Problem Analysis #26

DeepSeek V4 Pro · Run 1

Correct

2.96s

322 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 revised parabola-area problem, the boundary values for the parameter $k$ are

\frac19 \quad\text{and}\quad \frac13.

To avoid a range as the final answer, compute the integer

\frac{1}{1/9}+\frac{1}{1/3}.

Ground Truth

Recorded model response / solution

Reasoning Process

Let’s compute step by step.

We have:

\frac{1}{1/9} + \frac{1}{1/3}

First term:

\frac{1}{1/9} = 9

(because dividing by a fraction means multiplying by its reciprocal: $1 / (1/9) = 9$ ).

Second term:

\frac{1}{1/3} = 3

(same logic: $1 / (1/3) = 3$ ).

Now sum them:

9 + 3 = 12

The final integer is:

\boxed{12}

Final Model Output

Comparative Analysis (P26) (Average across runs)

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

Avg Time Taken

GPT-5.5

3.7

DeepSeek V4 Pro

3.2

K-EXAONE-236B-A23B

3.0

Gemini 3.5 Flash

2.9

Claude Opus 4.8

1.9

Solar Pro 3

0.8

KT Mi:dm 2.0 Base Instruct

0.6

Avg Token Usage

KT Mi:dm 2.0 Base Instruct

869.7

K-EXAONE-236B-A23B

555.0

Gemini 3.5 Flash

480.0

DeepSeek V4 Pro

346.7

Solar Pro 3

285.0

Claude Opus 4.8

273.0

GPT-5.5

242.7