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2619 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 15 | numeric | 2 | metric geometry - length | |
262 | [{"role": "user", "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 d... | A | mcq | 3 | solid geometry | |
2620 | [{"role": "user", "question": "Consider these two geoboard quadrilaterals. Which of the following statements is true?\n\n<image1>", "hint": "", "options": {"A": "$\\text{The area of quadrilateral I is more than the area of quadrilateral II.}$", "B": "$\\text{The area of quadrilateral I is less than the area of quadrila... | E | mcq | 4 | combinatorial geometry | |
2621 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$25$", "B": "$10 + 5\\pi$", "C": "$50$", "D": "$50 + 5\\pi$"... | C | mcq | 3 | metric geometry - area | |
2622 | [{"role": "user", "question": "A cube has edge length $2$. Suppose that we glue a cube of edge length $1$ on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed is... | 17 | numeric | 4 | solid geometry | |
2623 | [{"role": "user", "question": "If $\\angle A = 20^\\circ$ and $\\angle AFG = \\angle AGF$, then $\\angle B + \\angle D = $\n\n<image1>", "hint": "", "options": {"A": "$48^\\circ$", "B": "$60^\\circ$", "C": "$72^\\circ$", "D": "$80^\\circ$", "E": "$90^\\circ$"}, "choices": []}] | D | mcq | 5 | metric geometry - angle | |
2624 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 27 | numeric | 3 | metric geometry - area | |
2625 | [{"role": "user", "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... | 21 | numeric | 4 | combinatorial geometry | |
2626 | [{"role": "user", "question": "<image1>\n\nGenevieve puts bracing on her large kite in the form of a cross connecting opposite corners of the kite. How many inches of bracing material does she need?", "hint": "", "options": {}, "choices": []}] | 39 | numeric | 4 | combinatorial geometry | |
2627 | [{"role": "user", "question": "<image1>\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?", "hint": "", "options": {}, "choices": []}] | 189 | numeric | 4 | combinatorial geometry | |
2628 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 18 | numeric | 3 | analytic geometry | |
2629 | [{"role": "user", "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 larg... | E | mcq | 3 | transformation geometry | |
263 | [{"role": "user", "question": "If one removes some $1 \\times 1 \\times 1$ cubes from a $5 \\times 5 \\times 5$ cube, you obtain the solid shown. It consists of several equally high pillars that are built upon a common base. How many little cubes have been removed?\n<image1>", "hint": "", "options": {}, "choices": []}] | 64 | numeric | 3 | solid geometry | |
2630 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "... | D | mcq | 2 | statistics | |
2631 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 4 | combinatorial geometry | |
2632 | [{"role": "user", "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<imag... | 5 | numeric | 3 | transformation geometry | |
2633 | [{"role": "user", "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 o... | A | mcq | 2 | statistics | |
2634 | [{"role": "user", "question": "The students in Mrs. Sawyer's class were asked to do a taste test of five kinds of candy. Each student chose one kind of candy. A bar graph of their preferences is shown. What percent of her class chose candy E?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 20 | numeric | 2 | statistics | |
2635 | [{"role": "user", "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... | 24 | numeric | 2 | statistics | |
2636 | [{"role": "user", "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... | B | mcq | 2 | statistics | |
2637 | [{"role": "user", "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... | E | mcq | 2 | statistics | |
2638 | [{"role": "user", "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<image1>", "hint": "", "options": {}, ... | 13 | numeric | 4 | algebra | |
2639 | [{"role": "user", "question": "Which of the following polygons has the largest area?\n\n<image1>", "hint": "", "options": {"A": "$\\text{A}$", "B": "$\\text{B}$", "C": "$\\text{C}$", "D": "$\\text{D}$", "E": "$\\text{E}$"}, "choices": []}] | E | mcq | 4 | combinatorial geometry | |
264 | [{"role": "user", "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?\... | D | mcq | 3 | solid geometry | |
2640 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$X+Z=W+Y$", "B": "$W+X=Z$", "C": "$3X+4Y=5Z$", "D": "$X+W=\\... | E | mcq | 3 | metric geometry - area | |
2641 | [{"role": "user", "question": "The area of triangle $ XYZ$ is 8 square inches. Points $ A$ and $ B$ are midpoints of congruent segments $ \\overline{XY}$ and $ \\overline{XZ}$. Altitude $ \\overline{XC}$ bisects $ \\overline{YZ}$. What is the area (in square inches) of the shaded region?\n<image1>", "hint": "", "opt... | D | mcq | 3 | metric geometry - area | |
