Problem Analysis #23

Gemini 3.5 Flash · Run 1

Correct

3.91s

640 toks

API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.

Problem Statement

Return a single integer only. The problem has been revised so that no final answer is an irrational number, a parameterized expression, a range, a proof, a drawing, a graph, a locus equation, or a region description.

In the cubic tangent problem, the special value satisfying the area-ratio condition is

k=\frac{5\sqrt3}{12}.

Instead of giving $k$ , compute the integer

\frac{(12k)^2}{3}.

Ground Truth

Recorded model response / solution

Reasoning Process

To find the value of the expression, we start with the given value of $k$ :

k = \frac{5\sqrt{3}}{12}

First, we multiply $k$ by 12:

12k = 12 \left(\frac{5\sqrt{3}}{12}\right) = 5\sqrt{3}

Next, we square this result:

(12k)^2 = (5\sqrt{3})^2 = 25 \times 3 = 75

Finally, we divide by 3:

\frac{(12k)^2}{3} = \frac{75}{3} = 25

$\boxed{25}$

Final Model Output

Comparative Analysis (P23) (Average across runs)

Averages use reported measurements only. Missing usage is not treated as zero.

Avg Time Taken

K-EXAONE-236B-A23B

24.6

DeepSeek V4 Pro

5.0

GPT-5.5

4.1

Gemini 3.5 Flash

4.1

Claude Opus 4.8

1.7

Solar Pro 3

1.3

KT Mi:dm 2.0 Base Instruct

0.7

Avg Token Usage