write a \"+\" into four of the gaps and a \"−\" into one of the gaps so that the equation is correct. Where does she have to insert the \"-\"?\n\\n Options: A. between 6 and 9, B. between 9 and 12, C. between 12 and 15, D. between 15 and 18, E. between 18 and 21", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1228.png" }, { "solution": "\\boxed{184}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two parallel chords in a circle have lengths $10$ and $14$, and the distance between them is $6$. The chord parallel to these chords and midway between them is of length $\\sqrt{a}$ where $a$ is\n\n", "completion": "\\boxed{184}", "image_path": "dataset/math_vision/images/2421.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which will be the result?\n\\n Options: A. 111 111 111, B. 1 010 101 010, C. 100 000 000, D. 999 999 999, E. 1 000 000 000", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/737.png" }, { "solution": "\\boxed{65}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We define the $\\emph{weight}$ of a path to be the sum of the numbers written on each edge of the path. Find the minimum weight among all paths in the graph below that visit each vertex precisely once. \\n", "completion": "\\boxed{65}", "image_path": "dataset/math_vision/images/2820.png" }, { "solution": "\\boxed{\\sqrt{34}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $PAB$ and square $ABCD$ are in perpendicular planes. Given that $PA=3$, $PB=4$, and $AB=5$, what is $PD$? ", "completion": "\\boxed{\\sqrt{34}}", "image_path": "dataset/math_vision/images/2968.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Bernd produces steps for a staircase which are $15 \\mathrm{~cm}$ high and $15 \\mathrm{~cm}$ deep (see diagram). The staircase should reach from the ground floor to the first floor which is $3 \\mathrm{~m}$ higher. How many steps does Bernd have to produce?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1161.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The graph of the function $ f$ is shown below. How many solutions does the equation $ f(f(x)) = 6$ have?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2448.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Martinho made a bicolor kite with six pieces of a thin strip of bamboo. Two pieces were used for the diagonals, which are perpendicular. The other four pieces were used to connect the middle points on the sides of the kite, as shown in the picture. What is the ratio between the blue and yellow parts of the kite?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1440.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A path $D E F B$ with $D E \\perp E F$ and $E F \\perp F B$ lies within the square $A B C D$ as shown. We know that $D E=5, E F=1$ and $F B=2$. What is the side length of the square?\n\\n Options: A. $3 \\sqrt{2}$, B. $\\frac{7 \\sqrt{2}}{2}$, C. $\\frac{11}{2}$, D. $5 \\sqrt{2}$, E. another value", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/332.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Prab painted each of the eight circles in the diagram red, yellow or blue such that no two circles that are joined directly were painted the same colour. Which two circles must have been painted the same colour? \\n Options: A. 5 and 8, B. 1 and 6, C. 2 and 7, D. 4 and 5, E. 3 and 6", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1672.png" }, { "solution": "\\boxed{400}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $A B C D$ is comprised of one inner square (white) and four shaded congruent rectangles. Each shaded rectangle has a perimeter of $40 \\mathrm{~cm}$. What is the area (in $\\mathrm{cm}^{2}$ ) of square $A B C D$ ?\n", "completion": "\\boxed{400}", "image_path": "dataset/math_vision/images/705.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of the grey rectangle shown on the right is $13 \\mathrm{~cm}^{2}. X$ and $Y$ are the midpoints of the sides of the trapezium. How big is the area of the trapezium?\n\\n Options: A. $24 \\mathrm{~cm}^{2}$, B. $25 \\mathrm{~cm}^{2}$, C. $26 \\mathrm{~cm}^{2}$, D. $27 \\mathrm{~cm}^{2}$, E. $28 \\mathrm{~cm}^{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1343.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each corner cube is removed from this $3\\text{ cm}\\times 3\\text{ cm}\\times 3\\text{ cm}$ cube. The surface area of the remaining figure is\n\n\\n Options: A. $19\\text{ sq.cm}$, B. $24\\text{ sq.cm}$, C. $30\\text{ sq.cm}$, D. $54\\text{ sq.cm}$, E. $72\\text{ sq.cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2595.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Tom wants to completely cover his paper boat using the shapes\n\nWhat is the smallest number of shapes he needs for that?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/588.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many numbers are outside the square?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/47.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a circle with centre $O$ as well as a tangent that touches the circle in point $P$. The arc $A P$ has length 20, the arc $B P$ has length 16. What is the size of the angle $\\angle A X P$?\n\\n Options: A. $30^{\\circ}$, B. $24^{\\circ}$, C. $18^{\\circ}$, D. $15^{\\circ}$, E. $10^{\\circ}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/286.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A beetle walks along the edges of a cube. Starting from point $P$ it first moves in the direction shown. At the end of each edge it changes the direction in which it turns, turning first right then left, then right etc. Along how many edges will it walk before it returns to point $P$?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1057.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On each of the three separate pieces of paper there is a three-digit number. The sum of the three numbers is 826. What is the sum of the two hidden digits?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/905.png" }, { "solution": "\\boxed{47}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular piece of paper $F G H I$ with sides of length $4 \\mathrm{~cm}$ and $16 \\mathrm{~cm}$ is folded along the line $M N$ so that the vertex $G$ coincides with the vertex $I$ as shown. The outline of the paper now makes a pentagon $F M N H^{\\prime} I$. What is the area, in $\\mathrm{cm}^{2}$, of the pentagon $F M N H^{\\prime} I$ ? ", "completion": "\\boxed{47}", "image_path": "dataset/math_vision/images/1884.png" }, { "solution": "\\boxed{39}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Stan had 125 small cubes. He glued some of them together to form a large cube with nine tunnels, each perpendicular to two opposite faces and passing through the cube, as shown in the diagram.\nHow many of the small cubes did he not use? ", "completion": "\\boxed{39}", "image_path": "dataset/math_vision/images/1647.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the points $A$, $B$, $C$, $D$, $E$, and $F$ in the figure below represent a different digit from 1 to 6. Each of the five lines shown passes through some of these points. The digits along the line each are added to produce 5 sums, one for each line. The total of the sums is $47$. What is the digit represented by $B$?\n\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/2766.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the obtuse triangle $ABC$, $AM = MB, MD \\perp BC, EC \\perp BC$. If the area of $\\triangle ABC$ is 24, then the area of $\\triangle BED$ is\n\n\\n Options: A. $9$, B. $12$, C. $15$, D. $18$, E. $\\text{not uniquely determined}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2351.png" }, { "solution": "\\boxed{110}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Circle $C_0$ has radius $1$, and the point $A_0$ is a point on the circle. Circle $C_1$ has radius $r<1$ and is internally tangent to $C_0$ at point $A_0$. Point $A_1$ lies on circle $C_1$ so that $A_1$ is located $90^{\\circ}$ counterclockwise from $A_0$ on $C_1$. Circle $C_2$ has radius $r^2$ and is internally tangent to $C_1$ at point $A_1$. In this way a sequence of circles $C_1,C_2,C_3,...$ and a sequence of points on the circles $A_1,A_2,A_3,...$ are constructed, where circle $C_n$ has radius $r^n$ and is internally tangent to circle $C_{n-1}$ at point $A_{n-1}$, and point $A_n$ lies on $C_n$ $90^{\\circ}$ counterclockwise from point $A_{n-1}$, as shown in the figure below. There is one point $B$ inside all of these circles. When $r=\\frac{11}{60}$, the distance from the center of $C_0$ to $B$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\n\n", "completion": "\\boxed{110}", "image_path": "dataset/math_vision/images/2093.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The sides of the rectangle $A B C D$ are parallel to the co-ordinate axes. The rectangle is positioned below the $x$-axis and to the right of the $y$-axis, as shown in the picture. The co-ordinates of the points $A, B, C, D$ are whole numbers. For each of the points we calculate the value of ( $y$ co-ordinate) $\\div$(x co-ordinate). Which of the points will give the smallest value?\n\\n Options: A. A, B. B, C. C, D. D, E. It depends on the rectangle.", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1101.png" }, { "solution": "\\boxed{70}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $\\triangle PQR$ is isosceles. What is the value of $x$? ", "completion": "\\boxed{70}", "image_path": "dataset/math_vision/images/2895.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anna starts in the direction of the arrow. At each crossing she turns either right or left. At the first crossing she turns right, at the next left, then left again, then right, then left and left again. What will she find at the next crossing that she comes to?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/501.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In quadrilateral $ ABCD$, sides $ \\overline{AB}$ and $ \\overline{BC}$ both have length 10, sides $ \\overline{CD}$ and $ \\overline{DA}$ both have length 17, and the measure of angle $ ADC$ is $ 60^\\circ$. What is the length of diagonal $ \\overline{AC}$?\n", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/2663.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cub is $\\frac{1}{2}$ foot from the top face. The second cut is $\\frac{1}{3}$ foot below the first cut, and the third cut is $\\frac{1}{17}$ foot below the second cut. From the top to the bottom the pieces are labeled A, B, C, and D. The pieces are then glued together end to end as shown in the second diagram. What is the total surface area of this solid in square feet?\n\n\n\\n Options: A. 6$, $7$, $\\frac{419}{51}$, $\\frac{158}{17}$, $11$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2704.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Figure $OPQR$ is a square. Point $O$ is the origin, and point $Q$ has coordinates $(2,2)$. What are the coordinates for $T$ so that the area of triangle $PQT$ equals the area of square $OPQR$?\n\n\nNOT TO SCALE\\n Options: A. (-6, B. 0), C. (-4, D. 0), E. (-2, F. 0), G. (2, H. 0), I. (4, J. 0)", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2587.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The points $G$ and $I$ are on the circle with centre $H$, and $F I$ is tangent to the circle at $I$. The distances $F G$ and $H I$ are integers, and $F I=F G+6$. The point $G$ lies on the straight line through $F$ and $H$. How many possible values are there for $H I$ ? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1927.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The natural numbers from 1 to 120 were written as shown into a table with 15 columns. In which column (counting from left) is the sum of the numbers the largest?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1365.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Initially, a spinner points west. Chenille moves it clockwise $ 2 \\frac{1}{4}$ revolutions and then counterclockwise $ 3 \\frac{3}{4}$ revolutions. In what direction does the spinner point after the two moves?\n\n\\n Options: A. $\\text{north}$, B. $\\text{east}$, C. $\\text{south}$, D. $\\text{west}$, E. $\\text{northwest}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2670.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: My TV screen has sides in the ratio $16: 9$. My mother's TV screen has sides in the ratio $4: 3$. A picture which exactly fills the screen of my TV only fills the width of the screen of my mother's TV.\nWhat fraction of the screen on my mother's TV is not covered?\n\\n Options: A. $\\frac{1}{6}$, B. $\\frac{1}{5}$, C. $\\frac{1}{4}$, D. $\\frac{1}{3}$, E. It depends on the size of the screen.", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1757.png" }, { "solution": "\\boxed{80}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The points $P$ and $Q$ are opposite vertices of a regular hexagon and the points $R$ and $S$ are midpoints of opposite edges, as shown. The area of the hexagon is $60 \\mathrm{~cm}^{2}$. What is the product of the lengths, in cms, of $P Q$ and $R S$ ? ", "completion": "\\boxed{80}", "image_path": "dataset/math_vision/images/1892.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Werner wants to write a number at each vertex and on each edge of the rhombus shown. He wants the sum of the numbers at the two vertices at the ends of each edge to be equal to the number written on that edge. What number should he write on the edge marked with the question mark? ", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1707.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $4\\times 6$ grid should be cut along the black lines into several identical shapes. No piece is to be left over. Into which of the following shapes is it not possible to cut this grid in this way? \\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1243.png" }, { "solution": "\\boxed{2550}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $101\\times 101$ square grid is given with rows and columns numbered in order from $1$ to $101$. Each square that is contained in both an even-numbered row and an even-numbered column is cut out. A small section of the grid is shown below, with the cut-out squares in black. Compute the maximum number of $L$-triominoes (pictured below) that can be placed in the grid so that each $L$-triomino lies entirely inside the grid and no two overlap. Each $L$-triomino may be placed in the orientation pictured below, or rotated by $90^\\circ$, $180^\\circ$, or $270^\\circ$.\\n", "completion": "\\boxed{2550}", "image_path": "dataset/math_vision/images/2812.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many triangles can you find in the picture?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/41.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, $\\overline{AB}$ and $\\overline{CD}$ are diameters of the circle with center $O$, $\\overline{AB} \\perp \\overline{CD}$, and chord $\\overline{DF}$ intersects $\\overline{AB}$ at $E$. If $DE = 6$ and $EF = 2$, then the area of the circle is\n\\n Options: A. $23\\pi$, B. $\\frac{47}{2}\\pi$, C. $24\\pi$, D. $\\frac{49}{2}\\pi$, E. $25\\pi$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2420.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $ ABC$ has a right angle at $ B$. Point $ D$ is the foot of the altitude from $ B$, $ AD=3$, and $ DC=4$. What is the area of $ \\triangle{ABC}$?\n\\n Options: A. $4\\sqrt{3}$, B. $7\\sqrt{3}$, C. $21$, D. $14\\sqrt{3}$, E. $42$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2166.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In this diagram $AB$ and $AC$ are the equal sides of an isosceles triangle $ABC$, in which is inscribed equilateral triangle $DEF$. Designate angle $BFD$ by $a$, angle $ADE$ by $b$, and angle $FEC$ by $c$. Then:\n\\n Options: A. $b=\\frac{a+c}{2}$, B. $b=\\frac{a-c}{2}$, C. $a=\\frac{b-c}{2}$, D. $a=\\frac{b+c}{2}$, E. $\\text{none of these}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2276.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: From above, the corridor of a school looks like in the diagram. A cat walks along the dotted line drawn in the middle of the room. How many meters does the cat walk?\n\\n Options: A. $75 \\mathrm{~m}$, B. $77 \\mathrm{~m}$, C. $79 \\mathrm{~m}$, D. $81 \\mathrm{~m}$, E. $83 \\mathrm{~m}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/619.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We are going to make a spiral of isosceles triangles. We'll start with the shaded triangle $B A C$, which has a top angle $\\angle B A C=100^{\\circ}$, and move counterclockwise. Let $\\triangle A B C$ have number 0. Every of the next triangles (with numbers 1, 2, $3, \\ldots$ ) will have exactly one edge adjoining the previous one (see the picture). What will be the number of the first triangle which precisely covers triangle $\\mathrm{nr}$. 0?\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/1007.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An ant crawls along a closed line on the surface of a cube until it reaches its starting point. Which of the following nets of a cube belongs to the cube that the ant is crawling on?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1190.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $A B C D E F$ is a regular hexagon, as shown in the diagram. $G$ is the midpoint of $A B. H$ and I are the intercepts of the line segments GD and GE respectively, with the line segment FC. How big is the ratio of the areas of the triangle GIF and the trapezium IHDE?\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{1}{3}$, C. $\\frac{1}{4}$, D. $\\frac{\\sqrt{3}}{3}$, E. $\\frac{\\sqrt{3}}{4}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/320.png" }, { "solution": "\\boxed{144}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Delia is joining three vertices of a square to make four right-angled triangles.\nShe can create four triangles doing this, as shown.\n\nHow many right-angled triangles can Delia make by joining three vertices of a regular polygon with 18 sides?", "completion": "\\boxed{144}", "image_path": "dataset/math_vision/images/2003.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five cards are lying on the table in the order 5, 1, 4, 3, 2. You must get the cards in the order 1, 2, 3, 4, 5. Per move, any two cards may be interchanged. How many moves do you need at least?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/424.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the shapes to the right has the largest area?\n\\n Options: A. A, B. B, C. C, D. D, E. All shapes have the same area.", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1355.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A regular hexagon has side length 6. Congruent arcs with radius 3 are drawn with the center at each of the vertices, creating circular sectors as shown. The region inside the hexagon but outside the sectors is shaded as shown What is the area of the shaded region?\n\n\\n Options: A. $27\\sqrt{3}-9\\pi$, B. $27\\sqrt{3}-6\\pi$, C. $54\\sqrt{3}-18\\pi$, D. $54\\sqrt{3}-12\\pi$, E. $108\\sqrt{3}-9\\pi$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2192.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Choose the picture where the angle between the hands of a watch is $150^{\\circ}$.\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/730.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The water level in a port rises and falls on a certain day as shown in the diagram. How many hours on that day was the water level over $30 \\mathrm{~cm}$?\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/245.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Fridolin the hamster runs through the maze shown on the right. On the path there are 16 pumpkin seeds. He is only allowed to cross each junction once. What is the maximum number of pumpkin seeds that he can collect?\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/1074.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A semicircle is inscribed in an isosceles triangle with base $16$ and height $15$ so that the diameter of the semicircle is contained in the base of the triangle as shown. What is the radius of the semicircle?\n\n\\n Options: A. $4 \\sqrt{3}$, B. $\\frac{120}{17}$, C. $10$, D. $\\frac{17\\sqrt{2}}{2}$, E. $\\frac{17\\sqrt{3}}{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2740.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $ABC$ is equilateral with $AB=1$. Points $E$ and $G$ are on $\\overline{AC}$ and points $D$ and $F$ are on $\\overline{AB}$ such that both $\\overline{DE}$ and $\\overline{FG}$ are parallel to $\\overline{BC}$. Furthermore, triangle $ADE$ and trapezoids $DFGE$ and $FBCG$ all have the same perimeter. What is $DE+FG$?\n\\n Options: A. $1$, B. $\\frac{3}{2}$, C. $\\frac{21}{13}$, D. $\\frac{13}{8}$, E. $\\frac{5}{3}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2477.png" }, { "solution": "\\boxed{\\frac{3}{8}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A sphere is inscribed in a cone with height 4 and base radius 3. What is the ratio of the volume of the sphere to the volume of the cone?\n\n", "completion": "\\boxed{\\frac{3}{8}}", "image_path": "dataset/math_vision/images/2941.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the four vertices and six edges of the tetrahedron $P Q R S$ is marked with one of the numbers $1,2,3,4,5,6,7,8,9$ and 11 ; so the number 10 is not used. Each number is used exactly once. Each edge is marked with the sum of the numbers at the two vertices connected by that edge. Edge $P Q$ is marked with number 9 . Which number is used to mark edge RS? ", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1607.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Now it is 2008. What is the total sum of these digits?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/12.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many different digits can you find in this picture?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/4.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The twelve-sided figure shown has been drawn on $1 \\text{ cm}\\times 1 \\text{ cm}$ graph paper. What is the area of the figure in $\\text{cm}^2$?\n\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/2747.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rory uses four identical standard dice to build the solid shown in the diagram.\nWhenever two dice touch, the numbers on the touching faces are the same. The numbers on some of the faces of the solid are shown. What number is written on the face marked with question mark?\n(On a standard die, the numbers on opposite faces add to 7.)\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1747.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Seven sticks lay on top of each other. Stick 2 lays right at the bottom. Stick 6 lays right on top. Which stick lays exactly in the middle?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/35.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anna cuts the picture of a mushroom in two halves.\n\nShe then arranges the two pieces together to form a new picture. What could this new picture look like?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/139.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cuboid has been built using 3 shapes (not necessarily different) each made from 4 little cubes as shown. The shape shaded black is completely visible, but both of the others are only partially visible. Which of the following shapes is the unshaded one? \n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1507.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ria wants to write a number in each of the seven bounded regions in the diagram. Two regions are neighbours if they share part of their boundary. The number in each region is to be the sum of the numbers in all of its neighbours. Ria has already written in two of the numbers, as shown.\nWhat number must she write in the central region?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1624.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two squares with side 1 have a common vertex, and the edge of one of them lies along the diagonal of the other. What is the area of the overlap between the squares? \\n Options: A. $\\sqrt{2}-1$, B. $\\frac{\\sqrt{2}}{2}$, C. $\\frac{\\sqrt{2}+1}{2}$, D. $\\sqrt{2}+1$, E. $\\sqrt{3}-\\sqrt{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1831.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each participant in a cooking contest baked one tray of cookies like the one shown beside. What is the smallest number of trays of cookies needed to make the following plate?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/135.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The grey areas of the square with side length $a$ are bounded by a semi-circle and two quarter-circles respectively. What is their total area?\n\\n Options: A. $\\frac{\\pi a^{2}}{8}$, B. $\\frac{a^{2}}{2}$, C. $\\frac{\\pi a^{2}}{2}$, D. $\\frac{a^{2}}{4}$, E. $\\frac{\\pi a^{2}}{4}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1387.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $ABCD$ has side length 2. A semicircle with diameter $AB$ is constructed inside the square, and the tangent to the semicircle from $C$ intersects side $AD$ at $E$. What is the length of $CE$?\n\n\\n Options: A. $\\frac{2+\\sqrt{5}}2$, B. $\\sqrt{5}$, C. $\\sqrt{6}$, D. $\\frac{5}{2}$, E. $5-\\sqrt{5}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2137.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $3 \\mathrm{~cm}$ wide strip of paper is dark on one side and light on the other. The folded strip of paper lies exactly within a rectangle with length $27 \\mathrm{~cm}$ and width $9 \\mathrm{~cm}$ (see diagram). How long is the strip of paper?\n\\n Options: A. $36 \\mathrm{~cm}$, B. $48 \\mathrm{~cm}$, C. $54 \\mathrm{~cm}$, D. $57 \\mathrm{~cm}$, E. $81 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1138.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle of radius $ 2$ is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{\\pi}{6}$, C. $\\frac{2}{\\pi}$, D. $\\frac{2}{3}$, E. $\\frac{3}{\\pi}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2165.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A zig-zag line starts at the point $P$, at one end of the diameter $P Q$ of a circle. Each of the angles between the zig-zag line and the diameter $P Q$ is equal to $\\alpha$ as shown. After four peaks, the zig-zag line ends at the point $Q$. What is the size of angle $\\alpha$ ? \\n Options: A. $60^{\\circ}$, B. $72^{\\circ}$, C. $75^{\\circ}$, D. $80^{\\circ}$, E. $86^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1955.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows 5 equally big semicircles and the length of 5 distances. How big is the radius of one semicircle? ", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/1248.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The new TV screens have the sides $16: 9$ and the old ones have the sides 4:3.\n\nWe have a DVD that occupies exactly all the screen 16:9. We want to watch this film on the old 4:3 screen. If the width of the film occupies exactly the width of the old screen, then the empty part of the screen is:\\n Options: A. $\\frac{1}{2}$, B. $\\frac{1}{5}$, C. $\\frac{1}{4}$, D. $\\frac{1}{3}$, E. It depends on the size of the screen", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/769.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Using the connected sticks shown, Pia forms different shapes. Which shape can she not make?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/606.png" }, { "solution": "\\boxed{21}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The grid below contains the $16$ points whose $x$- and $y$-coordinates are in the set $\\{0,1,2,3\\}$: A square with all four of its vertices among these $16$ points has area $A$. What is the sum of all possible values of $A$?", "completion": "\\boxed{21}", "image_path": "dataset/math_vision/images/2917.png" }, { "solution": "\\boxed{1:2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A hexagon is drawn with its vertices at $$(0,0),(1,0),(2,1),(2,2),(1,2), \\text{ and } (0,1),$$ and all of its diagonals are also drawn, as shown below. The diagonals cut the hexagon into $24$ regions of various shapes and sizes. These $24$ regions are shown in pink and yellow below. If the smallest region (by area) has area $a$, and the largest has area $b$, then what is the ratio $a:b$? Give your answer in lowest terms. ", "completion": "\\boxed{1:2}", "image_path": "dataset/math_vision/images/2937.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lisa has mounted 7 postcards on her fridge door using 8 strong magnets (black dots). What is the maximum amount of magnets she can remove without any postcards falling on the floor?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/856.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many fish will have their heads pointing towards the ring when we straighten the line?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/641.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many white squares need to be coloured in black, so that there are exactly twice as many white squares as there are black squares?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/566.png" }, { "solution": "\\boxed{100}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram six circles of equal size touch adjacent circles and the sides of the large rectangle. Each of the corners of the small rectangle is the centre of one of the circles. The perimeter of the small rectangle is $60 \\mathrm{~cm}$. What is the perimeter of the large rectangle in centimetres? ", "completion": "\\boxed{100}", "image_path": "dataset/math_vision/images/1543.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If you hit the target board, you score points. The number of points depends on which one of the three areas you hit. Diana throws two darts, three times at the target board. On the first attempt she scores 14 points and on the second 16 points. How many points does she score on the third attempt?\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/884.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: John has made a building of unit cubes standing on a $4 \\times 4$ grid. The diagram shows the number of cubes standing on each cell. When John looks horizontally at the building from behind, what does he see? \n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1603.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The letter F shown below is rotated $90^\\circ$ clockwise around the origin, then reflected in the $y$-axis, and then rotated a half turn around the origin. What is the final image?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2204.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangles $ABC$ and $ABD$ are isosceles with $AB =AC = BD$, and $BD$ intersects $AC$ at $E$. If $BD$ is perpendicular to $AC$, then $\\angle C + \\angle D$ is\n\\n Options: A. $115^\\circ$, B. $120^\\circ$, C. $130^\\circ$, D. $135^\\circ$, E. $\\text{not uniquely determined}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2426.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a shape made from a regular hexagon of side one unit, six triangles and six squares. What is the perimeter of the shape? \\n Options: A. $6(1+\\sqrt{2})$, B. $6\\left(1+\\frac{1}{2} \\sqrt{3}\\right)$, C. $12$, D. $6+3 \\sqrt{2}$, E. $9$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1872.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The rectangle $A B C D$ is made up of 12 congruent rectangles (see diagram). How big is the ratio $\\frac{A D}{D C}$?\n\\n Options: A. $\\frac{8}{9}$, B. $\\frac{5}{6}$, C. $\\frac{7}{8}$, D. $\\frac{2}{3}$, E. $\\frac{9}{8}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1474.png" }, { "solution": "\\boxed{244}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $\\ell_A$ and $\\ell_B$ be two distinct parallel lines. For positive integers $m$ and $n$, distinct points $A_1, A_2, \\allowbreak A_3, \\allowbreak \\ldots, \\allowbreak A_m$ lie on $\\ell_A$, and distinct points $B_1, B_2, B_3, \\ldots, B_n$ lie on $\\ell_B$. Additionally, when segments $\\overline{A_iB_j}$ are drawn for all $i=1,2,3,\\ldots, m$ and $j=1,\\allowbreak 2,\\allowbreak 3, \\ldots, \\allowbreak n$, no point strictly between $\\ell_A$ and $\\ell_B$ lies on more than two of the segments. Find the number of bounded regions into which this figure divides the plane when $m=7$ and $n=5$. The figure shows that there are 8 regions when $m=3$ and $n=2$.\n", "completion": "\\boxed{244}", "image_path": "dataset/math_vision/images/2101.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the number 8. A dot stands for the number 1 and a line for the number 5. Which diagram represents the number 12?\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/602.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Right triangle $ACD$ with right angle at $C$ is constructed outwards on the hypotenuse $\\overline{AC}$ of isosceles right triangle $ABC$ with leg length $1$, as shown, so that the two triangles have equal perimeters. What is $\\sin(2\\angle BAD)$?\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{\\sqrt{2}}{2}$, C. $\\frac{3}{4}$, D. $\\frac{7}{9}$, E. $\\frac{\\sqrt{3}}{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2490.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: lines are drawn on a piece of paper and some of the lines are given numbers. The paper is cut along some of these lines and then folded as shown in the picture. Along which lines were the cuts made?\n\n\\n Options: A. $1,3,5,7$, B. $2,4,6,8$, C. $2,3,5,6$, D. $3,4,6,7$, E. $1,4,5,8$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/783.png" }, { "solution": "\\boxed{4.2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $ABCD$ is a quadrilateral with right angles at $A$ and $C$. Points $E$ and $F$ are on $AC$, and $DE$ and $BF$ are perpendicular to $AC$. If $AE=3$, $DE=5$, and $CE=7$, then $BF=$\n\n", "completion": "\\boxed{4.2}", "image_path": "dataset/math_vision/images/2388.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a square $P Q R S$ of side-length $1 . W$ is the centre of the square and $U$ is the midpoint of $R S$. Line segments $T W, U W$ and $V W$ split the square into three regions of equal area. What is the length of $S V$ ? \\n Options: A. $\\frac{1}{2}$, B. $\\frac{2}{3}$, C. $\\frac{3}{4}$, D. $\\frac{4}{5}$, E. $\\frac{5}{6}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1975.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Daniel sticks these two pieces of paper on this black circle: The two pieces of paper are not allowed to overlap. Which picture does he get?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/686.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below, all circles are tangent to each other as shown. The six outer circles are all congruent to each other, and the six inner circles are all congruent to each other. Compute the ratio of the area of one of the outer circles to the area of one of the inner circles.\\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/2810.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Cynthia paints each region of the figure in a single color: red, blue or yellow. She paints the regions that touch each other with different colors. In how many different ways can she color the figure?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/920.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The higher someone stands on the podium, the better the ranking. Which number got third place?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/601.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On a balance scale, three different masses were put at random on each pan and the result is shown in the picture. The masses are of 101, 102, 103, 104, 105 and 106 grams. What is the probability that the 106 gram mass stands on the heavier pan?\n\\n Options: A. $75 \\%$, B. $80 \\%$, C. $90 \\%$, D. $95 \\%$, E. $100 \\%$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1926.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the following figure, the heart and the arrow are arranged as pictured. At the same moment the heart and the arrow begin to move. The arrow moves around the figure 3 spaces clockwise and the heart 4 spaces anticlockwise and then they stop. This process repeats itself over and over again. After how many repetitions does the arrow find itself for the first time in the same triangle as the heart?\n\\n Options: A. 7, B. 8, C. 9, D. 10, E. That will never happen", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1112.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Points $E$ and $F$ are located on square $ABCD$ so that $\\Delta BEF$ is equilateral. What is the ratio of the area of $\\Delta DEF$ to that of $\\Delta ABE$?\n\n\\n Options: A. $\\frac{4}{3}$, B. $\\frac{3}{2}$, C. $\\sqrt{3}$, D. $2$, E. $1+\\sqrt{3}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2135.png" }, { "solution": "\\boxed{961}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each square in this cross-number can be filled with a non-zero digit such that all of the conditions in the clues are fulfilled. The digits used are not necessarily distinct.\nWhat is the answer to 3 ACROSS?\n\n\\section*{ACROSS}\n1. A multiple of 7\n3. The answer to this Question\n5. More than 10\n\\section*{DOWN}\n1. A multiple of a square of an odd prime; neither a square nor a cube\n2. The internal angle of a regular polygon; the exterior angle is between $10^{\\circ}$ and $20^{\\circ}$\n4. A proper factor of $5 \\mathrm{ACROSS}$ but not a proper factor of $1 \\mathrm{DOWN}$", "completion": "\\boxed{961}", "image_path": "dataset/math_vision/images/2024.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Riki wants to write one number in each of the seven sections of the diagram pictured. Two zones are adjacent if they share a part of their outline. The number in each zone should be the sum of all numbers of its adjacent zones. Riki has already placed numbers in two zones. Which number does she need to write in the zone marked \"?\".\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1128.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The large triangle shown has sides of length 5 units. What percentage of the area of the triangle is shaded? \\n Options: A. $80 \\%$, B. $85 \\%$, C. $88 \\%$, D. $90 \\%$, E. impossible to determine", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1914.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which is the graph of the function $y=\\sqrt{|(1+x)(1-|x|)|}$?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/202.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria has drawn some shapes on identical square pieces of paper, as shown. Each line she has drawn is parallel to an edge of her paper. How many of her shapes have the same perimeter as the sheet of paper itself? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1794.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Dennis takes off one of the squares of this shape \nHow many of these 5 shapes can he get?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/609.png" }, { "solution": "\\boxed{150}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The line segments $P Q R S$ and $W X Y S$ intersect circle $C_{1}$ at points $P, Q, W$ and $X$.\n\nThe line segments intersect circle $C_{2}$ at points $Q, R, X$ and $Y$. The lengths $Q R, R S$ and $X Y$ are 7, 9 and 18 respectively. The length $W X$ is six times the length $Y S$.\nWhat is the sum of the lengths of $P S$ and $W S$ ?", "completion": "\\boxed{150}", "image_path": "dataset/math_vision/images/2015.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A parallelogram is divided into 4 triangles as shown in the figure. Of the following possibilities for the areas of the triangles at most one can be true. Which one is it?\n\\n Options: A. $4,5,8,9$, B. $3,5,6,7$, C. $5,6,7,12$, D. $10,11,12,19$, E. $5,6,8,10$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/174.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Diameter $ACE$ is divided at $C$ in the ratio $2:3$. The two semicircles, $ABC$ and $CDE$, divide the circular region into an upper (shaded) region and a lower region. The ratio of the area of the upper region to that of the lower region is\n\n\\n Options: A. 2:3, B. 1:1, C. 3:2, D. 9:4, E. 5:2", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2596.png" }, { "solution": "\\boxed{\\frac{\\sqrt{21}}{5}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle{RST}$, shown, $\\sin{R}=\\frac{2}{5}$. What is $\\sin{T}$?\n\n", "completion": "\\boxed{\\frac{\\sqrt{21}}{5}}", "image_path": "dataset/math_vision/images/2983.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An $8 \\mathrm{~m}$ long rope is fastened to the corner of the house. A dog is fastened to the rope. Find the perimeter of the area, where the dog can be found.\n\\n Options: A. $15 \\pi+16$, B. $15 \\pi+20$, C. $15 \\pi$, D. $15 \\pi+18$, E. $30 \\pi+16$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1304.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four straight lines that intersect in one single point form eight equal angles (see diagram). Which one of the black arcs has the same length as the circumference of the little (grey) circle?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/369.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The following four statements, and only these are found on a card:\n\n(Assume each statement is either true or false.) Among them the number of false statements is exactly", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/2320.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Vania has a sheet of paper divided into nine equal squares. She wants to fold the sheet as shown in the picture, initially with horizontal folds and then with vertical folds, until she leaves the colored square on top of the layers. Vania wants to write the numbers from 1 to 9 , one in each square, so that these numbers are in ascending order, starting with the number 1 at the top, after the folds are made above. On the open sheet, indicated at the side, which numbers should she write in place of $a, b$ and $c$?\n\n\\n Options: A. $a=9, b=5, c=3$, B. $a=4, b=6, c=8$, C. $a=7, b=5, c=3$, D. $a=3, b=5, c=7$, E. $a=6, b=4, c=7$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/936.png" }, { "solution": "\\boxed{34426}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Carl writes down a five-digit number.\nHe then places a shape on each of the five digits (see picture).\nHe places different shapes on different digits.\nHe places the same shape on the same digits.\nWhich number did Carl hide?\n", "completion": "\\boxed{34426}", "image_path": "dataset/math_vision/images/146.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular piece of paper $A B C D$ with the measurements $4 \\mathrm{~cm} \\times 16 \\mathrm{~cm}$ is folded along the line $\\mathrm{MN}$ so that point $C$ coincides with point $A$ as shown. How big is the area of the quadrilateral ANMD'?\n\\n Options: A. $28 \\mathrm{~cm}^{2}$, B. $30 \\mathrm{~cm}^{2}$, C. $32 \\mathrm{~cm}^{2}$, D. $48 \\mathrm{~cm}^{2}$, E. $56 \\mathrm{~cm}^{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/247.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture any letter stands for some digit (different letters for different digits, equal letters for equal digits). Which digit is $\\mathrm{K}$?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1312.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One of the five coins $A, B, C, D$ or $E$ shall be placed in an empty square so that there are exactly two coins in each row and in each column. Which coin should be moved?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/661.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Peter looks at the picture hanging on the wall in more detail through a magnifying glass. Which section can he not see?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/844.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How big is the angle $\\alpha$ in the regular five-sided star shown?\n\\n Options: A. $24^{\\circ}$, B. $30^{\\circ}$, C. $36^{\\circ}$, D. $45^{\\circ}$, E. $72^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/248.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nAlbert places these 5 figures , , , , on a 5x5-grid. Each figure is only allowed to appear once in every column and in every row. Which figure does Albert have to place on the field with the question mark?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/587.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consider the $5\\times 5$ grid $Z^2_5 = \\{(a, b) : 0 \\le a, b \\le 4\\}$.\\nSay that two points $(a, b)$,$(x, y)$ are adjacent if $a - x \\equiv -1, 0, 1$ (mod $5$) and $b - y \\equiv -1, 0, 1$ (mod $5$) .\\nFor example, in the diagram, all of the squares marked with $\\cdot$ are adjacent to the square marked with $\\times$.\\n\\nWhat is the largest number of $\\times$ that can be placed on the grid such that no two are adjacent?\\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/2818.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There is a square with line segments drawn inside it. The line segments are drawn either from the vertices or the midpoints of other line segments. We coloured $\\frac{1}{8}$ of the large square. Which one is our coloring?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/946.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. THe remainder of the yard has a trapezoidal shape, as shown. The parallel sides of the trapezoid have lengths $ 15$ and $ 25$ meters. What fraction of the yard is occupied by the flower beds?\n\\n Options: A. $\\frac{1}{8}$, B. $\\frac{1}{6}$, C. $\\frac{1}{5}$, D. $\\frac{1}{4}$, E. $\\frac{1}{3}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2171.png" }, { "solution": "\\boxed{180}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the angle of rotation in degrees about point $C$ that maps the darker figure to the lighter image? ", "completion": "\\boxed{180}", "image_path": "dataset/math_vision/images/2994.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In right triangle $ABC$, $M$ and $N$ are midpoints of legs $\\overline{AB}$ and $\\overline{BC}$, respectively. Leg $\\overline{AB}$ is 6 units long, and leg $\\overline{BC}$ is 8 units long. How many square units are in the area of $\\triangle APC$? ", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/3010.png" }, { "solution": "\\boxed{90}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle ABC$, what is the value of $x + y$? ", "completion": "\\boxed{90}", "image_path": "dataset/math_vision/images/2930.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram opposite there is an object with 6 triangular faces. On each corner there is a number (two are shown). The sum of the numbers on the corners of each face is the same. What is the sum of all 5 numbers?\n", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/1053.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Twelve congruent rectangles are placed together to make a rectangle $P Q R S$ as shown. What is the ratio $P Q: Q R$ ? \\n Options: A. $2: 3$, B. $3: 4$, C. $5: 6$, D. $7: 8$, E. $8: 9$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1974.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $ EFGH$ is inside the square $ ABCD$ so that each side of $ EFGH$ can be extended to pass through a vertex of $ ABCD$. Square $ ABCD$ has side length $ \\sqrt{50}$ and $ BE = 1$. What is the area of the inner square $ EFGH$?\n", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/2143.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The rooms in Kanga's house are numbered. Eva enters the house through the main entrance. Eva has to walk through the rooms in such a way that each room that she enters has a number higher than the previous one. Through which door does Eva leave the house?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/595.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Circles $ A$, $ B$ and $ C$ are externally tangent to each other and internally tangent to circle $ D$. Circles $ B$ and $ C$ are congruent. Circle $ A$ has radius $ 1$ and passes through the center of $ D$. What is the radius of circle $ B$?\n\\n Options: A. $\\frac{2}{3}$, B. $\\frac{\\sqrt{3}}{2}$, C. $\\frac{7}{8}$, D. $\\frac{8}{9}$, E. $\\frac{1 + \\sqrt{3}}{3}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2459.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which number must be written into the circle with the question mark so that the calculation is correct?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/573.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: During a rough sailing trip, Jacques tried to sketch a map of his village. He managed to draw the four streets, the seven places where they cross and the houses of his friends. The houses are marked on the correct streets, and the intersections are correct, however, in reality, Arrow Street, Nail Street and Ruler Street are all absolutely straight. The fourth street is Curvy Street. Who lives on Curvy Street?\n\\n Options: A. Adeline, B. Benjamin, C. Carole, D. David, E. It is impossible to tell without a better map", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1876.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $P Q R S$ is a square of side $10 \\mathrm{~cm} . T$ is a point inside the square so that $\\angle S P T=75^{\\circ}$ and $\\angle T S P=30^{\\circ}$. What is the length of $T R$ ? \\n Options: A. $8 \\mathrm{~cm}$, B. $8.5 \\mathrm{~cm}$, C. $9 \\mathrm{~cm}$, D. $9.5 \\mathrm{~cm}$, E. $10 \\mathrm{~cm}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1745.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two identical equilateral triangles overlap with their sides parallel, so that the overlapping region is the hexagon shown shaded in the diagram. The perimeter length of each triangle is 18 . What is the perimeter length of the shaded hexagon? ", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1830.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the ten points in the diagram is labelled with one of the numbers 0,1 or 2. It is known that the sum of the numbers in the corner points of each white triangle is divisible by 3, while the sum of the numbers in the corner points of each black triangle is not divisible by 3. Three of the points are already labeled as shown in the diagram. With which numbers can the inner point be labeled?\n\\n Options: A. only 0, B. only 1, C. only 2, D. only 0 and 1, E. either 0 or 1 or 2", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/289.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rectangle $ ABCD$, we have $ AB=8$, $ BC=9$, $ H$ is on $ \\overline{BC}$ with $ BH=6$, $ E$ is on $ \\overline{AD}$ with $ DE=4$, line $ EC$ intersects line $ AH$ at $ G$, and $ F$ is on line $ AD$ with $ \\overline{GF}\\perp\\overline{AF}$. Find the length $ GF$.\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/2124.png" }, { "solution": "\\boxed{67}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a square $P Q R S$ with area $120 \\mathrm{~cm}^{2}$. Point $T$ is the mid-point of $P Q$. The ratio $Q U: U R=2: 1$, the ratio $R V: V S=3: 1$ and the ratio $S W: W P=4: 1$. What is the area, in $\\mathrm{cm}^{2}$, of quadrilateral $T U V W$? ", "completion": "\\boxed{67}", "image_path": "dataset/math_vision/images/1798.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a drawing we can see a three quarter circle with centre M and an indicated orientation arrow. This three-quarter circle is first turned $90^{\\circ}$ anti-clockwise about M and then reflected in the x - axis. Which is the resulting picture?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1370.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three lines intersect at one point. Two angles are given in the figure. How many degrees does the grey angle have?\n\\n Options: A. $52^{\\circ}$, B. $53^{\\circ}$, C. $54^{\\circ}$, D. $55^{\\circ}$, E. $56^{\\circ}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1041.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Turning a card around on the top side, we see the photo of the kangaroo. Instead, if we turn the card around on the right side, what will appear?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/112.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The given net is folded along the dotted lines to form an open box. The box is placed on the table so that the opening is on the top. Which side is facing the table?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/860.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anna has five circular discs that are all of different sizes. She wants to build a tower using three discs where a smaller disc always has to lie on top of a bigger disc. How many ways are there for Anna to build the tower? ", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/1246.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers in the five circles around each house add up to 20 . Some numbers are missing.\n\nWhich number does the question mark stand for?", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/149.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We consider a $5 \\times 5$ square that is split up into 25 fields. Initially all fields are white. In each move it is allowed to change the colour of two fields that are horizontally or vertically adjacent (i.e. white fields turn black and black ones turn white). What is the smallest number of moves needed to obtain the chessboard colouring shown in the diagram?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1402.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six different numbers, chosen from integers 1 to 9 , are written on the faces of a cube, one number per face. The sum of the numbers on each pair of opposite faces is always the same. Which of the following numbers could have been written on the opposite side with the number 8 ?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/115.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The closed curve in the figure is made up of $9$ congruent circular arcs each of length $\\frac{2\\pi}{3}$, where each of the centers of the corresponding circles is among the vertices of a regular hexagon of side $2$. What is the area enclosed by the curve?\n\n\\n Options: A. $2\\pi+6$, B. $2\\pi+4\\sqrt{3}$, C. $3\\pi+4$, D. $2\\pi+3\\sqrt{3}+2$, E. $\\pi+6\\sqrt{3}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2184.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Right isosceles triangles are constructed on the sides of a 3-4-5 right triangle, as shown. A capital letter represents the area of each triangle. Which one of the following is true?\n\n\\n Options: A. $X+Z=W+Y$, B. $W+X=Z$, C. $3X+4Y=5Z$, D. $X+W=\\frac{1}{2}(Y+Z)$, E. $X+Y=Z$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2640.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle $A B C D$ with dimensions $16 \\mathrm{~cm}$ by $4 \\mathrm{~cm}$ was folded along the line MN so that corner C meets corner A. What is the area of the Pentagon ABNMD'?\n\\n Options: A. $17 \\mathrm{~cm}^{2}$, B. $27 \\mathrm{~cm}^{2}$, C. $37 \\mathrm{~cm}^{2}$, D. $47 \\mathrm{~cm}^{2}$, E. $57 \\mathrm{~cm}^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1363.png" }, { "solution": "\\boxed{335}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two spheres with radii $36$ and one sphere with radius $13$ are each externally tangent to the other two spheres and to two different planes $\\mathcal{P}$ and $\\mathcal{Q}$. The intersection of planes $\\mathcal{P}$ and $\\mathcal{Q}$ is the line $\\ell$. The distance from line $\\ell$ to the point where the sphere with radius $13$ is tangent to plane $\\mathcal{P}$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\n\n", "completion": "\\boxed{335}", "image_path": "dataset/math_vision/images/2098.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sepideh is making a magic multiplication square using the numbers 1, 2, 4, 5, 10, 20, 25, 50 and 100 . The products of the numbers in each row, in each column and in the two diagonals should all be the same. In the figure you can see how she has started. Which number should Sepideh place in the cell with the question mark? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1915.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the floor plan of Renate's house. Renate enters her house from the terrace (Terrasse) and walks through every door of the house exactly once. Which room does she end up in?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/307.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram shown, you should follow the arrows to get from A to B. How many different ways are there that fulfill this condition?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1418.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Nico is learning to drive. He knows how to turn right but has not yet learned how to turn left. What is the smallest number of right turns he could make to travel from $\\mathrm{P}$ to $\\mathrm{Q}$, moving first in the direction shown? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1791.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, triangle $J K L$ is isosceles with $J K=J L, P Q$ is perpendicular to $J K$, angle $K P L$ is $120^{\\circ}$ and angle $J K P$ is $50^{\\circ}$. What is the size of angle $P K L$ ? \\n Options: A. $5^{\\circ}$, B. $10^{\\circ}$, C. $15^{\\circ}$, D. $20^{\\circ}$, E. $25^{\\circ}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1846.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the figures is shown most often in the sequence?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/453.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Barbara wants to place draughts on a $4 \\times 4$ board in such a way that the number of draughts in each row is equal to the number shown at the end of the row, and the number of draughts in each column is equal to the number shown at the bottom of the column. No more than one draught is to be placed in any cell. In how many ways can this be done? ", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1874.png" }, { "solution": "\\boxed{46}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the area of polygon $ ABCDEF$?\n\n", "completion": "\\boxed{46}", "image_path": "dataset/math_vision/images/2504.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are four cards on the table as in the picture. Every card has a letter on one side and a number on the other side. Peter said: \"For every card on the table it is true that if there is a vowel on one side, there is an even number on the other side.\" What is the smallest number of cards Alice must turn in order to check whether Peter said the truth?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/185.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shown can be folded into the shape of a cube. In the resulting cube, which of the lettered faces is opposite the face marked $x$?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2415.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Gray and white pearls are threaded onto a string. Tony pulls pearls from the ends of the chain. After pulling off the fifth gray pearl he stops. At most, how many white pearls could he have pulled off?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/1109.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What fraction of the square is grey?\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{1}{4}$, C. $\\frac{1}{5}$, D. $\\frac{3}{8}$, E. $\\frac{2}{9}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/790.png" }, { "solution": "\\boxed{192}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure below shows a polygon $ABCDEFGH$, consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that $AH = EF = 8$ and $GH = 14$. What is the volume of the prism?\n\n", "completion": "\\boxed{192}", "image_path": "dataset/math_vision/images/2781.png" }, { "solution": "\\boxed{50}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The solid shown in the diagram has 12 regular pentagonal faces, the other faces being either equilateral triangles or squares. Each pentagonal face is surrounded by 5 square faces and each triangular face is surrounded by 3 square faces. John writes 1 on each triangular face, 5 on each pentagonal face and -1 on each square. What is the total of the numbers written on the solid?\n", "completion": "\\boxed{50}", "image_path": "dataset/math_vision/images/362.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nEach of the three circles in the adjoining figure is externally tangent to the other two, and each side of the triangle is tangent to two of the circles. If each circle has radius three, then the perimeter of the triangle is\\n Options: A. $36+9\\sqrt{2}$, B. $36+6\\sqrt{3}$, C. $36+9\\sqrt{3}$, D. $18+18\\sqrt{3}$, E. $45$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2318.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows four cars 1, 2, 3 and 4. The arrows show where the cars move to in 5 seconds. Which cars will crash into each other?\n\\n Options: A. 1 and 2, B. 1 and 3, C. 1 and 4, D. 2 and 3, E. 3 and 4", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/689.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the $8 \\times 6$ grid pictured, there are 24 squares that have not been cut by either of the two diagonals. Now we draw the two diagonals on a $10 \\times 6$ grid. How many squares in this grid will not be cut by either of the two diagonals?\n", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/1099.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Bia has five coins as shown beside. She went to the grocery store to buy a fruit, using only three coins, without having to receive change. Among the prices of the following fruits, which one can she NOT buy?\n\\n Options: A. 1, B. 30, C. 1, D. 35, E. 1, F. 40, G. 1, H. 55, I. 1, J. 75", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/919.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anne has a few grey tiles like the one in the picture.\n\nWhat is the maximum number of these tiles that she can place on the $5 \\times 4$ rectangle without any overlaps?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/820.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The star shown in the picture is made by fitting together 12 congruent equilateral triangles. The perimeter of the star is $36 \\mathrm{~cm}$. What is the perimeter of the grey hexagon?\n\\n Options: A. $6 \\mathrm{~cm}$, B. $12 \\mathrm{~cm}$, C. $18 \\mathrm{~cm}$, D. $24 \\mathrm{~cm}$, E. $30 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1047.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle of diameter $1$ is removed from a $2\\times 3$ rectangle, as shown. Which whole number is closest to the area of the shaded region?\n\n\\n Options: A. 1, B. 2, C. 3, D. 4, E. 5", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2553.png" }, { "solution": "\\boxed{70}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two equilateral triangles of different sizes are placed on top of each other so that a hexagon is formed on the inside whose opposite sides are parallel. Four of the side lengths of the hexagon are stated in the diagram. How big is the perimeter of the hexagon? ", "completion": "\\boxed{70}", "image_path": "dataset/math_vision/images/386.png" }, { "solution": "\\boxed{14}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the star shaped figure below, if all side lengths are equal to $3$ and the three largest angles of the figure are $210$ degrees, its area can be expressed as $\\frac{a \\sqrt{b}}{c}$ , where $a, b$, and $c$ are positive integers such that $a$ and $c$ are relatively prime and that $b$ is square-free. Compute $a + b + c$.\\n", "completion": "\\boxed{14}", "image_path": "dataset/math_vision/images/2803.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: You need 3 pieces to build this shape. Each piece is made out of 4 , equally sized cubes of the same colour. What is the shape of the white piece?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/494.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each square in the grid shown is $1 \\mathrm{~cm}$ by $1 \\mathrm{~cm}$. What is the area of the shaded figure, in $\\mathrm{cm}^{2}$ ? ", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/1776.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Both the figures on the right were made out of the same 5 pieces. The rectangle has dimensions $5 \\mathrm{~cm} \\times 10 \\mathrm{~cm}$. The other pieces are quarter circles with 2 different sized radii. What is the difference between the perimeters of the two figures?\n\\n Options: A. $2.5 \\mathrm{~cm}$, B. $5 \\mathrm{~cm}$, C. $10 \\mathrm{~cm}$, D. $15 \\mathrm{~cm}$, E. $20 \\mathrm{~cm}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/814.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The kangaroo is inside how many circles?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/32.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An $ 8$-foot by $ 10$-foot floor is tiled with square tiles of size $ 1$ foot by $ 1$ foot. Each tile has a pattern consisting of four white quarter circles of radius $ 1/2$ foot centered at each corner of the tile. The remaining portion of the tile is shaded. How many square feet of the floor are shaded?\n\\n Options: A. $80-20\\pi$, B. $60-10\\pi$, C. $80-10\\pi$, D. $60+10\\pi$, E. $80+10\\pi$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2148.png" }, { "solution": "\\boxed{175}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The adjoining figure shows two intersecting chords in a circle, with $B$ on minor arc $AD$. Suppose that the radius of the circle is 5, that $BC = 6$, and that $AD$ is bisected by $BC$. Suppose further that $AD$ is the only chord starting at $A$ which is bisected by $BC$. It follows that the sine of the minor arc $AB$ is a rational number. If this fraction is expressed as a fraction $m/n$ in lowest terms, what is the product $mn$?\n", "completion": "\\boxed{175}", "image_path": "dataset/math_vision/images/2038.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The vertices of a $ 3 - 4 - 5$ right triangle are the centers of three mutually externally tangent circles, as shown. What is the sum of the areas of the three circles?\n\\n Options: A. $12\\pi$, B. $\\frac{25\\pi}{2}$, C. $13\\pi$, D. $\\frac{27\\pi}{2}$, E. $14\\pi$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2464.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the sum each letter stands for a different digit.\nWhat is the answer to the subtraction $ RN - KG $ ? ", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/1760.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: From which rectangular can you cut the figure shown on the right side out?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/429.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare?\n\n\\n Options: A. $\\text{The shaded areas in all three are equal.}$, B. $\\text{Only the shaded areas of }I\\text{ and }II\\text{ are equal.}$, C. $\\text{Only the shaded areas of }I\\text{ and }III\\text{ are equal.}$, D. $\\text{Only the shaded areas of }II\\text{ and }III\\text{ are equal.}$, E. $\\text{The shaded areas of }I, II\\text{ and }III\\text{ are all different.}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2572.png" }, { "solution": "\\boxed{160}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are 10 boxes in the first van. Every further van contains twice as many boxes as the previous one. How many boxes are there in the fifth van?\n", "completion": "\\boxed{160}", "image_path": "dataset/math_vision/images/396.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One of the line segments shown on the grid is the image produced by a rotation of the other line segment. Which of the points $T, U, V$, $W$ could be the centre of such a rotation? \\n Options: A. only $T$, B. only $U$, C. either of $U$ and $W$, D. any of $U, V$ and $W$, E. any of $T, U, V$ and $W$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1871.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each object shown is made up of 7 cubes. Which of $\\mathrm{P}, \\mathrm{Q}, \\mathrm{R}$ and $\\mathrm{S}$ can be obtained by rotating $\\mathrm{T}$ ?\n\\n Options: A. P and R, B. Q and S, C. only R, D. none of them, E. P, F. Q and R", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1547.png" }, { "solution": "\\boxed{14}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let there be a unit square initially tiled with four congruent shaded equilateral triangles, as seen below. The total area of all of the shaded regions can be expressed in the form $\\frac{a-b\\sqrt{c}}{d}$ , where $a, b, c$, and $d$ are positive integers and $c$ is not divisible by the square of any prime. Compute $a + b + c + d$.\\n", "completion": "\\boxed{14}", "image_path": "dataset/math_vision/images/2863.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Numbers 3,4 and two other unknown numbers are written in the cells of the $2 \\times 2$ table. It is known that the sums of numbers in the rows are equal to 5 and 10, and the sum of numbers in one of the columns is equal to 9. The larger number of the two unknown ones is\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/205.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: 5 congruent rectangles are positioned in a square with side length 24 as shown in the diagram. How big is the area of one of these rectangles?\n\\n Options: A. $12 \\mathrm{~cm}^{2}$, B. $16 \\mathrm{~cm}^{2}$, C. $18 \\mathrm{~cm}^{2}$, D. $24 \\mathrm{~cm}^{2}$, E. $32 \\mathrm{~cm}^{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1111.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The cube shown has sides of length 2 units. Holes in the shape of a hemisphere are carved into each face of the cube. The six hemispheres are identical and their centres are at the centres of the faces of the cube. The holes are just large enough to touch the hole on each neighbouring face. What is the diameter of each hole? \\n Options: A. 1, B. $\\sqrt{2}$, C. $2-\\sqrt{2}$, D. $3-\\sqrt{2}$, E. $3-\\sqrt{3}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1979.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram below shows a rectangle with side lengths $4$ and $8$ and a square with side length $5$. Three vertices of the square lie on three different sides of the rectangle, as shown. What is the area of the region inside both the square and the rectangle?\n\n\\n Options: A. $15\\frac{1}{8}$, B. $15\\frac{3}{8}$, C. $15\\frac{1}{2}$, D. $15\\frac{5}{8}$, E. $15\\frac{7}{8}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2250.png" }, { "solution": "\\boxed{\\frac{2}{5}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of the semicircle in Figure A is half the area of the circle in Figure B. The area of a square inscribed in the semicircle, as shown, is what fraction of the area of a square inscribed in the circle?\n\n", "completion": "\\boxed{\\frac{2}{5}}", "image_path": "dataset/math_vision/images/2956.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $ \\triangle ABC$, $ \\angle ABC = 45^\\circ$. Point $ D$ is on $ \\overline{BC}$ so that $ 2 \\cdot BD = CD$ and $ \\angle DAB = 15^\\circ$. Find $ \\angle ACB$.\n\\n Options: A. $54^\\circ$, B. $60^\\circ$, C. $72^\\circ$, D. $75^\\circ$, E. $90^\\circ$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2447.png" }, { "solution": "\\boxed{7685413092}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six numbers are written on the following cards, as shown:\n\nWhat is the largest number you can form with the given cards?", "completion": "\\boxed{7685413092}", "image_path": "dataset/math_vision/images/729.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Karo has a box of matches with 30 matches. Using some of the matches she forms the number 2022. She has already formed the first two digits (see picture). How many matches will be left in the box when she has finished the number?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1465.png" }, { "solution": "\\boxed{170}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure below depicts two congruent triangles with angle measures $40^\\circ$, $50^\\circ$, and $90^\\circ$. What is the measure of the obtuse angle $\\alpha$ formed by the hypotenuses of these two triangles?\\n", "completion": "\\boxed{170}", "image_path": "dataset/math_vision/images/2823.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In addition to the weight of the basket a single balloon can lift $80 \\mathrm{~kg}$. 2 balloons can lift $180 \\mathrm{~kg}$ in addition to the weight of the basket. How heavy is the basket?\n\\n Options: A. $60 \\mathrm{~kg}$, B. $50 \\mathrm{~kg}$, C. $40 \\mathrm{~kg}$, D. $30 \\mathrm{~kg}$, E. $20 \\mathrm{~kg}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/806.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Alice draws lines between the beetles. She starts with the beetle with the fewest points. Then she continues drawing to the beetle with one more point. Which figure is formed?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/72.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jan sticks these three pieces of paper Which picture can he not obtain?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/985.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Convex quadrilateral $ABCD$ has $AB = 3, BC = 4, CD = 13, AD = 12,$ and $\\angle ABC = 90^\\circ,$ as shown. What is the area of the quadrilateral?\n\n", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/2480.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $W X Y Z$ is a square, $M$ is the midpoint of $W Z$ and $M N$ is perpendicular to $W Y$. What is the ratio of the area of the shaded triangle $M N Y$ to the area of the square? \\n Options: A. 1:6, B. 1:5, C. 7:36, D. 3:16, E. 7:40", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1595.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The lengths of the sides of triangle $X Y Z$ are $X Z=\\sqrt{55}$, $X Y=8, Y Z=9$. Find the length of the diagonal $X A$ of the rectangular parallelepiped in the figure.\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/192.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the $6 \\times 8$ grid shown, 24 cells are not intersected by either diagonal. When the diagonals of a $6 \\times 10$ grid are drawn, how many cells are not intersected by either diagonal? ", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/1602.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The bee on the right has a few pieces missing. Each piece costs points (Punkte).\n\nHow many points does Maya need to complete the bee?", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/156.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The squares are formed by intersecting the segment $A B$ of $24 \\mathrm{~cm}$ by the broken line $A A_{1} A_{2} \\ldots A_{12} B$ (see the figure). Find the length of $A A_{1} A_{2} \\ldots A_{12} B$.\n\\n Options: A. $48 \\mathrm{~cm}$, B. $72 \\mathrm{~cm}$, C. $96 \\mathrm{~cm}$, D. $56 \\mathrm{~cm}$, E. $106 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/750.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure of a rectangular solid, $\\angle DHG=45^\\circ$ and $\\angle FHB=60^\\circ$. Find the cosine of $\\angle BHD$.\n\n\\n Options: A. $\\frac{\\sqrt{3}}{6}$, B. $\\frac{\\sqrt{2}}{6}$, C. $\\frac{\\sqrt{6}}{3}$, D. $\\frac{\\sqrt{6}}{4}$, E. $\\frac{\\sqrt{6}-\\sqrt{2}}{4}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2341.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A digital clock shows the following time: What time is it when it uses the exactly same digits again for the first time after that?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/901.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If all the statements in the box are true, which of $\\mathrm{A}, \\mathrm{B}, \\mathrm{C}$, $\\mathrm{D}$ or $\\mathrm{E}$ can be deduced? \\n Options: A. It's red, B. It's a blue square, C. It's red and round, D. It's yellow and round, E. It's blue and round", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1535.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We take three points from the grid so that they were collinear. How many possibilities do we have?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/210.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nIn this figure $AB$ is a diameter of a circle, centered at $O$, with radius $a$. A chord $AD$ is drawn and extended to meet the tangent to the circle at $B$ in point $C$. Point $E$ is taken on $AC$ so that $AE=DC$. Denoting the distances of $E$ from the tangent through $A$ and from the diameter $AB$ by $x$ and $y$, respectively, we can deduce the relation:\\n Options: A. $y^2=\\frac{x^3}{2a-x}$, B. $y^2=\\frac{x^3}{2a+x}$, C. $y^4=\\frac{x^2}{2-x} \\\\$, D. $x^2=\\frac{y^2}{2a-x}$, E. $x^2=\\frac{y^2}{2a+x}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2287.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A set of three points is randomly chosen from the grid shown. Each three point set has the same probability of being chosen. What is the probability that the points lie on the same straight line?\n\\n Options: A. $\\frac{1}{21}$, B. $\\frac{1}{14}$, C. $\\frac{2}{21}$, D. $\\frac{1}{7}$, E. $\\frac{2}{7}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2131.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many lines of symmetry does this figure have?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/1060.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following nets can be used to build the partial cube shown in the diagram?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1728.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We have cut off one corner of a cube. Which of the developments below is the development of the remaining part?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/717.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the given figure hexagon $ABCDEF$ is equiangular, $ABJI$ and $FEHG$ are squares with areas $18$ and $32$ respectively, $\\triangle JBK$ is equilateral and $FE=BC$. What is the area of $\\triangle KBC$?\n\\n Options: A. $6\\sqrt{2}$, B. $9$, C. $12$, D. $9\\sqrt{2}$, E. $32$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2736.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Grandma's watch has an hour, minute and second hand. We don't know which hand does which job, but we know that the watch tells the correct time. At 12:55:30 hours the watch looked as pictured. How will the watch look at 8:11:00 hours?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/497.png" }, { "solution": "\\boxed{\\frac{9}{5}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure below, quadrilateral $CDEG$ is a square with $CD = 3$, and quadrilateral $BEFH$ is a rectangle. If $BE = 5$, how many units is $BH$? Express your answer as a mixed number. ", "completion": "\\boxed{\\frac{9}{5}}", "image_path": "dataset/math_vision/images/2891.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which point in the labyrinth can we get to, starting at point $O$?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/52.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a grid made of vertical and horizontal lines. Which part was cut from the grid? \n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1239.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: 4 posts are placed along a $120 \\mathrm{~m}$ long running track. How many more posts have to be placed so that the running track is split into equally long sections that way? ", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/990.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the grid on the right, there are eight kangaroos. A kangaroo may jump into any empty square. Find the least number of the kangaroos which have to jump into an empty square so that in each row and column there are exactly two kangaroos. ", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1817.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The word \"'''HELP'''\" in block letters is painted in black with strokes $1$ unit wide on a $5$ by $15$ rectangular white sign with dimensions as shown. The area of the white portion of the sign, in square units, is\n\n", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/2567.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows an octagon consisting of $10$ unit squares. The portion below $\\overline{PQ}$ is a unit square and a triangle with base $5$. If $\\overline{PQ}$ bisects the area of the octagon, what is the ratio $\\frac{XQ}{QY}$?\n\n\\n Options: A. $\\frac{2}{5}$, B. $\\frac{1}{2}$, C. $\\frac{3}{5}$, D. $\\frac{2}{3}$, E. $\\frac{3}{4}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2706.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following indeformable pieces of wire, when duplicated, allows to make a closed piece without crosses, with the two pieces joined by their ends?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/926.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Baris has a few dominoes as shown in the picture. He wants to lay them in a line according to the rules of dominoes, that is that two dominoes can only be laid together if the neighbouring squares have the same number of dots in them. What is the biggest number of these dominoes that he can lay in a single line?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/507.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If $\\angle A = 20^\\circ$ and $\\angle AFG = \\angle AGF$, then $\\angle B + \\angle D = $\n\n\\n Options: A. $48^\\circ$, B. $60^\\circ$, C. $72^\\circ$, D. $80^\\circ$, E. $90^\\circ$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2623.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $ABC$ shown in the adjoining figure, $M$ is the midpoint of side $BC$, $AB=12$ and $AC=16$. Points $E$ and $F$ are taken on $AC$ and $AB$, respectively, and lines $EF$ and $AM$ intersect at $G$. If $AE=2AF$ then $\\frac{EG}{GF}$ equals\n\\n Options: A. $\\frac{3}{2}$, B. $\\frac{4}{3}$, C. $\\frac{5}{4}$, D. $\\frac{6}{5} \\$, E. $\\text{not enough information to solve the problem}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2312.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In an equilateral triangle with area 1, we draw the six perpendicular lines from the midpoints of each side to the other two sides as seen in the diagram. How big is the area of the grey hexagon that has been created this way?\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{2}{5}$, C. $\\frac{4}{9}$, D. $\\frac{1}{2}$, E. $\\frac{2}{3}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1407.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure triangle $ ABC$ is such that $ AB = 4$ and $ AC = 8$. If $ M$ is the midpoint of $ BC$ and $ AM = 3$, what is the length of $ BC$?\n\\n Options: A. $2\\sqrt{26}$, B. $2\\sqrt{31}$, C. $9$, D. $4+2\\sqrt{13}$, E. $\\text{not enough information given to solve the problem}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2310.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mike has built a construction, shown in the upper picture, from equal cubes. Lily has taken several cubes out of it, thus Mike's construction became such as we see in the lower picture. How many cubes has Lily taken?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/11.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Caroline wants to write the numbers $1,2,3,4$ in the square $4 \\times 4$ in such a way that every row and every column has each of the numbers. You see how she started. In how many different ways can she finish?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1278.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Tom has these nine cards:\n\nHe places these cards on the board next to each other so that each horizontal line and each vertical line has three cards with the three different shapes and the three different amounts of drawings. He has already placed three cards, as shown in the picture. Which card should he place in the colored box?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/113.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Leon has drawn a closed path on the surface of a cuboid. Which net can represent his path?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/388.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the nine paths in a park are $100 \\mathrm{~m}$ long. Anna wants to walk from $A$ to $B$ without using the same path twice. How long the longest path she can choose?\n\\n Options: A. $900 \\mathrm{~m}$, B. $800 \\mathrm{~m}$, C. $700 \\mathrm{~m}$, D. $500 \\mathrm{~m}$, E. $400 \\mathrm{~m}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1083.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Valentin draws a zig-zag line inside a rectangle as shown in the diagram. For that he uses the angles $10^{\\circ}, 14^{\\circ}, 33^{\\circ}$ and $26^{\\circ}$. How big is angle $\\varphi$?\n\\n Options: A. $11^{\\circ}$, B. $12^{\\circ}$, C. $16^{\\circ}$, D. $17^{\\circ}$, E. $33^{\\circ}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1167.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Point $F$ is taken in side $AD$ of square $ABCD$. At $C$ a perpendicular is drawn to $CF$, meeting $AB$ extended at $E$. The area of $ABCD$ is $256$ square inches and the area of triangle $CEF$ is $200$ square inches. Then the number of inches in $BE$ is:\n\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/2278.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Julia has 2017 round discs available: 1009 black ones and 1008 white ones. Using them, she wants to lay the biggest square pattern (as shown) possible and starts by using a black disc in the left upper corner. Subsequently she lays the discs in such a way that the colours alternate in each row and column. How many discs are left over\nwhen she has laid the biggest square possible?\n\\n Options: A. none, B. 40 of each colour, C. 40 black and 41 white ones, D. 41 of each colour, E. 40 white and 41 black ones", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/302.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In this addition each of the letters $X, Y$ and $Z$ represents a different non-zero digit. The letter $X$ will then have to stand for\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/1264.png" }, { "solution": "\\boxed{23}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure below is constructed from $11$ line segments, each of which has length $2$. The area of pentagon $ABCDE$ can be written as $\\sqrt{m}+\\sqrt{n},$ where $m$ and $n$ are positive integers. What is $m+n?$\n\n", "completion": "\\boxed{23}", "image_path": "dataset/math_vision/images/2240.png" }, { "solution": "\\boxed{256\\pi}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The lateral surface area of the frustum of a solid right cone is the product of one-half the slant height ($L$) and the sum of the circumferences of the two circular faces. What is the number of square centimeters in the total surface area of the frustum shown here? Express your answer in terms of $\\pi$.\n\n", "completion": "\\boxed{256\\pi}", "image_path": "dataset/math_vision/images/3004.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the non-convex quadrilateral $ABCD$ shown below, $\\angle BCD$ is a right angle, $AB=12$, $BC=4$, $CD=3$, and $AD=13$.\n\nWhat is the area of quadrilateral $ABCD$?", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/2744.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mother halves the birthday cake. One half she then halves again. Of that she again halves one of the smaller pieces. Of these smaller pieces she once more halves one of them (see diagram). One of the two smallest pieces weighs $100 \\mathrm{~g}$.\nHow much does the entire cake weigh?\n\\n Options: A. $600 \\mathrm{~g}$, B. $800 \\mathrm{~g}$, C. $1200 \\mathrm{~g}$, D. $1600 \\mathrm{~g}$, E. $2000 \\mathrm{~g}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/610.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Leo has built a stick made up of 27 building blocks.\n\nHe splits the stick into two pieces in a way so that one part is twice as long as the other. He keeps repeating this again and again. He takes one of the two pieces and splits it up so that one piece is twice as long as the other. Which of the following pieces can never result in this way?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/560.png" }, { "solution": "\\boxed{260}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a rectangle that has been dissected into nine non-overlapping squares. Given that the width and the height of the rectangle are relatively prime positive integers, find the perimeter of the rectangle.\n\n", "completion": "\\boxed{260}", "image_path": "dataset/math_vision/images/2061.png" }, { "solution": "\\boxed{28}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A game board consists of $64$ squares that alternate in color between black and white. The figure below shows square $P$ in the bottom and square $Q$ in the top row. A marker is placed at $P$. A step consists of moving the marker onto one of the adjoining white squares in the row above. How many $7$-step paths are there from $P$ to $Q$? (The figure shows a sample path.)\n\n", "completion": "\\boxed{28}", "image_path": "dataset/math_vision/images/2768.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Caroline wants to write the numbers 1, 2, 3, 4 in the square $4 \\times 4$ in such a way that every row and every column has each number. You see how she started. What number must be put in the place of $x$?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/712.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria drew the following figures on square sheets of paper.\n\nHow many of these figures have the same perimeter as the square sheet of paper itself?", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/821.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A kangaroo enters a building. He only passes through triangular rooms. Where does he leave the building?\n\\n Options: A. a, B. b, C. c, D. d, E. e", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/428.png" }, { "solution": "\\boxed{160}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nIn the diagram, $P T$ and $P S$ are tangents to a circle with centre $O$. The point $Y$ lies on the circumference of the circle; and the point $Z$ is where the line $P Y$ meets the radius $O S$.\nAlso, $\\angle S P Z=10^{\\circ}$ and $\\angle T O S=150^{\\circ}$.\nHow many degrees are there in the sum of $\\angle P T Y$ and $\\angle P Y T$ ?", "completion": "\\boxed{160}", "image_path": "dataset/math_vision/images/2001.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square with area $30 \\mathrm{~cm}^{2}$ is divided in two by a diagonal and then into triangles as shown. The areas of some of these triangles are given in the diagram (which is not drawn to scale). Which part of the diagonal is the longest? \\n Options: A. $a$, B. $b$, C. $C$, D. $d$, E. $e$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1625.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Julia puts the nine chips on the right in a box. She then takes one chip at a time, without looking, and notes down its digit, obtaining, at the end, a number of nine different digits. What is the probability that the number written by Julia is divisible by 45?\n\\n Options: A. $\\frac{1}{9}$, B. $\\frac{2}{9}$, C. $\\frac{1}{3}$, D. $\\frac{4}{9}$, E. $\\frac{8}{9}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1446.png" }, { "solution": "\\boxed{90}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $AD=BD=CD$ and $\\angle BCA = 40^\\circ.$ What is the measure of $\\angle BAC?$\n\n", "completion": "\\boxed{90}", "image_path": "dataset/math_vision/images/3019.png" }, { "solution": "\\boxed{68}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Emily makes four identical numbered cubes using the net shown. She then glues them together so that only faces with the same number on are glued together to form the $2 \\times 2 \\times 1$ block shown. What is the largest possible total of all the numbers on the faces of the block that Emily could achieve? ", "completion": "\\boxed{68}", "image_path": "dataset/math_vision/images/1799.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The square in the picture consists of two smaller squares and two rectangles of area $18 \\mathrm{~cm}^{2}$ each. The area of one of smaller rectangles is $81 \\mathrm{~cm}^{2}$. What is the length (in $\\mathrm{cm}$ ) of side of the biggest square?\n", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/702.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A furniture shop sells 3-seater, 2-seater and 1-seater sofas that each have an equally wide armrest on the left and the right hand side. Each seat is equally wide (see picture). Together with the armrests the 3-seater sofa is $220 \\mathrm{~cm}$ and the 2-seater sofa $160 \\mathrm{~cm}$ wide. How wide is the 1-seater sofa?\n\\n Options: A. $60 \\mathrm{~cm}$, B. $80 \\mathrm{~cm}$, C. $90 \\mathrm{~cm}$, D. $100 \\mathrm{~cm}$, E. $120 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/873.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If the area of the triangle shown is 40, what is $r$? ", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/2927.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two rectangles form the angles $40^{\\circ}$ and $30^{\\circ}$ respectively, with a straight line (see diagram). How big is angle $\\alpha$?\n\\n Options: A. $105^{\\circ}$, B. $120^{\\circ}$, C. $130^{\\circ}$, D. $135^{\\circ}$, E. another value", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/317.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three circles of radius $ s$ are drawn in the first quadrant of the $ xy$-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the $ x$-axis, and the third is tangent to the first circle and the $ y$-axis. A circle of radius $ r > s$ is tangent to both axes and to the second and third circles. What is $ r/s$?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/2462.png" }, { "solution": "\\boxed{90}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many different ways can you follow from point $A$ to point $B$ if you you can go only down, right or down diagonally by the sides of small triangles?\n", "completion": "\\boxed{90}", "image_path": "dataset/math_vision/images/1305.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many plums (see the picture) weigh as much as an apple?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/20.png" }, { "solution": "\\boxed{25}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The square $F G H I$ has area 80 . Points $J, K, L, M$ are marked on the sides of the square so that $F K=G L=H M=I J$ and $F K=3 K G$. What is the area of the shaded region? ", "completion": "\\boxed{25}", "image_path": "dataset/math_vision/images/1909.png" }, { "solution": "\\boxed{$6+4\\sqrt{3}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below, the three circles and the three line segments are tangent as shown. Given that the radius of all of the three circles is $1$, compute the area of the triangle.\\n", "completion": "\\boxed{$6+4\\sqrt{3}$}", "image_path": "dataset/math_vision/images/2811.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nThe large circle has diameter $ \\overline{AC}$. The two small circles have their centers on $ \\overline{AC}$ and just touch at $ O$, the center of the large circle. If each small circle has radius $ 1$, what is the value of the ratio of the area of the shaded region to the area of one of the small circles?\\n Options: A. $\\text{between }\\frac{1}{2} \\text{ and }1$, B. $1$, C. $\\text{between 1 and }\\frac{3}{2}$, D. $\\text{between }\\frac{3}{2} \\text{ and }2 \\\\$, E. $\\text{cannot be determined from the information given}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2515.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The six weights of a scale weigh $1 \\mathrm{~kg}, 2 \\mathrm{~kg}, 3 \\mathrm{~kg}, 4 \\mathrm{~kg}, 5 \\mathrm{~kg}$ and $6 \\mathrm{~kg}$. Rosi places five weights on the two scale pans so that they are balanced. The sixth weight is left aside. Which weight is left aside?\n\\n Options: A. $1 \\mathrm{~kg}$, B. $2 \\mathrm{~kg}$, C. $3 \\mathrm{~kg}$, D. $4 \\mathrm{~kg}$, E. $5 \\mathrm{~kg}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/688.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The distance between the top of the cat that is sitting on the table to the top of the cat that is sleeping on the floor is $150 \\mathrm{~cm}$. The distance from the top of the cat that is sleeping on the table to the top of the cat that is sitting on the floor is $110 \\mathrm{~cm}$. How high is the table?\n\\n Options: A. $110 \\mathrm{~cm}$, B. $120 \\mathrm{~cm}$, C. $130 \\mathrm{~cm}$, D. $140 \\mathrm{~cm}$, E. $150 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1415.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large cube is made from 64 small cubes. The 5 visible faces of the large cube are green, the bottom face is red. How many of the small cubes have 3 green faces?