id stringlengths 1 4 | question stringlengths 31 709 | options listlengths 6 6 | image_path stringlengths 12 15 | image imagewidth (px) 56 2.52k | answer stringclasses 5 values | solution stringclasses 259 values | level int64 1 5 | subject stringclasses 16 values | Answer(Option) stringclasses 5 values |
|---|---|---|---|---|---|---|---|---|---|
2527 | <image1>
The square in the first diagram "rolls" clockwise around the fixed regular hexagon until it reaches the bottom. In which position will the solid triangle be in diagram $4$?
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2527.jpg | E | null | 3 | transformation geometry | E | |
2529 | Which of the five "T-like shapes" would be symmetric to the one shown with respect to the dashed line?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2529.jpg | B | null | 3 | transformation geometry | B | |
2534 | 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 rectangle?
<image1> | [
"$\\frac{1}{2}$",
"$\\frac{2}{3}$",
"$\\frac{3}{4}$",
"$\\frac{4}{5}$",
"$\\frac{5}{6}$",
"I don't know"
] | images/2534.jpg | E | null | 3 | transformation geometry | E | |
2535 | 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?
<image1> | [
"$\\frac{1}{6}$",
"$\\frac{3}{7}$",
"$\\frac{1}{2}$",
"$\\frac{2}{3}$",
"$\\frac{5}{7}$",
"I don't know"
] | images/2535.jpg | C | null | 2 | combinatorics | C | |
2537 | What fraction of the square is shaded?
<image1> | [
"$\\frac{1}{3}$",
"$\\frac{2}{5}$",
"$\\frac{5}{12}$",
"$\\frac{3}{7}$",
"$\\frac{1}{2}$",
"I don't know"
] | images/2537.jpg | E | null | 3 | metric geometry - area | E | |
2538 | 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
<image1> | [
"$\\text{P}$",
"$\\text{Q}$",
"$\\text{R}$",
"$\\text{S}$",
"$\\text{T}$",
"I don't know"
] | images/2538.jpg | A | null | 4 | algebra | A | |
2540 | The area of this figure is $ 100\text{ cm}^{2} $. Its perimeter is
<image1> | [
"$\\text{20 cm}$",
"$\\text{25 cm}$",
"$\\text{30 cm}$",
"$\\text{40 cm}$",
"$\\text{50 cm}$",
"I don't know"
] | images/2540.jpg | E | null | 2 | metric geometry - length | E | |
2542 | The graph relates the distance traveled [in miles] to the time elapsed [in hours] on a trip taken by an experimental airplane. During which hour was the average speed of this airplane the largest?
<image1> | [
"$\\text{first (0-1)}$",
"$\\text{second (1-2)}$",
"$\\text{third (2-3)}$",
"$\\text{ninth (8-9)}$",
"$\\text{last (11-12)}$",
"I don't know"
] | images/2542.jpg | B | null | 2 | statistics | B | |
2545 | A "domino" is made up of two small squares:
<image1>
Which of the "checkerboards" illustrated below CANNOT be covered exactly and completely by a whole number of non-overlapping dominoes?
<image2> | [
"$3\\times 4$",
"$3\\times 5$",
"$4\\times 4$",
"$4\\times 5$",
"$6\\times 3$",
"I don't know"
] | images/2545.jpg | B | null | 4 | combinatorial geometry | B | |
2547 | 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?
<image1> | [
"$2\\text{ less}$",
"$1\\text{ less}$",
"$\\text{the same}$",
"$1\\text{ more}$",
"$2\\text{ more}$",
"I don't know"
] | images/2547.jpg | C | null | 4 | solid geometry | C | |
2549 | 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?
<image1> | [
"$9\\%$",
"$23\\frac{1}{3}\\%$",
"$30\\%$",
"$42\\frac{6}{7}\\%$",
"$50\\%$",
"I don't know"
] | images/2549.jpg | C | null | 2 | statistics | C | |
2551 | 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?
