id string | media images list | messages string | answer string | question_type string | catagory string |
|---|---|---|---|---|---|
rbench_v_full_00600 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 4 | numeric | Game | |
rbench_v_full_00601 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 4 | numeric | Game | |
rbench_v_full_00602 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 4 | numeric | Game | |
rbench_v_full_00603 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 4 | numeric | Game | |
rbench_v_full_00604 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 10 | numeric | Game | |
rbench_v_full_00605 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 6 | numeric | Game | |
rbench_v_full_00606 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 5 | numeric | Game | |
rbench_v_full_00607 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 4 | numeric | Game | |
rbench_v_full_00608 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 9 | numeric | Game | |
rbench_v_full_00609 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 4 | numeric | Game | |
rbench_v_full_00610 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 3 | numeric | Game | |
rbench_v_full_00611 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 3 | numeric | Game | |
rbench_v_full_00612 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 5 | numeric | Game | |
rbench_v_full_00613 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 4 | numeric | Game | |
rbench_v_full_00614 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 6 | numeric | Game | |
rbench_v_full_00615 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 5 | numeric | Game | |
rbench_v_full_00616 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 4 | numeric | Game | |
rbench_v_full_00617 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 4 | numeric | Game | |
rbench_v_full_00618 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 9 | numeric | Game | |
rbench_v_full_00619 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 6 | numeric | Game | |
rbench_v_full_00620 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 3 | numeric | Game | |
rbench_v_full_00621 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 5 | numeric | Game | |
rbench_v_full_00622 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 5 | numeric | Game | |
rbench_v_full_00623 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 8 | numeric | Game | |
rbench_v_full_00624 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 3 | numeric | Game | |
rbench_v_full_00625 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 4 | numeric | Game | |
rbench_v_full_00626 | [{"role": "user", "question": "In the given image:\n1. There are several blue circles, each containing a unique natural number starting from 1, representing the identifier of that circle;\n2. There are also several red arrows in the image, each with a specific direction.\n\nYour task is:\n\nDetermine how many blue circ... | 2 | numeric | Game | |
rbench_v_full_00627 | [{"role": "user", "question": "As shown in the figure, in the equilateral triangle △ABC, point D lies on segment AB, segment CD is drawn, point E lies on segment CD (with CE > DE), and segment CE is rotated 60° clockwise about point C to obtain segment CF; segment AF is then drawn. Let point G lie on the extension of s... | CE=2MF+DE | open | Math | |
rbench_v_full_00628 | [{"role": "user", "question": "In the equilateral triangle △ABC, point D is a moving point on side AC (excluding endpoints A and C). A ray BE is drawn such that it intersects ray AC at point E and ∠DBE = 30°. Segment DB is then rotated counterclockwise by 60° about point D to obtain segment DP. From point P, draw a per... | （1）AE=PC+BF; （2）sqrt(5)/2 | open | Math | |
rbench_v_full_00629 | [{"role": "user", "question": "As shown in the figure, the region between two straight lines represents a river, and the remaining area is land. A person moves at a speed of 4 m/s on land and 3 m/s in the river. Point A has coordinates (-4, 5) and point B has coordinates (5, -3.5). The riverbanks are represented by the... | P（0，2）Q（3，-2） | open | Math | |
rbench_v_full_00630 | [{"role": "user", "question": "As shown in the figure, given several points on a plane, please calculate how many of these points lie on their convex hull.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 7 | numeric | Math | |
