Identify the odd term out from the list: 121, 143, 165, 186, 209 — use divisibility structure and factor patterns to choose the exception.

Introduction / Context:
Odd-one-out questions often rely on a hidden common property shared by most terms, with one exception. Factorization and divisibility checks are effective first steps.

Given Data / Assumptions:

• Candidates: 121, 143, 165, 186, 209.
• We look for a unifying numeric property (e.g., perfect power, common factor).

Concept / Approach:
Test divisibility by a distinctive prime (such as 11) or identify special forms (like squares). Spot the majority pattern and isolate the outlier.

Step-by-Step Solution:

Verification / Alternative check:
Four of the five terms are exact multiples of 11; only 186 fails this test, confirming it as the odd one out.

Why Other Options Are Wrong:

• 143, 165, 209 all share the “multiple of 11” property; they are not exceptions.

Common Pitfalls:
Overcomplicating the search (e.g., summing digits or using advanced properties) when a simple prime-divisibility check reveals the pattern quickly.

Final Answer:
186