In each of these questions a number series is given. In each series only one…

Concept

In a 'find the wrong number' series, every term is produced from the previous one by a fixed rule. To locate the odd term, compute the differences between consecutive terms and look for the hidden pattern in those differences. Exactly one term breaks the pattern.

Application

Take the differences between consecutive terms, left to right:

1. 2194 - 2175 = 19

2. 2175 - 2152 = 23

3. 2152 - 2123 = 29

4. 2123 - 2092 = 31

5. 2092 - 2054 = 38

6. 2054 - 2014 = 40

The first four gaps are 19, 23, 29, 31 - these are consecutive prime numbers. The next prime after 31 is 37, so the fifth gap should be 37, giving 2092 - 37 = 2055. The series instead shows 2054, a gap of 38, which is not the required prime. So 2054 is the wrong term; it should be 2055.

Cross-check

Replace 2054 with 2055 and continue with the next prime, 41: 2055 - 41 = 2014, which matches the final term. The full corrected gap sequence is 19, 23, 29, 31, 37, 41 - six consecutive primes - confirming 2054 is the only term that violates the rule.