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/472.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Kathi folds a square piece of paper twice and subsequently cuts it along the two lines as shown in the picture. The resulting pieces of paper are then unfolded if possible. How many of the pieces of paper are squares?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1185.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The convex pentagon $ABCDE$ has $\\angle A=\\angle B=120^{\\circ}$, $EA=AB=BC=2$ and $CD=DE=4$. What is the area of $ABCDE$?\n\\n Options: A. $10$, B. $7\\sqrt{3}$, C. $15$, D. $9\\sqrt{3}$, E. $12\\sqrt{5}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2401.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Cynthia paints each region of the figure in a single color: red, blue or yellow. She paints with different colors the regions that touch each other. In how many different ways can Cyntia paint the figure?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/628.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six rectangles are arranged as shown. The top left-hand rectangle has height $6 \\mathrm{~cm}$. The numbers within the rectangles indicate their areas in $\\mathrm{cm}^{2}$. What is the height of the bottom right-hand rectangle?\n\\n Options: A. $4 \\mathrm{~cm}$, B. $5 \\mathrm{~cm}$, C. $6 \\mathrm{~cm}$, D. $7.5 \\mathrm{~cm}$, E. $10 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1453.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A strip of paper is folded three times as shown. Determine $\\beta$ if $\\alpha=70^{\\circ}$.\n\\n Options: A. $140^{\\circ}$, B. $130^{\\circ}$, C. $120^{\\circ}$, D. $110^{\\circ}$, E. $100^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/231.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cuboid is made of four pieces as shown. Each piece consists of four cubes and is a single colour. What is the shape of the white piece? \n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1879.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Henna has four hair ribbons of width $10 \\mathrm{~cm}$. When she measures them, she finds that each ribbon is $25 \\mathrm{~cm}$ longer than the next smallest ribbon. She then arranges the ribbons to form two different shapes as shown in the diagram. How much longer is the perimeter of the second shape than the perimeter of the first shape? \\n Options: A. $75 \\mathrm{~cm}$, B. $50 \\mathrm{~cm}$, C. $25 \\mathrm{~cm}$, D. $20 \\mathrm{~cm}$, E. $0 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1744.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A fifteen-meter log has to be sawn into three-meter pieces. How many cuts are needed for that?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/18.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $3 \\times 3$ square initially has the number 0 in each of its cells. In one step all four numbers in one $2 \\times 2$ sub-square such as the shaded one, for example, are then increased by 1. This operation is repeated several times to obtain the arrangement on the right. Unfortunately, some numbers in this arrangement are hidden. What number is in the square with the question mark?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1460.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The arrows on the two spinners shown below are spun. Let the number $N$ equal 10 times the number on Spinner $A$, added to the number on Spinner $B$. What is the probability that $N$ is a perfect square number?\n\\n Options: A. $\\frac{1}{16}$, B. $\\frac{1}{8}$, C. $\\frac{1}{4}$, D. $\\frac{3}{8}$, E. $\\frac{1}{2} $", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2775.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Steven wants to write each of the digits $2,0,1$ and 9 into the boxes of this addition:\n\nHe wants to obtain the biggest result possible. Which digit does he have to use for the single-digit number?\\n Options: A. either 0 or 1, B. either 0 or 2, C. only 0, D. only 1, E. only 2", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/612.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $\\text{ABCD}$ is a rectangle, $\\text{D}$ is the center of the circle, and $\\text{B}$ is on the circle. If $\\text{AD}=4$ and $\\text{CD}=3$, then the area of the shaded region is between\n\n\\n Options: A. $4\\text{ and }5$, B. $5\\text{ and }6$, C. $6\\text{ and }7$, D. $7\\text{ and }8$, E. $8\\text{ and }9$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2519.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Robin shoots three arrows at a target. He earns points for each shot as shown in the figure. However, if any of his arrows miss the target or if any two of his arrows hit adjacent regions of the target, he scores a total of zero. How many different scores can he obtain?\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/2010.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The triangle in the diagram contains a right angle. What is the sum of the other two marked angles on the diagram? \\n Options: A. $150^{\\circ}$, B. $180^{\\circ}$, C. $270^{\\circ}$, D. $320^{\\circ}$, E. $360^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1627.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $S$ be the set of points on the rays forming the sides of a $120^{\\circ}$ angle, and let $P$ be a fixed point inside the angle on the angle bisector. Consider all distinct equilateral triangles $PQR$ with $Q$ and $R$ in $S$. (Points $Q$ and $R$ may be on the same ray, and switching the names of $Q$ and $R$ does not create a distinct triangle.) There are\n\\n Options: A. $\\text{exactly 2 such triangles} \\$, B. $\\text{exactly 3 such triangles} \\$, C. $\\text{exactly 7 such triangles} \\$, D. $\\text{exactly 15 such triangles} \\$, E. $\\text{more than 15 such triangles}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2405.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Figure 1 is called a \"stack map.\" The numbers tell how many cubes are stacked in each position. Fig. 2 shows these cubes, and Fig. 3 shows the view of the stacked cubes as seen from the front.\n\nWhich of the following is the front view for the stack map in Fig. 4?\n\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2609.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: My little brother has a 4-digit bike lock with the digits 0 to 9 on each part of the lock as shown. He started on the correct combination and turned each part the same amount in the same direction and now the lock shows the combination 6348. Which of the following CANNOT be the correct combination of my brother's lock?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/957.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The vertical axis indicates the number of employees, but the scale was accidentally omitted from this graph. What percent of the employees at the Gauss company have worked there for $5$ years or more?\n\n\\n Options: A. $9\\%$, B. $23\\frac{1}{3}\\%$, C. $30\\%$, D. $42\\frac{6}{7}\\%$, E. $50\\%$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2549.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On the number line below, each gap equals one unit. Six integers are marked as shown. At least two of the integers are divisible by 3 , and at least two of them are divisible by 5 . Which of the integers are divisible by 15 ?\n\\n Options: A. $F$ and $K$, B. $G$ and $J$, C. $H$ and $I$, D. all six numbers, E. only one of them", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1845.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jenny writes numbers into a $3 \\times 3$ table so that the sums of the four numbers in each $2 \\times 2$ area of the table are the same. The numbers in three of the cells in the corner can already be seen in the diagram. Which number does she write into the cell in the fourth corner?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1235.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows two rectangles whose sides are parallel to each other. By how much is the perimeter of the bigger rectangle greater than the perimeter of the smaller rectangle?\n\\n Options: A. $12 \\mathrm{~m}$, B. $16 \\mathrm{~m}$, C. $20 \\mathrm{~m}$, D. $21 \\mathrm{~m}$, E. $24 \\mathrm{~m}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1146.png" }, { "solution": "\\boxed{790}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The $8$ eyelets for the lace of a sneaker all lie on a rectangle, four equally spaced on each of the longer sides. The rectangle has a width of $50$ mm and a length of $80$ mm. There is one eyelet at each vertex of the rectangle. The lace itself must pass between the vertex eyelets along a width side of the rectangle and then crisscross between successive eyelets until it reaches the two eyelets at the other width side of the rectrangle as shown. After passing through these final eyelets, each of the ends of the lace must extend at least $200$ mm farther to allow a knot to be tied. Find the minimum length of the lace in millimeters.\n\n", "completion": "\\boxed{790}", "image_path": "dataset/math_vision/images/2082.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: As shown in the figure, line segment $\\overline{AD}$ is trisected by points $B$ and $C$ so that $AB=BC=CD=2$. Three semicircles of radius $1,$ $\\overarc{AEB},\\overarc{BFC},$ and $\\overarc{CGD},$ have their diameters on $\\overline{AD},$ and are tangent to line $EG$ at $E,F,$ and $G,$ respectively. A circle of radius $2$ has its center on $F. $ The area of the region inside the circle but outside the three semicircles, shaded in the figure, can be expressed in the form\n\\[\\frac{a}{b}\\cdot\\pi-\\sqrt{c}+d,\\]where $a,b,c,$ and $d$ are positive integers and $a$ and $b$ are relatively prime. What is $a+b+c+d$?\n\n", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/2225.png" }, { "solution": "\\boxed{14}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Line $DE$ cuts through triangle $ABC$, with $DF$ parallel to $BE$. Given that $BD =DF = 10$ and $AD = BE = 25$, find $BC$.\\n", "completion": "\\boxed{14}", "image_path": "dataset/math_vision/images/2868.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square is split into 4 smaller squares. All small squares should either be coloured in white or black. How many ways are there to colour the big square? (patterns are the same if they can be - as shown in the picture transformed into one another by rotation.)\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1066.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five sparrows are sitting on a rope (see picture). Some of them are looking to the left, some of them are looking to the right. Every sparrow whistles as many times as the number of sparrows he can see sitting in front of him. For example, the third sparrow whistles exactly twice. How often do all sparrows whistle altogether?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/57.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Denis ties his dog, using an 11-meter rope, one meter away from a corner of about 7 meters by 5 meters, as illustrated. Denis places 5 bones near the fence, as shown in the picture. How many bones can the dog catch?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/629.png" }, { "solution": "\\boxed{70}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $ABC$, point $D$ is on segment $BC$, the measure of angle $BAC$ is 40 degrees, and triangle $ABD$ is a reflection of triangle $ACD$ over segment $AD$. What is the measure of angle $B$?\n\n", "completion": "\\boxed{70}", "image_path": "dataset/math_vision/images/3031.png" }, { "solution": "\\boxed{1+\\sqrt{3}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: (See the diagram below.) $ABCD$ is a square. Points $G$, $H$, $I$, and $J$ are chosen in the interior of $ABCD$ so that:\\n(i) $H$ is on $\\overline{AG}$, $I$ is on $\\overline{BH}$, $J$ is on $\\overline{CI}$, and $G$ is on $\\overline{DJ}$\\n(ii) $\\vartriangle ABH \\sim \\vartriangle BCI \\sim \\vartriangle CDJ \\sim \\vartriangle DAG$ and \\n(iii) the radii of the inscribed circles of $\\vartriangle ABH$, $\\vartriangle BCI$, $\\vartriangle CDJ$, $\\vartriangle DAK$, and $GHIJ$ are all the same.\\nWhat is the ratio of $\\overline{AB}$ to $\\overline{GH}$?\\n", "completion": "\\boxed{1+\\sqrt{3}}", "image_path": "dataset/math_vision/images/2849.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The die is a cube, the faces of which are numbered by $1,2, \\ldots, 6$, the sum of the numbers in any two opposite faces being 7. Using 4 such identical dice, Nick composed a parallelepiped $2 \\times 2 \\times 1$ as shown in the figure, the numbers on any two touching faces of the dice being equal. The numbers on some faces are shown in the figure. Which number is written in the face denoted by the question mark?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/755.png" }, { "solution": "\\boxed{48}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The quadrilateral on the right has the following side lengths: $A B=11, B C=$ $7, \\mathrm{CD}=9$ and $\\mathrm{DA}=3$. The angles at points $\\mathrm{A}$ and $\\mathrm{C}$ are right angles. What is the area of the quadrilateral?\n", "completion": "\\boxed{48}", "image_path": "dataset/math_vision/images/774.png" }, { "solution": "\\boxed{950}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Both rows of the following grid have the same sum. What is the value of $*$ ?\n", "completion": "\\boxed{950}", "image_path": "dataset/math_vision/images/2000.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Joseph writes the numbers 1 to 12 in the circles so that the numbers in adjacent circles differ by either 1 or 2 . Which pair of numbers does he write in adjacent circles? \\n Options: A. 3 and 4, B. 5 and 6, C. 6 and 7, D. 8 and 9, E. 8 and 10", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1786.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We want to paint each square in the grid with the colours P, Q, R and S, so that neighbouring squares always have different colours. (Squares which share the same corner point also count as neighbouring.) Some of the squares are already painted. In which colour(s) could the grey square be painted?\n\\n Options: A. only Q, B. only R, C. only S, D. either R or S, E. it is not possible.", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1054.png" }, { "solution": "\\boxed{14}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The different digits are build using sticks as shown. The ñweightò of a number describes the number of sticks used to build\nit. How heavy is the heaviest two digit number?\n", "completion": "\\boxed{14}", "image_path": "dataset/math_vision/images/772.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four of the numbers 1,3,4,5 and 7 are written into the boxes so that the calculation is correct.\nWhich number was not used?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/64.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a five-pointed star. How big is the angle $A$?\n\\n Options: A. $35^{\\circ}$, B. $42^{\\circ}$, C. $51^{\\circ}$, D. $65^{\\circ}$, E. $109^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1089.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The bar graph shows the results of a survey on color preferences. What percent preferred blue?\n\n\\n Options: A. $20\\%$, B. $24\\%$, C. $30\\%$, D. $36\\%$, E. $42\\%$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2557.png" }, { "solution": "\\boxed{61}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which number do you have to write in the last daisy?\n", "completion": "\\boxed{61}", "image_path": "dataset/math_vision/images/5.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five boys competed in a shooting challenge. Ricky scored the most points. Which target was Ricky's?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/644.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the sum of the 10 angles marked on the diagram on the right? \\n Options: A. $300^{\\circ}$, B. $450^{\\circ}$, C. $360^{\\circ}$, D. $600^{\\circ}$, E. $720^{\\circ}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1823.png" }, { "solution": "\\boxed{128}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a 16 metre by 16 metre wall. Three grey squares are painted on the wall as shown.\n\nThe two smaller grey squares are equal in size and each makes an angle of $45^{\\circ}$ with the edge of the wall. The grey squares cover a total area of $B$ metres squared.\nWhat is the value of $B$ ?", "completion": "\\boxed{128}", "image_path": "dataset/math_vision/images/2016.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The five shapes pictured were cut out of paper. Four of them can be folded to form a cube. For which shape is this not possible.\n\\n Options: A. Shape 1, B. Shape 2, C. Shape 3, D. Shape 4, E. Shape 5", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1098.png" }, { "solution": "\\boxed{54}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In chess, a knight can move by jumping to any square whose center is $\\sqrt{5}$ units away from the center of the square that it is currently on. For example, a knight on the square marked by the horse in the diagram below can move to any of the squares marked with an “X” and to no other squares. How many ways can a knight on the square marked by the horse in the diagram move to the square with a circle in exactly four moves?\\n", "completion": "\\boxed{54}", "image_path": "dataset/math_vision/images/2848.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Right isosceles triangle $T$ is placed in the first quadrant of the coordinate plane. Suppose that the projection of $T$ onto the $x$-axis has length $6$, while the projection of $T$ onto the $y$-axis has length $8$. What is the sum of all possible areas of the triangle $T$?\\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/2821.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a $3 \\times 4 \\times 5$ cuboid consisting of 60 identical small cubes. A termite eats its way along the diagonal from $P$ to $Q$. This diagonal does not intersect the edges of any small cube inside the cuboid. How many of the small cubes does it pass through on its journey? ", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/1693.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: James wrote a different integer from 1 to 9 in each cell of a table. He then calculated the sum of the integers in each of the rows and in each of the columns of the table. Five of his answers were 12, 13, 15, 16 and 17, in some order. What was his sixth answer? ", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/1656.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure $AB$ and $BC$ are adjacent sides of square $ABCD$; $M$ is the midpoint of $AB$; $N$ is the midpoint of $BC$; and $AN$ and $CM$ intersect at $O$. The ratio of the area of $AOCD$ to the area of $ABCD$ is\n\\n Options: A. $\\frac{5}{6}$, B. $\\frac{3}{4}$, C. $\\frac{2}{3}$, D. $\\frac{\\sqrt{3}}{2}$, E. $\\frac{(\\sqrt{3}-1)}{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2311.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are two holes in the cover of a book. The book lies on the table opened up (see diagram).\n\nAfter closing up the book which vehicles can Olaf see?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/603.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square that can be fitted into the remaining space?\n\\n Options: A. $9$, B. $12\\frac{1}{2}$, C. $15$, D. $15\\frac{1}{2}$, E. $17$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2737.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Some shapes are drawn on a piece of paper. The teacher folds the left-hand side of the paper over the central bold line. How many of the shapes on the left-hand side will fit exactly on top of a shape on the right-hand side? ", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1967.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $OABC$ be a unit square in the $xy$-plane with $O(0,0),A(1,0),B(1,1)$ and $C(0,1)$. Let $u=x^2-y^2$ and $v=2xy$ be a transformation of the $xy$-plane into the $uv$-plane. The transform (or image) of the square is:\n\n\n\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2292.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Andrea wraps a band around a piece of wood. She then turns the wood around as pictured. What does the wood now look like?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1065.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five squares are positioned as shown. The small square indicated has area 1. What is the value of $h$?\n\\n Options: A. $3 \\mathrm{~m}$, B. $3.5 \\mathrm{~m}$, C. $4 \\mathrm{~m}$, D. $4.2 \\mathrm{~m}$, E. $4.5 \\mathrm{~m}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1215.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A vertical stained glass square window of area $81 \\mathrm{~cm}^{2}$ is made out of six triangles of equal area (see figure). A fly is sitting on the exact spot where the six triangles meet. How far from the bottom of the window is the fly sitting? \\n Options: A. $3 \\mathrm{~cm}$, B. $5 \\mathrm{~cm}$, C. $5.5 \\mathrm{~cm}$, D. $6 \\mathrm{~cm}$, E. $7.5 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1952.png" }, { "solution": "\\boxed{255}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $S_{1}$ is $1\\times 1$. For $i\\ge 1,$ the lengths of the sides of square $S_{i+1}$ are half the lengths of the sides of square $S_{i},$ two adjacent sides of square $S_{i}$ are perpendicular bisectors of two adjacent sides of square $S_{i+1},$ and the other two sides of square $S_{i+1},$ are the perpendicular bisectors of two adjacent sides of square $S_{i+2}$. The total area enclosed by at least one of $S_{1}, S_{2}, S_{3}, S_{4}, S_{5}$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m-n$.\n\n", "completion": "\\boxed{255}", "image_path": "dataset/math_vision/images/2057.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Laura wants to colour in exactly one $2 \\times 2$ square in the figure given . How many ways are there for her to do that?", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/904.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Seven little dice were removed from a $3 \\times 3 \\times 3$ die, as can be seen in the diagram. The remaining (completely symmetrical) figure is cut along a plane through the centre and perpendicular to one of the four space diagonals. What does the cross-section look like?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1423.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In which shape is exactly one half coloured grey?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/839.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The segment $A E$ is divided into four equal parts and semicircles are drawn taking $A E, A D$ and $D E$ as diameters, creating two paths from $A$ to $E$ as shown. Determine the ratio of the length of the upper path to the length of the lower path.\n\\n Options: A. $1: 2$, B. $2: 3$, C. $2: 1$, D. $3: 2$, E. $1: 1$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/199.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each spinner is divided into $3$ equal parts. The results obtained from spinning the two spinners are multiplied. What is the probability that this product is an even number?\n\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{1}{2}$, C. $\\frac{2}{3}$, D. $\\frac{7}{9}$, E. $1$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2551.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the isosceles triangle $A B C$ (with base $A C$ ) the points $K$ and $L$ are added on the sides $A B$ and $B C$ respectively so that $A K=K L=\\angle B$ and $K B=A C$. How big is the angle $\\angle A B C$?\n\\n Options: A. $30^{\\circ}$, B. $35^{\\circ}$, C. $36^{\\circ}$, D. $40^{\\circ}$, E. $44^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1175.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the five vases shown has the same height and each has a volume of 1 litre. Half a litre of water is poured into each vase. In which vase would the level of the water be the highest?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1209.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: 3 rectangles of the same height are positioned as shown. The numbers within the rectangles indicate their areas in $\\mathrm{cm}^{2}$. If $A B=6 \\mathrm{~cm}$, how long is the distance $C D$?\n\\n Options: A. $7 \\mathrm{~cm}$, B. $7.5 \\mathrm{~cm}$, C. $8 \\mathrm{~cm}$, D. $8.2 \\mathrm{~cm}$, E. $8.5 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/950.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: This piece of paper was folded in half twice, and then had two equilateral triangles cut out of it. Which diagram shows how the paper will look when it is unfolded again? \n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1500.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five squirrels $A, B, C, D$ and $E$ are sitting on the points marked. The crosses indicate 6 nuts that they are collecting. The squirrels start to run at the same time with the same speed to the nearest nut in order to pick it up. As soon as a squirrel has picked up the first nut it immediately continues to run in order to get another nut. Which squirrel gets a second nut?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/862.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a quadrilateral divided into 4 smaller quadrilaterals with a common vertex $K$. The other labelled points divide the sides of the large quadrilateral into three equal parts. The numbers indicate the areas of the corresponding small quadrilaterals. What is the area of the shaded quadrilateral?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1221.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each cell of the $3 \\times 3$ grid shown has placed in it a positive number so that: in each row and each column, the product of the three numbers is equal to 1 ; and in each $2 \\times 2$ square, the product of the four numbers is equal to 2 . What number should be placed in the central cell?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1597.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn the adjoining figure, every point of circle $\\mathit{O'}$ is exterior to circle $\\mathit{O}$. Let $\\mathit{P}$ and $\\mathit{Q}$ be the points of intersection of an internal common tangent with the two external common tangents. Then the length of $PQ$ is\\n Options: A. $\\text{the average of the lengths of the internal and external common tangents}$, B. $\\text{equal to the length of an external common tangent if and only if circles }\\mathit{O}\\text{ and }\\mathit{O'}\\text{ have equal radii}$, C. $\\text{always equal to the length of an external common tangent}$, D. $\\text{greater than the length of an external common tangent}$, E. $\\text{the geometric mean of the lengths of the internal and external common tangents}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2315.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Unit squares of a squared board $2 \\times 3$ are coloured black and white like a chessboard (see picture). Determine the minimum number of steps necessary to achieve the reverse of the left board, following the rule: in each step, we must repaint two unit squares that have a joint edge, but we must repaint a black square with green, a green square with white and a white square with black.\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1271.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, equilateral hexagon $ABCDEF$ has three nonadjacent acute interior angles that each measure $30^\\circ$. The enclosed area of the hexagon is $6\\sqrt{3}$. What is the perimeter of the hexagon?\n\\n Options: A. 4, B. $4\\sqrt{3}$, C. 12, D. 18, E. $12\\sqrt{3}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2493.png" }, { "solution": "\\boxed{60}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many lines pass through exactly two points in the following hexagonal grid?\\n", "completion": "\\boxed{60}", "image_path": "dataset/math_vision/images/2859.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circular carpet is placed on a floor which is covered by equally big, square tiles. All tiles that have at least one point in common with the carpet are coloured in grey. Which of the following cannot be a result of this?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/258.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Bob folds a piece of paper, then punches a hole into the paper and unfolds it again. The unfolded paper then looks like this:\n\nAlong which dotted line has Bob folded the paper beforehand?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/571.png" }, { "solution": "\\boxed{80}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle with perimeter $ 176$ is divided into five congruent rectangles as shown in the diagram. What is the perimeter of one of the five congruent rectangles?\n", "completion": "\\boxed{80}", "image_path": "dataset/math_vision/images/2428.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows two adjoining squares with side lengths $a$ and $b$ (with $a\\n Options: A. $\\sqrt{a b}$, B. $\\frac{1}{2} a^{2}$, C. $\\frac{1}{2} b^{2}$, D. $\\frac{1}{4}\\left(a^{2}+b^{2}\\right)$, E. $\\frac{1}{2}\\left(a^{2}+b^{2}\\right)$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/330.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, the outer equilateral triangle has area $16$, the inner equilateral triangle has area $1$, and the three trapezoids are congruent. What is the area of one of the trapezoids?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/2686.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a regular 9-sided polygon (a nonagon or an enneagon) with two of the sides extended to meet at the point $X$. What is the size of the acute angle at $X$ ? \\n Options: A. $40^{\\circ}$, B. $45^{\\circ}$, C. $50^{\\circ}$, D. $55^{\\circ}$, E. $60^{\\circ}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1565.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A trip of the pupils to the zoo took 135 minutes.\n\nHow many hours and minutes does it make?\\n Options: A. 3 h 5 min, B. 2 h 15 min, C. 1 h 35 min, D. 2 h 35 min, E. 3 h 35 min", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/24.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows squares of different sizes. The side length of the smallest square is $20 \\mathrm{~cm}$. How long is the black line?\n\\n Options: A. $380 \\mathrm{~cm}$, B. $400 \\mathrm{~cm}$, C. $420 \\mathrm{~cm}$, D. $440 \\mathrm{~cm}$, E. $1680 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/771.png" }, { "solution": "\\boxed{80}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a net of an unfolded rectangular box. What is the volume of the box (in $\\mathrm{cm}^{3}$ )? ", "completion": "\\boxed{80}", "image_path": "dataset/math_vision/images/1657.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square piece of paper has been cut in three pieces. Two of them are in the picture on the right. What is the third one?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/179.png" }, { "solution": "\\boxed{7.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Angle $ABC$ of $\\triangle ABC$ is a right angle. The sides of $\\triangle ABC$ are the diameters of semicircles as shown. The area of the semicircle on $\\overline{AB}$ equals $8\\pi$, and the arc of the semicircle on $\\overline{AC}$ has length $8.5\\pi$. What is the radius of the semicircle on $\\overline{BC}$?\n", "completion": "\\boxed{7.5}", "image_path": "dataset/math_vision/images/2724.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the following four large congruent squares is subdivided into combinations of congruent triangles or rectangles and is partially bolded. What percent of the total area is partially bolded?\n\n\n\\n Options: A. $12\\frac{1}{2}$, B. $20$, C. $25$, D. $33 \\frac{1}{3}$, E. $37\\frac{1}{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2711.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In order to get to his bone, the dog has to follow the black line. In total he turns 3-times to the right and 2-times to the left.\nWhich path does he take?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/78.png" }, { "solution": "\\boxed{38}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A number is to be written into every vertex of the 18 -sided shape so that it is equal to the sum of the two numbers from the adjacent vertices. Two of these numbers are given. Which number is written in vertex $A$?\n", "completion": "\\boxed{38}", "image_path": "dataset/math_vision/images/1421.png" }, { "solution": "\\boxed{2.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The graph below shows the total accumulated dollars (in millions) spent by the Surf City government during $1988$. For example, about $.5$ million had been spent by the beginning of February and approximately $2$ million by the end of April. Approximately how many millions of dollars were spent during the summer months of June, July, and August?\n", "completion": "\\boxed{2.5}", "image_path": "dataset/math_vision/images/2531.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the sum of the six marked angles in the picture?\n\\n Options: A. $360^{\\circ}$, B. $900^{\\circ}$, C. $1080^{\\circ}$, D. $1120^{\\circ}$, E. $1440^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1461.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the four squares of a row there always have to be exactly two coins. In the four squares below each other there also always have to be exactly two coins.\n\nOn which square does one more coin have to be placed?\\n Options: A. square $A$, B. square $B$, C. square $C$, D. square $D$, E. square $E$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/140.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The vertices of a die are numbered 1 to 8, so that the sum of the four numbers on the vertices of each face are the same. The numbers 1, 4 and 6 are already indicated in the picture. Which number is in position $x$?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/266.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mr. Ramos gave a test to his class of $20$ students. The dot plot below shows the distribution of test scores.\n\nLater Mr. Ramos discovered that there was a scoring error on one of the questions. He regraded the tests, awarding some of the students $5$ extra points, which increased the median test score to $85$. What is the minimum number of students who received extra points?\n\n(Note that the median test score equals the average of the $2$ scores in the middle if the $20$ test scores are arranged in increasing order.)", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2777.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In front of a supermarket there are two rows of interconnected trolleys.The first one is $2.9 \\mathrm{~m}$ long and consists of 10 trolleys. The second one is $4.9 \\mathrm{~m}$ long and consists of twenty trolleys. How long is one trolley?\n\\n Options: A. $0.8 \\mathrm{~m}$, B. $1 \\mathrm{~m}$, C. $1.1 \\mathrm{~m}$, D. $1.2 \\mathrm{~m}$, E. $1.4 \\mathrm{~m}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1339.png" }, { "solution": "\\boxed{25}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The rectangle in the picture consists of 7 squares. The lengths of the sides of some of the squares are shown. Square $\\mathrm{K}$ is the biggest one, square $\\mathrm{L}$ -- the smallest one. How many times is the area of $\\mathrm{K}$ bigger than the area of L?\n", "completion": "\\boxed{25}", "image_path": "dataset/math_vision/images/704.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mr Beaver re-arranges the parts to build a kangaroo.\n\nWhich part is missing?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/154.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn the adjoining figure $\\measuredangle E=40^\\circ$ and arc $AB$, arc $BC$, and arc $CD$ all have equal length. Find the measure of $\\measuredangle ACD$.\\n Options: A. $10^\\circ$, B. $15^\\circ$, C. $20^\\circ$, D. $\\left(\\frac{45}{2}\\right)^\\circ$, E. $30^\\circ$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2317.png" }, { "solution": "\\boxed{37}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In each square of the maze there is a piece of cheese. Ronnie the mouse wants to enter and leave the maze as shown in the picture. He doesn't want to visit a square more than once, but would like to eat as much cheese as possible. What is the maximum number of pieces of cheese that he can eat?\n", "completion": "\\boxed{37}", "image_path": "dataset/math_vision/images/480.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If each side of the regular hexagon has length $\\sqrt{3}$ and $X A B C$ and $X P Q R$ are squares, what is the area of the shaded region?\n\\n Options: A. $\\frac{5-\\sqrt{3}}{4}$, B. $\\frac{\\sqrt{3}+1}{2}$, C. $\\frac{\\sqrt{3}}{4}$, D. $\\frac{2-\\sqrt{3}}{4}$, E. $\\frac{2+\\sqrt{3}}{4}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/196.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the right triangle shown the sum of the distances $ BM$ and $ MA$ is equal to the sum of the distances $ BC$ and $ CA$. If $ MB = x$, $ CB = h$, and $ CA = d$, then $ x$ equals:\n\\n Options: A. $\\frac{hd}{2h + d}$, B. $d - h$, C. $\\frac{1}{2}d$, D. $h + d - \\sqrt{2d}$, E. $\\sqrt{h^2 + d^2} - h$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2259.png" }, { "solution": "\\boxed{1.3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An isosceles trapezoid is inscribed in a semicircle as shown below, such that the three shaded regions are congruent. The radius of the semicircle is one meter. How many square meters are in the area of the trapezoid? Express your answer as a decimal to the nearest tenth.\n\n", "completion": "\\boxed{1.3}", "image_path": "dataset/math_vision/images/3016.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Alisha wrote an integer in each square of a $4 \\times 4$ grid. Integers in squares with a common edge differed by 1 . She wrote a 3 in the top left corner, as shown. She also wrote a 9 somewhere in the grid. How many different integers did she write? ", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/1797.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $AXYZ$ is inscribed in equiangular hexagon $ABCDEF$ with $X$ on $\\overline{BC}$, $Y$ on $\\overline{DE}$, and $Z$ on $\\overline{EF}$. Suppose that $AB=40$, and $EF=41(\\sqrt{3}-1)$. What is the side-length of the square?\n\n\\n Options: A. $29\\sqrt{3}$, B. $\\frac{21}{2}\\sqrt{2}+\\frac{41}{2}\\sqrt{3}$, C. $20\\sqrt{3}+16$, D. $20\\sqrt{2}+13\\sqrt{3}$, E. $21\\sqrt{6}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2475.png" }, { "solution": "\\boxed{147}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure below depicts a regular 7-gon inscribed in a unit circle.\n\nWhat is the sum of the 4th powers of the lengths of all 21 of its edges and diagonals?", "completion": "\\boxed{147}", "image_path": "dataset/math_vision/images/2499.png" }, { "solution": "\\boxed{116}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A barcode as pictured is made up of alternate black and white stripes. The code always starts and ends with a black stripee. Each strip (black or white) has the width 1 or 2 and the total width of the barcode is 12. How many different barcodes if this kind are there if one reads from left to right?\n", "completion": "\\boxed{116}", "image_path": "dataset/math_vision/images/232.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube has eight vertices (corners) and twelve edges. A segment, such as $x$, which joins two vertices not joined by an edge is called a diagonal. Segment $y$ is also a diagonal. How many diagonals does a cube have?\n\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/2594.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A terrace is covered with square tiles of different sizes. The smallest tile has a perimeter of $80 \\mathrm{~cm}$. A snake lay down along the edges of the tiles (see diagram). How long is the snake? \\n Options: A. $380 \\mathrm{~cm}$, B. $400 \\mathrm{~cm}$, C. $420 \\mathrm{~cm}$, D. $440 \\mathrm{~cm}$, E. $1680 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/986.png" }, { "solution": "\\boxed{45}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, $ABCD$ and $BEFG$ are squares, and $BCE$ is an equilateral triangle. What is the number of degrees in angle $GCE$?\n\n", "completion": "\\boxed{45}", "image_path": "dataset/math_vision/images/2972.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: When simon the squirrel comes down from his tree onto the floor, he never moves further than $5 \\mathrm{~m}$ away from the trunk of his tree. Furthermore, he stays at least $5 \\mathrm{~m}$ away from the dog kennel. Which picture shows most accurately the area in which Simon can be found?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1122.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram consists of three circles of equal radius $R$. The centre of those circles lie on a common straight line where the middle circle goes through the centres of the other two circles (see diagram). How big is the perimeter of the figure?\n\\n Options: A. $\\frac{10 \\pi R}{3}$, B. $\\frac{5 \\pi R}{3}$, C. $\\frac{2 \\pi R \\sqrt{3}}{3}$, D. $2 \\pi R \\sqrt{3}$, E. $4 \\pi R$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1432.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining plane figure, sides $AF$ and $CD$ are parallel, as are sides $AB$ and $EF$, and sides $BC$ and $ED$. Each side has length of 1. Also, $\\measuredangle FAB = \\measuredangle BCD = 60^\\circ$. The area of the figure is\n\n\\n Options: A. $\\frac{\\sqrt{3}}{2}$, B. $1$, C. $\\frac{3}{2}$, D. $\\sqrt{3}$, E. $2$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2345.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A card has a diagram printed on one side and the other side is plain white. The card is first flipped over downwards and then to the right (see diagram). Which picture is obtained?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1133.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular parallelepiped was composed of 4 pieces, each consisting of 4 little cubes. Then one piece was removed (see picture) Which one?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1265.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A ball with diameter 4 inches starts at point A to roll along the track shown. The track is comprised of 3 semicircular arcs whose radii are $R_1 = 100$ inches, $R_2 = 60$ inches, and $R_3 = 80$ inches, respectively. The ball always remains in contact with the track and does not slip. What is the distance the center of the ball travels over the course from A to B?\n\\n Options: A. $238\\pi$, B. $240\\pi$, C. $260\\pi$, D. $280\\pi$, E. $500\\pi$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2726.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A black disc with two holes is placed on top of a dial of a watch.\nThe black disc is turned.\nWhich two numbers can be seen at the same time?\n\\n Options: A. 4 and 9, B. 5 and 10, C. 5 and 9, D. 6 and 9, E. 7 and 12", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/681.png" }, { "solution": "\\boxed{55/2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular piece of paper with side lengths 5 by 8 is folded along the dashed lines shown below, so that the folded flaps just touch at the corners as shown by the dotted lines. Find the area of the resulting trapezoid.\\n", "completion": "\\boxed{55/2}", "image_path": "dataset/math_vision/images/2876.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On the number wall shown the number on each tile is equal to the sum of the numbers on the two tiles directly below it. Which number is on the tile marked with \"?\"?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/294.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $ ABC$ is a right triangle with $ \\angle ACB$ as its right angle, $ m\\angle ABC = 60^\\circ$, and $ AB = 10$. Let $ P$ be randomly chosen inside $ \\triangle ABC$, and extend $ \\overline{BP}$ to meet $ \\overline{AC}$ at $ D$. What is the probability that $ BD > 5\\sqrt{2}$?\n\n\\n Options: A. $\\frac{2 - \\sqrt{2}}{2}$, B. $\\frac{1}{3}$, C. $\\frac{3 - \\sqrt{3}}{3}$, D. $\\frac{1}{2}$, E. $\\frac{5 - \\sqrt{5}}{5}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2449.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In isosceles triangle $ABC$, if $BC$ is extended to a point $X$ such that $AC = CX$, what is the number of degrees in the measure of angle $AXC$? ", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/2934.png" }, { "solution": "\\boxed{45}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A wristwatch lies on the table with its face upwards. The minute hand points towards north-east. How many minutes have to pass for the minute hand to point towards northwest for the first time?\n", "completion": "\\boxed{45}", "image_path": "dataset/math_vision/images/1081.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In right triangle $ ABC$, $ BC = 5$, $ AC = 12$, and $ AM = x$; $ \\overline{MN} \\perp \\overline{AC}$, $ \\overline{NP} \\perp \\overline{BC}$; $ N$ is on $ AB$. If $ y = MN + NP$, one-half the perimeter of rectangle $ MCPN$, then:\n\\n Options: A. $y = \\frac{1}{2}(5 + 12)$, B. $y = \\frac{5x}{12} + \\frac{12}{5}$, C. $y = \\frac{144 - 7x}{12}$, D. $y = 12 \\,\\,$, E. $y = \\frac{5x}{12} + 6$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2266.png" }, { "solution": "\\boxed{80}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $P Q R$, the point $S$ is on $P Q$ so that the ratio of the length of $P S$ to the length of $S Q$ is $2: 3$. The point $T$ lies on $S R$ so that the area of triangle $P T R$ is 20 and the area of triangle $S Q T$ is 18 , as shown in the diagram.\n\nWhat is the area of triangle $P Q R$ ?", "completion": "\\boxed{80}", "image_path": "dataset/math_vision/images/1758.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a right-angled triangle with side lengths 5,12 and 13. What is the length of the radius of the inscribed semi-circle?\n\\n Options: A. $7 / 3$, B. $10 / 3$, C. $12 / 3$, D. $13 / 3$, E. $17 / 3$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1360.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the rectangles $\\mathbf{A}$ to $\\mathbf{E}$ can be covered by the pattern on the right-hand side in such a way that the result is a totally black rectangle?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/408.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the twenty dots on the graph below represents one of Sarah's classmates. Classmates who are friends are connected with a line segment. For her birthday party, Sarah is inviting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not be invited to Sarah's party?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2650.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Adam the Ant started at the left-hand end of a pole and crawled $\\frac{2}{3}$ of its length. Benny the Beetle started at the right-hand end of the same pole and crawled $\\frac{3}{4}$ of its length. What fraction of the length of the pole are Adam and Benny now apart?\n\\n Options: A. $\\frac{3}{8}$, B. $\\frac{1}{12}$, C. $\\frac{5}{7}$, D. $\\frac{1}{2}$, E. $\\frac{5}{12}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1641.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Martin has three cards that are labelled on both sides with a number. Martin places the three cards on the table without paying attention to back or front. He adds the three numbers that he can then see. How many different sums can Martin get that way?\n\\n Options: A. 3, B. 5, C. 6, D. 9, E. A different amount.", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/995.png" }, { "solution": "\\boxed{52}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A ball is propelled from corner $A$ of a square snooker table of side 2 metres. After bouncing off three cushions as shown, the ball goes into a pocket at $B$. The total distance travelled by the ball is $\\sqrt{k}$ metres. What is the value of $k$ ?\n\n(Note that when the ball bounces off a cushion, the angle its path makes with the cushion as it approaches the point of impact is equal to the angle its path makes with the cushion as it moves away from the point of impact as shown in the diagram below.)\n", "completion": "\\boxed{52}", "image_path": "dataset/math_vision/images/1996.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five equilateral triangles, each with side $2\\sqrt{3}$, are arranged so they are all on the same side of a line containing one side of each. Along this line, the midpoint of the base of one triangle is a vertex of the next. The area of the region of the plane that is covered by the union of the five triangular regions is\n\n\\n Options: A. $10$, B. $12$, C. $15$, D. $10\\sqrt{3}$, E. $12\\sqrt{3}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2396.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: When a positive integer $N$ is fed into a machine, the output is a number calculated according to the rule shown below.\n\n\nFor example, starting with an input of $N = 7$, the machine will output $3 \\cdot 7 + 1 = 22$. Then if the output is repeatedly inserted into the machine five more times, the final output is $26$. $$ 7 \\to 22 \\to 11 \\to 34 \\to 17 \\to 52 \\to 26$$When the same 6-step process is applied to a different starting value of $N$, the final output is $1$. What is the sum of all such integers $N$? $$ N \\to \\_\\_ \\to \\_\\_ \\to \\_\\_ \\to \\_\\_ \\to \\_\\_ \\to 1$$\\n Options: A. 73, B. 74, C. 75, D. 82, E. 83", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2769.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five equally big square pieces of card are placed on a table on top of each other. The picture on the side is created this way. The cards are collected up from top to bottom. In which order are they collected?\n\\n Options: A. 5-4-3-2-1, B. 5-2-3-4-1, C. 5-4-2-3-1, D. 5-3-2-1-4, E. 5-2-3-1-4", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/90.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The point $O$ is the centre of a regular pentagon. How much of the pentagon is shaded?\n\\n Options: A. $10 \\%$, B. $20 \\%$, C. $25 \\%$, D. $30 \\%$, E. $40 \\%$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1022.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the configuration below, $\\theta$ is measured in radians, $C$ is the center of the circle, $BCD$ and $ACE$ are line segments and $AB$ is tangent to the circle at $A$.\n\n\nA necessary and sufficient condition for the equality of the two shaded areas, given $0 < \\theta < \\frac{\\pi}{2}$, is\\n Options: A. $\\tan \\theta = \\theta$, B. $\\tan \\theta = 2\\theta$, C. $\\tan \\theta = 4\\theta$, D. $\\tan 2\\theta = \\theta \\$, E. $\\tan \\frac{\\theta}{2} = \\theta$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2363.png" }, { "solution": "\\boxed{2.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nA bar graph shows the number of hamburgers sold by a fast food chain each season. However, the bar indicating the number sold during the winter is covered by a smudge. If exactly $ 25 \\%$ of the chain's hamburgers are sold in the fall, how many million hamburgers are sold in the winter?", "completion": "\\boxed{2.5}", "image_path": "dataset/math_vision/images/2513.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram opposite shows a regular nonagon. What is the size of the angle marked $\\mathrm{X}$?\n\\n Options: A. $40^{\\circ}$, B. $45^{\\circ}$, C. $50^{\\circ}$, D. $55^{\\circ}$, E. $60^{\\circ}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1055.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture on the right has been drawn on paper and cut out to make a house. Which of the houses does it make?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/403.png" }, { "solution": "\\boxed{124}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Belinda is building squares with matches adding small squares that it already has built according to the schema of the figure. How many matches does she have to add to the 30th square to build the 31st?\n", "completion": "\\boxed{124}", "image_path": "dataset/math_vision/images/741.png" }, { "solution": "\\boxed{21}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. The kites look like the one in the diagram. For her small kite Genevieve draws the kite on a one-inch grid. For the large kite she triples both the height and width of the entire grid.\n\n\n\nWhat is the number of square inches in the area of the small kite?", "completion": "\\boxed{21}", "image_path": "dataset/math_vision/images/2625.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jörg is sorting his socks. Two socks with the same number are one pair.\n\nHow many pairs can he find?", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/89.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The edges of a regular tetrahedron with vertices $A ,~ B,~ C$, and $D$ each have length one. Find the least possible distance between a pair of points $P$ and $Q$, where $P$ is on edge $AB$ and $Q$ is on edge $CD$.\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{3}{4}$, C. $\\frac{\\sqrt{2}}{2}$, D. $\\frac{\\sqrt{3}}{2}$, E. $\\frac{\\sqrt{3}}{3}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2328.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A big square is made from 25 small squares put together. A few of the small squares have been lost. How many have been lost?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/29.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rachel has several square pieces of paper of area $4 \\mathrm{~cm}^{2}$. She cuts each of them into smaller squares and right-angled triangles in the manner shown in the first diagram. She takes some of the pieces and makes the shape shown in the second diagram.\nWhat is the area in $\\mathrm{cm}^{2}$ of the shape? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1609.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jenny decided to enter numbers into the cells of a $3 \\times 3$ table so that the sum of the numbers in all four possible $2 \\times 2$ cells will be the same. The numbers in three of the corner cells have already been written, as shown.\nWhich number should she write in the fourth corner cell?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1701.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large square is divided into smaller squares. In one of the smaller squares a diagonal is also drawn, as shown. What fraction of the large square is shaded? \\n Options: A. $\\frac{4}{5}$, B. $\\frac{3}{8}$, C. $\\frac{4}{9}$, D. $\\frac{1}{3}$, E. $\\frac{1}{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1674.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle is formed from 4 equally sized smaller rectangles. The shorter side is $10 \\mathrm{~cm}$ long. How long is the longer side?\n\\n Options: A. $40 \\mathrm{~cm}$, B. $30 \\mathrm{~cm}$, C. $20 \\mathrm{~cm}$, D. $10 \\mathrm{~cm}$, E. $5 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/848.png" }, { "solution": "\\boxed{4045}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each box in the strip shown is to contain one number. The first box and the eighth box each contain 2021. Numbers in adjacent boxes have $\\operatorname{sum} T$ or $T+1$ as shown. What is the value of $T$ ?\n", "completion": "\\boxed{4045}", "image_path": "dataset/math_vision/images/1961.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Theodor has built this tower made up of discs. He looks at the tower from above. How many discs does he see?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/76.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In tank I, whose base has an area of $2 \\mathrm{dm}^{2}$ and whose height is $10 \\mathrm{~cm}$, the water is $5 \\mathrm{~cm}$ high. An empty tank II with a base of area $1 \\mathrm{dm}^{2}$ and a height of $7 \\mathrm{~cm}$ is placed in tank I. The water of tank I rises, of course, and spills over into tank II. What level does the water reach in tank II?\n\\n Options: A. $1 \\mathrm{~cm}$, B. $2 \\mathrm{~cm}$, C. $3 \\mathrm{~cm}$, D. $4 \\mathrm{~cm}$, E. $5 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1276.png" }, { "solution": "\\boxed{180}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In circle $J$, $HO$ and $HN$ are tangent to the circle at $O$ and $N$. Find the number of degrees in the sum of $m\\angle J$ and $m\\angle H$. ", "completion": "\\boxed{180}", "image_path": "dataset/math_vision/images/2940.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six figures were drawn, one on each side of a cube, as shown beside, in different positions. On the side that does not appear beside is this drawing:\n\nWhat is the figure on the face opposite to it?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/110.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A figure is made up of three squares. The side length of the smallest square is $6 \\mathrm{~cm}$. How long is the side length of the biggest square?\n\\n Options: A. $8 \\mathrm{~cm}$, B. $10 \\mathrm{~cm}$, C. $12 \\mathrm{~cm}$, D. $14 \\mathrm{~cm}$, E. $16 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/888.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Every time these two wheels are spun, two numbers are selected by the pointers. What is the probability that the sum of the two selected numbers is even?\n\\n Options: A. $\\frac{1}{6}$, B. $\\frac{3}{7}$, C. $\\frac{1}{2}$, D. $\\frac{2}{3}$, E. $\\frac{5}{7}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2535.png" }, { "solution": "\\boxed{100}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The Olympic logo is made of $5$ circles of radius $1$, as shown in the figure. Suppose that the total area covered by these $5$ circles is $a+b\\pi$ where $a, b$ are rational numbers. Find $10a + 20b$.\\n", "completion": "\\boxed{100}", "image_path": "dataset/math_vision/images/2843.png" }, { "solution": "\\boxed{26}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three different one-digit positive integers are placed in the bottom row of cells. Numbers in adjacent cells are added and the sum is placed in the cell above them. In the second row, continue the same process to obtain a number in the top cell. What is the difference between the largest and smallest numbers possible in the top cell?\n\n\n", "completion": "\\boxed{26}", "image_path": "dataset/math_vision/images/2676.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the eight vertices of an octagon connected by line segments. Jodhvir wants to write one of the integers 1,2,3 or 4 at each of the vertices so that the two integers at the ends of every line segment are different. He has already written three integers as shown.\n\nHow many times will the integer 4 appear in his completed diagram?", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1777.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, what is the ratio of the area of the gray squares to the area of the white squares?\n\\n Options: A. 3:10, B. 3:8, C. 3:7, D. 3:5, E. 1:1", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2687.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram shown here (which is not drawn to scale), suppose that $\\triangle ABC \\sim \\triangle PAQ$ and $\\triangle ABQ \\sim \\triangle QCP$. If $m\\angle BAC = 70^\\circ$, then compute $m\\angle PQC$. ", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/3022.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square bit of paper is folded along the dashed lines in some order and direction. One of the corners of the resulting small square is cut off. The piece of paper is then unfolded. How many holes are on the inner area of the piece of paper?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/275.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Alfonso the Ostrich has been training for the Head in the Sand Competition in the Animolympiad. He buried his head in the sand last week and pulled it out at 8.15 am on Monday to find he had reached a new personal record - he had been underground for 98 hours and 56 minutes. When did Alfonso bury his head in the sand? \\n Options: A. On Thursday at 5.19 am, B. On Thursday at $5.41 \\mathrm{am}$, C. On Thursday at $11.11 \\mathrm{am}$, D. On Friday at 5.19 am, E. On Friday at 11.11 am", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1518.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Johann stacks $1 \\times 1$ cubes on the squares of a $4 \\times 4$ grid. The diagram on the right shows how many cubes were piled on top of each other on each square of the grid. What will Johann see if he looks from behind (hinten) at the tower?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/823.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In circle $ O$ chord $ AB$ is produced so that $ BC$ equals a radius of the circle. $ CO$ is drawn and extended to $ D$. $ AO$ is drawn. Which of the following expresses the relationship between $ x$ and $ y$?\n\n\\n Options: A. $x=3y \\\\$, B. $x=2y \\\\$, C. $x=60^\\circ \\\\$, D. $\\text{there is no special relationship between }x\\text{ and }y \\\\$, E. $x=2y \\text{ or }x=3y\\text{, depending upon the length of }AB$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2263.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Elizabetta wants to write the integers 1 to 9 in the regions of the shape shown, with one integer in each region. She wants the product of the integers in any two regions that have a common edge to be not more than 15 . In how many ways can she do this? ", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1714.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Roo has a very unusual chessboard of side 7, in which only the squares which lie on the diagonals are shaded. Kanga then asks the question \"What would be the total white area of your chessboard if each side was 2003 squares long?\" What is the correct answer? \\n Options: A. $2002^{2}$, B. $2002 \\times 2001$, C. $2003^{2}$, D. $2003 \\times 2004$, E. $2004^{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1808.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Leonie has hidden a Smiley behind some of the grey boxes. The numbers state how many Smileys there are in the neighbouring boxes. Two boxes are neighbouring if they have one side or one corner in common. How many Smileys has Leonie hidden?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/578.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square floor is made up of triangular and square tiles in grey and white. What is the smallest number of grey tiles that have to be swapped with white tiles, so that the floor looks the same from all four given viewing directions?\n\\n Options: A. three triangles, B. one square, C. one triangle, D. three squares, E. one triangle, F. one square, G. three triangles, H. three squares, I. three triangles, J. two squares", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/879.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six congruent rhombuses, each of area $5 \\mathrm{~cm}^{2}$, form a star. The tips of the star are joined to draw a regular hexagon, as shown. What is the area of the hexagon?\n\\n Options: A. $36 \\mathrm{~cm}^{2}$, B. $40 \\mathrm{~cm}^{2}$, C. $45 \\mathrm{~cm}^{2}$, D. $48 \\mathrm{~cm}^{2}$, E. $60 \\mathrm{~cm}^{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1454.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a convex quadrilateral $A B C D$ the diagonals are perpendicular to each other. The length of the edges are $A B=2017, B C=2018$ and $C D=2019$ (diagram not to scale). How long is side $A D$?\n\\n Options: A. 2016, B. 2018, C. $\\sqrt{2020^{2}-4}$, D. $\\sqrt{2018^{2}+2}$, E. 2020", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1410.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each letter in the sum shown represents a different digit and the digit for $\\mathrm{A}$ is odd. What digit does $\\mathrm{G}$ represent?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1829.png" }, { "solution": "\\boxed{41}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A natural number greater than 0 is written on each side of the die shown. All products of opposite numbers are of the same value. What is the smallest possible sum of all 6 numbers?\n", "completion": "\\boxed{41}", "image_path": "dataset/math_vision/images/911.png" }, { "solution": "\\boxed{144}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A point $P$ is chosen in the interior of $\\triangle ABC$ so that when lines are drawn through $P$ parallel to the sides of $\\triangle ABC$, the resulting smaller triangles, $t_1$, $t_2$, and $t_3$ in the figure, have areas 4, 9, and 49, respectively. Find the area of $\\triangle ABC$.\n", "completion": "\\boxed{144}", "image_path": "dataset/math_vision/images/2039.png" }, { "solution": "\\boxed{67}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Peter has bought a rug that is $36 \\mathrm{dm}$ wide and $60 \\mathrm{dm}$ long. On the rug you can see squares that contain either a sun or a moon, as shown in the picture. As you can see there are exactly nine squares along the width of the rug. The total length of the rug cannot be seen. How many moons would you see, if you could see the entire rug?\n", "completion": "\\boxed{67}", "image_path": "dataset/math_vision/images/508.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: As soon as he left his city towards Caecá, Charles saw the sign on the left. When he came back from Caecá, he saw the sign on the right. At that point, how far was it to get to his city?\n\\n Options: A. $12 \\mathrm{~km}$, B. $21 \\mathrm{~km}$, C. $29 \\mathrm{~km}$, D. $41 \\mathrm{~km}$, E. $52 \\mathrm{~km}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1197.png" }, { "solution": "\\boxed{26}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the map of a big park. The park is split into several sections and the number in each section states its perimeter in $\\mathrm{km}$. How big is the perimeter of the entire park in $\\mathrm{km}$ ? ", "completion": "\\boxed{26}", "image_path": "dataset/math_vision/images/1499.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle is twice as long as wide. Which fraction of the rectangle is coloured in grey?\n\\n Options: A. $\\frac{1}{4}$, B. $\\frac{3}{8}$, C. $\\frac{3}{4}$, D. $\\frac{1}{2}$, E. $\\frac{3}{5}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/872.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Every figure in the picture replaces some digit. What is the sum $\\square+\\bigcirc$ ?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/710.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On each of three pieces of paper a five-digit number is written as shown. Three of the digits are covered. The sum of the three numbers is 57263 . What are the covered digits? \\n Options: A. 0, B. 2 and 2, C. 1, D. 2 and 9, E. 2, F. 4 and 9, G. 2, H. 7 and 8, I. 5, J. 7 and 8", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1940.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Albin has put each of the digits from 1 to 9 in the fields of the table. In the diagram only 4 of these digits are visible. For the field containing the number 5, Albin noticed that the sum of the numbers in the neighbouring fields is 13. (neighbouring fields are fields which share a side). He noticed exactly the same for the field containing the digit 6 . Which digit had Albin written in the grey field?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/527.png" }, { "solution": "\\boxed{137}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $ABCD$ be a tetrahedron with $AB=41$, $AC=7$, $AD=18$, $BC=36$, $BD=27$, and $CD=13$, as shown in the figure. Let $d$ be the distance between the midpoints of edges $AB$ and $CD$. Find $d^{2}$.\n\n", "completion": "\\boxed{137}", "image_path": "dataset/math_vision/images/2050.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: With which square do you have to swap the question mark, so that the white area and the black area are the same size?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/514.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five children each have a black square, a grey triangle and a white circle made up of paper. The children place the three shapes on top of each other as seen in the pictures. In how many pictures was the triangles placed after the square?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/555.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle $K$ is inscribed in a quarter circle with radius 6 as shown in the figure. What is the radius of circle $K$?\n\\n Options: A. $\\frac{6-\\sqrt{2}}{2}$, B. $\\frac{3 \\sqrt{2}}{2}$, C. 2.5, D. 3, E. $6(\\sqrt{2}-1)$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/173.png" }, { "solution": "\\boxed{64}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of the shaded region $\\text{BEDC}$ in parallelogram $\\text{ABCD}$ is\n\n", "completion": "\\boxed{64}", "image_path": "dataset/math_vision/images/2530.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle ABC,$ a point $E$ is on $\\overline{AB}$ with $AE=1$ and $EB=2$. Point $D$ is on $\\overline{AC}$ so that $\\overline{DE} \\parallel \\overline{BC}$ and point $F$ is on $\\overline{BC}$ so that $\\overline{EF} \\parallel \\overline{AC}$. What is the ratio of the area of $CDEF$ to the area of $\\triangle ABC?$\n\n\\n Options: A. $\\frac{4}{9}$, B. $\\frac{1}{2}$, C. $\\frac{5}{9}$, D. $\\frac{3}{5}$, E. $\\frac{2}{3}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2751.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sonja's smartphone displays the diagram on the right. It shows how long she has worked with four different apps in the previous week. This week he has spent only half the amount of time using two of the apps and the same amount of time as last week using the other two apps. Which of the following pictures could be the diagram for the current week?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1469.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the area of the shaded pinwheel shown in the $5\\times 5$ grid?\n\n\\n Options: A. $4$, B. $6$, C. $8$, D. $10$, E. $12$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2684.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many different squares can be drawn in total by joining the dots with line segments in the part of the square lattice as shown on the right? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1552.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure below, semicircles with centers at $A$ and $B$ and with radii $2$ and $1$, respectively, are drawn in the interior of, and sharing bases with, a semicircle with diameter $\\overline{JK}$. The two smaller semicircles are externally tangent to each other and internally tangent to the largest semicircle. A circle centered at $P$ is drawn externally tangent to the two smaller semicircles and internally tangent to the largest semicircle. What is the radius of the circle centered at $P$?\n\n\\n Options: A. $\\frac{3}{4}$, B. $\\frac{6}{7}$, C. $\\frac{1}{2}\\sqrt{3}$, D. $\\frac{5}{8}\\sqrt{2}$, E. $\\frac{11}{12}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2486.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the square below the numbers 1,2 and 3 must be written in the cells. In each row and in each column each of the numbers 1 , 2 and 3 must appear. Harry started to fill in the square. In how many ways can he complete this task?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/743.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the triangle $P Q R$, the lengths of sides $P Q$ and $P R$ are the same. The point $S$ lies on $Q R$ so that $Q S=P S$ and $\\angle R P S=75^{\\circ}$. What is the size of $\\angle Q R P$ ? \\n Options: A. $35^{\\circ}$, B. $30^{\\circ}$, C. $25^{\\circ}$, D. $20^{\\circ}$, E. $15^{\\circ}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1751.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram the large square is divided into 25 smaller squares. Adding up the sizes of the five angles $X P Y, X Q Y, X R Y, X S Y$ and $X T Y$, what total is obtained? \\n Options: A. $30^{\\circ}$, B. $45^{\\circ}$, C. $60^{\\circ}$, D. $75^{\\circ}$, E. $90^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1510.png" }, { "solution": "\\boxed{22}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In acute triangle $ABC$, $\\angle A = 68^\\circ$. Let $O$ be the circumcenter of triangle $ABC$. Find $\\angle OBC$, in degrees.\n\n", "completion": "\\boxed{22}", "image_path": "dataset/math_vision/images/2914.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle of radius $4 \\mathrm{~cm}$ is divided into four congruent parts by arcs of radius $2 \\mathrm{~cm}$ as shown. What is the length of the perimeter of one of the parts, in $\\mathrm{cm}$ ? \\n Options: A. $2 \\pi$, B. $4 \\pi$, C. $6 \\pi$, D. $8 \\pi$, E. $12 \\pi$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1862.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nIn $\\triangle ABC$, $AB = 10~ AC = 8$ and $BC = 6$. Circle $P$ is the circle with smallest radius which passes through $C$ and is tangent to $AB$. Let $Q$ and $R$ be the points of intersection, distinct from $C$ , of circle $P$ with sides $AC$ and $BC$, respectively. The length of segment $QR$ is\\n Options: A. $4.75$, B. $4.8$, C. $5$, D. $4\\sqrt{2}$, E. $3\\sqrt{3}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2322.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, the five circles have the same radii and touch as shown. The square joins the centres of the four outer circles. The ratio of the area of the shaded part of all five circles to the area of the unshaded parts of the circles is:\n\\n Options: A. $1: 3$, B. $1: 4$, C. $2: 5$, D. $2: 3$, E. $5: 4$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1018.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria folds a square piece of paper in such a way that the kangaroos exactly overlap each other. Along how many of the lines shown is this possible?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/471.png" }, { "solution": "\\boxed{21}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A jump of a little kangaroo is three times shorter than its mother's. How many jumps should the little kangaroo make to cover the distance equal to 7 jumps of its mother?\n", "completion": "\\boxed{21}", "image_path": "dataset/math_vision/images/17.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are $20$ cities in the County of Newton. Their populations are shown in the bar chart below. The average population of all the cities is indicated by the horizontal dashed line. Which of the following is closest to the total population of all $20$ cities?\n\n\\n Options: A. 65{, B. }000, C. 75{, D. }000, E. 85{, F. }000, G. 95{, H. }000, I. 105{, J. }000", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2765.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An $n$-pyramid is defined to be a stack of $n$ layers of balls, with each layer forming a triangular array. The layers of a 3-pyramid are shown in the diagram.\nAn 8-pyramid is now formed where all the balls on the outside of the 8 -pyramid are black (including the base layer) and the balls on the inside are all white. How many layers are there in the white pyramid?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1849.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The digits $2$, $0$, $2$, and $3$ are placed in the expression below, one digit per box. What is the maximum possible value of the expression?\n\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/2784.png" }, { "solution": "\\boxed{126}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the circle with center $O$ and diameters $AC$ and $BD$, the angle $AOD$ measures $54$ degrees. What is the measure, in degrees, of angle $AOB$? ", "completion": "\\boxed{126}", "image_path": "dataset/math_vision/images/2938.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Max and Moritz have drawn out a $5 \\times 5$ grid on the playground, together with three obstacles. They want to walk from $P$ to $Q$ using the shortest route, avoiding the obstacles and always crossing a common edge to go from the centre of one square to the centre of the next. How many such shortest paths are there from $P$ to $Q$ ? ", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1537.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two chords $A B$ and $A C$ are drawn into a circle with diameter $\\mathrm{AD}. \\angle B A C=60^{\\circ}$, $\\overline{A B}=24 \\mathrm{~cm}$, $\\mathrm{E}$ lies on $\\mathrm{AC}$ so that $\\overline{E C}=3 \\mathrm{~cm}$, and $\\mathrm{BE}$ is perpendicular to $\\mathrm{AC}$. How long is the chord $\\mathrm{BD}$?\n\\n Options: A. $\\sqrt{3} \\mathrm{~cm}$, B. $2 \\mathrm{~cm}$, C. $3 \\mathrm{~cm}$, D. $2 \\sqrt{3} \\mathrm{~cm}$, E. $3 \\sqrt{2} \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1424.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle RZT is generated by rotating the equilateral triangle AZC about point Z. Angle $\\beta=\\angle \\mathrm{CZR}=70^{\\circ}$. Determine angle $\\alpha=\\angle \\mathrm{CAR}$.\n\\n Options: A. $20^{\\circ}$, B. $25^{\\circ}$, C. $30^{\\circ}$, D. $35^{\\circ}$, E. $40^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1371.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Joanna turns over the card shown about its lower edge and then about its right-hand edge, as indicated in the diagram.\n\nWhat does she see?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1628.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Peter has drawn this pattern:\n\nHe draws exactly the same pattern once more.\nWhich point is on his drawing?\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/75.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a semicircle with centre $O$. Two of the angles are given. What is the value of $x$ ? ", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1960.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rectangle $ ABCD$, $ AB=5$ and $ BC=3$. Points $ F$ and $ G$ are on $ \\overline{CD}$ so that $ DF=1$ and $ GC=2$. Lines $ AF$ and $ BG$ intersect at $ E$. Find the area of $ \\triangle{AEB}$.\n\\n Options: A. $10$, B. $\\frac{21}{2}$, C. $12$, D. $\\frac{25}{2}$, E. $15$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2129.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Max builds this construction using some small equally big cubes. If he looks at his construction from above, the plan on the right tells the number of cubes in every tower. How big is the sum of the numbers covered by the two hearts?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/574.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The pattern on a large square tile consists of eight congruent right-angled triangles and a small square. The area of the tile is $49 \\mathrm{~cm}^{2}$ and the length of the hypotenuse $P Q$ of one of the triangles is $5 \\mathrm{~cm}$. What is the area of the small square? \\n Options: A. $1 \\mathrm{~cm}^{2}$, B. $4 \\mathrm{~cm}^{2}$, C. $9 \\mathrm{~cm}^{2}$, D. $16 \\mathrm{~cm}^{2}$, E. $25 \\mathrm{~cm}^{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1679.png" }, { "solution": "\\boxed{140}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\bigtriangleup ABC$, $D$ is a point on side $\\overline{AC}$ such that $BD=DC$ and $\\angle BCD$ measures $70^\\circ$. What is the degree measure of $\\angle ADB$?\n\n", "completion": "\\boxed{140}", "image_path": "dataset/math_vision/images/2727.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A big spot of ink covers most of a calendar page of a certain month. Which day of the week does the 25th day of that month fall on?\n\\n Options: A. Monday, B. Wednesday, C. Thursday, D. Saturday, E. Sunday", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/887.png" }, { "solution": "\\boxed{58}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Point $A,B,C,D,$ and $E$ are equally spaced on a minor arc of a circle. Points $E,F,G,H,I$ and $A$ are equally spaced on a minor arc of a second circle with center $C$ as shown in the figure below. The angle $\\angle ABD$ exceeds $\\angle AHG$ by $12^\\circ$. Find the degree measure of $\\angle BAG$.", "completion": "\\boxed{58}", "image_path": "dataset/math_vision/images/2085.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The $16$ squares on a piece of paper are numbered as shown in the diagram. While lying on a table, the paper is folded in half four times in the following sequence:\n\nfold the top half over the bottom half\nfold the bottom half over the top half\nfold the right half over the left half\nfold the left half over the right half.\n\nWhich numbered square is on top after step $4$?\n\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/2548.png" }, { "solution": "\\boxed{21}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The construction in the picture is built of cubes of the same size and weighs 189 grams. How many grams does one cube weigh?\n", "completion": "\\boxed{21}", "image_path": "dataset/math_vision/images/400.png" }, { "solution": "\\boxed{45}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Quadrilateral $P Q R S$ has right angles at vertices $P$ and $Q$ only. The numbers show the areas in $\\mathrm{cm}^{2}$ of two of the triangles. What is the area in $\\mathrm{cm}^{2}$ of $P Q R S$ ? ", "completion": "\\boxed{45}", "image_path": "dataset/math_vision/images/1617.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The sum of the number in each line, column and diagonal in the Ămagic squareñon the right is always constant. Only two numbers are visible. Which number is missing in field $a$?\n\\n Options: A. 16, B. 51, C. 54, D. 55, E. 110", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/223.png" }, { "solution": "\\boxed{92}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the first three patterns in a sequence in which each pattern has a square hole in the middle. How many small shaded squares are needed to build the tenth pattern in the sequence?\n", "completion": "\\boxed{92}", "image_path": "dataset/math_vision/images/1566.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The following picture shows a necklace with six pearls:\n\nWhich of the following diagrams shows the same necklace?\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/568.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Tiles I, II, III and IV are translated so one tile coincides with each of the rectangles $A, B, C$ and $D$. In the final arrangement, the two numbers on any side common to two adjacent tiles must be the same. Which of the tiles is translated to Rectangle $C$?\n\n\\n Options: A. $I$, B. $II$, C. $III$, D. $IV$, E. $\\text{ cannot be determined}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2680.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture on the left we see three dice on top of each other. The sum of the points on opposite sides of the dice is 7 as usual. The sum of the points of areas that face each other is always 5. How many points are on the area marked $\\mathrm{X}$?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1347.png" }, { "solution": "\\boxed{2.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consider the L-shaped tromino below with 3 attached unit squares. It is cut into exactly two pieces of equal area by a line segment whose endpoints lie on the perimeter of the tromino. What is the longest possible length of the line segment?\\n", "completion": "\\boxed{2.5}", "image_path": "dataset/math_vision/images/2882.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anne has glued together some cubes and has obtained the solid shown on the right. She turns it around to check it out from different sides. Which view can she not obtain?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1137.png" }, { "solution": "\\boxed{280}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feet wide, and 5 feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?\n", "completion": "\\boxed{280}", "image_path": "dataset/math_vision/images/2722.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Johann stacked $1 \\times 1$ cubes on the squares of a $4 \\times 4$ grid. The diagram on the right shows the number of cubes that were stacked on top of each other above each square. What will Johann see if he looks from the back (hinten) at the tower?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1100.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria puts 4 liters of water in vase I, 3 liters of water in vase II and 4 liters of water in vase III, represented on the side. Seen from the front, these three vases seem to have the same size. Which of the following images can represent the three vases, when seen from above?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/929.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A bowl is formed by attaching four regular hexagons of side 1 to a square of side 1. The edges of adjacent hexagons coincide, as shown in the figure. What is the area of the octagon obtained by joining the top eight vertices of the four hexagons, situated on the rim of the bowl?\n\n\\n Options: A. $6$, B. $7$, C. $5+2\\sqrt{2}$, D. $8$, E. $9$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2246.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers 1 to 7 should be written in the small circles so that the sum of the numbers along each line is the same. Which number should be written in the uppermost circle on the triangle?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/811.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The cuboid shown has been built using four shapes, each made from four small cubes. Three of the shapes can be completely seen, but the dark one is only partly visible. Which of the following shapes could be the dark one? \n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1803.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: To complete the table, each cell must contain either 0 or 1 , and the total of each row and column must be 2 . What are the values of the entries $X$ and $Y$ ? \\n Options: A. $X=0, Y=0$, B. $X=0, Y=1$, C. $X=1, Y=0$, D. $X=1, Y=1$, E. It is impossible to complete.", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1834.png" }, { "solution": "\\boxed{46}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the perimeter of the figure shown (all angles are right angles)?\n", "completion": "\\boxed{46}", "image_path": "dataset/math_vision/images/784.png" }, { "solution": "\\boxed{421}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram below shows a sequence of shapes made up of black and white floor tiles where each shape after the first has two more rows and two more columns than the one before it.\n\nHow many black tiles would be required to create the 15th shape in the sequence?", "completion": "\\boxed{421}", "image_path": "dataset/math_vision/images/1725.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three four-digit numbers are written onto three separate pieces of paper as shown. The sum of the three numbers is 11126. Three of the digits in the picture are hidden. Which are the three hidden digits?\n\\n Options: A. 1, B. 4 and 7, C. 1, D. 5 and 7, E. 3, F. 3 and 3, G. 4, H. 5 and 6, I. 4, J. 5 and 7", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/326.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In this figure the radius of the circle is equal to the altitude of the equilateral triangle $ABC$. The circle is made to roll along the side $AB$, remaining tangent to it at a variable point $T$ and intersecting lines $AC$ and $BC$ in variable points $M$ and $N$, respectively. Let $n$ be the number of degrees in arc $MTN$.\n\nThen $n$, for all permissible positions of the circle:\\n Options: A. $\\text{varies from }30^{\\circ}\\text{ to }90^{\\circ}$, B. $\\text{varies from }30^{\\circ}\\text{ to }60^{\\circ}$, C. $\\text{varies from }60^{\\circ}\\text{ to }90^{\\circ}$, D. $\\text{remains constant at }30^{\\circ}$, E. $\\text{remains constant at }60^{\\circ}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2283.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The 5 balls shown begin to move simultaneously in the directions indicated by their arrows.\n\nWhen two balls going in opposite directions collide, the bigger ball swallows the smaller one and increases its value by the value of the smaller ball. The bigger ball continues to move in its original direction, as shown in the following example.\n\nWhat is the final result of the collisions of the 5 balls shown?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/650.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Tatiana's teacher drew a $3 \\times 3$ grid on the board, with zero in each cell. The students then took turns to pick a $2 \\times 2$ square of four adjacent cells, and to add 1 to each of the numbers in the four cells. After a while, the grid looked like the diagram on the right (some of the numbers in the cells have been rubbed out.)\n\nWhat number should be in the cell with the question mark?", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1963.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: At each of the vertices of a cube sits a Bunchkin. Two Bunchkins are said to be adjacent if and only if they sit at either end of one of the cube's edges. Each Bunchkin is either a 'truther', who always tells the truth, or a 'liar', who always lies. All eight Bunchkins say 'I am adjacent to exactly two liars'. What is the maximum number of Bunchkins who are telling the truth?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2011.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle is inscribed in the triangle $A B C$ (see the figure), $A C=5, A B=6, B C=3$. The segment $E D$ is tangent to the circle. The perimeter of the triangle $A D E$ is\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/212.png" }, { "solution": "\\boxed{84}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A farmer's rectangular field is partitioned into $2$ by $2$ grid of $4$ rectangular sections as shown in the figure. In each section the farmer will plant one crop: corn, wheat, soybeans, or potatoes. The farmer does not want to grow corn and wheat in any two sections that share a border, and the farmer does not want to grow soybeans and potatoes in any two sections that share a border. Given these restrictions, in how many ways can the farmer choose crops to plant in each of the four sections of the field?\n", "completion": "\\boxed{84}", "image_path": "dataset/math_vision/images/2232.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the 7 positions $1,2,3,4,5,6,7$ of the bottom side of a die which is rolled around its edge in this order. Which two of these positions were taken up by the same face of the die?\n\\n Options: A. 1 and 7, B. 1 and 6, C. 1 and 5, D. 2 and 7, E. 2 and 6", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1091.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $15 \\%$ of a round cake is cut as shown in the figure. How many degrees is the angle denoted by the question mark?\n\\n Options: A. $30^{\\circ}$, B. $45^{\\circ}$, C. $54^{\\circ}$, D. $15^{\\circ}$, E. $20^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1261.png" }, { "solution": "\\boxed{5\\sqrt{5}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Corner $A$ of a rectangular piece of paper of width 8 inches is folded over so that it coincides with point $C$ on the opposite side. If $BC = 5$ inches, find the length in inches of fold $l$.\n\n", "completion": "\\boxed{5\\sqrt{5}}", "image_path": "dataset/math_vision/images/2890.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, $\\mathrm{ABCE}$ is a square. $\\mathrm{CDE}$ and $\\mathrm{BCF}$ are equilateral triangles. The length of $\\mathrm{AB}$ is 1. How long is $\\mathrm{FD}$?\n\\n Options: A. $\\sqrt{2}$, B. $\\frac{\\sqrt{3}}{2}$, C. $\\sqrt{3}$, D. $\\sqrt{5}-1$, E. $\\sqrt{6}-1$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1333.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five kangaroos named A, B, C, D and E have one child each, named a, b, c, d and e, not necessarily in that order. In the first group photo shown exactly 2 of the children are standing next to their mothers. In the second group photo exactly 3 of the children are standing next to their mothers. Whose child is a?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/361.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the nets of a cube has a line drawn on. For which net does the line form a closed loop when the net is folded up to make a cube?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/910.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Using these tiles Robert makes different patterns. How many of the patterns shown below can he make?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/585.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the paths shown in the pictures is the longest?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/121.png" }, { "solution": "\\boxed{13837}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A student correctly added the two two-digit numbers on the left of the board and got the answer 137. What answer will she obtain if she adds the two four-digit numbers on the right of the board?\n", "completion": "\\boxed{13837}", "image_path": "dataset/math_vision/images/1686.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $A B C D$ has sides of length $3 \\mathrm{~cm}$. The points $M$ and $N$ lie on $A D$ and $A B$ so that $C M$ and $C N$ split the square into three pieces of the same area. What is the length of $D M$ ? \\n Options: A. $0.5 \\mathrm{~cm}$, B. $1 \\mathrm{~cm}$, C. $1.5 \\mathrm{~cm}$, D. $2 \\mathrm{~cm}$, E. $2.5 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1653.png" }, { "solution": "\\boxed{8\\sqrt{3}{squareinches}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: By joining alternate vertices of a regular hexagon with edges $4$ inches long, two equilateral triangles are formed, as shown. What is the area, in square inches, of the region that is common to the two triangles? Express your answer in simplest radical form. ", "completion": "\\boxed{8\\sqrt{3}{squareinches}}", "image_path": "dataset/math_vision/images/3007.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The three angle bisectors of triangle $L M N$ meet at a point $O$ as shown. Angle $L N M$ is $68^{\\circ}$. What is the size of angle $L O M$ ? \\n Options: A. $120^{\\circ}$, B. $124^{\\circ}$, C. $128^{\\circ}$, D. $132^{\\circ}$, E. $136^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1853.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, $ \\overline{CD}, \\overline{AE}$ and $ \\overline{BF}$ are one-third of their respective sides. It follows that $ \\overline{AN_2}: \\overline{N_2N_1}: \\overline{N_1D} = 3: 3: 1$, and similarly for lines $ BE$ and $ CF$. Then the area of triangle $ N_1N_2N_3$ is:\n\\n Options: A. $\\frac{1}{10} \\triangle ABC$, B. $\\frac{1}{9} \\triangle ABC$, C. $\\frac{1}{7} \\triangle ABC$, D. $\\frac{1}{6} \\triangle ABC$, E. $\\text{none of these}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2258.png" }, { "solution": "\\boxed{21}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the addition on the right, different letters represent different numbers. Assuming the account is correct, what is the highest possible value for the sum $\\mathrm{C}+\\mathrm{A}+\\mathrm{N}$?\n", "completion": "\\boxed{21}", "image_path": "dataset/math_vision/images/337.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a square with sides of length $6 \\mathrm{~cm}$ the points $A$ and $B$ are on one of the axes of symmetry, as shown. The shaded area is equal to each of the two unshaded areas.\n\nWhat is the length of $A B$ ?\\n Options: A. $3.6 \\mathrm{~cm}$, B. $3.8 \\mathrm{~cm}$, C. $4.0 \\mathrm{~cm}$, D. $4.2 \\mathrm{~cm}$, E. $4.4 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1520.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the ratio of the areas of the triangles $A D E$ and $A B C$ in the picture? \\n Options: A. $9: 4$, B. $7: 3$, C. $4: 5$, D. $15: 10$, E. $26: 9$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1805.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure, $AB$ is a diameter of the circle, $CD$ is a chord parallel to $AB$, and $AC$ intersects $BD$ at $E$, with $\\angle AED = \\alpha$. The ratio of the area of $\\triangle CDE$ to that of $\\triangle ABE$ is\n\n\\n Options: A. $\\cos \\alpha$, B. $\\sin \\alpha$, C. $\\cos^2\\alpha$, D. $\\sin^2\\alpha$, E. $1 - \\sin \\alpha$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2364.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The square was cut out from a page in a squared exercise book. Then two figures in the picture were cut out from the square. Which ones?\n\\n Options: A. 1 and 3, B. 2 and 4, C. 2 and 3, D. 1 and 4, E. Impossible to cut out", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/707.