2642 | [{"role": "user", "question": "Six cubes, each an inch on an edge, are fastened together, as shown. Find the total surface area in square inches. Include the top, bottom and sides.\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 26 | numeric | 4 | solid geometry | |
2643 | [{"role": "user", "question": "A portion of a corner of a tiled floor is shown. If the entire floor is tiled in this way and each of the four corners looks like this one, then what fraction of the tiled floor is made of darker tiles?\n\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{3}$", "B": "$\\frac{4}{9}$", ... | B | mcq | 4 | combinatorial geometry | |
2644 | [{"role": "user", "question": "Given the areas of the three squares in the figure, what is the area of the interior triangle?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 30 | numeric | 3 | metric geometry - area | |
2645 | [{"role": "user", "question": "$\\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<image1>\n\n$\\circ$ Roger's cookies are rectangles:\n<image2>\n\n$\\circ$ Paul's... | A | mcq | 3 | metric geometry - area | |
2646 | [{"role": "user", "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<image1>\n\n$\\circ$ Roger's cookies are rectangles:\n<image2>\n\n$\\circ$ Paul's... | 40 | numeric | 4 | algebra | |
2647 | [{"role": "user", "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<image1>\n\n$\\circ$ Roger's cookies are rectangles:\n<image2>\n\n$\\circ$ Paul's... | 24 | numeric | 3 | metric geometry - area | |
2648 | [{"role": "user", "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<image1>", "hint": "", "opt... | 6 | numeric | 4 | solid geometry | |
2649 | [{"role": "user", "question": "A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 4 | descriptive geometry | |
265 | [{"role": "user", "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<image1>", "hint": "", "options": {}... | 18 | numeric | 5 | metric geometry - length | |
2650 | [{"role": "user", "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 ... | 6 | numeric | 3 | graph theory | |
2651 | [{"role": "user", "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$, in centimeters?\n<image1>", "hint": "", "options": {}, "choices": []}] | 10 | numeric | 2 | metric geometry - length | |
2652 | [{"role": "user", "question": "The following figures are composed of squares and circles. Which figure has a shaded region with largest area?\n<image1>", "hint": "", "options": {"A": "$\\text{A only}$", "B": "$\\text{B only}$", "C": "$\\text{C only}$", "D": "$\\text{both A and B}$", "E": "$\\text{all are equal}$"}, "ch... | C | mcq | 3 | metric geometry - area | |
2653 | [{"role": "user", "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<image1>\n\nIf the pattern is con... | A | mcq | 3 | transformation geometry | |
2654 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "<image2>"... | B | mcq | 2 | statistics | |
2655 | [{"role": "user", "question": "In the figure, the area of square WXYZ is $25 \\text{cm}^2$. The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In $\\Delta ABC$, $AB = AC$, and when $\\Delta ABC$ is folded over side BC, point A coincides with O, the center... | C | mcq | 3 | metric geometry - area | |
2656 | [{"role": "user", "question": "What is the area enclosed by the geoboard quadrilateral below?\n\n<image1>", "hint": "", "options": {"A": "$15$", "B": "$18\\frac{1}{2}$", "C": "$22\\frac{1}{2}$", "D": "$27$", "E": "$41$"}, "choices": []}] | C | mcq | 4 | combinatorial geometry | |
2657 | [{"role": "user", "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 ... | 11 | numeric | 4 | combinatorial geometry | |
2658 | [{"role": "user", "question": "Spinners A and B are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability that the product of the two spinners' numbers is even?\n\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{4}$", "B": "$\\frac{1}{3}$", "C": "$\\frac{1}{2}$", "D": "$... | D | mcq | 2 | combinatorics | |
2659 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "<image2>", "B": "<image3>", "C": "<image4>", "D": "<image5>", "E": "<image6>"}, "choices": []}] | D | mcq | 2 | statistics | |
266 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 2 | numeric | 5 | algebra | |
2660 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 7.6 | numeric | 2 | metric geometry - length | |
2661 | [{"role": "user", "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<image1>", "hint": "", "... | D | mcq | 3 | metric geometry - area | |
2662 | [{"role": "user", "question": "What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal $ \\overline{BD}$ of square $ ABCD$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 4 | numeric | 4 | combinatorial geometry | |
2663 | [{"role": "user", "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<image1>", "hint": "", "optio... | 17 | numeric | 2 | metric geometry - length | |
2664 | [{"role": "user", "question": "The area of polygon $ ABCDEF$ is 52 with $ AB=8$, $ BC=9$ and $ FA=5$. What is $ DE+EF$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 9 | numeric | 2 | metric geometry - length | |
