Odd term in a decreasing pattern: 125, 123, 120, 115, 108, 100, 84, … Identify the wrong number that breaks the intended rule.

Introduction / Context:
“Odd-man-out” series require reconstructing the intended rule and locating the term that violates it. Many competitive-exam series use prime-based decrements, so checking prime differences is a productive first step here.

Given Data / Assumptions:

• Sequence: 125, 123, 120, 115, 108, 100, 84, …
• Expectation: a smooth numeric rule (often involving primes or consecutive odds).
• Only one term is wrong; others are consistent with a single rule.

Concept / Approach:
Test a “subtract consecutive primes” pattern. The first drops are 2, 3, 5, 7, so the next should be 11, then 13, etc. This is a common motif: 125 − 2 = 123; −3 = 120; −5 = 115; −7 = 108; next should be −11 ⇒ 108 − 11 = 97; then −13 ⇒ 97 − 13 = 84.

Step-by-Step Solution:
Start: 125125 − 2 = 123123 − 3 = 120120 − 5 = 115115 − 7 = 108Intended next: 108 − 11 = 97 (but the given term is 100)Continuing: 97 − 13 = 84 (matches later term)

Verification / Alternative check:
Once we correct the middle term to 97, the entire chain becomes perfectly consistent with prime decrements: 2, 3, 5, 7, 11, 13. The presence of 84 later strengthens that reconstruction (since 97 − 13 = 84 exactly).

Why Other Options Are Wrong:

• 125 / 115 / 84: each aligns with the prime-decrement pattern once 100 is replaced by 97.

Common Pitfalls:

• Averaging or forcing a mixed rule; here the elegant consecutive-primes subtraction explains all transitions except the erroneous 100.

Final Answer:
100