id stringlengths 1 4 | media images listlengths 1 1 | messages stringlengths 84 1.58k | answer stringclasses 371
values | question_type stringclasses 3
values | level int64 1 5 | subject stringclasses 16
values |
|---|---|---|---|---|---|---|
2709 | [{"role": "user", "question": "Semicircles $POQ$ and $ROS$ pass through the center of circle $O$. What is the ratio of the combined areas of the two semicircles to the area of circle $O$?\n<image1>", "hint": "", "options": {"A": "$\\frac{\\sqrt{2}}{4}$", "B": "$\\frac{1}{2}$", "C": "$\\frac{2}{\\pi}$", "D": "$\\frac{2}... | B | mcq | 3 | analytic geometry | |
271 | [{"role": "user", "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<image1>\n<image2>", ... | A | mcq | 3 | statistics | |
2710 | [{"role": "user", "question": "Extend the square pattern of $8$ black and $17$ white square tiles by attaching a border of black tiles around the square. What is the ratio of black tiles to white tiles in the extended pattern?\n<image1>", "hint": "", "options": {"A": "8:17", "B": "25:49", "C": "36:25", "D": "32:17", "E... | D | mcq | 4 | combinatorial geometry | |
2711 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$12\\frac{1}{2}$", "B": "$20$", "C": "$25$", "... | C | mcq | 4 | combinatorial geometry | |
2712 | [{"role": "user", "question": "Carmen takes a long bike ride on a hilly highway. The graph indicates the miles traveled during the time of her ride. What is Carmen's average speed for her entire ride in miles per hour?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 2 | statistics | |
2713 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 2 | statistics | |
2714 | [{"role": "user", "question": "Two congruent squares, $ABCD$ and $PQRS$, have side length $15$. They overlap to form the $15$ by $25$ rectangle $AQRD$ shown. What percent of the area of rectangle $AQRD$ is shaded?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 20 | numeric | 3 | metric geometry - area | |
2715 | [{"role": "user", "question": "How many rectangles are in this figure?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 11 | numeric | 4 | combinatorial geometry | |
2716 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 750 | numeric | 3 | metric geometry - area | |
2717 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{1}2$", "B": "$1$", "C": "$\\frac{3... | A | mcq | 3 | metric geometry - area | |
2718 | [{"role": "user", "question": "In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is $X$, in centimeters?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 2 | metric geometry - length | |
2719 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{4-\\pi}\\pi$", "B": "$\\frac{1}{\\pi}$", "... | A | mcq | 3 | metric geometry - area | |
272 | [{"role": "user", "question": "How many of the following shapes can be drawn using one continuous line (i.e. without lifting the pencil) and without going over a line twice?\n<image1>", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 5 | graph theory | |
2720 | [{"role": "user", "question": "A square with area 4 is inscribed in a square with area 5, with one vertex of the smaller square on each side of the larger square. A vertex of the smaller square divides a side of the larger square into two segments, one of length $a$, and the other of length $b$. What is the value of $a... | C | mcq | 2 | metric geometry - length | |
2721 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 4 | algebra | |
2722 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 280 | numeric | 4 | solid geometry | |
2723 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 3932 | numeric | 4 | algebra | |
2724 | [{"role": "user", "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 semic... | 7.5 | numeric | 2 | metric geometry - length | |
2725 | [{"role": "user", "question": "Squares $ABCD$, $EFGH$, and $GHIJ$ are equal in area. Points $C$ and $D$ are the midpoints of sides $IH$ ad $HE$, respectively. What is the ratio of the area of the shaded pentagon $AJICB$ to the sum of the areas of the three squares?\n\n<image1>", "hint": "", "options": {"A": "$\\frac{1}... | C | mcq | 4 | combinatorial geometry | |
2726 | [{"role": "user", "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. Wha... | A | mcq | 2 | metric geometry - length | |
2727 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 140 | numeric | 5 | metric geometry - angle | |
2728 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 13 | numeric | 2 | metric geometry - length | |
2729 | [{"role": "user", "question": "The circumference of the circle with center $O$ is divided into 12 equal arcs, marked the letters $A$ through $L$ as seen below. What is the number of degrees in the sum of the angles $x$ and $y$?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 90 | numeric | 5 | metric geometry - angle | |
273 | [{"role": "user", "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<image1>\n<image2>", "hint": "", "options": {"... | E | mcq | 1 | descriptive geometry | |
2730 | [{"role": "user", "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... | 4.0 | numeric | 3 | metric geometry - area | |