rbench_v_full_00631 | [{"role": "user", "question": "As shown in the diagram, the region between two straight lines represents a river, while the rest is land. A person travels at a speed of 4 m/s on land and 3 m/s in the river. Point A has coordinates (-4, 5) and point B has coordinates (5, -3.5). The riverbanks are defined by the function... | P（0，2）Q（3，-2） | open | Math | |
rbench_v_full_00632 | [{"role": "user", "question": "As shown in the figure, △ABC is an equilateral triangle. In Figure 2, segment AC is rotated 90 degrees clockwise around point A to obtain segment AD. Then segment BD is drawn. The angle bisector of ∠BAC intersects the extension of line segment DB at point E. Connect CE. Directly express t... | BD=sqrt2AE-2CE | open | Math | |
rbench_v_full_00633 | [{"role": "user", "question": "As shown in the figure, there is a convex hull with its vertices labeled A to H in counterclockwise order, and a red line passing through point A. Your task is to find a line L that is parallel to the red line, intersects the given convex hull, and is at the maximum possible distance from... | F | mcq | Math | |
rbench_v_full_00634 | [{"role": "user", "question": "As shown in the diagram, when the figure is folded into a cube, which number is on the face opposite to 5?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 3 | numeric | Math | |
rbench_v_full_00635 | [{"role": "user", "question": "Which of the following shapes can be folded into a cube?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | bd | open | Math | |
rbench_v_full_00636 | [{"role": "user", "question": "As shown in the diagram, each small square in the square grid has a side length of 1, and the vertices of the small squares are grid points. Points A, B, and C are grid points, and point D is the intersection point of line segment AC with a grid line. What is the value of ∠ADB - ∠ABD?", "... | 45° | open | Math | |
rbench_v_full_00637 | [{"role": "user", "question": "As shown in the figure, in a square grid, points A, B, C, D, and E are lattice points; what is the value of ∠ABD + ∠CBE?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 45° | open | Math | |
rbench_v_full_00638 | [{"role": "user", "question": "There are eight small circles each with a radius of 1 centimeter; as shown in the diagram, segments of their circumferences are used to form a petal-shaped figure, with the black dots representing the centers of these circles. What is the area of the resulting petal-shaped figure?", "hint... | 16+\pi | open | Math | |
rbench_v_full_00639 | [{"role": "user", "question": "As shown in the figure, there are two small squares and one large square; the side length of the large square is twice that of each small square. If the area of the shaded triangle is 240, what is the total area of the three squares?", "hint": "", "options": {}, "choices": [], "has_image"... | 360 | numeric | Math | |
rbench_v_full_00640 | [{"role": "user", "question": "Estimate how many of the small quadrilaterals shown in the figure are needed to completely fill the entire circumference of the circle.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 10 | numeric | Math | |
rbench_v_full_00641 | [{"role": "user", "question": "As shown in the figure, AD is the median of triangle ABC, and E is a point on AD such that AD = 3AE. Line segment CE intersects AB at point F. If AF = 1.2 cm, what is the length of AB?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 6cm | open | Math | |
rbench_v_full_00642 | [{"role": "user", "question": "What is the measure of the angle labeled x in the diagram?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 130° | open | Math | |
rbench_v_full_00643 | [{"role": "user", "question": "As shown in the figure, in the isosceles right triangle △ABC with AB = 1 and ∠A = 90°, point E is the midpoint of AC, and point F lies on BC such that line segment EF is perpendicular to BE. Find the area of triangle △CEF.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | \frac{1}{24} | open | Math | |
rbench_v_full_00644 | [{"role": "user", "question": "ABC is an equilateral triangle, with point P located such that PA = 6, PB = 8, and PC = 10; find the sum of the areas of triangles PAB and PAC.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 24+9√3 | open | Math | |
