In the series 18, 37, 76, 155, 314, 635, which number is the odd one out?

Introduction / Context:
This is an odd man out question based on a number series where the step sizes between terms grow rapidly according to a rule. The task is to find a consistent pattern among most of the terms and then identify the term that does not belong.

Given Data / Assumptions:

• Series: 18, 37, 76, 155, 314, 635.
• Exactly one term is incorrect or does not follow the series rule.
• The pattern appears to involve doubling and adding a small constant.

Concept / Approach:
In series where the numbers grow quite fast but not purely geometrically, check differences between terms. If those differences themselves follow a regular rule, such as doubling and then adding one, you can identify the intended pattern and then see where it breaks.

Step-by-Step Solution:
Step 1: Compute the differences: 37 − 18 = 19, 76 − 37 = 39, 155 − 76 = 79, 314 − 155 = 159, 635 − 314 = 321. Step 2: Observe the first four differences: 19, 39, 79, 159. Each term is almost double the previous one plus 1. Step 3: Check: 19 * 2 + 1 = 39, 39 * 2 + 1 = 79, 79 * 2 + 1 = 159. The pattern is consistent for these. Step 4: Continue the rule: the next difference should be 159 * 2 + 1 = 318 + 1 = 319. Step 5: Add this to 314 to get the next correct term: 314 + 319 = 633. Step 6: The series therefore should be 18, 37, 76, 155, 314, 633. The given term 635 does not match this value and is off by 2.

Verification / Alternative check:
With the corrected last term 633, the difference pattern 19, 39, 79, 159, 319 is perfectly consistent and follows difference_{n+1} = 2 * difference_n + 1. No other correction aligns with such a simple rule, so the logical conclusion is that 635 is the erroneous term.

Why Other Options Are Wrong:
If we remove 37, 155, or 314, the remaining series cannot be made to fit the clean difference doubling plus one pattern. For example, without 155 the transition between 76 and 314 does not fit the rule. Hence only 635 stands out as the incorrect term.

Common Pitfalls:
Learners sometimes check only the original numbers and miss the structure in the differences. Another error is to try multiplicative rules directly on the main terms, which here would produce ratios that are not as simple as the difference pattern. For series questions, always check both differences and ratios, and prefer the explanation that is simple and consistent across the longest stretch of terms.

Final Answer:
The number that does not fit the intended pattern is 635.