Mathematics

MATH-Vision

MATH-Vision (MATH-V): 3,040 competition mathematics problems with visual context, spanning 16 mathematical subjects and 5 difficulty levels. A model passes a problem iff its final answer matches the gold answer.

3,037items

13subjects

100%observed

MITlicense

mathematicsdomain

imagemodality

textmodality

Original source Paper Build script ← All benchmarks

Response matrix

Every model, scored item by item.

Each row is an AI model and each column an item, ordered so the strongest models and easiest items gather toward one corner. 13 subjects × 3,037 items, 100% of cells evaluated.

MATH-Vision response matrix: AI models (rows) against items (columns) — Correct (1)Incorrect (0)Unobserved
Scale: 1 = correct · 0 = incorrect

Sample items

What the questions look like — and how subjects answer.

A spread of items across the difficulty range, each shown with a few subjects' actual answers.

Item 10% solve rateanswer: 63

A large cube consists of 125 small black and white cubes, such that any two adjacent faces of the small cubes have different colors, the corner cubes being black. How many small black cubes are used? <image1>

How subjects answered

InternLM-XComposer2-VL incorrect
ShareGPT4V-7B incorrect
125
ShareGPT4V-13B incorrect
62
ChatGPT-3.5 incorrect
Let's analyze the given information:

The top face has 8 cubes in a 4x2 arrangement, with the pattern starting with a light-colored square.

The front face has 12 cubes in a 4x3 arrangement, with the pattern starting with a light-colored square.

The right face has 6 cubes in a 3x2 arrangement, with the pattern starting with a light-colored square.

Since the corner cubes are black, we know that the corner cubes of the large cube are black. Therefore, the top right corner cube, the front right corner cube, and the top front corner cube are black.

From the information given, we can deduce that the top face has 4 black cubes, the front face has 6 black cubes, and the right face has 3 …
Qwen-VL-Plus incorrect
40
Qwen-VL-Max incorrect
There are 8 corner cubes, so there are $125-8=117$ non-corner cubes. Each non-corner cube has two possible orientations, and half of these orientations have black on the top face (which is what we're trying to maximize). So there are $\frac{117}{2}$ ways to orient the non-corner cubes, and $\boxed{69}$ of them will have black on the top face.

Item 20% solve rate

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>

Options:

A.
$10\pi+20$
B.
$10\pi+30$
C.
$10\pi+40$
D.
$20\pi+20$
E.
$20\pi+40$

How subjects answered

InternLM-XComposer2-VL incorrect
The aardvark runs along the path shown, starting at $A$ and ending at $K$ . The aardvark runs along the path shown, starting at $A$ and ending at $K$ . The aardvark runs along the path shown, starting at $A$ and ending at $K$ .The aardvark runs along the path shown, starting at $A$ and ending at $K$ .The aardvark runs along the path shown, starting at $A$ and ending at $K$ .The aardvark runs along the path shown, starting at $A$ and ending at $K$ .The aardvark runs along the path shown, starting at $A$ and ending at $K$ .The aardvark runs along the path shown, starting at $A$ and ending at $K$ .The aardvark runs along the path shown, starting at $A$ and ending at $K$ .The aardvark runs along the …
ShareGPT4V-7B incorrect
A
ShareGPT4V-13B incorrect
D
ChatGPT-3.5 incorrect
To find the distance the aardvark runs from point A to point K, we need to calculate the length of the arc on the larger circle from A to K.

The formula to find the length of an arc on a circle is given by: [ \text{Arc Length} = \frac{n}{360} \times 2\pi r ] where:

( n ) is the central angle in degrees,

( r ) is the radius of the circle.

In this case, the central angle ( n ) is 90 degrees because the arc from A to K is a quarter of the circumference of the larger circle.