<image1> | [
"$\\frac{1}{3}$",
"$\\frac{1}{2}$",
"$\\frac{2}{3}$",
"$\\frac{7}{9}$",
"$1$",
"I don't know"
] | images/2551.jpg | D | null | 2 | combinatorics | D | |
2552 | 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?
<image1> | [
"$\\frac{1}{1024}$",
"$\\frac{15}{64}$",
"$\\frac{243}{1024}$",
"$\\frac{1}{4}$",
"$\\frac{81}{256}$",
"I don't know"
] | images/2552.jpg | C | null | 4 | algebra | C | |
2553 | 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?
<image1> | [
"1",
"2",
"3",
"4",
"5",
"I don't know"
] | images/2553.jpg | E | null | 3 | metric geometry - area | E | |
2557 | The bar graph shows the results of a survey on color preferences. What percent preferred blue?
<image1> | [
"$20\\%$",
"$24\\%$",
"$30\\%$",
"$36\\%$",
"$42\\%$",
"I don't know"
] | images/2557.jpg | B | null | 2 | statistics | B | |
2558 | <image1>
Which cylinder has twice the volume of the cylinder shown above?
<image2> | [
"A",
"B",
"C",
"D",
"None of the above",
"I don't know"
] | images/2558.jpg | B | null | 4 | solid geometry | B | |
2560 | Which pattern of identical squares could NOT be folded along the lines shown to form a cube?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2560.jpg | D | null | 4 | solid geometry | D | |
2561 | 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?
<image1> | [
"$\\text{Jan}$",
"$\\text{Feb}$",
"$\\text{Mar}$",
"$\\text{Apr}$",
"$\\text{May}$",
"I don't know"
] | images/2561.jpg | B | null | 2 | statistics | B | |
2562 | 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 figure. Which of the following could be the perimeter of the new figure?
<image1> | [
"15",
"17",
"18",
"19",
"20",
"I don't know"
] | images/2562.jpg | C | null | 4 | combinatorial geometry | C | |
2564 | Which one of the following bar graphs could represent the data from the circle graph?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2564.jpg | C | null | 2 | statistics | C | |
2565 | This line graph represents the price of a trading card during the first $6$ months of $1993$.
<image1>
The greatest monthly drop in price occurred during | [
"$\\text{January}$",
"$\\text{March}$",
"$\\text{April}$",
"$\\text{May}$",
"$\\text{June}$",
"I don't know"
] | images/2565.jpg | B | null | 2 | statistics | B | |
2570 | Which of the following represents the result when the figure shown below is rotated clockwise $120^\circ$ about its center?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2570.jpg | B | null | 3 | transformation geometry | B | |
2571 | If $\angle A = 60^\circ $, $\angle E = 40^\circ $ and $\angle C = 30^\circ $, then $\angle BDC = $
<image1> | [
"$40^\\circ$",
"$50^\\circ$",
"$60^\\circ$",
"$70^\\circ$",
"$80^\\circ$",
"I don't know"
] | images/2571.jpg | B | null | 5 | metric geometry - angle | B | |
2572 | 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?
<image1> | [
"$\\text{The shaded areas in all three are equal.}$",
"$\\text{Only the shaded areas of }I\\text{ and }II\\text{ are equal.}$",
"$\\text{Only the shaded areas of }I\\text{ and }III\\text{ are equal.}$",
"$\\text{Only the shaded areas of }II\\text{ and }III\\text{ are equal.}$",
"$\\text{The shaded areas of ... | images/2572.jpg | A | null | 4 | combinatorial geometry | A | |
2573 | If this path is to continue in the same pattern:
<image1>
then which sequence of arrows goes from point $425$ to point $427$?