2731 | [{"role": "user", "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<image1>", "hint": "", "opti... | B | mcq | 2 | metric geometry - length | |
2732 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{11}{32}$", "B": "$\\frac{3}{8}$", "C": "$\\frac{13}{32}$", "D": "$\\frac{7... | D | mcq | 3 | metric geometry - area | |
2733 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 18 | numeric | 4 | solid geometry | |
2734 | [{"role": "user", "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 th... | 31 | numeric | 4 | algebra | |
2735 | [{"role": "user", "question": "A triangle with vertices as $A=(1,3)$, $B=(5,1)$, and $C=(4,4)$ is plotted on a $6\\times5$ grid. What fraction of the grid is covered by the triangle?\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{6}$", "B": "$\\frac{1}{5}$", "C": "$\\frac{1}{4}$", "D": "$\\frac{1}{3}$", "E": "$\\... | A | mcq | 3 | analytic geometry | |
2736 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$6\\sqrt{2}$", "B": "$9$", "C": "$12$", "D... | C | mcq | 3 | metric geometry - area | |
2737 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$9$", "B": "$12\\frac{1}{2}$", "C": "$15$", "D": "$15\\frac{1}{2}$", "E": "$17$"... | C | mcq | 3 | metric geometry - area | |
2738 | [{"role": "user", "question": "The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these names?\n<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 2 | statistics | |
2739 | [{"role": "user", "question": "Rectangle $DEFA$ below is a $3 \\times 4$ rectangle with $DC=CB=BA$. The area of the \"bat wings\" is\n<image1>", "hint": "", "options": {"A": "$2$", "B": "$2 \\frac{1}{2}$", "C": "$3$", "D": "$3 \\frac{1}{2}$", "E": "$5$"}, "choices": []}] | C | mcq | 3 | metric geometry - area | |
274 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$X+Y<Z$", "B... | C | mcq | 5 | metric geometry - area | |
2740 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$4 \\sqrt{3}$", "B": "$\\frac{120}{... | B | mcq | 2 | metric geometry - length | |
2741 | [{"role": "user", "question": "Alicia, Brenda, and Colby were the candidates in a recent election for student president. The pie chart below shows how the votes were distributed among the three candidates. If Brenda received 36 votes, then how many votes were cast all together?\n\n<image1>", "hint": "", "options": {}, ... | 120 | numeric | 2 | statistics | |
2742 | [{"role": "user", "question": "In the arrangement of letters and numerals below, by how many different paths can one spell AMC8? Beginning at the A in the middle, a path allows only moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the ... | 24 | numeric | 2 | combinatorics | |
2743 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{3}{4}$", "B": "$\\frac{3}{2}$", "C": "$2$", "D": "$\\frac{12}{5}$", "E": "... | D | mcq | 3 | metric geometry - area | |
2744 | [{"role": "user", "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<image1>\nWhat is the area of quadrilateral $ABCD$?", "hint": "", "options": {}, "choices": []}] | 24 | numeric | 3 | metric geometry - area | |
2745 | [{"role": "user", "question": "In the right triangle $ABC$, $AC=12$, $BC=5$, and angle $C$ is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?\n<image1>", "hint": "", "options": {"A": "$\\frac{7}{6}$", "B": "$\\frac{13}{5}$", "C": "$\\frac{59}{18}$", "D": "$\\frac... | D | mcq | 2 | metric geometry - length | |
2746 | [{"role": "user", "question": "In the figure shown, $\\overline{US}$ and $\\overline{UT}$ are line segments each of length 2, and $m\\angle TUS = 60^\\circ$. Arcs $\\overarc{TR}$ and $\\overarc{SR}$ are each one-sixth of a circle with radius 2. What is the area of the region shown?\n<image1>", "hint": "", "options": {"... | B | mcq | 3 | metric geometry - area | |
2747 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 13 | numeric | 4 | combinatorial geometry | |
2748 | [{"role": "user", "question": "Mr. Garcia asked the members of his health class how many days last week they exercised for at least 30 minutes. The results are summarized in the following bar graph, where the heights of the bars represent the number of students.\n\n<image1>What was the mean number of days of exercise l... | 4.36 | numeric | 2 | statistics | |
2749 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{1}{4}$... | D | mcq | 3 | metric geometry - area | |
275 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices... | 1 | numeric | 5 | transformation geometry | |
2750 | [{"role": "user", "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 ... | 8 | numeric | 2 | combinatorics | |
2751 | [{"role": "user", "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 $CD... | A | mcq | 3 | metric geometry - area | |
2752 | [{"role": "user", "question": "Point $E$ is the midpoint of side $\\overline{CD}$ in square $ABCD,$ and $\\overline{BE}$ meets diagonal $\\overline{AC}$ at $F$. The area of quadrilateral $AFED$ is $45$. What is the area of $ABCD?$\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 108 | numeric | 3 | metric geometry - area | |
