In the series 7, 9, 19, 18, 31, 29, which number is the odd one out that does not fit the alternating pattern?

Introduction / Context:
This is an odd one out question involving an alternating pattern. Numbers at odd and even positions often form separate arithmetic progressions or follow different rules. Recognizing such interleaved patterns is a powerful technique for solving series questions quickly and accurately.

Given Data / Assumptions:

• The given sequence is 7, 9, 19, 18, 31, 29.
• Exactly one term is wrong or does not fit the pattern.
• We consider the possibility that odd and even positions form separate sub sequences.

Concept / Approach:
We separate the series into two subsequences: one consisting of numbers in odd positions and one of numbers in even positions. Often one is a simple arithmetic progression. If one subsequence is perfectly regular and the other is almost regular but has a single deviation, that deviation indicates the odd term.

Step-by-Step Solution:
Identify positions: 1st = 7, 2nd = 9, 3rd = 19, 4th = 18, 5th = 31, 6th = 29.Odd positioned terms: 7 (1st), 19 (3rd), 31 (5th).Even positioned terms: 9 (2nd), 18 (4th), 29 (6th).Check odd subsequence: 7, 19, 31. Differences are 19 - 7 = 12 and 31 - 19 = 12. So odd positions form an arithmetic progression with common difference 12.Check even subsequence: 9, 18, 29. Differences are 18 - 9 = 9 and 29 - 18 = 11. These are not equal and do not form a simple arithmetic progression.If we expect an arithmetic progression similar to the odd subsequence, we would want even differences to be consistent, for example 9 and then 9 or 11 and then 11. So one of the even terms is probably wrong.If we maintain the first two even terms 9 and 18 with difference 9, the third even term should be 18 + 9 = 27 instead of 29. That means 29 is the inconsistent number.

Verification / Alternative check:
Replace 29 with 27 to test the pattern. The full sequence becomes 7, 9, 19, 18, 31, 27. Now odd positions 7, 19, 31 form an arithmetic progression with difference 12, and even positions 9, 18, 27 form an arithmetic progression with difference 9. Both subsequences are clean and consistent, showing that 29 is the only value that breaks this two progression structure.

Why Other Options Are Wrong:
7, 19 and 31 belong to the odd subsequence and already form a perfect arithmetic progression, so none of them can be wrong without destroying that structure.

9 and 18 are the first two terms of the even subsequence and set the difference as 9. Removing either of them would force a more complicated adjustment than simply correcting the last term.

Common Pitfalls:
Some test takers attempt to look at the entire series as a single pattern of successive differences, which gives irregular values and leads nowhere. The better strategy is to check whether terms in odd and even positions form separate patterns. Doing this often reveals clean arithmetic or geometric progressions that make identifying the odd term much easier.

Final Answer:
The odd number in the series is 29.