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 numerical-answer problem. Solve it and put only the final integer value inside \boxed{}.
Problem 30 In the coordinate plane, letABbe a segment of length 10 √ 2, and consider the circle with diameterAB. PointsPandQlie on this circle and satisfy ( − →PA+− →PB)·(− →PQ+− →PB) = 2
− →PQ
2 . If
− →PB
= 14 and
− →QB
0, then
− →PA· − →QB
= q p, wherepandqare coprime natural numbers. Computep+q. [4 points] 19
Ground Truth
221
Recorded model response / solution
Reasoning Process
\boxed{221}
Final Model Output
221
Comparative Analysis (P45) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.
Avg Time Taken
Kimi K3
133.4
Solar Pro 4
58.2
Motif 3
52.3
K-EXAONE-2
11.0
Avg Token Usage
Solar Pro 4
4054.7
Kimi K3
3779.7
K-EXAONE-2
2969.3