2753 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{2}{7}$", "B": "$\\frac{5}{42}... | D | mcq | 2 | combinatorics | |
2754 | [{"role": "user", "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<image1>", "hi... | C | mcq | 4 | solid geometry | |
2755 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": ... | 150 | numeric | 3 | metric geometry - area | |
2756 | [{"role": "user", "question": "Quadrilateral $ABCD$ is a rhombus with perimeter $52$ meters. The length of diagonal $\\overline{AC}$ is $24$ meters. What is the area in square meters of rhombus $ABCD$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 120 | numeric | 3 | metric geometry - area | |
2757 | [{"role": "user", "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 t... | B | mcq | 2 | statistics | |
2758 | [{"role": "user", "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 symme... | C | mcq | 2 | combinatorics | |
2759 | [{"role": "user", "question": "The diagram shows the number of students at soccer practice each weekday during last week. After computing the mean and median values, Coach discovers that there were actually $21$ participants on Wednesday. Which of the following statements describes the change in the mean and median aft... | B | mcq | 2 | statistics | |
276 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "-5", "B": "-16", "... | E | mcq | 5 | algebra | |
2760 | [{"role": "user", "question": "The faces of a cube are painted in six different colors: red (R), white (W), green (G), brown (B), aqua (A), and purple (P). Three views of the cube are shown below. What is the color of the face opposite the aqua face?\n<image1>", "hint": "", "options": {"A": "$\\text{red}$", "B": "$\\te... | A | mcq | 4 | solid geometry | |
2761 | [{"role": "user", "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<image1... | 30 | numeric | 3 | metric geometry - area | |
2762 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 37 | numeric | 4 | algebra | |
2763 | [{"role": "user", "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 sma... | 20 | numeric | 4 | solid geometry | |
2764 | [{"role": "user", "question": "After school, Maya and Naomi headed to the beach, $6$ miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds?\n\n<image1... | 24 | numeric | 2 | statistics | |
2765 | [{"role": "user", "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<image1>", "hint": "", "... | D | mcq | 2 | statistics | |
2766 | [{"role": "user", "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 $47$. ... | 5 | numeric | 4 | algebra | |
2767 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 240 | numeric | 3 | metric geometry - area | |
2768 | [{"role": "user", "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. H... | 28 | numeric | 2 | combinatorics | |
2769 | [{"role": "user", "question": "When a positive integer $N$ is fed into a machine, the output is a number calculated according to the rule shown below.\n<image1>\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 fi... | E | mcq | 5 | arithmetic | |
277 | [{"role": "user", "question": "The diagram shows three concentric circles and two perpendicular, common diameters of the three circles. The three grey sections are of equal area, the small circle has radius 1. What is the product of the radii of the three circles?\n<image1>", "hint": "", "options": {"A": "$\\sqrt{6}$",... | A | mcq | 5 | metric geometry - length | |
2770 | [{"role": "user", "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 th... | A | mcq | 3 | metric geometry - area | |
2771 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 651 | numeric | 2 | metric geometry - length | |
2772 | [{"role": "user", "question": "The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 10 | numeric | 4 | combinatorial geometry | |
2773 | [{"role": "user", "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<image1>\n\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 3 | analytic geometry | |
2774 | [{"role": "user", "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 $60$ mile... | E | mcq | 2 | statistics | |
2775 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{1}{16}$", "B": "$\\frac{1}{... | B | mcq | 2 | combinatorics | |
2776 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices":... | 3 | numeric | 3 | analytic geometry | |
2777 | [{"role": "user", "question": "Mr. Ramos gave a test to his class of $20$ students. The dot plot below shows the distribution of test scores.\n<image1>\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 increas... | 4 | numeric | 2 | statistics | |
2778 | [{"role": "user", "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... | 8 | numeric | 4 | algebra | |
2779 | [{"role": "user", "question": "Steph scored $15$ baskets out of $20$ attempts in the first half of a game, and $10$ baskets out of $10$ attempts in the second half. Candace took $12$ attempts in the first half and $18$ attempts in the second. In each half, Steph scored a higher percentage of baskets than Candace. Surpr... | 9 | numeric | 2 | statistics | |
278 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "only 5", "B": "only 2", "C": "either ... | A | mcq | 3 | solid geometry | |
