Odd One Out — In the triples 3–4–14, 56–57–67, 102–103–113, 22–23–13, three end with a prime; one ends with a composite. Identify the exception.

Introduction / Context:Prime identification within short triples is a common classification trick. Here, the last term is decisive: three are primes; one is composite.

Given Data / Assumptions:

• Candidates for the third term: 14, 67, 113, 13.
• Primality checks: 67 (prime), 113 (prime), 13 (prime), 14 (composite = 2 * 7).

Concept / Approach:Check whether the final number of each triple is prime. If only one is composite, it is the odd one out.

Step-by-Step Solution:56–57–67 → 67 is prime.102–103–113 → 113 is prime.22–23–13 → 13 is prime.3–4–14 → 14 is composite (2 * 7).

Verification / Alternative check:Quick divisibility rules: 14 is even → divisible by 2; the others are not divisible by small primes (3, 5, 7) within their bounds, confirming primality.

Why Other Options Are Wrong:

• 56–57–67: ends with a prime.
• 102–103–113: ends with a prime.
• 22–23–13: ends with a prime.

Common Pitfalls:Overanalyzing the first two terms. The discriminant here is solely the primality of the third term.

Final Answer:3-4-14