For the larger circle with radius 20 meters: [ \text{Arc Length} = \frac{90}{360} \times 2\pi \times 20 = \frac{1}{4} \times 40\pi = 10\pi ]

Therefore, the aardvark runs ( 10\pi ) meters from point A to …
Qwen-VL-Plus incorrect
Circumference of larger circle is 60 pi; circumference of smaller circle is 20 pi. Distance traveled by A to K is sum of these two quantities.

Therefore, the answer is (C).
Qwen-VL-Max incorrect
The aardvark runs $10\pi$ meters along the circle with radius $10$ meters and $20$ meters from $A$ to $K$ . Therefore, the aardvark runs $\boxed{10\pi + 20}$ meters in total.

Item 30% solve rateanswer: 12

Max and Moritz have drawn out a $5 \times 5$ grid on the playground, together with three obstacles. They want to walk from $P$ to $Q$ using the shortest route, avoiding the obstacles and always crossing a common edge to go from the centre of one square to the centre of the next. How many such shortest paths are there from $P$ to $Q$ ? <image1>

How subjects answered

InternLM-XComposer2-VL incorrect
The answer is $\boxed{4}$ .
ShareGPT4V-7B incorrect
1
ShareGPT4V-13B incorrect
1
ChatGPT-3.5 incorrect
To find the number of shortest paths from $P$ to $Q$ while avoiding the obstacles, we can use the concept of combinations.

Since the obstacles are located in the second row, fourth row, and fourth column, we need to consider the paths that go around these obstacles.

Let's denote the obstacles as $O_1$ , $O_2$ , and $O_3$ respectively.

To go from $P$ to $Q$ while avoiding the obstacles, we need to go through the following steps:

Go from $P$ to the square above $O_1$ .

Go around $O_1$ by going either left or right.

Go from the square below $O_1$ to the square above $O_2$ .

Go around $O_2$ by going either left or right.

Go from the square below $O_2$ to $Q$ .

For steps 2 and …
Qwen-VL-Plus incorrect
24
Qwen-VL-Max incorrect
There are two ways to get from $P$ to $Q$ without passing through any obstacles. There are also two ways to get from $P$ to $Q$ that pass through one obstacle, two ways that pass through two obstacles, and one way that passes through all three obstacles. Thus, there are $\boxed{7}$ shortest paths from $P$ to $Q$ .

Item 40% solve rateanswer: 32

Equilateral triangle $T$ is inscribed in circle $A$ , which has radius $10$ . Circle $B$ with radius $3$ is internally tangent to circle $A$ at one vertex of $T$ . Circles $C$ and $D$ , both with radius $2$ , are internally tangent to circle $A$ at the other two vertices of $T$ . Circles $B$ , $C$ , and $D$ are all externally tangent to circle $E$ , which has radius $\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ . <image1>

How subjects answered

InternLM-XComposer2-VL incorrect
[asy] size(200); defaultpen(linewidth(0.7)+fontsize(10)); dot("A",dir(90),dir(90)); dot("B",dir(90-60),dir(90-60)); dot("C",dir(90-260),dir(90-260)); dot("D",dir(90-360),dir(90-360));

draw(Circle(dir(90),10),linewidth(0.7)); draw(Circle(dir(90-60),3),linewidth(0.7)); draw(Circle(dir(90-260),2),linewidth(0.7)); draw(Circle(dir(90-360),2),linewidth(0.7)); draw(Circle(dir(90-460),sqrt(10^2-2^2)),linewidth(0.7)); draw(Circle(dir(90-560),sqrt(10^2-3^2)),linewidth(0.7)); draw(Circle(dir(90-660),sqrt(10^2-4^2)),linewidth(0.7)); draw(Circle(dir(90-760),sqrt(3^2-2^2)),linewidth(0.7)); draw(Circle(dir(90-860),sqrt(3^2-4^2)),linewidth(0.7)); draw(Circle(dir(90-960),sqrt(2^2-2^2)),linewidth …
ShareGPT4V-7B incorrect
12
ShareGPT4V-13B incorrect
11
ChatGPT-3.5 incorrect
Let $O$ be the center of circle $A$ , $P$ be the center of circle $B$ , $Q$ be the center of circle $C$ , and $R$ be the center of circle $D$ . Let $X$ be the point of tangency between circles $A$ and $B$ , $Y$ be the point of tangency between circles $A$ and $C$ , and $Z$ be the point of tangency between circles $A$ and $D$ .