2780 | [{"role": "user", "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<image1>\n\nHow many configurations will have three $\\triangle$s in a line and three $\\bigcirc$s in a line?", "hint": "", "opt... | 84 | numeric | 2 | combinatorics | |
2781 | [{"role": "user", "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<image1>", "hint": "", "options": {},... | 192 | numeric | 4 | solid geometry | |
2782 | [{"role": "user", "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<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices":... | E | mcq | 3 | transformation geometry | |
2783 | [{"role": "user", "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... | 3 | numeric | 4 | algebra | |
2784 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 9 | numeric | 2 | combinatorics | |
2785 | [{"role": "user", "question": "A rectangle, with sides parallel to the $x-$axis and $y-$axis, has opposite vertices located at $(15, 3)$ and$(16, 5)$. A line is drawn through points $A(0, 0)$ and $B(3, 1)$. Another line is drawn through points $C(0, 10)$ and $D(2, 9)$. How many points on the rectangle lie on at least o... | 1 | numeric | 3 | analytic geometry | |
2786 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 8 | numeric | 2 | statistics | |
2787 | [{"role": "user", "question": "The figure below shows a large white circle with a number of smaller white and shaded circles in its interior. What fraction of the interior of the large white circle is shaded?\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{4}$", "B": "$\\frac{11}{36}$", "C": "$\\frac{1}{3}$", "D":... | B | mcq | 3 | metric geometry - area | |
2788 | [{"role": "user", "question": "Along the route of a bicycle race, $7$ water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also $2$ repair stations evenly spaced between the start and finish lines. The $3$rd water station is located $2$ miles after the $1$st repai... | 48 | numeric | 2 | metric geometry - length | |
2789 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$132~\\text{Ps}, 134~\\text{Qs}, 134~\\text{Rs}$", "B": "$133~\\text{Ps}, ... | C | mcq | 4 | algebra | |
279 | [{"role": "user", "question": "The curve in the diagram is defined by the equation\n$$\n\\left(x^{2}+y^{2}-2 x\\right)^{2}=2\\left(x^{2}+y^{2}\\right)\n$$\nWhich of the lines $a, b, c, d$ is the $y$-axis?\n<image1>", "hint": "", "options": {"A": "$a$", "B": "$b$", "C": "$c$", "D": "$d$", "E": "none of them"}, "choices"... | A | mcq | 4 | analytic geometry | |
2790 | [{"role": "user", "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<image1>", "hint": "", "option... | 1 | numeric | 4 | solid geometry | |
2791 | [{"role": "user", "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 a... | C | mcq | 3 | metric geometry - area | |
2792 | [{"role": "user", "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.<image1>\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<... | C | mcq | 4 | combinatorial geometry | |
2793 | [{"role": "user", "question": "Isosceles $\\triangle$ $ABC$ has equal side lengths $AB$ and $BC$. In the figure below, segments are drawn parallel to $\\overline{AC}$ so that the shaded portions of $\\triangle$ $ABC$ have the same area. The heights of the two unshaded portions are 11 and 5 units, respectively. What is ... | 14.6 | numeric | 2 | metric geometry - length | |
2794 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | $4 \pi$ | open | 5 | metric geometry - length | |
2795 | [{"role": "user", "question": "Consider the figure <image1>, where every small triangle is equilateral with side length $1$. Compute the area of the polygon $ AEKS $.", "hint": "", "options": {}, "choices": []}] | $5 \sqrt{3}$ | open | 5 | metric geometry - area | |
2796 | [{"role": "user", "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} = \\ov... | $\frac{\sqrt{6}}{6}$ | open | 5 | metric geometry - area | |
2797 | [{"role": "user", "question": "A group of aliens from Gliese $667$ Cc come to Earth to test the hypothesis that mathematics is indeed a universal language. To do this, they give you the following information about their mathematical system:\\n\\n$\\bullet$ For the purposes of this experiment, the Gliesians have decided... | $\frac{1}{3}$ | open | 5 | algebra | |
2798 | [{"role": "user", "question": "Right triangular prism $ABCDEF$ with triangular faces $\\vartriangle ABC$ and $\\vartriangle DEF$ and edges $\\overline{AD}$, $\\overline{BE}$, and $\\overline{CF}$ has $\\angle ABC = 90^o$ and $\\angle EAB = \\angle CAB = 60^o$ . Given that $AE = 2$, the volume of $ABCDEF$ can be written... | 5 | numeric | 3 | solid geometry | |
2799 | [{"role": "user", "question": "Alice is standing on the circumference of a large circular room of radius $10$. There is a circular pillar in the center of the room of radius $5$ that blocks Alice's view. The total area in the room Alice can see can be expressed in the form $\\frac{m\\pi}{n} +p\\sqrt{q}$, where $m$ and ... | 156 | numeric | 5 | metric geometry - area |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.