2025 · Paper 1 · Mathematics
Question 12
The printed question, the official key, and each model’s JSON answer plus the reasoning it wrote.
MathematicsPaper 1Numerical
Q12
Official 96
Model answers
Claude Fable 5.1
Anthropic
Correct4 / 4
96
Claude Fable 5.1 reasoning
f(x) = f(1)^x type exponential; f(a_i) forms a geometric progression with ratio r = f(d). f(a_31)/f(a_25) = r^6 = 64 ⇒ r = 2. Sum over i=1..50: f(a_1)(2^50 − 1) = 3(2^25+1) ⇒ f(a_1)(2^25−1)(2^25+1) = 3(2^25+1) ⇒ f(a_1) = 3/(2^25 − 1). Sum i=6..30: f(a_1)·2^5·(2^25 − 1) = 3·32 = 96.
GPT 6 Astra
OpenAI
Correct4 / 4
96
GPT 6 Astra reasoning
No written reasoning was returned for this item.
GPT 5.6 Luna
OpenAI
Correct4 / 4
96
GPT 5.6 Luna reasoning
No written reasoning was returned for this item.