Since triangle $T$ is equilateral, the center $O$ of circle $A$ is also the centroid of triangle $T$ . This means that $O$ is the intersection point of the medians of triangle $T$ , which is also the intersection point of the altitudes and the circumcenter of triangle $T$ . Therefore, $O$ is the circumcenter of triangle $T$ .

Let $r$ be the inradius of triangle $T$ . The area …
Qwen-VL-Plus incorrect
47
Qwen-VL-Max incorrect
Let $A(0,0)$ be at the origin. Then, the equation of the large circle is $x^2 + y^2 = 100$ . Solving for the intersection of this circle with $y = 3$ , we find that the points $B(-8,3)$ and $B'(8,3)$ are the two intersections of the large circle with the smaller circle centered at the origin. Similarly, solving for the intersections of the large circle with $y = -2$ , we find that the points $C(-4,-2)$ and $C'(-4,2)$ are the two intersections of the large circle with the circle centered at $B$ and $B'$ . The points $D$ and $D'$ , where the large circle intersects the circle centered at $C$ and $C'$ , respectively, are thus given by the intersections of the line $y = -\frac{1}{3}x - 2$ (the …

Item 56% solve rateanswer: 10

The regular pentagon $P Q R S T$ in the diagram has been reflected in the line $P Q$ so that vertex $T$ is reflected to point $U$ , as shown. Then the new pentagon is reflected in $P U$ , so that vertex $Q$ is reflected to point $V$ , as shown. This process is repeated, on each occasion reflecting in the line determined by the new edge through $P$ . What is the least number of such reflections that are needed to return pentagon $P Q R S T$ to its original position? <image1>

How subjects answered

InternLM-XComposer2-VL incorrect
The answer is 5.
ShareGPT4V-7B incorrect
3
ShareGPT4V-13B incorrect
3
ChatGPT-3.5 incorrect
To solve this problem, let's first analyze the reflections that have already been done.

The first reflection was in the line $PQ$ , reflecting $T$ to $U$ . This means that $T$ and $U$ are corresponding vertices after the first reflection.

The second reflection was in the line $PU$ , reflecting $Q$ to $V$ . This means that $Q$ and $V$ are corresponding vertices after the second reflection.

Since we want to return the pentagon $PQRST$ to its original position, we need to find the next reflection that will bring $R$ back to its original position.

The next reflection will be in the line determined by the new edge through $P$ , which is $PV$ . Therefore, we need to find the vertex that …
Qwen-VL-Plus incorrect
5
Qwen-VL-Max incorrect
It takes two reflections to return the pentagon to its original position. The first reflection is in $P Q$ , and the second is in $P U$ . These two lines intersect at $P$ , so the two reflections "flip" the pentagon back to its starting position. \boxed{2}.

Item 66% solve rateanswer: 18

How many distinct triangles can be drawn using three of the dots below as vertices?

How subjects answered

InternLM-XComposer2-VL incorrect
There are $\boxed{6}$ distinct triangles that can be drawn using three of the dots as vertices.
ShareGPT4V-7B incorrect
0
ShareGPT4V-13B incorrect
1
ChatGPT-3.5 incorrect
To find the number of distinct triangles that can be drawn using three of the dots as vertices, we need to consider all possible combinations of choosing 3 dots out of the 6.

There are a total of 6 dots, so we can calculate the number of ways to choose 3 dots out of 6 using the combination formula:

C(n, k) = n! / (k!(n-k)!)