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2573.jpg | A | null | 4 | algebra | A | |
2574 | Mike leaves home and drives slowly east through city traffic. When he reaches the highway he drives east more rapidly until he reaches the shopping mall where he stops. He shops at the mall for an hour. Mike returns home by the same route as he came, driving west rapidly along the highway and then slowly through city traffic. Each graph shows the distance from home on the vertical axis versus the time elapsed since leaving home on the horizontal axis. Which graph is the best representation of Mike's trip?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2574.jpg | B | null | 2 | statistics | B | |
2576 | The two wheels shown below are spun and the two resulting numbers are added. The probability that the sum is even is
<image1> | [
"$\\frac{1}{6}$",
"$\\frac{1}{4}$",
"$\\frac{1}{3}$",
"$\\frac{5}{12}$",
"$\\frac{4}{9}$",
"I don't know"
] | images/2576.jpg | D | null | 2 | combinatorics | D | |
2579 | 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
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2579.jpg | D | null | 4 | algebra | D | |
2580 | 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 = $
<image1> | [
"$75^\\circ$",
"$80^\\circ$",
"$85^\\circ$",
"$90^\\circ$",
"$95^\\circ$",
"I don't know"
] | images/2580.jpg | E | null | 5 | metric geometry - angle | E | |
2585 | The letters $P$, $Q$, $R$, $S$, and $T$ represent numbers located on the number line as shown.
<image1>
Which of the following expressions represents a negative number? | [
"$P-Q$",
"$P\\cdot Q$",
"$\\frac{S}{Q}\\cdot P$",
"$\\frac{R}{P\\cdot Q}$",
"$\\frac{S+T}{R}$",
"I don't know"
] | images/2585.jpg | A | null | 4 | algebra | A | |
2587 | 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 $OPQR$?
<image1>
NOT TO SCALE | [
"(-6,0)",
"(-4,0)",
"(-2,0)",
"(2,0)",
"(4,0)",
"I don't know"
] | images/2587.jpg | C | null | 3 | analytic geometry | C | |
2588 | 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
<image1> | [
"$30\\%$",
"$31\\%$",
"$32\\%$",
"$33\\%$",
"$34\\%$",
"I don't know"
] | images/2588.jpg | C | null | 2 | statistics | C | |
2589 | The horizontal and vertical distances between adjacent points equal $1$ unit. The area of triangle $ABC$ is
<image1> | [
"1/4",
"1/2",
"3/4",
"1",
"5/4",
"I don't know"
] | images/2589.jpg | B | null | 4 | combinatorial geometry | B | |
2590 | 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
<image1> | [
"$90^\\circ$",
"$100^\\circ$",
"$115^\\circ$",
"$122.5^\\circ$",
"$125^\\circ$",
"I don't know"
] | images/2590.jpg | C | null | 5 | metric geometry - angle | C | |
2591 | What fraction of this square region is shaded? Stripes are equal in width, and the figure is drawn to scale.
<image1> | [
"$\\frac{5}{12}$",
"$\\frac{1}{2}$",
"$\\frac{7}{12}$",
"$\\frac{2}{3}$",
"$\\frac{5}{6}$",
"I don't know"
] | images/2591.jpg | C | null | 3 | metric geometry - area | C | |
2592 | $\angle 1 + \angle 2 = 180^\circ $
$\angle 3 = \angle 4$
Find $\angle 4$.
<image1> | [
"$20^\\circ$",
"$25^\\circ$",
"$30^\\circ$",
"$35^\\circ$",
"$40^\\circ$",
"I don't know"
] | images/2592.jpg | D | null | 5 | metric geometry - angle | D | |
2593 | 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
<image1> | [
"$\\frac{\\sqrt{3}}{3}$",
"$\\frac{5}{9}$",
"$\\frac{2}{3}$",
"$\\frac{\\sqrt{5}}{3}$",
"$\\frac{7}{9}$",
"I don't know"
] | images/2593.jpg | B | null | 3 | metric geometry - area | B | |
2595 | 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
<image1> | [
"$19\\text{ sq.cm}$",
"$24\\text{ sq.cm}$",
"$30\\text{ sq.cm}$",
"$54\\text{ sq.cm}$",
"$72\\text{ sq.cm}$",
"I don't know"
] | images/2595.jpg | D | null | 4 | solid geometry | D | |
2596 | 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
<image1> | [
"2:3",
"1:1",
"3:2",
"9:4",
"5:2",
"I don't know"
] | images/2596.jpg | C | null | 3 | metric geometry - area | C | |
2599 | What is the ratio of the area of the shaded square to the area of the large square? (The figure is drawn to scale)
<image1> | [
"$\\frac{1}{6}$",
"$\\frac{1}{7}$",
"$\\frac{1}{8}$",
"$\\frac{1}{12}$",
"$\\frac{1}{16}$",
"I don't know"
] | images/2599.jpg | C | null | 3 | metric geometry - area | C | |
2600 | 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.
