Classification – Odd one out (unique prime among composites) Consider the following set of integers. Exactly one is prime, while the remaining three are composite. Identify the prime number and mark it as the odd one out.

Introduction / Context:
Prime-versus-composite classification is a staple of verbal–numerical reasoning. The fastest path is to apply small-prime divisibility tests (2, 3, 5, 7, 11, 13, …) and to recognize famous composite forms like perfect squares. The test-maker typically chooses one clean prime and surrounds it with composites that are easy to factor upon inspection, ensuring a single clear outlier.

Given Data / Assumptions:

• Options: 37, 45, 49, 65
• Goal: find the only prime.

Concept / Approach:
Run quick checks: evenness (for 2), last digit (for 5), digit sum (for 3 and 9), and recognition of perfect squares. If none of these reveal a divisor, conduct small trial divisions up to the approximate square root. Since sqrt(37) is a little over 6, testing divisibility by 2, 3, and 5 suffices for 37.

Step-by-Step Solution:
45 → ends with 5 and digit sum 4 + 5 = 9 → divisible by 5 and 9 → composite.49 → equals 7 * 7 → perfect square → composite.65 → equals 5 * 13 → composite.37 → not divisible by 2 (odd), not divisible by 3 (3 + 7 = 10), not divisible by 5 (ends with 7). With sqrt(37) < 7, no further small prime divides it → prime.

Verification / Alternative check:
Explicit factor checks confirm: 45 = 5 * 9, 49 = 7^2, 65 = 5 * 13. For 37, trial division by 2, 3, and 5 fails; since 7^2 = 49 > 37, the test set is complete. Therefore, 37 is prime beyond doubt.

Why Other Options Are Wrong:

• 45: Composite (multiple of 3 and 5).
• 49: Composite (square of 7).
• 65: Composite (product of 5 and 13).
• None of these: There is exactly one prime (37), so this distractor is incorrect.

Common Pitfalls:
Confusing “odd” with “prime,” or overlooking perfect squares like 49. Always confirm with small-prime tests and known patterns.

Final Answer:
37