2665 | [{"role": "user", "question": "The results of a cross-country team's training run are graphed below. Which student has the greatest average speed?\n<image1>", "hint": "", "options": {"A": "$\\text{Angela}$", "B": "$\\text{Briana}$", "C": "$\\text{Carla}$", "D": "$\\text{Debra}$", "E": "$\\text{Evelyn}$"}, "choices": []... | E | mcq | 3 | analytic geometry | |
2666 | [{"role": "user", "question": "What is the perimeter of trapezoid $ ABCD$?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 180 | numeric | 2 | metric geometry - length | |
2667 | [{"role": "user", "question": "How many distinct triangles can be drawn using three of the dots below as vertices?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 18 | numeric | 4 | combinatorial geometry | |
2668 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$6$", "B... | B | mcq | 3 | metric geometry - area | |
2669 | [{"role": "user", "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<image1>", "hin... | A | mcq | 2 | metric geometry - length | |
267 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$2: 1$", "B": "$\\sqrt{3}: 1$", "C": "$3: 2$", "D": "$\\sqrt{2}: 1$", "E": "$5: 4$"}, "choices": []}] | D | mcq | 5 | metric geometry - length | |
2670 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\text{north}$", "B": "$\\text{ea... | B | mcq | 3 | transformation geometry | |
2671 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 30 | numeric | 3 | metric geometry - area | |
2672 | [{"role": "user", "question": "The letter T is formed by placing two $ 2\\times 4$ inch rectangles next to each other, as shown. What is the perimeter of the T, in inches?\n\n<image1>", "hint": "", "options": {}, "choices": []}] | 20 | numeric | 2 | metric geometry - length | |
2673 | [{"role": "user", "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?", "hint": "", "options": {"A": "<image1>", "B": "<image2>", "C": "<image3>", "D": "<image4... | A | mcq | 3 | analytic geometry | |
2674 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{1}{4}$", "B": "$\\frac{1}{3}$", "C": "$\\frac{1}{2}$", "D": "$\\frac{2}{3}$", "E": "$\\frac{3}{4}$"}, "choic... | B | mcq | 2 | combinatorics | |
2675 | [{"role": "user", "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\... | 5.5 | numeric | 2 | metric geometry - length | |
2676 | [{"role": "user", "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 ... | 26 | numeric | 4 | algebra | |
2677 | [{"role": "user", "question": "Barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. The sums of the two numbers on each of the three cards are equal. The three numbers on the hidden sides are prime numbers. What is the average of the hidden prime numbers?\n\n<image1>", ... | 14 | numeric | 4 | algebra | |
2678 | [{"role": "user", "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 p... | E | mcq | 2 | statistics | |
2679 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 4.5 | numeric | 3 | metric geometry - area | |
268 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 10 | numeric | 5 | metric geometry - length | |
2680 | [{"role": "user", "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<image1>", "hint": "", "op... | D | mcq | 4 | combinatorial geometry | |
2681 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "1:1", "B": "6:5", "C": "3:2... | A | mcq | 3 | metric geometry - area | |
2682 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$03$", "B": "$1006$", "C": "$504$", "D": "$1507$", "E": "$1510$"... | C | mcq | 4 | algebra | |
2683 | [{"role": "user", "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?", "hint": "", "options": {"A": "<image1>", "B": "<image2>", "C": "<image3>", "D": "... | A | mcq | 2 | statistics | |
2684 | [{"role": "user", "question": "What is the area of the shaded pinwheel shown in the $5\\times 5$ grid?\n\n<image1>", "hint": "", "options": {"A": "$4$", "B": "$6$", "C": "$8$", "D": "$10$", "E": "$12$"}, "choices": []}] | B | mcq | 4 | combinatorial geometry | |
2685 | [{"role": "user", "question": "On the dart board shown in the figure, the outer circle has radius 6 and the inner circle has radius 3. Three radii divide each circle into the three congruent regions, with point values shown. The probability that a dart will hit a given region is proportional to to the area of the regio... | B | mcq | 2 | combinatorics | |
2686 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 3 | metric geometry - area | |
2687 | [{"role": "user", "question": "In the figure, what is the ratio of the area of the gray squares to the area of the white squares?\n<image1>", "hint": "", "options": {"A": "3:10", "B": "3:8", "C": "3:7", "D": "3:5", "E": "1:1"}, "choices": []}] | D | mcq | 4 | combinatorial geometry | |
2688 | [{"role": "user", "question": "Candy sales from the Boosters Club from January through April are shown. What were the average sales per month in dollars?\n<image1>", "hint": "", "options": {}, "choices": []}] | 80 | numeric | 2 | statistics | |