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a net of a cube, with three dotted lines added. If you folded the net into a cube and then cut along the dotted lines you would have a hole in the cube. What would be the shape of the hole? \\n Options: A. an equilateral triangle, B. a rectangle, C. but not a square, D. a right-angled triangle, E. a square, F. a hexagon", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1515.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four towns $P, Q, R$ and $S$ are connected by roads, as shown. A race uses each road exactly once. The race starts at $S$ and finishes at $Q$. How many possible routes are there for the race? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1630.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the triangle $P Q R$ in which $R H$ is a perpendicular height and $P S$ is the angle bisector at $P$. The obtuse angle between $R H$ and $P S$ is four times angle $S P Q$. What is angle $R P Q$ ? \\n Options: A. $30^{\\circ}$, B. $45^{\\circ}$, C. $60^{\\circ}$, D. $75^{\\circ}$, E. $90^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1614.png" }, { "solution": "\\boxed{0}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Instead of digits Hannes uses the letters A, B, C and D in a calculation. Different letters stand for different digits. Which digit does the letter B stand for?\n", "completion": "\\boxed{0}", "image_path": "dataset/math_vision/images/895.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many points are there in the three unseen sides of dice?\n", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/16.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers $1,4,7,10$ and 13 should be written into the squares so that the sum of the three numbers in the horizontal row is equal to the sum of the three numbers in the vertical column. What is the largest possible value of these sums?\n", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/787.png" }, { "solution": "\\boxed{132}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows an equilateral triangle and a regular pentagon. What is the value of $x$ ? ", "completion": "\\boxed{132}", "image_path": "dataset/math_vision/images/1527.png" }, { "solution": "\\boxed{60}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which number should be written in place of the question mark?\n", "completion": "\\boxed{60}", "image_path": "dataset/math_vision/images/1.png" }, { "solution": "\\boxed{60}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Marc builds the number 2022 as seen in the picture by glueing together 66 cubes of the same size. Afterwards he paints the entire surface of his work. On how many of the 66 cubes has Marc painted exactly four faces?\n", "completion": "\\boxed{60}", "image_path": "dataset/math_vision/images/968.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows an equilateral triangle RST and also the triangle $T U V$ obtained by rotating triangle $R S T$ about the point $T$. Angle $R T V=70^{\\circ}$. What is angle $R S V$ ? \\n Options: A. $20^{\\circ}$, B. $25^{\\circ}$, C. $30^{\\circ}$, D. $35^{\\circ}$, E. $40^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1890.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rolly wishes to secure his dog with an 8-foot rope to a square shed that is 16 feet on each side. His preliminary drawings are shown. Which of these arrangements gives the dog the greater area to roam, and by how many square feet?\n\n\\n Options: A. $\\text{ I, by }8\\pi$, B. $\\text{ I, by }6\\pi$, C. $\\text{ II, by }4\\pi$, D. $\\text{II, by }8\\pi$, E. $\\text{ II, by }10\\pi$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2151.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the starting position, the direction and the distance covered within 5 seconds by four bumper cars. Which two cars will first crash into each other? \\n Options: A. A and B, B. A and C, C. A and D, D. B and C, E. C and D", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1244.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Usain is walking for exercise by zigzagging across a $100$-meter by $30$-meter rectangular field, beginning at point $A$ and ending on the segment $\\overline{BC}$. He wants to increase the distance walked by zigzagging as shown in the figure below $(APQRS)$. What angle $\\theta=\\angle PAB=\\angle QPC=\\angle RQB=\\cdots$ will produce in a length that is $120$ meters? (Do not assume the zigzag path has exactly four segments as shown; there could be more or fewer.)\n\n\\n Options: A. $\\arccos\\frac{5}{6}$, B. $\\arccos\\frac{4}{5}$, C. $\\arccos\\frac{3}{10}$, D. $\\arcsin\\frac{4}{5}$, E. $\\arcsin\\frac{5}{6}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2501.png" }, { "solution": "\\boxed{23}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Construct a square on one side of an equilateral triangle. One on non-adjacent side of the square, construct a regular pentagon, as shown. One a non-adjacent side of the pentagon, construct a hexagon. Continue to construct regular polygons in the same way, until you construct an octagon. How many sides does the resulting polygon have?\n\n", "completion": "\\boxed{23}", "image_path": "dataset/math_vision/images/2699.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two squares have side 1. What is the area of the black quadrangle?\n\\n Options: A. $\\sqrt{2}-1$, B. $\\frac{\\sqrt{2}}{2}$, C. $\\frac{\\sqrt{2}+1}{2}$, D. $\\sqrt{2}+1$, E. $\\sqrt{3}-\\sqrt{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1297.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A flee stands on the floor and wants to climb the 10 steps. He can either jump 3 steps upwards or jump 4 steps downwards. What is is the smallest number of jumps he must make?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/495.png" }, { "solution": "\\boxed{120}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular board of 8 columns has squared numbered beginning in the upper left corner and moving left to right so row one is numbered 1 through 8, row two is 9 through 16, and so on. A student shades square 1, then skips one square and shades square 3, skips two squares and shades square 6, skips 3 squares and shades square 10, and continues in this way until there is at least one shaded square in each column. What is the number of the shaded square that first achieves this result?\n\n", "completion": "\\boxed{120}", "image_path": "dataset/math_vision/images/2603.png" }, { "solution": "\\boxed{0}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maja decided to enter numbers into the cells of a $3 \\times 3$ grid. She wanted to do this in such a way that the numbers in each of the four $2 \\times 2$ grids that form part of the $3 \\times 3$ grid have the same totals. She has already written numbers in three of the corner cells, as shown in the diagram. Which number does she need to write in the bottom right corner?\n", "completion": "\\boxed{0}", "image_path": "dataset/math_vision/images/1924.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the \"buildings\" A-E, each consisting of 5 cubes, cannot be obtained from the building on the right, if you are allowed to move only one cube?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/765.png" }, { "solution": "\\boxed{40}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Tom, John and Lily each shot six arrows at a target. Arrows hitting anywhere within the same ring scored the same number of points. Tom scored 46 points and John scored 34 points, as shown. How many points did Lily score? ", "completion": "\\boxed{40}", "image_path": "dataset/math_vision/images/1712.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rows 1, 2, 3, 4, and 5 of a triangular array of integers are shown below:\n\n\nEach row after the first row is formed by placing a 1 at each end of the row, and each interior entry is 1 greater than the sum of the two numbers diagonally above it in the previous row. What is the units digit of the sum of the 2023 numbers in the 2023rd row?", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/2502.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A wooden block has 8 vertices. One vertex is cut off now (see the picture).\n\nHow many vertices has the block now?", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/25.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Numbers are written in the $4 \\times 4$ grid: any two numbers in neighbouring squares should have a difference of 1 , that is squares that share an edge. The number 3 is already given. The number 9 will be used somewhere in the grid. How many different numbers will have been used once the grid is filled in completely?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/826.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture the large square has an area of 1. What is the area of the small black square?\n\\n Options: A. $\\frac{1}{100}$, B. $\\frac{1}{300}$, C. $\\frac{1}{600}$, D. $\\frac{1}{900}$, E. $\\frac{1}{1000}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1048.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many graphs of the functions $y=x^{2}, y=-x^{2}, y=+\\sqrt{x}, y=-\\sqrt{x}$, $y=+\\sqrt{-x}, y=-\\sqrt{-x}, y=+\\sqrt{|x|}, y=-\\sqrt{|x|}$ are included in the sketch on the right?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/239.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A semicircle is constructed along each side of a right triangle with legs 6 inches and 8 inches. The semicircle placed along the hypotenuse is shaded, as shown. What is the total area of the two non-shaded crescent-shaped regions? Express your answer in simplest form.\n\n", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/2990.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the $xy$-plane, consider the L-shaped region bounded by horizontal and vertical segments with vertices at $(0,0), (0,3), (3,3), (3,1), (5,1)$ and $(5,0)$. The slope of the line through the origin that divides the area of this region exactly in half is\n\\n Options: A. $\\frac{2}{7}$, B. $\\frac{1}{3}$, C. $\\frac{2}{3}$, D. $\\frac{3}{4}$, E. $\\frac{7}{9}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2412.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rectangle $ABCD$, $AD=1$, $P$ is on $\\overline{AB}$, and $\\overline{DB}$ and $\\overline{DP}$ trisect $\\angle ADC$. Write the perimeter of $\\triangle BDP$ in simplest form as: $w + \\frac{x \\cdot \\sqrt{y}}{z}$, where $w, x, y, z$ are nonnegative integers. What is $w + x + y + z$?\n\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/2931.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Natascha has some blue, red, yellow and green sticks of $1 \\mathrm{~cm}$ length. She wants to make a $3 \\times 3$ grid as shown in such a way that the four sides of each $1 \\times 1-$ square in the grid each are of a different colour. What is the minimum number of green sticks she can use?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1189.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six rectangles are arranged as shown. The number inside each rectangle gives the area, in $\\mathrm{cm}^{2}$, of that rectangle. The rectangle on the top left has height $6 \\mathrm{~cm}$.\n\nWhat is the height of the bottom right rectangle?\\n Options: A. $4 \\mathrm{~cm}$, B. $5 \\mathrm{~cm}$, C. $6 \\mathrm{~cm}$, D. $7.5 \\mathrm{~cm}$, E. $10 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1957.png" }, { "solution": "\\boxed{21}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The circles of the figure should be numbered from 0 to 10 , each with a different number. The five sums of the three numbers written on each diameter must be odd numbers. If one of these sums is the smallest possible, what will be the largest possible value of one of the remaining sums?\n", "completion": "\\boxed{21}", "image_path": "dataset/math_vision/images/922.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Eli drew a board on the floor with nine squares and wrote a number on each of them, starting from 1 and adding 3 units to each new number he wrote, until he filled the board. In the picture, three of the numbers that Eli wrote appear. Which number below can be one of the numbers she wrote in the colored box?\n\\n Options: A. 10, B. 14, C. 17, D. 20, E. 22", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/623.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the diagrams below cannot be drawn without lifting your pencil off the page and without drawing along the same line twice?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1663.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In trapezium $P Q R S, \\angle R S P=2 \\times \\angle S P Q$ and $\\angle S P Q=2 \\times \\angle P Q R$. Also $\\angle Q R S=k \\times \\angle P Q R$. What is the value of $k$ ? ", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1741.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The two colours of this picture are swapped. Then the picture is turned. Which of the pictures below is obtained?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/589.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rectangle $ ADEH$, points $ B$ and $ C$ trisect $ \\overline{AD}$, and points $ G$ and $ F$ trisect $ \\overline{HE}$. In addition, $ AH = AC = 2$. What is the area of quadrilateral $ WXYZ$ shown in the figure?\n\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{\\sqrt{2}}2$, C. $\\frac{\\sqrt{3}}2$, D. $\\frac{2\\sqrt{2}}3$, E. $\\frac{2\\sqrt{3}}3$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2154.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The two wheels shown below are spun and the two resulting numbers are added. The probability that the sum is even is\n\n\\n Options: A. $\\frac{1}{6}$, B. $\\frac{1}{4}$, C. $\\frac{1}{3}$, D. $\\frac{5}{12}$, E. $\\frac{4}{9}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2576.png" }, { "solution": "\\boxed{127}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Isosceles $ \\triangle ABC$ has a right angle at $ C$. Point $ P$ is inside $ \\triangle ABC$, such that $ PA = 11, PB = 7,$ and $ PC = 6$. Legs $ \\overline{AC}$ and $ \\overline{BC}$ have length $ s = \\sqrt{a + b\\sqrt{2}}$, where $ a$ and $ b$ are positive integers. What is $ a + b$?\n\n", "completion": "\\boxed{127}", "image_path": "dataset/math_vision/images/2467.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a square $A B C D M$ is the midpoint of $A B$. $M N$ is perpenticular to $A C$. Determine the ratio of the area of the grey triangle to the area of the square $A B C D$.\n\\n Options: A. $1: 6$, B. $1: 5$, C. $7: 36$, D. $3: 16$, E. $7: 40$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1092.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number $x$ in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of $x$?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/2778.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the five squares has the biggest proportion of black area?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/907.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of these clouds contain only numbers that are smaller than 7 ?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/85.png" }, { "solution": "\\boxed{170}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: As shown in the figure below, point $E$ lies on the opposite half-plane determined by line $CD$ from point $A$ so that $\\angle CDE = 110^\\circ$. Point $F$ lies on $\\overline{AD}$ so that $DE=DF$, and $ABCD$ is a square. What is the degree measure of $\\angle AFE?$\n", "completion": "\\boxed{170}", "image_path": "dataset/math_vision/images/2231.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maxi builds towers made up of little $1 \\mathrm{~cm} \\times 1 \\mathrm{~cm} \\times 2 \\mathrm{~cm}$ building blocks as can be seen in the picture.\n\nHe continues to build his towers in the same way. Finally he uses 28 building blocks for one tower. What is the height of this tower?\\n Options: A. $9 \\mathrm{~cm}$, B. $10 \\mathrm{~cm}$, C. $11 \\mathrm{~cm}$, D. $12 \\mathrm{~cm}$, E. $14 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/908.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Nathalie wanted to build a large cube out of lots of small cubes. How many cubes are missing from the picture on the right that would be needed to build the large cube on the left?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/817.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows an object made up of 12 dice glued-together. The object is dipped into some colour so that the entire outside is coloured in this new colour. How many of the small dice will have exactly four faces coloured in?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/308.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIf $a,b,$ and $d$ are the lengths of a side, a shortest diagonal and a longest diagonal, respectively, of a regular nonagon (see adjoining figure), then\\n Options: A. $d=a+b$, B. $d^2=a^2+b^2$, C. $d^2=a^2+ab+b^2$, D. $b=\\frac{a+d}{2}$, E. $b^2=ad$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2319.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The two circles pictured have the same center $C$. Chord $\\overline{AD}$ is tangent to the inner circle at $B$, $AC$ is $10$, and chord $\\overline{AD}$ has length $16$. What is the area between the two circles?\n\n\\n Options: A. $36 \\pi$, B. $49 \\pi$, C. $64 \\pi$, D. $81 \\pi$, E. $100 \\pi$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2708.png" }, { "solution": "\\boxed{22}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ann made a 3-step staircase using 18 toothpicks as shown in the figure. How many toothpicks does she need to add to complete a 5-step staircase? \n", "completion": "\\boxed{22}", "image_path": "dataset/math_vision/images/2202.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A child's toy hangs from the ceiling and it is in balance at all places. The same shapes have the same weight. The weight of a circle is 30 grams. What is the weight of a square?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/438.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two right circular cones with vertices facing down as shown in the figure below contain the same amount of liquid. The radii of the tops of the liquid surfaces are $3 \\text{ cm}$ and $6 \\text{ cm}$. Into each cone is dropped a spherical marble of radius $1 \\text{ cm}$, which sinks to the bottom and is completely submerged without spilling any liquid. What is the ratio of the rise of the liquid level in the narrow cone to the rise of the liquid level in the wide cone?\n\\n Options: A. 1:1, B. 47:43, C. 2:1, D. 40:13, E. 4:1", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2238.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The sides of the rectangle $A B C D$ are parallel to the co-ordinate axis. The rectangle lies below the $\\mathrm{x}$-axis and to the right of the $\\mathrm{y}$-axis, as shown in the diagram. For each of the points A, B, C, D the quotient (y-coordinate):(x-coordinate) is calculated. For which point will you obtain the smallest quotient?\n\\n Options: A. A, B. B, C. C, D. D, E. It depends on the position of the rectangle and its side lengths.", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1374.png" }, { "solution": "\\boxed{2\\pi}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A paper cone is to be made from a three-quarter circle having radius 4 inches (shaded). What is the length of the arc on the discarded quarter-circle (dotted portion)? Express your answer in terms of $\\pi$.\n\n", "completion": "\\boxed{2\\pi}", "image_path": "dataset/math_vision/images/2954.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Martin's smartphone displays the diagram on the right. It shows how long he has worked with four different apps in the previous week. The apps are sorted from top to bottom according to the amount of time they have been used. This week he has spent only half the amount of time using two of the apps and the same amount of time as last week using the other two apps. Which of the following pictures cannot be the diagram for the current week?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/366.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nThe bar graph shows the grades in a mathematics class for the last grading period. If A, B, C, and D are satisfactory grades, what fraction of the grades shown in the graph are satisfactory?\\n Options: A. $\\frac{1}{2}$, B. $\\frac{2}{3}$, C. $\\frac{3}{4}$, D. $\\frac{4}{5}$, E. $\\frac{9}{10}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2505.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three congruent circles with centers $P$, $Q$, and $R$ are tangent to the sides of rectangle $ABCD$ as shown. The circle centered at $Q$ has diameter $4$ and passes through points $P$ and $R$. The area of the rectangle is\n\n", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/2578.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The bee wants to get to the flower. Each arrow indicates a move to one neighbouring square. Which path can the bee fly to get to the flower?\n\\n Options: A. $\\downarrow \\rightarrow \\rightarrow \\downarrow \\downarrow \\downarrow$, B. $\\downarrow \\downarrow \\rightarrow \\downarrow \\downarrow \\rightarrow$, C. $\\rightarrow \\downarrow \\rightarrow \\downarrow \\rightarrow \\rightarrow$, D. $\\rightarrow \\rightarrow \\downarrow \\downarrow \\downarrow \\downarrow$, E. $\\rightarrow \\downarrow \\rightarrow \\downarrow \\downarrow \\rightarrow$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/660.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle with radius $1$ is inscribed in a square and circumscribed about another square as shown. Which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?\n\n\\n Options: A. $\\frac{1}2$, B. $1$, C. $\\frac{3}2$, D. $2$, E. $\\frac{5}2$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2717.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Oli coloured in the following 8 fields in the grid: A2, B1, B2, B3, B4, C3, D3 and D4. Which is his grid?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/490.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure the sum of the distances $AD$ and $BD$ is\n\\n Options: A. $\\text{between 10 and 11}$, B. $12$, C. $\\text{between 15 and 16}$, D. $\\text{between 16 and 17}$, E. $17$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2368.png" }, { "solution": "\\boxed{42}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: By drawing 9 lines, 5 horizontal and 4 vertical, one can form 12 small rectangles, as shown on the right. What is the greatest possible number of small rectangles one can form by drawing 15 lines, either horizontal or vertical? ", "completion": "\\boxed{42}", "image_path": "dataset/math_vision/images/1545.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Cuthbert is going to make a cube with each face divided into four squares. Each square must have one shape drawn on it; either a cross, a triangle or a circle. Squares that share an edge must have different shapes on them. One possible cube is shown in the diagram. Which of the following combinations of crosses and triangles is possible on such a cube (with the other shapes being circles)?\n\\n Options: A. 6 crosses, B. 8 triangles, C. 7 crosses, D. 8 triangles, E. 5 crosses, F. 8 triangles, G. 7 crosses, H. 7 triangles, I. none of these are possible", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1977.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Luisa draws a star. She cuts a piece out of the middle of the drawing. What does this piece look like?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/510.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Andrea has wound some rope around a piece of wood, as shown in the diagram on the right. She rotates the wood $180^{\\circ}$ as shown by the arrow in the diagram. What does she see after the rotation?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1574.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The 5 figures on the grid can only move in the directions indicated by the black arrows. Which figure can leave through gate G?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/944.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The rectangle $A B C D$ lies below the $x$-axis, and to the left of the $y$-axis. The edges of the rectangle are parallel to the coordinate axes. For each point $A, B, C, D$, the $y$-coordinate is divided by the $x$-coordinate. Which of the points yields the smallest value from this calculation? \\n Options: A. A, B. C, C. C, D. D, E. it depends on the size of the rectangle", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1893.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a plan of a town with various bus stops. There are four bus routes in the town.\nRoute 1 goes $\\mathrm{C}-\\mathrm{D}-\\mathrm{E}-\\mathrm{F}-\\mathrm{G}-\\mathrm{H}-\\mathrm{C}$ and is $17 \\mathrm{~km}$ long.\nRoute 2 goes $\\mathrm{A}-\\mathrm{B}-\\mathrm{C}-\\mathrm{F}-\\mathrm{G}-\\mathrm{H}-\\mathrm{A}$ and is $12 \\mathrm{~km}$ long.\nRoute 3 goes $\\mathrm{A}-\\mathrm{B}-\\mathrm{C}-\\mathrm{D}-\\mathrm{E}-\\mathrm{F}-\\mathrm{G}-\\mathrm{H}-\\mathrm{A}$ and is $20 \\mathrm{~km}$ long.\nRoute 4 goes $\\mathrm{C}-\\mathrm{F}-\\mathrm{G}-\\mathrm{H}-\\mathrm{C}$.\n\nHow long is route 4 ?\\n Options: A. $10 \\mathrm{~km}$, B. $9 \\mathrm{~km}$, C. $8 \\mathrm{~km}$, D. $7 \\mathrm{~km}$, E. $6 \\mathrm{~km}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1759.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Suppose that\n\nmeans $a+b-c$.\nFor example,\n\nis $5+4-6 = 3$.\nThen the sum\n\nis", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/2554.png" }, { "solution": "\\boxed{$4 \\pi$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: S-Corporation designs its logo by linking together $4$ semicircles along the diameter of a unit circle. Find the perimeter of the shaded portion of the logo.\\n", "completion": "\\boxed{$4 \\pi$}", "image_path": "dataset/math_vision/images/2794.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In which picture are there half as many circles as triangles and twice as many squares as triangles?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/67.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jeffrey fires three arrows at each of four archery targets. He scores 29 points on the first target, 43 on the second and 47 on the third. How many points does Jeffrey score on the fourth target? ", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/1505.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure triangle $ ABC$ is inscribed in a circle. Point $ D$ lies on $ \\stackrel{\\frown}{AC}$ with $ \\stackrel{\\frown}{DC} = 30^\\circ$, and point $ G$ lies on $ \\stackrel{\\frown}{BA}$ with $ \\stackrel{\\frown}{BG}\\, > \\, \\stackrel{\\frown}{GA}$. Side $ AB$ and side $ AC$ each have length equal to the length of chord $ DG$, and $ \\angle CAB = 30^\\circ$. Chord $ DG$ intersects sides $ AC$ and $ AB$ at $ E$ and $ F$, respectively. The ratio of the area of $ \\triangle AFE$ to the area of $ \\triangle ABC$ is\n\\n Options: A. $\\frac{2 - \\sqrt{3}}{3}$, B. $\\frac{2\\sqrt{3} - 3}{3}$, C. $7\\sqrt{3} - 12$, D. $3\\sqrt{3} - 5$, E. $\\frac{9 - 5\\sqrt{3}}{3}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2338.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square is cut into four pieces. Which shape can you not make with these four pieces?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/37.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If the pattern in the diagram continues, what fraction of the interior would be shaded in the eighth triangle?\n\n\\n Options: A. $\\frac{3}{8}$, B. $\\frac{5}{27}$, C. $\\frac{7}{16}$, D. $\\frac{9}{16}$, E. $\\frac{11}{45}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2602.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lina has placed two tiles on a square game board. Which one of the 5 counters shown, can she add, so that none of the remaining four counters can be placed anymore?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1078.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A monkey has torn off a piece of Captain Jack's map.\n\nWhat does the piece the monkey has torn off look like?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/141.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Katrin forms a path around each square. For that she uses stones like this\n\nHow many such stones does she need for a path around the square with side length 5?", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/147.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which piece is missing?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/50.png" }, { "solution": "\\boxed{\\frac{3}{4}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In right triangle $ABC$, shown below, $\\cos{B}=\\frac{6}{10}$. What is $\\tan{C}$?\n\n", "completion": "\\boxed{\\frac{3}{4}}", "image_path": "dataset/math_vision/images/3028.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: For triangle $ABC$, points $D$ and $E$ are the midpoints of sides $AB$ and $AC$, respectively. Side $BC$ measures six inches. What is the measure of segment $DE$ in inches?\n\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/2964.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $ABC$ is inscribed in a circle with center $O'$. A circle with center $O$ is inscribed in triangle $ABC$. $AO$ is drawn, and extended to intersect the larger circle in $D$.\n\n Then, we must have:\\n Options: A. $CD=BD=O'D$, B. $AO=CO=OD$, C. $CD=CO=BD \\\\$, D. $CD=OD=BD$, E. $O'B=O'C=OD $", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2286.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The sums of the all the three numbers on each side of the triangle are equal. Two numbers happened to be stained with ink. How much is the sum of these two numbers?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/8.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows four overlapping hearts. The areas of the hearts are $1 \\mathrm{~cm}^{2}, 4 \\mathrm{~cm}^{2}, 9 \\mathrm{~cm}^{2}$ and $16 \\mathrm{~cm}^{2}$. What is the total shaded area? \\n Options: A. $9 \\mathrm{~cm}^{2}$, B. $10 \\mathrm{~cm}^{2}$, C. $11 \\mathrm{~cm}^{2}$, D. $12 \\mathrm{~cm}^{2}$, E. $13 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1640.png" }, { "solution": "\\boxed{732}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure below shows a ring made of six small sections which you are to paint on a wall. You have four paint colors available and will paint each of the six sections a solid color. Find the number of ways you can choose to paint each of the six sections if no two adjacent section can be painted with the same color.\n\n", "completion": "\\boxed{732}", "image_path": "dataset/math_vision/images/2091.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn the adjoining figure, $AB$ is tangent at $A$ to the circle with center $O$; point $D$ is interior to the circle; and $DB$ intersects the circle at $C$. If $BC=DC=3$, $OD=2$, and $AB=6$, then the radius of the circle is\\n Options: A. $3+\\sqrt{3}$, B. $15/\\pi$, C. $9/2$, D. $2\\sqrt{6}$, E. $\\sqrt{22}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2313.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a logo made entirely from semicircular arcs, each with a radius of $2 \\mathrm{~cm}, 4 \\mathrm{~cm}$ or $8 \\mathrm{~cm}$. What fraction of the logo is shaded? \\n Options: A. $\\frac{1}{3}$, B. $\\frac{1}{4}$, C. $\\frac{1}{5}$, D. $\\frac{2}{3}$, E. $\\frac{3}{4}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1576.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A page is folded along the thick line as shown. Which letter will not be covered by a grey square?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/479.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anna made the figure on the right out of five cubes. Which of the following figures (when seen from any direction) cannot she get from the figure on the right side if she is allowed to move exactly one cube?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/452.png" }, { "solution": "\\boxed{8-2\\pi}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The two externally tangent circles each have a radius of 1 unit. Each circle is tangent to three sides of the rectangle. What is the area of the shaded region? Express your answer in terms of $\\pi$.\n\n", "completion": "\\boxed{8-2\\pi}", "image_path": "dataset/math_vision/images/3036.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which single digit should be placed in all three of the boxes shown to give a correct calculation? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1790.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The curved surfaces of two identical cylinders are cut open along the vertical dotted line, as shown and then stuck together to create the curved surface of one big cylinder. What can be said about the volume of the resulting cylinder compared to the volume of one of the small cylinders?\n\\n Options: A. It is 2-times as big., B. It is 3-times as big., C. It is $\\pi$-times as big., D. It is 4-times as big., E. It is 8-times as big.", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/264.png" }, { "solution": "\\boxed{-100}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: When the five pieces shown are fitted together correctly, the result is a rectangle with a calculation written on it. What is the answer to this calculation? ", "completion": "\\boxed{-100}", "image_path": "dataset/math_vision/images/1685.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An isosceles triangle $P Q R$, in which $P Q=P R$, is split into three separate isosceles triangles, as shown, so that $P S=S Q, R T=R S$ and $Q T=R T$.\nWhat is the size, in degrees, of angle $Q P R$ ? ", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/1705.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square with perimeter $48 \\mathrm{~cm}$ is cut into two equally big pieces with one cut. They are fitted together to make a rectangle as shown in the diagram. How big is the perimeter of that rectangle?\n\\n Options: A. $24 \\mathrm{~cm}$, B. $30 \\mathrm{~cm}$, C. $48 \\mathrm{~cm}$, D. $60 \\mathrm{~cm}$, E. $72 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/832.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Matias wrote 15 numbers on the wheel represented beside. Only one of them is visible, the 10 on top of the wheel. The sum of the numbers in any seven consecutive positions, such as the gray positions in the figure, does not vary. When seven numbers in consecutive positions are summed up, which of the following results is possible?\n\\n Options: A. 49, B. 70, C. 75, D. 105, E. 150", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/341.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The heart and the arrow are in the positions shown in the figure. At the same time the heart and the arrow start moving. The arrow moves three places clockwise and then stops and the heart moves four places anticlockwise and then stops. They repeat the same routine over and over again. After how many routines will the heart and the arrow land in the same place as each other for the first time? \\n Options: A. 7, B. 8, C. 9, D. 10, E. It will never happen", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1612.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each region in the figure is to be coloured with one of four colours: red $(\\mathrm{R})$, green $(\\mathrm{G})$, orange $(\\mathrm{O})$ or yellow $(\\mathrm{Y})$. The colours of only three regions are shown. Any two regions that touch must have different colours. The colour of the region $\\mathrm{X}$ is:\\n Options: A. red, B. orange, C. green, D. yellow, E. impossible to determine", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1582.png" }, { "solution": "\\boxed{70}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram on the right shows a large triangle divided up into squares and triangles. $S$ is the number of squares of any size in the diagram and $T$ is the number of triangles of any size in the diagram. What is the value of $S \\times T$ ?\n", "completion": "\\boxed{70}", "image_path": "dataset/math_vision/images/1720.png" }, { "solution": "\\boxed{7/3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A drunkard is randomly walking through a city when he stumbles upon a $2 \\times 2$ sliding tile puzzle. The puzzle consists of a $2 \\times 2$ grid filled with a blank square, as well as $3$ square tiles, labeled $1$, $2$, and $3$. During each turn you may fill the empty square by sliding one of the adjacent tiles into it. The following image shows the puzzle's correct state, as well as two possible moves you can make. Assuming that the puzzle is initially in an incorrect (but solvable) state, and that the drunkard will make completely random moves to try and solve it, how many moves is he expected to make before he restores the puzzle to its correct state?\\n", "completion": "\\boxed{7/3}", "image_path": "dataset/math_vision/images/2846.png" }, { "solution": "\\boxed{-2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We see in the diagram at the right a piece of the graphic of the function\n$$\nf(x)=a x^{3}+b x^{2}+c x+d.\n$$\nWhat is the value of $b$?\n", "completion": "\\boxed{-2}", "image_path": "dataset/math_vision/images/203.png" }, { "solution": "\\boxed{30}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the number of square centimeters in the shaded area? (The 10 represents the hypotenuse of the white triangle only.) ", "completion": "\\boxed{30}", "image_path": "dataset/math_vision/images/2997.png" }, { "solution": "\\boxed{34}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Cleuza assembled the $2 \\times 2 \\times 2$ block formed by equal balls beside, using one drop of glue at each contact point between two balls, in a total of 12 drops. She then glued a few more spheres until she completed a $4 \\times 3 \\times 2$ block. How many extra drops of glue did she get to use?\n", "completion": "\\boxed{34}", "image_path": "dataset/math_vision/images/1205.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three equilateral triangles are cut from the corners of a large equilateral triangle to form an irregular hexagon, as shown in the diagram.\nThe perimeter of the large equilateral triangle is $60 \\mathrm{~cm}$. The perimeter of the irregular hexagon is $40 \\mathrm{~cm}$. What is the sum of the perimeters of the triangles that were cut from the large triangle?\n\\n Options: A. $60 \\mathrm{~cm}$, B. $66 \\mathrm{~cm}$, C. $72 \\mathrm{~cm}$, D. $75 \\mathrm{~cm}$, E. $81 \\mathrm{~cm}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1631.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An annulus is a shape made from two concentric circles. The diagram shows an annulus consisting of two concentric circles of radii 2 and 9. Inside this annulus two circles are drawn without overlapping, each being tangent to both of the concentric circles that make the annulus. In a different annulus made by concentric circles of radii 1 and 9 , what would be the largest possible number of non-overlapping circles that could be drawn in this way?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1934.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ant Annie starts at the left end of the stick and crawls $\\frac{2}{3}$ of the length of the stick. Ladybird Bob starts at the right end of the stick und crawls $\\frac{3}{4}$ of the length of the stick. Which fraction of the length of the stick are they then apart from each other?\n\\n Options: A. $\\frac{3}{8}$, B. $\\frac{1}{12}$, C. $\\frac{5}{7}$, D. $\\frac{5}{12}$, E. $\\frac{7}{12}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1149.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Eight congruent semicircles are drawn inside a square of side-length 4 . Each semicircle begins at a vertex of the square and ends at a midpoint of an edge of the square. What is the area of the non-shaded part of the square? ", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/1933.png" }, { "solution": "\\boxed{124}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Belinda is making patterns using identical matchsticks. The $1 \\times 1,2 \\times 2$ and $3 \\times 3$ patterns are shown on the right. How many matchsticks should Belinda add to the $30 \\times 30$ pattern in order to make the $31 \\times 31$ pattern? ", "completion": "\\boxed{124}", "image_path": "dataset/math_vision/images/1538.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six identical circles fit together tightly in a rectangle of width $6 \\mathrm{~cm}$ as shown. What is the height, in $\\mathrm{cm}$, of the rectangle? \\n Options: A. 5, B. $2 \\sqrt{3}+2$, C. $3 \\sqrt{2}$, D. $3 \\sqrt{3}$, E. 6", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1881.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which pattern of identical squares could NOT be folded along the lines shown to form a cube?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2560.png" }, { "solution": "\\boxed{720}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle has sides of length $a$ and $36$. A hinge is installed at each vertex of the rectangle and at the midpoint of each side of length $36$. The sides of length $a$ can be pressed toward each other keeping those two sides parallel so the rectangle becomes a convex hexagon as shown. When the figure is a hexagon with the sides of length $a$ parallel and separated by a distance of $24,$ the hexagon has the same area as the original rectangle. Find $a^2$.\n\n\n", "completion": "\\boxed{720}", "image_path": "dataset/math_vision/images/2084.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nHow much does Dita weigh?\\n Options: A. $2 \\mathrm{~kg}$, B. $3 \\mathrm{~kg}$, C. $4 \\mathrm{~kg}$, D. $5 \\mathrm{~kg}$, E. $6 \\mathrm{~kg}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/843.png" }, { "solution": "\\boxed{367}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mr. Zhou places all the integers from $1$ to $225$ into a $15$ by $15$ grid. He places $1$ in the middle square (eight row and eight column) and places the other numbers one by one clockwise, as shown in part in the diagram below. What is the sum of the greatest and the least number that appear in the second row from the top?\n\n", "completion": "\\boxed{367}", "image_path": "dataset/math_vision/images/2239.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A creeping plant twists exactly 5 times around a post with circumference $15 \\mathrm{~cm}$ (as shown in the diagram) and thus reaches a height of $1 \\mathrm{~m}$. While the plant grows the height of the plant also grows with constant speed. How long is the creeping plant?\n\\n Options: A. $0.75 \\mathrm{~m}$, B. $1.0 \\mathrm{~m}$, C. $1.25 \\mathrm{~m}$, D. $1.5 \\mathrm{~m}$, E. $1.75 \\mathrm{~m}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1401.png" }, { "solution": "\\boxed{60}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: John has a chocolate tablet consisting of square pieces of $1 \\mathrm{~cm} \\times 1 \\mathrm{~cm}$. He has eaten already some pieces in a corner (see the picture). How many pieces John still have?\n", "completion": "\\boxed{60}", "image_path": "dataset/math_vision/images/418.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram Karl wants to add lines joining two of the marked points at a time, so that each of the seven marked points is joined to the same number of other marked points. What is the minimum number of lines he must draw?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1383.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: When Cosme correctly wears his new shirt, as shown on the left figure, the horizontal stripes form seven closed arches around his body. This morning he buttoned his shirt in the wrong way, as shown on the right. How many open arches were there around Cosme's body this morning?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1436.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cuboid-shaped container that is not filled completely contains $120 \\mathrm{~m}^{3}$ of water. The depth of the water is either $2 \\mathrm{~m}$ or $3 \\mathrm{~m}$ or $5 \\mathrm{~m}$, depending on which side the container is actually standing on (drawings not to scale). How big is the volume of the container?\n\\n Options: A. $160 \\mathrm{~m}^{3}$, B. $180 \\mathrm{~m}^{3}$, C. $200 \\mathrm{~m}^{3}$, D. $220 \\mathrm{~m}^{3}$, E. $240 \\mathrm{~m}^{3}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/328.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are 10 kangaroos in a row, as seen in the picture. Two kangaroos, that are standing next to each other and can see each other are allowed to change places by hopping past each other. This is carried out until no more jumps are allowed. How often do two kangaroos swap places?\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/1154.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Bart wrote the number 1015 as a sum of numbers using only the digit 7 . He used a 7 a total of 10 times, including using the number 77 three times, as shown. Now he wants to write the number 2023 as a sum of numbers using only the digit 7, using a 7 a total of 19 times. How many times will the number 77 occur in the sum? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1716.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria made a block using white cubes and colored cubes in equal amounts. How many of the white cubes cannot be seen in the picture?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/104.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, formed by a square and an equilateral triangle, the letters indicate the measurements of the angles. Which of the following equality is true?\n\\n Options: A. $a=d$, B. $b+c=d$, C. $a+c=d+e$, D. $a+b=d+e$, E. $e+d=a$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1196.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following pieces can be joined to the one pictured so that a rectangle is formed?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/505.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $K L M N$ is a unit square. Arcs of radius one unit are drawn using each of the four corners of the square as centres. The arcs centred at $K$ and $L$ intersect at $Q$; the arcs centred at $M$ and $N$ intersect at $P$. What is the length of $P Q$ ? \\n Options: A. $2-\\sqrt{2}$, B. $\\frac{3}{4}$, C. $\\sqrt{5}-\\sqrt{2}$, D. $\\frac{\\sqrt{3}}{3}$, E. $ \\sqrt{3}-1$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1851.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the five numbers 1, 4, 7, 10, and 13 is placed in one of the five squares so that the sum of the three numbers in the horizontal row equals the sum of the three numbers in the vertical column. The largest possible value for the horizontal or vertical sum is\n\n", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/2607.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square of area $40$ is inscribed in a semicircle as shown. What is the area of the semicircle?\n\n\\n Options: A. $20\\pi$, B. $25\\pi$, C. $30\\pi$, D. $40\\pi$, E. $50\\pi$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2157.png" }, { "solution": "\\boxed{81}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $R$ be the rectangle in the Cartesian plane with vertices at $(0,0), (2,0), (2,1),$ and $(0,1)$. $R$ can be divided into two unit squares, as shown; the resulting figure has seven edges. How many subsets of these seven edges form a connected figure?\\n", "completion": "\\boxed{81}", "image_path": "dataset/math_vision/images/2878.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Elena wants to write the numbers from 1 to 9 in the squares shown. The arrows always point from a smaller number to a larger one. She has already written 5 and 7. Which number should she write instead of the question mark?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/658.png" }, { "solution": "\\boxed{109}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below, $ABCD$ is a rectangle with side lengths $AB=3$ and $BC=11$, and $AECF$ is a rectangle with side lengths $AF=7$ and $FC=9,$ as shown. The area of the shaded region common to the interiors of both rectangles is $\\fracmn$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\n\n", "completion": "\\boxed{109}", "image_path": "dataset/math_vision/images/2096.png" }, { "solution": "\\boxed{43}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each cell of a $3 \\times 3$ square has a number written in it. Unfortunately the numbers are not visible because they are covered in ink. However, the sum of the numbers in each row and the sum of the numbers in two of the columns are all known, as shown by the arrows on the diagram. What is the sum of the numbers in the third column? ", "completion": "\\boxed{43}", "image_path": "dataset/math_vision/images/1676.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Evita wants to write the numbers 1 to 8 in the boxes of the grid shown, so that the sums of the numbers in the boxes in each row are equal and the sums of the numbers in the boxes in each column are equal. She has already written numbers 3,4 and 8 , as shown. What number should she write in the shaded box? ", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/1709.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle ABC$, $\\angle A=55^{\\circ}$, $\\angle C=75^{\\circ}$, $D$ is on side $\\overline{AB}$ and $E$ is on side $\\overline{BC}$. If $DB=BE$, then $\\angle BED=$\n\\n Options: A. $50^{\\circ}$, B. $55^{\\circ}$, C. $60^{\\circ}$, D. $65^{\\circ}$, E. $70^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2400.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the Kangaroo constellation, all stars have a number greater than 3 and their sum is 20 . Which is the Kangaroo constellation?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/125.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows a rectangle with four identical triangles. Determine the total area of the triangles.\n\\n Options: A. $46 \\mathrm{~cm}^{2}$, B. $52 \\mathrm{~cm}^{2}$, C. $54 \\mathrm{~cm}^{2}$, D. $56 \\mathrm{~cm}^{2}$, E. $64 \\mathrm{~cm}^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/802.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large set of weighing scales has two identical sets of scales placed on it, one on each pan. Four weights $W, X, Y, Z$ are placed on the weighing scales as shown in the left diagram.\n\nThen two of these weights are swapped, and the pans now appear as shown in the diagram on the right. Which two weights were swapped?\\n Options: A. $W$ and $Z$, B. $W$ and $Y$, C. $W$ and $X$, D. $X$ and $Z$, E. $X$ and $Y$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1910.png" }, { "solution": "\\boxed{96\\sqrt{3}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $R$ is on $QS$ and $QR=8$. Also, $PR=12$, $\\angle PRQ=120^\\circ$, and $\\angle RPS = 90^\\circ$. What is the area of $\\triangle QPS$? ", "completion": "\\boxed{96\\sqrt{3}}", "image_path": "dataset/math_vision/images/2946.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four cars drive into a roundabout at the same point in time, each one coming from a different direction (see diagram). No car drives all the way around the roundabout, and no two cars leave at the same exit. In how many different ways can the cars exit the roundabout?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1104.png" }, { "solution": "\\boxed{711}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many triangles can be drawn with vertices in the 18 points shown in the figure?\n", "completion": "\\boxed{711}", "image_path": "dataset/math_vision/images/176.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle of radius 1 is tangent to a circle of radius 2. The sides of $ \\triangle ABC$ are tangent to the circles as shown, and the sides $ \\overline{AB}$ and $ \\overline{AC}$ are congruent. What is the area of $ \\triangle ABC$?\n\n\\n Options: A. $\\frac{35}2$, B. $15\\sqrt{2}$, C. $\\frac{64}3$, D. $16\\sqrt{2}$, E. $24$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2153.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers from 1 to 6 are placed in the circles at the intersections of 3 rings. The position of number 6 is shown. The sums of the numbers on each ring are the same. What number is placed in the circle with the question mark?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1457.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One face of a cardboard cube is cut along its diagonals, as shown.\nWhich of the following are not nets for this cube?\n\n\\n Options: A. 1 and 3, B. 1 and 5, C. 2 and 4, D. 2 and 4, E. 3 and 5", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1843.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lisa has several sheets of construction paper like this\n\nand\n\nShe wants to make 7 identical crowns:\n\nFor that she cuts out the necessary parts.\nWhat is the minimum number of sheets of construction paper that she has to cut up?", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/69.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The perimeter of the figure pictured on the right is......\n\\n Options: A. $3 a+4 b$, B. $3 a+8 b$, C. $6 a+4 b$, D. $6 a+6 b$, E. $6 a+8 b$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1061.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows 3 hexagons with numbers at their vertices, but some numbers are invisible. The sum of the 6 numbers around each hexagon is 30. What is the number on the vertex marked with a question mark?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/949.png" }, { "solution": "\\boxed{616}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $ABC$ is isosceles, with $AB=AC$ and altitude $AM=11$. Suppose that there is a point $D$ on $\\overline{AM}$ with $AD=10$ and $\\angle BDC=3\\angle BAC$. Then the perimeter of $\\triangle ABC$ may be written in the form $a+\\sqrt{b},$ where $a$ and $b$ are integers. Find $a+b$.\n\n", "completion": "\\boxed{616}", "image_path": "dataset/math_vision/images/2058.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Thomas has made a table out of small cubes. How many small cubes did he use?\n", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/463.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Kristina has a piece of see-through foil on which some points and lines are drawn. She folds the foil along the dotted line. What can she see now?\\n Options: A. $2\\vdots6\\vdots9$, B. $2\\vdots6\\vdots6$, C. $5\\vdots6\\vdots6$, D. $2\\vdots8\\vdots6$, E. $5\\vdots8\\vdots9$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1242.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The regular pentagon $P Q R S T$ in the diagram has been reflected in the line $P Q$ so that vertex $T$ is reflected to point $U$, as shown. Then the new pentagon is reflected in $P U$, so that vertex $Q$ is reflected to point $V$, as shown. This process is repeated, on each occasion reflecting in the line determined by the new edge through $P$.\nWhat is the least number of such reflections that are needed to return pentagon $P Q R S T$ to its original position?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/1539.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $ \\overline{AB}$ be a diameter of a circle and $ C$ be a point on $ \\overline{AB}$ with $ 2 \\cdot AC = BC$. Let $ D$ and $ E$ be points on the circle such that $ \\overline{DC} \\perp \\overline{AB}$ and $ \\overline{DE}$ is a second diameter. What is the ratio of the area of $ \\triangle DCE$ to the area of $ \\triangle ABD$?\n\\n Options: A. $\\frac{1}{6}$, B. $\\frac{1}{4}$, C. $\\frac{1}{3}$, D. $\\frac{1}{2}$, E. $\\frac{2}{3}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2147.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each one of the four keys locks exactly one padlock. Every letter on a padlock stands for exactly one digit. Same letters mean same digits.\nWhich letters must be written on the fourth padlock?\n\\n Options: A. GDA, B. ADG, C. GAD, D. GAG, E. DAD", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/71.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the pictures below shows what you will see if you look from above the piece represented on the right?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1198.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The road from Anna's to Mary's house is $16 \\mathrm{~km}$ long. The road from Mary's to John's house is $20 \\mathrm{~km}$ long. The road from the crossing to Mary's house is $9 \\mathrm{~km}$ long. How long is the road from Anna's to John's house?\n\\n Options: A. $7 \\mathrm{~km}$, B. $9 \\mathrm{~km}$, C. $11 \\mathrm{~km}$, D. $16 \\mathrm{~km}$, E. $18 \\mathrm{~km}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/84.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The following figures are composed of squares and circles. Which figure has a shaded region with largest area?\n\\n Options: A. $\\text{A only}$, B. $\\text{B only}$, C. $\\text{C only}$, D. $\\text{both A and B}$, E. $\\text{all are equal}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2652.png" }, { "solution": "\\boxed{14}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Nick and Pete each chose four numbers from the nine numbers in the diagram on the right. There was one number which neither of them chose. Nick found that the total of his numbers was three times Pete's total. Which number was not chosen? ", "completion": "\\boxed{14}", "image_path": "dataset/math_vision/images/1549.png" }, { "solution": "\\boxed{\\frac{21}{8}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $ABC$, $AB = AC = 5$ and $BC = 6$. Let $O$ be the circumcenter of triangle $ABC$. Find the area of triangle $OBC$.\n\n", "completion": "\\boxed{\\frac{21}{8}}", "image_path": "dataset/math_vision/images/3024.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In this diagram, not drawn to scale, figures $\\text{I}$ and $\\text{III}$ are equilateral triangular regions with respective areas of $32\\sqrt{3}$ and $8\\sqrt{3}$ square inches. Figure $\\text{II}$ is a square region with area $32$ sq. in. Let the length of segment $AD$ be decreased by $12\\frac{1}{2} \\%$ of itself, while the lengths of $AB$ and $CD$ remain unchanged. The percent decrease in the area of the square is:\n\\n Options: A. $12\\frac{1}{2}$, B. $25$, C. $50$, D. $75$, E. $87\\frac{1}{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2289.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five equal rectangles are placed inside a square with side $24 \\mathrm{~cm}$, as shown in the diagram. What is the area in $\\mathrm{cm}^{2}$ of one rectangle? ", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/1613.png" }, { "solution": "\\boxed{118}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two thousand points are given on a circle. Label one of the points 1. From this point, count 2 points in the clockwise direction and label this point 2. From the point labeled 2, count 3 points in the clockwise direction and label this point 3. (See figure.) Continue this process until the labels $1, 2, 3, \\dots, 1993$ are all used. Some of the points on the circle will have more than one label and some points will not have a label. What is the smallest integer that labels the same point as 1993?\n\n", "completion": "\\boxed{118}", "image_path": "dataset/math_vision/images/2055.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the sum of the 10 angles marked in the picture?\n\\n Options: A. $720^{\\circ}$, B. $600^{\\circ}$, C. $450^{\\circ}$, D. $360^{\\circ}$, E. $300^{\\circ}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1284.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a cube with edges of length $12 \\mathrm{~cm}$. An ant crawls from the point $P$ to the point $Q$ along the route shown. What is the length of the ant's path? \\n Options: A. $40 \\mathrm{~cm}$, B. $48 \\mathrm{~cm}$, C. $50 \\mathrm{~cm}$, D. $60 \\mathrm{~cm}$, E. more information is needed", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1524.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A pentagon is cut into smaller parts as shown in the diagram. The numbers in the triangles state the area of the according triangle. How big is the area $P$ of the grey quadrilateral? ", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/389.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Natasha has many sticks of length 1 . Each stick is coloured blue, red, yellow or green. She wants to make a $3 \\times 3$ grid, as shown, so that each $1 \\times 1$ square in the grid has four sides of different colours. What is the smallest number of green sticks that she could use? ", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1670.png" }, { "solution": "\\boxed{100}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In quadrilateral $A B C D, \\angle A B C=\\angle A D C=90^{\\circ}, A D=D C$ and $A B+B C=20 \\mathrm{~cm}$.\n\nWhat is the area in $\\mathrm{cm}^{2}$ of quadrilateral $A B C D$ ?", "completion": "\\boxed{100}", "image_path": "dataset/math_vision/images/1998.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Martin placed 3 different types of objects, hexagons , squares and triangles , on sets of scales, as shown.\n\nWhat does he need to put on the left-hand side on the third set of scales for these scales to balance?\\n Options: A. 1 square, B. 2 squares, C. 1 hexagon, D. 1 triangle, E. 2 triangles", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/659.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram below shows five rectangles, each containing some of the letters $\\mathrm{P}, \\mathrm{R}, \\mathrm{I}, \\mathrm{S}$ and $\\mathrm{M}$.\n\nHarry wants to cross out letters so that each rectangle contains only one letter and each rectangle contains a different letter. Which letter does he not cross out in rectangle 2?\\n Options: A. P, B. R, C. I, D. S, E. M", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1754.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anna has four discs of different sizes. She wants to build a tower using 3 discs. A smaller disc always has to lie on top of a bigger disc. How many ways are there for Anna to build this tower?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/685.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each square in the shape has an area of $4 \\mathrm{~cm}^{2}$. How long is the thick line?\n\\n Options: A. $16 \\mathrm{~cm}$, B. $18 \\mathrm{~cm}$, C. $20 \\mathrm{~cm}$, D. $21 \\mathrm{~cm}$, E. $23 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/842.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On this monthly calendar, the date behind one of the letters is added to the date behind $C$. If this sum equals the sum of the dates behind $A$ and $B$, then the letter is\n\n\\n Options: A. $\\text{P}$, B. $\\text{Q}$, C. $\\text{R}$, D. $\\text{S}$, E. $\\text{T}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2538.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The robot starts walking over white cells of the table from the cell A2 in the direction of the arrow, as shown in the picture. It goes always forward. If it meets an obstacle (a black cell or the border of the table), it turns right. The robot stops in case, it cannot go forward after turning right (i.e., it stops in the cell where the obstacles appear in front of him and on the right). In which cell will it stop?\n\\n Options: A. B2, B. B1, C. A1, D. D1, E. It never stops", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/744.png" }, { "solution": "\\boxed{27}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Andy fills a $3 \\times 3$ table with all the digits from 1 to 9 so that each cell only contains one digit. He has already put the digits 1, 2, 3 and 4 in the table as shown in the diagram. Two numbers are 'neighbouring' when the cells they are in share one side. After he had finished filling in the table he noticed: The sum of the numbers neighbouring 9 equals 15. How big is the sum of the numbers neighbouring 8?\n", "completion": "\\boxed{27}", "image_path": "dataset/math_vision/images/1114.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: From an old model train set there are only identical pieces of track to use. Matthias puts 8 such pieces in a circle (picture on the left). Martin begins his track with 2 pieces as shown in the picture on the right. He also wants to build a closed track and use the smallest number of pieces possible. How many pieces will his track use?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/828.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Beattie wants to walk from $P$ to $Q$ along the paths shown, always moving in the direction from $P$ to $Q$.\n\nShe will add the numbers on the paths she walks along. How many different totals could she obtain?", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1738.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A mouse wants to escape a labyrinth. On her way out she is only allowed to go through each opening once at most. How many different ways can the mouse choose to go to get outside?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/553.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Using the pieces $A, B, C, D$ and $E$ one can fill this shape completely: Which of the pieces lies on the dot?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/687.png" }, { "solution": "\\boxed{240}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram below shows a $ 4\\times4$ rectangular array of points, each of which is $ 1$ unit away from its nearest neighbors.\nDefine a growing path to be a sequence of distinct points of the array with the property that the distance between consecutive points of the sequence is strictly increasing. Let $ m$ be the maximum possible number of points in a growing path, and let $ r$ be the number of growing paths consisting of exactly $ m$ points. Find $ mr$.", "completion": "\\boxed{240}", "image_path": "dataset/math_vision/images/2074.png" }, { "solution": "\\boxed{94}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the triangle $A B C$ the points $M$ and $N$ lie on the side $A B$ such that $A N=A C$ and $B M=B C$.\nWe know that $\\angle M C N=43^{\\circ}$.\nFind the size in degrees of $\\angle A C B$.\n", "completion": "\\boxed{94}", "image_path": "dataset/math_vision/images/2019.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In which figure can you find the largest number of small squares?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/440.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: You can place together the cards pictured, to make different three digit numbers, for instance 989 or 986. How many different three digit numbers can you make with these cards?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/483.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Peter colours in each of the eight circles in one of the colours red, yellow or blue. Two circles that are directly connected by a line, are not allowed to be of the same colour. Which two circles does Peter definitely have to colour in the same colour?\n\\n Options: A. 5 and 8, B. 1 and 6, C. 2 and 7, D. 4 and 5, E. 3 and 6", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1191.png" }, { "solution": "\\boxed{44}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The adjacent sides of the decagon shown meet at right angles. What is its perimeter?\n", "completion": "\\boxed{44}", "image_path": "dataset/math_vision/images/2427.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ellen wants to decorate the butterfly Which butterfly can she make?\n\nusing these 6 stickers\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/60.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: My umbrella has KANGAROO written on top as shown in the diagram. Which one of the following pictures also shows my umbrella?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1618.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nFelix the rabbit has 20 carrots. Every day he eats 2 of them. He has eaten the 12th carrot on a Wednesday. On which day of the week did he start eating the carrots?\\n Options: A. Monday, B. Tuesday, C. Wednesday, D. Thursday, E. Friday", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/590.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $a$ and $b$ be two shorter sides of the right-angled triangle. Then the sum of the diameter of the incircle and that of the circumcircle of this triangle is equal to:\n\\n Options: A. $\\sqrt{a^{2}+b^{2}}$, B. $\\sqrt{a b}$, C. $0.5(a+b)$, D. $2(a+b)$, E. $a+b$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1020.png" }, { "solution": "\\boxed{20201}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Figures $ 0$, $ 1$, $ 2$, and $ 3$ consist of $ 1$, $ 5$, $ 13$, and $ 25$ nonoverlapping squares, respectively. If the pattern were continued, how many nonoverlapping squares would there be in figure $ 100$?\n", "completion": "\\boxed{20201}", "image_path": "dataset/math_vision/images/2110.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Tobias glues 10 cubes together so that the following object is formed: He paints all of it, even the bottom. How many cubes then have exactly 4 faces coloured in?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/593.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure shown below, $ABCDE$ is a regular pentagon and $AG=1$. What is $FG+JH+CD$?\n\\n Options: A. $3$, B. $12-4\\sqrt{5}$, C. $\\frac{5+2\\sqrt{5}}{3}$, D. $1+\\sqrt{5}$, E. $\\frac{11+11\\sqrt{5}}{10}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2207.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?\n\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2648.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We make a sequence of figures by dividing a square. The first four figures have 1, 4, 7 and 10 parts, respectively.\n\nHow many parts will the fifth figure have?", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/447.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the figures shown bellow cannot be cut out of the figure illustrated nearby?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/21.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle of radius 2 is cut into four congruent arcs. The four arcs are joined to form the star figure shown. What is the ratio of the area of the star figure to the area of the original circle?\n\n\\n Options: A. $\\frac{4-\\pi}\\pi$, B. $\\frac{1}{\\pi}$, C. $\\frac{\\sqrt{2}}{\\pi}$, D. $\\frac{\\pi-1}\\pi$, E. $\\frac{3}{\\pi}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2719.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Thomas drew a pig and a shark. He cuts each animal into three pieces. Then he takes one of the two heads, one of the two middle sections and one of the two tails and lays them together to make another animal. How many different animals can he make in this way?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/546.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We consider the perimeter and the area of the region corresponding to the grey squares. How many more squares can we colour grey for the grey area to increase without increasing its perimeter?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/184.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Several non-overlapping isosceles triangles have vertex $O$ in common. Every triangle shares an edge with each immediate neighbour. The smallest of the angles at $O$ has size $m^{\\circ}$, where $m$ is a positive integer and the other triangles have angles at $O$ of size $2 m^{\\circ}, 3 m^{\\circ}, 4 m^{\\circ}$, and so on. The diagram shows an arrangement of five such triangles. What is the smallest value of $m$ for which such a set of triangles exists?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1896.png" }, { "solution": "\\boxed{7.7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four circles of radius $3$ are arranged as shown. Their centers are the vertices of a square. The area of the shaded region is closest to\n\n", "completion": "\\boxed{7.7}", "image_path": "dataset/math_vision/images/2563.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In which of the five pictures is the white area bigger than the grey area?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/488.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jeff rotates spinners $ P$, $ Q$ and $ R$ and adds the resulting numbers. What is the probability that his sum is an odd number?\n\n\\n Options: A. $\\frac{1}{4}$, B. $\\frac{1}{3}$, C. $\\frac{1}{2}$, D. $\\frac{2}{3}$, E. $\\frac{3}{4}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2674.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: n number of buttons are placed evenly around a circle. The buttons are labelled clockwise in order with the numbers 1 to $n$. The button with the number 7 is exactly opposite the button with the number 23. How big is $n$?\n", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/1188.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many rectangles are in this figure?\n\n", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/2715.png" }, { "solution": "\\boxed{$2(\\sqrt{2}-1)$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle inscribed in a square. Has two chords as shown in a pair. It has radius $2$, and $P$ bisects $TU$. The chords' intersection is where? Answer the question by giving the distance of the point of intersection from the center of the circle.\\n", "completion": "\\boxed{$2(\\sqrt{2}-1)$}", "image_path": "dataset/math_vision/images/2870.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many blocks are missing in this igloo?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/62.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of the shaded shape is equal to $2 \\pi$ (see the picture). What is the value of the chord $A B$?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1283.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $\\textbf{Bake Sale}$\nFour friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.\n\n$\\circ$ Art's cookies are trapezoids:\n\n\n$\\circ$ Roger's cookies are rectangles:\n\n\n$\\circ$ Paul's cookies are parallelograms:\n\n\n$\\circ$ Trisha's cookies are triangles:\n\n\nEach friend uses the same amount of dough, and Art makes exactly 12 cookies. Who gets the fewest cookies from one batch of cookie dough?\\n Options: A. $\\text{Art}$, B. $\\text{Roger}$, C. $\\text{Paul}$, D. $\\text{Trisha}$, E. $\\text{There is a tie for fewest.}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2645.png" }, { "solution": "\\boxed{30}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Points $ A, B, C$ and $ D$ are midpoints of the sides of the larger square. If the larger square has area 60, what is the area of the smaller square?\n\n", "completion": "\\boxed{30}", "image_path": "dataset/math_vision/images/2671.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A teacher wants to write the numbers from 1 to 7 into the circles. He writes exactly one number in each circle. When he adds up the two numbers of circles that are next to each other, he gets the number that is written between the two circles.\nWhich number does he write in the circle with the question mark?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/699.png" }, { "solution": "\\boxed{150}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three identical rectangles are put together to form rectangle $ABCD$, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles $5$ feet, what is the area in square feet of rectangle $ABCD$?\n", "completion": "\\boxed{150}", "image_path": "dataset/math_vision/images/2755.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Circles with centers $A ,~ B,$ and $C$ each have radius $r$, where $1 < r < 2$. The distance between each pair of centers is $2$.\n\nIf $B'$ is the point of intersection of circle $A$ and circle $C$ which is outside circle $B$, and if $C'$ is the point of intersection of circle $A$ and circle $B$ which is outside circle $C$, then length $B'C'$ equals\\n Options: A. $3r-2$, B. $r^2$, C. $r+\\sqrt{3(r-1)}$, D. $1+\\sqrt{3(r^2-1)}$, E. $\\text{none of these}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2329.png" }, { "solution": "\\boxed{50}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A particular right square-based pyramid has a volume of 63,960 cubic meters and a height of 30 meters. What is the number of meters in the length of the lateral height ($\\overline{AB}$) of the pyramid? Express your answer to the nearest whole number.\n\n", "completion": "\\boxed{50}", "image_path": "dataset/math_vision/images/3032.png" }, { "solution": "\\boxed{240}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangle $ABCD$ is inscribed in a semicircle with diameter $\\overline{FE},$ as shown in the figure. Let $DA=16,$ and let $FD=AE=9$. What is the area of $ABCD?$\n\n", "completion": "\\boxed{240}", "image_path": "dataset/math_vision/images/2767.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: As seen in the diagram, 3 darts are flying towards 9 fixed balloons. If a balloon is hit by a dart, it bursts and the dart continues in the same direction it had beforehand. How many balloons are hit by the darts?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/579.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: PQRS is a rectangle. $T$ is the midpoint of $R S. Q T$ is normal to the diagonal $P R$. What is the ratio of the lengths $P Q: Q R$?\n\\n Options: A. $2: 1$, B. $\\sqrt{3}: 1$, C. $3: 2$, D. $\\sqrt{2}: 1$, E. $5: 4$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/267.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, four circles of radius 1 with centres $P$, $Q$, $R$, and $S$ are tangent to one another and to the sides of $\\triangle ABC$, as shown. \n\nThe radius of the circle with center $R$ is decreased so that\n\n$\\bullet$ the circle with center $R$ remains tangent to $BC$,\n\n$\\bullet$ the circle with center $R$ remains tangent to the other three circles, and\n\n$\\bullet$ the circle with center $P$ becomes tangent to the other three circles.\n\nThe radii and tangencies of the other three circles stay the same. This changes the size and shape of $\\triangle ABC$. $r$ is the new radius of the circle with center $R$. $r$ is of the form $\\frac{a+\\sqrt{b}}{c}$. Find $a+b+c$.", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2896.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Susan has two pendants made of the same material. They are equally thick and weigh the same. One of them has the shape of an annulus created from two concentric circles with the radii $6 \\mathrm{~cm}$ and $4 \\mathrm{~cm}$ (see the diagram). The second has the shape of a solid circle. What is the radius of the second pendant?\n\\n Options: A. $4 \\mathrm{~cm}$, B. $2 \\sqrt{6} \\mathrm{~cm}$, C. $5 \\mathrm{~cm}$, D. $2 \\sqrt{5} \\mathrm{~cm}$, E. $\\sqrt{10} \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/186.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rita numbered the circles of the figure from 1 to 8 , so that the sum of the three numbers on each of the four sides of the square equals 13 . What is the sum of the four numbers written on the colored circles?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/116.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, $ABCD$ is a square of side length 1. The rectangles $JKHG$ and $EBCF$ are congruent. What is $BE$?\n\\n Options: A. $\\frac{1}{2}(\\sqrt{6}-2)$, B. $\\frac{1}{4}$, C. $2-\\sqrt{3}$, D. $\\frac{\\sqrt{3}}{6}$, E. $1-\\frac{\\sqrt{2}}{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2481.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle of radius 1 rolls along a straight line from the point $K$ to the point $L$, where $K L=11 \\pi$. Which of the following pictures shows the correct appearance of the circle when it reaches $L$ ?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1921.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a spiral of consecutive numbers starting with 1. In which order will the numbers 625, 626 and 627 appear in the spiral? \\n Options: A. $625 \\uparrow 626 \\uparrow 627$, B. $625 \\uparrow 626 \\rightarrow$, C. $625 \\rightarrow 626 \\rightarrow 627$, D. $625 \\rightarrow 626 \\uparrow 627$, E. $625 \\downarrow 626 \\downarrow 627$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/390.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangle $ABCD$ and right triangle $DCE$ have the same area. They are joined to form a trapezoid, as shown. What is $DE$?\n\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/2728.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two rectangles of dimensions $8 \\mathrm{~cm}$ by $10 \\mathrm{~cm}$ and $9 \\mathrm{~cm}$ by $12 \\mathrm{~cm}$ overlap as shown in the diagram. The area of the black region is $37 \\mathrm{~cm}^{2}$. What is the area of the grey region? \\n Options: A. $60 \\mathrm{~cm}^{2}$, B. $62 \\mathrm{~cm}^{2}$, C. $62.5 \\mathrm{~cm}^{2}$, D. $64 \\mathrm{~cm}^{2}$, E. $65 \\mathrm{~cm}^{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1762.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The adjacent diagram illustrates the graphs of the two functions f and g. How can we describe the relationship between f and g?\n\\n Options: A. $g(x-2)=-f(x)$, B. $g(x)=f(x+2)$, C. $g(x)=-f(-x+2)$, D. $g(-x)=-f(-x-2)$, E. $g(2-x)=-f(x)$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/221.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three circles with radius 2 are drawn in such a way that each time one of the points of intersection of two circles is identical with the centre of the third circle. How big is the area of the grey zone?\n\\n Options: A. $\\pi$, B. $3 \\pi$, C. $\\frac{\\pi}{2}$, D. $2 \\pi$, E. $4 \\pi$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/333.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the sum on the right, each of the letters $X, Y$ and $Z$ represents a different $X X$ non-zero digit. What does $X$ represent? ", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/1804.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a rectangle of size $7 \\mathrm{~cm} \\times 11 \\mathrm{~cm}$ containing two circles that each touch three of the sides of the rectangle. What is the distance between the centres of the two circles?\n\\n Options: A. $2 \\mathrm{~cm}$, B. $2.5 \\mathrm{~cm}$, C. $3 \\mathrm{~cm}$, D. $3.5 \\mathrm{~cm}$, E. $4 \\mathrm{~cm}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1652.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows two identical large circles and two identical smaller circles whose centres are at the corners of a square. The two large circles are touching, and they each touch the two smaller circles. The radius of the small circles is $1 \\mathrm{~cm}$. What is the radius of a large circle in centimetres? \\n Options: A. $1+\\sqrt{2}$, B. $\\sqrt{5}$, C. $\\sqrt{2}$, D. $\\frac{5}{2}$, E. $\\frac{4}{5} \\pi$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1854.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, if points $ A$, $ B$ and $ C$ are points of tangency, then $ x$ equals:\n\\n Options: A. $\\frac{3}{16}\"$, B. $\\frac{1}{8}\"$, C. $\\frac{1}{32}\"$, D. $\\frac{3}{32}\"$, E. $\\frac{1}{16}\"$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2261.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Segments $O A, O B, O C$ and $O D$ are drawn from the centre $O$ of the square $K L M N$ to its sides so that $O A \\perp O B$ and $O C \\perp O D$ (as shown in the figure). If the side of the square equals 2, the area of the shaded region equals\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/1037.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Malaika is skiing on a mountain. The graph below shows her elevation, in meters, above the base of the mountain as she skis along a trail. In total, how many seconds does she spend at an elevation between $4$ and $7$ meters?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/2786.png" }, { "solution": "\\boxed{41}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three dice with faces numbered 1 through 6 are stacked as shown. Seven of the eighteen faces are visible, leaving eleven faces hidden (back, bottom, between). The total number of dots NOT visible in this view is\n\n", "completion": "\\boxed{41}", "image_path": "dataset/math_vision/images/2615.png" }, { "solution": "\\boxed{35}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consider the L-shaped region formed by three unit squares joined at their sides, as shown below. Two points $A$ and $B$ are chosen independently and uniformly at random from inside this region. The probability that the midpoint of $\\overline{AB}$ also lies inside this L-shaped region can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\n", "completion": "\\boxed{35}", "image_path": "dataset/math_vision/images/2105.png" }, { "solution": "\\boxed{750}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: 1000 litres of water is passed through the water system as shown, into two identical tanks. At each junction the water separates into two equal amounts. How many litres of water end up in Tank Y?\n", "completion": "\\boxed{750}", "image_path": "dataset/math_vision/images/795.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The midpoints of both longer sides of a rectangle are connected with the vertices (see diagram). Which fraction of the rectangle is shaded?\n\\n Options: A. $\\frac{1}{5}$, B. $\\frac{1}{4}$, C. $\\frac{2}{7}$, D. $\\frac{1}{3}$, E. $\\frac{2}{5}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1468.png" }, { "solution": "\\boxed{22}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria writes a number on each face of the cube. Then, for each corner point of the cube, she adds the numbers on the faces which meet at that corner. (For corner B she adds the numbers on faces BCDA, BAEF and BFGC.) In this way she gets a total of 14 for corner C, 16 for corner D, and 24 for corner E. Which total, does she get for corner F?\n", "completion": "\\boxed{22}", "image_path": "dataset/math_vision/images/853.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Every one of these six building blocks consists of 5 little cubes. The little cubes are either white or grey. Cubes of equal colour don't touch each other. How many little white cubes are there in total?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/49.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Bridget folds a square piece of paper twice and subsequently cuts it along the two lines as shown in the picture.\n\nHow many pieces of paper does she obtain this way?", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/909.png" }, { "solution": "\\boxed{$2\\sqrt{2}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consider the figure below, not drawn to scale.\\nIn this figure, assume that$AB \\perp BE$ and $AD \\perp DE$. Also, let $AB = \\sqrt{6}$ and $\\angle BED =\\frac{\\pi}{6}$ . Find $AC$.\\n", "completion": "\\boxed{$2\\sqrt{2}$}", "image_path": "dataset/math_vision/images/2813.png" }, { "solution": "\\boxed{35}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: As shown in the diagram, $F G H I$ is a trapezium with side $G F$ parallel to $H I$. The lengths of $F G$ and $H I$ are 50 and 20 respectively. The point $J$ is on the side $F G$ such that the segment $I J$ divides the trapezium into two parts of equal area. What is the length of $F J$ ? ", "completion": "\\boxed{35}", "image_path": "dataset/math_vision/images/1922.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A sequence of squares is made of identical square tiles. The edge of each square is one tile length longer than the edge of the previous square. The first three squares are shown. How many more tiles does the seventh square require than the sixth?\n\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/2638.png" }, { "solution": "\\boxed{8\\pi-16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $ABCD$ is a square with $AB = 8$cm. Arcs $BC$ and $CD$ are semicircles. Express the area of the shaded region, in square centimeters, and in terms of $\\pi$. (As always, do not include units in your submitted answer.) ", "completion": "\\boxed{8\\pi-16}", "image_path": "dataset/math_vision/images/3000.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The graph shows the number of minutes studied by both Asha (black bar) and Sasha (grey bar) in one week. On the average, how many more minutes per day did Sasha study than Asha?\n\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2713.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Julia has 5 pieces of plastic and has stacked these pieces on a table, as shown beside. What was the second piece she put on the table?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/99.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: With how many ways one can get a number 2006 while following the arrows on the figure?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/731.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Emily has two identical cards in the shape of equilateral triangles. She places them both onto a sheet of paper so that they touch or overlap and draws around the shape she creates. Which one of the following is it impossible for her to draw?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1750.png" }, { "solution": "\\boxed{\\frac{1}{2}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure below, side $AE$ of rectangle $ABDE$ is parallel to the $x$-axis, and side $BD$ contains the point $C$. The vertices of triangle $ACE$ are $A(1, 1)$, $C(3, 3)$ and $E(4, 1)$. What is the ratio of the area of triangle $ACE$ to the area of rectangle $ABDE$?\n\n", "completion": "\\boxed{\\frac{1}{2}}", "image_path": "dataset/math_vision/images/2974.png" }, { "solution": "\\boxed{56}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle ABC$, $AB=AC=28$ and $BC=20$. Points $D,E,$ and $F$ are on sides $\\overline{AB}$, $\\overline{BC}$, and $\\overline{AC}$, respectively, such that $\\overline{DE}$ and $\\overline{EF}$ are parallel to $\\overline{AC}$ and $\\overline{AB}$, respectively. What is the perimeter of parallelogram $ADEF$?\n\n", "completion": "\\boxed{56}", "image_path": "dataset/math_vision/images/2189.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $ABCD$ has side length $30$. Point $P$ lies inside the square so that $AP = 12$ and $BP = 26$. The centroids of $\\triangle{ABP}$, $\\triangle{BCP}$, $\\triangle{CDP}$, and $\\triangle{DAP}$ are the vertices of a convex quadrilateral. What is the area of that quadrilateral?\n\n\\n Options: A. $100\\sqrt{2}$, B. $100\\sqrt{3}$, C. $200$, D. $200\\sqrt{2}$, E. $200\\sqrt{3}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2487.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If $ \\angle\\text{CBD} $ is a right angle, then this protractor indicates that the measure of $ \\angle\\text{ABC} $ is approximately\n\n\\n Options: A. $20^\\circ$, B. $40^\\circ$, C. $50^\\circ$, D. $70^\\circ$, E. $120^\\circ$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2522.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the five-sided star shown, the letters $A,B,C,D,$ and $E$ are replaced by the numbers $3,5,6,7,$ and $9$, although not necessarily in this order. The sums of the numbers at the ends of the line segments $\\overline{AB}$,$\\overline{BC}$,$\\overline{CD}$,$\\overline{DE}$, and $\\overline{EA}$ form an arithmetic sequence, although not necessarily in this order. What is the middle term of the arithmetic sequence?\n\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/2145.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, square $WXYZ$ has a diagonal of 12 units. Point $A$ is a midpoint of segment $WX$, segment $AB$ is perpendicular to segment $AC$ and $AB = AC.$ What is the length of segment $BC$? ", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/3030.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular garden was $50 \\mathrm{~m}$ long and $40 \\mathrm{~m}$ wide. An artificial lake was built next to it, so that the whole set forms a $60 \\mathrm{~m}$ square. Then a fence was stretched, separating both the garden and the lake in two parts with equal areas, as shown in the picture. How long is this fence?\n\\n Options: A. $60 \\mathrm{~m}$, B. $30 \\sqrt{5} \\mathrm{~m}$, C. $60 \\sqrt{2} \\mathrm{~m}$, D. $85 \\mathrm{~m}$, E. $60 \\sqrt{3} \\mathrm{~m}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/347.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diameters of three semi-circles form the sides of a right-angled triangle. Their areas are $X \\mathrm{~cm}^{2}, Y \\mathrm{~cm}^{2}$ and $Z \\mathrm{~cm}^{2}$ as pictured. Which of the following expressions is definitely correct?\n\\n Options: A. $X+Y", "completion": "\\boxed{69{degrees}}", "image_path": "dataset/math_vision/images/2947.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Andrew, the absent-minded mountain climber, climbed a mountain range, with a profile as shown in Figure 1 from point $P$ to point $Q$. From time to time he had to turn back to find bits of his equipment that he had dropped. The graph of the height $H$ of his position at time $t$ is shown in Figure 2 to the same scale as Figure 1. How many times did he turn back?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1814.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, $ \\angle EAB$ and $ \\angle ABC$ are right angles. $ AB = 4, BC = 6, AE = 8$, and $ \\overline{AC}$ and $ \\overline{BE}$ intersect at $ D$. What is the difference between the areas of $ \\triangle ADE$ and $ \\triangle BDC$?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2132.png" }, { "solution": "\\boxed{11.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular piece of paper $ABCD$ is folded so that edge $CD$ lies along edge $AD,$ making a crease $DP.$ It is unfolded, and then folded again so that edge $AB$ lies along edge $AD,$ making a second crease $AQ.$ The two creases meet at $R,$ forming triangles $PQR$ and $ADR$. If $AB=5\\mbox{ cm}$ and $AD=8\\mbox{ cm},$ what is the area of quadrilateral $DRQC,$ in $\\mbox{cm}^2?$\n\n", "completion": "\\boxed{11.5}", "image_path": "dataset/math_vision/images/3014.png" }, { "solution": "\\boxed{200}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a magic square, the sum of the three entries in any row, column, or diagonal is the same value. The figure shows four of the entries of a magic square. Find $x$.\n\n", "completion": "\\boxed{200}", "image_path": "dataset/math_vision/images/2059.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Carol is playing with two equilateral triangular cards shown. She puts one card beside or on the top of a part of the other and both on a sheet of paper. Then she draws on the paper around them, following the contour. She cannot get only one of the shapes. Which one is it?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/451.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An oval is constructed from four arcs of circles. Arc $P Q$ is the same as arc $R S$, and has radius $1 \\mathrm{~cm}$. Arc $Q R$ is the same as arc PS. At the points $P, Q, R, S$ where the arcs touch, they have a common tangent. The oval touches the midpoints of the sides of a rectangle with dimensions $8 \\mathrm{~cm}$ by $4 \\mathrm{~cm}$. What is the radius of the arc $P S$, in $\\mathrm{cm}$ ? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1868.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A regular octahedron has eight equilateral triangle faces with four faces meeting at each vertex. Jun will make the regular octahedron shown on the right by folding the piece of paper shown on the left. Which numbered face will end up to the right of $Q$?\n\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/2790.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. There are 2 red-white pairs. How many white pairs coincide?\n\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/2632.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The measure of angle $ABC$ is $50^\\circ $, $\\overline{AD}$ bisects angle $BAC$, and $\\overline{DC}$ bisects angle $BCA$. The measure of angle $ADC$ is\n\n\\n Options: A. $90^\\circ$, B. $100^\\circ$, C. $115^\\circ$, D. $122.5^\\circ$, E. $125^\\circ$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2590.png" }, { "solution": "\\boxed{189}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nThe large kite is covered with gold foil. The foil is cut from a rectangular piece that just covers the entire grid. How many square inches of waste material are cut off from the four corners?", "completion": "\\boxed{189}", "image_path": "dataset/math_vision/images/2627.png" }, { "solution": "\\boxed{222}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lily pours 296 litres of water into the top of the pipework shown in the diagram. Each time a pipe forks, half the water flows to one side and half to the other. How many litres of water will reach container $\\mathrm{Y}$ ? ", "completion": "\\boxed{222}", "image_path": "dataset/math_vision/images/1772.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A coin with diameter $1 \\mathrm{~cm}$ rolls around the contour outside of a regular hexagon with sides $1 \\mathrm{~cm}$ long, as shown. How long is the path traced by the centre of the coin (in $\\mathrm{cm}$ )?