Plugging in the values, we get:

C(6, 3) = 6! / (3!(6-3)!) C(6, 3) = 6! / (3!3!) C(6, 3) = (6 * 5 * 4) / (3 * 2 * 1) C(6, 3) = 20

Therefore, there are 20 distinct triangles that can be drawn using three of the dots as vertices.

\boxed{20}
Qwen-VL-Plus incorrect
5
Qwen-VL-Max incorrect
There are $\binom{6}{3} = \boxed{20}$ ways to choose 3 dots from the 6.

Item 711% solve rate

Tess runs counterclockwise around rectangular block JKLM. She lives at corner J. Which graph could represent her straight-line distance from home?

Options:

A.
<image2>
B.
<image3>
C.
<image4>
D.
<image5>
E.
<image6>

How subjects answered

LLaVA-v1.5-13B correct
D
Gemini-Pro correct
The correct answer is (C).

The graph (C) shows that Tess's distance from home increases as she runs along the block. This is because the graph is a straight line with a positive slope. The other graphs show that Tess's distance from home either decreases or stays the same as she runs along the block.
InternLM-XComposer2-VL incorrect
\boxed{(A)}
ChatGPT-3.5 incorrect
The straight-line distance from home will be the diagonal of the rectangle JKLM. This means that the distance will increase at a constant rate as Tess runs around the block.

Therefore, the distance-time graph that could represent her straight-line distance from home is Image 2, which shows a straight line sloping upwards to the right at a constant speed.

\boxed{2}
Qwen-VL-Plus incorrect
A
Qwen-VL-Max incorrect
The graph that represents Tess's straight-line distance from home is:

(E) <image6>

As Tess runs counterclockwise around the rectangular block JKLM, her straight-line distance from home (corner J) will increase as she moves away from J, decrease as she moves towards J, and remain constant when she is at corners K, L, or M. The graph in option (E) accurately depicts this pattern.

Item 811% solve rate

The diagram shows four circles each of which touches the largest square and two adjacent circles. A second square has its vertices at the midpoints of the sides of the largest square and the central square has its vertices at the centres of the circles. <image1> What is the ratio of the total shaded area to the area of the outer square?

Options:

A.
$\pi: 12$
B.
$1: 4$
C.
$(\pi+2): 16$
D.
$1: 3$
E.
$\pi: 4$

How subjects answered

SPHINX-MoE correct
(B)
ShareGPT4V-7B incorrect
E
ShareGPT4V-13B incorrect
C
ChatGPT-3.5 incorrect
To find the ratio of the total shaded area to the area of the outer square, we first need to calculate the areas of the shaded regions and the outer square.

Calculate the area of the outer square: Let the side length of the outer square be 2a (since the circles are tangent to the midpoint of each side, the side length of the outer square is twice the radius of the circles). The area of the outer square = (2a)^2 = 4a^2.

Calculate the area of the shaded regions: a. Calculate the area of the triangles in the corners: Each triangle is a right-angled triangle with legs of length a (half the side length of the outer square). The area of one triangle = (1/2) * a * a = a^2 / 2. Since there …
Qwen-VL-Plus incorrect
$\pi$ : $12$
Qwen-VL-Max incorrect
The shaded area consists of the four quarter-circles with radius $r$ and the central square with side length $s$ . The unshaded area consists of the four quarter-circles with radius $r-s$ .

The total shaded area is therefore [A = \frac{4}{4}\pi r^2 + s^2 = \pi r^2 + s^2,] and the total unshaded area is [B = \frac{4}{4}\pi (r-s)^2 = \pi r^2 - 2\pi rs + \pi s^2.]

The total area of the outer square is $4r^2$ , so the ratio of the shaded area to the area of the outer square is [\left(\pi r^2 + s^2\right) : 4r^2 = \boxed{\pi: 4}.]

