Problem Analysis #43

EXAONE-4.0.1-32B (high) · Run 1

25.00s
0 toks
Problem Statement

Let {an}\{a_n\} be an arithmetic sequence and {bn}\{b_n\} a geometric sequence whose first terms and common difference/ratio are equal. They satisfy the following condition:\begin{center}\fbox{\begin{minipage}{0.9\textwidth}For some natural number kk,

bk+i=1ai−1(i=1,2,3).b_{k+i} = \frac{1}{a_i} - 1 \quad (i = 1, 2, 3).

\end{minipage}}\end{center}Suppose that the inequality

0<∑n=1∞(bn−1anan+1)<300 < \sum_{n=1}^{\infty} \left(b_n - \frac{1}{a_n a_{n+1}}\right) < 30

holds. Then

a2×∑n=1∞b2n=qp,a_2 \times \sum_{n=1}^{\infty} b_{2n} = \dfrac{q}{p},

where a1eq0a_1 eq 0 and pp and qq are coprime natural numbers. Compute p+qp + q. [4 points]\

Ground Truth
97
Execution Trace
Reasoning Process
Final Model Output
No final answer recorded

Comparative Analysis (P43) (Average across runs)

Avg Time Taken

Grok-4.1-fast
2632.5
K-EXAONE-236B-A23B
2436.6
K-EXAONE-236B-A23B
2165.1
Gemini-3-Pro-Preview
417.3
Solar-Pro-2 (31B)(high)
277.7
Solar-Open-100B
270.6
Kanana-2-30B-Thinking
216.5
Kanana-2-30B-Thinking-2601
197.5
Deepseek-V3.2
191.1
GPT-5.1 (high)
191.1
Claude-Opus-4.5
156.4
Llama-VARCO-8B-Instruct
111.3
A.X-4.0 (72B)
106.4
GPT-5.2 (high)
34.0
HCX-007(high)
33.5
EXAONE-4.0.1-32B (high)
25.0

Avg Token Usage

Grok-4.1-fast
391,597
K-EXAONE-236B-A23B
259,249
Claude-Opus-4.5
93,759
Gemini-3-Pro-Preview
76,652
Solar-Open-100B
41,942
K-EXAONE-236B-A23B
36,846
Kanana-2-30B-Thinking-2601
36,468
Kanana-2-30B-Thinking
29,616
Solar-Pro-2 (31B)(high)
18,153
Deepseek-V3.2
14,077
GPT-5.1 (high)
13,809
Llama-VARCO-8B-Instruct
9,248
A.X-4.0 (72B)
6,554
GPT-5.2 (high)
5,731
HCX-007(high)
4,421
EXAONE-4.0.1-32B (high)
0