\n\\n Options: A. $6+\\frac{\\pi}{2}$, B. $6+\\pi$, C. $12+\\pi$, D. $6+2 \\pi$, E. $12+2 \\pi$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1306.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which part of the house is missing?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/42.png" }, { "solution": "\\boxed{\\frac{5}{16}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Squares $ABCD$ and $EFGH$ are equal in area. Vertices $B$, $E$, $C$, and $H$ lie on the same line. Diagonal $AC$ is extended to $J$, the midpoint of $GH$. What is the fraction of the two squares that is shaded? ", "completion": "\\boxed{\\frac{5}{16}}", "image_path": "dataset/math_vision/images/2969.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The suare in the diagram has side length 1. The radius of the small circle would\nthen be of the length\n\\n Options: A. $\\sqrt{2}-1$, B. $\\frac{1}{4}$, C. $\\frac{\\sqrt{2}}{4}$, D. $1-\\frac{\\sqrt{2}}{2}$, E. $(\\sqrt{2}-1)^{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/215.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Amy painted a dart board over a square clock face using the \"hour positions\" as boundaries. [See figure.] If $t$ is the area of one of the eight triangular regions such as that between $12$ o'clock and $1$ o'clock, and $q$ is the area of one of the four corner quadrilaterals such as that between $1$ o'clock and $2$ o'clock, then $\\frac{q}{t}=$\n\\n Options: A. $2\\sqrt{3}-2$, B. $\\frac{3}{2}$, C. $\\frac{\\sqrt{5}+1}{2}$, D. $\\sqrt{3}$, E. $2$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2402.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shown on the right consists of one square part and eight rectangular parts. Each part is $8 \\mathrm{~cm}$ wide. Peter assembles all parts to form one long, $8 \\mathrm{~cm}$ wide rectangle. How long is this rectangle?\n\\n Options: A. $150 \\mathrm{~cm}$, B. $168 \\mathrm{~cm}$, C. $196 \\mathrm{~cm}$, D. $200 \\mathrm{~cm}$, E. $232 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/898.png" }, { "solution": "\\boxed{4040}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The last two digits of a 2020 number are 9 and 9. At most, how many digits does the square of that number have?\n", "completion": "\\boxed{4040}", "image_path": "dataset/math_vision/images/340.png" }, { "solution": "\\boxed{130}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The glass gauge on a cylindrical coffee maker shows that there are 45 cups left when the coffee maker is $36\\%$ full. How many cups of coffee does it hold when it is full?\n\n", "completion": "\\boxed{130}", "image_path": "dataset/math_vision/images/2526.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Kengu likes to jump on the number line. He starts at 0 , then always starts with two big jumps and then three small jumps (see diagram). He keeps repeating this in the same way, over and over again. On which of the following numbers will he land in the course of his jumps?\n\\n Options: A. 82, B. 83, C. 84, D. 85, E. 86", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1224.png" }, { "solution": "\\boxed{110}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the calculation alongside, different letters represent different digits.\n\nFind the least possible answer to the subtraction shown.", "completion": "\\boxed{110}", "image_path": "dataset/math_vision/images/1835.png" }, { "solution": "\\boxed{173}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Stephen's calculator displays only one digit, as shown in the diagram. Unfortunately, the calculator is broken. Each time he switches it on, each of the seven bars will either illuminate (show up) or not, with probability 0.5 . The resultant display correctly shows one of the ten digits $0-9$ with probability $\\frac{a}{b}$.\n\nGiven that $\\frac{a}{b}$ is written in its lowest terms, what is the value of $9 a+2 b$ ?\n\n", "completion": "\\boxed{173}", "image_path": "dataset/math_vision/images/2033.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Andrew wants to write the letters of the word KANGAROO in the cells of a $2 \\times 4$ grid such that each cell contains exactly one letter. He can write the first letter in any cell he chooses but each subsequent letter can only be written in a cell with at least one common vertex with the cell in which the previous letter was written. Which of the following arrangements of letters could he not produce in this way?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1773.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Hansi sticks 12 cubes together to make this figure. He always puts one drop of glue between two cubes. How many drops of glue does he need?\n", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/158.png" }, { "solution": "\\boxed{80}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Candy sales from the Boosters Club from January through April are shown. What were the average sales per month in dollars?\n", "completion": "\\boxed{80}", "image_path": "dataset/math_vision/images/2688.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a shape made of arcs of three circles, each with radius $R$. The centres of the circles lie on the same straight line, and the middle circle passes through the centres of the other two circles. What is the perimeter of the shape? \\n Options: A. $\\frac{2 \\pi R \\sqrt{3}}{3}$, B. $\\frac{5 \\pi R}{3}$, C. $\\frac{10 \\pi R}{3}$, D. $2 \\pi R \\sqrt{3}$, E. $4 \\pi R$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1942.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nIn the picture above we see a cube in two different positions.\nThe six sides of the cube look like this:\n\nWhich side is opposite to ?\n", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/59.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A decorative window is made up of a rectangle with semicircles at either end. The ratio of $AD$ to $AB$ is $3:2$. And $AB$ is 30 inches. What is the ratio of the area of the rectangle to the combined area of the semicircle.\n\n\\n Options: A. $2:3$, B. $3:2$, C. $6:\\pi$, D. $9: \\pi$, E. $30 : \\pi$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2707.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Georg goes to the circus with his father. They have the seat numbers 71 and 72 . Which arrow do they have to follow to get to their seats?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/550.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Melanie has a square piece of paper with a $4 \\times 4$ grid drawn on it. She cuts along the gridlines and cuts several shapes out which all look either the same as the one pictured, or the same as its mirror image. How many squares are left over if she cuts out as many shapes as possible?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1096.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $ABC$ and $A'B'C'$ are equilateral triangles with parallel sides and the same center, as in the figure. The distance between side $BC$ and side $B'C'$ is $\\frac{1}{6}$ the altitude of $\\triangle ABC$. The ratio of the area of $\\triangle A'B'C'$ to the area of $\\triangle ABC$ is\n\\n Options: A. $\\frac{1}{36}$, B. $\\frac{1}{6}$, C. $\\frac{1}{4}$, D. $\\frac{\\sqrt{3}}{4}$, E. $\\frac{9+8\\sqrt{3}}{36}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2375.png" }, { "solution": "\\boxed{2.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Costa is building a new fence in his garden. He uses 25 planks of wood, each of which are $30 \\mathrm{~cm}$ long. He arranges these planks so that there is the same slight overlap between any two adjacent planks. The total length of Costa's new fence is 6.9 metres. What is the length in centimetres of the overlap between any pair of adjacent planks?\n", "completion": "\\boxed{2.5}", "image_path": "dataset/math_vision/images/1213.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four circles are always connected by a line to form chains of four in a drawing. The numbers 1, 2, 3 and 4 appear in each row, each column and each chain of four.\nWhich number is in the circle with the question mark?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/971.png" }, { "solution": "\\boxed{68}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square with side length $8$ is colored white except for $4$ black isosceles right triangular regions with legs of length $2$ in each corner of the square and a black diamond with side length $2\\sqrt{2}$ in the center of the square, as shown in the diagram. A circular coin with diameter $1$ is dropped onto the square and lands in a random location where the coin is completely contained within the square, The probability that the coin will cover part of the black region of the square can be written as $\\frac{1}{196}(a+b\\sqrt{2}+\\pi)$, where $a$ and $b$ are positive integers. What is $a+b$?\n\n", "completion": "\\boxed{68}", "image_path": "dataset/math_vision/images/2242.png" }, { "solution": "\\boxed{200}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle of radius $5$ is inscribed in a rectangle as shown. The ratio of the the length of the rectangle to its width is $2\\ :\\ 1$. What is the area of the rectangle?\n\n", "completion": "\\boxed{200}", "image_path": "dataset/math_vision/images/2185.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Pegs are put in a board $ 1$ unit apart both horizontally and vertically. A reubber band is stretched over $ 4$ pegs as shown in the figure, forming a quadrilateral. Its area in square units is\n\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2355.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture we have 11 fields.\n\nIn the first field there is a 7, and in the ninth field we have a 6. What positive integer has to be written in the second field for the following condition to be valid: the sum of any three adjoining fields is equal to 21?", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/1015.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mr Hofer has drawn a picture of flowers on the inside of a display window (large picture). What do these flowers look like when you look at the picture from the outside?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/513.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The midpoints of the sides of a regular hexagon $ABCDEF$ are joined to form a smaller hexagon. What fraction of the area of $ABCDEF$ is enclosed by the smaller hexagon?\n\\n Options: A. $\\displaystyle \\frac{1}{2}$, B. $\\displaystyle \\frac{\\sqrt{3}}{3}$, C. $\\displaystyle \\frac{2}{3}$, D. $\\displaystyle \\frac{3}{4}$, E. $\\displaystyle \\frac{\\sqrt{3}}{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2425.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Florian has 10 identical metal strips, each with the same amount of holes (picture above). He bolts these strips in pairs. That way he gets the 5 long strips in the picture below. Which of the long strips is the longest?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/529.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Points $R, S$ and $T$ are vertices of an equilateral triangle, and points $X, Y$ and $Z$ are midpoints of its sides. How many noncongruent triangles can be drawn using any three of these six points as vertices?\n\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2631.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anna has glued together several cubes of the same size to form a solid (see picture). Which of the following pictures shows a different view of this solid?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/973.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram you can see a very ragged island. Some of the frogs are sitting in the water. How many are sitting on the island?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/534.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following cubes can be folded from the net on the right?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1526.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A dart board is a regular octagon divided into regions as shown. Suppose that a dart thrown at the board is equally likely to land anywhere on the board. What is probability that the dart lands within the center square?\n\n\\n Options: A. $\\frac{\\sqrt{2} - 1}{2}$, B. $\\frac{1}{4}$, C. $\\frac{2 - \\sqrt{2}}{2}$, D. $\\frac{\\sqrt{2}}{4}$, E. $2 - \\sqrt{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2181.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A unit cube is cut twice to form three triangular prisms, two of which are congruent, as shown in Figure 1. The cube is then cut in the same manner along the dashed lines shown in Figure 2. This creates nine pieces. What is the volume of the piece that contains vertex $ W$?\n\\n Options: A. $\\frac{1}{12}$, B. $\\frac{1}{9}$, C. $\\frac{1}{8}$, D. $\\frac{1}{6}$, E. $\\frac{1}{4}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2463.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ten people form a circle. Each picks a number and tells it to the two neighbors adjacent to him in the circle. Then each person computes and announces the average of the numbers of his two neighbors. The figure shows the average announced by each person (not the original number the person picked). The number picked by the person who announced the average $6$ was\n\\n Options: A. $1$, B. $5$, C. $6$, D. $10$, E. $\\text{not uniquely determined from the given information}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2389.png" }, { "solution": "\\boxed{90}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Numbers in the picture are ticket prices between neighbouring towns. Peter wants to go from $A$ to $B$ as cheaply as possible. What is the lowest price he has to pay?\n", "completion": "\\boxed{90}", "image_path": "dataset/math_vision/images/430.png" }, { "solution": "\\boxed{1290}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The following diagram uses $126$ sticks of length $1$ to form a “triangulated hollow hexagon” with inner side length $2$ and outer side length $4$. How many sticks would be needed for a triangulated hollow hexagon with inner side length $20$ and outer side length $23$?\\n", "completion": "\\boxed{1290}", "image_path": "dataset/math_vision/images/2829.png" }, { "solution": "\\boxed{23}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If you add the numbers on opposite faces of this special die, you will get the same total three times. The numbers on the hidden faces of the die are prime numbers. Which number is on the face opposite to 14?\n", "completion": "\\boxed{23}", "image_path": "dataset/math_vision/images/1382.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On a square grid made up of unit squares, six points are marked as shown on the right. Three of which form a triangle with the least area. How big is this smallest area?\n\\n Options: A. $1 / 2$, B. $1 / 3$, C. $1 / 4$, D. 1, E. 2", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1368.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangle $A B C D$ intersects the circle at points $E, F$, $G, H$. If $A E=4 \\mathrm{~cm}, E F=5 \\mathrm{~cm}, D H=3 \\mathrm{~cm}$, then the length of $H B$ is\n\\n Options: A. $6 \\mathrm{~cm}$, B. $7 \\mathrm{~cm}$, C. $\\frac{20}{3} \\mathrm{~cm}$, D. $8 \\mathrm{~cm}$, E. $9 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1313.png" }, { "solution": "\\boxed{29}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Daniela fills a $3 \\times 3$ table using the digits 1 to 9 so that each field contains only one digit. She has already placed the digits 1, 2, 3 and 4 in the table as shown in the diagram. Two numbers count as \"adjacent\" if the fields which they fill have one common side. When she has finished filling the table she realised: the sum of the numbers adjacent to 5 is 9 . How big is the sum of the numbers adjacent to 6?\n", "completion": "\\boxed{29}", "image_path": "dataset/math_vision/images/838.png" }, { "solution": "\\boxed{280}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: At each of the sixteen circles in the network below stands a student. A total of 3360 coins are distributed among the sixteen students. All at once, all students give away all their coins by passing an equal number of coins to each of their neighbors in the network. After the trade, all students have the same number of coins as they started with. Find the number of coins the student standing at the center circle had originally.\n\n", "completion": "\\boxed{280}", "image_path": "dataset/math_vision/images/2077.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $A 10 \\mathrm{~cm}$ long piece if wire is folded so that every part is equally long (see diagram). The wire is then cut through in the two positions marked. How long are the three pieces created in this way?\n\\n Options: A. $2 \\mathrm{~cm}, 3 \\mathrm{~cm}, 5 \\mathrm{~cm}$, B. $2 \\mathrm{~cm}, 2 \\mathrm{~cm}, 6 \\mathrm{~cm}$, C. $1 \\mathrm{~cm}, 4 \\mathrm{~cm}, 5 \\mathrm{~cm}$, D. $1 \\mathrm{~cm}, 3 \\mathrm{~cm}, 6 \\mathrm{~cm}$, E. $3 \\mathrm{~cm}, 3 \\mathrm{~cm}, 4 \\mathrm{~cm}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/855.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two vertices of a square lie on a semi-circle as shown, while the other two lie on its diameter. The radius of the circle is $1 \\mathrm{~cm}$. How big is the area of the square?\n\\n Options: A. $\\frac{4}{5} \\mathrm{~cm}^{2}$, B. $\\frac{\\pi}{4} \\mathrm{~cm}^{2}$, C. $1 \\mathrm{~cm}^{2}$, D. $\\frac{4}{3} \\mathrm{~cm}^{2}$, E. $\\frac{2}{\\sqrt{3}} \\mathrm{~cm}^{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1434.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which number is hidden behind the square?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/531.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two rectangular blocks and a cube are joined to form a larger rectangular block, which volume is $280 \\mathrm{~cm}^{3}$. The cube, in dark gray in the picture, has volume equal to $125 \\mathrm{~cm}^{3}$ and the smaller rectangular block has volume equal to $75 \\mathrm{~cm}^{3}$. What is the area of the face marked with the question mark?\n\\n Options: A. $16 \\mathrm{~cm}^{2}$, B. $18 \\mathrm{~cm}^{2}$, C. $20 \\mathrm{~cm}^{2}$, D. $24 \\mathrm{~cm}^{2}$, E. $56 \\mathrm{~cm}^{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/344.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Some edges of a cube are coloured in red so that each sides of the cube has at least one red edge. What is the minimum number of red edges that the cube has? ", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1249.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A folded napkin was cut through (see picture). What does it look like when unfolded?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/998.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $ \\triangle ABC$, $ AB = BC$, and $ BD$ is an altitude. Point $ E$ is on the extension of $ \\overline{AC}$ such that $ BE = 10$. The values of $ \\tan CBE$, $ \\tan DBE$, and $ \\tan ABE$ form a geometric progression, and the values of $ \\cot DBE$, $ \\cot CBE$, $ \\cot DBC$ form an arithmetic progression. What is the area of $ \\triangle ABC$?\n\\n Options: A. $16$, B. $\\frac{50}{3}$, C. $10\\sqrt{3}$, D. $8\\sqrt{5}$, E. $18$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2461.png" }, { "solution": "\\boxed{21}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Emily wants to write a number into every free small triangle. The sum of the numbers in two triangles with a common side should always be the same. Two numbers are already given. How big is the sum of all numbers in the figure?\n", "completion": "\\boxed{21}", "image_path": "dataset/math_vision/images/894.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On a tall building there are 4 fire escape ladders, as shown. The heights of 3 ladders are at their tops. What is the height of the shortest ladder?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/651.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Paul folds a piece of paper, then punches a hole into the paper and unfolds it again. The unfolded paper then looks like the picture on the right. Along which dotted line can Paul have folded the paper beforehand?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1147.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The next window is a square of area $1 \\mathrm{~m}^{2}$ and is composed of four triangles, which areas, indicated in the figure, follow the ratios $3 A=4 B$ and $2 C=3 D$. A fly is placed exactly at the point where these four triangles touch each other. The fly flies directly to the side closest to the window. How much does it fly?\n\\n Options: A. $40 \\mathrm{~cm}$, B. $30 \\mathrm{~cm}$, C. $25 \\mathrm{~cm}$, D. $20 \\mathrm{~cm}$, E. $10 \\mathrm{~cm}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1445.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: All six sides of a rectangular solid were rectangles. A one-foot cube was cut out of the rectangular solid as shown. The total number of square feet in the surface of the new solid is how many more or less than that of the original solid?\n\n\\n Options: A. $2\\text{ less}$, B. $1\\text{ less}$, C. $\\text{the same}$, D. $1\\text{ more}$, E. $2\\text{ more}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2547.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Find the length of the arc denoted by the interrogation sign.\n\\n Options: A. $\\frac{5 \\pi}{4}$, B. $\\frac{5 \\pi}{3}$, C. $\\frac{\\pi}{2}$, D. $\\frac{3 \\pi}{2}$, E. $\\frac{2 \\pi}{3}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1317.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangle $ ABCD$, pictured below, shares $50\\%$ of its area with square $ EFGH$. Square $ EFGH$ shares $20\\%$ of its area with rectangle $ ABCD$. What is $ \\frac{AB}{AD}$?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/2471.png" }, { "solution": "\\boxed{27}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of rectangle $ABCD$ is $72$. If point $A$ and the midpoints of $\\overline{BC}$ and $\\overline{CD}$ are joined to form a triangle, the area of that triangle is\n\n", "completion": "\\boxed{27}", "image_path": "dataset/math_vision/images/2624.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mr. Hide wants to find a treasure that he buried years before. He can only remember that he buried the treasure at least $5 \\mathrm{~m}$ away from the hedge and no more than $5 \\mathrm{~m}$ away from the old pear tree. Which picture shows best the area where Mr. Hide has to look for the treasure?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1388.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a length of string wound over and under $n$ equal circles. The sum of the diameters of the circles is $d \\mathrm{~cm}$. What is the length of the string in $\\mathrm{cm}$ ?\n\\n Options: A. $\\frac{1}{2} \\pi d$, B. $\\pi d n$, C. $2 \\pi d n$, D. $\\pi d$, E. $d n$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1528.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jim and Ben are sitting in a ferris wheel (see picture on the right). The ferris wheel is turning. Now Ben is in the position where Jim was beforehand. Where is Jim now?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/65.png" }, { "solution": "\\boxed{7.6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, $ABCD$ is a rectangle and $EFGH$ is a parallelogram. Using the measurements given in the figure, what is the length $d$ of the segment that is perpendicular to $HE$ and $FG$?\n\n", "completion": "\\boxed{7.6}", "image_path": "dataset/math_vision/images/2660.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $P Q=P R=Q S$ and $\\angle Q P R=20^{\\circ}$. What is $\\angle R Q S$ ? \\n Options: A. $50^{\\circ}$, B. $60^{\\circ}$, C. $65^{\\circ}$, D. $70^{\\circ}$, E. $75^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1666.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows two different views of the same cube. The cube is made from 27 small cubes, which are either white or black. At most how many black cubes are there?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1384.png" }, { "solution": "\\boxed{145}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A hexagon is inscribed in a circle: What is the measure of $\\alpha$, in degrees?", "completion": "\\boxed{145}", "image_path": "dataset/math_vision/images/3006.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A triangular array of numbers has a first row consisting of the odd integers $ 1,3,5,\\ldots,99$ in increasing order. Each row below the first has one fewer entry than the row above it, and the bottom row has a single entry. Each entry in any row after the top row equals the sum of the two entries diagonally above it in the row immediately above it. How many entries in the array are multiples of $ 67$?\n", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/2072.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two pieces of land are separated by the borderline $A B C D$, as shown in the figure. The line segments $A B, B C$ and $C D$ are parallel to the sides of the rectangle and have lengths $30 \\mathrm{~m}, 24 \\mathrm{~m}$ and $10 \\mathrm{~m}$, respectively. We want to straighten the borderline by replacing it with a line $A E$, such that the areas of the two pieces of land do not change. How far from $D$ must be $E$?\n\\n Options: A. $8 \\mathrm{~m}$, B. $10 \\mathrm{~m}$, C. $12 \\mathrm{~m}$, D. $14 \\mathrm{~m}$, E. $16 \\mathrm{~m}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1288.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $ ABCD$ is a rectangle (see the accompanying diagram) with $ P$ any point on $ \\overline{AB}$. $ \\overline{PS} \\perp \\overline{BD}$ and $ \\overline{PR} \\perp \\overline{AC}$. $ \\overline{AF} \\perp \\overline{BD}$ and $ \\overline{PQ} \\perp \\overline{AF}$. Then $ PR + PS$ is equal to:\n\\n Options: A. PQ, B. AE, C. PT + AT, D. AF, E. EF", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2273.png" }, { "solution": "\\boxed{72}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a square and an equilateral right-angled crossshaped dodecagon. The length of the perimeter of the dodecagon is $36 \\mathrm{~cm}$. What, in $\\mathrm{cm}^{2}$, is the area of the square?\n", "completion": "\\boxed{72}", "image_path": "dataset/math_vision/images/1281.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An ant walked $6 \\mathrm{~m}$ every day to go from point $A$ to point $B$ in a straight line. One day Johnny put a straight cylinder of one meter high in that way. Now the ant walks on the same straight line or above it, having to go up and down the cylinder, as shown in the picture. How much does she have to walk now to go from $A$ to $B$?\n\\n Options: A. $8 \\mathrm{~m}$, B. $9 \\mathrm{~m}$, C. $6+\\pi \\mathrm{~m}$, D. $12-\\pi \\mathrm{~m}$, E. $10 \\mathrm{~m}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/335.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nEquilateral triangle $ABP$ (see figure) with side $AB$ of length $2$ inches is placed inside square $AXYZ$ with side of length $4$ inches so that $B$ is on side $AX$. The triangle is rotated clockwise about $B$, then $P$, and so on along the sides of the square until $P$ returns to its original position. The length of the path in inches traversed by vertex $P$ is equal to\\n Options: A. $20\\pi/3$, B. $32\\pi/3$, C. $12\\pi$, D. $40\\pi/3$, E. $15\\pi$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2304.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nEquilateral $ \\triangle ABC$ is inscribed in a circle. A second circle is tangent internally to the circumcircle at $ T$ and tangent to sides $ AB$ and $ AC$ at points $ P$ and $ Q$. If side $ BC$ has length $ 12$, then segment $ PQ$ has length\\n Options: A. $6$, B. $6\\sqrt{3}$, C. $8$, D. $8\\sqrt{3}$, E. $9$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2336.png" }, { "solution": "\\boxed{42}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A chain is made from circular links, with external radius $3 \\mathrm{~cm}$ and internal radius $2 \\mathrm{~cm}$, as shown in the diagram. The length of the chain is $1.7 \\mathrm{~m}$.\n\nHow many rings are used?", "completion": "\\boxed{42}", "image_path": "dataset/math_vision/images/1516.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A (very small) ball is kicked off from point A on a square billiard table with side length $2 \\mathrm{~m}$. After moving along the shown path and touching the sides three times as indicated, the path ends in point $B$. How long is the path that the bal travels from A to B? (As indicated on the right: incident angle = emergent angle.)\n\\n Options: A. 7, B. $2 \\sqrt{13}$, C. 8, D. $4 \\sqrt{3}$, E. $2 \\cdot(\\sqrt{2}+\\sqrt{3})$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/218.png" }, { "solution": "\\boxed{54}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, what is the area of $\\triangle ABC$? ", "completion": "\\boxed{54}", "image_path": "dataset/math_vision/images/3020.png" }, { "solution": "\\boxed{37}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The first diagram on the right shows a shape constructed from two rectangles. The lengths of two sides are marked: 11 and 13. The shape is cut into three parts and the parts are rearranged, as shown in the second diagram on the right. What is the length marked $x$ ?\n", "completion": "\\boxed{37}", "image_path": "dataset/math_vision/images/1586.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular box is 4 cm thick, and its square bases measure 16 cm by 16 cm. What is the distance, in centimeters, from the center point $P$ of one square base to corner $Q$ of the opposite base? Express your answer in simplest terms.\n\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/2982.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The first kangaroo is repeatedly mirrored along the dotted lines. Two reflections were already carried out. In which position is the kangaroo in the grey triangle?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/881.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following polygons has the largest area?\n\n\\n Options: A. $\\text{A}$, B. $\\text{B}$, C. $\\text{C}$, D. $\\text{D}$, E. $\\text{E}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2639.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a square with sides of length $4 \\mathrm{~mm}$, a square with sides of length $5 \\mathrm{~mm}$, a triangle with area $8 \\mathrm{~mm}^{2}$, and a parallelogram. What is the area, in $\\mathrm{mm}^{2}$, of the parallelogram? ", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1885.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Tarzan wanted to draw a rhombus made up of two equilateral triangles. He drew the line segments inaccurately. When Jane checked the measurements of the four angles shown, she sees that they are not equally big (see diagram). Which of the five line segments in this diagram is the longest?\n\\n Options: A. AD, B. AC, C. AB, D. BC, E. BD", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1375.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the pattern below, the cat (denoted as a large circle in the figures below) moves clockwise through the four squares and the mouse (denoted as a dot in the figures below) moves counterclockwise through the eight exterior segments of the four squares.\n\n\nIf the pattern is continued, where would the cat and mouse be after the 247th move?\\n Options: A. , B. , C. , D. , E. ", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2653.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the net of a cube whose faces are numbered. Sascha adds the numbers that are on opposite faces of the cube. Which three results does he get?\n\\n Options: A. $4,6,11$, B. $4,5,12$, C. $5,6,10$, D. $5,7,9$, E. $5,8,8$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1120.png" }, { "solution": "\\boxed{103}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five cards have the numbers $101,102,103,104$ and 105 on their fronts.\n\nOn the reverse, each card has one of five different positive integers: $a, b, c, d$ and $e$ respectively.\nWe know that $c=b e, a+b=d$ and $e-d=a$.\nFrankie picks up the card which has the largest integer on its reverse. What number is on the front of Frankie's card?", "completion": "\\boxed{103}", "image_path": "dataset/math_vision/images/2026.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular sheet of paper which measures $6 \\mathrm{~cm} \\times 12 \\mathrm{~cm}$ is folded along its diagonal (Diagram A). The shaded areas in Diagram B are then cut off and the paper is unfolded leaving the rhombus shown in Diagram C. What is the length of the side of the rhombus? \\n Options: A. $\\frac{7}{2} \\sqrt{5} \\mathrm{~cm}$, B. $7.35 \\mathrm{~cm}$, C. $7.5 \\mathrm{~cm}$, D. $7.85 \\mathrm{~cm}$, E. $8.1 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1806.png" }, { "solution": "\\boxed{4028}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure on the right is made up of six unit squares. Its perimeter is $14 \\mathrm{~cm}$. Squares will be added to this figure in the same way until it is made up of 2013 unit squares (zigzag: alternating bottom right and top right). How big is the perimeter of the newly created figure?\n", "completion": "\\boxed{4028}", "image_path": "dataset/math_vision/images/1372.png" }, { "solution": "\\boxed{7.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular sheet of paper with measures $6 \\times 12$ is folded along its diagonal. The shaded parts sticking out over the edge of the overlapping area are cut off and the sheet is unfolded. Now it has the shape of a rhombus. Find the length of the side of the rhombus.\n", "completion": "\\boxed{7.5}", "image_path": "dataset/math_vision/images/1270.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The faces of the brick have the areas A, B and C as shown. How big is the volume of the brick?\n\\n Options: A. $A B C$, B. $\\sqrt{A B C}$, C. $\\sqrt{A B+B C+C A}$, D. $\\sqrt[3]{A B C}$, E. $2(A+B+C)$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/310.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Thirteen black and six white hexagonal tiles were used to create the figure below. If a new figure is created by attaching a border of white tiles with the same size and shape as the others, what will be the difference between the total number of white tiles and the total number of black tiles in the new figure?\n\n", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/2657.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Joana has several sheets of paper with the drawing of a parrot . She wants to paint only the head, tail and wing of the parrot, red, blue or green, and the head and tail may have the same color, but the wing may not have the same color as the head or tail. How many leaves can she paint, so that there are not two parrots painted the same way?", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/638.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Farmer Pythagoras has a field in the shape of a right triangle. The right triangle's legs have lengths 3 and 4 units. In the corner where those sides meet at a right angle, he leaves a small unplanted square $S$ so that from the air it looks like the right angle symbol. The rest of the field is planted. The shortest distance from $S$ to the hypotenuse is 2 units. What fraction of the field is planted?\n\n\\n Options: A. $\\frac{25}{27}$, B. $\\frac{26}{27}$, C. $\\frac{73}{75}$, D. $\\frac{145}{147}$, E. $\\frac{74}{75}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2217.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Peter wants to colour the cells of a $3 \\times 3$ square in such a way that each of the rows, each of the columns and both diagonals have cells of three different colours. What is the least number of colours Peter could use? ", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1916.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The graph of the line $ y = mx + b$ is shown. Which of the following is true?\n\\n Options: A. mb < - 1, B. - 1 < mb < 0, C. mb = 0, D. 0 < mb < 1, E. mb > 1", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2456.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube with the edge $3 \\mathrm{~cm}$ long is painted grey and cut into smaller cubes each with an edge of $1 \\mathrm{~cm}$ long. How many smaller cubes will have exactly 2 faces painted?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/444.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four objects $a, b, c, d$ are placed on a double balance as shown. Then two of the objects are exchanged, which results in the change of position of the balance as shown. Which two objects were exchanged?\n\\n Options: A. $a$ and $b$, B. $b$ and $d$, C. $b$ and $c$, D. $a$ and $d$, E. $a$ and $c$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1392.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The line $P Q$ is divided into six parts by the points $V, W, X, Y$ and $Z$. Squares are drawn on $P V, V W, W X, X Y, Y Z$ and $Z Q$ as shown in the diagram. The length of line $P Q$ is $24 \\mathrm{~cm}$. What is the length of the path from $P$ to $Q$ indicated by the arrows?\n\\n Options: A. $48 \\mathrm{~cm}$, B. $60 \\mathrm{~cm}$, C. $66 \\mathrm{~cm}$, D. $72 \\mathrm{~cm}$, E. $96 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1743.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Given an isosceles triangle $A B C, C A=C B, A D=$ $=A C, D B=D C$ (see the fig.). Find the value of the angle $A C B$.\n\\n Options: A. $98^{\\circ}$, B. $100^{\\circ}$, C. $104^{\\circ}$, D. $108^{\\circ}$, E. $110^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/207.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the five \"T-like shapes\" would be symmetric to the one shown with respect to the dashed line?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2529.png" }, { "solution": "\\boxed{1.4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure shown, a perpendicular segment is drawn from B in rectangle ABCD to meet diagonal AC at point X. Side AB is 6 cm and diagonal AC is 10 cm. How many centimeters away is point X from the midpoint M of the diagonal AC? Express your answer as a decimal to the nearest tenth.\n\n", "completion": "\\boxed{1.4}", "image_path": "dataset/math_vision/images/2959.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A birdbath is designed to overflow so that it will be self-cleaning. Water flows in at the rate of 20 milliliters per minute and drains at the rate of 18 milliliters per minute. One of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time. Which one is it?\n\n\\n Options: A. $\\text{A}$, B. $\\text{B}$, C. $\\text{C}$, D. $\\text{D}$, E. $\\text{E}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2633.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square piece of paper is cut in a straight line into two pieces. Which of the following shapes can not be created?\n\\n Options: A. A Square, B. A rectangle, C. A pentagon, D. An equilateral triangle, E. A right-angled triangle", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/793.png" }, { "solution": "\\boxed{1047}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the smallest sum of two $3$-digit numbers that can be obtained by placing each of the six digits $ 4,5,6,7,8,9 $ in one of the six boxes in this addition problem?\n\n", "completion": "\\boxed{1047}", "image_path": "dataset/math_vision/images/2536.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square piece of paper is cut into six rectangular pieces as shown in the diagram. When the lengths of the perimeters of the six rectangular pieces are added together, the result is $120 \\mathrm{~cm}$. What is the area of the square piece of paper? \\n Options: A. $48 \\mathrm{~cm}^{2}$, B. $64 \\mathrm{~cm}^{2}$, C. $110.25 \\mathrm{~cm}^{2}$, D. $144 \\mathrm{~cm}^{2}$, E. $256 \\mathrm{~cm}^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1583.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram QSR is a straight line. $\\angle \\mathrm{QPS}=12^{\\circ}$ and $\\mathrm{PQ}=\\mathrm{PS}=\\mathrm{RS}$. How big is $\\angle \\mathrm{QPR}$?\n\\n Options: A. $36^{\\circ}$, B. $42^{\\circ}$, C. $54^{\\circ}$, D. $60^{\\circ}$, E. $84^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1049.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Inside the cube lattice pictured on the side one can see a solid, non-seethrough pyramid $A B C D S$ with square base $A B C D$, whose top $S$ is exactly in the middle of one edge of the cube. If you look at the pyramid from above, from below, from the front, from the back, from the right and from the left - which of the following views cannot be possible?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/256.png" }, { "solution": "\\boxed{336}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On Misha's new phone, a passlock consists of six circles arranged in a $2\\times 3$ rectangle. The lock is opened by a continuous path connecting the six circles; the path cannot pass through a circle on the way between two others (e.g. the top left and right circles cannot be adjacent). For example, the left path shown below is allowed but the right path is not. (Paths are considered to be oriented, so that a path starting at $A$ and ending at $B$ is different from a path starting at $B$ and ending at $A$. However, in the diagrams below, the paths are valid/invalid regardless of orientation.) How many passlocks are there consisting of all six circles?\\n", "completion": "\\boxed{336}", "image_path": "dataset/math_vision/images/2824.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows an isosceles triangle, where the height is marked and its area is split up into equally wide white and grey stripes. Which fraction of the area of the triangle is white?\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{1}{3}$, C. $\\frac{2}{3}$, D. $\\frac{3}{4}$, E. $\\frac{2}{5}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1145.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $ ABCD$ has side length $ 2$. A semicircle with diameter $ \\overline{AB}$ is constructed inside the square, and the tangent to the semicricle from $ C$ intersects side $ \\overline{AD}$ at $ E$. What is the length of $ \\overline{CE}$?\n\n\\n Options: A. $\\frac{2 + \\sqrt{5}}{2}$, B. $\\sqrt{5}$, C. $\\sqrt{6}$, D. $\\frac{5}{2}$, E. $5 - \\sqrt{5}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2458.png" }, { "solution": "\\boxed{2040}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $K$, $O$ and $M$ are the centers of the three semi-circles. Also, $OC = 32$ and $CB = 36$.\n\n Line $l$ is drawn to touch the smaller semi-circles at points $S$ and $E$ so that $KS$ and $ME$ are both perpendicular to $l$. Determine the area of quadrilateral $KSEM$.", "completion": "\\boxed{2040}", "image_path": "dataset/math_vision/images/2906.png" }, { "solution": "\\boxed{$\\frac{90}{23}^{\\circ}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On the first day of school, Ashley the teacher asked some of her students what their favorite color was and used those results to construct the pie chart pictured below. During this first day, $165$ students chose yellow as their favorite color. The next day, she polled $30$ additional students and was shocked when none of them chose yellow. After making a new pie chart based on the combined results of both days, Ashley noticed that the angle measure of the sector representing the students whose favorite color was yellow had decreased. Compute the difference, in degrees, between the old and the new angle measures.\\n", "completion": "\\boxed{$\\frac{90}{23}^{\\circ}$}", "image_path": "dataset/math_vision/images/2804.png" }, { "solution": "\\boxed{19}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The $ 5\\times 5$ grid shown contains a collection of squares with sizes from $ 1\\times 1$ to $ 5\\times 5$. How many of these squares contain the black center square?\n", "completion": "\\boxed{19}", "image_path": "dataset/math_vision/images/2133.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: 18 cubes are coloured white or grey or black and are arranged as shown.\n\nThe figures below show the white and the black parts. Which of the following is the grey part?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/649.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the net of a regular octahedron. In a Magic Octahedron, the four numbers on the faces that meet at a vertex add up to make the same total for every vertex. If the letters $F, G, H, J$ and $K$ are replaced with the numbers $2,4,6,7$, and 8 , in some order, to make a Magic Octahedron, what is the value of $G+J$ ? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1848.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: This line graph represents the price of a trading card during the first $6$ months of $1993$.\n\n\nThe greatest monthly drop in price occurred during\\n Options: A. $\\text{January}$, B. $\\text{March}$, C. $\\text{April}$, D. $\\text{May}$, E. $\\text{June}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2565.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular garden is surrounded by a path of constant width. The perimeter of the garden is $24 \\mathrm{~m}$ shorter than the distance along the outside edge of the path. What is the width of the path? \\n Options: A. $1 \\mathrm{~m}$, B. $2 \\mathrm{~m}$, C. $3 \\mathrm{~m}$, D. $4 \\mathrm{~m}$, E. $5 \\mathrm{~m}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1724.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points $W$, $X$, $Y$, and $Z$ is a vertex of one of the small squares. Square $ABCD$ can be constructed with sides passing through $W$, $X$, $Y$, and $Z$. What is the maximum possible distance from $A$ to $P$? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2916.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many pieces of string are there in the picture?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1039.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each side of the large square in the figure is trisected (divided into three equal parts). The corners of an inscribed square are at these trisection points, as shown. The ratio of the area of the inscribed square to the area of the large square is\n\n\\n Options: A. $\\frac{\\sqrt{3}}{3}$, B. $\\frac{5}{9}$, C. $\\frac{2}{3}$, D. $\\frac{\\sqrt{5}}{3}$, E. $\\frac{7}{9}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2593.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sophie wants to complete the grid shown so that each row and each column of the grid contains the digits 1, 2 and 3 exactly once. What is the sum of the digits she will write in the shaded cells? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1737.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The integers from 1 to $n$, inclusive, are equally spaced in order round a circle. The diameter through the position of the integer 7 also goes through the position of 23 , as shown. What is the value of $n$ ? ", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/1671.png" }, { "solution": "\\boxed{63}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ria wants to write a number into each box. She has already written two numbers. The sum of all five numbers should be 35, the sum of the first three numbers should be 22, the sum of the last three numbers should be 25. What is the product Ria gets, if she multiplies the two numbers in the grey boxes?\n", "completion": "\\boxed{63}", "image_path": "dataset/math_vision/images/1151.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An equilateral triangle is placed inside a larger equilateral triangle so that the region between them can be divided into three congruent trapezoids, as shown below. The side length of the inner triangle is $\\frac{2}{3}$ the side length of the larger triangle. What is the ratio of the area of one trapezoid to the area of the inner triangle?\n\\n Options: A. 1:3, B. 3:8, C. 5:12, D. 7:16, E. 4:9", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2791.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular section was cut out of a rectangular block as shown in the diagram. Find the decrease percentage of the surface area.\n\\n Options: A. Less than $12.5 \\%$, B. $12.5 \\%$, C. More than $12.5 \\%$, D. but less than $25 \\%$, E. $25 \\%$, F. More than $25 \\%$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/754.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Out of how many circles is the beaver made of?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/151.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube has all its corners cut off, as shown. How many edges does the resulting shape have?\n", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/1040.png" }, { "solution": "\\boxed{592}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $\\triangle ABC$ be an acute triangle with circumcenter $O$ and centroid $G$. Let $X$ be the intersection of the line tangent to the circumcircle of $\\triangle ABC$ at $A$ and the line perpendicular to $GO$ at $G$. Let $Y$ be the intersection of lines $XG$ and $BC$. Given that the measures of $\\angle ABC, \\angle BCA, $ and $\\angle XOY$ are in the ratio $13 : 2 : 17, $ the degree measure of $\\angle BAC$ can be written as $\\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\n", "completion": "\\boxed{592}", "image_path": "dataset/math_vision/images/2099.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shows the lines $r$ and $s$, which equations are, respectively, $y=a x\n+b$ e $y=c x+d$. Which of the following statements is true?\n\\n Options: A. $a b+c d<0$, B. $a+b+c+d<0$, C. $a c+b d \\geq 0$, D. $a+b+c+d>0$, E. $a b c d>0$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/345.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following is made using more than one piece of string?\n\\n Options: A. I, B. III, C. IV and V, D. III, E. IV and V, F. I, G. III and V, H. all, I. None of these answers", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/773.png" }, { "solution": "\\boxed{761}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figures $ F_1$, $ F_2$, $ F_3$, and $ F_4$ shown are the first in a sequence of figures. For $ n\\ge3$, $ F_n$ is constructed from $ F_{n - 1}$ by surrounding it with a square and placing one more diamond on each side of the new square than $ F_{n - 1}$ had on each side of its outside square. For example, figure $ F_3$ has $ 13$ diamonds. How many diamonds are there in figure $ F_{20}$?\n", "completion": "\\boxed{761}", "image_path": "dataset/math_vision/images/2169.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Betsy designed a flag using blue triangles, small white squares, and a red center square, as shown. Let $ B$ be the total area of the blue triangles, $ W$ the total area of the white squares, and $ R$ the area of the red square. Which of the following is correct?\n\n\\n Options: A. B = W, B. W = R, C. B = R, D. 3B = 2R, E. 2R = W", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2119.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Johannes wrote the numbers 6,7 and 8 in the circles as shown. He wants to write the numbers 1, 2, 3, 4 and 5 in the remaining circles so that the sum of the numbers along each side of the square is 13. What will be the sum of the numbers in the grey circles?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/486.png" }, { "solution": "\\boxed{$5 \\sqrt{3}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consider the figure , where every small triangle is equilateral with side length $1$. Compute the area of the polygon $ AEKS $.", "completion": "\\boxed{$5 \\sqrt{3}$}", "image_path": "dataset/math_vision/images/2795.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram you see the rectangular garden of Green's family. It has an area of $30 \\mathrm{~m}^{2}$ and is divided into three rectangular parts. One side of the part where flowers are growing has a length of $2 \\mathrm{~m}$. Its area is $10 \\mathrm{~m}^{2}$. The part with strawberries has one side of length $3 \\mathrm{~m}$. What is the area of the part where vegetables are growing?\n\\n Options: A. $4 \\mathrm{~m}^{2}$, B. $6 \\mathrm{~m}^{2}$, C. $8 \\mathrm{~m}^{2}$, D. $10 \\mathrm{~m}^{2}$, E. $12 \\mathrm{~m}^{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/724.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the $\\triangle ABC$ shown, $D$ is some interior point, and $x, y, z, w$ are the measures of angles in degrees. Solve for $x$ in terms of $y, z$ and $w$.\n\\n Options: A. $w-y-z$, B. $w-2y-2z$, C. $180-w-y-z \\$, D. $2w-y-z$, E. $180-w+y+z$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2367.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Leon has drawn a closed loop on the surface of a cuboid.\nWhich net cannot show his loop? \\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1498.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram a closed polygon can be seen whose vertices are the midpoints of the edges of the die. The interior angles are as usual defined as the angle that two sides of the polygon describe in a common vertex. How big is the sum of all interior angles of the polygon?\n\\n Options: A. $720^{\\circ}$, B. $1080^{\\circ}$, C. $1200^{\\circ}$, D. $1440^{\\circ}$, E. $1800^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/270.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Suppose you make a trip over the squared board shown, and you visit every square exactly once. Where must you start, if you can move only horizontally or vertically, but not diagonally?\n\\n Options: A. Only in the middle square, B. Only at a corner square, C. Only at an unshaded square, D. Only at a shaded square, E. At any square", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/766.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram on the right, $Q S R$ is a straight line, $\\angle Q P S=12^{\\circ}$ and $P Q=P S=R S$.\nWhat is the size of $\\angle Q P R$ ? \\n Options: A. $36^{\\circ}$, B. $42^{\\circ}$, C. $54^{\\circ}$, D. $60^{\\circ}$, E. $84^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1559.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An acute isosceles triangle, $ABC$ is inscribed in a circle. Through $B$ and $C$, tangents to the circle are drawn, meeting at point $D$. If $\\angle ABC=\\angle ACB=2\\angle D$ and $x$ is the radian measure of $\\angle A$, then $x=$\n\n\\n Options: A. $\\frac{3}{7}\\pi$, B. $\\frac{4}{9}\\pi$, C. $\\frac{5}{11}\\pi$, D. $\\frac{6}{13}\\pi$, E. $\\frac{7}{15}\\pi$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2387.png" }, { "solution": "\\boxed{486}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers 1, 2, 3 are written on the circumference of a circle. Then the sum of each pair of neighbouring numbers is written between them, so 6 numbers are obtained (1,3,2,5,3 and 4). This operation is repeated 4 more times, resulting in 96 numbers on the circle. What is the sum of these numbers?\n", "completion": "\\boxed{486}", "image_path": "dataset/math_vision/images/1298.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A game is played on a board as shown in the picture. I move the counter from square to square according to the following rules. First, one square to the right, then one square up, then one square left, then one square down, and then once again one square right. Which picture shows where the counter can then be found?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/476.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three four-digit numbers are written onto three separate pieces of paper as shown. The sum of the three numbers is 10126. Three of the digits in the picture are hidden. Which are the hidden digits?\n\\n Options: A. 5, B. 6 and 7, C. 4, D. 5 and 7, E. 4, F. 6 and 7, G. 4, H. 5 and 6, I. 3, J. 5 and 6", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1182.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $ABC$ lines $CE$ and $AD$ are drawn so that\n\n$\\frac{CD}{DB}=\\frac{3}{1}$ and $\\frac{AE}{EB}=\\frac{3}{2}$. Let $r=\\frac{CP}{PE}$\n\nwhere $P$ is the intersection point of $CE$ and $AD$. Then $r$ equals:\n\n\\n Options: A. $3$, B. $\\frac{3}{2}$, C. $4$, D. $5$, E. $\\frac{5}{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2280.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a square $P Q R S$ with side length 1. The point $U$ is the midpoint of the side $R S$ and the point $W$ is the midpoint of the square. The three line segments, $T W, U W$ and $V W$ split the square into three equally big areas. How long is the line segment $S V$?\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{2}{3}$, C. $\\frac{3}{4}$, D. $\\frac{4}{5}$, E. $\\frac{5}{6}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1476.png" }, { "solution": "\\boxed{50}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Figure $\\mathrm{S}$ is made from four paper ribbons $10 \\mathrm{~cm}$ wide. Each of the ribbons is $25 \\mathrm{~cm}$ longer than the previous one (see the picture). By how many centimetres will the perimeter of figure $\\mathrm{T}$ (made from the same ribbons) exceed that of figure $\\mathrm{S}$?\n", "completion": "\\boxed{50}", "image_path": "dataset/math_vision/images/751.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nEach of the sides of the five congruent rectangles is labeled with an integer, as shown above. These five rectangles are placed, without rotating or reflecting, in positions $I$ through $V$ so that the labels on coincident sides are equal.\n\nWhich of the rectangles is in position $I$?\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2434.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the ground plan of a room. Adjoining walls are perpendicular to each other. The letters $a$ and $b$ on the plan show the lengths of some of the walls. What is the area of the room? \\n Options: A. $3 a b+a^{2}$, B. $8 a+2 b$, C. $3 a b-a^{2}$, D. $b^{2}-a^{2}$, E. $3 a b$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1525.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The ratio of the radii of two concentric circles is $1:3$. If $\\overline{AC}$ is a diameter of the larger circle, $\\overline{BC}$ is a chord of the larger circle that is tangent to the smaller circle, and $AB = 12$, then the radius of the larger circle is\n\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/2397.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Marta sticks several triangles on top of each other and makes a star that way. What is the minimum number of triangles she has used?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/618.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure, the triangle $ABC$ is a right triangle with $\\angle BCA=90^\\circ$. Median $CM$ is perpendicular to median $BN$, and side $BC=s$. The length of $BN$ is\n\n\\n Options: A. $s\\sqrt{2}$, B. $\\frac{3}{2}s\\sqrt{2}$, C. $2s\\sqrt{2}$, D. $\\frac{1}{2}s\\sqrt{5}$, E. $\\frac{1}{2}s\\sqrt{6}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2342.png" }, { "solution": "\\boxed{2304}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the area in square units of the quadrilateral XYZW shown below? ", "completion": "\\boxed{2304}", "image_path": "dataset/math_vision/images/3005.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Alice subtracts one two-digit number from another two-digit number. Afterwards she paints over two digits in the calculation. How big is the sum of the two painted digits?\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/889.png" }, { "solution": "\\boxed{284}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each one of the 5 keys locks exactly one padlock. Every letter on a padlock stands for exactly one digit, same letters mean same digits. Which digits are on the key with the question mark?\n", "completion": "\\boxed{284}", "image_path": "dataset/math_vision/images/880.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six points are placed and numbered as shown on the right. Two triangles are drawn: one by connecting the even numbered points, and one by connecting the odd numbered points. Which of the following shapes is the result?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/960.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which number has to be put into the dark cloud to have all the given calculations right?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/442.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The shaded part of the regular octagon has an area of $3 \\mathrm{~cm}^{2}$. How big is the area of the octagon?\n\\n Options: A. $8+4 \\sqrt{2} \\mathrm{~cm}^{2}$, B. $9 \\mathrm{~cm}^{2}$, C. $8 \\sqrt{2} \\mathrm{~cm}^{2}$, D. $12 \\mathrm{~cm}^{2}$, E. $14 \\mathrm{~cm}^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1381.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rabbit, a beaver and a kangaroo are having a competition. All three begin at the same time from the \"Start\" and hop in the same direction. The beaver always moves one position forwards with each jump. The rabbit always moves two positions forwards with one jump and the kangaroo always three positions. Whoever takes the least amount of jumps to land exactly in the position labelled \"Ziel“ is the winner. Who wins the competition?\\n Options: A. Kangaroo and rabbit, B. Rabbit, C. Kangaroo, D. Beaver, E. Kangaroo and beaver", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/992.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which tile below completes the wall next to it?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/916.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In this diagram a scheme is indicated for associating all the points of segment $ \\overline{AB}$ with those of segment $ \\overline{A'B'}$, and reciprocally. To described this association scheme analytically, let $ x$ be the distance from a point $ P$ on $ \\overline{AB}$ to $ D$ and let $ y$ be the distance from the associated point $ P'$ of $ \\overline{A'B'}$ to $ D'$. Then for any pair of associated points, if $ x = a,\\, x + y$ equals:\n\\n Options: A. $13a$, B. $17a - 51$, C. $17 - 3a$, D. $\\frac{17 - 3a}{4}$, E. $12a - 34$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2274.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shows the graph of a function $f:[-5,5] \\rightarrow R$. How many distinct solutions does the equation $f(f(x))=0$ have?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/360.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Matchsticks can be used to write digits, as shown in the diagram. How many different positive integers can be written using exactly six matchsticks in this way? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1710.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon?\n\n\\n Options: A. $\\frac{2}{7}$, B. $\\frac{5}{42}$, C. $\\frac{11}{14}$, D. $\\frac{5}{7}$, E. $\\frac{6}{7}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2753.png" }, { "solution": "\\boxed{40}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $\\textbf{Bake Sale}$\nFour friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.\n\n$\\circ$ Art's cookies are trapezoids:\n\n\n$\\circ$ Roger's cookies are rectangles:\n\n\n$\\circ$ Paul's cookies are parallelograms:\n\n\n$\\circ$ Trisha's cookies are triangles:\n\n\nEach friend uses the same amount of dough, and Art makes exactly 12 cookies. Art's cookies sell for 60 cents each. To earn the same amount from a single batch, how much should one of Roger's cookies cost in cents?", "completion": "\\boxed{40}", "image_path": "dataset/math_vision/images/2646.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The sides of $\\triangle ABC$ have lengths $6, 8$ and $10$. A circle with center $P$ and radius $1$ rolls around the inside of $\\triangle ABC$, always remaining tangent to at least one side of the triangle. When $P$ first returns to its original position, through what distance has $P$ traveled?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/2406.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Carl tries to divide the large shape of squares into smaller pieces using only copies of the T-piece and the F-piece shown on the right. (Pieces may be turned over or around.) What is the smallest possible number of the T-pieces that he can achieve? ", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/1509.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows the same cube from two different views. It is built from 27 smaller cubes, some of which are grey and some white.\nWhat is the largest number of grey cubes there could be?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1902.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Marco's father took a picture of his son in front of the car shown beside. Which of the drawings below could represent this picture?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/100.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Numbers are to be placed into the table shown, one number in each cell, in such a way that each row has the same total, and each column has the same total. Some of the numbers are already given. What number is $x$ ? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1883.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: John paints the squares of the board next to it if the result of the calculation inside them is 24. How did the painting of the board look?\n\\begin{tabular}{|l|l|l|}\n\\hline $28-4$ & $4 \\times 6$ & $18+6$ \\\\\n\\hline $19+6$ & $8 \\times 3$ & $29-6$ \\\\\n\\hline\n\\end{tabular}\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/621.png" }, { "solution": "\\boxed{79}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Charlotte is playing the hit new web number game, Primle. In this game, the objective is to guess a two-digit positive prime integer between $10$ and $99$, called the Primle. For each guess, a digit is highlighted blue if it is in the Primle, but not in the correct place. A digit is highlighted orange if it is in the Primle and is in the correct place. Finally, a digit is left unhighlighted if it is not in the Primle. If Charlotte guesses $13$ and $47$ and is left with the following game board, what is the Primle?\\n", "completion": "\\boxed{79}", "image_path": "dataset/math_vision/images/2852.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many little squares at least do we have to shade in the picture on the right in order that it have an axis of symmetry?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1032.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $A B C D$ be a convex quadrilateral with an area of 1 where $A B$ and $B D$ are the bases of two isosceles triangles $A D B$ and $B C D$ respectively (as shown). The product $A C \\cdot B D$ is equal to:\n\\n Options: A. $\\frac{\\sqrt{3}}{3}$, B. $\\frac{2 \\sqrt{3}}{3}$, C. $\\sqrt{3}$, D. $\\frac{4 \\sqrt{3}}{3}$, E. other answer", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/177.png" }, { "solution": "\\boxed{120}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $ABCDEFGH$ shown below is a right rectangular prism. If the volume of pyramid $ABCH$ is 20, then what is the volume of $ABCDEFGH$?\n\n", "completion": "\\boxed{120}", "image_path": "dataset/math_vision/images/2995.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diameter of the circle from the picture is $10 \\mathrm{~cm}$. What is the perimeter of the figure which is marked with double line, if the rectangles in the picture are coincident?\n\\n Options: A. $8 \\mathrm{~cm}$, B. $16 \\mathrm{~cm}$, C. $20 \\mathrm{~cm}$, D. $25 \\mathrm{~cm}$, E. $30 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/738.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A parallelogram is divided in two parts $P_{1}$ and $P_{2}$, as shown in the picture. Which sentence is always true?\n\\n Options: A. $P_{2}$ has a longer perimeter than $P_{1}$, B. $P_{2}$ has a smaller perimeter than $P_{1}$, C. $P_{2}$ has a smaller area than $P_{1}$, D. $P_{1}$ and $P_{2}$ have the same perimeter, E. $P_{1}$ and $P_{2}$ have the same area", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/749.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large square touches another two squares, as shown in the picture. The numbers inside the smaller squares indicate their areas. What is the area of the largest square?\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/342.png" }, { "solution": "\\boxed{19}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure below, $N$ congruent semicircles lie on the diameter of a large semicircle, with their diameters covering the diameter of the large semicircle with no overlap. Let $A$ be the combined area of the small semicircles and $B$ be the area of the region inside the large semicircle but outside the semicircles. The ratio $A:B$ is $1:18$. What is $N$?\n", "completion": "\\boxed{19}", "image_path": "dataset/math_vision/images/2218.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The point $O$ is the center of the circle in the picture. What is the diameter of the circle?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/1012.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One slice of a circular cake is $15 \\%$ of the whole cake. What is the size of the angle marked with the question mark? \\n Options: A. $30^{\\circ}$, B. $45^{\\circ}$, C. $54^{\\circ}$, D. $15^{\\circ}$, E. $20^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1800.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A triangular pyramid is built with 20 cannon balls, as shown. Each cannon ball is labelled with one of $A, B, C, D$ or $E$. There are 4 cannon balls with each type of label. The picture shows the labels on the cannon balls on 3 of the faces of the pyramid. What is the label on the hidden cannon ball in the middle of the fourth face?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1218.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The centres of the four illustrated circles are in the corners of the square. The two big circles touch each other and also the two little circles. With which factor do you have to multiply the radii of the little circles to obtain the radius of the big circles?\n\\n Options: A. $\\frac{2}{9}$, B. $\\sqrt{5}$, C. $0.8 \\cdot \\pi$, D. 2.5, E. $1+\\sqrt{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1327.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If the letters of the Word MAMA are written underneath each other then the word has a vertical axis of symmetry. For which of these words does that also hold true?\n\\n Options: A. ADAM, B. BAUM, C. BOOT, D. LOGO, E. TOTO", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1159.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $V W X$ and $X Y Z$ are congruent equilateral triangles and angle $V X Y=80^{\\circ}$. What is the size of angle $V W Y$ ? \\n Options: A. $25^{\\circ}$, B. $30^{\\circ}$, C. $35^{\\circ}$, D. $40^{\\circ}$, E. $45^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1546.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Point $O$ is the center of the regular octagon $ABCDEFGH$, and $X$ is the midpoint of the side $\\overline{AB}$. What fraction of the area of the octagon is shaded?\n\\n Options: A. $\\frac{11}{32}$, B. $\\frac{3}{8}$, C. $\\frac{13}{32}$, D. $\\frac{7}{16}$, E. $\\frac{15}{32}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2732.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What fraction of the large $12$ by $18$ rectangular region is shaded?\n\n\\n Options: A. $\\frac{1}{108}$, B. $\\frac{1}{18}$, C. $\\frac{1}{12}$, D. $\\frac{2}{9}$, E. $\\frac{1}{3}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2518.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Max has cut a rectangle into two pieces. One piece looks like:\n\nWhat does the other piece look like?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/34.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows four circles each of which touches the largest square and two adjacent circles. A second square has its vertices at the midpoints of the sides of the largest square and the central square has its vertices at the centres of the circles.\n\nWhat is the ratio of the total shaded area to the area of the outer square?\\n Options: A. $\\pi: 12$, B. $1: 4$, C. $(\\pi+2): 16$, D. $1: 3$, E. $\\pi: 4$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1562.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram we see 10 islands that are connected by 15 bridges. What is the minimum number of bridges that need to be closed off so that there is no connection from $A$ to $B$ anymore?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/295.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria has six equally big square pieces of plain paper. On each piece of paper she draws one of the figures shown below. How many of these figures have the same perimeter as the plain piece of paper itself?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1366.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the net of a box consisting only of rectangles. How big is the volume of the box?\n\\n Options: A. $43 \\mathrm{~cm}^{3}$, B. $70 \\mathrm{~cm}^{3}$, C. $80 \\mathrm{~cm}^{3}$, D. $100 \\mathrm{~cm}^{3}$, E. $1820 \\mathrm{~cm}^{3}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1170.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two of the 5 ladybirds in the picture are always friends with each other if the difference between their number of dots is exactly 1. Today every ladybird has sent an SMS to each of their friends. How many SMS messages were sent?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/538.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Seven pairwise different single-digit numbers are distributed among the circles shown so that the product of the three numbers that are connected by a straight line is the same in all three cases. Which number is written in the circle with the question mark? ", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/1496.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a rectangle $A B C D$, the points $P, Q, R$ and $S$ are the midpoints of sides $A B, B C, C D$ and $A D$ respectively, and $T$ is the midpoint of the line $R S$. What fraction of the area of $A B C D$ is the triangle $P Q T$ ? \\n Options: A. $\\frac{5}{16}$, B. $\\frac{1}{4}$, C. $\\frac{1}{5}$, D. $\\frac{1}{6}$, E. $\\frac{3}{8}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1508.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each square in a $3 \\times 3$ grid is randomly filled with one of the $4$ gray-and-white tiles shown below on the right.\nWhat is the probability that the tiling will contain a large gray diamond in one of the smaller $2\\times 2$ grids? Below is an example of one such tiling.\n\\n Options: A. $\\frac{1}{1024}$, B. $\\frac{1}{256}$, C. $\\frac{1}{64}$, D. $\\frac{1}{16}$, E. $\\frac{1}{4}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2792.png" }, { "solution": "\\boxed{84}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, points $X$, $Y$ and $Z$ are on the sides of $\\triangle UVW$, as shown. Line segments $UY$, $VZ$ and $WX$ intersect at $P$. Point $Y$ is on $VW$ such that $VY:YW=4:3$. If $\\triangle PYW$ has an area of 30 and $\\triangle PZW$ has an area of 35, determine the area of $\\triangle UXP$. ", "completion": "\\boxed{84}", "image_path": "dataset/math_vision/images/2976.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Veronika wears five rings as shown. How many, different ways are there for her to take off the rings one by one?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1477.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A right hexagonal prism has a height of 3 feet and each edge of the hexagonal bases is 6 inches. What is the sum of the areas of the non-hexagonal faces of the prism, in square feet?\n\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/2935.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle centered at $ O$ has radius $ 1$ and contains the point $ A$. Segment $ AB$ is tangent to the circle at $ A$ and $ \\angle{AOB} = \\theta$. If point $ C$ lies on $ \\overline{OA}$ and $ \\overline{BC}$ bisects $ \\angle{ABO}$, then $ OC =$\n\n\\n Options: A. $\\sec^2\\theta - \\tan\\theta$, B. $\\frac{1}{2}$, C. $\\frac{\\cos^2\\theta}{1 + \\sin\\theta}$, D. $\\frac{1}{1 + \\sin\\theta}$, E. $\\frac{\\sin\\theta}{\\cos^2\\theta}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2440.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube $3 \\times 3 \\times 3$ is made from $1 \\times 1 \\times 1$ white, grey and black cubes, as shown in the first diagram. The other two diagrams show the white part and the black part of the cube. Which of the following diagrams shows the grey part?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1210.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five cards are lying on the table in the order 1, 3, 5, 4, 2. You must get the cards in the order 1, 2, 3, 4, 5. Per move, any two cards may be interchanged. How many moves do you need at least?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/723.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two buttons with smiling faces and two buttons with sad faces are in a row as shown in the picture. When you press a button the face changes, and so do the faces of the neighbouring buttons. What is the minimum number of button presses needed so that only smiling faces can be seen?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/827.png" }, { "solution": "\\boxed{751}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube-shaped container has vertices $A$, $B$, $C$, and $D$ where $\\overline{AB}$ and $\\overline{CD}$ are parallel edges of the cube, and $\\overline{AC}$ and $\\overline{BD}$ are diagonals of the faces of the cube. Vertex $A$ of the cube is set on a horizontal plane $\\mathcal P$ so that the plane of the rectangle $ABCD$ is perpendicular to $\\mathcal P$, vertex $B$ is $2$ meters above $\\mathcal P$, vertex $C$ is $8$ meters above $\\mathcal P$, and vertex $D$ is $10$ meters above $\\mathcal P$. The cube contains water whose surface is $7$ meters above $\\mathcal P$. The volume of the water is $\\frac{m}{n}$ cubic meters, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\n", "completion": "\\boxed{751}", "image_path": "dataset/math_vision/images/2107.png" }, { "solution": "\\boxed{35}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Snail quadruplets have gone hiking on a path paved with identical rectangular tiles. The shape and length of each snail's trip is shown below.\n\nHow many decimeters has the snail Tin hiked?", "completion": "\\boxed{35}", "image_path": "dataset/math_vision/images/718.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a cube with sides of length $12 \\mathrm{~cm}$. An ant moves on the cube surface from point $M$ to point $N$ following the route shown. Find the length of ant's path.\n\\n Options: A. 40 cm, B. 48 cm, C. 50 cm, D. 60 cm, E. It is impossible to determine", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/722.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rectangle $ ABCD$, points $ F$ and $ G$ lie on $ \\overline{AB}$ so that $ AF = FG = GB$ and $ E$ is the midpoint of $ \\overline{DC}$. Also, $ \\overline{AC}$ intersects $ \\overline{EF}$ at $ H$ and $ \\overline{EG}$ at $ J$. The area of the rectangle $ ABCD$ is $ 70$. Find the area of triangle $ EHJ$.\n\\n Options: A. $\\frac{5}{2}$, B. $\\frac{35}{12}$, C. $3$, D. $\\frac{7}{2}$, E. $\\frac{35}{8}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2446.png" }, { "solution": "\\boxed{30}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle is split into 11 smaller rectangles as shown. All 11 small rectangles are similar to the initial rectangle. The smallest rectangles are aligned like the original rectangle (see diagram). The lower sides of the smallest rectangles have length 1. How big is the perimeter of the big rectangle?\n", "completion": "\\boxed{30}", "image_path": "dataset/math_vision/images/376.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In how many ways can all the numbers $1,2,3,4,5,6$ be written in the squares of the figure (one in each square) so that there are no adjacent squares in which the difference of the numbers written is equal to 3? (Squares that share only a corner are not considered adjacent.)\n\\n Options: A. $3 \\cdot 2^{5}$, B. $3^{6}$, C. $6^{3}$, D. $2 \\cdot 3^{5}$, E. $3 \\cdot 5^{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/194.png" }, { "solution": "\\boxed{90}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Blahaj has two rays with a common endpoint A0 that form an angle of $1^o$. They construct a sequence of points $A_0$, $. . . $, $A_n$ such that for all $1 \\le i \\le n$, $|A_{i-1}A_i | = 1$, and $|A_iA_0| > |A_{i-1}A_0|$. Find the largest possible value of $n$.\\n", "completion": "\\boxed{90}", "image_path": "dataset/math_vision/images/2835.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The acronym AMC is shown in the rectangular grid below with grid lines spaced $1$ unit apart. In units, what is the sum of the lengths of the line segments that form the acronym AMC$?$\n\n\\n Options: A. $17$, B. $15 + 2\\sqrt{2}$, C. $13 + 4\\sqrt{2}$, D. $11 + 6\\sqrt{2}$, E. $21$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2491.png" }, { "solution": "\\boxed{40}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The rabbit family Hoppel eat cabbages and carrots. Each day they eat either 10 carrots or 2 cabbages. In the whole of last week they ate 6 cabbages. How many carrots did the rabbit family eat last week?\n", "completion": "\\boxed{40}", "image_path": "dataset/math_vision/images/36.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five rectangles, $A$, $B$, $C$, $D$, and $E$, are arranged in a square as shown below. These rectangles have dimensions $1\\times6$, $2\\times4$, $5\\times6$, $2\\times7$, and $2\\times3$, respectively. (The figure is not drawn to scale.) Which of the five rectangles is the shaded one in the middle?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2497.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a sign pyramid a cell gets a \"+\" if the two cells below it have the same sign, and it gets a \"-\" if the two cells below it have different signs. The diagram below illustrates a sign pyramid with four levels. How many possible ways are there to fill the four cells in the bottom row to produce a \"+\" at the top of the pyramid?\n\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/2750.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the area enclosed by the geoboard quadrilateral below?\n\n\\n Options: A. $15$, B. $18\\frac{1}{2}$, C. $22\\frac{1}{2}$, D. $27$, E. $41$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2656.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A right triangle $ABC$ with hypotenuse $AB$ has side $AC = 15$. Altitude $CH$ divides $AB$ into segments $AH$ And $HB$, with $HB = 16$. The area of $\\triangle ABC$ is:\n\\n Options: A. $120$, B. $144$, C. $150$, D. $216$, E. $144\\sqrt{5}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2350.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Aisha has a strip of paper with the numbers $1,2,3,4$ and 5 written in five cells as shown. She folds the strip so that the cells overlap, forming 5 layers. Which of the following configurations, from top layer to bottom layer, is it not possible to obtain? \\n Options: A. $3,5,4,2,1$, B. $3,4,5,1,2$, C. $3,2,1,4,5$, D. $3,1,2,4,5$, E. $3,4,2,1,5$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1680.png" }, { "solution": "\\boxed{81}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square is cut into three rectangles along two lines parallel to a side, as shown. If the perimeter of each of the three rectangles is 24, then the area of the original square is\n\n", "completion": "\\boxed{81}", "image_path": "dataset/math_vision/images/2378.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn the adjoining figure, $ABCD$ is a square, $ABE$ is an equilateral triangle and point $E$ is outside square $ABCD$. What is the measure of $\\measuredangle AED$ in degrees?", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/2325.png" }, { "solution": "\\boxed{34}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A company makes a six-sided hollow aluminum container in the shape of a rectangular prism as shown. The container is $10^{''}$ by $10^{''}$ by $12^{''}$. Aluminum costs $\\$0.05$ per square inch. What is the cost, in dollars, of the aluminum used to make one container?\n\n", "completion": "\\boxed{34}", "image_path": "dataset/math_vision/images/2971.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A straight one-mile stretch of highway, $40$ feet wide, is closed. Robert rides his bike on a path composed of semicircles as shown. If he rides at $5$ miles per hour, how many hours will it take to cover the one-mile stretch?\n\nNote: $1$ mile= $5280$ feet\n\n\\n Options: A. $\\frac{\\pi}{11}$, B. $\\frac{\\pi}{10}$, C. $\\frac{\\pi}{5}$, D. $\\frac{2\\pi}{5}$, E. $\\frac{2\\pi}{3}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2731.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A pyramid is built from cubes (see diagram)\nAll cubes have side length $10 \\mathrm{~cm}$.\nAn ant crawls along the line drawn across the pyramid (see diagram).\nHow long is the path taken by the ant?\n\\n Options: A. $30 \\mathrm{~cm}$, B. $60 \\mathrm{~cm}$, C. $70 \\mathrm{~cm}$, D. $80 \\mathrm{~cm}$, E. $90 \\mathrm{~cm}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/674.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the box are seven blocks. It is possible to slide the blocks around so that another block can be added to the box. What is the minimum number of blocks that must be moved?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/782.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A big square is divided up into smaller squares of different sizes as shown. Some of the smaller squares are shaded in grey. Which fraction of the big square is shaded in grey?\n\\n Options: A. $\\frac{2}{3}$, B. $\\frac{2}{5}$, C. $\\frac{4}{7}$, D. $\\frac{4}{9}$, E. $\\frac{5}{12}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1181.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the triangle illustrated one internal angle measures $68^{\\circ}$. The three angle bisectors of the triangle are shown. What is the size of the angle indicated with a question mark?\n\\n Options: A. $120^{\\circ}$, B. $124^{\\circ}$, C. $128^{\\circ}$, D. $132^{\\circ}$, E. $136^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1325.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The object pictured is made up of four equally sized cubes. Each cube has a surface area of $24 \\mathrm{~cm}^{2}$. What is the surface area of the object pictured?\n\\n Options: A. $80 \\mathrm{~cm}^{2}$, B. $64 \\mathrm{~cm}^{2}$, C. $40 \\mathrm{~cm}^{2}$, D. $32 \\mathrm{~cm}^{2}$, E. $24 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1330.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In this square there are 9 dots. The distance between the points is always the same. You can draw a square by joining 4 points. How many different sizes can such squares have?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/545.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The points of intersection of the network of bars shown are labelled with the numbers 1 to 10. The sums $S$ of the four numbers on the vertices of each square are\nall the same. What is the minimum value of $S$?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/331.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Several mice live in three houses. Last night every mouse left their house and moved directly to one of the other two houses. The diagram shows how many mice were in each house yesterday and today. How many mice used the path that is indicated with an arrow? ", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/1257.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A 3-pyramid is a stack of the following 3 layers of balls. In the same way we have a 4-pyramid, a 5-pyramid, etc. All the outside balls of an 8-pyramid are removed. What kind of figure form the rest balls?\n\\n Options: A. 3-pyramid, B. 4-pyramid, C. 5-pyramid, D. 6-pyramid, E. 7-pyramid", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1319.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the 9 sides of the triangles in the picture will be coloured blue, green or red. Three of the sides are already coloured. Which colour can side $\\mathrm{x}$ have, if the sides of each triangle must be coloured in three different colours?\n\\n Options: A. only blue, B. only green, C. only red, D. Each of the three colours is possible., E. The colouring described is not possible", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/849.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A mushroom grows up every day. For five days Maria took a picture of this mushroom, but she wrongly ordered the photos beside. What is the sequence of photos that correctly shows the mushroom growth, from left to right?\n\\n Options: A. 2-5-3-1-4, B. 2-3-4-5-1, C. 5-4-3-2-1, D. 1-2-3-4-5, E. 2-3-5-1-4", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/620.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In right $ \\triangle ABC$ with legs $ 5$ and $ 12$, arcs of circles are drawn, one with center $ A$ and radius $ 12$, the other with center $ B$ and radius $ 5$. They intersect the hypotenuse at $ M$ and $ N$. Then, $ MN$ has length:\n\n\\n Options: A. $2$, B. $\\frac{13}{5}$, C. $3$, D. $4$, E. $\\frac{24}{5}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2353.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A graph consists of 16 points and several connecting lines as shown in the diagram. An ant is at point $A$. With every move the ant can move from the point where it currently is, along one of the connecting lines, to an adjacent point. At which of the points $P, Q, R, S$ and $T$ can the ant be after 2019 moves?\n\\n Options: A. only at $P, R$ or $S$, B. not at $Q$ or $T$, C. only at $P$, D. $R$, E. $S$ or $T$, F. not at $Q$, G. only at $Q$, H. only at $T$, I. At all of the points", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1435.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each shape represents exactly one digit. The sum of the digits in each row is stated on the right hand-side of each row.\n\nWhich digit does the star stand for?", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/615.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: As indicated by the diagram below, a rectangular piece of paper is folded bottom to top, then left to right, and finally, a hole is punched at X.\nWhat does the paper look like when unfolded?\n\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2600.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A small square with side length $4 \\mathrm{~cm}$ is drawn within a big square with side length $10 \\mathrm{~cm}$; their sides are parallel to each other (see diagram). What percentage of the figure is shaded? \\n Options: A. $25 \\%$, B. $30 \\%$, C. $40 \\%$, D. $42 \\%$, E. $45 \\%$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1485.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A regular hexagon is split into four quadrilaterals and a smaller regular hexagon. The ratio $\\frac{\\text { Area of the dark sections }}{\\text { Area of the small hexagon }}=\\frac{4}{3}$. How big is the ratio $\\frac{\\text { Area of the small hexagon }}{\\text { Area of the big hexagon }}$ ? \\n Options: A. $\\frac{3}{11}$, B. $\\frac{1}{3}$, C. $\\frac{2}{3}$, D. $\\frac{3}{4}$, E. $\\frac{3}{5}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1259.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Nathalie wanted to build a large cube out of lots of small cubes, just like in picture 1. How many cubes are missing from picture 2 that would be needed to build the large cube?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/502.png" }, { "solution": "\\boxed{75}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture $A B C D$ is a rectangle with $A B=16, B C=12$. Let $E$ be such a point that $A C \\perp C E, C E=15$. If $F$ is the point of intersection of segments $A E$ and $C D$, then the area of the triangle $A C F$ is equal to\n", "completion": "\\boxed{75}", "image_path": "dataset/math_vision/images/168.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which three puzzle pieces do you need to complete the large puzzle?\n\\n Options: A. 1, B. 3, C. 4, D. 1, E. 3, F. 6, G. 2, H. 3, I. 5, J. 2, 3, 6, 2, 5, 6", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/807.png" }, { "solution": "\\boxed{125}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each face of two noncongruent parallelepipeds is a rhombus whose diagonals have lengths $\\sqrt{21}$ and $\\sqrt{31}$. The ratio of the volume of the larger of the two polyhedra to the volume of the smaller is $\\fracmn$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. A parallelepiped is a solid with six parallelogram faces such as the one shown below.\n", "completion": "\\boxed{125}", "image_path": "dataset/math_vision/images/2103.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the rectangular parallelpiped shown, $AB = 3, BC= 1,$ and $CG = 2$. Point $M$ is the midpoint of $\\overline{FG}$. What is the volume of the rectangular pyramid with base $BCHE$ and apex $M$?\n\n\\n Options: A. $1$, B. $\\frac{4}{3}$, C. $\\frac{3}{2}$, D. $\\frac{5}{3}$, E. $2$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2220.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: John uses some building blocks to form a work of art. What does John see when he looks at his work of art from above?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/665.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: When the bat Elisa left its cave at night, the digital clock showed . When she came back in the morning and hung herself upside down, she looked at her watch and saw . How long did she stay out of the cave?\\n Options: A. 2h 48m, B. 2h 59m, C. 3h 39m, D. 3h 41m, E. 3h 49m", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/923.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The five vases shown are filled with water. The filling rate is constant. For which of the five vases does the graph shown describe the height of the water $h$ as a function of the time t?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/312.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In this picture there is what I saw on four different clocks at the same time. Only one of them had the right time. One was 20 minutes fast. Another 20 minutes slow. One had stopped some time ago.\n\nWhat was the right time?\\n Options: A. 4:45, B. 5:05, C. 5:25, D. 5:40, E. 12:00", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/409.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the square you can see the digits from 1 to 9 . A number is created by starting at the star, following the line and writing down the digits along the line while passing. For example, the line shown represents the number 42685 . Which of the following lines represents the largest number?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/940.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: This diagram shows two see-through sheets. You place the sheets on top of each other.Which pattern do you get?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/77.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure below shows line $\\ell$ with a regular, infinite, recurring pattern of squares and line segments.\n\nHow many of the following four kinds of rigid motion transformations of the plane in which this figure is drawn, other than the identity transformation, will transform this figure into itself?\n\nsome rotation around a point of line $\\ell$\nsome translation in the direction parallel to line $\\ell$\nthe reflection across line $\\ell$\nsome reflection across a line perpendicular to line $\\ell$", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/2222.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consecutive numbers have been entered diagonally criss-crossing the square on the right. Which of the following numbers could $x$ not be? \\n Options: A. 128, B. 256, C. 81, D. 121, E. 400", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1521.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram (which is not drawn to scale) shows a box measuring $5 \\mathrm{~cm}$ by $5 \\mathrm{~cm}$. There are seven bars in the box, each measuring $1 \\mathrm{~cm}$ by $3 \\mathrm{~cm}$. Kanga wants to slide the bars in the box so there is room for one more bar. What is the minimum number of bars that Kanga needs to move?\n\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1571.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An 8-inch by 8-inch square is folded along a diagonal creating a triangular region. This resulting triangular region is then folded so that the right angle vertex just meets the midpoint of the hypotenuse. What is the area of the resulting trapezoidal figure in square inches?