rbench_v_full_00645 | [{"role": "user", "question": "As shown in the figure, point P lies inside triangle ABC. Lines AP, BP, and CP are extended to intersect the opposite sides BC, AC, and AB at points D, E, and F respectively. It is given that AP = 6, BP = 9, PD = 6, PE = 3, and CF = 20. Find the area of triangle ABC.", "hint": "", "option... | 108 | numeric | Math | |
rbench_v_full_00646 | [{"role": "user", "question": "As shown in the figure, in triangle ABC, ∠ABC = 50°, ∠ACB = 30°, and point M lies inside the triangle such that ∠MCB = 20° and ∠MAC = 40°. Find the measure of ∠MBC.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 30° | open | Math | |
rbench_v_full_00647 | [{"role": "user", "question": "As shown in the figure, in triangle ABC, AB = AC and ∠A = 80°, point D lies inside the triangle such that ∠DAB = ∠DBA = 10°; find the measure of angle ∠ACD.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 30° | open | Math | |
rbench_v_full_00648 | [{"role": "user", "question": "In which of the following options is the bold line on the surface not closed when the depicted shape is folded into a rectangular prism?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | C | mcq | Math | |
rbench_v_full_00649 | [{"role": "user", "question": "Which of the following options shows the image above after being reflected as a mirror image?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | A | mcq | Math | |
rbench_v_full_00650 | [{"role": "user", "question": "On the left is the unfolded diagram (net) of the outer surface of a cube; which of the following options can be formed by folding it into a cube?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | B | mcq | Math | |
rbench_v_full_00651 | [{"role": "user", "question": "On the left is the outer surface of a paper box; which of the following can be formed by folding it?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | D | mcq | Math | |
rbench_v_full_00652 | [{"role": "user", "question": "As shown in the figure, triangle ABC is a right triangle; segment GE is the perpendicular bisector of segment FD and is parallel to AB. After folding the triangle along GE, calculate the area of the resulting figure. Express the final answer using the lowercase letters a, b, c, and d as l... | b+d | open | Math | |
rbench_v_full_00653 | [{"role": "user", "question": "A square piece of paper is folded in half twice and then a small hole is cut out as shown in the diagram; what will the resulting pattern look like when the paper is fully unfolded?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | C | mcq | Math | |
rbench_v_full_00654 | [{"role": "user", "question": "After folding a rectangular sheet of paper once and cutting it into the shape shown, which of the following options is NOT a possible shape when the paper is unfolded?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | D | mcq | Math | |
rbench_v_full_00655 | [{"role": "user", "question": "Using the dashed line as the axis of symmetry, identify the three corresponding points on the other half of the symmetric figure; which of the following options is correct?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | A | mcq | Math | |
rbench_v_full_00656 | [{"role": "user", "question": "Among the following options, all except ( ) can be unfolded into the planar figure shown on the left.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | B | mcq | Math | |
rbench_v_full_00657 | [{"role": "user", "question": "Which letter will not be covered by the gray shaded area when the paper is folded along the bold line?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | E | mcq | Math | |
rbench_v_full_00658 | [{"role": "user", "question": "As shown in the figure, if a (transparent) piece of paper is folded along the dashed line, which of the four options will be visible afterward?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | A | mcq | Math | |
rbench_v_full_00659 | [{"role": "user", "question": "Which one of the blocks A, B, C, or D, when combined with the blocks numbered 1 and 2, can form the polyhedron shown in the left diagram?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | D | mcq | Math | |
