id stringlengths 1 4 | media images listlengths 1 1 | messages stringlengths 84 1.58k | answer stringclasses 371
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2529 | [{"role": "user", "question": "Which of the five \"T-like shapes\" would be symmetric to the one shown with respect to the dashed line?\n\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 3 | transformation geometry | |
253 | [{"role": "user", "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 followin... | C | mcq | 3 | solid geometry | |
2530 | [{"role": "user", "question": "The area of the shaded region $\\text{BEDC}$ in parallelogram $\\text{ABCD}$ is\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 64 | numeric | 3 | metric geometry - area | |
2531 | [{"role": "user", "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 we... | 2.5 | numeric | 2 | statistics | |
2532 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 14 | numeric | 4 | solid geometry | |
2533 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 33 | numeric | 4 | solid geometry | |
2534 | [{"role": "user", "question": "Suppose a square piece of paper is folded in half vertically. The folded paper is then cut in half along the dashed line. Three 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 rectangl... | E | mcq | 3 | transformation geometry | |
2535 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{1}{6}$", "B": "$\\frac{3}{7}$", "C": "$\\frac{1}{2}$", "D": "$\\frac{2}{3}$", "E": "... | C | mcq | 2 | combinatorics | |
2536 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 1047 | numeric | 2 | combinatorics | |
2537 | [{"role": "user", "question": "What fraction of the square is shaded?\n\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{3}$", "B": "$\\frac{2}{5}$", "C": "$\\frac{5}{12}$", "D": "$\\frac{3}{7}$", "E": "$\\frac{1}{2}$"}, "choices": []}] | E | mcq | 3 | metric geometry - area | |
2538 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\text{P}$", "B": "$\\text{Q}$", "C": "$\\text{R}$", "D": "$\\text{S}$"... | A | mcq | 4 | algebra | |
2539 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 81 | numeric | 4 | solid geometry | |
254 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$4 \\pi$", "B": "$\\frac{28}{3} \\pi$", "C": "$8 ... | B | mcq | 5 | transformation geometry | |
2540 | [{"role": "user", "question": "The area of this figure is $ 100\\text{ cm}^{2} $. Its perimeter is\n\n\n<image1>", "hint": "", "options": {"A": "$\\text{20 cm}$", "B": "$\\text{25 cm}$", "C": "$\\text{30 cm}$", "D": "$\\text{40 cm}$", "E": "$\\text{50 cm}$"}, "choices": []}] | E | mcq | 2 | metric geometry - length | |
2541 | [{"role": "user", "question": "Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have?\n<image1>", "hint": "", "options": {}, "choices": []}] | 36 | numeric | 4 | solid geometry | |
2542 | [{"role": "user", "question": "The graph relates the distance traveled [in miles] to the time elapsed [in hours] on a trip taken by an experimental airplane. During which hour was the average speed of this airplane the largest?\n\n<image1>", "hint": "", "options": {"A": "$\\text{first (0-1)}$", "B": "$\\text{second (1-... | B | mcq | 2 | statistics | |
2543 | [{"role": "user", "question": "Three $ \\Delta $'s and a $ \\diamondsuit $ will balance nine $ \\bullet $'s. One $ \\Delta $ will balance a $ \\diamondsuit $ and a $ \\bullet $.\n<image1>\n\nHow many $ \\bullet $'s will balance the two $ \\diamondsuit $'s in this balance?\n<image2>", "hint": "", "options": {}, "choices... | 3 | numeric | 4 | algebra | |
2544 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 8 | numeric | 4 | combinatorial geometry | |
2545 | [{"role": "user", "question": "A \"domino\" is made up of two small squares:\n<image1>\nWhich of the \"checkerboards\" illustrated below CANNOT be covered exactly and completely by a whole number of non-overlapping dominoes?\n\n<image2>", "hint": "", "options": {"A": "$3\\times 4$", "B": "$3\\times 5$", "C": "$4\\times... | B | mcq | 4 | combinatorial geometry | |