\n\n", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/2928.png" }, { "solution": "\\boxed{750}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Quadrilateral $ABCD$ is a trapezoid, $AD = 15$, $AB = 50$, $BC = 20$, and the altitude is $12$. What is the area of the trapezoid?\n\n", "completion": "\\boxed{750}", "image_path": "dataset/math_vision/images/2716.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The points $M$ and $N$ are the midpoints of two sides of the big rectangle (see diagram). Which part of the area of the big rectangle is shaded? \\n Options: A. $\\frac{1}{6}$, B. $\\frac{1}{5}$, C. $\\frac{1}{4}$, D. $\\frac{1}{3}$, E. $\\frac{1}{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1489.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nSuppose one of the eight lettered identical squares is included with the four squares in the T-shaped figure outlined. How many of the resulting figures can be folded into a topless cubical box?", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2514.png" }, { "solution": "\\boxed{412}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The smallest four two-digit primes are written in different squares of a $2 \\times 2$ table.\n\nThe sums of the numbers in each row and column are calculated.\n\nTwo of these sums are 24 and 28.\n\nThe other two sums are $c$ and $d$, where $c", "completion": "\\boxed{412}", "image_path": "dataset/math_vision/images/2032.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria switches the lights on and off according to the given plan.\n\nFor how many minutes in total are there exactly two lights on at the same time?", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/683.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The five pieces shown below can be arranged to form four of the five figures shown in the choices. Which figure cannot be formed?\n\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2697.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Wanda has lots of pages of square paper, whereby each page has an area of 4. She cuts each of the pages into right-angled triangles and squares (see the left hand diagram). She takes a few of these pieces and forms the shape in the right hand diagram. How big is the area of this shape?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1107.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: When the 5 pieces are fitted together correctly, the result is a rectangle with a calculation written on it. What is the answer to this calculation?", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/942.png" }, { "solution": "\\boxed{206}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five cards have the numbers $101,102,103,104$ and 105 on their fronts. \nOn the reverse, each card has a statement printed as follows:\n101: The statement on card 102 is false\n102: Exactly two of these cards have true statements\n103: Four of these cards have false statements\n104: The statement on card 101 is false\n105: The statements on cards 102 and 104 are both false\nWhat is the total of the numbers shown on the front of the cards with TRUE statements?", "completion": "\\boxed{206}", "image_path": "dataset/math_vision/images/2031.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A regular pentagon is cut out of a page of lined paper. Step by step this pentagon is then rotated $21^{\\circ}$ counter clockwise about its midpoint. The result after step one is shown in the diagram. Which of the diagrams shows the situation when the pentagon fills the hole entirely again for the first time?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/315.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Chantal has placed numbers in two of the nine cells (see diagram). She wants to place the numbers 1, 2, 3 in every row and every column exactly once. How big is the sum of the two numbers in the grey cells?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/556.png" }, { "solution": "\\boxed{26}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: John is building houses of cards. On the picture there are houses of one, two, and three layers that John built. How many cards does he need to build a 4-layer house?\n", "completion": "\\boxed{26}", "image_path": "dataset/math_vision/images/435.png" }, { "solution": "\\boxed{40}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One square is drawn inside each of the two congruent isosceles right-angled triangles. The area of square $P$ is 45 units. How many units is the area of square R?\n", "completion": "\\boxed{40}", "image_path": "dataset/math_vision/images/1478.png" }, { "solution": "\\boxed{225}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Simone has a cube with sides of length $10 \\mathrm{~cm}$, and a pack of identical square stickers. She places one sticker in the centre of each face of the cube, and one across each edge so that the stickers meet at their corners, as shown in the diagram. What is the total area in $\\mathrm{cm}^{2}$ of the stickers used by Simone? ", "completion": "\\boxed{225}", "image_path": "dataset/math_vision/images/1877.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On the faces of a cube are written letters. First figure represents one possibility of its net. What letter should be written instead of the question mark in the other version of its net?\n\\n Options: A. A, B. B, C. C, D. E, E. Impossible to determine", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/742.png" }, { "solution": "\\boxed{4.2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Diagonal $ DB$ of rectangle $ ABCD$ is divided into $ 3$ segments of length $ 1$ by parallel lines $ L$ and $ L'$ that pass through $ A$ and $ C$ and are perpendicular to $ DB$. The area of $ ABCD$, rounded to the nearest tenth, is\n\n", "completion": "\\boxed{4.2}", "image_path": "dataset/math_vision/images/2356.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nVertex $E$ of equilateral triangle $ABE$ is in the interior of square $ABCD$, and $F$ is the point of intersection of diagonal $BD$ and line segment $AE$. If length $AB$ is $\\sqrt{1+\\sqrt{3}}$ then the area of $\\triangle ABF$ is\\n Options: A. $1$, B. $\\frac{\\sqrt{2}}{2}$, C. $\\frac{\\sqrt{3}}{2}$, D. $4-2\\sqrt{3}$, E. $\\frac{1}{2}+\\frac{\\sqrt{3}}{4}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2321.png" }, { "solution": "\\boxed{21}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The square pictured, is split into two squares and two rectangles. The vertices of the shaded quadrilateral with area 3 are the midpoints of the sides of the smaller squares. What is the area of the non-shaded part of the big square?\n", "completion": "\\boxed{21}", "image_path": "dataset/math_vision/images/371.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jorge's teacher asks him to plot all the ordered pairs $ (w, l)$ of positive integers for which $ w$ is the width and $ l$ is the length of a rectangle with area 12. What should his graph look like?\\n Options: A. , B. , C. , D. , E. ", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2673.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle with perimeter $30 \\mathrm{~cm}$ is divided into four parts by a vertical line and a horizontal line. One of the parts is a square of area $9 \\mathrm{~cm}^{2}$, as shown in the figure. What is the perimeter of rectangle $A B C D$?\n\\n Options: A. $14 \\mathrm{~cm}$, B. $16 \\mathrm{~cm}$, C. $18 \\mathrm{~cm}$, D. $21 \\mathrm{~cm}$, E. $24 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1455.png" }, { "solution": "\\boxed{40}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Peter shared a bar of chocolate. First he broke off a row with five pieces for his brother. Then he broke off a column with 7 pieces for his sister. How many pieces were there in the entire bar of chocolate?\n", "completion": "\\boxed{40}", "image_path": "dataset/math_vision/images/461.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The results of a cross-country team's training run are graphed below. Which student has the greatest average speed?\n\\n Options: A. $\\text{Angela}$, B. $\\text{Briana}$, C. $\\text{Carla}$, D. $\\text{Debra}$, E. $\\text{Evelyn}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2665.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure below, choose point $D$ on $\\overline{BC}$ so that $\\triangle ACD$ and $\\triangle ABD$ have equal perimeters. What is the area of $\\triangle ABD$?\n\\n Options: A. $\\frac{3}{4}$, B. $\\frac{3}{2}$, C. $2$, D. $\\frac{12}{5}$, E. $\\frac{5}{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2743.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows a mouse and a piece of cheese. The mouse is only allowed to move to the neighbouring fields in the direction of the arrows. How many paths are there from the mouse to the cheese?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/92.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The little caterpillar rolls up to go to sleep. What could it look like then?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/673.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We check the water meter and see that all digits on the display are different. What is the minimum amount of water that has to be used before this happens again?\n\\n Options: A. $0.006 \\mathrm{~m}^{3}$, B. $0.034 \\mathrm{~m}^{3}$, C. $0.086 \\mathrm{~m}^{3}$, D. $0.137 \\mathrm{~m}^{3}$, E. $1.048 \\mathrm{~m}^{3}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/370.png" }, { "solution": "\\boxed{$3\\sqrt{2}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consider a $1$ by $2$ by $3$ rectangular prism. Find the length of the shortest path between opposite corners $A$ and $B$ that does not leave the surface of the prism.\\n", "completion": "\\boxed{$3\\sqrt{2}$}", "image_path": "dataset/math_vision/images/2814.png" }, { "solution": "\\boxed{34}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A small square is inscribed in a big one as shown in the figure. Find the area of the small square.\n", "completion": "\\boxed{34}", "image_path": "dataset/math_vision/images/1031.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Karin places tables of size $2 \\times 1$ according to the number of participants in a meeting. The diagram shows the table arrangements from above for a small, a medium and a large meeting. How many tables are used in a large meeting?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1467.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Julia has two pots with flowers, as shown. She keeps the flowers exactly where they are. She buys more flowers and puts them in the pots. After that, each pot has the same number of each type of flower. What is the smallest number of flowers she needs to buy?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/128.png" }, { "solution": "\\boxed{72}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Suppose we have a hexagonal grid in the shape of a hexagon of side length $4$ as shown at left. Define a “chunk” to be four tiles, two of which are adjacent to the other three, and the other two of which are adjacent to just two of the others. The three possible rotations of these are shown at right.\\n\\nIn how many ways can we choose a chunk from the grid?\\n", "completion": "\\boxed{72}", "image_path": "dataset/math_vision/images/2816.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which beetle has to fly away so that the remaining beetles have 20 dots altogether?\n\\n Options: A. Beetle with 4 points, B. Beetle with 7 points, C. Beetle with 5 points, D. Beetle with 6 points, E. no beetle", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/74.png" }, { "solution": "\\boxed{61}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sylvia draws patterns with hexagons as shown. If she carries on drawing in this way, how many hexagons will there be in the fifth pattern?\n", "completion": "\\boxed{61}", "image_path": "dataset/math_vision/images/487.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows three squares. The medium square is formed by joining the midpoints of the sides of the large square. The small square is formed by joining the midpoints of the sides of the medium square. The area of the small square is $6 \\mathrm{~cm}^{2}$. What is the difference between the area of the medium square and the area of the large square? \\n Options: A. $3 \\mathrm{~cm}^{2}$, B. $6 \\mathrm{~cm}^{2}$, C. $9 \\mathrm{~cm}^{2}$, D. $12 \\mathrm{~cm}^{2}$, E. $15 \\mathrm{~cm}^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1581.png" }, { "solution": "\\boxed{24+4\\pi}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, what is the perimeter of the sector of the circle with radius 12?\n\n", "completion": "\\boxed{24+4\\pi}", "image_path": "dataset/math_vision/images/2901.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $\\mathrm{M}$ and $\\mathrm{N}$ are the midpoints of the equal sides of an isosceles triangle. How big is the area of the quadrilateral (marked?)?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1356.png" }, { "solution": "\\boxed{22}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Emily wants to insert nine numbers into the $3 \\times 3$ table so that the sum of the numbers in two adjacent cells (with a common side) is always the same. She has already written two numbers into the table. How big is the sum of all nine numbers?\n", "completion": "\\boxed{22}", "image_path": "dataset/math_vision/images/1153.png" }, { "solution": "\\boxed{30}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, four circles of radius 1 with centres $P$, $Q$, $R$, and $S$ are tangent to one another and to the sides of $\\triangle ABC$, as shown. \n\n\nWhat is the degree measure of the smallest angle in triangle $PQS$?", "completion": "\\boxed{30}", "image_path": "dataset/math_vision/images/2905.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four people can be seated at a square table. How many people at most could be seated if we pushed four tables of this kind together in one row?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/10.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nWhat is the final result?", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/548.png" }, { "solution": "\\boxed{384}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure below, isosceles $\\triangle ABC$ with base $\\overline{AB}$ has altitude $CH = 24$ cm. $DE = GF$, $HF = 12$ cm, and $FB = 6$ cm. What is the number of square centimeters in the area of pentagon $CDEFG$? ", "completion": "\\boxed{384}", "image_path": "dataset/math_vision/images/2911.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows three squares, $P Q R S, T U V R$ and $U W X Y$. They are placed together, edge to edge. Points $P, T$ and $X$ lie on the same straight line. The area of $P Q R S$ is 36 and the area of TUVR is 16. What is the area of triangle PXV?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/359.png" }, { "solution": "\\boxed{28}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $ABC$, $AB = 13$, $AC = 15$, and $BC = 14$. Let $I$ be the incenter. The incircle of triangle $ABC$ touches sides $BC$, $AC$, and $AB$ at $D$, $E$, and $F$, respectively. Find the area of quadrilateral $AEIF$.\n\n", "completion": "\\boxed{28}", "image_path": "dataset/math_vision/images/2993.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two rectangles are inscribed into a triangle as shown in the diagram. The dimensions of the rectangles are $1 \\times 5$ and $2 \\times 3$ respectively. How big is the height of the triangle in $A$?\n\\n Options: A. 3, B. $\\frac{7}{2}$, C. $\\frac{8}{3}$, D. $\\frac{6}{5}$, E. another number", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/377.png" }, { "solution": "\\boxed{594}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The rectangle $ABCD$ below has dimensions $AB = 12 \\sqrt{3}$ and $BC = 13 \\sqrt{3}$. Diagonals $\\overline{AC}$ and $\\overline{BD}$ intersect at $P$. If triangle $ABP$ is cut out and removed, edges $\\overline{AP}$ and $\\overline{BP}$ are joined, and the figure is then creased along segments $\\overline{CP}$ and $\\overline{DP}$, we obtain a triangular pyramid, all four of whose faces are isosceles triangles. Find the volume of this pyramid.\n\n", "completion": "\\boxed{594}", "image_path": "dataset/math_vision/images/2052.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each plant in Johns garden has exactly 5 leaves or exactly 2 leaves and a flower. In total the plants have 6 flowers and 32 leaves. How many plants are growing in the garden?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/845.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a circle with centre $O$ and the diameters $A B$ and $C X$. Let $O B=$ $B C$. Which fraction of the circle area is shaded?\n\\n Options: A. $\\frac{2}{5}$, B. $\\frac{1}{3}$, C. $\\frac{2}{7}$, D. $\\frac{3}{8}$, E. $\\frac{4}{11}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/297.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If John looks out the window he can see half of the kangaroos in the park. How many kangaroos in total are there in the park?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/563.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sonja builds the cube shown, out of equally sized bricks. The shortest side of one brick is $4 \\mathrm{~cm}$ long. What dimensions in $\\mathrm{cm}$ does one brick have?\n\\n Options: A. $4 \\times 6 \\times 12$, B. $4 \\times 6 \\times 16$, C. $4 \\times 8 \\times 12$, D. $4 \\times 8 \\times 16$, E. $4 \\times 12 \\times 16$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1225.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a net of an octahedron. When this is folded to form the octahedron, which of the labelled line segments will coincide with the line segment labelled $x$ ? \\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1943.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $A B C$ (see picture) $A B=A C, A E=A D$, and $\\angle B A D=30^{\\circ}$. What is the measure of angle $C D E$?\n\\n Options: A. $10^{\\circ}$, B. $15^{\\circ}$, C. $20^{\\circ}$, D. $25^{\\circ}$, E. $30^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1008.png" }, { "solution": "\\boxed{0}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shows seven regions enclosed by three circles. We call two regions neighbouring if their boundaries have more than one common point. In each region a number is written. The number in any region is equal to the sum of the numbers of its neighbouring regions. Two of the numbers are shown. What number is written in the central region? ", "completion": "\\boxed{0}", "image_path": "dataset/math_vision/images/1911.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Between two points four routes are drawn. Which route is the shortest?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/432.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large square is divided into 4 equal-sized smaller squares. All the smaller squares are either shaded or unshaded. How many different ways are there to colour the large square? (Two colourings are considered to be the same if one can be rotated to look exactly like the other, as in the example shown.)\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1572.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows 3 semicircular arcs with the endpoints $A, B$ of one arc and the centres $E, F$ of the other two arcs at the vertices of a rectangle. What is the area of the shaded region when the radius of each semicircle is $2 \\mathrm{~cm}$ ? \\n Options: A. $2 \\pi+2 \\mathrm{~cm}^{2}$, B. $8 \\mathrm{~cm}^{2}$, C. $2 \\pi+1 \\mathrm{~cm}^{2}$, D. $7 \\mathrm{~cm}^{2}$, E. $2 \\pi \\mathrm{cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1822.png" }, { "solution": "\\boxed{-4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four regular hexagons surround a square with a side length $1$, each one sharing an edge with the square, as shown in the figure below. The area of the resulting 12-sided outer nonconvex polygon can be written as $m\\sqrt{n} + p$, where $m$, $n$, and $p$ are integers and $n$ is not divisible by the square of any prime. What is $m + n + p$?\n\n", "completion": "\\boxed{-4}", "image_path": "dataset/math_vision/images/2500.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The chord $A B$ touches the smaller of the two concentric circles. The length $A B=$ 16. How big is the area of the grey part?\n\\n Options: A. $32 \\pi$, B. $63 \\pi$, C. $64 \\pi$, D. $32 \\pi^{2}$, E. It depends on the radius of the circles.", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/228.png" }, { "solution": "\\boxed{140}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle ABC$, $AC=BC$, and $m\\angle BAC=40^\\circ$. What is the number of degrees in angle $x$? ", "completion": "\\boxed{140}", "image_path": "dataset/math_vision/images/3035.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the four balls weighs either 10 or 20 or 30 or 40 grams. Which ball weighs 30 grams?\n\\n Options: A. A, B. B, C. C, D. D, E. It can be A or B.", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/600.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Eve has taken 2 bananas to school. At first she changed each of them into 4 apples, later on she exchanged each apple into 3 mandarins. How many mandarins has Eve got? \\n Options: A. $2+4+3$, B. $2 \\cdot 4+3$, C. $2+4 \\cdot 3$, D. $2 \\cdot 4 \\cdot 3$, E. $2+4-3$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/19.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The plane is tiled by congruent squares and congruent pentagons as indicated.\n\nThe percent of the plane that is enclosed by the pentagons is closest to\\n Options: A. 50, B. 52, C. 54, D. 56, E. 58", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2116.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Some of the digits in the following correct addition have been replaced by the letters $P, Q, R$ and $S$ , as shown. What is the value of $P+Q+R+S$ ?\n", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/1931.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mike sets the table for 8 people: The fork has to lie to the left and the knife to the right of the plate. For how many people is the cutlery set correctly?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/584.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There were five candidates in the school election. After $90 \\%$ of the votes had been counted, the preliminary results were as shown on the right. How many students still had a chance of winning the election?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1970.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $3 \\times 3$ field is made up of 9 unit squares. In two of these squares, circles are inscribed as shown in the diagram. How big is the shortest distance between these circles?\n\\n Options: A. $2 \\sqrt{2}-1$, B. $\\sqrt{2+1}$, C. $2 \\sqrt{2}$, D. 2, E. 3", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1395.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet?\n\n\\n Options: A. $120$, B. $180$, C. $240$, D. $360$, E. $480$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2134.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture, three strips of the same horizontal width $a$ are marked 1,2,3. These strips connect the two parallel lines. Which strip has the biggest area?\n\\n Options: A. All three strips have the same area, B. Strip 1, C. Strip 2, D. Strip 3, E. Impossible to answer without knowing $a$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1262.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows 2 mushrooms. What is the difference between their heights?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/120.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Under cards with the same colour, the same number is always found. If the three hidden numbers in one row are added, one obtains the number to the right of the row. Which number is hidden under the black card?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/678.png" }, { "solution": "\\boxed{92}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A pattern is made out of white, square tiles. The first three patterns are shown. How many tiles will be needed for the tenth pattern?\n", "completion": "\\boxed{92}", "image_path": "dataset/math_vision/images/1056.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The flag of Kangaria is a rectangle with side-lengths in the ratio $3: 5$. The flag is divided into four rectangles of equal area as shown. What is the ratio of the length of the shorter sides of the white rectangle to the length of its longer sides? \\n Options: A. $1: 3$, B. $1: 4$, C. $2: 7$, D. $3: 10$, E. $4: 15$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1941.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Emma should colour in the three strips of the flag shown. She has four colours available. She can only use one colour for each strip and immediately adjacent strips are not to be of the same colour. How many different ways are there for her to colour in the flag? ", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/382.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the box are seven blockss. You want to rearrange the blocks so that another block can placed. What is the minimum number of blocks that have to be moved?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/225.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A triangle is folded along the dashed line as shown. The area of the triangle is 1.5 times the area of the resulting figure. We know that the total area of the grey parts is 1. Determine the area of the starting triangle.\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1338.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The parallel sides of a trapezoid are $ 3$ and $ 9$. The non-parallel sides are $ 4$ and $ 6$. A line parallel to the bases divides the trapezoid into two trapezoids of equal perimeters. The ratio in which each of the non-parallel sides is divided is:\n\\n Options: A. 4: 3, B. 3: 2, C. 4: 1, D. 3: 1, E. 6: 1", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2270.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five identical right-angled triangles can be arranged so that their larger acute angles touch to form the star shown in the diagram. It is also possible to form a different star by arranging more of these triangles so that their smaller acute angles touch. How many triangles are needed to form the second star?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1214.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a shape made up of 36 identical small equilateral triangles. What is the smallest number of small triangles identical to these that could be added to the shape to turn it into a hexagon? ", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/1675.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A building block is made up of five identical rectangles: \nHow many of the patterns shown below can be made with two such building blocks without overlap?\n\n\n\n\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/693.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the length of line $A B$ if the side of each of the four squares shown is 1?\n\\n Options: A. 5, B. $\\sqrt{13}$, C. $\\sqrt{5}+\\sqrt{2}$, D. $\\sqrt{5}$, E. None of the previous", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1311.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a $2 \\times 4$ table in which the numbers in each column except the first column are the sum and the difference of the numbers in the previous column.\n\nCarl completes a $2 \\times 7$ table in the same way and obtains the numbers 96 and 64 in the final column. What is the sum of the numbers in the first column of Carl's table?", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1769.png" }, { "solution": "\\boxed{95}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the digits 2, 3, 4 and 5 will be placed in a square. Then there will be two numbers, which will be added together. What is the biggest number that they could make?\n", "completion": "\\boxed{95}", "image_path": "dataset/math_vision/images/38.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many faces has the object shown? (Prism with a hole)\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/770.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Katja throws darts at the target pictured on the right. If she does not hit the target she gets no points. She throws twice and adds her points. What can her total not be?\n\\n Options: A. 60, B. 70, C. 80, D. 90, E. 100", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/517.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A plastic snap-together cube has a protruding snap on one side and receptacle holes on the other five sides as shown. What is the smallest number of these cubes that can be snapped together so that only receptacle holes are showing?\n\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2583.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In this figure $\\angle RFS = \\angle FDR$, $FD = 4$ inches, $DR = 6$ inches, $FR = 5$ inches, $FS = 7\\frac{1}{2}$ inches. The length of $RS$, in inches, is:\n\n\\n Options: A. $\\text{undetermined}$, B. $4$, C. $5\\frac{1}{2}$, D. $6$, E. $6\\frac{1}{4}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2281.png" }, { "solution": "\\boxed{64}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Medians $ BD$ and $ CE$ of triangle $ ABC$ are perpendicular, $ BD = 8$, and $ CE = 12$. The area of triangle $ ABC$ is\n", "completion": "\\boxed{64}", "image_path": "dataset/math_vision/images/2430.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The \"Borromaic Rings\" have an extraordinary property. Although no two are interlocked, they are strongly connected within each other. If one ring is cut through, the other two fall apart. Which of the following diagrams shows the picture of \"Borromaic Rings\"?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1326.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ruth and Sarah decide to have a race. Ruth runs around the perimeter of the pool shown in the diagram while Sarah swims lengths of the pool.\nRuth runs three times as fast as Sarah swims. Sarah swims six lengths of the pool in the same time Ruth runs around the pool five times. How wide is the pool?\n\\n Options: A. $25 \\mathrm{~m}$, B. $40 \\mathrm{~m}$, C. $50 \\mathrm{~m}$, D. $80 \\mathrm{~m}$, E. $180 \\mathrm{~m}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1658.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Monika plans to travel across the network in the diagram from point $P$ to point $Q$, travelling only in the direction of the arrows. How many different routes are possible? ", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1932.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the shapes cannot be split into two triangles using a single straight line?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/979.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, lines $Q T$ and $R S$ are parallel and $P Q$ and $Q T$ are equal. Angle $S T Q$ is $154^{\\circ}$. What is the size of angle $S R Q$ ? \\n Options: A. $120^{\\circ}$, B. $122^{\\circ}$, C. $124^{\\circ}$, D. $126^{\\circ}$, E. $128^{\\circ}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1783.png" }, { "solution": "\\boxed{829}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each square in this cross-number can be filled with a non-zero digit such that all of the conditions in the clues are fulfilled. The digits used are not necessarily distinct.\n\nACROSS\n1. A square\n3. The answer to this Kangaroo question\n5. A square\nDOWN\n1. 4 down minus eleven\n2. One less than a cube\n4. The highest common factor of 1 down and 4 down is greater than one", "completion": "\\boxed{829}", "image_path": "dataset/math_vision/images/2013.png" }, { "solution": "\\boxed{372}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below, how many distinct paths are there from January 1 to December 31, moving from one adjacent dot to the next either to the right, down, or diagonally down to the right?\\n", "completion": "\\boxed{372}", "image_path": "dataset/math_vision/images/2869.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure of side 1 is formed by six equal triangles, made with 12 sticks. How many matchsticks are needed to complete the figure of side 2, partially represented?\n", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/1194.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Carl composed the figure shown on the left side of the drawing from the smaller three-square and four-square figures shown on the right side. The smaller figures can be turned around, but not turned over. What is the smallest number of three-square figures needed for that?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/1005.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nA parabolic arch has a height of $16$ inches and a span of $40$ inches. The height, in inches, of the arch at a point $5$ inches from the center of $M$ is:\\n Options: A. $1$, B. $15$, C. $15\\frac{1}{3}$, D. $15\\frac{1}{2}$, E. $15\\frac{3}{4}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2291.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangle $DEFA$ below is a $3 \\times 4$ rectangle with $DC=CB=BA$. The area of the \"bat wings\" is\n\\n Options: A. $2$, B. $2 \\frac{1}{2}$, C. $3$, D. $3 \\frac{1}{2}$, E. $5$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2739.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Akash's birthday cake is in the form of a $4 \\times 4 \\times 4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into $64$ smaller cubes, each measuring $1 \\times 1 \\times 1$ inch, as shown below. How many of the small pieces will have icing on exactly two sides?\n\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/2763.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Gardener Toni plants tulips and sunflowers in a square flowerbed with side length $12 \\mathrm{~m}$, as shown in the diagram. How big is the entire area where sunflowers are planted?\n\\n Options: A. $36 \\mathrm{~m}^{2}$, B. $40 \\mathrm{~m}^{2}$, C. $44 \\mathrm{~m}^{2}$, D. $46 \\mathrm{~m}^{2}$, E. $48 \\mathrm{~m}^{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1232.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each side of each triangle in the diagram is painted either blue, green or red. Four of the sides are already painted. Which colour can the line marked \"x\" have, if each triangle must have all sides in different colours?\n\\n Options: A. only green, B. only red, C. only blue, D. either red or blue, E. The question cannot be solved.", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1126.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Circles with centers $ O$ and $ P$ have radii 2 and 4, respectively, and are externally tangent. Points $ A$ and $ B$ are on the circle centered at $ O$, and points $ C$ and $ D$ are on the circle centered at $ P$, such that $ \\overline{AD}$ and $ \\overline{BC}$ are common external tangents to the circles. What is the area of hexagon $ AOBCPD$?\n\\n Options: A. $18\\sqrt{3}$, B. $24\\sqrt{2}$, C. $36$, D. $24\\sqrt{3}$, E. $32\\sqrt{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2161.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows six identical squares, each containing a shaded region.\n How many of the regions have perimeter equal in length to the perimeter of one of the squares?", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1887.png" }, { "solution": "\\boxed{4.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The triangular plot of ACD lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the railroad runs north and south. The numbers in the diagram indicate distances in miles. The width of the railroad track can be ignored. How many square miles are in the plot of land ACD?\n", "completion": "\\boxed{4.5}", "image_path": "dataset/math_vision/images/2698.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Katrin arranges tables measuring $2 \\mathrm{~m}$ by $1 \\mathrm{~m}$ according to the number of participants in a meeting. The diagrams show the plan view for a small, a medium and a large meeting. How many tables are needed for a large meeting? ", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1968.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A collection of circles in the upper half-plane, all tangent to the $x$-axis, is constructed in layers as follows. Layer $L_0$ consists of two circles of radii $70^2$ and $73^2$ that are externally tangent. For $k\\geq 1$, the circles in $\\textstyle\\bigcup_{j=0}^{k-1} L_j$ are ordered according to their points of tangency with the $x$-axis. For every pair of consecutive circles in this order, a new circle is constructed externally tangent to each of the two circles in the pair. Layer $L_k$ consists of the $2^{k-1}$ circles constructed in this way. Let $S=\\textstyle\\bigcup_{j=0}^6 L_j$, and for every circle $C$ denote by $r(C)$ its radius. What is \\[\\sum_{C\\in S}\\frac{1}{\\sqrt{r(C)}}?\\]\n\n\\n Options: A. $\\frac{286}{35}$, B. $\\frac{583}{70}$, C. $\\frac{715}{73}$, D. $\\frac{143}{14}$, E. $\\frac{1573}{146}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2482.png" }, { "solution": "\\boxed{$\\boxed{\\frac{16}{7}}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $7$ congruent squares are arranged into a 'C,' as shown below. If the perimeter and area of the 'C' are equal (ignoring units), compute the (nonzero) side length of the squares.\\n", "completion": "\\boxed{$\\boxed{\\frac{16}{7}}$}", "image_path": "dataset/math_vision/images/2828.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Circles $A, B,$ and $C$ each have radius 1. Circles $A$ and $B$ share one point of tangency. Circle $C$ has a point of tangency with the midpoint of $\\overline{AB}$. What is the area inside Circle $C$ but outside circle $A$ and circle $B$ ?\n\n\\n Options: A. $3 - \\frac{\\pi}{2}$, B. $\\frac{\\pi}{2}$, C. $2$, D. $\\frac{3\\pi}{4}$, E. $1+\\frac{\\pi}{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2179.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Seven children stand in a circle. Nowhere are two boys found standing next to each other. Nowhere are three girls found standing next to each other. What is possible for the number of girls? The number of girls can...\n\\n Options: A. ... only be 3., B. ... be 3 or 4., C. ... be 4 or 5., D. ... only be 5., E. ... only be 4.", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/521.png" }, { "solution": "\\boxed{\\frac{1}{3}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the ratio of the area of triangle $BDC$ to the area of triangle $ADC$?\n\n", "completion": "\\boxed{\\frac{1}{3}}", "image_path": "dataset/math_vision/images/3023.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sammy has a wooden board, shaped as a rectangle with length $2^{2014}$ and height $3^{2014}$. The board is divided into a grid of unit squares. A termite starts at either the left or bottom edge of the rectangle, and walks along the gridlines by moving either to the right or upwards, until it reaches an edge opposite the one from which the termite started. Depicted below are two possible paths of the termite. The termite's path dissects the board into two parts. Sammy is surprised to find that he can still arrange the pieces to form a new rectangle not congruent to the original rectangle. This rectangle has perimeter $P$. How many possible values of $P$ are there?\\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2858.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six regular hexagons surround a regular hexagon of side length $1$ as shown. What is the area of $\\triangle ABC$?\n\n\\n Options: A. $2\\sqrt{3}$, B. $3\\sqrt{3}$, C. $1+3\\sqrt{2}$, D. $2+2\\sqrt{3}$, E. $3+2\\sqrt{3}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2198.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: At noon the minute hand of a clock is in the position shown on the left and after the quarter of an hour -- in the position shown on the right. Which position the minute hand will take after seventeen quarters from the noon?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/416.png" }, { "solution": "\\boxed{39}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mike has 125 small, equally big cubes. He glues some of them together in such a way that one big cube with exactly nine tunnels is created (see diagram). The tunnels go all the way straight through the cube. How many of the 125 cubes is he not using?\n", "completion": "\\boxed{39}", "image_path": "dataset/math_vision/images/1156.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On Nadya's smartphone, the diagram shows how much time she spent last week on four of her apps. This week she halved the time spent on two of these apps, but spent the same amount of time as the previous week on the other two apps.\n\nWhich of the following could be the diagram for this week?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1969.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $\\triangle ABC$ in the figure has area $10$. Points $D$, $E$ and $F$, all distinct from $A$, $B$ and $C$, are on sides $AB$, $BC$ and $CA$ respectively, and $AD = 2$, $DB = 3$. If triangle $\\triangle ABE$ and quadrilateral $DBEF$ have equal areas, then that area is\n\n\\n Options: A. $4$, B. $5$, C. $6$, D. $\\frac{5}{3}\\sqrt{10}$, E. $\\text{not uniquely determined}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2347.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five big and four small elephants are marching along a path. Since the path is narrow the elephants cannot change their order. At the fork in the path each elephant either goes to the right or to the left. Which of the following situations cannot happen?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/967.png" }, { "solution": "\\boxed{13.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle ABC$, medians $\\overline{AD}$ and $\\overline{CE}$ intersect at $P$, $PE=1.5$, $PD=2$, and $DE=2.5$. What is the area of $AEDC?$\n", "completion": "\\boxed{13.5}", "image_path": "dataset/math_vision/images/2190.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five sparrows on a rope look in one or the other direction (see diagram). Every sparrow whistles as many times as the number of sparrows he can see in front of him. Azra therefore whistles four times. Then one sparrow turns in the opposite direction and again all sparrows whistle according to the same rule. The second time the sparrows whistle more often in total than the first time. Which sparrow has turned around?\n\\n Options: A. Azra, B. Bernhard, C. Christa, D. David, E. Elsa", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/561.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the isosceles triangle $A B C$, points $K$ and $L$ are marked on the equal sides $A B$ and $B C$ respectively so that $A K=K L=L B$ and $K B=A C$.\n\nWhat is the size of angle $A B C$ ?\\n Options: A. $36^{\\circ}$, B. $38^{\\circ}$, C. $40^{\\circ}$, D. $42^{\\circ}$, E. $44^{\\circ}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1662.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mary had a piece of paper. She folded it exactly in half. Then she folded it exactly in half again. She got this shape . Which of the shapes P, Q or R could have been the shape of her original piece of paper?\n\\n Options: A. only P, B. only Q, C. only R, D. only P or Q, E. any of P, F. Q or R", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/945.png" }, { "solution": "\\boxed{60}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $A B C$ be a triangle with area 30. Let $D$ be any point in its interior and let $e, f$ and $g$ denote the distances from $D$ to the sides of the triangle. What is the value of the expression $5 e+12 f+13 g$?\n", "completion": "\\boxed{60}", "image_path": "dataset/math_vision/images/165.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a square with sides of length 2. Four semicircles are drawn whose centres are the four vertices of the square. These semicircles meet at the centre of the square, and adjacent semicircles meet at their ends. Four circles are drawn whose centres lie on the edges of the square and which each touch two semicircles. What is the total shaded area? \\n Options: A. $4 \\pi(3-2 \\sqrt{2})$, B. $4 \\pi \\sqrt{2}$, C. $\\frac{16}{9} \\pi$, D. $\\pi$, E. $\\frac{4}{\\sqrt{2}} \\pi$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1867.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle ABC$, $AB = 5, BC = 7, AC = 9$ and $D$ is on $\\overline{AC}$ with $BD = 5$. Find the ratio of $AD: DC$.\n\n\\n Options: A. 4:3, B. 7:5, C. 11:6, D. 13:5, E. 19:8", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2383.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the sum shown, different shapes represent different digits.\n\nWhat digit does the square represent?", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1722.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The triangle pictured is right-angled. $M$ is the midoint of the hypotenuse $\\mathrm{AB}$ and $\\angle \\mathrm{BCA}=90^{\\circ}$. How big is $\\angle \\mathrm{BMC}$?\n\\n Options: A. $105^{\\circ}$, B. $108^{\\circ}$, C. $110^{\\circ}$, D. $120^{\\circ}$, E. $125^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/226.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The ladybird would like to sit on his flower. The flower has five petals and the stem has three leaves. On which flower should the ladybird sit?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/26.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Isosceles right triangle $ ABC$ encloses a semicircle of area $ 2\\pi$. The circle has its center $ O$ on hypotenuse $ \\overline{AB}$ and is tangent to sides $ \\overline{AC}$ and $ \\overline{BC}$. What is the area of triangle $ ABC$?\n\n\\n Options: A. $6$, B. $8$, C. $3\\pi$, D. $10$, E. $4\\pi$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2668.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the small circles in the figure has radius one. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the area of the shaded region.\n\\n Options: A. $\\pi$, B. $1.5\\pi$, C. $2\\pi$, D. $3\\pi$, E. $3.5\\pi$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2118.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Old McDonald has a horse, two cows and three pigs.\n\nHow many more cows does he need, so that exactly half of all his animals are cows?", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/68.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Heinzi the kangaroo has bought some toys. For this he gave 150 Kangoo-coins (KC) and received 20 kangoo-coins back. Just before leaving the shop he changed his mind, and exchanged one of the toys he had bought with another one. Therefore he received a further 5 kangoo-coins back from the shopkeeper. Which of the toys in the picture has Heinzi taken home with him?\n\\n Options: A. Carriage and Aeroplane, B. Carriage and Bus, C. Carriage and Tram, D. Motorbike and Tram, E. Bus, F. Motorbike and Tram", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/524.png" }, { "solution": "\\boxed{34}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Dino walks from the entrance to the exit. He is only allowed to go through each room once. The rooms have numbers (see diagram). Dino adds up all the numbers of the rooms he walks through.\n\nWhat is the biggest result he can get this way?", "completion": "\\boxed{34}", "image_path": "dataset/math_vision/images/150.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the piece that fits completely to the given one to form a rectangle?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/441.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Kengu jumps on the number line to the right (see diagram). He first makes one big jump and then two little jumps in a row and keeps repeating the same thing over and over again. He starts at 0 and ends at 16. How many jumps does Kengu make in total?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/663.png" }, { "solution": "\\boxed{120}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, two circles, each with center $D$, have radii of $1$ and $2$. The total area of the shaded region is $\\frac{5}{12}$ of the area of the larger circle. How many degrees are in the measure of (the smaller) $\\angle ADC$?\n", "completion": "\\boxed{120}", "image_path": "dataset/math_vision/images/2898.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The symbols stand for one of the digits 1, 2, 3, 4 or 5. It is known that\n\nWhich symbol stands for the digit 3?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/596.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nThe square in the first diagram \"rolls\" clockwise around the fixed regular hexagon until it reaches the bottom. In which position will the solid triangle be in diagram $4$?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2527.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A unit cube has vertices $P_1, P_2, P_3, P_4, P_1', P_2', P_3'$, and $P_4'$. Vertices $P_2, P_3$, and $P_4$ are adjacent to $P_1$, and for $1\\leq i\\leq 4$, vertices $P_i$ and $P_i'$ are opposite to each other. A regular octahedron has one vertex in each of the segments $P_1P_2, P_1P_3, P_1P_4, P_1'P_2', P_1'P_3'$, and $P_1'P_4'$. What is the octahedron's side length?\n\\n Options: A. $\\frac{3\\sqrt{2}}{4}$, B. $\\frac{7\\sqrt{6}}{16}$, C. $\\frac{\\sqrt{5}}{2}$, D. $\\frac{2\\sqrt{3}}{3}$, E. $\\frac{\\sqrt{6}}{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2474.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture on the right a number should be written next to each point. The sum of the numbers on the corners of each side of the hexagon should be equal. Two numbers have already been inserted. Which number should be in the place marked '$x$'?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/234.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Renate wants to glue together a number of ordinary dice (whose number of points on opposite sides always adds up to 7) to form a \"dicebar\" as shown. Doing this she only wants to glue sides together with an equal number of points. She wants to make sure that the sum of all points on the non-glued sides equals 2012. How many dice does she have to glue together?\n\\n Options: A. 70, B. 71, C. 142, D. 143, E. It is impossible to obtain exactly 2012 points on the non-glued together sides.", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/252.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $a>b$. If the ellipse shown rotates about the $x$-axis an ellipsoid $E_{x}$ with volume $\\operatorname{Vol}\\left(E_{x}\\right)$ is obtained. If it rotates about the $y$-axis an ellipsoid $E_{y}$ with volume $\\operatorname{Vol}\\left(E_{y}\\right)$ is obtained. Which of the following statements is true?\n\\n Options: A. $\\mathrm{E}_{\\mathrm{x}}=\\mathrm{E}_{\\mathrm{y}}$ and $\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{x}}\\right)=\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{y}}\\right)$, B. $\\mathrm{E}_{\\mathrm{x}}=\\mathrm{E}_{\\mathrm{y}}$ but $\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{x}}\\right) \\neq \\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{y}}\\right)$, C. $\\mathrm{E}_{\\mathrm{x}} \\neq \\mathrm{E}_{\\mathrm{y}}$ and $\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{x}}\\right)>\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{y}}\\right)$, D. $\\mathrm{E}_{\\mathrm{x}} \\neq \\mathrm{E}_{\\mathrm{y}}$ and $\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{x}}\\right)<\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{y}}\\right)$, E. $\\mathrm{E}_{\\mathrm{x}} \\neq \\mathrm{E}_{\\mathrm{y}}$ but $\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{x}}\\right)=\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{y}}\\right)$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/253.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Adam and Bruna try to find out which is Carla's favorite figure, amongst the figures beside. Adam knows that Carla told Bruna what the shape of the figure was. Bruna knows that Carla told Adam what color the figure was. The following conversation takes place. Adam: \"I don't know what Carla's favorite figure is and I know that Bruna doesn't know either\". Bruna: \"At first I didn't know what Carla's favorite figure was, but now I know\". Adam: \"Now I know too\". What is Carla's favorite figure?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/350.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle ABC, \\angle A = 100^\\circ, \\angle B = 50^\\circ, \\angle C = 30^\\circ, \\overline{AH}$ is an altitude, and $\\overline{BM}$ is a median. Then $\\angle MHC =$\n\n\\n Options: A. $15^\\circ$, B. $22.5^\\circ$, C. $30^\\circ$, D. $40^\\circ$, E. $45^\\circ$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2381.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The rectangle shown is divided into six squares. The length of the sides of the smallest square is 1 . What is the length of the sides of the largest square? ", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/1828.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Amanda Reckonwith draws five circles with radii 1, 2, 3, 4 and 5. Then for each circle she plots the point (C; A), where C is its circumference and A is its area. Which of the following could be her graph?\\n Options: A. , B. , C. , D. , E. ", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2683.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Gerhard has the same number of white, grey and black counters. He has thrown some of these circular pieces together onto a pile. All the pieces he has used for this, can be seen in the picture. He has however, got 5 counters left that will not stay on the pile. How many black counters did he have to begin with?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/519.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One square was divided into four equal squares, containing other equal colored squares and equal colored triangles, as shown in the picture. What fraction of the original square does the colored part represent?\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{1}{2}$, C. $\\frac{4}{9}$, D. $\\frac{5}{8}$, E. $\\frac{3}{4}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1193.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five points on a circle are numbered 1,2,3,4, and 5 in clockwise order. A bug jumps in a clockwise direction from one point to another around the circle; if it is on an odd-numbered point, it moves one point, and if it is on an even-numbered point, it moves two points. If the bug begins on point 5, after 1995 jumps it will be on point\n\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2418.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three circles $C_{1}, C_{2}$ and $C_{3}$ of radii $1 \\mathrm{~cm}, 2 \\mathrm{~cm}$ and $3 \\mathrm{~cm}$ respectively touch as shown. $C_{1}$ meets $C_{2}$ at $P$ and meets $C_{3}$ at $Q$. What is the length in centimetres of the longer arc of circle $C_{1}$ between $P$ and $Q$ ? \\n Options: A. $\\frac{5 \\pi}{4}$, B. $\\frac{5 \\pi}{3}$, C. $\\frac{\\pi}{2}$, D. $\\frac{2 \\pi}{3}$, E. $\\frac{3 \\pi}{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1847.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A part of a polynomial of degree five is illegible due to an ink stain. It is known that all zeros of the polynomial are integers. What is the highest power of $x-1$ that divides this polynomial? \\n Options: A. $(x-1)^{1}$, B. $(x-1)^{2}$, C. $(x-1)^{3}$, D. $(x-1)^{4}$, E. $(x-1)^{5}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/392.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many pairs of parallel edges, such as $\\overline{AB}$ and $\\overline{GH}$ or $\\overline{EH}$ and $\\overline{FG}$, does a cube have?\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/2733.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two circles are externally tangent. Lines $\\overline{PAB}$ and $\\overline{PA'B'}$ are common tangents with $A$ and $A'$ on the smaller circle and $B$ and $B'$ on the larger circle. If $PA = AB = 4$, then the area of the smaller circle is\n\\n Options: A. $1.44\\pi$, B. $2\\pi$, C. $2.56\\pi$, D. $\\sqrt{8}\\pi$, E. $4\\pi$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2392.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A shape is made up of a triangle and a circle that partially overlap. The grey area is $45 \\%$ of the entire area of the shape. The white part of the triangle is $40 \\%$ of the total area of the shape. What percent of the area of the circle is the white part, outside the triangle?\n\\n Options: A. $20 \\%$, B. $25 \\%$, C. $30 \\%$, D. $35 \\%$, E. $50 \\%$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1236.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many triangles are in this figure? (Some triangles may overlap other triangles.)\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/2597.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The vertices of a triangle are the points of intersection of the line $y = -x-1$, the line $x=2$, and $y = \\frac{1}{5}x+\\frac{13}{5}$. Find an equation of the circle passing through all three vertices.\n\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/2957.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nChords $AB$ and $CD$ in the circle above intersect at $E$ and are perpendicular to each other. If segments $AE$, $EB$, and $ED$ have measures $2$, $3$, and $6$ respectively, then the length of the diameter of the circle is\\n Options: A. $4\\sqrt{5}$, B. $\\sqrt{65}$, C. $2\\sqrt{17}$, D. $3\\sqrt{7}$, E. $6\\sqrt{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2303.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have?\n", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/2541.png" }, { "solution": "\\boxed{-2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The point $A(3,3)$ is reflected across the $x$-axis to $A^{'}$. Then $A^{'}$ is translated two units to the left to $A^{''}$. The coordinates of $A^{''}$ are $(x,y)$. What is the value of $x+y$? ", "completion": "\\boxed{-2}", "image_path": "dataset/math_vision/images/2909.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What fraction of this square region is shaded? Stripes are equal in width, and the figure is drawn to scale.\n\n\\n Options: A. $\\frac{5}{12}$, B. $\\frac{1}{2}$, C. $\\frac{7}{12}$, D. $\\frac{2}{3}$, E. $\\frac{5}{6}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2591.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The floor of a room is covered with equally big rectangular tiles (see picture). How long is the room? \\n Options: A. $6 \\mathrm{~m}$, B. $8 \\mathrm{~m}$, C. $10 \\mathrm{~m}$, D. $11 \\mathrm{~m}$, E. $12 \\mathrm{~m}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/91.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The sums of the numbers in the white and in the grey fields should be equally big. Which two numbers have to be swapped so that the sums are equally big? \\n Options: A. 1 and 11, B. 2 and 8, C. 3 and 7, D. 4 and 13, E. 7 and 13", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/988.png" }, { "solution": "\\boxed{10100}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the length (in $\\mathrm{cm}$ ) of the line (see picture) connecting vertices $M$ and $N$ of the square?\n", "completion": "\\boxed{10100}", "image_path": "dataset/math_vision/images/709.png" }, { "solution": "\\boxed{108}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the figure. She plants one flower per square foot in each region. Asters cost $ \\$$1 each, begonias $ \\$$1.50 each, cannas $ \\$$2 each, dahlias $ \\$$2.50 each, and Easter lilies $ \\$$3 each. What is the least possible cost, in dollars, for her garden?\n", "completion": "\\boxed{108}", "image_path": "dataset/math_vision/images/2126.png" }, { "solution": "\\boxed{25\\pi}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle with center $C$ is shown. Express the area of the circle in terms of $\\pi$. ", "completion": "\\boxed{25\\pi}", "image_path": "dataset/math_vision/images/2903.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram (which $\\underline{\\text { is }}$ drawn to scale) shows two triangles. In how many ways can you choose two vertices, one in each triangle, so that the straight line through the two vertices does not cross either triangle? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1588.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which shape has the biggest area?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/478.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five identical measuring jugs are filled with water. Four of them contain exactly the same amount of water. Which measuring jug contains a different amount?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1426.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area in square units of the region enclosed by parallelogram $ABCD$ is\n\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/2546.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn this diagram semi-circles are constructed on diameters $\\overline{AB}$, $\\overline{AC}$, and $\\overline{CB}$, so that they are mutually tangent. If $\\overline{CD} \\bot \\overline{AB}$, then the ratio of the shaded area to the area of a circle with $\\overline{CD}$ as radius is:\\n Options: A. $1:2$, B. $1:3$, C. $\\sqrt{3}:7$, D. $1:4$, E. $\\sqrt{2}:6$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2288.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two $1 \\mathrm{~cm}$ long segments are marked on opposite sides of a square with side length 8 $\\mathrm{cm}$. The end points of the segments are connected with each other as shown in the diagram. How big is the area of the grey part?\n\\n Options: A. $2 \\mathrm{~cm}^{2}$, B. $4 \\mathrm{~cm}^{2}$, C. $6.4 \\mathrm{~cm}^{2}$, D. $8 \\mathrm{~cm}^{2}$, E. $10 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1152.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nGiven that all angles shown are marked, the perimeter of the polygon shown is\\n Options: A. $14$, B. $20$, C. $28$, D. $48$, E. $\\text{cannot be determined from the information given}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2512.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Julia drew the picture on the side of a cardboard sheet, cut, folded and glued to form a cube. Which of the cubes below can be the one she did?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/632.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three five-digit numbers are written onto three separate pieces of paper as shown. Three of the digits in the picture are hidden. The sum of the three numbers is 57263. Which are the hidden digits?\n\\n Options: A. 0, B. 2 and 2, C. 1, D. 2 and 9, E. 2, F. 4 and 9, G. 2, H. 7 and 8, I. 5, J. 7 and 8", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1429.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following pictures can you NOT do with all the pieces beside?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/622.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A belt can be joined together in 5 different ways.\n\nHow many $\\mathrm{cm}$ is the belt longer if it is only closed in the first hole instead of in all 5 holes?\n\\n Options: A. $4 \\mathrm{~cm}$, B. $8 \\mathrm{~cm}$, C. $10 \\mathrm{~cm}$, D. $16 \\mathrm{~cm}$, E. $20 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/597.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The square $A B C D$ has a side of length 1 and $M$ is the midpoint of $A B$. The area of the shaded region is\n\\n Options: A. $\\frac{1}{24}$, B. $\\frac{1}{16}$, C. $\\frac{1}{8}$, D. $\\frac{1}{12}$, E. $\\frac{2}{13}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/213.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two identical equilateral triangles with perimeters 18 are overlapped with their respective sides parallel. What is the perimeter of the resulting hexagon?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1295.png" }, { "solution": "\\boxed{$16 \\sqrt{3}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Equilateral triangle $ABC$ has $AD = DB = FG = AE = EC = 4$ and $BF = GC = 2$. From $D$ and $G$ are drawn perpendiculars to $EF$ intersecting at $H$ and $I$, respectively. The three polygons $ECGI$, $FGI$, and $BFHD$ are rearranged to $EANL$, $MNK$, and $AMJD$ so that the rectangle $HLKJ$ is formed. Find its area.\\n", "completion": "\\boxed{$16 \\sqrt{3}$}", "image_path": "dataset/math_vision/images/2867.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the kangaroo cards shown below can be turned around so that it then looks the same as the card shown on the right?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/45.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A triangular corner with side lengths $DB=EB=1$ is cut from equilateral triangle $ABC$ of side length $3$. The perimeter of the remaining quadrilateral is\n\n\\n Options: A. $6$, B. $6\\frac{1}{2}$, C. $7$, D. $7\\frac{1}{2}$, E. $8$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2366.png" }, { "solution": "\\boxed{160}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The population of a small town is $480$. The graph indicates the number of females and males in the town, but the vertical scale-values are omitted. How many males live in the town?\n\n", "completion": "\\boxed{160}", "image_path": "dataset/math_vision/images/2555.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime?\n\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{2}{3}$, C. $\\frac{3}{4}$, D. $\\frac{7}{9}$, E. $\\frac{5}{6}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2701.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The rectangle shown in the diagram on the right is divided into 7 squares. The sides of the grey squares on the right are all $8 \\mathrm{~cm}$ long. What is the length in $\\mathrm{cm}$ of the side of the black square? ", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/1536.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Gaspar has these seven different pieces, formed by equal little squares.\n\nHe uses all these pieces to assemble rectangles with different perimeters, that is, with different shapes. How many different perimeters can he find?", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/626.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube with side length $ 1$ is sliced by a plane that passes through two diagonally opposite vertices $ A$ and $ C$ and the midpoints $ B$ and $ D$ of two opposite edges not containing $ A$ and $ C$, ac shown. What is the area of quadrilateral $ ABCD$?\n\\n Options: A. $\\frac{\\sqrt{6}}{2}$, B. $\\frac{5}{4}$, C. $\\sqrt{2}$, D. $\\frac{3}{2}$, E. $\\sqrt{3}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2163.png" }, { "solution": "\\boxed{38}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: At each vertex of the 18 -gon in the picture a number should be written which is equal to the sum of the numbers at the two adjacent vertices. Two of the numbers are given. What number should be written at the vertex $P$ ? ", "completion": "\\boxed{38}", "image_path": "dataset/math_vision/images/1936.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle on the right is divided into 7 squares. The sides of the grey squares are all 8. What is the side of the great white square?\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/1025.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The solid shown on the right is made from two cubes. The small cube with edges $1 \\mathrm{~cm}$ long sits on top of a bigger cube with edges $3 \\mathrm{~cm}$ long. What is the surface area of the whole solid? \\n Options: A. $56 \\mathrm{~cm}^{2}$, B. $58 \\mathrm{~cm}^{2}$, C. $60 \\mathrm{~cm}^{2}$, D. $62 \\mathrm{~cm}^{2}$, E. $64 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1534.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ella wants to write a number into each circle in the diagram on the right, in such a way that each number is equal to the sum, of its two direct neighbours. Which number does Ella need to write into the circle marked with \"?\".\n\\n Options: A. -5, B. -16, C. -8, D. -3, E. This question has no solution.", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/276.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Hannes has a game board with 11 spaces. He places one coin each on eight spaces that lie next to each other. He can choose on which space to place his first coin. No matter where Hannes starts some spaces will definitely be filled. How many spaces will definitely be filled?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/557.png" }, { "solution": "\\boxed{\\frac{25}{7}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $ABCD$ be a rectangle with $AB = 20$, $BC = 15$. Let $X$ and $Y$ be on the diagonal $\\overline{BD}$ of $ABCD$ such that $BX > BY$ . Suppose $A$ and $X$ are two vertices of a square which has two sides on lines $\\overline{AB}$ and $\\overline{AD}$, and suppose that $C$ and $Y$ are vertices of a square which has sides on $\\overline{CB}$ and $\\overline{CD}$. Find the length $XY$.\\n", "completion": "\\boxed{\\frac{25}{7}}", "image_path": "dataset/math_vision/images/2847.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which one of the following bar graphs could represent the data from the circle graph?\n\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2564.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of polygon $ ABCDEF$ is 52 with $ AB=8$, $ BC=9$ and $ FA=5$. What is $ DE+EF$?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/2664.png" }, { "solution": "\\boxed{384}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure shown there are three concentric circles and two perpendicular diameters. The three shaded regions have equal area. The radius of the small circle is 2 . The product of the three radii is $Y$.\nWhat is the value of $Y^{2}$ ?\n", "completion": "\\boxed{384}", "image_path": "dataset/math_vision/images/2027.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure, CDE is an equilateral triangle and ABCD and DEFG are squares.\n\nThe measure of $\\angle GDA$ is\\n Options: A. $90^\\circ$, B. $105^\\circ$, C. $120^\\circ$, D. $135^\\circ$, E. $150^\\circ$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2331.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, an arrow pointing from one person to another means that the first person is shorter than the second. For example, person $B$ is shorter than person $A$. Which person is the tallest?\n\\n Options: A. Person A, B. Person B, C. Person C, D. Person D, E. Person E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/117.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The large rectangle shown is made up of nine identical rectangles whose longest sides are $10 \\mathrm{~cm}$ long. What is the perimeter of the large rectangle? \\n Options: A. $40 \\mathrm{~cm}$, B. $48 \\mathrm{~cm}$, C. $76 \\mathrm{~cm}$, D. $81 \\mathrm{~cm}$, E. $90 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1651.png" }, { "solution": "\\boxed{14}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure may be folded along the lines shown to form a number cube. Three number faces come together at each corner of the cube. What is the largest sum of three numbers whose faces come together at a corner?\n\n", "completion": "\\boxed{14}", "image_path": "dataset/math_vision/images/2532.png" }, { "solution": "\\boxed{441}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $P$ be an interior point of triangle $ABC$ and extend lines from the vertices through $P$ to the opposite sides. Let $a$, $b$, $c$, and $d$ denote the lengths of the segments indicated in the figure. Find the product $abc$ if $a + b + c = 43$ and $d = 3$.\n\n", "completion": "\\boxed{441}", "image_path": "dataset/math_vision/images/2048.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mike leaves home and drives slowly east through city traffic. When he reaches the highway he drives east more rapidly until he reaches the shopping mall where he stops. He shops at the mall for an hour. Mike returns home by the same route as he came, driving west rapidly along the highway and then slowly through city traffic. Each graph shows the distance from home on the vertical axis versus the time elapsed since leaving home on the horizontal axis. Which graph is the best representation of Mike's trip?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2574.png" }, { "solution": "\\boxed{\\frac{4}{3}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the volume of a pyramid whose base is one face of a cube of side length $2$, and whose apex is the center of the cube? Give your answer in simplest form.\n\n", "completion": "\\boxed{\\frac{4}{3}}", "image_path": "dataset/math_vision/images/3013.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a circle with center $ O$, $ AD$ is a diameter, $ ABC$ is a chord, $ BO = 5$, and $ \\angle ABO = \\stackrel{\\frown}{CD} = 60^{\\circ}$. Then the length of $ BC$ is:\n\n\\n Options: A. $3$, B. $3 + \\sqrt{3}$, C. $5 - \\frac{\\sqrt{3}}{2}$, D. $5$, E. $\\text{none of the above}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2357.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Evita wants to write the numbers from 1 to 8 with one number in each field. The sum of the numbers in each row should be equal. The sum of the numbers in the four columns should also be the same. She has already written in the numbers 3, 4 and 8 (see diagram). Which number does she have to write in the dark field?", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/1247.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the maximum number of $T$-shaped polyominos (shown below) that we can put into a $6 \\times 6$ grid without any overlaps. The blocks can be rotated.\\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/2845.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Clown Pipo looks like this:\n\nHe looks at himself in the mirror. Which picture does he see?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/549.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ten kangaroos stood in a line as shown in the diagram.\n\nAt a particular moment, two kangaroos standing nose-to-nose exchanged places by jumping past each other. Each of the two kangaroos involved in an exchange continued to face the same way as it did before the exchange. This was repeated until no further exchanges were possible. How many exchanges were made?", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/1645.png" }, { "solution": "\\boxed{144}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Given regular pentagon $ABCDE,$ a circle can be drawn that is tangent to $\\overline{DC}$ at $D$ and to $\\overline{AB}$ at $A.$ In degrees, what is the measure of minor arc $AD$? ", "completion": "\\boxed{144}", "image_path": "dataset/math_vision/images/2922.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure below, $ABDC,$ $EFHG,$ and $ASHY$ are all squares; $AB=EF =1$ and $AY=5$.\n\nWhat is the area of quadrilateral $DYES$?\n\n", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/2961.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the $4 \\times 4$ table some cells must be painted black. The numbers next to and below the table show how many cells in that row or column must be black. In how many ways can this table be painted?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1464.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Kirsten has written numbers into 5 of the 10 circles. She wants to write numbers into the remaining circles so that the sum of the three numbers along every side of the pentagon is always the same. Which number does she have to write into the circle marked\n$X$?\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/867.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram every of the eight kangaroos can jump to any empty square. What is the least number of kangaroos that must jump so that each row and each column have exactly two kangaroos?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/417.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The upper coin rolls without sliding around the fixed lower coin. Which position will the two coins have afterwards?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/810.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle ABC$, $M$ is the midpoint of side $BC$, $AN$ bisects $\\angle BAC$, $BN\\perp AN$ and $\\theta$ is the measure of $\\angle BAC$. If sides $AB$ and $AC$ have lengths $14$ and $19$, respectively, then length $MN$ equals\n\n\\n Options: A. $2$, B. $\\frac{5}{2}$, C. $\\frac{5}{2} - \\sin \\theta$, D. $\\frac{5}{2} - \\frac{1}{2} \\sin \\theta$, E. $\\frac{5}{2} - \\frac{1}{2} \\sin \\left(\\frac{1}{2} \\theta\\right)$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2335.png" }, { "solution": "\\boxed{11.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Zilda will use six equal cubes and two different rectangular blocks to form the structure beside with eight faces. Before gluing the pieces, she will paint each one entirely and calculated that she will need 18 liters of paint (the color does not matter). How many liters of paint would she use if she painted the whole structure only after gluing the parts?\n", "completion": "\\boxed{11.5}", "image_path": "dataset/math_vision/images/339.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram on the right shows an L-shape made from four small squares. Ria wants to add an extra small square in order to form a shape with a line of symmetry. In how many different ways can she do this? ", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1580.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Hanni wants to colour in the circles in the diagram. When two circles are connected by a line they should have different colours. What is the minimum number of colours she needs?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/692.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Picture $X$ is paired with picture $Y$. Which of the following pictures is paired with picture $G$ ?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/462.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Martina multiplies two, two-digit numbers and then paints over some of the digits. How big is the sum of the three digits that Martina has painted over?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1166.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An equilateral triangle and a regular hexagon are inscribed in a circle which is itself inscribed in an equilateral triangle. $L$ is the area of the large triangle, $S$ is the area of the smaller triangle and $H$ is the area of the hexagon. Which of these statements is true? \\n Options: A. $L=H+3 S$, B. $H=L S$, C. $H=\\frac{1}{2}(L+S)$, D. $H=L-S$, E. $H=\\sqrt{L S}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1839.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which figure can be made from the 2 pieces shown on the right?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/130.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four identical dice were put together to make a tower as shown. The sum of the numbers on opposite faces of each dice is always 7. What would the tower look like from behind?\n\n\\n Options: A. A), B. B), C. C), D. D), E. E)", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/482.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ellen wants to colour some of the cells of a $4 \\times 4$ grid. She wants to do this so that each coloured cell shares at least one side with an uncoloured cell and each uncoloured cell shares at least one side with a coloured cell.\nWhat is the largest number of cells she can colour?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1648.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The shaded region formed by the two intersecting perpendicular rectangles, in square units, is\n\n\\n Options: A. $23$, B. $38$, C. $44$, D. $46$, E. $\\text{unable to be determined from the information given}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2525.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An equilateral triangle is being rolled around a unit square as shown. How long is the path that the point shown covers, if the point and the triangle are both back at the start for the first time?\n\\n Options: A. $4 \\pi$, B. $\\frac{28}{3} \\pi$, C. $8 \\pi$, D. $\\frac{14}{3} \\pi$, E. $\\frac{21}{2} \\pi$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/254.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the figures can be cut into these 3 pieces?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/93.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers from $1$ to $49$ are arranged in a spiral pattern on a square grid, beginning at the center. The first few numbers have been entered into the grid below. Consider the four numbers that will appear in the shaded squares, on the same diagonal as the number $7$. How many of these four numbers are prime?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/2783.png" }, { "solution": "\\boxed{25}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The square $A B C D$ has area 80. The points $E, F, G$ and $H$ are on the sides of the square and $\\mathrm{AE}=\\mathrm{BF}=\\mathrm{CG}=\\mathrm{DH}$. How big is the area of the grey part, if $\\mathrm{AE}=3 \\times \\mathrm{EB}$?\n", "completion": "\\boxed{25}", "image_path": "dataset/math_vision/images/1391.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jane can walk any distance in half the time it takes Hector to walk the same distance. They set off in opposite directions around the outside of the 18-block area as shown. When they meet for the first time, they will be closest to\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2579.png" }, { "solution": "\\boxed{45}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The right pyramid shown has a square base and all eight of its edges are the same length. What is the degree measure of angle $ABD$?", "completion": "\\boxed{45}", "image_path": "dataset/math_vision/images/2981.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are seven squares in the picture. How many more triangles than squares are there in the picture?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/725.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the overlapping triangles $ \\triangle{ABC}$ and $ \\triangle{ABE}$ sharing common side $ AB$, $ \\angle{EAB}$ and $ \\angle{ABC}$ are right angles, $ AB = 4$, $ BC = 6$, $ AE = 8$, and $ \\overline{AC}$ and $ \\overline{BE}$ intersect at $ D$. What is the difference between the areas of $ \\triangle{ADE}$ and $ \\triangle{BDC}$?\n\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2457.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Every time the witch has 3 apples she turns them in to 1 banana. Every time she has 3 bananas she turns them in to 1 apple. What will she finish with if she starts with 4 apples and 5 bananas?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/133.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The graph shows the distribution of the number of children in the families of the students in Ms. Jordan's English class. The median number of children in the family for this distribution is\n\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2582.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $a, b$ and $c$ show the lengths of the different of pieces of wire pictured. Which of the following inequalities is correct?\n\\n Options: A. $a\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/137.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A shape is made by cutting all the corners off a cube, as shown in the diagram. How many edges does the shape have? ", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/1554.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: As shown in the figure below, six semicircles lie in the interior of a regular hexagon with side length $2$ so that the diameters of the semicircles coincide with the sides of the hexagon. What is the area of the shaded region—inside the hexagon but outside all of the semicircles?\n\n\\n Options: A. $6\\sqrt{3}-3\\pi$, B. $\\frac{9\\sqrt{3}}{2}-2\\pi$, C. $\\frac{3\\sqrt{3}}{2}-\\frac{\\pi}{3}$, D. $3\\sqrt{3}-\\pi \\$, E. $\\frac{9\\sqrt{3}}{2}-\\pi$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2229.png" }, { "solution": "\\boxed{44}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle{ABC}$ medians $\\overline{AD}$ and $\\overline{BE}$ intersect at $G$ and $\\triangle{AGE}$ is equilateral. Then $\\cos(C)$ can be written as $\\frac{m\\sqrtp}n$, where $m$ and $n$ are relatively prime positive integers and $p$ is a positive integer not divisible by the square of any prime. What is $m+n+p?$\n", "completion": "\\boxed{44}", "image_path": "dataset/math_vision/images/2498.png" }, { "solution": "\\boxed{293}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $ABCD$ is a rectangular sheet of paper that has been folded so that corner $B$ is matched with point $B'$ on edge $AD$. The crease is $EF$, where $E$ is on $AB$ and $F$is on $CD$. The dimensions $AE=8$, $BE=17$, and $CF=3$ are given. The perimeter of rectangle $ABCD$ is $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\n", "completion": "\\boxed{293}", "image_path": "dataset/math_vision/images/2065.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure on the right has a perimeter of $42 \\mathrm{~cm}$. The figure was made from eight equally sized squares. What is the area of the figure?\n\\n Options: A. $8 \\mathrm{~cm}^{2}$, B. $9 \\mathrm{~cm}^{2}$, C. $24 \\mathrm{~cm}^{2}$, D. $72 \\mathrm{~cm}^{2}$, E. $128 \\mathrm{~cm}^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/809.png" }, { "solution": "\\boxed{8178}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Suppose that 13 cards numbered $1, 2, 3, \\dots, 13$ are arranged in a row. The task is to pick them up in numerically increasing order, working repeatedly from left to right. In the example below, cards 1, 2, 3 are picked up on the first pass, 4 and 5 on the second pass, 6 on the third pass, 7, 8, 9, 10 on the fourth pass, and 11, 12, 13 on the fifth pass. For how many of the $13!$ possible orderings of the cards will the $13$ cards be picked up in exactly two passes?\n\n", "completion": "\\boxed{8178}", "image_path": "dataset/math_vision/images/2247.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the triangle, $\\angle A=\\angle B$. What is $x$? ", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/2986.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following objects can be obtained by rotating in space the grey object?\n\n\\n Options: A. W and Y, B. X and Z, C. Only Y, D. None of these, E. W, F. X ir Y", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1036.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $A B C, A B=6 \\mathrm{~cm}, A C=8 \\mathrm{~cm}$ and $B C=10 \\mathrm{~cm}$. $M$ is the midpoint of the side $B C$. $A M D E$ is a square and $M D$ intersects $A C$ at point $F$. What is the area of the quadrilateral $A F D E$ in $\\mathrm{cm}^{2}$?\n\\n Options: A. $\\frac{124}{8}$, B. $\\frac{125}{8}$, C. $\\frac{126}{8}$, D. $\\frac{127}{8}$, E. $\\frac{128}{8}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1386.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There used to be 5 parrots in my cage. Their average value was $€ 6000$. One day while I was cleaning out the cage the most beautiful parrot flew away. The average value of the remaining four parrots was $€ 5000$. What was the value of the parrot that escaped? \\n Options: A. $€ 1000$, B. $€ 2000$, C. $€ 5500$, D. $€ 6000$, E. $€ 10000$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1502.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $3 \\times 3 \\times 3$ cube weighs 810 grams. If we drill three holes through it as shown, each of which is a $1 \\times 1 \\times 3$ rectangular parallelepiped, the weight of the remaining solid is:\n\\n Options: A. $540 \\mathrm{~g}$, B. $570 \\mathrm{~g}$, C. $600 \\mathrm{~g}$, D. $630 \\mathrm{~g}$, E. $660 \\mathrm{~g}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/180.png" }, { "solution": "\\boxed{50}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are two different isosceles triangles whose side lengths are integers and whose areas are $120.$ One of these two triangles, $\\triangle XYZ,$ is shown. Determine the perimeter of the second triangle.\n\n", "completion": "\\boxed{50}", "image_path": "dataset/math_vision/images/2892.png" }, { "solution": "\\boxed{1144}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Teddy works at Please Forget Meat, a contemporary vegetarian pizza chain in the city of Gridtown, as a deliveryman. Please Forget Meat (PFM) has two convenient locations, marked with “$X$” and “$Y$ ” on the street map of Gridtown shown below. Teddy, who is currently at $X$, needs to deliver an eggplant pizza to $\\nabla$ en route to $Y$ , where he is urgently needed. There is currently construction taking place at $A$, $B$, and $C$, so those three intersections will be completely impassable. How many ways can Teddy get from $X$ to $Y$ while staying on the roads (Traffic tickets are expensive!), not taking paths that are longer than necessary (Gas is expensive!), and that let him pass through $\\nabla$ (Losing a job is expensive!)?\\n", "completion": "\\boxed{1144}", "image_path": "dataset/math_vision/images/2851.png" }, { "solution": "\\boxed{45}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A marble of radius 15 is rolled into a cone-shaped hole. It fits in perfectly. From the side the cone looks like an equilateral triangle. How deep is the hole?\n", "completion": "\\boxed{45}", "image_path": "dataset/math_vision/images/1348.png" }, { "solution": "\\boxed{110}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The large equilateral triangle shown consists of 36 smaller equilateral triangles. Each of the smaller equilateral triangles has area $10 \\mathrm{~cm}^{2}$.\nThe area of the shaded triangle is $K \\mathrm{~cm}^{2}$. Find $K$.\n", "completion": "\\boxed{110}", "image_path": "dataset/math_vision/images/2004.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: When you put the 4 puzzle pieces together correctly, they form a rectangle with a calculation on it. What is the result of this calculation?\n", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/642.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The \"tower\" in the diagram on the left is made up of a sqaure, a rectangle and an equlateral triangle. Each of those three shapes has the same perimeter. The side length of the square is $9 \\mathrm{~cm}$. How long is the side of the rectangle indicated?\n\\n Options: A. $4 \\mathrm{~cm}$, B. $5 \\mathrm{~cm}$, C. $6 \\mathrm{~cm}$, D. $7 \\mathrm{~cm}$, E. $8 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/775.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In circle $ O$, the midpoint of radius $ OX$ is $ Q$; at $ Q$, $ \\overline{AB} \\perp \\overline{XY}$. The semi-circle with $ \\overline{AB}$ as diameter intersects $ \\overline{XY}$ in $ M$. Line $ \\overline{AM}$ intersects circle $ O$ in $ C$, and line $ \\overline{BM}$ intersects circle $ O$ in $ D$. Line $ \\overline{AD}$ is drawn. Then, if the radius of circle $ O$ is $ r$, $ AD$ is:\n\\n Options: A. $r\\sqrt{2}$, B. $r$, C. $\\text{not a side of an inscribed regular polygon}$, D. $\\frac{r\\sqrt{3}}{2}$, E. $r\\sqrt{3}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2268.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the number pyramid shown each number is the sum of the two numbers immediately below. What number should appear in the lefthand cell of the bottom row?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1919.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rose the cat walks along the wall. She starts at point $B$ and follows the direction of the arrows shown in the picture. The cat walks a total of 20 metres. Where does she end up?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/127.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure $ TP$ and $ T'Q$ are parallel tangents to a circle of radius $ r$, with $ T$ and $ T'$ the points of tangency. $ PT''Q$ is a third tangent with $ T''$ as point of tangency. If $ TP=4$ and $ T'Q=9$ then $ r$ is\n\n\\n Options: A. $25/6$, B. $6$, C. $25/4 \\$, D. $\\text{a number other than }25/6, 6, 25/4 \\$, E. $\\text{not determinable from the given information}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2308.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The solid in the diagram is made out of 8 identical cubes. What does the solid look like when viewed from above?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/515.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A dark disc with two holes is placed on top of a dial of a watch as shown. The dark disc is now rotated so that the number 8 can be seen through one of the holes. Which of the numbers could one see through the other hole now? \\n Options: A. 4 and 12, B. 1 and 5, C. 1 and 4, D. 7 and 11, E. 5 and 12", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1241.png" }, { "solution": "\\boxed{80}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A belt is drawn tightly around three circles of radius $10$ cm each, as shown. The length of the belt, in cm, can be written in the form $a + b\\pi$ for rational numbers $a$ and $b$. What is the value of $a + b$? ", "completion": "\\boxed{80}", "image_path": "dataset/math_vision/images/2908.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Karin wants to place five bowls on a table so that they are ordered according to their weight. She has already placed the bowls $Q, R, S$ and $T$ in order, where $Q$ is lightest and $T$ is heaviest. Where does she have to place bowl Z?\n\\n Options: A. to the left of bowl Q, B. between bowls Q and R, C. between bowls R and S, D. between bowls S and T, E. to the right of bowl T", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/559.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $Q R=P S$. What is the size of $\\angle P S R$ ? \\n Options: A. $30^{\\circ}$, B. $50^{\\circ}$, C. $55^{\\circ}$, D. $65^{\\circ}$, E. $70^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1807.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each bowl has 4 balls. Add up the numbers on the balls. In which bowl is the result biggest?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/153.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Paul hangs rectangular pictures on a wall. For each picture he hammers a nail into the wall $2.5 \\mathrm{~m}$ above the floor. He ties a $2 \\mathrm{~m}$ long string to the upper corners of each picture (see diagram). which picture size (width in $\\mathrm{cm} \\times$ height in $\\mathrm{cm}$ ) has its lower edge nearest to the floor?\n\\n Options: A. $60 \\times 40$, B. $120 \\times 50$, C. $120 \\times 90$, D. $160 \\times 60$, E. $160 \\times 100$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1380.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four equally big squares are partially coloured in black. In which of the four squares is the total area of the black parts biggest?\n\\n Options: A. A, B. B, C. C, D. D, E. The total area of the black parts is always equally big.", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/891.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure below, every inscribed triangle has vertices that are on the midpoints of its circumscribed triangle's sides. If the area of the largest triangle is $64$, what is the area of the shaded region?\\n", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/2862.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A decorated glass tile is mirrored several times along the boldly printed edge. The first mirror image is shown.\n\nWhat does the tile on the far right look like after the third reflection?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/598.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Several figures can be made by attaching two equilateral triangles to the regular pentagon $ ABCDE$ in two of the five positions shown. How many non-congruent figures can be constructed in this way?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/2453.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The digits 0 to 9 can be formed using matchsticks (see diagram). How many different positive whole numbers can be formed this way with exactly 6 matchsticks? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1250.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large equilateral triangle is constructed by using toothpicks to create rows of small equilateral triangles. For example, in the figure we have $ 3$ rows of small congruent equilateral triangles, with $ 5$ small triangles in the base row. How many toothpicks would be needed to construct a large equilateral triangle if the base row of the triangle consists of $ 2003$ small equilateral triangles?