Problem Analysis #5

Kimi K3 · Run 1

Correct

14.65s

733 toks

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

Problem Statement

This is a Korean CSAT mathematics multiple-choice problem. Solve it and put only the correct choice symbol, one of ①, ②, ③, ④, ⑤, inside \boxed{}.

Problem 6 Letaandbbe real numbers greater than 1 such that loga b= 3,log 3 b a = 1 2 . Determine the value of log 9(ab). [3 points] ① 3 8 ② 1 2 ③ 5 8 ④ 3 4 ⑤ 7 8 2

Ground Truth

②

Recorded model response / solution

Reasoning Process

Let $x=\log_3 a$ and $y=\log_3 b$ .

From $\log_a b=3$ , we get $\dfrac{y}{x}=3$ , so $y=3x$ .

From $\log_3 \dfrac{b}{a}=\dfrac12$ , we get $y-x=\dfrac12$ .

Substituting $y=3x$ : $3x-x=2x=\dfrac12$ , so $x=\dfrac14$ , $y=\dfrac34$ .

Then

\log_9(ab)=\frac{\log_3(ab)}{\log_3 9}=\frac{x+y}{2}=\frac{\frac14+\frac34}{2}=\frac12.

\boxed{②}

Final Model Output

②

Comparative Analysis (P5) (Average across runs)

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

Avg Time Taken

Motif 3

136.3

Kimi K3

57.5

Solar Pro 4

54.6

K-EXAONE-2

7.3

Avg Token Usage

Solar Pro 4

2490.7

Kimi K3

2058.0

K-EXAONE-2

1936.7