2546 | [{"role": "user", "question": "The area in square units of the region enclosed by parallelogram $ABCD$ is\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 8 | numeric | 3 | analytic geometry | |
2547 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$2\\... | C | mcq | 4 | solid geometry | |
2548 | [{"role": "user", "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\n... | 9 | numeric | 3 | transformation geometry | |
2549 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$9\\%$", "B": "$23\\frac{1}{3}\\%$", "C": "... | C | mcq | 2 | statistics | |
255 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 5 | metric geometry - length | |
2550 | [{"role": "user", "question": "In the addition problem, each digit has been replaced by a letter. If different letters represent different digits then $C=$\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 1 | numeric | 4 | algebra | |
2551 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{1}{3}$", "B": "$\\frac{1}{2}$", "C": "$\\frac{2}{3}$", "D": ... | D | mcq | 2 | combinatorics | |
2552 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\... | C | mcq | 4 | algebra | |
2553 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "1", "B": "2", "C": "3", "D": "4", "E": "5"}, "choices": []}] | E | mcq | 3 | metric geometry - area | |
2554 | [{"role": "user", "question": "Suppose that\n<image1>\nmeans $a+b-c$.\nFor example,\n<image2>\nis $5+4-6 = 3$.\nThen the sum\n<image3>\nis", "hint": "", "options": {}, "choices": []}] | 1 | numeric | 4 | algebra | |
2555 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 160 | numeric | 2 | statistics | |
2556 | [{"role": "user", "question": "An isosceles right triangle with legs of length $8$ is partitioned into $16$ congruent triangles as shown. The shaded area is\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 20 | numeric | 3 | metric geometry - area | |
2557 | [{"role": "user", "question": "The bar graph shows the results of a survey on color preferences. What percent preferred blue?\n\n<image1>", "hint": "", "options": {"A": "$20\\%$", "B": "$24\\%$", "C": "$30\\%$", "D": "$36\\%$", "E": "$42\\%$"}, "choices": []}] | B | mcq | 2 | statistics | |
2558 | [{"role": "user", "question": "<image1>\n\nWhich cylinder has twice the volume of the cylinder shown above?\n\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "None of the above"}, "choices": []}] | B | mcq | 4 | solid geometry | |
2559 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 2 | metric geometry - length | |
256 | [{"role": "user", "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... | E | mcq | 1 | descriptive geometry | |
2560 | [{"role": "user", "question": "Which pattern of identical squares could NOT be folded along the lines shown to form a cube?\n\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 4 | solid geometry | |
2561 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\text{Ja... | B | mcq | 2 | statistics | |
2562 | [{"role": "user", "question": "Eight $1\\times 1$ square tiles are arranged as shown so their outside edges form a polygon with a perimeter of $14$ units. Two additional tiles of the same size are added to the figure so that at least one side of each tile is shared with a side of one of the squares in the original fig... | C | mcq | 4 | combinatorial geometry | |
2563 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 7.7 | numeric | 3 | metric geometry - area | |
2564 | [{"role": "user", "question": "Which one of the following bar graphs could represent the data from the circle graph?\n<image1>\n\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | C | mcq | 2 | statistics | |
2565 | [{"role": "user", "question": "This line graph represents the price of a trading card during the first $6$ months of $1993$.\n<image1>\n\nThe greatest monthly drop in price occurred during", "hint": "", "options": {"A": "$\\text{January}$", "B": "$\\text{March}$", "C": "$\\text{April}$", "D": "$\\text{May}$", "E": "$\\... | B | mcq | 2 | statistics | |