What does the paper look like when unfolded?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2600.jpg | B | null | 3 | transformation geometry | B | |
2602 | If the pattern in the diagram continues, what fraction of the interior would be shaded in the eighth triangle?
<image1> | [
"$\\frac{3}{8}$",
"$\\frac{5}{27}$",
"$\\frac{7}{16}$",
"$\\frac{9}{16}$",
"$\\frac{11}{45}$",
"I don't know"
] | images/2602.jpg | C | null | 4 | algebra | C | |
2605 | 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
<image1> | [
"$\\text{B}$",
"$\\text{G}$",
"$\\text{O}$",
"$\\text{R}$",
"$\\text{Y}$",
"I don't know"
] | images/2605.jpg | A | null | 4 | solid geometry | A | |
2609 | 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.
Which of the following is the front view for the stack map in Fig. 4?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2609.jpg | B | null | 4 | descriptive geometry | B | |
2611 | Square $ABCD$ has sides of length 3. Segments $CM$ and $CN$ divide the square's area into three equal parts. How long is segment $CM$ ?
<image1> | [
"$\\sqrt{10}$",
"$\\sqrt{12}$",
"$\\sqrt{13}$",
"$\\sqrt{14}$",
"$\\sqrt{15}$",
"I don't know"
] | images/2611.jpg | C | null | 2 | metric geometry - length | C | |
2613 | 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
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2613.jpg | E | null | 2 | statistics | E | |
2618 | In triangle $CAT$, we have $\angle ACT = \angle ATC$ and $\angle CAT = 36^\circ$. If $\overline{TR}$ bisects $\angle ATC$, then $\angle CRT =$
<image1> | [
"$36^\\circ$",
"$54^\\circ$",
"$72^\\circ$",
"$90^\\circ$",
"$108^\\circ$",
"I don't know"
] | images/2618.jpg | C | null | 5 | metric geometry - angle | C | |
2620 | Consider these two geoboard quadrilaterals. Which of the following statements is true?
<image1> | [
"$\\text{The area of quadrilateral I is more than the area of quadrilateral II.}$",
"$\\text{The area of quadrilateral I is less than the area of quadrilateral II.}$",
"$\\text{The quadrilaterals have the same area and the same perimeter.}$",
"$\\text{The quadrilaterals have the same area, but the perimeter o... | images/2620.jpg | E | null | 4 | combinatorial geometry | E | |
2621 | 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?
<image1> | [
"$25$",
"$10 + 5\\pi$",
"$50$",
"$50 + 5\\pi$",
"$25\\pi$",
"I don't know"
] | images/2621.jpg | C | null | 3 | metric geometry - area | C | |
2623 | If $\angle A = 20^\circ$ and $\angle AFG = \angle AGF$, then $\angle B + \angle D = $
<image1> | [
"$48^\\circ$",
"$60^\\circ$",
"$72^\\circ$",
"$80^\\circ$",
"$90^\\circ$",
"I don't know"
] | images/2623.jpg | D | null | 5 | metric geometry - angle | D | |
2629 | A square piece of paper, 4 inches on a side, is folded in half vertically. Both layers are then cut in half parallel to the fold. Three new rectangles are formed, a large one and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?
