2025 · Paper 2 · Mathematics
Question 10
The printed question, the official key, and each model’s JSON answer plus the reasoning it wrote.
MathematicsPaper 2Numerical
Q10
Official 6
Model answers
Claude Fable 5.1
Anthropic
Correct4 / 4
6
Claude Fable 5.1 reasoning
a_i = C(23,i)(2/5)^i. Ratio a_{i+1}/a_i = (23-i)/(i+1) · 2/5 ≥ 1 ⇔ 2(23-i) ≥ 5(i+1) ⇔ 46-2i ≥ 5i+5 ⇔ 41 ≥ 7i ⇔ i ≤ 5.857. So a_6 > a_5, and a_7 < a_6. Maximum at r = 6.
GPT 6 Astra
OpenAI
Correct4 / 4
6
GPT 6 Astra reasoning
No written reasoning was returned for this item.
GPT 5.6 Luna
OpenAI
Correct4 / 4
6
GPT 5.6 Luna reasoning
No written reasoning was returned for this item.