\n\\n Options: A. $1,\\!004,\\!004$, B. $1,\\!005,\\!006$, C. $1,\\!507,\\!509$, D. $3,\\!015,\\!018$, E. $6,\\!021,\\!018$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2125.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lina has placed two shapes on a $5 \\times 5$ board, as shown in the picture on the right. Which of the following five shapes should she place on the empty part of the board so that none of the remaining four shapes will fit in the empty space that is left? (The shapes may be rotated or turned over, but can only be placed so that they cover complete squares.)\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1584.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the minimum number of cells of a $5 \\times 5$ grid that have to be coloured in so that every possible $1 \\times 4$ rectangle and every $4 \\times 1$ rectangle respectively in the grid has at least one cell coloured in?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1238.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The $ 8\\times 18$ rectangle $ ABCD$ is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is $ y$?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2150.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lisa needs exactly 3 pieces to complete her jigsaw.\nWhich of the 4 pieces is left over?\n\n\\n Options: A. A, B. B, C. C, D. D, E. C or D", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/79.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The word KANGAROO is written on the top side of my umbrella. Which of the following pictures does not show my umbrella?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/840.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the largest number of \" $\\mathrm{T}$ \" shaped pieces, as shown, that can be placed on the $4 \\times 5$ grid in the diagram, without any overlap of the pieces? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1793.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The square $A B C D$ has side length $3 \\mathrm{~cm}$. The points $M$ and $N$, which lie on the sides $A D$ and $A B$ respectively, are joined to the corner $C$. That way the square is split up into three parts with equal area. How long is the line segment DM?\n\\n Options: A. $0.5 \\mathrm{~cm}$, B. $1 \\mathrm{~cm}$, C. $1.5 \\mathrm{~cm}$, D. $2 \\mathrm{~cm}$, E. $2.5 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1165.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram on the right the following can be seen: a straight line, which is the common tangent of two touching circles with radius 1, and a square with one edge on the straight line and the other vertices one on each of the two circles. How big is the side length of the square?\n\\n Options: A. $\\frac{2}{5}$, B. $\\frac{1}{4}$, C. $\\frac{1}{\\sqrt{2}}$, D. $\\frac{1}{\\sqrt{5}}$, E. $\\frac{1}{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/269.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Arno lays out the word KANGAROO using 8 cards. However, some cards are turned.\n\nBy turning it twice the letter $\\mathrm{K}$ can be corrected, letter $\\mathrm{A}$ can be corrected by turning it once (see drawing). How often does he have to turn so that the word KANGAROO can be read correctly?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/829.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Different figures represent different digits. Find the digit corresponding to the square.\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/715.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are several figures that can be formed by nine squares of $1 \\mathrm{~cm}$ side by side (see an example beside) and one of them has the biggest perimeter. What is this perimeter?\n\\n Options: A. $12 \\mathrm{~cm}$, B. $14 \\mathrm{~cm}$, C. $16 \\mathrm{~cm}$, D. $18 \\mathrm{~cm}$, E. $20 \\mathrm{~cm}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1438.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $P Q R S$ and $W X Y Z$ are congruent squares. The sides $P S$ and $W Z$ are parallel. The shaded area is equal to $1 \\mathrm{~cm}^{2}$. What is the area of square $P Q R S$ ? \\n Options: A. $1 \\mathrm{~cm}^{2}$, B. $2 \\mathrm{~cm}^{2}$, C. $\\frac{1}{2} \\mathrm{~cm}^{2}$, D. $1 \\frac{1}{2} \\mathrm{~cm}^{2}$, E. $\\frac{3}{4} \\mathrm{~cm}^{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1746.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square piece of paper is folded twice into four equal quarters, as shown below, then cut along the dashed line. When unfolded, the paper will match which of the following figures?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2782.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A belt system is made up of wheels $A, B$ and $C$, which rotate without sliding. $B$ rotates 4 times around, while $A$ turns 5 times around, and $B$ rotates 6 times around, while $C$ turns 7 times around. The circumference of $C$ is $30 \\mathrm{~cm}$. How big is the circumference of $A$?\n\\n Options: A. $27 \\mathrm{~cm}$, B. $28 \\mathrm{~cm}$, C. $29 \\mathrm{~cm}$, D. $30 \\mathrm{~cm}$, E. $31 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1408.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rectangle $ABCD$, $AB=1$, $BC=2$, and points $E$, $F$, and $G$ are midpoints of $\\overline{BC}$, $\\overline{CD}$, and $\\overline{AD}$, respectively. Point $H$ is the midpoint of $\\overline{GE}$. What is the area of the shaded region?\n\n\\n Options: A. $\\frac{1}{12}$, B. $\\frac{\\sqrt{3}}{18}$, C. $\\frac{\\sqrt{2}}{12}$, D. $\\frac{\\sqrt{3}}{12}$, E. $\\frac{1}{6}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2194.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube is coloured on the outside as if it was made up of four white and four black cubes where no cubes of the same colour are next to each other (see picture). Which of the following figures represents a possible net of the coloured cube?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1369.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A small square is constructed inside a square of area 1 by dividing each side of the unit square into $n$ equal parts, and then connecting the vertices to the division points closest to the opposite vertices. Find the value of $n$ if the the area of the small square is exactly 1/1985.\n", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/2040.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows the same die in three different positions. When the die is rolled, what is the probability of rolling a 'YES'?\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{1}{2}$, C. $\\frac{5}{9}$, D. $\\frac{2}{3}$, E. $\\frac{5}{6}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1907.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Marta wants to use 16 square tiles like the one shown to form a $4 \\times 4$ square design. The tiles may be turned. Each arc bisects the sides it meets and has length $p \\mathrm{~cm}$. She is trying to make the arcs connect to make a long path. What is the length, in centimetres, of the longest possible path? \\n Options: A. $15 p$, B. $20 p$, C. $21 p$, D. $22 p$, E. $25 p$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1550.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The horizontal and vertical distances between adjacent points equal $1$ unit. The area of triangle $ABC$ is\n\n\\n Options: A. 1/4, B. 1/2, C. 3/4, D. 1, E. 5/4", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2589.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Betty keeps drawing three different figures in the same order. Which figure should be the next?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/426.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the designs shown is initially divided into squares. For how many of the designs is the total area of the shaded region equal to three-fifths of the area of the whole design?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/1749.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram alongside, the five circles have the same radii and touch as shown. The square joins the centres of the four outer circles. \nThe ratio of the area of the shaded parts of all five circles to the area of the unshaded parts of all five circles is\\n Options: A. $5: 4$, B. $2: 3$, C. $2: 5$, D. $1: 4$, E. $1: 3$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1818.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two rectangles $A B C D$ and $D B E F$ are shown in the diagram. What is the area of the rectangle $D B E F$ ? \\n Options: A. $10 \\mathrm{~cm}^{2}$, B. $12 \\mathrm{~cm}^{2}$, C. $13 \\mathrm{~cm}^{2}$, D. $14 \\mathrm{~cm}^{2}$, E. $16 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1529.png" }, { "solution": "\\boxed{540}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nThe diagram above shows the front and right-hand views of a solid made up of cubes of side $3 \\mathrm{~cm}$. The maximum volume that the solid could have is $\\mathrm{V} \\mathrm{cm}^{3}$. What is the value of $\\mathrm{V}$ ?", "completion": "\\boxed{540}", "image_path": "dataset/math_vision/images/1726.png" }, { "solution": "\\boxed{100}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the total area in $\\mathrm{cm}^{2}$ of the shaded region? ", "completion": "\\boxed{100}", "image_path": "dataset/math_vision/images/1629.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The carpenter's machine can perform two operations: $\\mathrm{P}$ and $\\mathrm{T}$. The operation $\\mathrm{P}$ is \"printing\" and $\\mathrm{T}$ is \"turning\" (see the figure). What is the right sequence of operations to obtain starting from ?\n\\n Options: A. TTP, B. PTT, C. TPT, D. TPP, E. TPTTT", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/745.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows part of a scale of a measuring device. The arrow indicates an approximate reading of\n\\n Options: A. 10.05, B. 10.15, C. 10.25, D. 10.3, E. 10.6", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2520.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: These five animals are made up from different shapes. There is one shape which is only used on one animal. On which animal is this shape used?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/142.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lucy folds a piece of paper exactly half way and then cuts out a figure:\n\nThen she unfolds the paper again. Which of the five pictures can she see?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/583.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Carolina has a box of 30 matches. She begins to make the number 2022 using matchsticks. The diagram shows the first two digits.\n\nHow many matchsticks will be left in the box when she has finished?", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1966.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $ \\triangle ABC$ points $ D$ and $ E$ lie on $ \\overline{BC}$ and $ \\overline{AC}$, respectively. If $ \\overline{AD}$ and $ \\overline{BE}$ intersect at $ T$ so that $ AT/DT = 3$ and $ BT/ET = 4$, what is $ CD/BD$?\n\\n Options: A. $\\frac{1}{8}$, B. $\\frac{2}{9}$, C. $\\frac{3}{10}$, D. $\\frac{4}{11}$, E. $\\frac{5}{12}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2141.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An equilateral triangle is originally painted black. Each time the triangle is changed, the middle fourth of each black triangle turns white. After five changes, what fractional part of the original area of the black triangle remains black?\n\n\\n Options: A. $\\frac{1}{1024}$, B. $\\frac{15}{64}$, C. $\\frac{243}{1024}$, D. $\\frac{1}{4}$, E. $\\frac{81}{256}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2552.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Circles of radius $ 2$ and $ 3$ are externally tangent and are circumscribed by a third circle, as shown in the figure. Find the area of the shaded region.\n\n\\n Options: A. $3\\pi$, B. $4\\pi$, C. $6\\pi$, D. $9\\pi$, E. $12\\pi$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2121.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The side lengths of the large regular hexagon are twice the length of those of the small regular hexagon. What is the area of the large hexagon if the small hexagon has an area of $4 \\mathrm{~cm}^{2}$?\n\\n Options: A. $16 \\mathrm{~cm}^{2}$, B. $14 \\mathrm{~cm}^{2}$, C. $12 \\mathrm{~cm}^{2}$, D. $10 \\mathrm{~cm}^{2}$, E. $8 \\mathrm{~cm}^{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1378.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria colours exactly 5 cells of this grid in grey. Then she has her 5 friends guess which cells she has coloured in and their answers are the five patterns $A, B, C, D$ and $E$. Maria looks at the patterns and says: \"One of you is right. The others have each guessed exactly four cells correctly.\" Which pattern did Maria paint?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/700.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Points $B$,$D$ , and $J$ are midpoints of the sides of right triangle $ACG$ . Points $K$, $E$, $I$ are midpoints of the sides of triangle , etc. If the dividing and shading process is done 100 times (the first three are shown) and $ AC=CG=6 $, then the total area of the shaded triangles is nearest\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2612.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nPoints $A , B, C$, and $D$ are distinct and lie, in the given order, on a straight line. Line segments $AB, AC$, and $AD$ have lengths $x, y$, and $z$ , respectively. If line segments $AB$ and $CD$ may be rotated about points $B$ and $C$, respectively, so that points $A$ and $D$ coincide, to form a triangle with positive area, then which of the following three inequalities must be satisfied?\n\n$\\textbf{I. }x<\\frac{z}{2}\\qquad\\textbf{II. }y", "completion": "\\boxed{315}", "image_path": "dataset/math_vision/images/2041.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rebecca folds a square piece of paper twice. Then she cuts off one corner as you can see in the diagram.\n\nThen she unfolds the paper. What could the paper look like now?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/695.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Kanga likes jumping on the number line. She always makes two large jumps of length 3 , followed by three small jumps of length 1 , as shown, and then repeats this over and over again. She starts jumping at 0 .\n\nWhich of these numbers will Kanga land on?\\n Options: A. 82, B. 83, C. 84, D. 85, E. 86", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1695.png" }, { "solution": "\\boxed{0}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram we can see seven sections which are bordered by three circles. One number is written into each section. It is known that each number is equal to the sum of all the numbers in the adjacent zones. (Two zones are called adjacent if they have more than one corner point in common.) Which number is written into the inner area?\n", "completion": "\\boxed{0}", "image_path": "dataset/math_vision/images/1393.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture opposite we see that $1+3+5+7=4 \\times 4$. How big is $1+3+5+7+\\ldots+17+19$?\n\\n Options: A. $10 \\times 10$, B. $11 \\times 11$, C. $12 \\times 12$, D. $13 \\times 13$, E. $14 \\times 14$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1332.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the addition problem, each digit has been replaced by a letter. If different letters represent different digits then $C=$\n\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/2550.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four of the following five diagrams can be drawn without lifting the pencil and without going over a line twice. For one diagram this is not true. Which one is it?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1180.png" }, { "solution": "\\boxed{14}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Carlos wants to put numbers in the number pyramid shown in such a way that each number above the bottom row is the sum of the two numbers immediately below it. What is the largest number of odd numbers that Carlos could put in the pyramid?\n", "completion": "\\boxed{14}", "image_path": "dataset/math_vision/images/1925.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jenny looks at her weather app that shows the predicted weather and maximum temperatures for the next five days. Which of the following represents the corresponding graph of maximum temperatures?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1451.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two squares of different sizes are drawn inside an equilateral triangle. One side of one of these squares lies on one of the sides of the triangle as shown. What is the size of the angle marked by the question mark? \\n Options: A. $25^{\\circ}$, B. $30^{\\circ}$, C. $35^{\\circ}$, D. $45^{\\circ}$, E. $50^{\\circ}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1951.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If the length of the side of a little square is 1, what is the area of the letter N?\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/401.png" }, { "solution": "\\boxed{22}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows the clown Dave dancing on top of two balls and one cubic box. The radius of the lower ball is $6 \\mathrm{dm}$, the radius of the upper ball is three times less. The side of the cubic box is $4 \\mathrm{dm}$ longer than the radius of the upper ball. At what height (in $\\mathrm{dm}$ ) above the ground is the clown Dave standing?\n", "completion": "\\boxed{22}", "image_path": "dataset/math_vision/images/703.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Nik wants to write integers in the cells of a $3 \\times 3$ table so that the sum of the numbers in any $2 \\times 2$ square is 10 . He has already written five numbers in the table as shown. What is the sum of the four missing numbers?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1875.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On the right you can see a picture of ladybird Sophie. Sophie turns. Which of the pictures below is not Sophie?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/582.png" }, { "solution": "\\boxed{110}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: This table shows the quantity of different types of flowers in the botanical garden. Ted was told by the gardener that there were 35 azaleas, 50 irises and 85 roses in the garden. What is the number of gerberas growing in the garden?\n", "completion": "\\boxed{110}", "image_path": "dataset/math_vision/images/399.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many of the hands pictured show a right hand?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/81.png" }, { "solution": "\\boxed{150}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $ABCD$ be a parallelogram with $\\angle BAD < 90^{\\circ}$. A circle tangent to sides $\\overline{DA}$, $\\overline{AB}$, and $\\overline{BC}$ intersects diagonal $\\overline{AC}$ at points $P$ and $Q$ with $AP < AQ$, as shown. Suppose that $AP = 3$, $PQ = 9$, and $QC = 16$. Then the area of $ABCD$ can be expressed in the form $m\\sqrtn$, where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n$.\n\n", "completion": "\\boxed{150}", "image_path": "dataset/math_vision/images/2100.png" }, { "solution": "\\boxed{900\\pi}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $K$, $O$ and $M$ are the centers of the three semi-circles. Also, $OC = 32$ and $CB = 36$. What is the area of the shaded region?", "completion": "\\boxed{900\\pi}", "image_path": "dataset/math_vision/images/2992.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Margie's winning art design is shown. The smallest circle has radius 2 inches, with each successive circle's radius increasing by 2 inches. Approximately what percent of the design is black?\n\n\\n Options: A. 42, B. 44, C. 45, D. 46, E. 48", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2695.png" }, { "solution": "\\boxed{\\frac{40}{3}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $ABC$ and triangle $DEF$ are congruent, isosceles right triangles. The square inscribed in triangle $ABC$ has an area of 15 square centimeters. What is the area of the square inscribed in triangle $DEF$?\n\n", "completion": "\\boxed{\\frac{40}{3}}", "image_path": "dataset/math_vision/images/3025.png" }, { "solution": "\\boxed{\\frac{3}{5}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In right triangle $XYZ$, shown below, what is $\\sin{X}$?\n\n", "completion": "\\boxed{\\frac{3}{5}}", "image_path": "dataset/math_vision/images/2980.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each letter represents a different digit, and each digit a different letter. What digit could G represent?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1294.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An ant is standing at the bottom left corner of a $3$ by $3$ grid. How many ways can it get to the top right corner if it can only move up, right, and left, and it is not allowed to cross the same edge twice?\\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/2854.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The letters $P$, $Q$, and $R$ are entered in a $20\\times 20$ grid according to the pattern shown below. How many $P$s, $Q$s, and $R$s will appear in the completed table?\n\n\\n Options: A. $132~\\text{Ps}, 134~\\text{Qs}, 134~\\text{Rs}$, B. $133~\\text{Ps}, 133~\\text{Qs}, 134~\\text{Rs}$, C. $133~\\text{Ps}, 134~\\text{Qs}, 133~\\text{Rs}$, D. $134~\\text{Ps}, 132~\\text{Qs}, 134~\\text{Rs}$, E. $134~\\text{Ps}, 133~\\text{Qs}, 133~\\text{Rs}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2789.png" }, { "solution": "\\boxed{11 }", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure consists of alternating light and dark squares.\n\nThe number of dark squares exceeds the number of light squares by", "completion": "\\boxed{11 }", "image_path": "dataset/math_vision/images/2521.png" }, { "solution": "\\boxed{150}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a grey rectangle that lies within a bigger rectangle which sides it touches. Two corner points of the grey rectangle are the midpoints of the shorter sides of the bigger rectangle. The grey rectangle is made up of three squares that each have an area of $25 \\mathrm{~cm}^{2}$. How big is the area of the bigger rectangle in $\\mathrm{cm}^{2}$ ? ", "completion": "\\boxed{150}", "image_path": "dataset/math_vision/images/1253.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle centered at $ A$ with a radius of 1 and a circle centered at $ B$ with a radius of 4 are externally tangent. A third circle is tangent to the first two and to one of their common external tangents as shown. The radius of the third circle is\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{2}{5}$, C. $\\frac{5}{12}$, D. $\\frac{4}{9}$, E. $\\frac{1}{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2445.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $4\\times 4\\times h$ rectangular box contains a sphere of radius $2$ and eight smaller spheres of radius $1$. The smaller spheres are each tangent to three sides of the box, and the larger sphere is tangent to each of the smaller spheres. What is $h$?\n\n\\n Options: A. $2+2\\sqrt{7}$, B. $3+2\\sqrt{5}$, C. $4+2\\sqrt{7}$, D. $4\\sqrt{5}$, E. $4\\sqrt{7}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2479.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An isosceles right triangle with legs of length $8$ is partitioned into $16$ congruent triangles as shown. The shaded area is\n\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/2556.png" }, { "solution": "\\boxed{3932}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks wide. How many toothpicks are used altogether?\n\n", "completion": "\\boxed{3932}", "image_path": "dataset/math_vision/images/2723.png" }, { "solution": "\\boxed{39}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In circle $O$, $\\overline{PN}$ and $\\overline{GA}$ are diameters and m$\\angle GOP=78^\\circ$. How many degrees are in the measure of $\\angle NGA$? ", "completion": "\\boxed{39}", "image_path": "dataset/math_vision/images/2979.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A ship sails $ 10$ miles in a straight line from $ A$ to $ B$, turns through an angle between $ 45^{\\circ}$ and $ 60^{\\circ}$, and then sails another $ 20$ miles to $ C$. Let $ AC$ be measured in miles. Which of the following intervals contains $ AC^2$?\n\\n Options: A. [400, B. 500], C. [500, D. 600], E. [600, F. 700], G. [700, H. 800], I. [800, J. 900]", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2469.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers from 1 to 9 are to be distributed to the nine squares in the diagram according to the following rules: There is to be one number in each square. The sum of three adjacent numbers is always a multiple of 3 . The numbers 7 and 9 are already written in. How many ways are there to insert the remaining numbers? ", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/385.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Freda wants to write a number in each of the nine cells of this figure so that the sum of the three numbers on each diameter is 13 and the sum of the eight numbers on the circumference is 40. What number must be written in the central cell? ", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1950.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram there are 7 squares. What is the difference between the number of triangles and the number of squares in the diagram? ", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1819.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two dice with volumes $V$ and $W$ intersect each other as shown. $90 \\%$ of the volume of the die with volume $V$ does not belong to both dice. $85 \\%$ of the volume of the die with volume $W$ does not belong to both dice. What is the relationship between the volumes of the two dice?\n\\n Options: A. $V=\\frac{2}{3} W$, B. $V=\\frac{3}{2} W$, C. $V=\\frac{85}{90} \\mathrm{~W}$, D. $V=\\frac{90}{85} W$, E. $V=W$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/311.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture, $A B C D$ and $E F G H$, with $A B$ parallel to $E F$, are two equal squares. The shaded area is equal to 1. What is the area of the square $A B C D$?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/753.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ahmed and Sara move from point $A$ in the direction shown with the same speed. Ahmed walks around the square garden and Sara walks around the rectangular garden. How many rounds does Ahmed have to walk to meet Sara in point $A$ again for the first time?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/676.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which pattern will you get if you join the centres of each of the neighbouring hexagons.\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/805.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A triangular pyramid is built with 10 identical balls, like this . Each ball has one of the letters A, $B, C, D$ and $E$ on it. There are 2 balls marked with each letter. The picture shows 3 side views of the pyramid. What is the letter on the ball with the question mark?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/951.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An octahedron is inscribed into a die with side length 1. The vertices of the octahedron are the midpoints of the faces of the die. How big is the volume of the octahedron?\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{1}{4}$, C. $\\frac{1}{5}$, D. $\\frac{1}{6}$, E. $\\frac{1}{8}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/313.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The graph of the function $f(x)$, defined for all real numbers, is formed by two half-lines and one segment, as illustrated in the picture. Clearly, -8 is a solution of the equation $f(f(x))=0$, because $f(f(-8))=f(-4)=0$. Find all the solutions of the equation $f(f(f(x)))=0$.\n\\n Options: A. -4 ; 0, B. -8 ;-4 ; 0, C. -12 ;-8 ;-4 ; 0, D. -16 ;-12 ;-8 ;-4 ; 0, E. No solutions", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1268.png" }, { "solution": "\\boxed{446}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We used metal rods to build this nice ensemble. We know there are 61 octagons. How many rods are there?\n", "completion": "\\boxed{446}", "image_path": "dataset/math_vision/images/214.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A tower is made up of bricks that are labelled with the numbers from 1 to 50 from bottom to top. Bob uses these bricks to build a new tower. Each time he takes the two topmost bricks off the old tower and places them down on top of the new tower without changing their order (see diagram). Which two bricks lie on top of each other when he is finished with the re-arrangement? \\n Options: A. 29 and 28, B. 34 and 35, C. 29 and 26, D. 31 and 33, E. 27 and 30", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/994.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Grey and white pearls are threaded on a piece of string.\n\nMonika wants to have 5 grey pearls. However, she can only pull off pearls from the end of the string. Therefore she has to pull off some white pearls as well. What is the minimum number of white pearls she has to pull off, to get 5 grey pearls?", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/833.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are more grey squares than white. How many more?\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/28.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows three big circles of equal size and four small circles. Each small circle touches two big circles and has radius 1. How big is the shaded area?\n\\n Options: A. $\\pi$, B. $2 \\pi$, C. $3 \\pi$, D. $4 \\pi$, E. $6 \\pi$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1472.png" }, { "solution": "\\boxed{55}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $PRT$ and $QRS$ are straight lines. What is the value of $x$? ", "completion": "\\boxed{55}", "image_path": "dataset/math_vision/images/2985.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Points $ K$, $ L$, $ M$, and $ N$ lie in the plane of the square $ ABCD$ so that $ AKB$, $ BLC$, $ CMD$, and $ DNA$ are equilateral triangles. If $ ABCD$ has an area of $ 16$, find the area of $ KLMN$.\n\n\\n Options: A. $32$, B. $16 + 16\\sqrt{3}$, C. $48$, D. $32 + 16\\sqrt{3}$, E. $64$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2451.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a square of side $s$, where $s$ is an odd integer, the squares of side 1 on the diagonals are colored (like in the picture, where the square is of side 7). How many white squares are there?\n\\n Options: A. $s^{2}+1-2 s$, B. $s^{2}+4-4 s$, C. $2 s^{2}+1-4 s$, D. $s^{2}-1-2 s$, E. $s^{2}-2 s$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/169.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Boris has a big box of building bricks. Each brick is $1 \\mathrm{~cm}$ long, $2 \\mathrm{~cm}$ wide and $3 \\mathrm{~cm}$ high. What is the smallest number of bricks he would need to build a cube? ", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/1519.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram shown, sides $P Q$ and $P R$ are equal. Also $\\angle Q P R=40^{\\circ}$ and $\\angle T Q P=\\angle S R Q$. What is the size of $\\angle T U R$ ? \\n Options: A. $55^{\\circ}$, B. $60^{\\circ}$, C. $65^{\\circ}$, D. $70^{\\circ}$, E. $75^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1711.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are five houses on Color Street: a blue, a red, a yellow, a pink, and a green one. The houses are numbered from 1 to 5 (see picture). The red house is the neighbor of the blue house only. The blue house stands between the green and red houses.\n\nWhich color is the house with number 3?\\n Options: A. Blue, B. Red, C. Yellow, D. Pink, E. Green", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/412.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: 5 friends talk about their collected . Xenia says: \"I have an even number of pins\", Zach: \"Half of my pins are planets, Sue: \"I don't have any moons\", Paul: \"I have more moons than stars\" and Yvonne: \"I have more stars than planets\". Below are the collections of the 5 friends. Which set of pins belongs to Yvonne?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1217.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square of side-length $30 \\mathrm{~cm}$ is divided into nine smaller identical squares. The large square contains three circles with radii $5 \\mathrm{~cm}$ (bottom right), $4 \\mathrm{~cm}$ (top left) and $3 \\mathrm{~cm}$ (top right), as shown. What is the total area of the shaded part? \\n Options: A. $400 \\mathrm{~cm}^{2}$, B. $500 \\mathrm{~cm}^{2}$, C. $(400+50 \\pi) \\mathrm{cm}^{2}$, D. $(500-25 \\pi) \\mathrm{cm}^{2}$, E. $(500+25 \\pi) \\mathrm{cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1986.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Laszlo went online to shop for black pepper and found thirty different black pepper options varying in weight and price, shown in the scatter plot below. In ounces, what is the weight of the pepper that offers the lowest price per ounce?\n\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/2776.png" }, { "solution": "\\boxed{54}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two identical bricks can be placed side by side in three different ways as shown in the diagrams. The surface areas of the resulting cuboids are 72, 96 and $102 \\mathrm{~cm}^{2}$. What is the surface area (in $\\mathrm{cm}^{2}$ ) of one brick?\n", "completion": "\\boxed{54}", "image_path": "dataset/math_vision/images/1234.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A bike lock has four wheels numbered with the digits 0 to 9 in order. Each of the four wheels is rotated by $180^{\\circ}$ from the code shown in the first diagram to get the correct code. What is the correct code for the bike lock?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1211.png" }, { "solution": "\\boxed{193}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangle $ABCD$ is divided into four parts of equal area by five segments as shown in the figure, where $XY = YB + BC + CZ = ZW = WD + DA + AX$, and $PQ$ is parallel to $AB$. Find the length of $AB$ (in cm) if $BC = 19$ cm and $PQ = 87$ cm.\n\n", "completion": "\\boxed{193}", "image_path": "dataset/math_vision/images/2043.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The points $A$ and $B$ lie on a circle with centre $M$. The point $P$ lies on the straight line through $A$ and $M. P B$ touches the circle in $B$. The lengths of the segments $P A$ and $M B$ are whole numbers, and $P B=P A+6$. How many possible values for $M B$ are there?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1413.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six squares are colored, front and back, (R = red, B = blue, O = orange, Y = yellow, G = green, and W = white). They are hinged together as shown, then folded to form a cube. The face opposite the white face is\n\n\\n Options: A. $\\text{B}$, B. $\\text{G}$, C. $\\text{O}$, D. $\\text{R}$, E. $\\text{Y}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2605.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $A B C$ and $C D E$ are equal equilateral triangles. If $\\angle A C D=80^{\\circ}$, what is $\\angle A B D$?\n\\n Options: A. $25^{\\circ}$, B. $30^{\\circ}$, C. $35^{\\circ}$, D. $40^{\\circ}$, E. $45^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1034.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangles $ABC$, $ADE$, and $EFG$ are all equilateral. Points $D$ and $G$ are midpoints of $\\overline{AC}$ and $\\overline{AE}$, respectively. If $AB = 4$, what is the perimeter of figure $ABCDEFG$?\n\n", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/2619.png" }, { "solution": "\\boxed{39}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sujay sees a shooting star go across the night sky, and took a picture of it. The shooting star consists of a star body, which is bounded by four quarter-circle arcs, and a triangular tail. Suppose $AB = 2$, $AC = 4$. Let the area of the shooting star be $X$. If $6X = a-b\\pi$ for positive integers $a, b$, find $a + b$.\\n", "completion": "\\boxed{39}", "image_path": "dataset/math_vision/images/2841.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One of the two sides of a rectangle has length $6 \\mathrm{~cm}$. In the rectangle circles are drawn next to each other in such a way that their centres form an equilateral triangle. What is the shortest distance between the two grey circles (in $\\mathrm{cm}$ )?\n\\n Options: A. 1, B. $\\sqrt{2}$, C. $2 \\sqrt{3}-2$, D. $\\frac{\\pi}{2}$, E. 2", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1359.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: For the game of Chess a new piece, the Kangaroo, has been invented. With each jump the kangaroo jumps either 3 squares vertically and 1 Horizontally, or 3 horizontally and 1 vertically, as pictured. What is the smallest number of jumps the kangaroo must make to move from its current position to position $\\mathrm{A}$ ?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/850.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A triangular pyramid is built with 20 cannonballs, as shown. Each cannonball is labelled with one of A, B, C, D or E. There are four cannonballs with each type of label.\n\nThe diagrams show the labels on the cannonballs on three of the faces of the pyramid. What is the label on the hidden cannonball in the middle of the fourth face?\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1691.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: This picture shows a bracelet with pearls.\n\nWhich of the bands below shows the same bracelet as above?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/63.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Alaya draws a picture of the sun. Which of the following answers is part of her picture?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/643.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria wants to write whole numbers in the squares of the figure, so that the sum of the numbers in three consecutive squares is always 10. She has already written a number. What number should she write on the gray square?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/111.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $3 \\mathrm{~cm}$ wide strip is grey on one side and white on the other. Maria folds the strip, so that it fits inside a rectangle of length $27 \\mathrm{~cm}$, as shown. The grey trapeziums are identical. What is the length of the original strip?\n\\n Options: A. $36 \\mathrm{~cm}$, B. $48 \\mathrm{~cm}$, C. $54 \\mathrm{~cm}$, D. $57 \\mathrm{~cm}$, E. $81 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1632.png" }, { "solution": "\\boxed{864}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture any letter stands for some digit (different letters for different digits, equal letters for equal digits). Find the largest possible value of the number KAN.\n", "completion": "\\boxed{864}", "image_path": "dataset/math_vision/images/1045.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure, the circle meets the sides of an equilateral triangle at six points. If $AG=2$, $GF=13$, $FC=1$, and $HJ=7$, then $DE$ equals\n\n\\n Options: A. $2\\sqrt{22}$, B. $7\\sqrt{3}$, C. $9$, D. $10$, E. $13$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2343.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: ", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/528.png" }, { "solution": "\\boxed{160}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the perimeter of the star (in centimetres) if you know that the star on the picture is formed by four equal circles with radius $5 \\mathrm{~cm}$, one square and four equilateral triangles?\n", "completion": "\\boxed{160}", "image_path": "dataset/math_vision/images/733.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram on the right shows a solid made up of 6 triangles. Each vertex is assigned a number, two of which are indicated. The total of the three numbers on each triangle is the same. What is the total of all five numbers?\n", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/1323.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, angle $P Q R$ is $20^{\\circ}$, and the reflex angle at $P$ is $330^{\\circ}$. The line segments $Q T$ and $S U$ are perpendicular. What is the size of angle RSP? \\n Options: A. $10^{\\circ}$, B. $20^{\\circ}$, C. $30^{\\circ}$, D. $40^{\\circ}$, E. $50^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1861.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of $1$ square unit, then what is the area of the shaded region, in square units?\n\n\\n Options: A. $\\frac{1}{4}$, B. $\\frac{1}{3}$, C. $\\frac{1}{2}$, D. $1$, E. $\\frac{\\pi}{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2749.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The faces of a die are either white, grey or black. Opposite faces are always a different colour. Which of the following nets does not belong to such a die?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/893.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The flag of Kangoraland is a rectangle which is split into three equal rectangles as shown. How big is the ratio of the side lengths of the white rectangle?\n\\n Options: A. $1: 2$, B. $2: 3$, C. $2: 5$, D. $3: 7$, E. $4: 9$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/322.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The shortest path from Atown to Cetown runs through Betown. Two of the signposts that can be seen on this path are shown, but one of them is broken and a number missing. What distance was written on the broken sign? \\n Options: A. $2 \\mathrm{~km}$, B. $3 \\mathrm{~km}$, C. $4 \\mathrm{~km}$, D. $5 \\mathrm{~km}$, E. $6 \\mathrm{~km}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1949.png" }, { "solution": "\\boxed{$\\frac{7^3}{2^{12} 13^2}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Adam has a circle of radius $1$ centered at the origin.\\n\\n- First, he draws $6$ segments from the origin to the boundary of the circle, which splits the upper (positive $y$) semicircle into $7$ equal pieces.\\n\\n- Next, starting from each point where a segment hit the circle, he draws an altitude to the $x$-axis.\\n\\n- Finally, starting from each point where an altitude hit the $x$-axis, he draws a segment directly away from the bottommost point of the circle $(0,-1)$, stopping when he reaches the boundary of the circle.\\n\\nWhat is the product of the lengths of all $18$ segments Adam drew?\\n", "completion": "\\boxed{$\\frac{7^3}{2^{12} 13^2}$}", "image_path": "dataset/math_vision/images/2825.png" }, { "solution": "\\boxed{71}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A beam of light strikes $\\overline{BC}$ at point $C$ with angle of incidence $\\alpha=19.94^\\circ$ and reflects with an equal angle of reflection as shown. The light beam continues its path, reflecting off line segments $\\overline{AB}$ and $\\overline{BC}$ according to the rule: angle of incidence equals angle of reflection. Given that $\\beta=\\alpha/10=1.994^\\circ$ and $AB=AC,$ determine the number of times the light beam will bounce off the two line segments. Include the first reflection at $C$ in your count.\n\n", "completion": "\\boxed{71}", "image_path": "dataset/math_vision/images/2056.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six cars are parked on a parking. Someone wants to move from $S$ to $F$. His route must be as short as possible. Which of the following routes is the shortest?\n\\n Options: A. A, B. B, C. C, D. D, E. All routes are equal", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/739.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A hen lays white and brown eggs. Lisa takes six of them and puts them in a box as shown. The brown eggs are not allowed to touch each other. What is the maximum number of brown eggs Lisa can place in the box?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/54.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The distance between two shelves in Monika's kitchen is $36 \\mathrm{~cm}$. She knows that a stack of 8 identical glasses is $42 \\mathrm{~cm}$ high and a stack of 2 such glasses is $18 \\mathrm{~cm}$ high. How many glasses has the biggest stack that will fit between two shelves?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1230.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, $AB \\perp BC$, $BC \\perp CD$, and $BC$ is tangent to the circle with center $O$ and diameter $AD$. In which one of the following cases is the area of $ABCD$ an integer?\n\n\\n Options: A. AB=3, B. CD=1, C. AB=5, D. CD=2, E. AB=7, F. CD=3, G. AB=9, H. CD=4, I. AB=11, J. CD=5", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2377.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: It takes 9 litres of paint to cover the surface of the cube on the left.\n\nHow much paint would it take to cover the surface of the shape on the right?\\n Options: A. 9 litres, B. 8 litres, C. 6 litres, D. 4 litres, E. 2 litres", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1727.png" }, { "solution": "\\boxed{540}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle is partitioned into 5 regions as shown. Each region is to be painted a solid color - red, orange, yellow, blue, or green - so that regions that touch are painted different colors, and colors can be used more than once. How many different colorings are possible?\n", "completion": "\\boxed{540}", "image_path": "dataset/math_vision/images/2244.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The outside of a $2 \\times 2 \\times 2$ cube is painted with black and white squares in such a way that it appears as if it was built using alternate black cubes and white cubes, as shown. Which of the following is a net of the painted cube?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1888.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two concentric circles with radii 1 and 9 form an annulus. $n$ circles without overlap are drawn inside this annulus, where every circle touches both circles of the annulus. (The diagram shows an example for $\\mathrm{n}=1$ and the other radii as given.) What is the biggest possible value of $n$?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1420.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Irene made a \"city\" using identical wooden cubes. We have, beside, a view from above and a side view of this \"city\". We do not know which side of the \"city\" is being shown. What is the smallest amount of cubes Irene may have used to make its assembly?\n", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/1202.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $\\textbf{Juan's Old Stamping Grounds}$\nJuan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.)\n\n\nThe average price of his '70s stamps is closest to\\n Options: A. $3.5 \\text{ cents}$, B. $4 \\text{ cents}$, C. $4.5 \\text{ cents}$, D. $5 \\text{ cents}$, E. $5.5 \\text{ cents}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2637.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four identical pieces of paper are placed as shown. Michael wants to punch a hole that goes through all four pieces. At which point should Michael punch the hole?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/122.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangle $ABCD$ has $AB=5$ and $BC=4$. Point $E$ lies on $\\overline{AB}$ so that $EB=1$, point $G$ lies on $\\overline{BC}$ so that $CG=1$. and point $F$ lies on $\\overline{CD}$ so that $DF=2$. Segments $\\overline{AG}$ and $\\overline{AC}$ intersect $\\overline{EF}$ at $Q$ and $P$, respectively. What is the value of $\\frac{PQ}{EF}$?\n\n\n\\n Options: A. $\\frac{\\sqrt{13}}{16}$, B. $\\frac{\\sqrt{2}}{13}$, C. $\\frac{9}{82}$, D. $\\frac{10}{91}$, E. $\\frac{1}{9}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2211.png" }, { "solution": "\\boxed{45}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure in the drawing consists of five isosceles right triangles of the same size. Find the area (in $\\mathrm{cm}^{2}$ ) of the shaded figure.\n", "completion": "\\boxed{45}", "image_path": "dataset/math_vision/images/711.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The multiplication uses each of the digits from 1 to 9 exactly once. What is digit $Y$?", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/756.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jane shoots two arrows at the target. In the drawing we see that her score is 5. If both arrows hit the target, how many different scores can she obtain?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/455.png" }, { "solution": "\\boxed{2400}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A bug travels from $A$ to $B$ along the segments in the hexagonal lattice pictured below. The segments marked with an arrow can be traveled only in the direction of the arrow, and the bug never travels the same segment more than once. How many different paths are there?\n\n", "completion": "\\boxed{2400}", "image_path": "dataset/math_vision/images/2187.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A regular octagon is folded three times down the middle as shown, until a triangle is formed. Then the rightmost corner is cut away. Which of the following shapes is formed when the paper is unfolded?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/813.png" }, { "solution": "\\boxed{2499}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sujay and Rishabh are taking turns marking lattice points within a square board in the Cartesian plane with opposite vertices $(1, 1)$,$(n, n)$ for some constant $n$. Sujay loses when the two-point pattern $P$ below shows up. That is, Sujay loses when there exists a pair of points $(x, y)$ and $(x + 2, y + 1)$. He and Rishabh stop marking points when the pattern $P$ appears on the board. If Rishabh goes first, let $S$ be the set of all integers $3 \\le n \\le 100$ such that Rishabh has a strategy to always trick Sujay into being the one who creates $P$. Find the sum of all elements of $S$.\\n", "completion": "\\boxed{2499}", "image_path": "dataset/math_vision/images/2840.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Using a table of a certain height, two identical blocks of wood are placed as shown in Figure 1. Length $r$ is found to be $32$ inches. After rearranging the blocks as in Figure 2, length $s$ is found to be $28$ inches. How high is the table?\n\n\\n Options: A. $28\\text{ inches}$, B. $29\\text{ inches}$, C. $30\\text{ inches}$, D. $31\\text{ inches}$, E. $32\\text{ inches}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2360.png" }, { "solution": "\\boxed{750}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the accompanying figure, the outer square has side length 40. A second square S' of side length 15 is constructed inside S with the same center as S and with sides parallel to those of S. From each midpoint of a side of S, segments are drawn to the two closest vertices of S'. The result is a four-pointed starlike figure inscribed in S. The star figure is cut out and then folded to form a pyramid with base S'. Find the volume of this pyramid.\n", "completion": "\\boxed{750}", "image_path": "dataset/math_vision/images/2079.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jack wants to keep six tubes each of diameter $2 \\mathrm{~cm}$ together using a rubber band. He chooses between the two possible variations shown. How are the lengths of the rubber bands related to each other?\n\\n Options: A. In the left picture the band is $\\pi \\mathrm{cm}$ shorter., B. In the left picture the band is $4 \\mathrm{~cm}$ shorter., C. In the right picture the band is $\\pi \\mathrm{cm}$ shorter., D. In the right picture the band is $4 \\mathrm{~cm}$ shorter., E. Both bands are equally long.", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1398.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Caroline wants to write the numbers $1,2,3,4$ in the square $4 \\times 4$ in such a way that every row and every column has each of the numbers. You see how she started. How many of the 4 numbers can be written in place of $x$?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/1010.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a square $2003 \\times 2003$, the squares $1 \\times 1$ on the diagonals are colored (like in the picture, where the square is $7 \\times 7$). How many white squares are there?\n\\n Options: A. $2002^{2}$, B. $2002 \\times 2001$, C. $2001^{2}$, D. $2003 \\times 2002$, E. $2003^{2}-2004$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1273.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The digits of the sequence $123451234512345 \\ldots$ fill the cells on a sheet of paper in a spiral-like manner beginning with the marked cell (see the figure). Which digit is written in the cell being 100 cells above the marked one?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/204.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are $4$ mirrors facing the inside of a $5\\times 7$ rectangle as shown in the figure. A ray of light comes into the inside of a rectangle through $A$ with an angle of $45^o$. When it hits the sides of the rectangle, it bounces off at the same angle, as shown in the diagram. How many times will the ray of light bounce before it reaches any one of the corners $A$, $B$, $C$, $D$? A bounce is a time when the ray hit a mirror and reflects off it.\\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/2842.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three weights are randomly placed on each tray of a beam balance. The balance dips to the right hand side as shown on the picture. The masses of the weights are 101, 102, 103, 104, 105 and 106 grams. For how many percent of the possible distributions is the 106grams-weight on the right (heavier) side?\n\\n Options: A. $75 \\%$, B. $80 \\%$, C. $90 \\%$, D. $95 \\%$, E. $100 \\%$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1412.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers from 1 to 6 are to be placed at the intersections of three circles, one number in each of the six squares. The number 6 is already placed. Which number must replace $x$, so that the sum of the four numbers on each circle is the same? ", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1959.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Olivia and a friend are playing a game of 'battleships' on a $5 \\times 5$ board. Olivia has already placed two ships as shown. She still has to place a $3 \\times 1$ ship so that it covers exactly three cells. No two ships can have a boundary point in common. How many positions are there for her $3 \\times 1$ ship? ", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/1599.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The 8 corners of the shape in the picture are to be labelled with the numbers 1, 2, 3 or 4 , so that the numbers at the ends of each of the lines shown are different. How often does the number 4 appear on the shape?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/800.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Beatriz has five sisters with ages of 2, 3, 5, 8, 10 and 17. Beatriz writes these ages in the circles of the opposite diagram, so that the sum of the ages in the four corners of the square is equal to the sum of the ages in the four circles aligned horizontally. What is this sum?\n", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/928.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three squares are placed together as shown. The lines $A E$ and $C H$ intersect at point $P$. What is the angle $\\angle C P E$?\n\\n Options: A. $30^{\\circ}$, B. $45^{\\circ}$, C. $60^{\\circ}$, D. $50^{\\circ}$, E. $40^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1291.png" }, { "solution": "\\boxed{295}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each square in this cross-number can be filled with a non-zero digit such that all of the conditions in the clues are fulfilled. The digits used are not necessarily distinct. What is the answer to 3 ACROSS?\n\n\\section*{ACROSS}\n1. A composite factor of 1001\n3. Not a palindrome\n5. $p q^{3}$ where $p, q$ prime and $p \\neq q$\n\\section*{DOWN}\n1. One more than a prime, one less than a prime\n2. A multiple of 9\n4. $p^{3} q$ using the same $p, q$ as 5 ACROSS", "completion": "\\boxed{295}", "image_path": "dataset/math_vision/images/2020.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five children should paint three quarters of the total amount of the little squares on their trays. One of the children A, B, C, D or E was wrong. Which one?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/625.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nPlacing no more than one $x$ in each small square, what is the greatest number of $x$'s that can be put on the grid shown without getting three $x$'s in a row vertically, horizontally, or diagonally?", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/2524.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Leonie has one stamp for each of the digits $0,1,2,3,4,5,6,7,8,9$. Using them, she stamps the date of the kangaroocompetition. How many of the stamps does Leonie use to do that?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/581.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which one of the domino piece's A to $E$ has to be placed in between the shown pieces, so that both calculations are correct?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/562.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The centres of the seven circles shown all lie on the same line. The four smaller circles have radius $1 \\mathrm{~cm}$. The circles touch, as shown.\n\nWhat is the total area of the shaded regions?\\n Options: A. $\\pi \\mathrm{cm}^{2}$, B. $2 \\pi \\mathrm{cm}^{2}$, C. $3 \\pi \\mathrm{cm}^{2}$, D. $4 \\pi \\mathrm{cm}^{2}$, E. $5 \\pi \\mathrm{cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1973.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What percentage of the area of the triangle is coloured in grey in the adjacent diagram?\n\\n Options: A. $80 \\%$, B. $85 \\%$, C. $88 \\%$, D. $90 \\%$, E. It cannot be calculated.", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1396.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two rays starting in $S$ form a right angle. More rays starting in $S$ are drawn within the right angle so that each angle $10^{\\circ}, 20^{\\circ}, 30^{\\circ}, 40^{\\circ}, 50^{\\circ}, 60^{\\circ}, 70^{\\circ}$ and $80^{\\circ}$ is enclosed by two rays. What is the minimum number of rays that have to be drawn? ", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1252.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sol is having fun playing with water in two tanks. Tank $X$ has a base of area of $200 \\mathrm{~cm}^{2}$.\nTank $Y$ has a base of area $100 \\mathrm{~cm}^{2}$ and height $7 \\mathrm{~cm}$. Sol has partly filled Tank X to a depth of $5 \\mathrm{~cm}$. He then places Tank Y, which is empty, on the bottom of Tank X. The water in Tank X rises, of course, and spills over into in Tank Y. What level does the water reach in Tank Y ? \\n Options: A. $1 \\mathrm{~cm}$, B. $2 \\mathrm{~cm}$, C. $3 \\mathrm{~cm}$, D. $4 \\mathrm{~cm}$, E. $5 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1811.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The big rectangle is made up of five small rectangles (see diagram). Lukas wants to colour in the small rectangles in red, blue and yellow. Two rectangles next to each other should be coloured in different colours.\n How many ways are there for Lukas to do that?", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/989.png" }, { "solution": "\\boxed{100}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The keystone arch is an ancient architectural feature. It is composed of congruent isosceles trapezoids fitted together along the non-parallel sides, as shown. The bottom sides of the two end trapezoids are horizontal. In an arch made with $ 9$ trapezoids, let $ x$ be the angle measure in degrees of the larger interior angle of the trapezoid. What is $ x$?\n", "completion": "\\boxed{100}", "image_path": "dataset/math_vision/images/2177.png" }, { "solution": "\\boxed{181}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many dots are in the picture?\n", "completion": "\\boxed{181}", "image_path": "dataset/math_vision/images/520.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows 5 cubes from the front. What do they look like from above?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/152.png" }, { "solution": "\\boxed{651}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangles $R_1$ and $R_2,$ and squares $S_1,\\,S_2,\\,$ and $S_3,$ shown below, combine to form a rectangle that is $3322$ units wide and $2020$ units high. What is the side length of $S_2$ in units?\n", "completion": "\\boxed{651}", "image_path": "dataset/math_vision/images/2771.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Linda fixes 3 photos on a pin board next to each other. She uses 8 pins to do so. Peter wants to fix 7 photos in the same way. How many pins does he need for that?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/608.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube has diagonals drawn on three adjacent faces as shown in the diagram. Which of the following nets could Usman use to make the cube shown?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1739.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nWhich cylinder has twice the volume of the cylinder shown above?\n\n\\n Options: A. A, B. B, C. C, D. D, E. None of the above", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2558.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jan sends five postcards to his friends during his holiday.\nThe card for Michael does not have ducks.\nThe card for Lexi shows a dog.\nThe card for Clara shows the sun.\nThe card for Heidi shows kangaroos.\nThe card for Paula shows exactly two animals.\nWhich card does Jan send to Michael?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/671.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A card has a diagram printed on one side and the other side is plain white. The card is first flipped over to the left and then upwards (see diagram). Which picture do you get this way?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/558.png" }, { "solution": "\\boxed{30}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anna has connected all the upper and lower points with straight lines. How many lines has she drawn?\n", "completion": "\\boxed{30}", "image_path": "dataset/math_vision/images/781.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Adam has 9 marbles and Brenda also has 9 marbles. Together they have 8 white and 10 black marbles. Brenda has twice as many black marbles as white marbles. How many black marbles does Adam have?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/697.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Werner inserts numbers in various ways into the empty squares in such a way that the calculation is correct. He always uses four of the numbers 2,3, 4, 5 or 6 where in each calculation each number is only allowed to appear once. How many of the five numbers can Werner insert into the grey square?", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/974.png" }, { "solution": "\\boxed{0}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the addition sum to the right, three digits have been replaced with stars. How big is the sum of the three missing digits?\n", "completion": "\\boxed{0}", "image_path": "dataset/math_vision/images/831.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following pieces do I need to complete the cuboid?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/794.png" }, { "solution": "\\boxed{142}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: It is possible to place positive integers into the vacant twenty-one squares of the $5 \\times 5$ square shown below so that the numbers in each row and column form arithmetic sequences. Find the number that must occupy the vacant square marked by the asterisk (*).\n\n", "completion": "\\boxed{142}", "image_path": "dataset/math_vision/images/2047.png" }, { "solution": "\\boxed{603}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a semicircle with diameter $P Q$ inscribed in a rhombus $A B C D$. The rhombus is tangent to the arc of the semicircle in two places. Points $P$ and $Q$ lie on sides $B C$ and $C D$ of the rhombus respectively. The line of symmetry of the semicircle is coincident with the diagonal $A C$ of the rhombus. It is given that $\\angle C B A=60^{\\circ}$. The semicircle has radius 10 . The area of the rhombus can be written in the form $a \\sqrt{b}$ where $a$ and $b$ are integers and $b$ is prime. What is the value of\n\n$a b+a+b ?$", "completion": "\\boxed{603}", "image_path": "dataset/math_vision/images/2014.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $\\angle 1 + \\angle 2 = 180^\\circ $\n\n$\\angle 3 = \\angle 4$\n\nFind $\\angle 4$.\n\n\\n Options: A. $20^\\circ$, B. $25^\\circ$, C. $30^\\circ$, D. $35^\\circ$, E. $40^\\circ$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2592.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The odd positive integers $1,3,5,7,\\cdots,$ are arranged into in five columns continuing with the pattern shown on the right. Counting from the left, the column in which $ 1985$ appears in is the\n\n\\n Options: A. $\\text{ first}$, B. $\\text{ second}$, C. $\\text{ third}$, D. $\\text{ fourth}$, E. $\\text{ fifth}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2354.png" }, { "solution": "\\boxed{150}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a smaller rectangle made from three squares, each of area $25 \\mathrm{~cm}^{2}$, inside a larger rectangle. Two of the vertices of the smaller rectangle lie on the mid-points of the shorter sides of the larger rectangle. The other two vertices of the smaller rectangle lie on the other two sides of the larger rectangle. What is the area, in $\\mathrm{cm}^{2}$, of the larger rectangle? ", "completion": "\\boxed{150}", "image_path": "dataset/math_vision/images/1713.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Some identical rectangles are drawn on the floor. A triangle of base $10 \\mathrm{~cm}$ and height $6 \\mathrm{~cm}$ is drawn over them, as shown, and the region inside the rectangles and outside the triangle is shaded. What is the area of the shaded region? \\n Options: A. $10 \\mathrm{~cm}^{2}$, B. $12 \\mathrm{~cm}^{2}$, C. $14 \\mathrm{~cm}^{2}$, D. $15 \\mathrm{~cm}^{2}$, E. $21 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1669.png" }, { "solution": "\\boxed{114}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A barcode as pictured is made up of alternate black and white stripes. The code always starts and ends with a black stripe. Each stripe (black or white) has the width 1 or 2 and the total width of the barcode is 12. How many different barcodes of this kind are there if one reads from left to right?\n", "completion": "\\boxed{114}", "image_path": "dataset/math_vision/images/1342.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Else has two machines R and S. If she puts a square piece of paper into machine $R$ it is rotated: \nIf she puts the piece of paper in machine $S$ it is printed on: \nShe wants to produce the following picture: \nIn which order does Else use the two machines so that she gets this picture?\n\\n Options: A. SRR, B. RSR, C. RSS, D. RRS, E. SRS", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/698.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the plane figure shown below, $3$ of the unit squares have been shaded. What is the least number of additional unit squares that must be shaded so that the resulting figure has two lines of symmetry$?$\n\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/2492.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Some mice live in three neighbouring houses. Last night, every mouse left its house and moved to one of the other two houses, always taking the shortest route. The numbers in the diagram show the number of mice per house, yesterday and today. How many mice used the path at the bottom of the diagram? ", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/1715.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three one-inch squares are palced with their bases on a line. The center square is lifted out and rotated $ 45^\\circ$, as shown. Then it is centered and lowered into its original location until it touches both of the adjoining squares. How many inches is the point $ B$ from the line on which the bases of the original squares were placed?\n\\n Options: A. $1$, B. $\\sqrt{2}$, C. $\\frac{3}{2}$, D. $\\sqrt{2} + \\frac{1}{2}$, E. $2$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2146.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Edmund cut a ribbon as shown in the picture. How many pieces of the ribbon did he finish with?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/126.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are 5 boxes and each box contains some cards labeled K, M, H, P, T, as shown below. Peter wants to remove cards out of each box so that at the end each box contained only one card, and different boxes contained cards with different letters. Which card remains in the first box?\n\\n Options: A. It is impossible to do this, B. T, C. M, D. H, E. P", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/761.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The large cube shown is made up of $27$ identical sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of smaller cubes that must have at least one face shaded is\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/2517.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large rectangle is partitioned into four rectangles by two segments parallel to its sides. The areas of three of the resulting rectangles are shown. What is the area of the fourth rectangle?\n", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/2407.png" }, { "solution": "\\boxed{42}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: By drawing 9 segments (5 horizontal and 4 vertical) one can make a table of 12 cells. How many cells can you get maximally if you draw 15 segments?\n", "completion": "\\boxed{42}", "image_path": "dataset/math_vision/images/1035.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Many Gothic cathedrals have windows with portions containing a ring of congruent circles that are circumscribed by a larger circle, In the figure shown, the number of smaller circles is four. What is the ratio of the sum of the areas of the four smaller circles to the area of the larger circle?\n\\n Options: A. $3-2\\sqrt{2}$, B. $2-\\sqrt{2}$, C. $4(3-2\\sqrt{2})$, D. $\\frac{1}{2}(3-\\sqrt{2})$, E. $2\\sqrt{2}-2$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2170.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How often in a day does a digital clock display four identical digits? The picture shows a digital clock that is displaying exactly two different digits.\n\\n Options: A. 1 time, B. 24 times, C. 3 times, D. 5 times, E. 12 times", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/481.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The scatter graph shows the distance run and time taken by five students during a training session. Who ran with the fastest average speed? \\n Options: A. Alicia, B. Bea, C. Carlos, D. Dani, E. Ernesto", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1863.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular piece of paper whose length is $\\sqrt{3}$ times the width has area $A$. The paper is divided into equal sections along the opposite lengths, and then a dotted line is drawn from the first divider to the second divider on the opposite side as shown. The paper is then folded flat along this dotted line to create a new shape with area $B$. What is the ratio $B:A$?\n\n\\n Options: A. 1:2, B. 3:5, C. 2:3, D. 3:4, E. 4:5", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2196.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Max and Moritz have drawn a square $5 \\times 5$ and marked the centres of the small squares. Afterwards, they draw obstacles and then find out in how many ways it is possible to go from $A$ to $B$ using the shortest way avoiding the obstacles and going from centre to centre only vertically and horizontally. How many shortest paths are there from $A$ to $B$ under these conditions?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1026.png" }, { "solution": "\\boxed{156}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a triangle $A B C$ with area $12 \\mathrm{~cm}^{2}$. The sides of the triangle are extended to points $P, Q, R, S, T$ and $U$ as shown so that $P A=A B=B S, Q A=A C=C T$ and $R B=B C=C U$.\n\nWhat is the area (in $\\mathrm{cm}^{2}$ ) of hexagon $P Q R S T U$ ?", "completion": "\\boxed{156}", "image_path": "dataset/math_vision/images/1995.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anna has placed matches along the dotted lines to create a path. She has placed the first match as shown in the diagram. The path is in such a way that in the end it leads back to the left end of the first match. The numbers in the small squares state how many sides of the square she has placed matches on. What is the minimum number of matches she has used?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1187.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a rectangle $A B C D$ in which $A B=1$ metre and $A D=4$ metres. The points $E$ and $G$ are the midpoints of $A D$ and $A B$ and the points $F$ and $H$ are the midpoints of $A E$ and $A G$.\n\nWhat is the area of the shaded rectangle?\\n Options: A. $\\frac{1}{16} \\mathrm{~m}^{2}$, B. $\\frac{1}{8} \\mathrm{~m}^{2}$, C. $\\frac{1}{4} \\mathrm{~m}^{2}$, D. $\\frac{1}{2} \\mathrm{~m}^{2}$, E. $1 \\mathrm{~m}^{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1731.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Points $M$ and $N$ are the midpoints of two sides of the rectangle, shown in the diagram. What fraction of the rectangle's area is shaded? \\n Options: A. $\\frac{1}{6}$, B. $\\frac{1}{5}$, C. $\\frac{1}{4}$, D. $\\frac{1}{3}$, E. $\\frac{1}{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1983.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The cube pictured on the side is intersected by a plane that passes through the three points adjacent to $A$, that is $D, E$ and $B$. In a similar way the cube is also intersected by those planes that go through the three points adjacent to each of the other seven vertices. These planes dissect the cube into several pieces. What does the piece that contains the centre of the cube look like?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/262.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five unit squares are arranged in the coordinate plane as shown, with the lower left corner at the origin. The slanted line, extending from $ (a,0)$ to $ (3,3)$, divides the entire region into two regions of equal area. What is $ a$?\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{3}{5}$, C. $\\frac{2}{3}$, D. $\\frac{3}{4}$, E. $\\frac{4}{5}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2174.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two squares $9 \\mathrm{~cm} \\times 9 \\mathrm{~cm}$ overlap so as to form a rectangle $9 \\mathrm{~cm} \\times 13 \\mathrm{~cm}$ as shown. Find the area of the region in which the two squares overlap.\n\\n Options: A. $36 \\mathrm{~cm}^{2}$, B. $45 \\mathrm{~cm}^{2}$, C. $54 \\mathrm{~cm}^{2}$, D. $63 \\mathrm{~cm}^{2}$, E. $72 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/748.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the cones listed below can be formed from a $ 252^\\circ$ sector of a circle of radius $ 10$ by aligning the two straight sides?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2115.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the grid, each small square has side of length 1 . What is the minimum distance from 'Start' to 'Finish' travelling only on edges or diagonals of the squares? \\n Options: A. $2 \\sqrt{2}$, B. $\\sqrt{10}+\\sqrt{2}$, C. $2+2 \\sqrt{2}$, D. $4 \\sqrt{2}$, E. $6$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1908.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Kelly had a paper ribbon of $27 \\mathrm{~cm}$ long. She divided it into four rectangles of different size and drew two segments both of which connected the centres of the two adjacent rectangles (see the picture). Find the sum of lengths of the two segments.\n\\n Options: A. $12 \\mathrm{~cm}$, B. $13.5 \\mathrm{~cm}$, C. $14 \\mathrm{~cm}$, D. $14.5 \\mathrm{~cm}$, E. The number depends on the division", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/747.png" }, { "solution": "\\boxed{120}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Julia wrote four positive integers, one at each vertex of a triangular base pyramid. She calculated the sum of the numbers written on the vertices of one face and the product of the numbers written on the vertices of other two faces, obtaining 15, 20 and 30, respectively. What is the highest possible value of the product of the four numbers?\n", "completion": "\\boxed{120}", "image_path": "dataset/math_vision/images/1448.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following diagrams shows the locus of the midpoint of the wheel when the wheel rolls along the zig-zag curve shown?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1920.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the smallest number of little squares that need to be painted to get at least one axis of symmetry in the picture?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/716.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On each horizontal line in the figure below, the five large dots indicate the populations of cities $A$, $B$, $C$, $D$ and $E$ in the year indicated. Which city had the greatest percentage increase in population from 1970 to 1980?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2374.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Peter has drawn the graph of a function $f: R \\rightarrow R$ which consists of two rays and a line segment as indicated on the right. How many solutions has the equation $f(f(f(x)))=0$ ?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/260.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The flag shown in the diagram consists of three stripes, each of equal height, which are divided into two, three and four equal parts, respectively. What fraction of the area of the flag is shaded? \\n Options: A. $\\frac{1}{2}$, B. $\\frac{2}{3}$, C. $\\frac{3}{5}$, D. $\\frac{4}{7}$, E. $\\frac{5}{9}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1826.png" }, { "solution": "\\boxed{19}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An archer tries his art on the target shown below on the right. With each of his three arrows he always hits the target. How many different scores could he total with three arrows?\n", "completion": "\\boxed{19}", "image_path": "dataset/math_vision/images/243.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many ropes can you see in this picture?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/51.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A mathematically skilled spider spins a cobweb and some of the strings have lengths as shown in the picture. If $x$ is an integer, determine the value of $x$.\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/200.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $|A B|=4 \\mathrm{~m},|B C|=1 \\mathrm{~m}$. $E$ is a midpoint of $A B, F$ is a midpoint of $A E, G$ is a midpoint of $A D$ and $H$ is a midpoint of $A G$. The area of the black rectangle is equal to:\n\\n Options: A. $\\frac{1}{4} \\mathrm{~m}^{2}$, B. $1 \\mathrm{~m}^{2}$, C. $\\frac{1}{8} \\mathrm{~m}^{2}$, D. $\\frac{1}{2} \\mathrm{~m}^{2} $, E. $\\frac{1}{16} \\mathrm{~m}^{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/736.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Julia folds the paper net pictured on the right, into a cube. Which number is on the face that is opposite to the face with the number 3?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/535.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square piece of paper has side length $1$ and vertices $A,B,C,$ and $D$ in that order. As shown in the figure, the paper is folded so that vertex $C$ meets edge $\\overline{AD}$ at point $C'$, and edge $\\overline{BC}$ intersects edge $\\overline{AB}$ at point $E$. Suppose that $C'D=\\frac{1}{3}$. What is the perimeter of $\\triangle AEC'$?\n\n\\n Options: A. $2$, B. $1+\\frac{2}{3}\\sqrt{3}$, C. $\\frac{13}{6}$, D. $1+\\frac{3}{4}\\sqrt{3}$, E. $\\frac{7}{3}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2241.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure below, $3$ of the $6$ disks are to be painted blue, $2$ are to be painted red, and $1$ is to be painted green. Two paintings that can be obtained from one another by a rotation or a reflection of the entire figure are considered the same. How many different paintings are possible?\n\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/2213.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Benjamin writes a number into the first circle. He then carries out the calculations as instructed and each time writes down the results in the respective circles. How many of the six numbers are divisible by 3?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/913.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The following diagonal is drawn in a regular decagon, creating an octagon and a quadrilateral. What is the measure of $x$?\n\n", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/2884.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a list of five numbers the first number is 2 and the last one is 12. The product of the first three numbers is 30 , of the middle three 90 and of the last three 360. What is the middle number in that list?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/246.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below two neighbouring squares are never allowed to have the same number. Which puzzle piece has to be placed in the gap so that this rule is followed?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/664.png" }, { "solution": "\\boxed{4045}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are eight boxes in the strip shown. Numbers in adjacent boxes have suma or $a+1$ as shown. The numbers in the first box and the eighth box are both 2021. What is the value of $a$?\n", "completion": "\\boxed{4045}", "image_path": "dataset/math_vision/images/1462.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A game marker in the shape of a regular tetrahedron has one marked area. That side is placed on the triangle marked START. The marker is then moved within the diagram always to the next adjacent triangle by rolling it around an edge. On which triangle is the marker when it is on the marked side again for the first time? \\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/391.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following is made using more than one piece of string?\n\\n Options: A. I, B. III, C. IV and V, D. I, E. III and V, F. III, G. IV and V, H. all, I. None of these answers", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1050.png" }, { "solution": "\\boxed{810}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: As shown in the figure below a regular dodecahedron (the polyhedron consisting of 12 congruent regular pentagonal faces) floats in space with two horizontal faces. Note that there is a ring of five slanted faces adjacent to the top face, and a ring of five slanted faces adjacent to the bottom face. How many ways are there to move from the top face to the bottom face via a sequence of adjacent faces so that each face is visited at most once and moves are not permitted from the bottom ring to the top ring?\n\n", "completion": "\\boxed{810}", "image_path": "dataset/math_vision/images/2227.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A flag consists of three stripes of equal width, which are divided into two, three and four equal parts, respectively. What fraction of the area of the flag is coloured grey?\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{2}{3}$, C. $\\frac{3}{5}$, D. $\\frac{4}{7}$, E. $\\frac{5}{9}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1292.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many quadrilaterals of any size are to be found in the diagram pictured.\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1105.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the trapezium $P Q R S$ the sides $P Q$ and $S R$ are parallel. Also $\\angle \\mathrm{RSP}=120^{\\circ}$ and $\\overline{R S}=\\overline{S P}=\\frac{1}{3} \\overline{P Q}$. What is the size of angle $\\angle \\mathrm{PQR}$ ?\n\\n Options: A. $15^{\\circ}$, B. $22.5^{\\circ}$, C. $25^{\\circ}$, D. $30^{\\circ}$, E. $45^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1130.png" }, { "solution": "\\boxed{392}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are two natural ways to inscribe a square in a given isosceles right triangle. If it is done as in Figure 1 below, then one finds that the area of the square is $441 \\text{cm}^2$. What is the area (in $\\text{cm}^2$) of the square inscribed in the same $\\triangle ABC$ as shown in Figure 2 below?\n", "completion": "\\boxed{392}", "image_path": "dataset/math_vision/images/2370.png" }, { "solution": "\\boxed{130}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure, two circles of radii 6 and 8 are drawn with their centers 12 units apart. At $P$, one of the points of intersection, a line is drawn in such a way that the chords $QP$ and $PR$ have equal length. Find the square of the length of $QP$.\n\n", "completion": "\\boxed{130}", "image_path": "dataset/math_vision/images/2037.png" }, { "solution": "\\boxed{180}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sohom constructs a square $BERK$ of side length $10$. Darlnim adds points $T$, $O$, $W$, and $N$, which are the midpoints of $\\overline{BE}$, $\\overline{ER}$, $\\overline{RK}$, and $\\overline{KB}$, respectively. Lastly, Sylvia constructs square $CALI$ whose edges contain the vertices of $BERK$, such that $\\overline{CA}$ is parallel to $\\overline{BO}$. Compute the area of $CALI$.\\n", "completion": "\\boxed{180}", "image_path": "dataset/math_vision/images/2809.png" }, { "solution": "\\boxed{81}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers on the faces of this cube are consecutive whole numbers. The sums of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is\n\n", "completion": "\\boxed{81}", "image_path": "dataset/math_vision/images/2539.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A kangaroo laid out 3 sticks like this to make a shape. It is not allowed to break or to bend the sticks. Which shape could the kangaroo make?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/119.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a rectangle we draw both diagonals and the segment which joins a vertex with the midpoint of one of the sides, as shown in the picture. What is the result of dividing the length of the diagonal by the length of segment $O P$?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1280.png" }, { "solution": "\\boxed{100}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square can be divided into four congruent figures as shown. For how many $n$ with $1 \\le n \\le 100$ can a unit square be divided into $n$ congruent figures?\\n", "completion": "\\boxed{100}", "image_path": "dataset/math_vision/images/2857.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $ABCD$ is rotated $20^\\circ$ clockwise about its center to obtain square $EFGH$, as shown below. What is the degree measure of $\\angle EAB$?\n\\n Options: A. $20^\\circ$, B. $30^\\circ$, C. $32^\\circ$, D. $35^\\circ$, E. $45^\\circ$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2256.png" }, { "solution": "\\boxed{$\\pi-\\tan ^{-1}\\left(\\frac{1}{d}\\right)$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two parallel lines $\\ell_1$ and $\\ell_2$ lie on a plane, distance $d$ apart. On $\\ell_1$ there are an infinite number of points $A_1, A_2, A_3, ...$ , in that order, with $A_nA_{n+1} = 2$ for all $n$. On $\\ell_2$ there are an infinite number of points $B_1, B_2, B_3,...$ , in that order and in the same direction, satisfying $B_nB_{n+1} = 1$ for all $n$. Given that $A_1B_1$ is perpendicular to both $\\ell_1$ and $\\ell_2$, express the sum $\\sum_{i=1}^{\\infty} \\angle A_iB_iA_{i+1}$ in terms of $d$.\\n", "completion": "\\boxed{$\\pi-\\tan ^{-1}\\left(\\frac{1}{d}\\right)$}", "image_path": "dataset/math_vision/images/2866.png" }, { "solution": "\\boxed{90}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangle $WXYZ$ is drawn on $\\triangle ABC$, such that point $W$ lies on segment $AB$, point $X$ lies on segment $AC$, and points $Y$ and $Z$ lies on segment $BC$, as shown. If $m\\angle BWZ=26^{\\circ}$ and $m\\angle CXY=64^{\\circ}$, what is $m\\angle BAC$, in degrees? ", "completion": "\\boxed{90}", "image_path": "dataset/math_vision/images/2999.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The kangaroo wants to visit the koala. On its way it is not allowed to jump through a square with water. Each arrow shows one jump on to a neighbouring field.\n\nWhich path is the kangaroo allowed to take?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/145.png" }, { "solution": "\\boxed{1152}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The regular octagon $ABCDEFGH$ has its center at $J$. Each of the vertices and the center are to be associated with one of the digits $1$ through $9$, with each digit used once, in such a way that the sums of the numbers on the lines $AJE$, $BJF$, $CJG$, and $DJH$ are equal. In how many ways can this be done? \n", "completion": "\\boxed{1152}", "image_path": "dataset/math_vision/images/2191.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $ABCD$ be an isosceles trapezoid with $\\overline{BC}\\parallel \\overline{AD}$ and $AB=CD$. Points $X$ and $Y$ lie on diagonal $\\overline{AC}$ with $X$ between $A$ and $Y$, as shown in the figure. Suppose $\\angle AXD = \\angle BYC = 90^\\circ$, $AX = 3$, $XY = 1$, and $YC = 2$. What is the area of $ABCD?$\n\n\\n Options: A. $15$, B. $5\\sqrt{11}$, C. $3\\sqrt{35}$, D. $18$, E. $7\\sqrt{7}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2494.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two circles are inscribed into an $11 \\mathrm{~cm}$ long and $7 \\mathrm{~cm}$ wide rectangle so that they each touch three sides of the rectangle. How big is the distance between the centres of the two circles?\n\\n Options: A. $1 \\mathrm{~cm}$, B. $2 \\mathrm{~cm}$, C. $3 \\mathrm{~cm}$, D. $4 \\mathrm{~cm}$, E. $5 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1164.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria has exactly 9 white cubes, 9 light gray cubes and 9 dark gray cubes, all the same size. She glues all these cubes together to form a larger cube. Which of the cubes below is the one she made?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/924.png" }, { "solution": "\\boxed{42}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Elsa has 3 tetrahedra and 5 dice. How many faces do these eight objects have altogether?\n", "completion": "\\boxed{42}", "image_path": "dataset/math_vision/images/1071.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, the area of each circle is $1 \\mathrm{~cm}^{2}$. The area common to any two overlapping circles is $\\frac{1}{8} \\mathrm{~cm}^{2}$. What is the area of the region covered by the five circles? \\n Options: A. $4 \\mathrm{~cm}^{2}$, B. $\\frac{9}{2} \\mathrm{~cm}^{2}$, C. $\\frac{35}{8} \\mathrm{~cm}^{2}$, D. $\\frac{39}{8} \\mathrm{~cm}^{2}$, E. $\\frac{19}{4} \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1611.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A little kangaroo draws a line passing through point $P$ of the grid and then paints three triangles in black as shown in the picture. The areas of these triangles are proportional to which numbers?\n\\n Options: A. $1: 4: 9$, B. $1: 2: 9$, C. $1: 3: 9$, D. $1: 2: 3$, E. $2: 3: 4$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/346.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four identical squares and one rectangle are placed together to form one large square as shown. The length of the rectangle is how many times as large as its width?\n\\n Options: A. $\\frac{5}{4}$, B. $\\frac{4}{3}$, C. $\\frac{3}{2}$, D. $2$, E. $3$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2178.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three equally sized equilateral triangles are cut from the vertices of a large equilateral triangle of side length $6 \\mathrm{~cm}$. The three little triangles together have the same perimeter as the remaining grey hexagon. What is the side-length of one side of one small triangle?\n\\n Options: A. $1 \\mathrm{~cm}$, B. $1.2 \\mathrm{~cm}$, C. $1.25 \\mathrm{~cm}$, D. $1.5 \\mathrm{~cm}$, E. $2 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1090.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Northside's Drum and Bugle Corps raised money for a trip. The drummers and bugle players kept separate sales records. According to the double bar graph, in what month did one group's sales exceed the other's by the greatest percent?\n\n\\n Options: A. $\\text{Jan}$, B. $\\text{Feb}$, C. $\\text{Mar}$, D. $\\text{Apr}$, E. $\\text{May}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2561.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Paulo took a rectangular sheet of paper, yellow on one side and green on the other side and, with several folds shown in the dotted lines in the figure below, made a little paper plane. To give the airplane a charm, Paulo made a circular hole, marked on the last figure.\n\nAfter playing a lot with the plane, Paulo unfolded the sheet and realized that there were several holes in it. How many holes did he count?", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/624.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $T$ has side lengths $1$, $2$, and $\\sqrt{7}$. It turns out that one can arrange three copies of triangle $T$ to form two equilateral triangles, one inside the other, as shown below. Compute the ratio of the area of the outer equilaterial triangle to the area of the inner equilateral triangle.\\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/2831.png" }, { "solution": "\\boxed{216}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shows a shape consisting of a regular hexagon of side $18 \\mathrm{~cm}$, six triangles and six squares. The outer perimeter of the shape is $P \\mathrm{~cm}$. What is the value of $P$ ?\n", "completion": "\\boxed{216}", "image_path": "dataset/math_vision/images/2007.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If $r, s$, and $t$ denote the lengths of the 'lines' in the picture, then which of the following inequalities is correct? \\n Options: A. $r\\n Options: A. 4, B. $3+\\sqrt{3}$, C. 3, D. $3+\\sqrt{2}$, E. $4+\\sqrt{3}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/288.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram $P Q R S$ is a rhombus. Point $T$ is the mid-point of $P S$ and point $W$ is the mid-point of $S R$.\n\nWhat is the ratio of the unshaded area to the shaded area?\\n Options: A. $1: 1$, B. $2: 3$, C. $3: 5$, D. $4: 7$, E. $5: 9$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1778.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nIn the diagram above there are 11 cards, each printed with two letters. The diagram below shows a rearangement of the cards, but only the top letters are shown.\n\nWhich one of the following sequences of letters could appear on the bottom row of the second diagram?\\n Options: A. ANJAMKILIOR, B. RLIIMKOJNAA, C. JANAMKILIRO, D. RAONJMILIKA, E. ANMAIKOLIRJ", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1540.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A bee called Maja wants to hike from honeycomb $X$ to honeycomb $Y$. She can only move from one honeycomb to the neighbouring honeycomb if they share an edge. How many, different ways are there for Maja to go from $X$ to $Y$ if she has to step onto every one of the seven honeycombs exactly once?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1473.