<image1> | [
"$\\frac{1}{3}$",
"$\\frac{1}{2}$",
"$\\frac{3}{4}$",
"$\\frac{4}{5}$",
"$\\frac{5}{6}$",
"I don't know"
] | images/2629.jpg | E | null | 3 | transformation geometry | E | |
2630 | 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?
<image1> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2630.jpg | D | null | 2 | statistics | D | |
2633 | A birdbath is designed to overflow so that it will be self-cleaning. Water flows in at the rate of 20 milliliters per minute and drains at the rate of 18 milliliters per minute. One of these graphs shows the volume of water in the birdbath during the filling time and continuing into the overflow time. Which one is it?
<image1> | [
"$\\text{A}$",
"$\\text{B}$",
"$\\text{C}$",
"$\\text{D}$",
"$\\text{E}$",
"I don't know"
] | images/2633.jpg | A | null | 2 | statistics | A | |
2636 | $\textbf{Juan's Old Stamping Grounds}$
Juan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.)
<image1>
In dollars and cents, how much did his South American stampes issued before the '70s cost him? | [
"$\\textdollar 0.40$",
"$\\textdollar 1.06$",
"$\\textdollar 1.80$",
"$\\textdollar 2.38$",
"$\\textdollar 2.64$",
"I don't know"
] | images/2636.jpg | B | null | 2 | statistics | B | |
2637 | $\textbf{Juan's Old Stamping Grounds}$
Juan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.)
<image1>
The average price of his '70s stamps is closest to | [
"$3.5 \\text{ cents}$",
"$4 \\text{ cents}$",
"$4.5 \\text{ cents}$",
"$5 \\text{ cents}$",
"$5.5 \\text{ cents}$",
"I don't know"
] | images/2637.jpg | E | null | 2 | statistics | E | |
2639 | Which of the following polygons has the largest area?
<image1> | [
"$\\text{A}$",
"$\\text{B}$",
"$\\text{C}$",
"$\\text{D}$",
"$\\text{E}$",
"I don't know"
] | images/2639.jpg | E | null | 4 | combinatorial geometry | E | |
2640 | 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?
<image1> | [
"$X+Z=W+Y$",
"$W+X=Z$",
"$3X+4Y=5Z$",
"$X+W=\\frac{1}{2}(Y+Z)$",
"$X+Y=Z$",
"I don't know"
] | images/2640.jpg | E | null | 3 | metric geometry - area | E | |
2641 | 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?
<image1> | [
"$1\\frac{1}{2}$",
"$2$",
"$2\\frac{1}{2}$",
"$3$",
"$3\\frac{1}{2}$",
"I don't know"
] | images/2641.jpg | D | null | 3 | metric geometry - area | D | |
2643 | 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?
<image1> | [
"$\\frac{1}{3}$",
"$\\frac{4}{9}$",
"$\\frac{1}{2}$",
"$\\frac{5}{9}$",
"$\\frac{5}{8}$",
"I don't know"
] | images/2643.jpg | B | null | 4 | combinatorial geometry | B | |
2645 | $\textbf{Bake Sale}$
Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
$\circ$ Art's cookies are trapezoids:
<image1>
$\circ$ Roger's cookies are rectangles:
<image2>
$\circ$ Paul's cookies are parallelograms:
<image3>
$\circ$ Trisha's cookies are triangles:
<image4>
Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Who gets the fewest cookies from one batch of cookie dough? | [
"$\\text{Art}$",
"$\\text{Roger}$",
"$\\text{Paul}$",
"$\\text{Trisha}$",
"$\\text{There is a tie for fewest.}$",
"I don't know"
] | images/2645.jpg | A | null | 3 | metric geometry - area | A | |
2652 | The following figures are composed of squares and circles. Which figure has a shaded region with largest area?
<image1> | [
"$\\text{A only}$",
"$\\text{B only}$",
"$\\text{C only}$",
"$\\text{both A and B}$",
"$\\text{all are equal}$",
"I don't know"
] | images/2652.jpg | C | null | 3 | metric geometry - area | C | |
2653 | 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.