rbench_v_full_00660 | [{"role": "user", "question": "As shown in the figure, in quadrilateral ABCD, sides AD and BC have lengths of 10 and 20 respectively, angles ∠BAD and ∠BCD are both right angles, and angle ∠ABC is 45°, find the area of quadrilateral ABCD.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 150 | numeric | Math | |
rbench_v_full_00661 | [{"role": "user", "question": "Square ABCD and square CEFG have side lengths of 8 and 5 respectively; calculate the area of triangle ACF shown in the figure.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 38 | numeric | Math | |
rbench_v_full_00662 | [{"role": "user", "question": "In the quadrilateral $ABCD$, it is given that $\\angle BAD = \\angle D = 90^\\circ$, and that $BM = CM = CD$; determine the relationship between $\\angle AMC$ and $\\angle BAM$.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | $\angle A M C=3 \angle B A M$ | open | Math | |
rbench_v_full_00663 | [{"role": "user", "question": "In triangle $\\triangle ABC$, the bisector of angle $\\angle B$ and the bisector of the exterior angle at vertex $C$ intersect at point $D$. Given that $\\angle A = 27^\\circ$, what is the measure of angle $\\angle BDC$?", "hint": "", "options": {}, "choices": [], "has_image": 0}] | 13.5 | numeric | Math | |
rbench_v_full_00664 | [{"role": "user", "question": "As shown in the figure, $AD$ is the median of triangle $\\triangle ABC$, and point $E$ lies on segment $AD$ such that $AE = \\frac{1}{3}AD$. Line segment $CE$ intersects $AB$ at point $F$. If $AF = 1.2cm$, what is the length of $AB$?", "hint": "", "options": {}, "choices": [], "has_image"... | 6cm | open | Math | |
rbench_v_full_00665 | [{"role": "user", "question": "In triangle $ABC$, let $BD$ and $CE$ be the medians to sides $AC$ and $AB$, respectively, such that $BD \\perp CE$, $BD = 4$, and $CE = 6$. What is the area of triangle $ABC$?", "hint": "", "options": {}, "choices": [], "has_image": 0}] | 16 | numeric | Math | |
rbench_v_full_00666 | [{"role": "user", "question": "As shown in the figure, in triangle $ABC$, $EF \\parallel BC$ and the area of triangle $AEF$ is equal to the area of triangle $BCE$; if the area of triangle $ABC$ is 1, then what is the area of triangle $CEF$?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | $\sqrt{5}-2$ | open | Math | |
rbench_v_full_00667 | [{"role": "user", "question": "In the cyclic quadrilateral ABCD, ∠A = 60°, ∠B = 90°, AD = 3, and CD = 2. (1) Find the length of BC; (2) Find the area of quadrilateral ABCD; (3) Compare the sum AB + BC with the sum AD + CD.", "hint": "", "options": {}, "choices": [], "has_image": 0}] | 3√3/2 - 1；5√3/8 + 9/2；< | open | Math | |
rbench_v_full_00668 | [{"role": "user", "question": "Given that ABCD is a cyclic quadrilateral inscribed in a circle with radius R, where AB = 12 and CD = 6, and AB and DC are extended to intersect at point P, with BP = 8 and ∠APD = 60°, find the value of R.", "hint": "", "options": {}, "choices": [], "has_image": 0}] | 2√21 | open | Math | |
rbench_v_full_00669 | [{"role": "user", "question": "In trapezoid ABCD with AB ∥ CD and AB = 3CD, let E be the midpoint of diagonal AC, and let line BE intersect line AD at point F. What is the value of the ratio AF:FD?", "hint": "", "options": {}, "choices": [], "has_image": 0}] | \frac{3}{2} | open | Math | |
rbench_v_full_00670 | [{"role": "user", "question": "In right triangle \\( \\triangle ACB \\), where \\( \\angle ACB = 90^{\\circ} \\), \\( BC = 12 \\), and \\( AC = 8 \\), a rhombus \\( BCDE \\) is constructed outside of triangle \\( ACB \\) with \\( BC \\) as one of its sides and \\( \\angle BCD = 60^{\\circ} \\); the diagonals \\( BD \\)... | 36 | numeric | Math | |
rbench_v_full_00671 | [{"role": "user", "question": "In quadrilateral ABCD, ∠B = ∠C = 90°, AB > CD, and AD = AB + CD. The angle bisector of ∠ADC intersects BC at point E, and AE is drawn. Given that CD = 2 and AB = 4, let points M and N be variable points on segments AE and AB, respectively. Find the minimum value of BM + MN.", "hint": "", ... | \(\frac{8\sqrt{2}}{3}\)。 | open | Math | |
rbench_v_full_00672 | [{"role": "user", "question": "In equilateral triangle △ABC, a ray AP is drawn from point A to the right side of segment AB such that ∠BAP = α (where 60° < α < 90°); point E is the reflection of point B across line AP; segments AE, BE, and CE are drawn, with BE and CE intersecting ray AP at points D and F respectively;... | 60° | open | Math | |