2566 | [{"role": "user", "question": "Consider this histogram of the scores for $81$ students taking a test:\n<image1>\n\nThe median is in the interval labeled", "hint": "", "options": {}, "choices": []}] | 70 | numeric | 2 | statistics | |
2567 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 36 | numeric | 3 | metric geometry - area | |
2568 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 500 | numeric | 4 | solid geometry | |
2569 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 320 | numeric | 3 | metric geometry - area | |
257 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 10 | numeric | 5 | combinatorial geometry | |
2570 | [{"role": "user", "question": "Which of the following represents the result when the figure shown below is rotated clockwise $120^\\circ$ about its center?\n<image1>\n\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 3 | transformation geometry | |
2571 | [{"role": "user", "question": "If $\\angle A = 60^\\circ $, $\\angle E = 40^\\circ $ and $\\angle C = 30^\\circ $, then $\\angle BDC = $\n\n<image1>", "hint": "", "options": {"A": "$40^\\circ$", "B": "$50^\\circ$", "C": "$60^\\circ$", "D": "$70^\\circ$", "E": "$80^\\circ$"}, "choices": []}] | B | mcq | 5 | metric geometry - angle | |
2572 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\text{The shaded areas in all three are... | A | mcq | 4 | combinatorial geometry | |
2573 | [{"role": "user", "question": "If this path is to continue in the same pattern:\n<image1>\n\nthen which sequence of arrows goes from point $425$ to point $427$?\n\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 4 | algebra | |
2574 | [{"role": "user", "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 high... | B | mcq | 2 | statistics | |
2575 | [{"role": "user", "question": "Around the outside of a $4$ by $4$ square, construct four semicircles (as shown in the figure) with the four sides of the square as their diameters. Another square, $ABCD$, has its sides parallel to the corresponding sides of the original square, and each side of $ABCD$ is tangent to one... | 64 | numeric | 3 | metric geometry - area | |
2576 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{1}{6}$", "B": "$\\frac{1}{4}$", "C": "$\\frac{1}{3}$", "D": "$\\frac{5}{12}$", "E": "$\\frac{4}{9}$"}, "choices": []}] | D | mcq | 2 | combinatorics | |
2577 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 36 | numeric | 2 | metric geometry - length | |
2578 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 32 | numeric | 3 | metric geometry - area | |
2579 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "A", "B": "B... | D | mcq | 4 | algebra | |
258 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C",... | E | mcq | 5 | combinatorial geometry | |
2580 | [{"role": "user", "question": "In the figure, $\\angle A$, $\\angle B$, and $\\angle C$ are right angles. If $\\angle AEB = 40^\\circ $ and $\\angle BED = \\angle BDE$, then $\\angle CDE = $\n\n<image1>", "hint": "", "options": {"A": "$75^\\circ$", "B": "$80^\\circ$", "C": "$85^\\circ$", "D": "$90^\\circ$", "E": "$95^... | E | mcq | 5 | metric geometry - angle | |
2581 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 50 | numeric | 4 | combinatorial geometry | |
2582 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 2 | statistics | |
2583 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}... | 4 | numeric | 4 | solid geometry | |
2584 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 7.2 | numeric | 2 | metric geometry - length | |
2585 | [{"role": "user", "question": "The letters $P$, $Q$, $R$, $S$, and $T$ represent numbers located on the number line as shown.\n<image1>\n\nWhich of the following expressions represents a negative number?", "hint": "", "options": {"A": "$P-Q$", "B": "$P\\cdot Q$", "C": "$\\frac{S}{Q}\\cdot P$", "D": "$\\frac{R}{P\\cdot ... | A | mcq | 4 | algebra | |
2586 | [{"role": "user", "question": "Six different digits from the set\n\\[\\{ 1,2,3,4,5,6,7,8,9\\}\\]\nare placed in the squares in the figure shown so that the sum of the entries in the vertical column is 23 and the sum of the entries in the horizontal row is 12.\nThe sum of the six digits used is\n\n<image1>", "hint": "",... | 29 | numeric | 2 | combinatorics | |