<image1>
If the pattern is continued, where would the cat and mouse be after the 247th move? | [
"<image2>",
"<image3>",
"<image4>",
"<image5>",
"<image6>",
"I don't know"
] | images/2653.jpg | A | null | 3 | transformation geometry | A | |
2654 | 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?
<image1> | [
"<image2>",
"<image3>",
"<image4>",
"<image5>",
"<image6>",
"I don't know"
] | images/2654.jpg | B | null | 2 | statistics | B | |
2655 | 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 of square WXYZ. What is the area of $\Delta ABC$, in square centimeters?
<image1> | [
"$\\frac{15}4$",
"$\\frac{21}4$",
"$\\frac{27}4$",
"$\\frac{21}2$",
"$\\frac{27}2$",
"I don't know"
] | images/2655.jpg | C | null | 3 | metric geometry - area | C | |
2656 | What is the area enclosed by the geoboard quadrilateral below?
<image1> | [
"$15$",
"$18\\frac{1}{2}$",
"$22\\frac{1}{2}$",
"$27$",
"$41$",
"I don't know"
] | images/2656.jpg | C | null | 4 | combinatorial geometry | C | |
2658 | 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?
<image1> | [
"$\\frac{1}{4}$",
"$\\frac{1}{3}$",
"$\\frac{1}{2}$",
"$\\frac{2}{3}$",
"$\\frac{3}{4}$",
"I don't know"
] | images/2658.jpg | D | null | 2 | combinatorics | D | |
2659 | Tess runs counterclockwise around rectangular block JKLM. She lives at corner J. Which graph could represent her straight-line distance from home?
<image1> | [
"<image2>",
"<image3>",
"<image4>",
"<image5>",
"<image6>",
"I don't know"
] | images/2659.jpg | D | null | 2 | statistics | D | |
2661 | 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?
<image1> | [
"$16-4\\pi$",
"$16-2\\pi$",
"$28-4\\pi$",
"$28-2\\pi$",
"$32-2\\pi$",
"I don't know"
] | images/2661.jpg | D | null | 3 | metric geometry - area | D | |
2665 | The results of a cross-country team's training run are graphed below. Which student has the greatest average speed?
<image1> | [
"$\\text{Angela}$",
"$\\text{Briana}$",
"$\\text{Carla}$",
"$\\text{Debra}$",
"$\\text{Evelyn}$",
"I don't know"
] | images/2665.jpg | E | null | 3 | analytic geometry | E | |
2668 | 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$?
<image1> | [
"$6$",
"$8$",
"$3\\pi$",
"$10$",
"$4\\pi$",
"I don't know"
] | images/2668.jpg | B | null | 3 | metric geometry - area | B | |
2669 | 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?
<image1> | [
"$\\frac{2}{\\sqrt{\\pi}}$",
"$\\frac{1+\\sqrt{2}}{2}$",
"$\\frac{3}{2}$",
"$\\sqrt{3}$",
"$\\sqrt{\\pi}$",
"I don't know"
] | images/2669.jpg | A | null | 2 | metric geometry - length | A | |
2670 | 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?
<image1> | [
"$\\text{north}$",
"$\\text{east}$",
"$\\text{south}$",
"$\\text{west}$",
"$\\text{northwest}$",
"I don't know"
] | images/2670.jpg | B | null | 3 | transformation geometry | B | |
2673 | 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? | [
"<image1>",
"<image2>",
"<image3>",
"<image4>",
"<image5>",
"I don't know"
] | images/2673.jpg | A | null | 3 | analytic geometry | A | |
2674 | Jeff rotates spinners $ P$, $ Q$ and $ R$ and adds the resulting numbers. What is the probability that his sum is an odd number?
<image1> | [
"$\\frac{1}{4}$",
"$\\frac{1}{3}$",
"$\\frac{1}{2}$",
"$\\frac{2}{3}$",
"$\\frac{3}{4}$",
"I don't know"
] | images/2674.jpg | B | null | 2 | combinatorics | B | |
2678 | Six-hundred fifty students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. The results of the survey are displayed in the bar graph. What is the ratio of the number of students who preferred spaghetti to the number of students who preferred manicotti?