rbench_v_full_00673 | [{"role": "user", "question": "Given a square ABCD, a line AP is drawn outside the square such that the point E is the reflection of point B across line AP; segments BE and DE are connected, and DE intersects line AP at point F. If the angle ∠PAB satisfies 45° < ∠PAB < 90°, AB = 4, and FE = 5, find the length of FD.", ... | √7 | open | Math | |
rbench_v_full_00674 | [{"role": "user", "question": "In triangle \\(ABC\\), \\(\\angle BAC = 80^\\circ\\) and \\(\\angle ABC = 60^\\circ\\); point \\(D\\) lies inside the triangle such that \\(\\angle DAB = 10^\\circ\\) and \\(\\angle DBA = 20^\\circ\\); find the measure of angle \\(\\angle ACD\\) in degrees.", "hint": "", "options": {}, "c... | 30° | open | Math | |
rbench_v_full_00675 | [{"role": "user", "question": "The median AD of triangle ABC intersects its incircle O at points X and Y; given that AC = AB + AD, find the measure of angle ∠XOY.", "hint": "", "options": {}, "choices": [], "has_image": 0}] | 120° | open | Math | |
rbench_v_full_00676 | [{"role": "user", "question": "In trapezoid ABCD, where AD is parallel to BC, with BC = BD = 1, AB = AC, CD < 1, and ∠BAC + ∠BDC = 180°, find the length of CD.", "hint": "", "options": {}, "choices": [], "has_image": 0}] | √2-1 | open | Math | |
rbench_v_full_00677 | [{"role": "user", "question": "In triangle ABC, AB = AC and ∠A = 100°. Let I be the incenter of the triangle, and let D be a point on segment AB such that BD = BI. Find the measure of angle ∠BCD.", "hint": "", "options": {}, "choices": [], "has_image": 0}] | 30° | open | Math | |
rbench_v_full_00678 | [{"role": "user", "question": "There are 11 empty circles in the diagram. You are to fill the numbers from 1 to 13 into these circles (with 3 and 4 already filled in) such that the sum of the two numbers in the upper circles equals the number in the connected lower circle, and the sum of the numbers in the bottom four ... | 2 | numeric | Math | |
rbench_v_full_00679 | [{"role": "user", "question": "Divide the given figure along the grid lines into several squares, aiming to use as few squares as possible; what is the minimum number of squares needed?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 6 | numeric | Math | |
rbench_v_full_00680 | [{"role": "user", "question": "What is the minimum number of squares that the figure can be divided into by cutting along the grid lines?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 13 | numeric | Math | |
rbench_v_full_00681 | [{"role": "user", "question": "In a 15×15 square grid, 30 points are to be connected into 15 line segments, with lengths ranging from 1 to 15 (the side length of each small square is 1). The following conditions must be satisfied: (1) Each point must serve as the endpoint of exactly one line segment; (2) The 15 connect... | 6 | numeric | Math | |
rbench_v_full_00682 | [{"role": "user", "question": "As shown in Figure 28-7, there is a 6×6 square grid with three numbers—2, 5, and 4—written inside it. Figure 28-8 shows two \"tanks\", each consisting of 7 unit squares. The task is to place both tanks into the 6×6 square grid such that: (1) the outer edges of each tank align with the gri... | up | open | Math | |
rbench_v_full_00683 | [{"role": "user", "question": "Draw squares along the grid lines in the diagram, ensuring that no two squares share any common point. Continue drawing until it is no longer possible to add any more squares. What is the minimum number of squares that must be drawn?", "hint": "", "options": {}, "choices": [], "has_image"... | 3 | numeric | Math | |
rbench_v_full_00684 | [{"role": "user", "question": "Draw squares along the grid lines in the diagram, ensuring that no two squares share any common point. Continue drawing until it is no longer possible to add any more squares. What is the minimum number of squares that must be drawn?", "hint": "", "options": {}, "choices": [], "has_image"... | 8 | numeric | Math | |
rbench_v_full_00685 | [{"role": "user", "question": "As shown in the figure, there is a 5×5 square grid, with a total of 10 small squares each containing one circle. Please assign the numbers 1 through 10 to these circles. Then, draw line segments to consecutively connect circle 1 to circle 2, circle 2 to circle 3, and so on up to circle 9 ... | 9 | numeric | Math | |