2689 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": ... | 4 | numeric | 2 | combinatorics | |
269 | [{"role": "user", "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<ima... | A | mcq | 5 | metric geometry - length | |
2690 | [{"role": "user", "question": "A shape is created by joining seven unit cubes, as shown. What is the ratio of the volume in cubic units to the surface area in square units?\n\n<image1>", "hint": "", "options": {"A": "1 : 6", "B": "7 : 36", "C": "1 : 5", "D": "7 : 30", "E": "6 : 25"}, "choices": []}] | D | mcq | 4 | solid geometry | |
2691 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$10\\pi+20$", "B": "$10\\pi+30$", "C": "$10\\pi+40$", "... | E | mcq | 2 | metric geometry - length | |
2692 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{1}{4}$", "B": "$\\frac{2}{7}$", "C... | B | mcq | 2 | combinatorics | |
2693 | [{"role": "user", "question": "Jerry cuts a wedge from a $6$-cm cylinder of bologna as shown by the dashed curve. Which answer choice is closest to the volume of his wedge in cubic centimeters?\n<image1>", "hint": "", "options": {"A": "48", "B": "75", "C": "151", "D": "192", "E": "603"}, "choices": []}] | C | mcq | 4 | solid geometry | |
2694 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{1}{6}$", "B": "$\\frac{2}{9}$", "C": "$\\frac{5}{18}$", "D": "$\\frac{1}{3}$", "E": "$\\frac{7}{20}$"}, "choices": []}... | C | mcq | 3 | metric geometry - area | |
2695 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "42", "B": "44", "C": "45", "D": "46", "E": "48"}, "cho... | A | mcq | 3 | metric geometry - area | |
2696 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 2 | statistics | |
2697 | [{"role": "user", "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<image1>\n\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | B | mcq | 4 | combinatorial geometry | |
2698 | [{"role": "user", "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... | 4.5 | numeric | 3 | metric geometry - area | |
2699 | [{"role": "user", "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. ... | 23 | numeric | 3 | counting | |
27 | [{"role": "user", "question": "Theresa moves a pencil along the line. She starts at the arrow shown. In which order will she go past the shapes?\n<image1>", "hint": "", "options": {"A": "$\\Delta, \\square, \\bullet$", "B": "$\\Delta, \\bullet, \\square$", "C": "$\\bullet, \\Delta, \\square$", "D": "$\\square, \\Delta,... | A | mcq | 5 | topology | |
270 | [{"role": "user", "question": "In the diagram a closed polygon can be seen whose vertices are the midpoints of the edges of the die. The interior angles are as usual defined as the angle that two sides of the polygon describe in a common vertex. How big is the sum of all interior angles of the polygon?\n<image1>", "hin... | B | mcq | 3 | solid geometry | |
2700 | [{"role": "user", "question": "On a checkerboard composed of 64 unit squares, what is the probability that a randomly chosen unit square does not touch the outer edge of the board?\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{16}$", "B": "$\\frac{7}{16}$", "C": "$\\frac{1}{2}$", "D": "$\\frac{9}{16}$", "E": ... | D | mcq | 5 | arithmetic | |
2701 | [{"role": "user", "question": "The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime?\n<image1>\n<image2>", "hint": "", "options": {"A": "$\\frac{1}{2}$", "B": "$\\frac{2}{3}$", "C": "$\\frac{3}{4}$", "D": "$\\... | D | mcq | 2 | combinatorics | |
2702 | [{"role": "user", "question": "The diagram represents a $ 7$-foot-by-$ 7$-foot floor that is tiled with $ 1$-square-foot black tiles and white tiles. Notice that the corners have white tiles. If a $ 15$-foot-by-$ 15$-foot floor is to be tiled in the same manner, how many white tiles will be needed?\n<image1>", "hint": ... | 64 | numeric | 4 | algebra | |
2703 | [{"role": "user", "question": "How many non-congruent triangles have vertices at three of the eight points in the array shown below?\n<image1>", "hint": "", "options": {}, "choices": []}] | 8 | numeric | 4 | combinatorial geometry | |
2704 | [{"role": "user", "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... | E | mcq | 4 | solid geometry | |
2705 | [{"role": "user", "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<image1>", "hint": "", "options": {}, "choices": []}] | 70 | numeric | 2 | statistics | |
2706 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$\\frac{2}{5... | D | mcq | 4 | combinatorial geometry | |
2707 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$2:3$", "B": "$3:2$",... | C | mcq | 3 | metric geometry - area | |
2708 | [{"role": "user", "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<image1>", "hint": "", "options": {"A": "$36 \\pi$", "B": "$49 \\pi$", "C... | C | mcq | 3 | metric geometry - area |
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