Item 917% solve rate

A large square is divided into smaller squares, as shown. A shaded circle is inscribed inside each of the smaller squares. What proportion of the area of the large square is shaded? <image1>

Options:

A.
$\frac{8 \pi}{9}$
B.
$\frac{13 \pi}{16}$
C.
$\frac{3}{\pi}$
D.
$\frac{3}{4}$
E.
$\frac{\pi}{4}$

How subjects answered

LLaVA-v1.5-13B correct
E
Qwen-VL-Max correct
Let the side length of the large square be $s$ . The radius of the largest inscribed circle is $\frac{s}{2}$ , so its area is $\pi \left(\frac{s}{2}\right)^2 = \frac{\pi s^2}{4}$ . The side length of each smaller square is $\frac{s}{2}$ , so the radius of each inscribed circle is $\frac{s}{4}$ . The area of each inscribed circle is $\pi \left(\frac{s}{4}\right)^2 = \frac{\pi s^2}{16}$ . There are 9 smaller squares, so the total area of all the inscribed circles is $9 \cdot \frac{\pi s^2}{16} = \frac{9 \pi s^2}{16}$ . The area of the large square is $s^2$ , so the proportion of the area that is shaded is $\frac{\frac{9 \pi s^2}{16}}{s^2} = \boxed{\frac{9 \pi}{16}}$ .
SPHINX-MoE correct
(E)
GPT-4 incorrect
To solve this problem, we need to calculate the total shaded area (the area covered by the circles) and divide it by the area of the large square. The description provides enough information to determine the sizes of the circles and their arrangement within the large square.

Step 1: Calculate the Area of the Large Square

The large square is divided into a 4x4 grid of smaller squares, so if we consider the side length of each smaller square to be (s), the side length of the large square is (4s). Therefore, the area of the large square ((A_{\text{large square}})) is: [A_{\text{large square}} = (4s)^2 = 16s^2]

Step 2: Calculate the Total Area Covered by the Circles

…
ChatGPT-3.5 incorrect
To find the proportion of the area of the large square that is shaded, we need to calculate the total area of the shaded circles and then divide it by the total area of the large square.

Let's start by calculating the total area of the shaded circles:

The large circle in the top right corner has a diameter equal to 2 smaller squares, so its radius is equal to the side length of one smaller square. The area of this circle is πr^2 = π(1)^2 = π.

The medium-sized circle below the large circle has a diameter equal to 1 smaller square, so its radius is 0.5 times the side length of one smaller square. The area of this circle is πr^2 = π(0.5)^2 = 0.25π.

The three small circles to the …
Qwen-VL-Plus incorrect
$\frac{20 \pi}{25} = \frac{4 \cdot 5 \pi}{5^2}= \frac{4 \pi}{5}=\frac{16 \pi}{20} = \frac{4 \pi}{5}$

Item 1022% solve rateanswer: 20

A $3 \times 3 \times 3$ cube is made up of small $1 \times 1 \times 1$ cubes. Then the middle cubes from front to back, from top to bottom and from right to left are removed (see diagram). How many $1 \times 1 \times 1$ - cubes remain? <image1>

How subjects answered

InternLM-XComposer2-VL correct
There are $3 \times 3 \times 3 = 27$ small cubes in the $3 \times 3 \times 3$ cube. After removing the middle cubes from front to back, from top to bottom, and from right to left, there are $3 \times 3 \times 3 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 \times 1 \times 1 - 1 …
Qwen-VL-Plus correct
20
GPT-4V correct
Let's start by calculating the total number of $1 \times 1 \times 1$ cubes in the $3 \times 3 \times 3$ cube. Since the cube is $3$ small cubes long on each side, the total is $3 \cdot 3 \cdot 3 = 27$ .

Now, let's figure out how many cubes have been removed. Three middle cubes are removed: one from the front to the back, one from the top to the bottom, and one from right to left. However, we must keep in mind that the cube in the very center of the large cube gets counted three times since it is the middle cube in all three directions. Therefore, we are removing $3 - 1 = 2$ unique cubes in addition to the center cube.