<image1> | [
"$\\frac{2}{5}$",
"$\\frac{1}{2}$",
"$\\frac{5}{4}$",
"$\\frac{5}{3}$",
"$\\frac{5}{2}$",
"I don't know"
] | images/2678.jpg | E | null | 2 | statistics | E | |
2680 | 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 $C$?
<image1> | [
"$I$",
"$II$",
"$III$",
"$IV$",
"$\\text{ cannot be determined}$",
"I don't know"
] | images/2680.jpg | D | null | 4 | combinatorial geometry | D | |
2681 | 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?
<image1> | [
"1:1",
"6:5",
"3:2",
"2:1",
"3:1",
"I don't know"
] | images/2681.jpg | A | null | 3 | metric geometry - area | A | |
2682 | 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.
<image1> | [
"$03$",
"$1006$",
"$504$",
"$1507$",
"$1510$",
"I don't know"
] | images/2682.jpg | C | null | 4 | algebra | C | |
2683 | 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? | [
"<image1>",
"<image2>",
"<image3>",
"<image4>",
"<image5>",
"I don't know"
] | images/2683.jpg | A | null | 2 | statistics | A | |
2684 | What is the area of the shaded pinwheel shown in the $5\times 5$ grid?
<image1> | [
"$4$",
"$6$",
"$8$",
"$10$",
"$12$",
"I don't know"
] | images/2684.jpg | B | null | 4 | combinatorial geometry | B | |
2685 | 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 region. What two darts hit this board, the score is the sum of the point values in the regions. What is the probability that the score is odd?
<image1> | [
"$\\frac{17}{36}$",
"$\\frac{35}{72}$",
"$\\frac{1}{2}$",
"$\\frac{37}{72}$",
"$\\frac{19}{36}$",
"I don't know"
] | images/2685.jpg | B | null | 2 | combinatorics | B | |
2687 | In the figure, what is the ratio of the area of the gray squares to the area of the white squares?
<image1> | [
"3:10",
"3:8",
"3:7",
"3:5",
"1:1",
"I don't know"
] | images/2687.jpg | D | null | 4 | combinatorial geometry | D | |
2690 | 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?
<image1> | [
"1 : 6",
"7 : 36",
"1 : 5",
"7 : 30",
"6 : 25",
"I don't know"
] | images/2690.jpg | D | null | 4 | solid geometry | D | |
2691 | 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?
<image1> | [
"$10\\pi+20$",
"$10\\pi+30$",
"$10\\pi+40$",
"$20\\pi+20$",
"$20\\pi+40$",
"I don't know"
] | images/2691.jpg | E | null | 2 | metric geometry - length | E | |
2692 | 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?
<image1> | [
"$\\frac{1}{4}$",
"$\\frac{2}{7}$",
"$\\frac{4}{11}$",
"$\\frac{1}{2}$",
"$\\frac{4}{7}$",
"I don't know"
] | images/2692.jpg | B | null | 2 | combinatorics | B | |
2693 | 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?
<image1> | [
"48",
"75",
"151",
"192",
"603",
"I don't know"
] | images/2693.jpg | C | null | 4 | solid geometry | C | |
2694 | In square $ABCE$, $AF=2FE$ and $CD=2DE$. What is the ratio of the area of $\triangle BFD$ to the area of square $ABCE$?
<image1> | [
"$\\frac{1}{6}$",
"$\\frac{2}{9}$",
"$\\frac{5}{18}$",
"$\\frac{1}{3}$",
"$\\frac{7}{20}$",
"I don't know"
] | images/2694.jpg | C | null | 3 | metric geometry - area | C | |
2695 | 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?
<image1> | [
"42",
"44",
"45",
"46",
"48",
"I don't know"
] | images/2695.jpg | A | null | 3 | metric geometry - area | A | |
2697 | The five pieces shown below can be arranged to form four of the five figures shown in the choices. Which figure cannot be formed?
