Problem Analysis #13

Gemini 3.5 Flash · Run 1

Correct
4.92s
885 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.

For the relevant optimization problem, the maximum value is 19/619/6. If the maximum is p/qp/q in lowest terms, find p+qp+q.

Ground Truth
25
Recorded model response / solution
Reasoning Process

To find the value of p+qp+q where the maximum value of the optimization problem is 196\frac{19}{6} in lowest terms:

  1. The given maximum value is pq=196\frac{p}{q} = \frac{19}{6}.
  2. Since 19 is a prime number and does not divide 6, the fraction 196\frac{19}{6} is already in its lowest terms.
  3. Therefore, p=19p = 19 and q=6q = 6.
  4. Calculating p+qp+q: p+q=19+6=25p+q = 19 + 6 = 25

\boxed{25}

Final Model Output
25

Comparative Analysis (P13) (Average across runs)

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

Avg Time Taken

K-EXAONE-236B-A23B
24.2
Gemini 3.5 Flash
5.3
DeepSeek V4 Pro
4.7
GPT-5.5
4.1
Solar Pro 3
2.4
Claude Opus 4.8
1.7
KT Mi:dm 2.0 Base Instruct
0.5

Avg Token Usage

Gemini 3.5 Flash
956.3
KT Mi:dm 2.0 Base Instruct
777.0
K-EXAONE-236B-A23B
639.3
Solar Pro 3
464.0
DeepSeek V4 Pro
367.3
GPT-5.5
254.3
Claude Opus 4.8
229.7
    Tokyo · Problem 13 · Gemini 3.5 Flash | EntropyMath