So we subtract three (rather than four) from the total to account for …
GPT-4 incorrect
Given the description, we can calculate the number of $1 \times 1 \times 1$ cubes that remain after removing the center cube and the six cubes adjacent to it in the $3 \times 3 \times 3$ cube structure.

Total number of cubes in a solid $3 \times 3 \times 3$ cube: Since it's a $3 \times 3 \times 3$ cube, there are $3 \times 3 \times 3 = 27$ smaller cubes in total if the structure were solid.

Number of cubes removed: The center cube is removed, along with the six cubes adjacent to it (one on each face of the center cube). So, $1 + 6 = 7$ cubes are removed.

Number of cubes remaining: To find the number of cubes remaining, subtract the number of cubes removed from the …
ChatGPT-3.5 incorrect
To find the number of remaining $1 \times 1 \times 1$ cubes, we can calculate the total number of cubes in the original $3 \times 3 \times 3$ cube and subtract the number of cubes that were removed.

Total number of cubes in the original $3 \times 3 \times 3$ cube = $3 \times 3 \times 3 = 27$ cubes

Number of cubes removed:

The center cube is removed.

6 cubes adjacent to the center cube on each face are removed, which is a total of $6 \times 6 = 36$ cubes.

Total number of cubes removed = 1 (center cube) + 36 (adjacent cubes) = 37 cubes

Number of remaining cubes = Total number of cubes - Number of cubes removed Number of remaining cubes = 27 - 37 = -10

Since we cannot have a negative …
Qwen-VL-Max incorrect
There are $3-2=1$ small cube in the middle layer, so there are $3^3-1=26$ small cubes remaining. The answer is \boxed{26}.

Item 1128% solve rate

Triangles $ABC$ and $ABD$ are isosceles with $AB =AC = BD$ , and $BD$ intersects $AC$ at $E$ . If $BD$ is perpendicular to $AC$ , then $\angle C + \angle D$ is <image1>

Options:

A.
$115^\circ$
B.
$120^\circ$
C.
$130^\circ$
D.
$135^\circ$
E.
$\text{not uniquely determined}$

How subjects answered

InternLM-XComposer2-VL correct
The answer is (D).
SPHINX-v2 correct
D
SPHINX-MoE correct
(D)
ChatGPT-3.5 incorrect
Given that triangles $ABC$ and $ABD$ are isosceles with $AB = AC = BD$ , and $BD$ intersects $AC$ at $E$ , and $BD$ is perpendicular to $AC$ , we can see that $\angle A = \angle B = 90^\circ$ .

Since $AB = AC = BD$ , we can conclude that triangle $ABD$ is an equilateral triangle. Therefore, $\angle D = 60^\circ$ .

Since $\angle A = 90^\circ$ and $\angle D = 60^\circ$ , we can find $\angle C$ by using the fact that the sum of angles in a triangle is $180^\circ$ .

Therefore, $\angle C = 180^\circ - \angle A - \angle D = 180^\circ - 90^\circ - 60^\circ = 30^\circ$ .

Finally, $\angle C + \angle D = 30^\circ + 60^\circ = 90^\circ$ .

Therefore, $\boxed{90^\circ}$ .
Qwen-VL-Plus incorrect
130
Qwen-VL-Max incorrect
Since $\triangle ABC$ and $\triangle ABD$ are isosceles, we have $\angle BAC = \angle BCA$ and $\angle BAD = \angle ADB$ . Since $BD$ is perpendicular to $AC$ , we have $\angle AEB = 90^\circ$ . Therefore, $\angle AEB = \angle AED = 45^\circ$ . Since $\angle AEB = \angle AED = 45^\circ$ , we have $\angle BED = 90^\circ$ . Therefore, $\angle BED = \angle BDE = 45^\circ$ . Since $\angle BDE = \angle ADB = 45^\circ$ , we have $\angle ADB = 45^\circ$ . Therefore, $\angle ADB = \angle ABD = 45^\circ$ . Since $\angle ABD = \angle ADB = 45^\circ$ , we have $\angle ABD = \angle ADB = 45^\circ$ . Since $\angle ABD = \angle ADB = 45^\circ$ , we have $\angle ABD = \angle ADB = 45^\circ$ . Since $\angle ABD = \angle …

