[tab] evaluation/gpt-5-verfict-easy.out (plaintext)

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Processing file: evaluation/easy_problems.jsonl
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Entry 1:
Problem:
 Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}.

The probability of snow on 1st January is 1/20. What is the probability that snow will fall on the next 1st January?
OpenAI GPT-5 Difficulty verdict: 1/10 — It’s a direct application of the given probability (assumed the same each year) with no computation or additional reasoning required.
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Entry 2:
Problem:
 Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}.

When orange trees are planted to the acre, each tree yields 100 pounds of fruit. For each additional tree over 100, the yield per tree is reduced by 1 pound. How many trees should be planted so that the yield per acre is 4816 pounds?
OpenAI GPT-5 Difficulty verdict: 3 — It’s a straightforward quadratic modeling problem with a simple domain check to choose the valid root.
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Entry 3:
Problem:
 Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}.

Find the smallest prime number \( p \) such that \( p \) divides \( n^2 + 7n + 23 \).
OpenAI GPT-5 Difficulty verdict: 3/10 — It’s a routine modular-arithmetic check over small primes (using parity and simple quadratic-residue/discriminant reasoning) to find the first prime that can divide the quadratic.
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Entry 4:
Problem:
 Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}.

Is there a geometric transformation that maps every point to exactly one point such that any triangle can be transformed into another triangle with the same area? (Alternatively, can any triangle be transformed into a regular triangle with the same area?)
OpenAI GPT-5 Difficulty verdict: 3 — It’s a straightforward affine-geometry fact: any two triangles are affinely equivalent, and if their areas match the affine map has determinant 1 (area-preserving), so you can also map any triangle to an equilateral of the same area.
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Entry 5:
Problem:
 Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}.

How many natural numbers greater than 6 but less than 60 are relatively prime to 15?
OpenAI GPT-5 Difficulty verdict: 3/10 — It’s a straightforward inclusion–exclusion/counting-multiples problem with small numbers and minimal computation.
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Entry 6:
Problem:
 Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}.

Resolve the expression $\frac{x^5 + x^4 - x^3 + 2x^2 + x}{(x-1)^2 (x^2 + 1)^2}$.
OpenAI GPT-5 Difficulty verdict: 6 — It’s a routine partial-fraction decomposition with repeated linear and irreducible quadratic squared factors, requiring solving several coefficients (algebraically tedious but standard).
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Entry 7:
Problem:
 Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}.

What is the total volume in cubic feet of three boxes if each box is a cube with edge length 4 feet?
OpenAI GPT-5 Difficulty verdict: 1 — It’s a direct application of the cube volume formula (a^3) followed by a simple multiplication by 3, with no tricky steps.
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