<image1>
<image2> | [
"A",
"B",
"C",
"D",
"E",
"I don't know"
] | images/2697.jpg | B | null | 4 | combinatorial geometry | B | |
2700 | 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?
<image1> | [
"$\\frac{1}{16}$",
"$\\frac{7}{16}$",
"$\\frac{1}{2}$",
"$\\frac{9}{16}$",
"$\\frac{49}{64}$",
"I don't know"
] | images/2700.jpg | D | null | 5 | arithmetic | D | |
2701 | 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?
<image1>
<image2> | [
"$\\frac{1}{2}$",
"$\\frac{2}{3}$",
"$\\frac{3}{4}$",
"$\\frac{7}{9}$",
"$\\frac{5}{6}$",
"I don't know"
] | images/2701.jpg | D | null | 2 | combinatorics | D | |
2704 | A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cub is $\frac{1}{2}$ foot from the top face. The second cut is $\frac{1}{3}$ foot below the first cut, and the third cut is $\frac{1}{17}$ foot below the second cut. From the top to the bottom the pieces are labeled A, B, C, and D. The pieces are then glued together end to end as shown in the second diagram. What is the total surface area of this solid in square feet?
<image1>
<image2> | [
"6$",
"$7$",
"$\\frac{419}{51}$",
"$\\frac{158}{17}$",
"$11$",
"I don't know"
] | images/2704.jpg | E | null | 4 | solid geometry | E | |
2706 | 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 $\frac{XQ}{QY}$?
<image1> | [
"$\\frac{2}{5}$",
"$\\frac{1}{2}$",
"$\\frac{3}{5}$",
"$\\frac{2}{3}$",
"$\\frac{3}{4}$",
"I don't know"
] | images/2706.jpg | D | null | 4 | combinatorial geometry | D | |
2707 | 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.
<image1> | [
"$2:3$",
"$3:2$",
"$6:\\pi$",
"$9: \\pi$",
"$30 : \\pi$",
"I don't know"
] | images/2707.jpg | C | null | 3 | metric geometry - area | C | |
2708 | 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?
<image1> | [
"$36 \\pi$",
"$49 \\pi$",
"$64 \\pi$",
"$81 \\pi$",
"$100 \\pi$",
"I don't know"
] | images/2708.jpg | C | null | 3 | metric geometry - area | C | |
2709 | 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 $O$?
<image1> | [
"$\\frac{\\sqrt{2}}{4}$",
"$\\frac{1}{2}$",
"$\\frac{2}{\\pi}$",
"$\\frac{2}{3}$",
"$\\frac{\\sqrt{2}}{2}$",
"I don't know"
] | images/2709.jpg | B | null | 3 | analytic geometry | B | |
2710 | 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?
<image1> | [
"8:17",
"25:49",
"36:25",
"32:17",
"36:17",
"I don't know"
] | images/2710.jpg | D | null | 4 | combinatorial geometry | D | |
2711 | 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?
<image1> | [
"$12\\frac{1}{2}$",
"$20$",
"$25$",
"$33 \\frac{1}{3}$",
"$37\\frac{1}{2}$",
"I don't know"
] | images/2711.jpg | C | null | 4 | combinatorial geometry | C | |
2717 | 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?
<image1> | [
"$\\frac{1}2$",
"$1$",
"$\\frac{3}2$",
"$2$",
"$\\frac{5}2$",
"I don't know"
] | images/2717.jpg | A | null | 3 | metric geometry - area | A | |
2719 | 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?
<image1> | [
"$\\frac{4-\\pi}\\pi$",
"$\\frac{1}{\\pi}$",
"$\\frac{\\sqrt{2}}{\\pi}$",
"$\\frac{\\pi-1}\\pi$",
"$\\frac{3}{\\pi}$",
"I don't know"
] | images/2719.jpg | A | null | 3 | metric geometry - area | A |
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