2587 | [{"role": "user", "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<image1>\n\nNOT TO SCALE", "hint": "", "options": {"A": "(-6,0)", "B": "(-4,0)", "C": "(-2,0)... | C | mcq | 3 | analytic geometry | |
2588 | [{"role": "user", "question": "The pie charts below indicate the percent of students who prefer golf, bowling, or tennis at East Junior High School and West Middle School. The total number of students at East is $2000$ and at West, $2500$. In the two schools combined, the percent of students who prefer tennis is\n\n<... | C | mcq | 2 | statistics | |
2589 | [{"role": "user", "question": "The horizontal and vertical distances between adjacent points equal $1$ unit. The area of triangle $ABC$ is\n\n<image1>", "hint": "", "options": {"A": "1/4", "B": "1/2", "C": "3/4", "D": "1", "E": "5/4"}, "choices": []}] | B | mcq | 4 | combinatorial geometry | |
259 | [{"role": "user", "question": "Amongst the graphs shown below there is the graph of the function $f(x)=(a-x)(b-x)^{2}$ with $a<b$. Which is it?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 4 | analytic geometry | |
2590 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$90^\\circ$", "B": "$100^\\circ$", "C": "$115^\\circ$", "D": "$122.5^\\circ$", "E": "$125^... | C | mcq | 5 | metric geometry - angle | |
2591 | [{"role": "user", "question": "What fraction of this square region is shaded? Stripes are equal in width, and the figure is drawn to scale.\n\n<image1>", "hint": "", "options": {"A": "$\\frac{5}{12}$", "B": "$\\frac{1}{2}$", "C": "$\\frac{7}{12}$", "D": "$\\frac{2}{3}$", "E": "$\\frac{5}{6}$"}, "choices": []}] | C | mcq | 3 | metric geometry - area | |
2592 | [{"role": "user", "question": "$\\angle 1 + \\angle 2 = 180^\\circ $\n\n$\\angle 3 = \\angle 4$\n\nFind $\\angle 4$.\n\n<image1>", "hint": "", "options": {"A": "$20^\\circ$", "B": "$25^\\circ$", "C": "$30^\\circ$", "D": "$35^\\circ$", "E": "$40^\\circ$"}, "choices": []}] | D | mcq | 5 | metric geometry - angle | |
2593 | [{"role": "user", "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<image1>", "hint": "", "options": {... | B | mcq | 3 | metric geometry - area | |
2594 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 16 | numeric | 4 | solid geometry | |
2595 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$19\\text{ sq.cm}$", "B": "$24\\text{ sq.cm}$", "C": "$30\\text{ sq.cm}$", "D": "$54\\text{ sq.cm}$",... | D | mcq | 4 | solid geometry | |
2596 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "2:... | C | mcq | 3 | metric geometry - area | |
2597 | [{"role": "user", "question": "How many triangles are in this figure? (Some triangles may overlap other triangles.)\n<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 4 | combinatorial geometry | |
2598 | [{"role": "user", "question": "Dots are spaced one unit apart, horizontally and vertically. The number of square units enclosed by the polygon is\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 4 | combinatorial geometry | |
2599 | [{"role": "user", "question": "What is the ratio of the area of the shaded square to the area of the large square? (The figure is drawn to scale)\n\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{6}$", "B": "$\\frac{1}{7}$", "C": "$\\frac{1}{8}$", "D": "$\\frac{1}{12}$", "E": "$\\frac{1}{16}$"}, "choices": []}] | C | mcq | 3 | metric geometry - area | |
26 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 1 | counting | |
260 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 4 | analytic geometry | |
2600 | [{"role": "user", "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<image1>\n\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}... | B | mcq | 3 | transformation geometry | |
2601 | [{"role": "user", "question": "Let $PQRS$ be a square piece of paper. $P$ is folded onto $R$ and then $Q$ is folded onto $S$. The area of the resulting figure is 9 square inches. Find the perimeter of square $PQRS$.\n<image1>", "hint": "", "options": {}, "choices": []}] | 24 | numeric | 3 | transformation geometry | |
