Odd One Out — In the series 32, 13, 51, 24, 46, 20, 72, 45, identify the single number that is prime while all the others are composite.

Introduction / Context:
Series classification can hinge on individual term properties instead of inter-term differences. Here we focus on primality within a list of two-digit numbers.

Given Data / Assumptions:

• Numbers: 32, 13, 51, 24, 46, 20, 72, 45.
• Prime definition: exactly two positive divisors.

Concept / Approach:
Check each term for composite status by testing small prime factors.

Step-by-Step Solution:
32: composite (2 * 16).13: prime (no divisors other than 1 and 13).51: composite (3 * 17).24: composite (2 * 12).46: composite (2 * 23).20: composite (2 * 10).72: composite (8 * 9 or 2 * 36).45: composite (5 * 9).

Verification / Alternative check:
Only 13 resists factorization by 2, 3, 5, and 7 given its size, confirming it as prime.

Why Other Options Are Wrong:

• 20, 46, 72: clearly even composites.
• 32, 24: powers or multiples of 2.
• 51, 45: have small odd prime factors.

Common Pitfalls:
Looking for complex inter-term patterns and missing the single prime among composites.

Final Answer:
13