rbench_v_full_00686 | [{"role": "user", "question": "As shown in the diagram, nine identical right-angled triangle cards are arranged to form a flat geometric figure; among the three angles of each triangle card, what is the degree measure of the smallest angle?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 36^\circ | open | Math | |
rbench_v_full_00687 | [{"role": "user", "question": "As shown in the figure, a hexagon has all six interior angles equal to 120 degrees; find the perimeter of this hexagon.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 45 | numeric | Math | |
rbench_v_full_00688 | [{"role": "user", "question": "In the figure, the outer quadrilateral is a square with side length 10; find the area of the shaded region.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 53 | numeric | Math | |
rbench_v_full_00689 | [{"role": "user", "question": "As shown in the figure, a circular disk with a radius of 2 centimeters starts at position ① and rolls along the line segments AB, BC, and CD sequentially until it reaches position ②. If the lengths of AB, BC, and CD are all 20 centimeters, what is the area, in square centimeters, swept by... | 228.07 | numeric | Math | |
rbench_v_full_00690 | [{"role": "user", "question": "As shown in the figure, a pentagon has one interior angle measuring 60°, while each of the other angles measures 120°. What is the perimeter of this pentagon?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 14 | numeric | Math | |
rbench_v_full_00691 | [{"role": "user", "question": "The rectangle in the diagram is divided into several smaller sections, with the areas of four of these sections already labeled; what is the area of the shaded region?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 25 | numeric | Math | |
rbench_v_full_00692 | [{"role": "user", "question": "As shown in the figure, in quadrilateral ABCD, AB = 30, AD = 48, BC = 14, and ∠ABD + ∠BDC = 90°, ∠ADB + ∠DBC = 90°. What is the area of quadrilateral ABCD?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 936 | numeric | Math | |
rbench_v_full_00693 | [{"role": "user", "question": "As shown in the figure, a hexagon has all its six interior angles equal to 120°. A straight line segment is drawn to divide the hexagon into two parts. What is the ratio of the areas of the upper and lower resulting shapes?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 0.885416666666667 | numeric | Math | |
rbench_v_full_00694 | [{"role": "user", "question": "There are seven identical circles arranged as shown in the diagram. If the area of each circle is 10, what is the area of the shaded region?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 20 | numeric | Math | |
rbench_v_full_00695 | [{"role": "user", "question": "As shown in the figure, the area of triangle DEF is 1, with AD equal to 2 times the length of DF, BE equal to 3 times the length of DE, and CE equal to 2 times the length of EF; what is the area of triangle ABC?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 18 | numeric | Math | |
rbench_v_full_00696 | [{"role": "user", "question": "As shown in the figure, a puppy is tied to point B, the midpoint of one side of a square building with a side length of 4 meters; the surrounding area is open space. The leash is 8 meters long. What is the total area, in square meters, within which the puppy can move? (The puppy cannot pa... | 156 | numeric | Math | |
rbench_v_full_00697 | [{"role": "user", "question": "In the figure, the distance between any two adjacent grid points is 1 centimeter; what is the area, in square centimeters, of each of the shaded shapes?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 3 | numeric | Math | |
rbench_v_full_00698 | [{"role": "user", "question": "As shown in the figure, the distance between any two adjacent grid points is 1 centimeter; what is the area, in square centimeters, of the shaded region?", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 6.5 | numeric | Math | |
rbench_v_full_00699 | [{"role": "user", "question": "Quadrilateral ABCD is a rectangle and quadrilateral AEFG is a square with a side length of 10; given that the area of the shaded region is 18, find the area of rectangle ABCD.", "hint": "", "options": {}, "choices": [], "has_image": 1}] | 64 | numeric | Math |
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