Problem Analysis #23

K-EXAONE-236B-A23B · Run 1

Correct

65.19s

865 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

We are given the value of $k = $$\frac{5\sqrt{3}}{12}$$$ , and asked to compute the integer value of:

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

Step 1: Compute $12k$

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

Step 2: Square $12k$

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

Step 3: Divide by 3

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

This result is an integer, as required.

\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

K-EXAONE-236B-A23B

828.3

KT Mi:dm 2.0 Base Instruct

828.0

Gemini 3.5 Flash

640.0

DeepSeek V4 Pro

395.0

Solar Pro 3

366.3

Claude Opus 4.8

285.0