In this number series odd man out question, find the odd number from the series: 222, 271, 308, 332, 348, 357.

Introduction / Context:
This question presents the series 222, 271, 308, 332, 348, 357 and asks you to find the odd number out. Here the series is intended to be generated by adding descending perfect squares, but one number is inconsistent with that pattern. Identifying the break in the pattern is the key to solving the problem.

Given Data / Assumptions:

• Series: 222, 271, 308, 332, 348, 357
• We expect a consistent difference pattern between consecutive terms.
• The intended differences are based on perfect squares.
• Exactly one term fails to respect this structure.

Concept / Approach:
Many advanced series use differences that follow a squared pattern, such as 7^2, 6^2, 5^2, 4^2, 3^2. If three or more gaps between terms match such a pattern and one gap does not, the term causing the incorrect gap is the odd one out. We therefore examine the consecutive differences and compare them to descending perfect squares.

Step-by-Step Solution:
Step 1: Compute actual differences.271 - 222 = 49, which equals 7^2.308 - 271 = 37.332 - 308 = 24.348 - 332 = 16, which equals 4^2.357 - 348 = 9, which equals 3^2.Step 2: Infer the intended pattern.We can reasonably infer that the intended series should add descending squares: 7^2, 6^2, 5^2, 4^2, 3^2, that is 49, 36, 25, 16, 9.Step 3: Construct the ideal series using these squares.Start from 222: 222 + 49 = 271.Then add 6^2 = 36: 271 + 36 = 307.Then add 5^2 = 25: 307 + 25 = 332.Then add 4^2 = 16: 332 + 16 = 348.Then add 3^2 = 9: 348 + 9 = 357.Step 4: Compare the ideal and given series.The only discrepancy is at the third term: the series should contain 307, but instead has 308.

Verification / Alternative check:
The first difference 49 and the later differences 16 and 9 already match perfect squares 7^2, 4^2 and 3^2. This strongly suggests the full set of differences should be 49, 36, 25, 16 and 9. Inserting 308 into the series disrupts this pattern because 308 - 271 = 37, which is not a perfect square. If we replace 308 with 307, every step aligns with the intended descending square rule, confirming that 308 is the inconsistent term.

Why Other Options Are Wrong:
271: Follows directly from 222 by adding 7^2 = 49, so it fits the pattern.
332: Can be obtained from the corrected intermediate value 307 by adding 5^2 = 25, so it matches the rule.
348: Follows from 332 by adding 4^2 = 16 and is therefore consistent.

Common Pitfalls:
Candidates may focus only on the raw differences 49, 37, 24, 16, 9 and fail to notice that several of them are exact squares. Without inferring the intended 36 and 25, the presence of 37 and 24 can be confusing. The key is to recognize known patterns involving perfect squares and adjust for a likely misprint or anomaly. Here that anomaly is 308.

Final Answer:
The odd number out in the given series is 308.