Classification – Odd one out (prime vs composite) Among the following integers, three are composite while exactly one is prime. Identify the prime and mark it as the odd one out.

Introduction / Context:Prime detection is a staple in verbal–numerical classification. When three options are clearly composite, the single prime becomes the odd one out.

Given Data / Assumptions:

• Options: 21, 69, 81, 83
• Basic divisibility checks (2, 3, 5, 7, 9, 11) will quickly separate composites from primes.

Concept / Approach:Apply small-prime tests: sums of digits for 3 and 9, last digit for 2 and 5, simple division for 7 and 11 as needed.

Step-by-Step Solution:21 → 3 * 7 → composite.69 → 3 * 23 → composite.81 → 9 * 9 = 3^4 → composite.83 → not divisible by 2, 3, 5, 7, 11 → prime.

Verification / Alternative check:Testing primes up to sqrt(83) ≈ 9.1 confirms no divisors among 2, 3, 5, 7. Hence 83 is prime.

Why Other Options Are Wrong:

• 21: Composite.
• 69: Composite.
• 81: Composite.
• None of these: There is exactly one prime (83).

Common Pitfalls:Misclassifying 81 as prime because it is odd. Remember 81 = 9^2 = 3^4 is highly composite.

Final Answer:83