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Both of the shapes shown in the diagram are formed from the same five pieces, a $5 \\mathrm{~cm}$ by $10 \\mathrm{~cm}$ rectangle, two large quarter circles and two small quarter circles. What is the difference in $\\mathrm{cm}$ between their perimeters? ", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1782.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the maximum number of such pieces that can be cut from a 5 x 5 square?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/864.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the addition sum below, $a, b$ and $c$ stand for different digits.\n\nWhat is the value of $a+b+c$ ?", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1736.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Andrew has seven pieces of wire of lengths $1 \\mathrm{~cm}, 2 \\mathrm{~cm}, 3 \\mathrm{~cm}, 4 \\mathrm{~cm}$, $5 \\mathrm{~cm}, 6 \\mathrm{~cm}$ and $7 \\mathrm{~cm}$. He bends some of the pieces to form a wire frame in the shape of a cube with edges of length $1 \\mathrm{~cm}$ without any overlaps. What is the smallest number of these pieces that he can use? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1626.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the final of a dancing competition, each of the three members of the jury gives each of the five competitors 0 points, 1 point, 2 points, 3 points or 4 points. No two competitors get the same mark from any individual judge. Adam knows all the sums of the marks and a few single marks, as shown. How many points does Adam get from judge III? ", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1682.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are five big trees and three paths in a park. It has been decided to plant a sixth tree so that there are the same number of trees on either side of each path. In which region of the park should the sixth tree be planted? \\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1696.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The fractions $\\frac{1}{3}$ and $\\frac{1}{5}$ have been placed on the\n\nnumber-line shown on the right. At which position should the fraction $\\frac{1}{4}$ be placed?\\n Options: A. $a$, B. $b$, C. $C$, D. $d$, E. $e$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1568.png" }, { "solution": "\\boxed{-\\frac{24}{25}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below, we have $\\sin \\angle RPQ = \\frac{7}{25}$. What is $\\cos \\angle RPS$?\n\n", "completion": "\\boxed{-\\frac{24}{25}}", "image_path": "dataset/math_vision/images/2915.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $ ABC$ and point $ P$ in the same plane are given. Point $ P$ is equidistant from $ A$ and $ B$, angle $ APB$ is twice angle $ ACB$, and $ \\overline{AC}$ intersects $ \\overline{BP}$ at point $ D$.\n\nIf $ PB = 3$ and $ PD = 2$, then $ AD\\cdot CD =$", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/2433.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sid is colouring the cells in the grid using the four colours red, blue, yellow and green in such a way that any two cells that share a vertex are coloured differently. He has already coloured some of the cells as shown.\nWhat colour will he use for the cell marked $X$ ?\n\\n Options: A. Red, B. Blue, C. Yellow, D. Green, E. You can't be certain", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1771.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Points $M$ and $N$ are the midpoints of sides $PA$ and $PB$ of $\\triangle PAB$. As $P$ moves along a line that is parallel to side $AB$, how many of the four quantities listed below change?\n\n$\\mathrm{a.}\\ \\text{the length of the segment} MN$\n\n$\\mathrm{b.}\\ \\text{the perimeter of }\\triangle PAB$\n\n$\\mathrm{c.}\\ \\text{ the area of }\\triangle PAB$\n\n$\\mathrm{d.}\\ \\text{ the area of trapezoid} ABNM$\n\n\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/2108.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture below you can see a road from town $M$ to town $N$ (a solid line) and a detour (a dashed line) of segment $K L$, which is under repair. How many more kilometers does one have to travel from $M$ to $N$ using the detour?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/405.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Jane, Kate and Lynn go for a walk. Jane walks at the very front, Kate in the middle and Lynn at the very back. Jane weighs $500 \\mathrm{~kg}$ more than Kate and Kate weighs $1000 \\mathrm{~kg}$ less than Lynn. Which of the following pictures shows Jane, Kate and Lynn in the right order?\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/870.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A semicircle of diameter $ 1$ sits at the top of a semicircle of diameter $ 2$, as shown. The shaded area inside the smaller semicircle and outside the larger semicircle is called a lune. Determine the area of this lune.\n\\n Options: A. $\\frac{1}{6}\\pi - \\frac{\\sqrt{3}}{4}$, B. $\\frac{\\sqrt{3}}{4} - \\frac{1}{12}\\pi$, C. $\\frac{\\sqrt{3}}{4} - \\frac{1}{24}\\pi$, D. $\\frac{\\sqrt{3}}{4} + \\frac{1}{24}\\pi$, E. $\\frac{\\sqrt{3}}{4} + \\frac{1}{12}\\pi$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2123.png" }, { "solution": "\\boxed{25}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram on the right shows a triangle $A B C$ where two lines are drawn to the opposite sides from each of the two vertices $A$ and $B$. This divides the triangle into nine non-overlapping sections. If eight lines are drawn to the opposite sides, four from $A$ and four from $B$, what is the number of nonoverlapping sections the triangle is divided into?\n", "completion": "\\boxed{25}", "image_path": "dataset/math_vision/images/1303.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sets A and B, shown in the venn diagram, have the same number of elements. Thier union has 2007 elements and their intersection has 1001 elements. Find the number of elements in A.\n\n\\n Options: A. $03$, B. $1006$, C. $504$, D. $1507$, E. $1510$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2682.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A drinking glass is made in the shape of a truncated cone. The outside of the glass (without the upper or lower circle) should be covered with coloured paper. How do you need to cut the paper to completely cover the glass without an overlap?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/273.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the quadrilateral $P Q R S$, the length of $P Q$ is $11 \\mathrm{~cm}$, the length of $Q R$ is $7 \\mathrm{~cm}$, the length of $R S$ is $9 \\mathrm{~cm}$ and the length of $S P$ is $3 \\mathrm{~cm}$. Both $\\angle Q R S$ and $\\angle S P Q$ are $90^{\\circ}$. What is the area of the quadrilateral $P Q R S$ ? \\n Options: A. $30 \\mathrm{~cm}^{2}$, B. $48 \\mathrm{~cm}^{2}$, C. $50 \\mathrm{~cm}^{2}$, D. $52 \\mathrm{~cm}^{2}$, E. $60 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1763.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What fraction of the largest square is grey?\n\\n Options: A. $\\frac{1}{4}$, B. $\\frac{1}{5}$, C. $\\frac{2}{5}$, D. $\\frac{3}{8}$, E. $\\frac{1}{3}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1052.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure below is a map showing $12$ cities and $17$ roads connecting certain pairs of cities. Paula wishes to travel along exactly $13$ of those roads, starting at city $A$ and ending at city $L,$ without traveling along any portion of a road more than once. (Paula is allowed to visit a city more than once.) How many different routes can Paula take?\n\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2489.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIf $\\triangle A_1A_2A_3$ is equilateral and $A_{n+3}$ is the midpoint of line segment $A_nA_{n+1}$ for all positive integers $n$, then the measure of $\\measuredangle A_{44}A_{45}A_{43}$ equals\\n Options: A. $30^\\circ$, B. $45^\\circ$, C. $60^\\circ$, D. $90^\\circ$, E. $120^\\circ$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2323.png" }, { "solution": "\\boxed{4028}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a shape made from six squares, each measuring $1 \\mathrm{~cm}$ by $1 \\mathrm{~cm}$. The shape has perimeter of length $14 \\mathrm{~cm}$. The zigzag shape is then continued until it has 2013 squares. What is the length, in $\\mathrm{cm}$, of the perimeter of the new shape? ", "completion": "\\boxed{4028}", "image_path": "dataset/math_vision/images/1891.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers 1 to 8 are written into the circles shown so that there is one number in each circle. Along each of the five straight arrows the three numbers in the circles are multiplied. Their product is written next to the tip of the arrow. How big is the sum of the numbers in the three circles on the lowest row of the diagram?\n", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/1237.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five line segments are drawn inside a rectangle as shown.\n\nWhat is the sum of the six marked angles?\\n Options: A. $360^{\\circ}$, B. $720^{\\circ}$, C. $900^{\\circ}$, D. $1080^{\\circ}$, E. $1120^{\\circ}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1958.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows three adjacent squares with side lengths $3 \\mathrm{~cm}, 5 \\mathrm{~cm}$ and $8 \\mathrm{~cm}$. How big is the area of the shaded in trapezium? \\n Options: A. $13 \\mathrm{~cm}^{2}$, B. $\\frac{55}{4} \\mathrm{~cm}^{2}$, C. $\\frac{61}{4} \\mathrm{~cm}^{2}$, D. $\\frac{65}{4} \\mathrm{~cm}^{2}$, E. $\\frac{69}{4} \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1488.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three triangles are connected to each other as shown. In which of the following pictures are the three triangles connected in the same way?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/325.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the minimum number of dots that must be taken away from the picture so that no three of the remaining dots lie on a straight line?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1051.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the smallest number of cells that need to be coloured in a $5 \\times 5$ square grid so that every $1 \\times 4$ or $4 \\times 1$ rectangle in the grid has at least one coloured cell? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1704.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two circles that share the same center have radii $10$ meters and $20$ meters. An aardvark runs along the path shown, starting at $A$ and ending at $K$. How many meters does the aardvark run?\n\\n Options: A. $10\\pi+20$, B. $10\\pi+30$, C. $10\\pi+40$, D. $20\\pi+20$, E. $20\\pi+40$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2691.png" }, { "solution": "\\boxed{$\\boxed{\\frac{3}{4}}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $R$ be the rectangle in the Cartesian plane with vertices at $(0,0)$, $(2,0)$, $(2,1)$, and $(0,1)$. $R$ can be divided into two unit squares, as shown. Pro selects a point $P$ at random in the interior of $R$. Find the probability that the line through $P$ with slope $\\frac{1}{2}$ will pass through both unit squares.\\n", "completion": "\\boxed{$\\boxed{\\frac{3}{4}}$}", "image_path": "dataset/math_vision/images/2877.png" }, { "solution": "\\boxed{144}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three congruent isosceles triangles $DAO$, $AOB$ and $OBC$ have $AD=AO=OB=BC=10$ and $AB=DO=OC=12$. These triangles are arranged to form trapezoid $ABCD$, as shown. Point $P$ is on side $AB$ so that $OP$ is perpendicular to $AB$.\n\n\n\nWhat is the area of trapezoid $ABCD$?", "completion": "\\boxed{144}", "image_path": "dataset/math_vision/images/2899.png" }, { "solution": "\\boxed{1150}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three flower beds overlap as shown. Bed A has 500 plants, bed B has 450 plants, and bed C has 350 plants. Beds A and B share 50 plants, while beds A and C share 100. The total number of plants is\n\n", "completion": "\\boxed{1150}", "image_path": "dataset/math_vision/images/2606.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two of the following four facts about a positive integer $N$ are true and two are false. \nWhat is the value of $N$ ?", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1764.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn the adjoining figure, $CD$ is the diameter of a semi-circle with center $O$. Point $A$ lies on the extension of $DC$ past $C$; point $E$ lies on the semi-circle, and $B$ is the point of intersection (distinct from $E$ ) of line segment $AE$ with the semi-circle. If length $AB$ equals length $OD$, and the measure of $\\measuredangle EOD$ is $45^\\circ$, then the\nmeasure of $\\measuredangle BAO$ is\\n Options: A. $10^\\circ$, B. $15^\\circ$, C. $20^\\circ$, D. $25^\\circ$, E. $30^\\circ$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2326.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In right triangle $ \\triangle ACE$, we have $ AC = 12$, $ CE = 16$, and $ EA = 20$. Points $ B$, $ D$, and $ F$ are located on $ \\overline{AC}$, $ \\overline{CE}$, and $ \\overline{EA}$, respectively, so that $ AB = 3$, $ CD = 4$, and $ EF = 5$. What is the ratio of the area of $ \\triangle DBF$ to that of $ \\triangle ACE$?\n\\n Options: A. $\\frac{1}{4}$, B. $\\frac{9}{25}$, C. $\\frac{3}{8}$, D. $\\frac{11}{25}$, E. $\\frac{7}{16}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2140.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following sentences fits to the picture?\n\\n Options: A. There are equally many circles as squares., B. There are fewer circles than triangles., C. There are twice as many circles as triangles., D. There are more squares than triangles., E. There are two more triangles than circles.", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/552.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A transparent square sheet of film lies on a table. The letter $\\mathbf{Y}$ is drawn (like this) on the sheet. We turn the sheet clockwise through $90^{\\circ}$, then turn it over what is now the left edge of the sheet, and then turn it through $180^{\\circ}$. Which figure can we now see?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1504.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consider the dark square in an array of unit squares, part of which is shown. The first ring of squares around this center square contains $ 8$ unit squares. The second ring contains $ 16$ unit squares.\n\nIf we continue this process, the number of unit squares in the $ 100^\\text{th}$ ring is\\n Options: A. $396$, B. $404$, C. $800$, D. $10,\\!000$, E. $10,\\!404$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2114.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Andrea made the pattern in the picture out of several identical tiles. None of the tiles overlap each other. Which of the following tiles could she definitely not have used?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/484.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following road signs has the most axes of symmetry?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/854.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers 1 to 9 are placed in the squares shown with a number in each square. The sums of all pairs of neighbouring numbers are shown. Which number is placed in the shaded square?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/655.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram you can see the calendar page of a certain month. Unfortunately ink has run across parts of the page. Which day of the week does the 27th of that month fall on?\n\\n Options: A. Monday, B. Wednesday, C. Thursday, D. Saturday, E. Sunday", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/306.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In square $ABCD$, points $E$ and $H$ lie on $\\overline{AB}$ and $\\overline{DA}$, respectively, so that $AE=AH$. Points $F$ and $G$ lie on $\\overline{BC}$ and $\\overline{CD}$, respectively, and points $I$ and $J$ lie on $\\overline{EH}$ so that $\\overline{FI} \\perp \\overline{EH}$ and $\\overline{GJ} \\perp \\overline{EH}$. See the figure below. Triangle $AEH$, quadrilateral $BFIE$, quadrilateral $DHJG$, and pentagon $FCGJI$ each has area $1$. What is $FI^2$?\n\\n Options: A. $\\frac{7}{3}$, B. $8-4\\sqrt{2}$, C. $1+\\sqrt{2}$, D. $\\frac{7}{4}\\sqrt{2}$, E. $2\\sqrt{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2230.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $3 \\times 4 \\times 5$ cuboid consists of 60 identical small cubes. A termite eats its way along the diagonal from $P$ to $Q$. This diagonal does not intersect the edges of any small cube inside the cuboid. How many of the small cubes does it pass through on its journey?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/1219.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers $1,2,3,4$ and 5 have to be written into the five fields of this diagram according to the following rules: If one number is below another number, it has to be greater; if one number is to the right of another, it has to be greater. How many ways are there to place the numbers?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/877.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rebecca has drawn a point on a sheet of paper. She now draws four straight lines that pass through this point. Into how many sections do these lines divide the paper?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/449.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three circles of radius $ 1$ are externally tangent to each other and internally tangent to a larger circle. What is the radius of the large circle?\n\n\\n Options: A. $\\frac{2 + \\sqrt{6}}{3}$, B. $2$, C. $\\frac{2 + 3\\sqrt{2}}{3}$, D. $\\frac{3 + 2\\sqrt{3}}{3}$, E. $\\frac{3 + \\sqrt{3}}{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2139.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram on the right we want to colour the fields with the colours A, B, C and D so that adjacent fields are always in different colours. (Even fields that share only one corner, count as adjacent.) Some fields have already been coloured in. In which colour can the grey field be coloured in?\n\\n Options: A. either A or B, B. only C, C. only D, D. either C or D, E. A, F. B, G. C or D", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/217.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nThe map shows the roundtrip that Captain Bluebear covers during his journey. Three distances are given on the map. He sails from island to island and starts at the island Berg. In total he covers a distance of $100 \\mathrm{~km}$. The distances between the islands Wüste and Wald is equal to the distance between the islands Berg and Blume via Vulkan. How big is the distance between Berg and Wald?\\n Options: A. $17 \\mathrm{~km}$, B. $23 \\mathrm{~km}$, C. $26 \\mathrm{~km}$, D. $33 \\mathrm{~km}$, E. $35 \\mathrm{~km}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/592.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The sum of the dots on opposite sides of an ordinary die is 7. Which of the following dice could be an ordinary die?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/902.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three circles with centres $A, B, C$ touch each other in pairs from the outside (see diagram). Their radii are 3,2 and 1. How big is the area of the triangle $A B C$?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/300.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The fractions $\\frac{1}{3}$ und $\\frac{1}{5}$ are shown on the number line. In which position should $\\frac{1}{4}$ be shown?\n\\n Options: A. a, B. b, C. c, D. d, E. e", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1058.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of trapezoid $ ABCD$ is $ 164 \\text{cm}^2$. The altitude is $ 8 \\text{cm}$, $ AB$ is $ 10 \\text{cm}$, and $ CD$ is $ 17 \\text{cm}$. What is $ BC$, in centimeters?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/2651.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square with side length 2 and a circle share the same center. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square. What is the radius of the circle?\n\n\\n Options: A. $\\frac{2}{\\sqrt{\\pi}}$, B. $\\frac{1+\\sqrt{2}}{2}$, C. $\\frac{3}{2}$, D. $\\sqrt{3}$, E. $\\sqrt{\\pi}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2669.png" }, { "solution": "\\boxed{19}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sheila is making a regular-hexagon-shaped sign with side length $ 1$. Let $ABCDEF$ be the regular hexagon, and let $R, S,T$ and U be the midpoints of $FA$, $BC$, $CD$ and $EF$, respectively. Sheila splits the hexagon into four regions of equal width: trapezoids $ABSR$, $RSCF$ , $FCTU$, and $UTDE$. She then paints the middle two regions gold. The fraction of the total hexagon that is gold can be written in the form $m/n$ , where m and n are relatively prime positive integers. Compute $m + n$.\\n", "completion": "\\boxed{19}", "image_path": "dataset/math_vision/images/2802.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Florian has seven pieces of wire of lengths $1 \\mathrm{~cm}, 2 \\mathrm{~cm}, 3 \\mathrm{~cm}, 4 \\mathrm{~cm}, 5 \\mathrm{~cm}, 6 \\mathrm{~cm}$ and $7 \\mathrm{~cm}$. He uses some of those pieces to form a wire model of a cube with side length 1. He does not want any overlapping wire parts. What is the smallest number of wire pieces that he can use?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1129.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $ ABCD$ has sides of length $ 4$, and $ M$ is the midpoint of $ \\overline{CD}$. A circle with radius $ 2$ and center $ M$ intersects a circle with raidus $ 4$ and center $ A$ at points $ P$ and $ D$. What is the distance from $ P$ to $ \\overline{AD}$?\n\\n Options: A. $3$, B. $\\frac{16}{5}$, C. $\\frac{13}{4}$, D. $2\\sqrt{3}$, E. $\\frac{7}{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2452.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lines drawn parallel to the base of the triangle pictured, separate the other two sides into 10 equally large parts. What percentage of the triangle is grey?\n\\n Options: A. $41.75 \\%$, B. $42.5 \\%$, C. $45 \\%$, D. $46 \\%$, E. $47.5 \\%$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1340.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Patricia drives one afternoon at a constant speed to her friend. She looks at her watch as she leaves and when she arrives.\n\nIn which position will the minute hand be when she has completed one third of her journey?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/822.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The following information is known about triangle PSQ: $\\angle Q P S=20^{\\circ}$. The triangle PSQ has been split up into two smaller triangles by the line $Q R$ as shown. It is known that $P Q=P R=Q S$. How big is the angle RQS?\n\\n Options: A. $50^{\\circ}$, B. $60^{\\circ}$, C. $65^{\\circ}$, D. $70^{\\circ}$, E. $75^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1183.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the minimum number of points which have to be removed from the adjacent diagram so that in the remaining picture no three points lie in one line?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1322.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The composite board shown in the picture consists of 44 fields $1 \\times 1$. How many possibilities are there to cover all 40 white fields with 20 rectangular stones $1 \\times 2$? (The board cannot be turned. Two possibilities are different if at least one stone lies in another way.)\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/999.png" }, { "solution": "\\boxed{14}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Paul wants to write a positive whole number onto every tile in the number wall shown, so that every number is equal to the sum of the two numbers on the tiles that are directly below. What is the maximum number of odd numbers he can write on the tiles?\n", "completion": "\\boxed{14}", "image_path": "dataset/math_vision/images/1411.png" }, { "solution": "\\boxed{150}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rectangle $ABCD$, angle $C$ is trisected by $\\overline{CF}$ and $\\overline{CE}$, where $E$ is on $\\overline{AB}$, $F$ is on $\\overline{AD}$, $BE = 6,$ and $AF = 2$. Which of the following is closest to the area of the rectangle $ABCD$?\n", "completion": "\\boxed{150}", "image_path": "dataset/math_vision/images/2424.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram one can see my decision-die in three different positions. What is the probability I get a \"YES\", when rolling this die once.\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{1}{2}$, C. $\\frac{5}{9}$, D. $\\frac{2}{3}$, E. $\\frac{5}{6}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1389.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: At a pirate school, each student had to sew a black and white flag. The condition was, that the black colour had to cover exactly three fifths of the flag. How many of the following flags fulfilled this condition?\n\\n Options: A. None, B. One, C. Two, D. Three, E. Four", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/758.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the arrow-shaped polygon [see figure], the angles at vertices $A$, $C$, $D$, $E$ and $F$ are right angles, $BC = FG = 5$, $CD = FE = 20$, $DE = 10$, and $AB = AG$. The area of the polygon is closest to\n\n\\n Options: A. 288, B. 291, C. 294, D. 297, E. 300", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2390.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A caterpillar crawled up a smooth slope from $A$ to $B$, and crept down the stairs from $B$ to $C$. What is the ratio of the distance the caterpillar travelled from $B$ to $C$ to the distance it travelled from $A$ to $B$ ? \\n Options: A. $1: 1$, B. 2:1, C. 3:1, D. $\\sqrt{2}: 1$, E. $\\sqrt{3}: 1$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1965.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the $5 \\times 5$ square shown the sum of the numbers in each row and in each column is the same. There is a number in every cell, but some of the numbers are not shown. What is the number in the cell marked with a question mark?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/356.png" }, { "solution": "\\boxed{408}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An angle is drawn on a set of equally spaced parallel lines as shown. The ratio of the area of shaded region $\\mathcal{C}$ to the area of shaded region $\\mathcal{B}$ is $11/5$. Find the ratio of shaded region $\\mathcal{D}$ to the area of shaded region $\\mathcal{A}$.\n\n", "completion": "\\boxed{408}", "image_path": "dataset/math_vision/images/2066.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An ant walks along the sides of an equilateral triangle (see diagram). Its velocity is $5 \\mathrm{~cm} / \\mathrm{min}$ along the first side, $15 \\mathrm{~cm} / \\mathrm{min}$ along the second and $20 \\mathrm{~cm} / \\mathrm{min}$ along the third. With which average velocity in $\\mathrm{cm} / \\mathrm{min}$ does the ant walk once around the entire triangle? \\n Options: A. $10$, B. $\\frac{80}{11}$, C. $\\frac{180}{19}$, D. $15$, E. $\\frac{40}{3}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1255.png" }, { "solution": "\\boxed{25}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a triangle $J K L$ where two lines are drawn from each of the vertices $J$ and $K$ to points on the opposite sides. This divides the triangle into nine nonoverlapping sections. If instead, eight lines are drawn to the opposite sides, four from $J$ and four from $K$, how many nonoverlapping sections would the triangle be divided into? ", "completion": "\\boxed{25}", "image_path": "dataset/math_vision/images/1836.png" }, { "solution": "\\boxed{19}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large cube is formed by stacking $27$ unit cubes. A plane is perpendicular to one of the internal diagonals of the large cube and bisects that diagonal. The number of unit cubes that the plane intersects is\n", "completion": "\\boxed{19}", "image_path": "dataset/math_vision/images/2422.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn triangle $ ABC$ in the adjoining figure, $ AD$ and $ AE$ trisect $ \\angle BAC$. The lengths of $ BD$, $ DE$ and $ EC$ are $ 2$, $ 3$, and $ 6$, respectively. The length of the shortest side of $ \\triangle ABC$ is\\n Options: A. $2\\sqrt{10}$, B. $11$, C. $6\\sqrt{6}$, D. $6$, E. $\\text{not uniquely determined by the given information}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2337.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are white, grey and black squares. Three children use these to make this pattern.\n\nFirst Anni replaces all black squares with white squares.\nThen Bob replaces all grey squares with black squares.\nFinally Chris replaces all white squares with grey squares.\nWhich picture have the three children now created?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/95.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Some of the small squares on each of the square transparencies have been coloured black. If you slide the three transparencies on top of each other, without lifting them from the table, a new pattern can be seen. What is the maximum number of black squares which could be seen in the new pattern?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/541.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square flag has a red cross of uniform width with a blue square in the center on a white background as shown. (The cross is symmetric with respect to each of the diagonals of the square.) If the entire cross (both the red arms and the blue center) takes up $36\\%$ of the area of the flag, what percent of the area of the flag is blue?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/2384.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $ABCD$ has sides of length 3. Segments $CM$ and $CN$ divide the square's area into three equal parts. How long is segment $CM$ ?\n\n\\n Options: A. $\\sqrt{10}$, B. $\\sqrt{12}$, C. $\\sqrt{13}$, D. $\\sqrt{14}$, E. $\\sqrt{15}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2611.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: You can make only one rectangle with the perimeter consisting of 6 matches (see the picture). How many different rectangles with the perimeter consisting of 14 matches can you compose?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/421.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four identical dice are arranged in a row (see the fig.).\n\nEach dice has faces with 1, 2, 3, 4, 5 and 6 points, but the dice are not standard, i.e., the sum of the points on the opposite faces of the dice is not necessarily equal to 7. What is the total sum of the points in all the 6 touching faces of the dice?", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1046.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The dartboard shown consists of an inner black circle and 2 rings around it. The width of each ring is equal to the radius of the black circle. How many times greater is the area of the grey ring than the area of the inner black circle?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1274.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Carl built the shape shown using seven unit cubes. How many such cubes does he have to add to make a cube with edges of length 3 ? ", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1610.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the children Ali, Lea, Josef, Vittorio and Sophie get a birthday cake. The number on top of the cake shows how old the child is. Lea is two years older than Josef, but one year younger than Ali. Vittorio is the youngest. Which cake belongs to Sophie?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/162.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The Kangaroo Hotel has 30 floors numbered from 1 to 30 and each floor has 20 rooms numbered from 1 to 20. The code to enter the room is formed by joining the floor number with the room number, in that order. But this code can be confusing, as shown in the picture. Note that the code 101 is not confusing, as it can only refer to floor 10 and room 1 and never to floor 1 and room 1, as it has the code 11. How many codes are confusing, including the one in the figure?\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/639.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Max wants to complete the jigsaw shown. He has different pieces.\n\nWhich pieces does he have to use?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/160.png" }, { "solution": "\\boxed{1536}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On the $8 \\times 8$ board beside, in how many ways can you place two chips, one green and one red, in different colored cells, so that the chips are not in the same row or in the same column of the board?\n", "completion": "\\boxed{1536}", "image_path": "dataset/math_vision/images/1450.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A paper in the shape of a regular hexagon, as the one shown, is folded in such a way that the three marked corners touch each other at the centre of the hexagon. What is the obtained figure?\n\\n Options: A. Six corner star, B. Dodecagon, C. Hexagon, D. Square, E. Triangle", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/734.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Zilda took a square sheet of paper of side 1 and made two folds taking two consecutive sides of the sheet to a diagonal of it, as shown in the picture, obtaining a quadrilateral (highlighted outline). What is the area of this quadrilateral?\n\\n Options: A. $\\frac{7}{10}$, B. $2-\\sqrt{2}$, C. $\\frac{3}{5}$, D. $\\sqrt{2}-1$, E. $\\frac{\\sqrt{2}}{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1204.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, $\\triangle ABC$ has $\\angle A =45^{\\circ}$ and $\\angle B =30^{\\circ}$. A line $DE$, with $D$ on $AB$ and $\\angle ADE =60^{\\circ}$, divides $\\triangle ABC$ into two pieces of equal area. (Note: the figure may not be accurate; perhaps $E$ is on $CB$ instead of $AC$.) The ratio $\\frac{AD}{AB}$ is\n\\n Options: A. $\\frac{1}{\\sqrt{2}}$, B. $\\frac{2}{2+\\sqrt{2}}$, C. $\\frac{1}{\\sqrt{3}}$, D. $\\frac{1}{\\sqrt[3]{6}}$, E. $\\frac{1}{\\sqrt[4]{12}}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2371.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are $5$ yellow pegs, $4$ red pegs, $3$ green pegs, $2$ blue pegs, and $1$ orange peg on a triangular peg board. In how many ways can the pegs be placed so that no (horizontal) row or (vertical) column contains two pegs of the same color?\n\n\\n Options: A. $0$, B. $1$, C. $5!\\cdot4!\\cdot3!\\cdot2!\\cdot1!$, D. $\\frac{15!}{5!\\cdot4!\\cdot3!\\cdot2!\\cdot1!}$, E. $15!$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2111.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows a hanging mobile. The mobile weighs 112 grams in total. (The weight of the sticks and threads is not taken into account.) How much does the star weigh?\n\\n Options: A. $6 \\mathrm{~g}$, B. $7 \\mathrm{~g}$, C. $12 \\mathrm{~g}$, D. $16 \\mathrm{~g}$, E. It cannot be calculated.", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/791.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $A B$ has length $1 ; \\angle A B C=\\angle A C D=90^{\\circ}$; $\\angle C A B=\\angle D A C=\\theta$. What is the length of $A D$?\n\\n Options: A. $\\cos \\beta+\\tg \\beta$, B. $\\frac{1}{\\cos (2 \\beta)}$, C. $\\cos ^{2} \\beta$, D. $\\cos (2 \\beta)$, E. $\\frac{1}{\\cos ^{2} \\beta}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/187.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram on the right shows nine points in a square array. What is the smallest number of points that need to be removed in order that no three of the remaining points are in a straight line? ", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1561.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the middle of the big diagram one piece is missing and should be replaced. You are only allowed to do this by connecting light-grey lines with light-grey lines, dark-grey lines with dark-grey lines and black lines with black lines. Which piece fits?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/554.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The parallelogram has area 1. The two diagonals intersect each other at point M. Another point $P$ lies on the side DC. $E$ is the point of intersection of the segments $A P$ and $B D$, and $F$ is the point of intersection of the segments $B P$ and $A C$. What is the area of the quadrilateral EMFP, if the sum of the areas of the triangles $A E D$ and BFC is $\\frac{1}{3}$?\n\\n Options: A. $\\frac{1}{6}$, B. $\\frac{1}{8}$, C. $\\frac{1}{10}$, D. $\\frac{1}{12}$, E. $\\frac{1}{14}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1158.png" }, { "solution": "\\boxed{\\frac{40}{9}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two right triangles share a side as follows: What is the area of $\\triangle ABE$?", "completion": "\\boxed{\\frac{40}{9}}", "image_path": "dataset/math_vision/images/2910.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a square of side $2 \\mathrm{~m}$ with lines drawn to its sides from the centre $O$. The points $A, B, C$ and $D$ are all on different sides of the square. The lines $O A$ and $O B$ are perpendicular as are the lines $O C$ and $O D$. What is the shaded area in square metres? ", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/1548.png" }, { "solution": "\\boxed{$\\frac{3 \\sqrt{6}}{2}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below, $A$ and $B$ trisect $DE$, $C$ and $A$ trisect $F G$, and $B$ and $C$ trisect $HI$. Given that $DI = 5$, $EF = 6$, $GH = 7$, find the area of $\\vartriangle ABC$.\\n", "completion": "\\boxed{$\\frac{3 \\sqrt{6}}{2}$}", "image_path": "dataset/math_vision/images/2815.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a spiral of isosceles triangles. The largest angle in each of the triangles is $100^{\\circ}$. The grey triangle is number 0 . Each of the following triangles (numbered 1, 2, 3, ...) join by one edge to the previous one, as shown. As you can see triangle 3 only partially covers triangle 0. What is the number of the first triangle that exactly covers triangle 0 ? ", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/1511.png" }, { "solution": "\\boxed{30}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $ABC$, point $D$ divides side $\\overline{AC}$ so that $AD:DC=1:2$. Let $E$ be the midpoint of $\\overline{BD}$ and let $F$ be the point of intersection of line $BC$ and line $AE$. Given that the area of $\\triangle ABC$ is $360$, what is the area of $\\triangle EBF$?\n", "completion": "\\boxed{30}", "image_path": "dataset/math_vision/images/2761.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $\\textbf{Juan's Old Stamping Grounds}$\nJuan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.)\n\n\nHow many of his European stamps were issued in the '80s?", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/2635.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers from 1 to 11 are written in the empty hexagons. The sums of the three numbers in three hexagons with a common bold point are always equal. Three of the eleven numbers are already written in (see diagram). Which number is written in the hexagon with the question mark? ", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/394.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $\\triangle ABC$ is right-angled at $C$. Also, points $M$, $N$ and $P$ are the midpoints of sides $BC$, $AC$ and $AB$, respectively. If the area of $\\triangle APN$ is $2\\mbox{ cm}^2$, then what is the area, in square centimeters, of $\\triangle ABC$? ", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/2900.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Figure $ABCD$ is a square. Inside this square three smaller squares are drawn with the side lengths as labeled. The area of the shaded L-shaped region is\n\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/2614.png" }, { "solution": "\\boxed{35}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $A B C D$ is a trapezium with parallel sides $A B$ and $C D$. Let $A B=50$ and $C D=20$. Point $E$ lies on side $A B$ in such a way that the straight line $D E$ divides the trapezium into two shapes of equal area. How long is the straight line $A E$?\n", "completion": "\\boxed{35}", "image_path": "dataset/math_vision/images/1406.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of these figures differs from the rest four?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/13.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure below shows a square and four equilateral triangles, with each triangle having a side lying on a side of the square, such that each triangle has side length 2 and the third vertices of the triangles meet at the center of the square. The region inside the square but outside the triangles is shaded. What is the area of the shaded region?\n\n\\n Options: A. $4$, B. $12 - 4\\sqrt{3}$, C. $3\\sqrt{3}$, D. $4\\sqrt{3}$, E. $16 - \\sqrt{3}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2224.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three rings are connected to each other as shown. Which of the following pictures also shows three rings connected in the same way?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1179.png" }, { "solution": "\\boxed{288}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The solid shown has a square base of side length $s$. The upper edge is parallel to the base and has length $2s$. All other edges have length $s$. Given that $s = 6 \\sqrt{2}$, what is the volume of the solid?\n", "completion": "\\boxed{288}", "image_path": "dataset/math_vision/images/2036.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The same amount of kangaroos should be in both parks. How many kangaroos have to be moved from the left park to the right park for that to happen?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/73.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two circles are tangent to each other and also to two sides of a square. What is the measure of the $A \\hat{O} B$ angle, determined by three of these points of tangency, as shown in the figure?\n\\n Options: A. $110^{\\circ}$, B. $112^{\\circ}$, C. $120^{\\circ}$, D. $128^{\\circ}$, E. $135^{\\circ}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1443.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Kai has to insert the numbers $3,4,5,6$ and 7 into the five circles of the diagram on the right in the following way: The product of the three numbers in the vertices of each triangle has to be equal to the number stated within the triangle. How big is the sum of the numbers in the vertices of the triangle with the number 168?\n", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/977.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The bases of the two touching squares shown lie on the same straight line. The lengths of the diagonals of the larger square and the smaller square are $10 \\mathrm{~cm}$ and $8 \\mathrm{~cm}$ respectively. $P$ is the centre of the smaller square. What is the area, in $\\mathrm{cm}^{2}$, of the shaded triangle $P Q R$ ? ", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1978.png" }, { "solution": "\\boxed{100}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the polygon shown, each side is perpendicular to its adjacent sides, and all 28 of the sides are congruent. The perimeter of the polygon is $56$. The area of the region bounded by the polygon is\n", "completion": "\\boxed{100}", "image_path": "dataset/math_vision/images/2409.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle ABC$, $\\angle C = 90^\\circ, AC = 6$ and $BC = 8$. Points $D$ and $E$ are on $\\overline{AB}$ and $\\overline{BC}$, respectively, and $\\angle BED = 90^\\circ$. If $DE = 4$, then $BD =$\n\n\\n Options: A. $5$, B. $\\frac{16}{3}$, C. $\\frac{20}{3}$, D. $\\frac{15}{2}$, E. $8$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2416.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Seven different single-digit numbers are written in the circles of the diagram shown with one number in each circle. The product of the three numbers in each of the three lines of three numbers is the same. Which number is written in the circle containing the question mark? ", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/1988.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ana plays with $n \\times n$ boards by placing a token in each of the cells with no common points with other cells containing tokens. In the picture beside we see how to place as many chips as possible on $5 \\times 5$ and $6 \\times 6$ boards. In this way, how many chips can Ana possibly put on a $2020 \\times 2020$ board?\n\\n Options: A. 2020, B. 4039, C. $674^{2}$, D. $1010^{2}$, E. $2020^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1444.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Eight congruent semi-circles are drawn inside a square with side length 4. How big is the area of the white part?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/1419.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular piece of paper is wrapped around a cylinder. Then an angled straight cut is made through the points $\\mathrm{X}$ and $\\mathrm{Y}$ of the cylinder as shown on the left. The lower part of the piece of paper is then unrolled. Which of the following pictures could show the result?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/236.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many triangles can be seen in the picture on the right? (Be careful! A triangle can be also be made by joining several smaller triangles together.)\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/504.png" }, { "solution": "\\boxed{75}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure below $AB = BC$, $m \\angle ABD = 30^{\\circ}$, $m \\angle C = 50^{\\circ}$ and $m \\angle CBD = 80^{\\circ}$. What is the number of degrees in the measure of angle $A$?\n\n", "completion": "\\boxed{75}", "image_path": "dataset/math_vision/images/2932.png" }, { "solution": "\\boxed{121}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Using this picture we can observe that\n$1+3+5+7=4 \\times 4$.\nWhat is the value of\n$1+3+5+7+9+11+13+15+17+19+21$ ?\n", "completion": "\\boxed{121}", "image_path": "dataset/math_vision/images/1999.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The vertices of a triangle have the co-ordinates $A(p \\mid q), B(r \\mid s)$ and $C(t \\mid u)$ as shown. The midpoints of the sides of the triangle are the points $\\mathrm{M}(-2 \\mid 1), \\mathrm{N}(2 \\mid-1)$ and $\\mathrm{P}(3 \\mid 2)$. Determine the value of the expression $p+q+r+s+t+u$\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/314.png" }, { "solution": "\\boxed{4.0}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rectangle $ABCD$ has sides $CD=3$ and $DA=5$. A circle of radius $1$ is centered at $A$, a circle of radius $2$ is centered at $B$, and a circle of radius $3$ is centered at $C$. Which of the following is closest to the area of the region inside the rectangle but outside all three circles?\n\n", "completion": "\\boxed{4.0}", "image_path": "dataset/math_vision/images/2730.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The giants Tim and Tom build a sandcastle and decorate it with a flag. They insert half the flagpole into the highest point of the sandcastle. The highest point of the flagpole is now $16 \\mathrm{~m}$ above the floor, the lowest $6 \\mathrm{~m}$ (see diagram). How high is the sandcastle? \\n Options: A. $11 \\mathrm{~m}$, B. $12 \\mathrm{~m}$, C. $13 \\mathrm{~m}$, D. $14 \\mathrm{~m}$, E. $15 \\mathrm{~m}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/94.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rose bush has 8 flowers on which butterflies and dragonflies are sitting. On every flower there is at most one insect sitting on it. More than half of the flowers are occupied. The number of butterflies is twice as big as the number of dragonflies. How many butterflies are sitting on the rose blossoms?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/591.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a triangle joined to a square to form an irregular pentagon. The triangle has the same perimeter as the square.\n\nWhat is the ratio of the perimeter of the pentagon to the perimeter of the square?\\n Options: A. 2: 1, B. 3: 2, C. 4: 3, D. 5: 4, E. 6: 5", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1756.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six paper strips are used to weave a pattern (see diagram). What do you see when you look at the pattern from behind?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/617.png" }, { "solution": "\\boxed{55}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A semi-circle of radius 8 cm, rocks back and forth along a line. The distance between the line on which the semi-circle sits and the line above is 12 cm. As it rocks without slipping, the semi-circle touches the line above at two points. (When the semi-circle hits the line above, it immediately rocks back in the other direction.) What is the distance between these two points, in millimetres, rounded off to the nearest whole number? (Note: After finding the exact value of the desired distance, you may find a calculator useful to round this value off to the nearest whole number.)", "completion": "\\boxed{55}", "image_path": "dataset/math_vision/images/3040.png" }, { "solution": "\\boxed{116}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A barcode of the type shown in the two examples is composed of alternate strips of black and white, where the leftmost and rightmost strips are always black. Each strip (of either colour) has a width of 1 or 2 . The total width of the barcode is 12 . The barcodes are always read from left to right. How many distinct barcodes are possible?\n", "completion": "\\boxed{116}", "image_path": "dataset/math_vision/images/2005.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Eight points are spaced around at intervals of one unit around a $2 \\times 2$ square, as shown. Two of the $8$ points are chosen at random. What is the probability that the two points are one unit apart?\n\\n Options: A. $\\frac{1}{4}$, B. $\\frac{2}{7}$, C. $\\frac{4}{11}$, D. $\\frac{1}{2}$, E. $\\frac{4}{7}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2692.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are three paths running through our park in the city (see diagram). A tree is situated in the centre of the park. What is the minimum number of trees that have to be planted additionally so that there are the same number of trees on either side of each path?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1475.png" }, { "solution": "\\boxed{21}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are 10 balls, numbered 0 to 9 in a basket. John and George play a game. Each person is allowed to take three balls from the basket and calculate the total of the numbers on the balls. What is the biggest possible difference between the john and Georges totals?\n", "completion": "\\boxed{21}", "image_path": "dataset/math_vision/images/539.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: If I join the midpoints of the sides of the large triangle in the picture, a small triangle is formed. If I join the midpoints of the sides of this small triangle, a tiny triangle is formed. How many of these tiny triangles can fit into the largest triangle at the same time?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/506.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many squares can be drawn by joining the dots with line segments?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1042.png" }, { "solution": "\\boxed{\\frac{11}{7}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four semi-circles are shown with $AB:BC:CD = 1:2:3$. What is the ratio of the shaded area to the unshaded area in the semi circle with diameter $AD$? ", "completion": "\\boxed{\\frac{11}{7}}", "image_path": "dataset/math_vision/images/2998.png" }, { "solution": "\\boxed{\\sqrt{22}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure shown, $AC=13$ and $DC=2$ units. What is the length of the segment $BD$? Express your answer in simplest radical form.\n\n", "completion": "\\boxed{\\sqrt{22}}", "image_path": "dataset/math_vision/images/2977.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square piece of paper is cut into six rectangular pieces as shown on the right. The sum of the perimeters of the six pieces is $120 \\mathrm{~cm}$. How big is the area of the square?\n\\n Options: A. $48 \\mathrm{~cm}^{2}$, B. $64 \\mathrm{~cm}^{2}$, C. $110.25 \\mathrm{~cm}^{2}$, D. $144 \\mathrm{~cm}^{2}$, E. $256 \\mathrm{~cm}^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1076.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three villages are connected by paths as shown. From Downend to Uphill, the detour via Middleton is $1 \\mathrm{~km}$ longer than the direct path. From Downend to Middleton, the detour via Uphill is $5 \\mathrm{~km}$ longer than the direct path. From Uphill to Middleton, the detour via Downend is $7 \\mathrm{~km}$ longer than the direct path. What is the length of the shortest of the three direct paths between the villages?\n\\n Options: A. $1 \\mathrm{~km}$, B. $2 \\mathrm{~km}$, C. $3 \\mathrm{~km}$, D. $4 \\mathrm{~km}$, E. $5 \\mathrm{~km}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1690.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A sphere is inscribed in a truncated right circular cone as shown. The volume of the truncated cone is twice that of the sphere. What is the ratio of the radius of the bottom base of the truncated cone to the radius of the top base of the truncated cone?\n\n\n\\n Options: A. $\\frac{3}{2}$, B. $\\frac{1+\\sqrt{5}}{2}$, C. $\\sqrt{3}$, D. $2$, E. $\\frac{3+\\sqrt{5}}{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2201.png" }, { "solution": "\\boxed{500}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square with side length $30 \\mathrm{~cm}$ is split into 9 squares. The big square contains three circles with radii $5 \\mathrm{~cm}$ (bottom right), $4 \\mathrm{~cm}$ (top left) as well as $3 \\mathrm{~cm}$ (top right) as seen in the diagram. How many $\\mathrm{cm}^{2}$ are shaded in grey?\n", "completion": "\\boxed{500}", "image_path": "dataset/math_vision/images/1493.png" }, { "solution": "\\boxed{45}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A quarter-circle of radius 3 units is drawn at each of the vertices of a square with sides of 6 units. The area of the shaded region can be expressed in the form $a-b\\pi$ square units, where $a$ and $b$ are both integers. What is the value of $a+b?$", "completion": "\\boxed{45}", "image_path": "dataset/math_vision/images/2963.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the 4 vertices and 6 edges of a tetrahedron is labelled with one of the numbers $1,2,3,4,5,6,7,8,9$ and 11. (The number 10 is left out). Each number is only used once. The number on each edge is the sum of the numbers on the two vertices which are connected by that edge. The edge $A B$ has the number 9. With which number is the edge $C D$ labelled?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1103.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows the plan of a room. Adjoining walls are perpendicular to each other and the lengths of some of the walls are shown. What is the length of the perimeter of the room? \\n Options: A. $3 a+4 b$, B. $3 a+8 b$, C. $6 a+4 b$, D. $6 a+6 b$, E. $6 a+8 b$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1570.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A regular octagon is folded exactly in half three times until a triangle is obtained. The bottom corner of the triangle is then cut off with a cut perpendicular to one side of the triangle as shown.\n\nWhich of the following will be seen when the triangle is unfolded?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1784.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular sheet with one side of $12 \\mathrm{~cm}$ is folded along its $20 \\mathrm{~cm}$ diagonal. What is the overlapping area of the folded parts, indicated in gray in the picture beside?\n\\n Options: A. $24 \\mathrm{~cm}^{2}$, B. $36 \\mathrm{~cm}^{2}$, C. $48 \\mathrm{~cm}^{2}$, D. $50 \\mathrm{~cm}^{2}$, E. $75 \\mathrm{~cm}^{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1447.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Florian has 10 equally long metal strips with equally many holes.\n\nHe bolts the metal strips together in pairs. Now he has five long strips (see the diagram).\n\nWhich of the long strips is the shortest?\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/44.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In each box exactly one of the digits $0,1,2,3,4,5$ and 6 is to be written. Each digit will only be used once. Which digit has to be written in the grey box so that the sum is correct?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/525.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $T$ be $7$. The diagram below features two concentric circles of radius $1$ and $T$ (not necessarily to scale). Four equally spaced points are chosen on the smaller circle, and rays are drawn from these points to the larger circle such that all of the rays are tangent to the smaller circle and no two rays intersect. If the area of the shaded region can be expressed as $k\\pi$ for some integer $k$, find $k$.\\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/2832.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two semicircles are drawn as shown in the figure. The chord $C D$, of length 4 , is parallel to the diameter $A B$ of the greater semicircle and touches the smaller semicircle. Then the area of the shaded region equals\n\\n Options: A. $\\pi$, B. $1.5 \\pi$, C. $2 \\pi$, D. $3 \\pi$, E. Not enough data", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/201.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, polygons $ A$, $ E$, and $ F$ are isosceles right triangles; $ B$, $ C$, and $ D$ are squares with sides of length $ 1$; and $ G$ is an equilateral triangle. The figure can be folded along its edges to form a polyhedron having the polygons as faces.\n\nThe volume of this polyhedron is\\n Options: A. 1/2, B. 2/3, C. 3/4, D. 5/6, E. 4/3", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2432.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows 3 gears with a black gear tooth on each. Which picture shows the correct position of the black teeth after the small gear has turned a full turn clockwise?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/955.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $A B C D$ is a square with side length $10 \\mathrm{~cm}$. The distance of $\\mathrm{N}$ to $\\mathrm{M}$ measures $6 \\mathrm{~cm}$. Each area not shaded grey is either a sqaure or an isosceles triangle. How big is the area shaded in grey?\n\\n Options: A. $42 \\mathrm{~cm}^{2}$, B. $46 \\mathrm{~cm}^{2}$, C. $48 \\mathrm{~cm}^{2}$, D. $52 \\mathrm{~cm}^{2}$, E. $58 \\mathrm{~cm}^{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/777.png" }, { "solution": "\\boxed{336}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Equilateral triangle $ABC$ has side length $840$. Point $D$ lies on the same side of line $BC$ as $A$ such that $\\overline{BD} \\perp \\overline{BC}$. The line $\\ell$ through $D$ parallel to line $BC$ intersects sides $\\overline{AB}$ and $\\overline{AC}$ at points $E$ and $F$, respectively. Point $G$ lies on $\\ell$ such that $F$ is between $E$ and $G$, $\\triangle AFG$ is isosceles, and the ratio of the area of $\\triangle AFG$ to the area of $\\triangle BED$ is $8:9$. Find $AF$.\n\n", "completion": "\\boxed{336}", "image_path": "dataset/math_vision/images/2097.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The black-white caterpillar shown, rolls up to go to sleep. Which diagram could show the rolled-up caterpillar?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1226.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure each asterisk stands for one digit. The sum of the digits of the product is equal to\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/211.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a large equilateral triangle divided into 36 small equilateral triangles, each with area $1 \\mathrm{~cm}^{2}$. What is the area of the shaded triangle, in $\\mathrm{cm}^{2}$ ? ", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/1579.png" }, { "solution": "\\boxed{768}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many ways are there to choose a white square and a black square, such as those shown, from an $8 \\times 8$ chess board so that these squares do not lie in either the same row or the same column? ", "completion": "\\boxed{768}", "image_path": "dataset/math_vision/images/1825.png" }, { "solution": "\\boxed{64}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Nina made a wall around a square area, using 36 identical cubes. A section of the wall is shown in the picture. How many cubes will she now need to completely fill the square area.\n", "completion": "\\boxed{64}", "image_path": "dataset/math_vision/images/798.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each figure is made up of 4 equally big cubes and coloured in. Which figure needs the least amount of colour?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/96.png" }, { "solution": "\\boxed{64}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture there are four overlapping squares with sides 11, 9, 7 and 5 long. How much greater is the sum of the two grey areas than the sum of the two black areas?\n", "completion": "\\boxed{64}", "image_path": "dataset/math_vision/images/1266.png" }, { "solution": "\\boxed{72}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Points $A,$ $B,$ and $C$ are placed on a circle centered at $O$ as in the following diagram: If $AC = BC$ and $\\angle OAC = 18^\\circ,$ then how many degrees are in $\\angle AOB$?", "completion": "\\boxed{72}", "image_path": "dataset/math_vision/images/2918.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram drawn on the square grid, find the ratio of the unshaded area to the shaded area.\n\\n Options: A. $\\frac{1}{4}$, B. $\\frac{1}{5}$, C. $\\frac{1}{6}$, D. $\\frac{2}{5}$, E. $\\frac{2}{7}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/719.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lina has already laid two shapes on a square playing board. Which of the 5 shapes can she add to the board so that none of the remaining four shapes will have space to fit.\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/803.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the least possible number of small squares that we should shade in the diagram on the right for the whole diagram to have a line of symmetry? ", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/1542.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: 9 points, numbered 1 to 9 are marked on a circle. Point 1 is joined to point 3, 3 to 5. Continue the drawing, always joining to the next but one point along. Which drawing do you get if you keep going until you get back to point 1?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/533.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The sides of the square $A B C D$ are $10 \\mathrm{~cm}$ long. What is the total area of the shaded part?\n\\n Options: A. $40 \\mathrm{~cm}^{2}$, B. $45 \\mathrm{~cm}^{2}$, C. $50 \\mathrm{~cm}^{2}$, D. $55 \\mathrm{~cm}^{2}$, E. $60 \\mathrm{~cm}^{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/966.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A dog is tied to the outside corner of a house by a rope of length $10 \\mathrm{~m}$. The house is a rectangle with sides of length $6 \\mathrm{~m}$ and $4 \\mathrm{~m}$. What is the length (in metres) of the curved boundary of the area in which the dog can roam? \\n Options: A. $20 \\pi$, B. $22 \\pi$, C. $40 \\pi$, D. $88 \\pi$, E. $100 \\pi$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1837.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following diagrams is impossible to make with the two dominos?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/464.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nA piece of paper containing six joined squares labeled as shown in the diagram is folded along the edges of the squares to form a cube. The label of the face opposite the face labeled $ \\text{X}$ is:\\n Options: A. $\\text{Z}$, B. $\\text{U}$, C. $\\text{V}$, D. $\\text{W}$, E. $\\text{Y}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2507.png" }, { "solution": "\\boxed{69}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two circles of radius 5 are externally tangent to each other and are internally tangent to a circle of radius 13 at points $A$ and $B$, as shown in the diagram. The distance $AB$ can be written in the form $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?\n\n", "completion": "\\boxed{69}", "image_path": "dataset/math_vision/images/2216.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An equilateral triangle with side length 3 and a circle with radius 1 have the same centre. What is the perimeter of the figure that is created when the two are being put together?\n\\n Options: A. $6+\\pi$, B. $3+2 \\pi$, C. $9+\\frac{\\pi}{3}$, D. $3 \\pi$, E. $9+\\pi$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/220.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube is cut in three directions as shown, to produce eight cuboids (each cut is parallel to one of the faces of the cube). What is the ratio of the total surface area of the eight cuboids to the surface area of the original cube?\n\\n Options: A. 1:1, B. 4:3, C. 3:2, D. 2:1, E. 4:1", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1059.png" }, { "solution": "\\boxed{4\\sqrt{2}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four diagonals of a regular octagon with side length 2 intersect as shown. Find the area of the shaded region. ", "completion": "\\boxed{4\\sqrt{2}}", "image_path": "dataset/math_vision/images/2924.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The cells of the table are being coloured red (R) and green (G). In each row and in each column there must be two red and two green cells. What will the lowest row look like after colouring the table?\n\\n Options: A. GRGR, B. RGRG, C. GRRG, D. RGGR, E. GGRR", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1302.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the smallest number of dots that need be removed from the pattern shown, so that no three of the remaining dots are at the vertices of an equilateral triangle?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1028.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maia the bee can only walk on colorful houses. How many ways can you color exactly three white houses with the same color so that Maia can walk from $A$ to $B$ ?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/118.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Equilateral $\\triangle ABC$ has side length $1$, and squares $ABDE$, $BCHI$, $CAFG$ lie outside the triangle. What is the area of hexagon $DEFGHI$?\n\n\\n Options: A. $\\frac{12+3\\sqrt{3}}4$, B. $\\frac{9}{2}$, C. $3+\\sqrt{3}$, D. $\\frac{6+3\\sqrt{3}}2$, E. $6$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2193.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of these two pieces of wire is made of 8 segments of length 1. One of the pieces is placed one above the other so that they coincide partially. What is the largest possible length of their common part?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/728.png" }, { "solution": "\\boxed{128}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: You write a number in each square as shown in the square figure. Then, the number $x$ cannot be:\n", "completion": "\\boxed{128}", "image_path": "dataset/math_vision/images/720.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A gray square with an area of $36 \\mathrm{~cm}^{2}$ and a black square with an area of $25 \\mathrm{~cm}^{2}$ are superimposed, as shown beside. What is the perimeter of the overlapping region, represented by the white quadrilateral, which has a vertex on the side of the gray square?\n\\n Options: A. It is not determined., B. $11 \\mathrm{~cm}$, C. $16 \\mathrm{~cm}$, D. $18 \\mathrm{~cm}$, E. $20 \\mathrm{~cm}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/338.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Daniel wants to make a complete square using pieces only like those shown. What is the minimum number of pieces he must use?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/801.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance $d$ traveled by the two animals over time $t$ from start to finish?$\\phantom{h}$\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2757.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a rectangle JKLM the angle bisector in $\\mathrm{J}$ intersects the diagonal KM in $\\mathrm{N}$. The distance of $\\mathrm{N}$ to $\\mathrm{LM}$ is 1 and the distance of $\\mathrm{N}$ to $\\mathrm{KL}$ is 8. How long is LM?\n\\n Options: A. $8+2 \\sqrt{2}$, B. $11-\\sqrt{2}$, C. 10, D. $8+3 \\sqrt{2}$, E. $11+\\frac{\\sqrt{2}}{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/224.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Simon has two identical tiles, whose front look like this: The back is white.\n\nWhich pattern can he make with those two tiles?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/70.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Petra crafts a piece of jewellery out of two black and two white hearts. The hearts have areas of $1 \\mathrm{~cm}^{2}, 4 \\mathrm{~cm}^{2}, 9 \\mathrm{~cm}^{2}$ and $16 \\mathrm{~cm}^{2}$ respectively. She places the hearts on top of each other as shown in the diagram and glues them together. How big is the total area of the visible black parts?\n\\n Options: A. $9 \\mathrm{~cm}^{2}$, B. $10 \\mathrm{~cm}^{2}$, C. $11 \\mathrm{~cm}^{2}$, D. $12 \\mathrm{~cm}^{2}$, E. $13 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1148.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rhombus $ ABCD$ is similar to rhombus $ BFDE$. The area of rhombus $ ABCD$ is 24, and $ \\angle BAD = 60^\\circ$. What is the area of rhombus $ BFDE$?\n\n\\n Options: A. $6$, B. $4\\sqrt{3}$, C. $8$, D. $9$, E. $6\\sqrt{3}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2158.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The 10 islands are connected by 12 bridges (see diagram). All bridges are open for traffic. What is the minimum number of bridges that need to be closed off, so that the traffic between $A$ and $B$ comes to a halt?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/869.png" }, { "solution": "\\boxed{3025}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Diana drew a rectangular grid of 12 squares on squared paper. Some of the squares were then painted black. In each white square she wrote the number of black squares that shared an edge with it (a whole edge, not just a vertex). The figure shows the result. Then she did the same with a rectangular grid of 2 by 1009 squares. What is the maximum value that she could obtain as the result of the sum of all the numbers in this grid? ", "completion": "\\boxed{3025}", "image_path": "dataset/math_vision/images/1935.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two $4\\times 4$ squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the area of the shaded region created by removing the circle from the squares?\n\n\\n Options: A. $16-4\\pi$, B. $16-2\\pi$, C. $28-4\\pi$, D. $28-2\\pi$, E. $32-2\\pi$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2661.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many cubes have been taken from the block?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/427.png" }, { "solution": "\\boxed{145}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of the smallest equilateral triangle with one vertex on each of the sides of the right triangle with side lengths $2\\sqrt{3}$, $5$, and $\\sqrt{37}$, as shown, is $\\frac{m\\sqrt{p}}{n}$, where $m$, $n$, and $p$ are positive integers, $m$ and $n$ are relatively prime, and $p$ is not divisible by the square of any prime. Find $m+n+p$.\n", "completion": "\\boxed{145}", "image_path": "dataset/math_vision/images/2092.png" }, { "solution": "\\boxed{6.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Luana builds a fence using pieces of wood 2 meters long by half a meter wide, just like this one: . The picture beside shows this fence, after it is ready. How long is the fence, in meters?\n", "completion": "\\boxed{6.5}", "image_path": "dataset/math_vision/images/630.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Inside a square of area $36 \\mathrm{~cm}^{2}$, there are shaded regions as shown. The total shaded area is $27 \\mathrm{~cm}^{2}$. What is the value of $p+q+r+s$ ? \\n Options: A. $4 \\mathrm{~cm}$, B. $6 \\mathrm{~cm}$, C. $8 \\mathrm{~cm}$, D. $9 \\mathrm{~cm}$, E. $10 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1634.png" }, { "solution": "\\boxed{45}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The quadrilateral $A B C D$ has right angles only in corners $A$ and $D$. The numbers in the diagram give the respective areas of the triangles in which they are located. How big is the area of $A B C D$?\n", "completion": "\\boxed{45}", "image_path": "dataset/math_vision/images/1115.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The shaded region below is called a shark's fin falcata, a figure studied by Leonardo da Vinci. It is bounded by the portion of the circle of radius $3$ and center $(0,0)$ that lies in the first quadrant, the portion of the circle with radius $\\frac{3}{2}$ and center $(0,\\frac{3}{2})$ that lies in the first quadrant, and the line segment from $(0,0)$ to $(3,0)$. What is the area of the shark's fin falcata?\n\n\\n Options: A. $\\frac{4\\pi}{5}$, B. $\\frac{9\\pi}{8}$, C. $\\frac{4\\pi}{3}$, D. $\\frac{7\\pi}{5}$, E. $\\frac{3\\pi}{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2205.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the quadrilateral $\\mathrm{ABCD}, \\mathrm{AD}=\\mathrm{BC}, \\angle \\mathrm{DAC}=50^{\\circ}$, $\\angle \\mathrm{DCA}=65^{\\circ}$ and $\\angle \\mathrm{ACB}=70^{\\circ}$. How big is $\\angle \\mathrm{ABC}$?\n\\n Options: A. $50^{\\circ}$, B. $55^{\\circ}$, C. $60^{\\circ}$, D. $65^{\\circ}$, E. It is not clear.", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1064.png" }, { "solution": "\\boxed{30}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a wooden cube of side $3 \\mathrm{~cm}$ with a smaller cube of side $1 \\mathrm{~cm}$ cut out at one corner. A second cube of side $3 \\mathrm{~cm}$ has a cube of side $1 \\mathrm{~cm}$ cut out at each corner. How many faces does the shape formed from the second cube have? ", "completion": "\\boxed{30}", "image_path": "dataset/math_vision/images/1796.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle with sides $6 \\mathrm{~cm}$ as shown. The sum of the perimeters of the three small triangles is equal to the perimeter of the remaining hexagon. What is the side-length of one of the small triangles? \\n Options: A. $1 \\mathrm{~cm}$, B. $1.2 \\mathrm{~cm}$, C. $1.25 \\mathrm{~cm}$, D. $1.5 \\mathrm{~cm}$, E. $2 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1593.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rectangle $ ABCD$, $ AD = 1$, $ P$ is on $ \\overline{AB}$, and $ \\overline{DB}$ and $ \\overline{DP}$ trisect $ \\angle ADC$. What is the perimeter of $ \\triangle BDP$?\n\\n Options: A. $3 + \\frac{\\sqrt{3}}{3}$, B. $2 + \\frac{4\\sqrt{3}}{3}$, C. $2 + 2\\sqrt{2}$, D. $\\frac{3 + 3\\sqrt{5}}{2}$, E. $2 + \\frac{5\\sqrt{3}}{3}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2109.png" }, { "solution": "\\boxed{-100}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: When the 5 pieces are fitted together correctly, the result is a rectangle with a calculation written on it. What is the answer to this calculation?", "completion": "\\boxed{-100}", "image_path": "dataset/math_vision/images/1208.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three of the cards shown will be dealt to Nadia, the rest to Riny. Nadia multiplies the three values of her cards and Riny multiplies the two values of his cards. It turns out that the sum of those two products is a prime number. Determine the sum of the values of Nadia's cards.\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/316.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture on the right you see a map. In the middle a piece is missing. The cat should be able to reach the milk, and the mouse the cheese, but the cat and the mouse must not meet each other. What should the piece in the middle look like?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/467.png" }, { "solution": "\\boxed{180}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the perimeter of trapezoid $ ABCD$?\n\n", "completion": "\\boxed{180}", "image_path": "dataset/math_vision/images/2666.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $ ABC$ has a right angle at $ B$, $ AB = 1$, and $ BC = 2$. The bisector of $ \\angle BAC$ meets $ \\overline{BC}$ at $ D$. What is $ BD$?\n\\n Options: A. $\\frac{\\sqrt{3} - 1}{2}$, B. $\\frac{\\sqrt{5} - 1}{2}$, C. $\\frac{\\sqrt{5} + 1}{2}$, D. $\\frac{\\sqrt{6} + \\sqrt{2}}{2}$, E. $2\\sqrt{3} - 1$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2175.png" }, { "solution": "\\boxed{51}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, what is the value of $x$ ? ", "completion": "\\boxed{51}", "image_path": "dataset/math_vision/images/1592.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three congruent isosceles triangles $DAO,$ $AOB,$ and $OBC$ have $AD=AO=OB=BC=10$ and $AB=DO=OC=12.$ These triangles are arranged to form trapezoid $ABCD,$ as shown. Point $P$ is on side $AB$ so that $OP$ is perpendicular to $AB.$ What is the length of $OP?$", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/2887.png" }, { "solution": "\\boxed{39}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn a magic triangle, each of the six whole numbers $ 10-15$ is placed in one of the circles so that the sum, $ S$, of the three numbers on each side of the triangle is the same. The largest possible value for $ S$ is", "completion": "\\boxed{39}", "image_path": "dataset/math_vision/images/2508.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the $4 \\times 4$ grid some cells must be painted black. The numbers to the right of the grid and those below the grid show how many cells in that row or column must be black.\n\nIn how many ways can this grid be painted?", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1962.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Dirce built the sculpture on the side by gluing cubic boxes of half a meter on the side. Then she painted the sculpture minus the support base, with a special paint sold in cans. Each can allow to paint 4 square meters of surface. How many cans of paint did she have to buy?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/935.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A portion of a corner of a tiled floor is shown. If the entire floor is tiled in this way and each of the four corners looks like this one, then what fraction of the tiled floor is made of darker tiles?\n\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{4}{9}$, C. $\\frac{1}{2}$, D. $\\frac{5}{9}$, E. $\\frac{5}{8}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2643.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Peter writes the word KANGAROO on a see-through piece of glass, as seen on the right. What can he see when he first flips over the glass onto its back along the right-hand side edge and then turns it about $180^{\\circ}$ while it is lying on the table?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1403.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In how many ways can the three kangaroos be placed in three different squares so that no kangaroo has an immediate neighbour?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/852.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The large rectangle $W X Y Z$ is divided into seven identical rectangles, as shown. What is the ratio $W X: X Y$ ? \\n Options: A. $3: 2$, B. $4: 3$, C. $8: 5$, D. $12: 7$, E. $7: 3$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1702.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The big rectangle shown is divided into 30 equally big squares. The perimeter of the area shaded in grey is $240 \\mathrm{~cm}$. How big is the area of the big rectangle? \\n Options: A. $480 \\mathrm{~cm}^{2}$, B. $750 \\mathrm{~cm}^{2}$, C. $1080 \\mathrm{~cm}^{2}$, D. $1920 \\mathrm{~cm}^{2}$, E. $2430 \\mathrm{~cm}^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1486.png" }, { "solution": "\\boxed{15}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Every box shows the result of the addition of the numbers on the very left and on the very top (for example: $6+2=8$ ). Which number is written behind the question mark?\n", "completion": "\\boxed{15}", "image_path": "dataset/math_vision/images/570.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two circles are centered at the origin, as shown. The point $P(8,6)$ is on the larger circle and the point $S(0,k)$ is on the smaller circle. If $QR=3$, what is the value of $k$? ", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/3021.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $3 \\times 3 \\times 3$ cube is made up of small $1 \\times 1 \\times 1$ cubes. Then the middle cubes from front to back, from top to bottom and from right to left are removed (see diagram). How many $1 \\times 1 \\times 1$ - cubes remain?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1178.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each shelf holds a total of 64 deciliters of apple juice. The bottles have three different sizes: large, medium and small. How many deciliters of apple juice does a medium bottle contain?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/958.png" }, { "solution": "\\boxed{70}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The graph shows the price of five gallons of gasoline during the first ten months of the year. By what percent is the highest price more than the lowest price?\n\n", "completion": "\\boxed{70}", "image_path": "dataset/math_vision/images/2705.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The two markers with a question mark have the same value.\n\nWhich value do you have to use instead of the question mark so that the calculation is correct?", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/680.png" }, { "solution": "\\boxed{154}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows twenty congruent circles arranged in three rows and enclosed in a rectangle. The circles are tangent to one another and to the sides of the rectangle as shown in the diagram. The ratio of the longer dimension of the rectangle to the shorter dimension can be written as $\\frac{1}{2}\\left(\\sqrt{p}-q\\right),$ where $p$ and $q$ are positive integers. Find $p+q$.\n\n", "completion": "\\boxed{154}", "image_path": "dataset/math_vision/images/2062.png" }, { "solution": "\\boxed{60}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Barbara wants to complete the diagram below by inserting three numbers, one into each empty cell. She wants the sum of the first three numbers to be 100 , the sum of the middle three numbers to be 200 and the sum of the last three numbers to be 300 . What number should Barbara insert into the middle cell of the diagram? ", "completion": "\\boxed{60}", "image_path": "dataset/math_vision/images/1591.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three semicircles of radius $ 1$ are constructed on diameter $ AB$ of a semicircle of radius $ 2$. The centers of the small semicircles divide $ \\overline{AB}$ into four line segments of equal length, as shown. What is the area of the shaded region that lies within the large semicircle but outside the smaller semicircles?\n\\n Options: A. $\\pi-\\sqrt{3}$, B. $\\pi-\\sqrt{2}$, C. $\\frac{\\pi+\\sqrt{2}}{2}$, D. $\\frac{\\pi+\\sqrt{3}}{2}$, E. $\\frac{7}{6}\\pi-\\frac{\\sqrt{3}}{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2128.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One of the following nets cannot be folded along the dashed lines shown to form a cube. Which one?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1605.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The function $J(x)$ is defined by:\n$$\nJ(x)= \\begin{cases}4+x & \\text { for } x \\leq-2 \\\\ -x & \\text { for }-20\\end{cases}\n$$\n\nHow many distinct real solutions has the equation $J(J(J(x)))=0$ ?", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2018.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lisas aviation club designs a flag with a flying \"dove\" on a $4 \\times 6$-grid. The area of the \"dove\" is $192 \\mathrm{~cm}^{2}$. The perimeter of the \"dove\" is made up of straight lines and circular arcs. What measurements does the flag have?\n\\n Options: A. $6 \\mathrm{~cm} \\times 4 \\mathrm{~cm}$, B. $12 \\mathrm{~cm} \\times 8 \\mathrm{~cm}$, C. $20 \\mathrm{~cm} \\times 12 \\mathrm{~cm}$, D. $24 \\mathrm{~cm} \\times 16 \\mathrm{~cm}$, E. $30 \\mathrm{~cm} \\times 20 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1173.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Diagonals are drawn in three adjacent faces of a cube as shown in the picture. Which of the following nets is that of the given cube?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/746.png" }, { "solution": "\\boxed{13}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each side of a triangle $A B C$ is being extended to the points $\\mathrm{P}, \\mathrm{Q}, \\mathrm{R}, \\mathrm{S}, \\mathrm{T}$ and $\\mathrm{U}$, so that $\\mathrm{PA}=\\mathrm{AB}=\\mathrm{BS}, \\mathrm{TC}=\\mathrm{CA}$ $=\\mathrm{AQ}$ and $\\mathrm{UC}=\\mathrm{CB}=\\mathrm{BR}$. The area of $\\mathrm{ABC}$ is 1. How big is the area of the hexagon PQRSTU?\n", "completion": "\\boxed{13}", "image_path": "dataset/math_vision/images/216.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The regular eight-sided shape on the right has sides of length 10. A circle touches all inscribed diagonals of this eight-sided shape. What is the radius of this circle?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/255.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The parabola in the figure has an equation of the form $y=a x^{2}+b x+c$ for some distinct real numbers $a, b$ and $c$. Which of the following equations could be an equation of the line in the figure?\n\\n Options: A. $y=b x+c$, B. $y=c x+b$, C. $y=a x+b$, D. $y=a x+c$, E. $y=c x+a$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/354.png" }, { "solution": "\\boxed{21}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ellis's Eel Emporium contains a large tank holding three different types of eel: electric eels, moray eels and freshwater eels. A notice on the tank reads as follows:\n\nHow many eels are in the tank?", "completion": "\\boxed{21}", "image_path": "dataset/math_vision/images/1770.png" }, { "solution": "\\boxed{11}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The five small shaded squares inside this unit square are congruent and have disjoint interiors. The midpoint of each side of the middle square coincides with one of the vertices of the other four small squares as shown. The common side length is $\\frac{a-\\sqrt{2}}{b}$, where $a$ and $b$ are positive integers. What is $a+b$ ?\n\n", "completion": "\\boxed{11}", "image_path": "dataset/math_vision/images/2483.png" }, { "solution": "\\boxed{47}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The vertices of a convex pentagon are $(-1, -1), (-3, 4), (1, 7), (6, 5)$ and $(3, -1)$. What is the area of the pentagon? ", "completion": "\\boxed{47}", "image_path": "dataset/math_vision/images/2973.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A barber wants to write the word SHAVE on a board so that a customer who sees the word in the mirror can read the word normally. How does he have to write the word on the board?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1425.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cylindrical tin is $15 \\mathrm{~cm}$ high. The circumference of the base circle is $30 \\mathrm{~cm}$. An ant walks from point $A$ at the base to point $B$ at the top. Its path is partly vertically upwards and partly along horizontal circular arcs. Its path is drawn in bold on the diagram (with a solid line on the front and a dashed line at the back). How long is the total distance covered by the ant? \\n Options: A. $45 \\mathrm{~cm}$, B. $55 \\mathrm{~cm}$, C. $60 \\mathrm{~cm}$, D. $65 \\mathrm{~cm}$, E. $75 \\mathrm{~cm}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/381.png" }, { "solution": "\\boxed{77}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The big rectangle consists of various squares of different sizes. Each of the three smallest squares has area 1. How big is the area of the big rectangle?\n", "completion": "\\boxed{77}", "image_path": "dataset/math_vision/images/594.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers on each pair of opposite faces on a die add up to 7 . A die is rolled without slipping around the circuit shown. At the start the top face is 3 . What number will be displayed on the top face at the end point? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1824.png" }, { "solution": "\\boxed{28}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $\\overline{BC}$ is parallel to the segment through $A$, and $AB = BC$. What is the number of degrees represented by $x$?\n\n", "completion": "\\boxed{28}", "image_path": "dataset/math_vision/images/2920.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn $\\triangle ABC$, $E$ is the midpoint of side $BC$ and $D$ is on side $AC$. If the length of $AC$ is $1$ and $\\measuredangle BAC = 60^\\circ$, $\\measuredangle ABC = 100^\\circ$, $\\measuredangle ACB = 20^\\circ$ and $\\measuredangle DEC = 80^\\circ$, then the area of $\\triangle ABC$ plus twice the area of $\\triangle CDE$ equals\\n Options: A. $\\frac{1}{4}\\cos 10^\\circ$, B. $\\frac{\\sqrt{3}}{8}$, C. $\\frac{1}{4}\\cos 40^\\circ$, D. $\\frac{1}{4}\\cos 50^\\circ$, E. $\\frac{1}{8}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2330.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Numbers are to be placed into the square grid shown, so that each of the numbers $1,2,3,4$ and 5 appears exactly once in each row and in each column. Furthermore sthe sum of all numbers in the three black-bordered sections should always be the same. Which number has to be written into the top right cell?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/334.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Distinct points $A$ and $B$ are on a semicircle with diameter $MN$ and center $C$. The point $P$ is on $CN$ and $\\angle CAP = \\angle CBP = 10^{\\circ}$. If $\\stackrel{\\frown}{MA} = 40^{\\circ}$, then $\\stackrel{\\frown}{BN}$ equals\n\n\\n Options: A. $10^{\\circ}$, B. $15^{\\circ}$, C. $20^{\\circ}$, D. $25^{\\circ}$, E. $30^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2348.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five children each light a candle at the same time. Lisa blows out the candles at different times. Now they look as shown in the picture.\n\nWhich candle did Lisa blow out first?\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/679.png" }, { "solution": "\\boxed{24.2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rays $r_1$ and $r_2$ share a common endpoint. Three squares have sides on one of the rays and vertices on the other, as shown in the diagram. If the side lengths of the smallest two squares are $20$ and $22$, find the side length of the largest square.\\n", "completion": "\\boxed{24.2}", "image_path": "dataset/math_vision/images/2834.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square piece of paper of area $64 \\mathrm{~cm}^{2}$ is folded twice, as shown in the diagram. What is the sum of the areas of the two shaded rectangles?\n\\n Options: A. $10 \\mathrm{~cm}^{2}$, B. $14 \\mathrm{~cm}^{2}$, C. $15 \\mathrm{~cm}^{2}$, D. $16 \\mathrm{~cm}^{2}$, E. $24 \\mathrm{~cm}^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1789.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shows a rectangular garden with dimensions $16 \\mathrm{~m}$ and $20 \\mathrm{~m}$. The gardener has planted six identical flowerbeds (they are gray in the diagram). What is the perimeter (in metres) of each of the flowerbeds?\n", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/423.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $A B C$ is equilateral and has area 9. The dividing lines are parallel to the sides, and divide the sides into three equal lengths. What is the area of the grey shaded part of the triangle?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1095.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, it is given that angle $ C = 90^{\\circ}, \\overline{AD} = \\overline{DB}, DE \\perp AB, \\overline{AB} = 20$, and $ \\overline{AC} = 12$. The area of quadrilateral $ ADEC$ is:\n\\n Options: A. $75$, B. $58\\frac{1}{2}$, C. $48$, D. $37\\frac{1}{2}$, E. $\\text{none of these}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2257.png" }, { "solution": "\\boxed{56}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows a Fortress made from cubes. How many cubes were used to make it?\n", "completion": "\\boxed{56}", "image_path": "dataset/math_vision/images/485.png" }, { "solution": "\\boxed{2309415687}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six numbers are written on the following cards, as shown.\n\nWhat is the smallest number you can form with the given cards?", "completion": "\\boxed{2309415687}", "image_path": "dataset/math_vision/images/431.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a wooden block with 5 screws. 4 of which are equally long, one screw is shorter.\n\nWhich is the shorter screw?", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/580.png" }, { "solution": "\\boxed{72}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a square and an equilateral right-angled crossshaped dodecagon. The length of the perimeter of the dodecagon is $36 \\mathrm{~cm}$. What is the area of the square in $\\mathrm{cm}^{2}$ ? ", "completion": "\\boxed{72}", "image_path": "dataset/math_vision/images/1815.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which cloud contains even numbers only?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1177.png" }, { "solution": "\\boxed{68}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of square $ABCD$ is 100 square centimeters, and $AE = 2$ cm. What is the area of square $EFGH$, in square centimeters?\n\n", "completion": "\\boxed{68}", "image_path": "dataset/math_vision/images/2945.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The net on the right can be cut out and folded to make a cube. Which face will then be opposite the face marked $\\mathbf{x}$ ? \\n Options: A. a, B. b, C. c, D. d, E. e", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1503.png" }, { "solution": "\\boxed{\\frac{25}{3}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Coplanar squares $ABGH$ and $BCDF$ are adjacent, with $CD = 10$ units and $AH = 5$ units. Point $E$ is on segments $AD$ and $GB$. What is the area of triangle $ABE$, in square units?\n\n", "completion": "\\boxed{\\frac{25}{3}}", "image_path": "dataset/math_vision/images/2978.png" }, { "solution": "\\boxed{37}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagon?\n\n", "completion": "\\boxed{37}", "image_path": "dataset/math_vision/images/2762.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The two-sided mirrors reflect the laser beams as shown in the\nsmall picture: . At which letter does the laser beam leave the picture: ?\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/962.png" }, { "solution": "\\boxed{52}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Inside the gray square there are three white squares and the numbers inside them indicate their areas. The white squares have sides parallel to the sides of the gray square. If the area of the gray square is 81, what is the area of the gray area not covered by the white squares?\n", "completion": "\\boxed{52}", "image_path": "dataset/math_vision/images/930.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An ant climbs from $C$ to $A$ on path $C A$ and descends from $A$ to $B$ on the stairs, as shown in the diagram. What is the ratio of the lengths of the ascending and descending paths?