Item 1233% solve rate

In the trapezium $P Q R S$ the sides $P Q$ and $S R$ are parallel. Also $\angle \mathrm{RSP}=120^{\circ}$ and $\overline{R S}=\overline{S P}=\frac{1}{3} \overline{P Q}$ . What is the size of angle $\angle \mathrm{PQR}$ ? <image1>

Options:

A.
$15^{\circ}$
B.
$22.5^{\circ}$
C.
$25^{\circ}$
D.
$30^{\circ}$
E.
$45^{\circ}$

How subjects answered

InternLM-XComposer2-VL correct
The answer is (D).
SPHINX-v2 correct
D
GPT-4V correct
We are given a trapezium (PQRS) with (PQ \parallel SR). We know that (\angle RSP = 120^{\circ}) and (RS = SP = \frac{1}{3}PQ).

Since (RS) and (SP) are equal, triangle (RSP) is an isosceles triangle. Therefore, the angles at (R) and (S) (other than the (120^{\circ}) angle) must be equal.

Let's call the angle at (R) and (S) (inside the triangle (RSP)) (x). Therefore, we have:

[x + x + 120^{\circ} = 180^{\circ}] [2x = 180^{\circ} - 120^{\circ}] [2x = 60^{\circ}] [x = 30^{\circ}]

So both (\angle R) and (\angle S) in triangle (RSP) are (30^{\circ}).

The angle (x = 30^{\circ}) at (R) in (\triangle RSP) corresponds to the angle at (R) in the …
ChatGPT-3.5 incorrect
To solve this problem, we can use the properties of trapezoids and the given information.

Since $\overline{RS} = \overline{SP} = \frac{1}{3} \overline{PQ}$ , we can denote the length of $\overline{PQ}$ as $3x$ . Therefore, $\overline{RS} = \overline{SP} = x$ .

Now, since $\angle RSP = 120^\circ$ , we can find $\angle PSR$ by subtracting 120 from 180 (since the sum of angles in a triangle is 180 degrees). Therefore, $\angle PSR = 180 - 120 = 60^\circ$ .

Since opposite angles in a trapezoid are equal, we have $\angle PSR = \angle QRP$ . Therefore, $\angle QRP = 60^\circ$ .

Finally, to find $\angle PQR$ , we can use the fact that the sum of angles in a quadrilateral is 360 degrees. Therefore, …
Qwen-VL-Plus incorrect
67.5
Qwen-VL-Max incorrect
Let $x=\angle S P Q$ . Since $\angle R S P=120^{\circ}$ , we have $\angle R P Q=60^{\circ}$ . Since $P Q \parallel S R$ , we have $\angle S R Q=180^{\circ}-x$ . Finally, since $S R=S P$ and $Q$ lies on the perpendicular bisector of $S R$ , we have $\angle S R Q=\angle S P Q=x$ . Thus $2 x=180^{\circ}-x$ , so $x=60^{\circ}$ . Hence $\angle P Q R=180^{\circ}-2 x=180^{\circ}-120^{\circ}=\boxed{60^{\circ}}$ .

Subjects

The models, agents, and reward models evaluated.

13 subjects, ranked by mean response (accuracy) across this benchmark's items.

1GPT-4V0.2337
2Gemini-Pro0.16
3InternLM-XComposer2-VL0.1446
4SPHINX-MoE0.1418
5Qwen-VL-Max0.1411
6ShareGPT4V-13B0.1187
7LLaVA-v1.5-13B0.1112
8Qwen-VL-Plus0.1072
9GPT-40.1061
10ShareGPT4V-7B0.1053
11ChatGPT-3.50.0974
12SPHINX-v20.097
13LLaVA-v1.5-7B0.0852

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