2602 | [{"role": "user", "question": "If the pattern in the diagram continues, what fraction of the interior would be shaded in the eighth triangle?\n\n<image1>", "hint": "", "options": {"A": "$\\frac{3}{8}$", "B": "$\\frac{5}{27}$", "C": "$\\frac{7}{16}$", "D": "$\\frac{9}{16}$", "E": "$\\frac{11}{45}$"}, "choices": []}] | C | mcq | 4 | algebra | |
2603 | [{"role": "user", "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 squ... | 120 | numeric | 4 | algebra | |
2604 | [{"role": "user", "question": "The diagram shows the miles traveled by bikers Alberto and Bjorn. After four hours, about how many more miles has Alberto biked than Bjorn?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 15 | numeric | 2 | statistics | |
2605 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\text{B}$", "B": "$\\text{G}$", ... | A | mcq | 4 | solid geometry | |
2606 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 1150 | numeric | 4 | algebra | |
2607 | [{"role": "user", "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<image1>", "hint": "... | 24 | numeric | 2 | combinatorics | |
2608 | [{"role": "user", "question": "In trapezoid $ABCD$ , the sides $AB$ and $CD$ are equal. The perimeter of $ABCD$ is\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 34 | numeric | 2 | metric geometry - length | |
2609 | [{"role": "user", "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<image1>\n\n<image2>... | B | mcq | 4 | descriptive geometry | |
261 | [{"role": "user", "question": "In a triangle $A B C$ the points $M$ and $N$ are placed on side $A B$ so that $A N=A C$ and $B M=$ $B C$. Determine $\\angle A C B$ if $\\angle M C N=43^{\\circ}$\n<image1>", "hint": "", "options": {"A": "$86^{\\circ}$", "B": "$89^{\\circ}$", "C": "$90^{\\circ}$", "D": "$92^{\\circ}$", "E... | E | mcq | 4 | metric geometry - angle | |
2610 | [{"role": "user", "question": "The degree measure of angle $A$ is\n<image1>", "hint": "", "options": {}, "choices": []}] | 30 | numeric | 5 | metric geometry - angle | |
2611 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\sqrt{10}$", "B": "$\\sqrt{12}$", "C": "$\\sqrt{13}$", "D": "$\\sqrt{14}$", "E": "$\\sqrt{15}$"}, "choice... | C | mcq | 2 | metric geometry - length | |
2612 | [{"role": "user", "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 i... | 6 | numeric | 4 | algebra | |
2613 | [{"role": "user", "question": "In $1960$ only $5\\%$ of the working adults in Carlin City worked at home. By $1970$ the \"at-home\" work force increased to $8\\%$. In $1980$ there were approximately $15\\%$ working at home, and in $1990$ there were $30\\%$. The graph that best illustrates this is\n\n<image1>", "hint": ... | E | mcq | 2 | statistics | |
2614 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 7 | numeric | 3 | metric geometry - area | |
2615 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 41 | numeric | 4 | solid geometry | |
2616 | [{"role": "user", "question": "Three-digit powers of 2 and 5 are used in this ''cross-number'' puzzle. What is the only possible digit for the outlined square?\n\\begin{tabular}{lcl}\n\\textbf{ACROSS} & & \\textbf{DOWN} \\\\\n\\textbf{2}. $2^m$ & & \\textbf{1}. $5^n$\n\\end{tabular}\n<image1>", "hint": "", "options": {... | 6 | numeric | 2 | combinatorics | |
2617 | [{"role": "user", "question": "A block wall $100$ feet long and $7$ feet high will be constructed using blocks that are $1$ foot high and either $2$ feet long or $1$ foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest... | 353 | numeric | 4 | combinatorial geometry | |
2618 | [{"role": "user", "question": "In triangle $CAT$, we have $\\angle ACT = \\angle ATC$ and $\\angle CAT = 36^\\circ$. If $\\overline{TR}$ bisects $\\angle ATC$, then $\\angle CRT =$\n\n<image1>", "hint": "", "options": {"A": "$36^\\circ$", "B": "$54^\\circ$", "C": "$72^\\circ$", "D": "$90^\\circ$", "E": "$108^\\circ$"},... | C | mcq | 5 | metric geometry - angle |
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