\n\\n Options: A. 1, B. $\\frac{1}{2}$, C. $\\frac{1}{3}$, D. $\\frac{\\sqrt{2}}{2}$, E. $\\frac{\\sqrt{3}}{3}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1463.png" }, { "solution": "\\boxed{841}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each cell in this cross-number can be filled with a non-zero digit so that all of the conditions in the clues are satisfied. The digits used are not necessarily distinct.\n\n\\section*{ACROSS}\n1. Four less than a factor of 105.\n3. One more than a palindrome.\n5. The square-root of the answer to this Kangaroo question.\n\\section*{DOWN}\n1. Two less than a square.\n2. Four hundred less than a cube.\n4. Six less than the sum of the answers to two of the other clues.\nWhat is the square of the answer to 5 ACROSS?", "completion": "\\boxed{841}", "image_path": "dataset/math_vision/images/2034.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangle intersects a circle as shown: $AB=4$, $BC=5$, and $DE=3$. Then $EF$ equals:\n\n\\n Options: A. $6$, B. $7$, C. $\\frac{20}{3}$, D. $8$, E. $9$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2349.png" }, { "solution": "\\boxed{130}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Identical regular pentagons are arranged in a ring. The partially completed ring is shown in the diagram. Each of the regular pentagons has a perimeter of 65 . The regular polygon formed as the inner boundary of the ring has a perimeter of $P$. What is the value of $P$ ?\n", "completion": "\\boxed{130}", "image_path": "dataset/math_vision/images/2017.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The board beside is formed by little white and dark squares. After a ninety-degree turn, how can this board appear?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/918.png" }, { "solution": "\\boxed{400}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a church there is a rose window as in the figure, where the letters R, G and B represent glass of red colour, green colour and blue colour, respectively. Knowing that $400 \\mathrm{~cm}^{2}$ of green glass have been used, how many $\\mathrm{cm}^{2}$ of blue glass are necessary?\n", "completion": "\\boxed{400}", "image_path": "dataset/math_vision/images/191.png" }, { "solution": "\\boxed{5.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Triangle $ ABC$ is an isosceles triangle with $ \\overline{AB} =\\overline{BC}$. Point $ D$ is the midpoint of both $ \\overline{BC}$ and $ \\overline{AE}$, and $ \\overline{CE}$ is 11 units long. Triangle $ ABD$ is congruent to triangle $ ECD$. What is the length of $ \\overline{BD}$?\n\n", "completion": "\\boxed{5.5}", "image_path": "dataset/math_vision/images/2675.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Beatrice has a few grey tiles that all look exactly like the one pictured. At least how many of these tiles does she need in order to make a complete square?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/509.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five blocks are built with equal cubes glued face to face. In which of them was the smallest number of cubes used?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/108.png" }, { "solution": "\\boxed{81}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, point $A$ is the center of the circle, the measure of angle $RAS$ is 74 degrees, and the measure of angle $RTB$ is 28 degrees. What is the measure of minor arc $BR$, in degrees? ", "completion": "\\boxed{81}", "image_path": "dataset/math_vision/images/3018.png" }, { "solution": "\\boxed{864}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the subtraction calculation on the right, each of the letters $\\mathrm{K}, \\mathrm{A}, \\mathrm{N}, \\mathrm{G}, \\mathrm{R}$ and $\\mathrm{O}$ represents a different digit.\nWhat is the largest possible value of the number 'KAN'?\n", "completion": "\\boxed{864}", "image_path": "dataset/math_vision/images/1556.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An underground line has the six stations A, B, C, D, E and F. The train stops at every station. After reaching the end of the line $A$ or $F$ the train continues in the opposite direction. The train conductor starts his journey in station B. His first stop is in station C. In which station will be his $46^{\\text {th}}$ stop?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/694.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Misty the cat has five kittens: two of them are striped, one spotty, the rest of them are absolutely white. In which picture can we see the kittens of Misty, knowing that the ears of one of them are of different colour?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/6.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Kate has four flowers, which have $6,7,8$ and 11 petals respectively. She now tears off one petal from each of three different flowers. She repeats this until it is no longer possible to tear off one petal from each of three different flowers. What is the minimum number of petals left over?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/577.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: When she drew two intersecting circles, as shown, Tatiana divided the space inside the circles into three regions. When drawing two intersecting squares, what is the largest number of regions inside one or both of the squares that Tatiana could create? ", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1792.png" }, { "solution": "\\boxed{116}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A bar code of the type shown is composed of alternate strips of black and white, always beginning and ending with a black strip. Each strip in the bar code has width either 1 or 2 , and the total width of the bar code is 12 . Two bar codes are different if they read differently from left to right. How many different bar codes of this type can be made? ", "completion": "\\boxed{116}", "image_path": "dataset/math_vision/images/1869.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, two regular hexagons are equal to each other. What part of the parallelogram's area is shaded?\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{1}{3}$, C. $\\frac{1}{4}$, D. $\\frac{1}{5}$, E. $\\frac{1}{6}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1314.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Semicircle $\\stackrel{\\frown}{AB}$ has center $C$ and radius $1$. Point $D$ is on $\\stackrel{\\frown}{AB}$ and $\\overline{CD} \\perp \\overline{AB}$. Extend $\\overline{BD}$ and $\\overline{AD}$ to $E$ and $F$, respectively, so that circular arcs $\\stackrel{\\frown}{AE}$ and $\\stackrel{\\frown}{BF}$ have $B$ and $A$ as their respective centers. Circular arc $\\stackrel{\\frown}{EF}$ has center $D$. The area of the shaded \"smile\", $AEFBDA$, is\n\n\\n Options: A. $(2 - \\sqrt{2})\\pi$, B. $2\\pi - \\pi\\sqrt{2} - 1$, C. $\\left(1 - \\frac{\\sqrt{2}}{2}\\right)\\pi$, D. $\\frac{5\\pi}{2} - \\pi\\sqrt{2} - 1$, E. $(3 - 2\\sqrt{2})\\pi$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2399.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Aladdin's carpet has the shape of a square. Along each edge there are two rows of dots (see diagram). The number of points is the same along each edge. How many dots in total does the carpet have?\n", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/669.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Diana produces a bar chart which shows the number of four different types of trees which she has counted on a biology trip. Heinz believes that a pie chart would represent the ratio of the different types of trees in a better way. What would the pie chart look like?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/271.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Vumos wants to write the integers 1 to 9 in the nine boxes shown so that the sum of the integers in any three adjacent boxes is a multiple of 3 . In how many ways can he do this? \\n Options: A. $6 \\times 6 \\times 6 \\times 6$, B. $6 \\times 6 \\times 6$, C. $2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2$, D. $6 \\times 5 \\times 4 \\times 3 \\times 2 \\times 1$, E. $9 \\times 8 \\times 7 \\times 6 \\times 5 \\times 4 \\times 3 \\times 2 \\times 1$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1992.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The shape pictured, is made out of two squares with side lengths $4 \\mathrm{~cm}$ and $5 \\mathrm{~cm}$ respectively, a triangle with area $8 \\mathrm{~cm}^{2}$ and the grey parallelogram. What is the area of the parallelogram?\n\\n Options: A. $15 \\mathrm{~cm}^{2}$, B. $16 \\mathrm{~cm}^{2}$, C. $18 \\mathrm{~cm}^{2}$, D. $20 \\mathrm{~cm}^{2}$, E. $21 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1364.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A full glass of water weighs 400 grams. An empty glass weighs 100 grams.\n\nHow much does a half-full glass of water weigh?\\n Options: A. $150 \\mathrm{~g}$, B. $200 \\mathrm{~g}$, C. $225 \\mathrm{~g}$, D. $250 \\mathrm{~g}$, E. $300 \\mathrm{~g}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/613.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Equilateral $ \\triangle ABC$ has side length $ 2$, $ M$ is the midpoint of $ \\overline{AC}$, and $ C$ is the midpoint of $ \\overline{BD}$. What is the area of $ \\triangle CDM$?\n\\n Options: A. $\\frac{\\sqrt{2}}{2}$, B. $\\frac{3}{4}$, C. $\\frac{\\sqrt{3}}{2}$, D. $1$, E. $\\sqrt{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2149.png" }, { "solution": "\\boxed{42}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What entry should replace $x$ in the table so that the numbers in each row, each column and each diagonal form an arithmetic sequence?\n(In an arithmetic sequence, there is a constant difference between successive terms.) ", "completion": "\\boxed{42}", "image_path": "dataset/math_vision/images/1821.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of the intersection of a triangle and a circle is $45 \\%$ of the total area of the diagram. The area of the triangle outside the circle is $40 \\%$ of the total area of the diagram. What percentage of the circle lies outside the triangle? \\n Options: A. $20 \\%$, B. $25 \\%$, C. $30 \\%$, D. $33 \\frac{1}{3} \\%$, E. $35 \\%$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1700.png" }, { "solution": "\\boxed{1250\\pi}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $K$, $O$ and $M$ are the centers of the three semi-circles. Also, $OC = 32$ and $CB = 36$.\n\n\n\nWhat is the area of the semi-circle with center $K$?", "completion": "\\boxed{1250\\pi}", "image_path": "dataset/math_vision/images/3038.png" }, { "solution": "\\boxed{114}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Twenty cubical blocks are arranged as shown. First, $10$ are arranged in a triangular pattern; then a layer of $6$, arranged in a triangular pattern, is centered on the $10$; then a layer of $3$, arranged in a triangular pattern, is centered on the $6$; and finally one block is centered on top of the third layer. The blocks in the bottom layer are numbered $1$ through $10$ in some order. Each block in layers $2, 3$ and $4$ is assigned the number which is the sum of the numbers assigned to the three blocks on which it rests. Find the smallest possible number which could be assigned to the top block.\n", "completion": "\\boxed{114}", "image_path": "dataset/math_vision/images/2403.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Suppose Annie the Ant is walking on a regular icosahedron (as shown). She starts on point $A$ and will randomly create a path to go to point $Z$ which is the point directly opposite to $A$. Every move she makes never moves further from Z, and she has equal probability to go down every valid move. What is the expected number of moves she can make?\\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2836.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \nIn the picture above five ladybirds can be seen. Each one is sitting on a certain flower. A ladybird is only allowed to sit on a flower if the following conditions are met:\n1) The difference between the number of points on each wing is equal to the number of leaves on the stem.\n2) The number of points on the wings of the ladybird is equal to the number of petals on the flower. Which of the following flowers is without a ladybird?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/58.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large square of side-length $10 \\mathrm{~cm}$ contains a smaller square of side-length $4 \\mathrm{~cm}$, as shown in the diagram. The corresponding sides of the two squares are parallel. What percentage of the area of the large square is shaded? \\n Options: A. $25 \\%$, B. $30 \\%$, C. $40 \\%$, D. $42 \\%$, E. $45 \\%$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1980.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The big square shown is split into four small squares. The circle touches the right side of the square in its midpoint. How big is the side length of the big square? (Hint: The diagram is not drawn to scale.) \\n Options: A. $18 \\mathrm{~cm}$, B. $20 \\mathrm{~cm}$, C. $24 \\mathrm{~cm}$, D. $28 \\mathrm{~cm}$, E. $30 \\mathrm{~cm}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/393.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $A B C D$ is a parallelogram. If $A A_{1}=4 \\mathrm{~cm}, D D_{1}=5 \\mathrm{~cm}$ and $C C_{1}=7 \\mathrm{~cm}$, what is the length of $B B_{1}$ ? \\n Options: A. $9 \\mathrm{~cm}$, B. $11 \\mathrm{~cm}$, C. $12 \\mathrm{~cm}$, D. $16 \\mathrm{~cm}$, E. $21 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1523.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new rectangles are formed, a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?\n\\n Options: A. $\\frac{1}{3}$, B. $\\frac{1}{2}$, C. $\\frac{3}{4}$, D. $\\frac{4}{5}$, E. $\\frac{5}{6}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2629.png" }, { "solution": "\\boxed{27}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Janet enters all the digits from 1 to 9 in the cells of a $3 \\times 3$ table, so that each cell contains one digit. She has already entered 1,2,3 and 4, as shown. Two numbers are considered to be 'neighbours' if their cells share an edge. After entering all the numbers, she notices that the sum of the neighbours of 9 is 15 . What is the sum of the neighbours of 8 ? ", "completion": "\\boxed{27}", "image_path": "dataset/math_vision/images/1615.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Konrad has some pieces of cardboard which all look like this:\n\nWhich of the shapes below can he not make out of these pieces?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/56.png" }, { "solution": "\\boxed{25}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Determine the area of the quadrilateral PQRS pictured on the right, where $\\mathrm{PS}=\\mathrm{RS}$, $\\angle \\mathrm{PSR}=\\angle \\mathrm{PQR}=90^{\\circ}, \\mathrm{ST} \\perp \\mathrm{PQ}$, and $\\mathrm{ST}=5$.\n", "completion": "\\boxed{25}", "image_path": "dataset/math_vision/images/237.png" }, { "solution": "\\boxed{500}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A butterfly sat down on a correctly solved exercise. What number is the butterfly covering?\n", "completion": "\\boxed{500}", "image_path": "dataset/math_vision/images/415.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An equilateral triangle and a regular hexagon are inscribed in a circle, the latter beeing inscribed in an equilateral triangle (see the picture). $S$ is the area of the big triangle, $s$ the area of the little one and $Q$ is the area of the hexagon. What is true?\n\\n Options: A. $Q=\\sqrt{S \\cdot s}$, B. $Q=\\frac{S+s}{2}$, C. $S=s+Q$, D. $Q=\\sqrt{S^{2}+s^{2}}$, E. $S=Q+3 s$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1307.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Christoph folds a see-through piece of foil along the dashed line. What can he then see?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/684.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On a standard die the sum of the numbers on opposite faces is always 7. Two identical standard dice are shown in the figure. How many dots could there be on the non-visible right-hand face (marked with \"?\")?\n\\n Options: A. only 5, B. only 2, C. either 2 or 5, D. either 1, E. 2, F. 3 or 5, G. either 2, H. 3 or 5", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/278.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The adjacent map is part of a city: the small rectangles are rocks, and the paths in between are streets. Each morning, a student walks from intersection A to intersection B, always walking along streets shown, and always going east or south. For variety, at each intersection where he has a choice, he chooses with probability $\\frac{1}{2}$ whether to go east or south. Find the probability that through any given morning, he goes through $C$.\n\n\\n Options: A. $\\frac{11}{32}$, B. $\\frac{1}{2}$, C. $\\frac{4}{7}$, D. $\\frac{21}{32}$, E. $\\frac{3}{4}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2344.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two circles have their centres on the same diagonal of a square. They touch each other and the sides of the square as shown. The side of the square is $1 \\mathrm{~cm}$ long. What is the sum of the lengths of the radii of the circles in centimetres?\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{1}{\\sqrt{2}}$, C. $\\sqrt{2}-1$, D. $2-\\sqrt{2}$, E. It depends on sizes of the circles", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1308.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Freda's flying club designed a flag of a flying dove on a square grid as shown.\nThe area of the dove is $192 \\mathrm{~cm}^{2}$. All parts of the perimeter of the dove are either quarter-circles or straight lines. What are the dimensions of the flag?\n\\n Options: A. $6 \\mathrm{~cm} \\times 4 \\mathrm{~cm}$, B. $12 \\mathrm{~cm} \\times 8 \\mathrm{~cm}$, C. $21 \\mathrm{~cm} \\times 14 \\mathrm{~cm}$, D. $24 \\mathrm{~cm} \\times 16 \\mathrm{~cm}$, E. $27 \\mathrm{~cm} \\times 18 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1659.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sara makes a staircase out of toothpicks as shown:\nThis is a 3-step staircase and uses 18 toothpicks. How many steps would be in a staircase that used 180 toothpicks?", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/2219.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three $\\text{A's}$, three $\\text{B's}$, and three $\\text{C's}$ are placed in the nine spaces so that each row and column contain one of each letter. If $\\text{A}$ is placed in the upper left corner, how many arrangements are possible?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2689.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a regular hexagon with side length 1. The grey flower is outlined by circular arcs with radius 1 whose centre's lie in the vertices of the hexagon. How big is the area of the grey flower?\n\\n Options: A. $\\frac{\\pi}{2}$, B. $\\frac{2 \\pi}{3}$, C. $2 \\sqrt{3}-\\pi$, D. $\\frac{\\pi}{2}+\\sqrt{3}$, E. $2 \\pi-3 \\sqrt{3}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/303.png" }, { "solution": "\\boxed{2143}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Betty walked around the park once, starting from the marked point in the direction of the arrow. She took 4 pictures. In which order did she take the pictures?\n", "completion": "\\boxed{2143}", "image_path": "dataset/math_vision/images/768.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A dark disc with three holes is placed on top of a dial of a watch (see diagram). Then the disc is rotated around its centre. Which numbers can be seen at the same time? \\n Options: A. 4, B. 6 and 12, C. 1, D. 5 and 10, E. 2, F. 4 and 9, G. 3, H. 6 and 9, I. 5, J. 7 and 12", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/984.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Peter places three building blocks on a table, as shown. What does he see when he is looking at them from above?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/883.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two strips of width 1 overlap at an angle of $\\alpha$ as shown. The area of the overlap (shown shaded) is\n\n\\n Options: A. $\\sin \\alpha$, B. $\\frac{1}{\\sin \\alpha}$, C. $\\frac{1}{1 - \\cos \\alpha}$, D. $\\frac{1}{\\sin^2 \\alpha}$, E. $\\frac{1}{(1 - \\cos \\alpha)^2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2382.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In square $ABCE$, $AF=2FE$ and $CD=2DE$. What is the ratio of the area of $\\triangle BFD$ to the area of square $ABCE$?\n\\n Options: A. $\\frac{1}{6}$, B. $\\frac{2}{9}$, C. $\\frac{5}{18}$, D. $\\frac{1}{3}$, E. $\\frac{7}{20}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2694.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The map shows three bus stations at points $A, B$ and $C$. A tour from station $A$ to the Zoo and the Port and back to $A$ is $10 \\mathrm{~km}$ long. $A$ tour from station $B$ to the Park and the Zoo and back to B is $12 \\mathrm{~km}$ long. A tour from station C to the Port and the Park and back to $C$ is $13 \\mathrm{~km}$ long. Also, A tour from the Zoo to the Park and the Port and back to the Zoo is $15 \\mathrm{~km}$ long. How long is the shortest tour from A to B to $C$ and back to $A$?\n\\n Options: A. $18 \\mathrm{~km}$, B. $20 \\mathrm{~km}$, C. $25 \\mathrm{~km}$, D. $35 \\mathrm{~km}$, E. $50 \\mathrm{~km}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/947.png" }, { "solution": "\\boxed{$\\frac{1}{60}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A regular dodecahedron is a figure with $12$ identical pentagons for each of its faces. Let x be the number of ways to color the faces of the dodecahedron with $12$ different colors, where two colorings are identical if one can be rotated to obtain the other. Compute $\\frac{x}{12!}$.\\n", "completion": "\\boxed{$\\frac{1}{60}$}", "image_path": "dataset/math_vision/images/2827.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The number in each box below is the product of the numbers in the two boxes that touch it in the row above. For example, $30 = 6\\times5$. What is the missing number in the top row?\n\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/2721.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The rectangular mirror has broken. Which piece is missing?\n\n\\n Options: A. (A), B. (B), C. (C), D. (D), E. (E)", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/503.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which stone should Mr Flintstone place on the right side of the scales, so that both sides weigh the same?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/475.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lydia draws a flower with 5 petals. She wants to colour in the flower using the colours white and black. How many different flowers can she draw with these two colours if the flower can also be just one colour?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/789.png" }, { "solution": "\\boxed{19}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On a circle 15 points are equally spaced. We can form triangles by joining any 3 of these. Congruent triangles, by rotation or reflection, are counted as only one triangle. How many different triangles can be drawn?\n", "completion": "\\boxed{19}", "image_path": "dataset/math_vision/images/363.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Part of an \"$n$-pointed regular star\" is shown. It is a simple closed polygon in which all $2n$ edges are congruent, angles $A_{1}$, $A_{2}$, $\\ldots$, $A_{n}$ are congruent and angles $B_{1}$, $B_{2}$, $\\ldots$, $B_{n}$ are congruent. If the acute angle at $A_{1}$ is $10^{\\circ}$ less than the acute angle at $B_{1}$, then $n = $\n", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/2398.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A star consist of a square and four triangles. All sides of the triangles are equally long. The perimeter of the square is $36 \\mathrm{~cm}$. What is the perimeter of the star?\n\\n Options: A. $144 \\mathrm{~cm}$, B. $120 \\mathrm{~cm}$, C. $104 \\mathrm{~cm}$, D. $90 \\mathrm{~cm}$, E. $72 \\mathrm{~cm}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/886.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A ship travels from point A to point B along a semicircular path, centered at Island X. Then it travels along a straight path from B to C. Which of these graphs best shows the ship's distance from Island X as it moves along its course?\n\n\\n Options: A. , B. , C. , D. , E. ", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2654.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Nick can turn right but not left on his bicycle. What is the least number of right turns he must make in order to get from $A$ to $B$?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/819.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows a cube with four marked angles, $\\angle W X Y$, $\\angle X Y Z, \\angle Y Z W$ and $\\angle Z W X$. What is the sum of these angles? \\n Options: A. $315^{\\circ}$, B. $330^{\\circ}$, C. $345^{\\circ}$, D. $360^{\\circ}$, E. $375^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1917.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four circles with radius 1 intersect each other as seen in the diagram. What is the perimeter of the grey area?\n\\n Options: A. $\\pi$, B. $\\frac{3 \\pi}{2}$, C. a number between $\\frac{3 \\pi}{2}$ and $2 \\pi$, D. $2 \\pi$, E. $\\pi^{2}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/367.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: $\\triangle ABC$ is a right angle at $C$ and $\\angle A = 20^\\circ$. If $BD$ is the bisector of $\\angle ABC$, then $\\angle BDC =$\n\\n Options: A. $40^\\circ$, B. $45^\\circ$, C. $50^\\circ$, D. $55^\\circ$, E. $60^\\circ$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2359.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sides $AB,BC,CD$ and $DA$ of convex polygon $ABCD$ have lengths 3,4,12, and 13, respectively, and $\\measuredangle CBA$ is a right angle. The area of the quadrilateral is\n\n", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/2333.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Thomas has made the following shape with 6 squares of side length 1. What is the perimeter of the shape?\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/847.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure shows three concentric circles with four lines passing through their common centre. What percentage of the figure is shaded?\n\\n Options: A. $30 \\%$, B. $35 \\%$, C. $40 \\%$, D. $45 \\%$, E. $50 \\%$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1207.png" }, { "solution": "\\boxed{40}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, if $\\triangle ABC$ and $\\triangle PQR$ are equilateral, then what is the measure of $\\angle CXY$ in degrees? ", "completion": "\\boxed{40}", "image_path": "dataset/math_vision/images/2888.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows three congruent regular hexagons. Some diagonals have been drawn, and some regions then shaded. The total shaded areas of the hexagons are $X, Y, Z$ as shown. Which of the following statements is true? \\n Options: A. $X, Y$ and $Z$ are all the same, B. $\\quad Y$ and $Z$ are equal, C. but $X$ is different, D. $X$ and $Z$ are equal, E. but $Y$ is different, F. $X$ and $Y$ are equal, G. but $Z$ is different, H. $X, Y, Z$ are all different", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1930.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A ball is made of white hexagons and black pentagons, as seen in the picture. There are 12 pentagons in total. How many hexagons are there? ", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1692.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: This picture shows you Anna's house from the front: At the back it has three windows but no door. Which picture shows Anna's house from the back?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/569.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In parallelogram $ABCD$ of the accompanying diagram, line $DP$ is drawn bisecting $BC$ at $N$ and meeting $AB$ (extended) at $P$. From vertex $C$, line $CQ$ is drawn bisecting side $AD$ at $M$ and meeting $AB$ (extended) at $Q$. Lines $DP$ and $CQ$ meet at $O$. If the area of parallelogram $ABCD$ is $k$, then the area of the triangle $QPO$ is equal to\n\\n Options: A. $k$, B. $\\frac{6k}{5}$, C. $\\frac{9k}{8}$, D. $\\frac{5k}{4}$, E. $2k$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2309.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows an isosceles triangle with $A B=A C$. If $\\angle B P C=120^{\\circ}, \\angle A B P=50^{\\circ}$, then what is angle $P B C$?\n\\n Options: A. $5^{\\circ}$, B. $10^{\\circ}$, C. $15^{\\circ}$, D. $20^{\\circ}$, E. $25^{\\circ}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1316.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sara says: \"My boat has more than one circle. It also has 2 triangles more than squares.\" Which boat belongs to Sara?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/155.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Erik has 4 bricks of the same size: . Which of the cubes shown below can he make with his 4 bricks?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/640.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each animal in the picture on the right represents a natural number greater than zero. Different animals represent a different numbers. The sum of the two numbers of each column is written underneath each column. What is the maximum value the sum of the four numbers in the upper row can have?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/976.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The robot in the diagram has been programmed to move in a straight line and, if it meets a wall (shown by bold lines), to turn right by $90^{\\circ}$ and then to continue straight on. If it cannot go straight or turn right it will stop. What will happen to this robot? \\n Options: A. It will stop at $\\mathrm{P} 2$., B. It will stop at P1., C. It will stop at $\\mathrm{T} 1$., D. It will stop at $S 1$., E. It will never stop.", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1541.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rhombus $ABCD$, point $P$ lies on segment $\\overline{AD}$ such that $BP\\perp AD$, $AP = 3$, and $PD = 2$. What is the area of $ABCD$?\n\n\\n Options: A. $3\\sqrt{5}$, B. $10$, C. $6\\sqrt{5}$, D. $20$, E. $25$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2249.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The straight line $g$ runs through the vertex $A$ of the rectangle $A B C D$ shown. The perpendicular distance from $C$ to $g$ is 2 and from $D$ to $g$ is $6. A D$ is twice as long as $A B$. Determine the length of $A D$.\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/268.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure $A B C D$ is a rectangle and $P Q R S$ a square. The area of the grey part is half as big as the area of ABCD. How long is the side PX?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1067.png" }, { "solution": "\\boxed{147}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three identical square sheets of paper each with side length $6{ }$ are stacked on top of each other. The middle sheet is rotated clockwise $30^\\circ$ about its center and the top sheet is rotated clockwise $60^\\circ$ about its center, resulting in the $24$-sided polygon shown in the figure below. The area of this polygon can be expressed in the form $a-b\\sqrt{c}$, where $a$, $b$, and $c$ are positive integers, and $c$ is not divisible by the square of any prime. What is $a+b+c?$\n\n", "completion": "\\boxed{147}", "image_path": "dataset/math_vision/images/2236.png" }, { "solution": "\\boxed{552}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Circles $\\omega_1$, $\\omega_2$, and $\\omega_3$ each have radius $4$ and are placed in the plane so that each circle is externally tangent to the other two. Points $P_1$, $P_2$, and $P_3$ lie on $\\omega_1$, $\\omega_2$, and $\\omega_3$ respectively such that $P_1P_2=P_2P_3=P_3P_1$ and line $P_iP_{i+1}$ is tangent to $\\omega_i$ for each $i=1,2,3$, where $P_4 = P_1$. See the figure below. The area of $\\triangle P_1P_2P_3$ can be written in the form $\\sqrt{a}+\\sqrt{b}$ for positive integers $a$ and $b$. What is $a+b$?\n\n", "completion": "\\boxed{552}", "image_path": "dataset/math_vision/images/2488.png" }, { "solution": "\\boxed{63}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large cube consists of 125 small black and white cubes, such that any two adjacent faces of the small cubes have different colors, the corner cubes being black. How many small black cubes are used?\n", "completion": "\\boxed{63}", "image_path": "dataset/math_vision/images/413.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A unit hexagon is composed of a regular haxagon of side length 1 and its equilateral triangular extensions, as shown in the diagram. What is the ratio of the area of the extensions to the area of the original hexagon?\n\n\\n Options: A. 1:1, B. 6:5, C. 3:2, D. 2:1, E. 3:1", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2681.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Elisabeth wants to write the numbers 1 to 9 in the fields of the diagram shown so that the product of the numbers of two fields next to each other is no greater than 15. Two fields are called „next to each other“ if they share a common edge. How many ways are there for Elisabeth to label the fields? ", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1256.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The pictures show how much 2 pieces of fruit cost altogether.\n\\n Options: A. 8 Taler, B. 9 Taler, C. 10 Taler, D. 11 Taler, E. 12 Taler", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/614.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Points $A, B, C$ and $D$ have these coordinates: $A(3,2), B(3,-2), C(-3,-2)$ and $D(-3, 0)$. The area of quadrilateral $ABCD$ is\n\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/2628.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture on the right we can see three squares. The corners of the middle square are on the midpoints of the sides of the larger square, and the corners of the smaller square are on the midpoints of the sides of the middle square. The area of the small square is $6 \\mathrm{~cm}^{2}$. What is the area of the big square?\n\\n Options: A. $24 \\mathrm{~cm}^{2}$, B. $18 \\mathrm{~cm}^{2}$, C. $15 \\mathrm{~cm}^{2}$, D. $12 \\mathrm{~cm}^{2}$, E. $9 \\mathrm{~cm}^{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1072.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Alice has four jigsaw pieces. Which two can be fitted together to form a hexagon?\\n Options: A. 1 and 2, B. 1 and 3, C. 2 and 3, D. 2 and 4, E. 1 and 4", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/983.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square has two of its vertices on a semicircle and the other two on the diameter of the semicircle as shown. The radius of the circle is 1 . What is the area of the square? \\n Options: A. $\\frac{4}{5}$, B. $\\frac{\\pi}{4}$, C. 1, D. $\\frac{4}{3}$, E. $\\frac{2}{\\sqrt{3}}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1944.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many distinct triangles can be drawn using three of the dots below as vertices?\n\n", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/2667.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: 6 beavers and 2 kangaroos are standing on the fields in this order: Of three animals in a row there is always exactly one kangaroo. On which of these numbers stands a kangaroo?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/691.png" }, { "solution": "\\boxed{224}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The truncated right circular cone below has a large base radius 8 cm and a small base radius of 4 cm. The height of the truncated cone is 6 cm. The volume of this solid is $n \\pi$ cubic cm, where $n$ is an integer. What is $n$? ", "completion": "\\boxed{224}", "image_path": "dataset/math_vision/images/2949.png" }, { "solution": "\\boxed{19}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five boys share 10 bags of marbles between themselves. Everyone gets exactly two bags:\n\nAlex gets 5 marbles, Bob 7, Charles 9 and Dennis 15. Eric gets the two bags that are left over. How many marbles does he get?", "completion": "\\boxed{19}", "image_path": "dataset/math_vision/images/576.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the picture there is a square tile with two fourths of a circle. The radius of every fourth is half the side of the tile and its length equals $5 \\mathrm{dm}$. We form a large square from 16 such tiles and try to get the longest unbroken curve consisting of the fourths. How long can this continuous curve be at most?\n\\n Options: A. $75 \\mathrm{dm}$, B. $100 \\mathrm{dm}$, C. $105 \\mathrm{dm}$, D. $110 \\mathrm{dm}$, E. $80 \\mathrm{dm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1038.png" }, { "solution": "\\boxed{167}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sam spends his days walking around the following $2\\times 2$ grid of squares. Say that two squares are adjacent if they share a side. He starts at the square labeled $1$ and every second walks to an adjacent square. How many paths can Sam take so that the sum of the numbers on every square he visits in his path is equal to $20$ (not counting the square he started on)?\\n", "completion": "\\boxed{167}", "image_path": "dataset/math_vision/images/2880.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the multiplication grid displayed, each white cell should show the product of the numbers in the grey cells that are in the same row and column respectively. One number is already entered. The integer $x$ is bigger than the positive integer $y$. What is the value of $y$?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1470.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There is an animal asleep in each of the five baskets. The koala and the fox sleep in baskets with the same pattern and the same shape. The kangaroo and the rabbit sleep in baskets with the same pattern.\n\nIn which basket does the mouse sleep?\\n Options: A. Basket 1, B. Basket 2, C. Basket 3, D. Basket 4, E. Basket 5", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/143.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are 81 grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point $P$ is the center of the square. Given that point $Q$ is randomly chosen from among the other 80 points, what is the probability that line $PQ$ is a line of symmetry for the square?\n\\n Options: A. $\\frac{1}{5}$, B. $\\frac{1}{4}$, C. $\\frac{2}{5}$, D. $\\frac{9}{20}$, E. $\\frac{1}{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2758.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A clock has three hands in different lengths (for seconds, minutes and hours). We don't know the length of each hand but we know that the clock shows the correct time. At 12:55:30 the hands are in the positions shown on the right. What does the clockface look like at 8:10:00?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/244.png" }, { "solution": "\\boxed{17.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagonals of the squares $A B C D$ and $E F G B$ are $7 \\mathrm{~cm}$ and $10 \\mathrm{~cm}$ long respectively (see diagram). The point $P$ is the point of intersection of the two diagonals of the square $A B C D$. How big is the area of the triangle $F P D$ (in $\\mathrm{cm}^{2}$)?\n", "completion": "\\boxed{17.5}", "image_path": "dataset/math_vision/images/1480.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a regular octagon, with a line drawn between two of its vertices. The shaded area measures $3 \\mathrm{~cm}^{2}$.\nWhat is the area of the octagon in square centimetres? ", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1899.png" }, { "solution": "\\boxed{36}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Figures $I$, $II$, and $III$ are squares. The perimeter of $I$ is $12$ and the perimeter of $II$ is $24$. The perimeter of $III$ is\n\n", "completion": "\\boxed{36}", "image_path": "dataset/math_vision/images/2577.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture beside shows two cogs, each with a black tooth. Where will the black teeth be after the small cog has made one full turn?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/134.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which square contains 3 quadrilaterals, 3 circles and 4 hearts?\n\\n Options: A. A), B. B), C. C), D. D), E. E)", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/468.png" }, { "solution": "\\boxed{$\\frac{8}{25}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $T$ be the answer from the previous part. Rectangle $R$ has length $T$ times its width. $R$ is inscribed in a square $S$ such that the diagonals of $ S$ are parallel to the sides of $R$. What proportion of the area of $S$ is contained within $R$?\\n", "completion": "\\boxed{$\\frac{8}{25}$}", "image_path": "dataset/math_vision/images/2839.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Square $ ABCD$ has side length $ s$, a circle centered at $ E$ has radius $ r$, and $ r$ and $ s$ are both rational. The circle passes through $ D$, and $ D$ lies on $ \\overline{BE}$. Point $ F$ lies on the circle, on the same side of $ \\overline{BE}$ as $ A$. Segment $ AF$ is tangent to the circle, and $ AF = \\sqrt{9 + 5\\sqrt{2}}$. What is $ r/s$?\n\\n Options: A. $\\frac{1}{2}$, B. $\\frac{5}{9}$, C. $\\frac{3}{5}$, D. $\\frac{5}{3}$, E. $\\frac{9}{5}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2465.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A cube of edge length $s > 0$ has the property that its surface area is equal to the sum of its volume and five times its edge length. Compute the sum of all possible values of $s$.\n\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2913.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large triangle is divided into four smaller triangles and three quadrilaterals by three straight line segments. The sum of the perimeters of the three quadrilaterals is $25 \\mathrm{~cm}$. The sum of the perimeters of the four triangles is $20 \\mathrm{~cm}$. The perimeter of the original triangle is $19 \\mathrm{~cm}$. What is the sum of the lengths of the three straight line segments?\n\\n Options: A. $11 \\mathrm{~cm}$, B. $12 \\mathrm{~cm}$, C. $13 \\mathrm{~cm}$, D. $15 \\mathrm{~cm}$, E. $16 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1596.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, the small equilateral triangles have area $4 \\mathrm{~cm}^{2}$. What is the area of the shaded region? \\n Options: A. $80 \\mathrm{~cm}^{2}$, B. $90 \\mathrm{~cm}^{2}$, C. $100 \\mathrm{~cm}^{2}$, D. $110 \\mathrm{~cm}^{2}$, E. $120 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1721.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The smaller square in the picture has area 16 and the grey triangle has area 1. What is the area of the larger square? ", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/1964.png" }, { "solution": "\\boxed{56}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows four congruent right-angled triangles inside a rectangle. What is the total area, in $\\mathrm{cm}^{2}$, of the four triangles? ", "completion": "\\boxed{56}", "image_path": "dataset/math_vision/images/1774.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anna and Peter live in the same street. On one side of Anna's house there are 27 houses, and on the other side 13 houses. Peter lives in the house right in the middle of the street. How many houses are there between Anna's and Peter's houses?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/465.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the figure, $ ABCD$ is a $ 2\\times 2$ square, $ E$ is the midpoint of $ \\overline{AD}$, and $ F$ is on $ \\overline{BE}$. If $ \\overline{CF}$ is perpendicular to $ \\overline{BE}$, then the area of quadrilateral $ CDEF$ is\n\\n Options: A. $2$, B. $3 - \\frac{\\sqrt{3}}{2}$, C. $\\frac{11}{5}$, D. $\\sqrt{5}$, E. $\\frac{9}{4}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2429.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A goldsmith has 12 double-links of chain. Out of these he wants to make a single closed chain with 24 links. What is the minimum number of links that he must open (and close again)?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/1362.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The numbers 1 to 8 are to be placed, one per circle, in the circles shown. The number next to each arrow shows what the product of the numbers in the circles on that straight line should be.\nWhat will be the sum of the numbers in the three circles at the bottom of the diagram?\n", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/1699.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In an arcade game, the \"monster\" is the shaded sector of a circle of radius $ 1$ cm, as shown in the figure. The missing piece (the mouth) has central angle $ 60^{\\circ}$. What is the perimeter of the monster in cm?\n\n\\n Options: A. $\\pi + 2$, B. $2\\pi$, C. $\\frac{5}{3} \\pi$, D. $\\frac{5}{6} \\pi + 2$, E. $\\frac{5}{3} \\pi + 2$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2352.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the shapes below cannot be divided into two trapeziums by a single straight line?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1706.png" }, { "solution": "\\boxed{18}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Five squares and two right-angled triangles are positioned as shown. The areas of three squares are $3 \\mathrm{~m}^{2}, 7 \\mathrm{~m}^{2}$ and $22 \\mathrm{~m}^{2}$ as shown. What is the area, in $\\mathrm{m}^{2}$, of the square with the question mark? ", "completion": "\\boxed{18}", "image_path": "dataset/math_vision/images/1971.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, the centre of the top square is directly above the common edge of the lower two squares. Each square has sides of length $1 \\mathrm{~cm}$. What is the area of the shaded region? \\n Options: A. $\\frac{3}{4} \\mathrm{~cm}^{2}$, B. $\\frac{7}{8} \\mathrm{~cm}^{2}$, C. $1 \\mathrm{~cm}^{2}$, D. $1 \\frac{1}{4} \\mathrm{~cm}^{2}$, E. $1 \\frac{1}{2} \\mathrm{~cm}^{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1620.png" }, { "solution": "\\boxed{22}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each square in a $5 \\times 5$ grid is either filled or empty, and has up to eight adjacent neighboring squares, where neighboring squares share either a side or a corner. The grid is transformed by the following rules:\n\nAny filled square with two or three filled neighbors remains filled.\nAny empty square with exactly three filled neighbors becomes a filled square.\nAll other squares remain empty or become empty.\n\nA sample transformation is shown in the figure below.\n\n\nSuppose the $5 \\times 5$ grid has a border of empty squares surrounding a $3 \\times 3$ subgrid. How many initial configurations will lead to a transformed grid consisting of a single filled square in the center after a single transformation? (Rotations and reflections of the same configuration are considered different.)\n", "completion": "\\boxed{22}", "image_path": "dataset/math_vision/images/2251.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: To meet the New Year day 2008, Basil put on a T-shirt with on it, and stood in front of a mirror on his hands, with his feet up. What number did Nick standing on his feet behind Basil see in the mirror?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1310.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ann has the square sheet of paper shown in the left-hand diagram. By cutting along lines of the square, she produces copies of the shape shown in the right-hand diagram. What is the smallest possible number of cells she can leave unused? ", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/1598.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A particle moves through the first quadrant as follows. During the first minute it moves from the origin to $(1,0)$. Thereafter, it continues to follow the directions indicated in the figure, going back and forth between the positive $x$ and $y$ axes, moving one unit of distance parallel to an axis in each minute. At which point will the particle be after exactly $1989$ minutes?\n\\n Options: A. (35, B. 44), C. (36, D. 45), E. (37, F. 45), G. (44, H. 35), I. (45, J. 36)", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2385.png" }, { "solution": "\\boxed{71}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Parallelograms $ABGF$, $CDGB$ and $EFGD$ are drawn so that $ABCDEF$ is a convex hexagon, as shown. If $\\angle ABG = 53^o$ and $\\angle CDG = 56^o$, what is the measure of $\\angle EFG$, in degrees?\\n", "completion": "\\boxed{71}", "image_path": "dataset/math_vision/images/2806.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The ratio of the radii of the sector and the incircle in the picture is $3: 1$. Than the ratio of their areas is:\n\\n Options: A. $3: 2$, B. $4: 3$, C. $\\sqrt{3}: 1$, D. $2: 1$, E. $9: 1$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/189.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sofie wants to write the word KENGU by using letters from the boxes. She can only take one letter from each box. What letter must Sofie take from box 4?\n\\n Options: A. K, B. E, C. N, D. G, E. U", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/941.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following symbols for signs of the Zodiac has an axis of symmetry?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1206.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following $4 \\times 4$ tiles cannot be formed by combining the two given pieces?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1667.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A rectangular piece of paper $A B C D$ is $5 \\mathrm{~cm}$ wide and $50 \\mathrm{~cm}$ long. The paper is white on one side and grey on the other. Christina folds the strip as shown so that the vertex $B$ coincides with $M$ the midpoint of the edge $C D$. Then she folds it so that the vertex $D$ coincides with $N$ the midpoint of the edge $A B$. How big is the area of the visible white part in the diagram?\n\n\n\\n Options: A. $50 \\mathrm{~cm}^{2}$, B. $60 \\mathrm{~cm}^{2}$, C. $62.5 \\mathrm{~cm}^{2}$, D. $100 \\mathrm{~cm}^{2}$, E. $125 \\mathrm{~cm}^{2}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/292.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $ \\triangle ABC$ , $ AB = 13$, $ AC = 5$, and $ BC = 12$. Points $ M$ and $ N$ lie on $ \\overline{AC}$ and $ \\overline{BC}$, respectively, with $ CM = CN = 4$. Points $ J$ and $ K$ are on $ \\overline{AB}$ so that $ \\overline{MJ}$ and $ \\overline{NK}$ are perpendicular to $ \\overline{AB}$. What is the area of pentagon $ CMJKN$?\n\\n Options: A. $15$, B. $\\frac{81}{5}$, C. $\\frac{205}{12}$, D. $\\frac{240}{13}$, E. $20$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2460.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Raphael has three squares. The first one has side length $2 \\mathrm{~cm}$, the second one has side length $4 \\mathrm{~cm}$ and one corner is the centre of the first square. The third square has side length $6 \\mathrm{~cm}$ and one corner is the centre of the second square. What is the total area of the figure shown?\n\\n Options: A. $51 \\mathrm{~cm}^{2}$, B. $32 \\mathrm{~cm}^{2}$, C. $27 \\mathrm{~cm}^{2}$, D. $16 \\mathrm{~cm}^{2}$, E. $6 \\mathrm{~cm}^{2}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/875.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four unit squares are placed edge to edge as shown. What is the length of the line $P Q$ ? \\n Options: A. 5, B. $\\sqrt{13}$, C. $\\sqrt{5}+\\sqrt{2}$, D. $\\sqrt{5}$, E. 13", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1842.png" }, { "solution": "\\boxed{1}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a tournament each of the six teams plays one match against every other team. In each round of matches, three take place simultaneously. A TV station has already decided which match it will broadcast for each round, as shown in the diagram. In which round will team $\\mathrm{S}$ play against team U?\n", "completion": "\\boxed{1}", "image_path": "dataset/math_vision/images/1694.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram on the right, the triangle is equilateral.\n\nWhat is the area of the large circle divided by the area of the small circle?", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1522.png" }, { "solution": "\\boxed{28}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Will stands at a point $P$ on the edge of a circular room with perfectly reflective walls. He shines two laser pointers into the room, forming angles of $n^o$ and $(n + 1)^o$ with the tangent at $P$, where $n$ is a positive integer less than $90$. The lasers reflect off of the walls, illuminating the points they hit on the walls, until they reach $P$ again. ($P$ is also illuminated at the end.) What is the minimum possible number of illuminated points on the walls of the room?\\n", "completion": "\\boxed{28}", "image_path": "dataset/math_vision/images/2856.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are rectangular cards divided into 4 equal cells with different shapes drawn in each cell. Cards can be placed side by side only if the same shapes appear in adjacent cells on their common side. 9 cards are used to form a rectangle as shown in the figure. Which of the following cards was definitely NOT used to form this rectangle?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/959.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle of radius 2 is centered at $ O$. Square $ OABC$ has side length 1. Sides $ \\overline{AB}$ and $ \\overline{CB}$ are extended past $ b$ to meet the circle at $ D$ and $ E$, respectively. What is the area of the shaded region in the figure, which is bounded by $ \\overline{BD}$, $ \\overline{BE}$, and the minor arc connecting $ D$ and $ E$?\n\n\\n Options: A. $\\frac{\\pi}3 + 1 - \\sqrt{3}$, B. $\\frac{\\pi}2\\left( 2 - \\sqrt{3}\\right)$, C. $\\pi\\left(2 - \\sqrt{3}\\right)$, D. $\\frac{\\pi}{6} + \\frac{\\sqrt{3} - 1}{2} \\ \\indent$, E. $\\frac{\\pi}{3} - 1 + \\sqrt{3}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2159.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Lea should write the numbers 1 to 7 in the fields of the given figure. There is only one number allowed in every field. Two consecutive numbers are not allowed to be in adjacent fields. Two fields are adjacent if they have one edge or one corner in common. Which numbers can she write into the field with the question mark?\n\\n Options: A. all 7 numbers, B. only odd numbers, C. only even numbers, D. the number 4, E. the numbers 1 or 7", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/599.png" }, { "solution": "\\boxed{320}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The rectangle shown has length $AC=32$, width $AE=20$, and $B$ and $F$ are midpoints of $\\overline{AC}$ and $\\overline{AE}$, respectively. The area of quadrilateral $ABDF$ is\n\n", "completion": "\\boxed{320}", "image_path": "dataset/math_vision/images/2569.png" }, { "solution": "\\boxed{45^2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In right $\\triangle ABC$, shown here, $AB = 15 \\text{ units}$, $AC = 24 \\text{ units}$ and points $D,$ $E,$ and $F$ are the midpoints of $\\overline{AC}, \\overline{AB}$ and $\\overline{BC}$, respectively. In square units, what is the area of $\\triangle DEF$?\n\n", "completion": "\\boxed{45^2}", "image_path": "dataset/math_vision/images/2925.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Equilateral triangle $ABC$ has been creased and folded so that vertex $A$ now rests at $A'$ on $\\overline{BC}$ as shown. If $BA' = 1$ and $A'C = 2$ then the length of crease $\\overline{PQ}$ is\n\\n Options: A. $\\frac{8}{5}$, B. $\\frac{7}{20}\\sqrt{21}$, C. $\\frac{1+\\sqrt{5}}{2}$, D. $\\frac{13}{8}$, E. $\\sqrt{3}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2394.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rectangle $J K L M$, the bisector of angle $K J M$ cuts the diagonal $K M$ at point $N$ as shown. The distances between $N$ and sides $L M$ and $K L$ are $8 \\mathrm{~cm}$ and $1 \\mathrm{~cm}$ respectively. The length of $K L$ is $(a+\\sqrt{b}) \\mathrm{cm}$. What is the value of $a+b$ ?\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/1997.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: After the storm last night, the flagpole on our school building is leaning over. Looking from northwest, its tip is to the right of its bottom point. Looking from the east, its tip is also to the right of its bottom point. In which direction could the flagpole be leaning over?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/353.png" }, { "solution": "\\boxed{140}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two externally tangent circles $\\omega_1$ and $\\omega_2$ have centers $O_1$ and $O_2$, respectively. A third circle $\\Omega$ passing through $O_1$ and $O_2$ intersects $\\omega_1$ at $B$ and $C$ and $\\omega_2$ at $A$ and $D$, as shown. Suppose that $AB = 2$, $O_1O_2 = 15$, $CD = 16$, and $ABO_1CDO_2$ is a convex hexagon. Find the area of this hexagon.\n", "completion": "\\boxed{140}", "image_path": "dataset/math_vision/images/2102.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below, $\\triangle ABC$ is isosceles and its area is 240. What is the $y$-coordinate of $A?$\n\n", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/3026.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: We have a large number of blocks of $1 \\mathrm{~cm} \\times$ $2 \\mathrm{~cm} \\times 4 \\mathrm{~cm}$. We will try to put as many of these blocks as possible into a box of $4 \\mathrm{~cm} \\times$ $4 \\mathrm{~cm} \\times 4 \\mathrm{~cm}$ so that we were able to close the box with a lid. How many blocks fit in?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/454.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A three-quarter sector of a circle of radius $4$ inches together with its interior can be rolled up to form the lateral surface area of a right circular cone by taping together along the two radii shown. What is the volume of the cone in cubic inches?\n\\n Options: A. $3\\pi \\sqrt{5}$, B. $4\\pi \\sqrt{3}$, C. $3 \\pi \\sqrt{7}$, D. $6\\pi \\sqrt{3}$, E. $6\\pi \\sqrt{7}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2228.png" }, { "solution": "\\boxed{63}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ellie wants to write a number in each box of the diagram shown. She has already written in two of the numbers. She wants the sum of all the numbers to be 35, the sum of the numbers in the first three boxes to be 22, and the sum of the numbers in the last three boxes to be 25. What is the product of the numbers she writes in the shaded boxes?", "completion": "\\boxed{63}", "image_path": "dataset/math_vision/images/1642.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A square is divided into 25 small squares (see the picture). Find the measure of the angle which is the sum of the angles $M A N, M B N, M C N, M D N, M E N$.\n\\n Options: A. 30°, B. 45°, C. 60°, D. 75°, E. 90°", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1006.png" }, { "solution": "\\boxed{72}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, the centre of the circle is $O.$ The area of the shaded region is $20\\%$ of the area of the circle. What is the value of $x?$ ", "completion": "\\boxed{72}", "image_path": "dataset/math_vision/images/2967.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Rosa wants to start at the arrow, follow the line, and get out at the other arrow. Which piece is it NOT possible to put in the middle to obtain that?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/948.png" }, { "solution": "\\boxed{72}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each square in a $3\\times 3$ grid of squares is colored red, white, blue, or green so that every $2\\times 2$ square contains one square of each color. One such coloring is shown on the right below. How many different colorings are possible?\n", "completion": "\\boxed{72}", "image_path": "dataset/math_vision/images/2253.png" }, { "solution": "\\boxed{7}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Amira is traveling from Atown to Betown and passes by two indicative signs along the road. One of them has a hidden number. What is this number?\n", "completion": "\\boxed{7}", "image_path": "dataset/math_vision/images/917.png" }, { "solution": "\\boxed{318}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $ABC$, $BC = 23$, $CA = 27$, and $AB = 30$. Points $V$ and $W$ are on $\\overline{AC}$ with $V$ on $\\overline{AW}$, points $X$ and $Y$ are on $\\overline{BC}$ with $X$ on $\\overline{CY}$, and points $Z$ and $U$ are on $\\overline{AB}$ with $Z$ on $\\overline{BU}$. In addition, the points are positioned so that $\\overline{UV} \\parallel \\overline{BC}$, $\\overline{WX} \\parallel \\overline{AB}$, and $\\overline{YZ} \\parallel \\overline{CA}$. Right angle folds are then made along $\\overline{UV}$, $\\overline{WX}$, and $\\overline{YZ}$. The resulting figure is placed on a level floor to make a table with triangular legs. Let $h$ be the maximum possible height of a table constructed from triangle $ABC$ whose top is parallel to the floor. Then $h$ can be written in the form $\\frac{k \\sqrt{m}}{n}$, where $k$ and $n$ are relatively prime positive integers and $m$ is a positive integer that is not divisible by the square of any prime. Find $k + m + n$.\n\n", "completion": "\\boxed{318}", "image_path": "dataset/math_vision/images/2076.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Nick wants to write whole numbers into the cells of the $3 \\times 3$-table on the right so that the sum of the digits in each in each $2 \\times 2$-sub-table is always 10. Five numbers have already been written. Determine the sum of the remaining four numbers.\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/1350.png" }, { "solution": "\\boxed{276}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Priti is learning a new language called Tedio. During her one hour lesson, which started at midday, she looks at the clock and notices that the hour hand and the minute hand make exactly the same angle with the vertical, as shown in the diagram. How many whole seconds remain until the end of the lesson?\n", "completion": "\\boxed{276}", "image_path": "dataset/math_vision/images/2009.png" }, { "solution": "\\boxed{10}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ralf has a number of equally big plastic plates each in the form of a regular five sided shape. He glues them together along the sides to form a complete ring (see picture). Out of how many of these plates is the ring made up?\n", "completion": "\\boxed{10}", "image_path": "dataset/math_vision/images/257.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three circular arcs of radius $5$ units bound the region shown. Arcs $AB$ and $AD$ are quarter-circles, and arc $BCD$ is a semicircle. What is the area, in square units, of the region?\n\n\\n Options: A. $25$, B. $10 + 5\\pi$, C. $50$, D. $50 + 5\\pi$, E. $25\\pi$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2621.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of $\\triangle ABC$?\n\n\\n Options: A. $\\frac{1}{6}$, B. $\\frac{1}{5}$, C. $\\frac{2}{9}$, D. $\\frac{1}{3}$, E. $\\frac{\\sqrt{2}}{4}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2183.png" }, { "solution": "\\boxed{17}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a solid with six triangular faces. At each vertex there is a number and two of the numbers are 1 and 5, as shown. For each face the sum of the numbers at the three vertices of each face is calculated, and all the sums are the same. What is the sum of all five numbers at the vertices? ", "completion": "\\boxed{17}", "image_path": "dataset/math_vision/images/1563.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two plane mirrors $O P$ and $O Q$ are inclined at an acute angle (diagram is not to scale). A ray of light $X Y$ parallel to $O Q$ strikes mirror $O P$ at $Y$. The ray is reflected and hits mirror $O Q$, is reflected again and hits mirror $O P$ and is reflected for a third time and strikes mirror $O Q$ at right angles at $R$ as shown. If $O R=5 \\mathrm{~cm}$, what is the distance $d$ of the ray $X Y$ from the mirror $O Q$?\n\\n Options: A. $4 \\mathrm{~cm}$, B. $4.5 \\mathrm{~cm}$, C. $5 \\mathrm{~cm}$, D. $5.5 \\mathrm{~cm}$, E. $6 \\mathrm{~cm}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/365.png" }, { "solution": "\\boxed{64}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Four cubes, each with surface area $24 \\mathrm{~cm}^{2}$, are placed together to form a cuboid as shown. What is the surface area of this cuboid, in $\\mathrm{cm}^{2}$ ? ", "completion": "\\boxed{64}", "image_path": "dataset/math_vision/images/1857.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which picture shows a single large loop?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/544.png" }, { "solution": "\\boxed{50}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The point $ O$ is the center of the circle circumscribed about $ \\triangle ABC$, with $ \\angle BOC = 120^\\circ$ and $ \\angle AOB = 140^\\circ$, as shown. What is the degree measure of $ \\angle ABC$?\n", "completion": "\\boxed{50}", "image_path": "dataset/math_vision/images/2468.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What do you see if you look at the tower, which is made up of two building blocks, exactly from above?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/46.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large square region is paved with $n^2$ gray square tiles, each measuring $s$ inches on a side. A border $d$ inches wide surrounds each tile. The figure below shows the case for $n = 3$. When $n = 24$, the $576$ gray tiles cover $64\\%$ of the area of the large square region. What is the ratio $\\frac{d}{s}$ for this larger value of $n$?\n\n\\n Options: A. $\\frac{6}{25}$, B. $\\frac{1}{4}$, C. $\\frac{9}{25}$, D. $\\frac{7}{16}$, E. $\\frac{9}{16}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2770.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Three circular hoops are joined together so that they intersect at rightangles as shown. A ladybird lands on an intersection and crawls around the outside of the hoops by repeating this procedure: she travels along a quarter-circle, turns $90^{\\circ}$ to the right, travels along a quarter-circle and turns $90^{\\circ}$ to the left. Proceeding in this way, how many quarter-circles will she travel along before she first returns to her starting point? ", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1855.png" }, { "solution": "\\boxed{31}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example, $2,5,8,11,14$ is an arithmetic sequence with five terms, in which the first term is $2$ and the constant added is $3$. Each row and each column in this $5\\times5$ array is an arithmetic sequence with five terms. What is the value of $X$?\n", "completion": "\\boxed{31}", "image_path": "dataset/math_vision/images/2734.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In kangaroo land you pay with \"Kangas\". Lucy has a few Kangas in her purse. She buys a ball and pays 7 Kangas. How many Kangas does she have left over, after she has paid fort he ball?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/530.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: What is the sum of the two marked angles?\n\\n Options: A. $150^{\\circ}$, B. $180^{\\circ}$, C. $270^{\\circ}$, D. $320^{\\circ}$, E. $360^{\\circ}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1132.png" }, { "solution": "\\boxed{148}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram below, angle $ABC$ is a right angle. Point $D$ is on $\\overline{BC}$, and $\\overline{AD}$ bisects angle $CAB$. Points $E$ and $F$ are on $\\overline{AB}$ and $\\overline{AC}$, respectively, so that $AE=3$ and $AF=10$. Given that $EB=9$ and $FC=27$, find the integer closest to the area of quadrilateral $DCFG$.\n\n", "completion": "\\boxed{148}", "image_path": "dataset/math_vision/images/2063.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Tess runs counterclockwise around rectangular block JKLM. She lives at corner J. Which graph could represent her straight-line distance from home?\n\n\\n Options: A. , B. , C. , D. , E. ", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2659.png" }, { "solution": "\\boxed{72}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The distance of two not-crossing edges of a regular tetrahedron (triangular pyramid with all the six edges equal) is $6 \\mathrm{~cm}$. What is the volume of the tetrahedron $\\left(\\right.$ in $\\left.\\mathrm{cm}^{3}\\right)$?\n", "completion": "\\boxed{72}", "image_path": "dataset/math_vision/images/1309.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: An \"n-pointed star\" is formed as follows: the sides of a convex polygon are numbered consecutively $1,2,\\cdots,k,\\cdots,n$, $n\\geq 5$; for all $n$ values of $k$, sides $k$ and $k+2$ are non-parallel, sides $n+1$ and $n+2$ being respectively identical with sides $1$ and $2$; prolong the $n$ pairs of sides numbered $k$ and $k+2$ until they meet. (A figure is shown for the case $n=5$)\n\n\nLet $S$ be the degree-sum of the interior angles at the $n$ points of the star; then $S$ equals:\\n Options: A. 180, B. 360, C. 180(n+2), D. 180(n-2), E. 180(n-4)", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2285.png" }, { "solution": "\\boxed{$\\frac{1}{2}+\\frac{\\sqrt{3}}{3}$}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Let $ABC$ be an equilateral triangle and $CDEF$ a square such that $E$ lies on segment $AB$ and $F$ on segment $BC$. If the perimeter of the square is equal to $4$, what is the area of triangle $ABC$?\\n", "completion": "\\boxed{$\\frac{1}{2}+\\frac{\\sqrt{3}}{3}$}", "image_path": "dataset/math_vision/images/2844.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How many white squares must you paint grey so that the number of grey squares is exactly half that of the white squares?\n", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/407.png" }, { "solution": "\\boxed{\\frac{4}{5}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In $\\triangle{ABC}$, shown, $\\cos{B}=\\frac{3}{5}$. What is $\\cos{C}$?\n\n", "completion": "\\boxed{\\frac{4}{5}}", "image_path": "dataset/math_vision/images/2894.png" }, { "solution": "\\boxed{850}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: On square $ABCD,$ points $E,F,G,$ and $H$ lie on sides $\\overline{AB},\\overline{BC},\\overline{CD},$ and $\\overline{DA},$ respectively, so that $\\overline{EG} \\perp \\overline{FH}$ and $EG=FH = 34$. Segments $\\overline{EG}$ and $\\overline{FH}$ intersect at a point $P,$ and the areas of the quadrilaterals $AEPH, BFPE, CGPF,$ and $DHPG$ are in the ratio $269:275:405:411$. Find the area of square $ABCD$.\n\n\n", "completion": "\\boxed{850}", "image_path": "dataset/math_vision/images/2083.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Ronja had four white tokens and Wanja had four grey tokens. They played a game in which they took turns to place one of their tokens to create two piles. Ronja placed her first token first. Which pair of piles could they not create?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/952.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Each of the 5 boxes contains either apples or bananas, but not both. The total weight of all the bananas is 3 times the weight of all the apples. Which boxes contain apples?\n\\n Options: A. 1 and 2, B. 2 and 3, C. 2 and 4, D. 3 and 4, E. 1 and 4", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/657.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Pia has a folding yardstick consisting of 10 equally long pieces. Which of the following figures can she not make?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/906.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consider the figure consisting of a square, its diagonals, and the segments joining the midpoints of opposite sides. The total number of triangles of any size in the figure is\n\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/2417.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Peter wants to colour in the cells of a $3 \\times 3$ square so that every row, every column and both diagonals each have three cells with three different colours. What is the smallest number of colours with which Peter can achieve this?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1399.png" }, { "solution": "\\boxed{52}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The trapezoid shown has a height of length $12\\text{ cm},$ a base of length $16\\text{ cm},$ and an area of $162\\text{ cm}^2.$ What is the perimeter of the trapezoid? ", "completion": "\\boxed{52}", "image_path": "dataset/math_vision/images/2952.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram shows a triangle and three circles whose centres are at the vertices of the triangle. The area of the triangle is $80 \\mathrm{~cm}^{2}$ and each of the circles has radius $2 \\mathrm{~cm}$. What is the area, in $\\mathrm{cm}^{2}$, of the shaded area? \\n Options: A. 76, B. $80-2 \\pi$, C. $40-4 \\pi$, D. $80-\\pi$, E. $78 \\pi$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1852.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The diagram on the right shows a cube of side $18 \\mathrm{~cm}$. A giant ant walks across the cube's surface from $\\mathrm{X}$ to $\\mathrm{Y}$ along the route shown. How far does it walk? \\n Options: A. $54 \\mathrm{~cm}$, B. $72 \\mathrm{~cm}$, C. $80 \\mathrm{~cm}$, D. $88 \\mathrm{~cm}$, E. $90 \\mathrm{~cm}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1717.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A $5 \\times 5$ square is covered with $1 \\times 1$ tiles. The design on each tile is made up of three dark triangles and one light triangle (see diagram). The triangles of neighbouring tiles always have the same colour where they join along an edge. The border of the large square is made of dark and light triangles. What is the smallest number of dark triangles that could be amongst them?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/1118.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Consider the five circles with midpoints $A, B, C, D$ and $E$ respectively, which touch each other as displayed in the diagram. The line segments, drawn in, connect the midpoints of adjacent circles. The distances between the midpoints are $A B=16, B C=14, C D=17, D E=13$ and $A E=14$ Which of the points is the midpoint of the circle with the biggest radius?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/1481.png" }, { "solution": "\\boxed{430}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Toothpicks of equal length are used to build a rectangular grid as shown. If the grid is 20 toothpicks high and 10 toothpicks wide, then the number of toothpicks used is\n\n", "completion": "\\boxed{430}", "image_path": "dataset/math_vision/images/2380.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nA rectangular piece of paper $6$ inches wide is folded as in the diagram so that one corner touches the opposite side. The length in inches of the crease $L$ in terms of angle $\\theta$ is\\n Options: A. $3\\sec ^2\\theta\\csc\\theta$, B. $6\\sin\\theta\\sec\\theta$, C. $3\\sec\\theta\\csc\\theta$, D. $6\\sec\\theta\\csc ^2\\theta$, E. $\\text{None of these}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2302.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The target shown consists of an inner black circle with two rings, one black and one white, around it. The width of each ring is equal to the radius of the black circle. What is the ratio of the area of the black ring to the area of the inner black circle? \\n Options: A. $2: 1$, B. $3: 1$, C. $4: 1$, D. $5: 1$, E. $6: 1$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/1809.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the addition beside, different letters represent different numbers and equal letters represent equal numbers. The resulting sum is a number of four digits, B being different from zero. What is the sum of the numbers of this number?\n\\n Options: A. AA, B. BB, C. AB, D. BE, E. EA", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1437.png" }, { "solution": "\\boxed{225}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The set $ G$ is defined by the points $ (x,y)$ with integer coordinates, $ 3\\le|x|\\le7$, $ 3\\le|y|\\le7$. How many squares of side at least $ 6$ have their four vertices in $ G$?\n", "completion": "\\boxed{225}", "image_path": "dataset/math_vision/images/2470.png" }, { "solution": "\\boxed{12}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: John made a construction with wooden cubes of the same size, with the three views shown beside, using as many cubes as possible. Ana, John's sister, wants to remove all the cubes she can, without modifying these three views. At most, how many cubes can she remove?\nfront:\n\nright side:\n\nabove:\n", "completion": "\\boxed{12}", "image_path": "dataset/math_vision/images/931.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn the adjoining figure, circle $\\mathit{K}$ has diameter $\\mathit{AB}$; cirlce $\\mathit{L}$ is tangent to circle $\\mathit{K}$ and to $\\mathit{AB}$ at the center of circle $\\mathit{K}$; and circle $\\mathit{M}$ tangent to circle $\\mathit{K}$, to circle $\\mathit{L}$ and $\\mathit{AB}$. The ratio of the area of circle $\\mathit{K}$ to the area of circle $\\mathit{M}$ is\\n Options: A. $12$, B. $14$, C. $16$, D. $18$, E. $\\text{not an integer}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2314.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The graph shows the constant rate at which Suzanna rides her bike. If she rides a total of a half an hour at the same speed, how many miles would she have ridden?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2696.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mrs Gardner has beds for peas and strawberries in her rectangular garden. This year, by moving the boundary between them, she changed her rectangular pea bed to a square by lengthening one of its sides by 3 metres. As a result of this change, the area of the strawberry bed reduced by $15 \\mathrm{~m}^{2}$. What was the area of the pea bed before the change? \\n Options: A. $5 \\mathrm{~m}^{2}$, B. $9 \\mathrm{~m}^{2}$, C. $10 \\mathrm{~m}^{2}$, D. $15 \\mathrm{~m}^{2}$, E. $18 \\mathrm{~m}^{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1590.png" }, { "solution": "\\boxed{2}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Maria wants there to be a knife to the right of every plate and a fork to the left of it. In order to get the right order she always swaps one fork with one knife. What is the minimum number of swaps necessary?\n", "completion": "\\boxed{2}", "image_path": "dataset/math_vision/images/858.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In triangle $ABC, AB=AC, AE=AD$ and angle $BAD=30^{\\circ}$. What is the size of angle $CDE$ ? \\n Options: A. $10^{\\circ}$, B. $15^{\\circ}$, C. $20^{\\circ}$, D. $25^{\\circ}$, E. $30^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1512.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A triangle is partitioned into three triangles and a quadrilateral by drawing two lines from vertices to their opposite sides. The areas of the three triangles are 3, 7, and 7, as shown. What is the area of the shaded quadrilateral?\n\n\n\\n Options: A. $15$, B. $17$, C. $\\frac{35}{2}$, D. $18$, E. $\\frac{55}{3}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2160.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The billiard ball meets the board under $45^{\\circ}$ as shown. Which pocket will it fall into?\n\\n Options: A. $A$, B. $B$, C. $C$, D. $D$, E. Neither of the pockets", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/198.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Andrew bought 27 little cubes of the same color, each with three adjacent faces painted red and the other three of another color. He wants to use all these little cubes to build a bigger cube. What is the largest number of completely red faces that he can get for this cube?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/1200.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The following figures show five paths, indicated by the thickest lines, between the $X$ and $Y$ points. Which of these paths is the longest?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/925.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In rectangle $ABCD$, $DC = 2CB$ and points $E$ and $F$ lie on $\\overline{AB}$ so that $\\overline{ED}$ and $\\overline{FD}$ trisect $\\angle ADC$ as shown. What is the ratio of the area of $\\triangle DEF$ to the area of rectangle $ABCD$?\n\n\\n Options: A. $\\frac{\\sqrt{3}}{6}$, B. $\\frac{\\sqrt{6}}{8}$, C. $\\frac{3\\sqrt{3}}{16}$, D. $\\frac{1}{3}$, E. $\\frac{\\sqrt{2}}{4}$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2199.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One corner of a square piece of paper is folded into the middle of the square That way an irregular pentagon is created. The numerical values of the areas of the Pentagon and the square are consecutive whole numbers. What is the area of the square?\n", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/1123.png" }, { "solution": "\\boxed{5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A regular polygon of $m$ sides is exactly enclosed (no overlaps, no gaps) by $m$ regular polygons of $n$ sides each. (Shown here for $m=4, n=8$.) If $m=10$, what is the value of $n$?\n", "completion": "\\boxed{5}", "image_path": "dataset/math_vision/images/2413.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: One sunny day, Ling decided to take a hike in the mountains. She left her house at $8 \\, \\textsc{am}$, drove at a constant speed of $45$ miles per hour, and arrived at the hiking trail at $10 \\, \\textsc{am}$. After hiking for $3$ hours, Ling drove home at a constant speed of $60$ miles per hour. Which of the following graphs best illustrates the distance between Ling's car and her house over the course of her trip?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2774.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Meike paddles around five buoys with her boat (see diagram). Which of the buoys does she paddle around in a clockwise direction?\n\\n Options: A. 2, B. 3 and 4, C. 1, D. 2 and 3, E. 1, F. 3 and 5, G. 2, H. 4 and 5, I. 2, J. 3 and 5", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1222.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nUsing only the paths and the directions shown, how many different routes are there from $ M$ to $ N$?", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/2510.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Some identical glasses are stacked on top of each other. A stack with eight glasses is $42 \\mathrm{~cm}$ high. A stack with two glasses is $18 \\mathrm{~cm}$ high. How high is a stack with six glasses?\n\\n Options: A. $22 \\mathrm{~cm}$, B. $24 \\mathrm{~cm}$, C. $28 \\mathrm{~cm}$, D. $34 \\mathrm{~cm}$, E. $40 \\mathrm{~cm}$", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/972.png" }, { "solution": "\\boxed{20}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: George builds the sculpture shown from seven cubes each of edge length 1. How many more of these cubes must he add to the sculpture so that he builds a large cube of edge length 3?\n", "completion": "\\boxed{20}", "image_path": "dataset/math_vision/images/1108.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The points $A, B, C$ and $D$ are marked on a straight line in this order as shown in the diagram. We know that $A$ is $12 \\mathrm{~cm}$ from $C$ and that $B$ is $18 \\mathrm{~cm}$ from $D$. How far apart from each other are the midpoints of the line segments $A B$ and $C D$?\n\\n Options: A. $6 \\mathrm{~cm}$, B. $9 \\mathrm{~cm}$, C. $12 \\mathrm{~cm}$, D. $13 \\mathrm{~cm}$, E. $15 \\mathrm{~cm}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/368.png" }, { "solution": "\\boxed{50}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of each of the four congruent L-shaped regions of this 100-inch by 100-inch square is 3/16 of the total area. How many inches long is the side of the center square?\n\n", "completion": "\\boxed{50}", "image_path": "dataset/math_vision/images/2581.png" }, { "solution": "\\boxed{400}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Two identical cylindrical sheets are cut open along the dotted lines and glued together to form one bigger cylindrical sheet, as shown. The smaller sheets each enclose a volume of 100. What volume is enclosed by the larger\n", "completion": "\\boxed{400}", "image_path": "dataset/math_vision/images/2021.png" }, { "solution": "\\boxed{8}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, $D$ and $E$ are the midpoints of $\\overline{AB}$ and $\\overline{BC}$ respectively. Determine the area of quadrilateral $DBEF$. ", "completion": "\\boxed{8}", "image_path": "dataset/math_vision/images/2950.png" }, { "solution": "\\boxed{6}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Father hangs towels on the washing as shown in the picture. For three towels he uses 4 clothes pegs. How many clothes pegs would he use for 5 towels?\n", "completion": "\\boxed{6}", "image_path": "dataset/math_vision/images/489.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large square is divided into smaller squares, as shown. A shaded circle is inscribed inside each of the smaller squares. What proportion of the area of the large square is shaded?\n\\n Options: A. $\\frac{8 \\pi}{9}$, B. $\\frac{13 \\pi}{16}$, C. $\\frac{3}{\\pi}$, D. $\\frac{3}{4}$, E. $\\frac{\\pi}{4}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/352.png" }, { "solution": "\\boxed{14}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In a shop selling toys a four-storey black and white \"brickflower\" is displayed (see picture on the left). Each storey is made of bricks of the same colour. In the picture on the right, the flower is shown from the top. How many white bricks were used to make the flower?\n", "completion": "\\boxed{14}", "image_path": "dataset/math_vision/images/760.png" }, { "solution": "\\boxed{32}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Anastasia's tablecloth has a regular pattern, as shown in the diagram. What percentage of her tablecloth is black? ", "completion": "\\boxed{32}", "image_path": "dataset/math_vision/images/1646.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A circle is tangent to one side of a rectangle and passes through two of its vertices, as shown beside. A square of $20 \\mathrm{~cm}^{2}$ area has one side over the side of the rectangle and two vertices over the circle, as shown in the figure. What is the area of the rectangle?\n\\n Options: A. $40 \\mathrm{~cm}^{2}$, B. $45 \\mathrm{~cm}^{2}$, C. $50 \\mathrm{~cm}^{2}$, D. $55 \\mathrm{~cm}^{2}$, E. $60 \\mathrm{~cm}^{2}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/343.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The kangaroo goes up three steps each time the rabbit goes down two steps. When the kangaroo is on step 9, on which step will the rabbit be?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/98.png" }, { "solution": "\\boxed{16}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Point $F$ is taken on the extension of side $AD$ of parallelogram $ABCD$. $BF$ intersects diagonal $AC$ at $E$ and side $DC$ at $G$. If $EF = 32$ and $GF = 24$, then $BE$ equals:\n\n\n", "completion": "\\boxed{16}", "image_path": "dataset/math_vision/images/2279.png" }, { "solution": "\\boxed{225}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Simon has a cube with side length $1 \\mathrm{dm}$ made of glass. He sticks several equally big black squares on it, as shown on the right so that all faces look the same. How many $\\mathrm{cm}^{2}$ were covered over?\n", "completion": "\\boxed{225}", "image_path": "dataset/math_vision/images/1352.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Kristina has a piece of transparent paper with some lines marked on it. She folds it along the central dashed line, as indicated. What can she now see? \\n Options: A. $2: 6: 9$, B. $2: 6: 6$, C. $5: 6: 9$, D. $2: 8: 6$, E. $5: 8: 9$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1708.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Twelve weights have integer masses of $1 \\mathrm{~g}, 2 \\mathrm{~g}, 3 \\mathrm{~g}, \\ldots, 11 \\mathrm{~g}$ and $12 \\mathrm{~g}$ respectively. A vendor divides those weights up into 3 groups of 4 weights each. The total mass of the first group is $41 \\mathrm{~g}$, the mass of the second group is $26 \\mathrm{~g}$ (see diagram). Which of the following weights is in the same group as the weight with $9 \\mathrm{~g}$?\n\\n Options: A. $3 \\mathrm{~g}$, B. $5 \\mathrm{~g}$, C. $7 \\mathrm{~g}$, D. $8 \\mathrm{~g}$, E. $10 \\mathrm{~g}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1479.png" }, { "solution": "\\boxed{52.5}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Segment $ BD$ and $ AE$ intersect at $ C$, as shown, $ AB=BC=CD=CE$, and $ \\angle A=\\frac{5}{2}\\angle B$. What is the degree measure of $ \\angle D$?\n", "completion": "\\boxed{52.5}", "image_path": "dataset/math_vision/images/2172.png" }, { "solution": "\\boxed{34}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A large triangle is divided into smaller triangles as shown. The number inside each small triangle indicates its perimeter. What is the perimeter of the large\ntriangle?\n", "completion": "\\boxed{34}", "image_path": "dataset/math_vision/images/355.png" }, { "solution": "\\boxed{3}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: There are 12 children in front of a zoo. Susi is the 7th from the front and Kim the $2 \\mathrm{nd}$ from the back. \nHow many children are there between Susi and Kim?", "completion": "\\boxed{3}", "image_path": "dataset/math_vision/images/88.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: \n\nIn triangle $ABC$, point $F$ divides side $AC$ in the ratio $1:2$. Let $E$ be the point of intersection of side $BC$ and $AG$ where $G$ is the midpoints of $BF$. The point $E$ divides side $BC$ in the ratio\\n Options: A. 1:4, B. 1:3, C. 2:5, D. 4:11, E. 3:8", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/2296.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Six-hundred fifty students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. The results of the survey are displayed in the bar graph. What is the ratio of the number of students who preferred spaghetti to the number of students who preferred manicotti?\n\n\\n Options: A. $\\frac{2}{5}$, B. $\\frac{1}{2}$, C. $\\frac{5}{4}$, D. $\\frac{5}{3}$, E. $\\frac{5}{2}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2678.png" }, { "solution": "\\boxed{56}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Black and white tiles can be laid on square floors as shown in the pictures. We can see floors with 4 black and 9 black tiles respectively. In each corner there is a black tile, and each black tile touches only white tiles. How many white tiles would there be on a floor that had 25 black tiles?\n", "completion": "\\boxed{56}", "image_path": "dataset/math_vision/images/799.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: How much does this Ferris wheel need to turn so that a white gondola is on top for\nthe first time?\n\\n Options: A. $\\frac{1}{2}$ turn, B. $\\frac{1}{3}$ turn, C. $\\frac{1}{6}$ turn, D. $\\frac{1}{12}$ turn, E. $\\frac{5}{6}$ turn", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/965.png" }, { "solution": "\\boxed{\\frac{4}{25}}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the diagram, the two triangles shown have parallel bases. What is the ratio of the area of the smaller triangle to the area of the larger triangle? ", "completion": "\\boxed{\\frac{4}{25}}", "image_path": "dataset/math_vision/images/2885.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: In the adjoining figure, points $B$ and $C$ lie on line segment $AD$, and $AB$, $BC$, and $CD$ are diameters of circle $O$, $N$, and $P$, respectively. Circles $O$, $N$, and $P$ all have radius $15$ and the line $AG$ is tangent to circle $P$ at $G$. If $AG$ intersects circle $N$ at points $E$ and $F$, then chord $EF$ has length\n\n\\n Options: A. $20$, B. $15\\sqrt{2}$, C. $24$, D. $25$, E. $\\text{none of these}$", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/2340.png" }, { "solution": "\\boxed{B}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following statements is definitely true for the angle marked in the diagram which is made up of nine squares?\n\\n Options: A. $\\alpha=\\beta$, B. $2 \\alpha+\\beta=90^{\\circ}$, C. $\\alpha+\\beta=60^{\\circ}$, D. $2 \\beta+\\alpha=90^{\\circ}$, E. $\\alpha+\\beta=45^{\\circ}$", "completion": "\\boxed{B}", "image_path": "dataset/math_vision/images/1427.png" }, { "solution": "\\boxed{A}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The figure below shows $13$ circles of radius $1$ within a larger circle. All the intersections occur at points of tangency. What is the area of the region, shaded in the figure, inside the larger circle but outside all the circles of radius $1 ?$\n\n\\n Options: A. $4 \\pi \\sqrt{3}$, B. $7 \\pi$, C. $\\pi(3\\sqrt{3} +2)$, D. $10 \\pi (\\sqrt{3} - 1)$, E. $\\pi(\\sqrt{3} + 6)$", "completion": "\\boxed{A}", "image_path": "dataset/math_vision/images/2223.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Alfred turns his building block 10 times. The first three times can be seen in the picture.\nWhat is the final position of the building block?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/66.png" }, { "solution": "\\boxed{4}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A panel is composed of 4 circles. When Lucy touches a circle, this circle and the others that touch this circle change their color from white to black or from black to white, as shown in the picture. Starting with all white circles, at least how many circles must Lucy touch, one after the other, so that all circles turn black?\n", "completion": "\\boxed{4}", "image_path": "dataset/math_vision/images/932.png" }, { "solution": "\\boxed{C}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Which of the following is a net for the cube with two holes shown alongside?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{C}", "image_path": "dataset/math_vision/images/1533.png" }, { "solution": "\\boxed{D}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Car M traveled at a constant speed for a given time. This is shown by the dashed line. Car N traveled at twice the speed for the same distance. If Car N's speed and time are shown as solid line, which graph illustrates this?\n\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{D}", "image_path": "dataset/math_vision/images/2630.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Mike and Jake play darts. Each of them throws three darts. Who won, and by how many points?\nMike: \nJake: \\n Options: A. Mike won. He had 3 points more., B. Jake won. He had 4 points more., C. Mike won. He had 2 points more., D. Jake won. He had 2 points more., E. Mike won. He had 4 points more.", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/491.png" }, { "solution": "\\boxed{24}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: Sacha's garden has the shape shown. All the sides are either parallel or perpendicular to each other. Some of the dimensions are shown in the diagram. What is the length of the perimeter of Sacha's garden? ", "completion": "\\boxed{24}", "image_path": "dataset/math_vision/images/1678.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: A wheel rolls along a zigzag curve as can be seen below. Which of the following pictures shows the curve that is described by the centre of the wheel?\n\\n Options: A. A, B. B, C. C, D. D, E. E", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/1404.png" }, { "solution": "\\boxed{9}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The picture shows seven points and the connections between them. What is the least number of connecting lines that could be added to the picture so that each of the seven points has the same number of connections with other points? (Connecting lines are allowed to cross each other.)\n", "completion": "\\boxed{9}", "image_path": "dataset/math_vision/images/1901.png" }, { "solution": "\\boxed{E}", "prompt": "Solve the problem and output the answer in the format of \\boxed{your answer}.\\n Question: The area of this figure is $ 100\\text{ cm}^{2} $. Its perimeter is\n\n\n\\n Options: A. $\\text{20 cm}$, B. $\\text{25 cm}$, C. $\\text{30 cm}$, D. $\\text{40 cm}$, E. $\\text{50 cm}$", "completion": "\\boxed{E}", "image_path": "dataset/math_vision/images/2540.png" } ]