In this aptitude reasoning question on number series, find the odd number out from the list: 61, 66, 83, 121, 185.

Introduction / Context:
This question asks you to identify the odd number out from the list 61, 66, 83, 121, 185. Instead of a forward series pattern, the focus is on a distinctive numeric property that one number has and the others do not. Such classification questions are common in the number reasoning section of aptitude tests.

Given Data / Assumptions:

• Numbers given: 61, 66, 83, 121, 185
• Exactly one number must be considered different based on a clear mathematical property.
• The property should be simple, such as being a perfect square or cube, or relating to prime or composite status.

Concept / Approach:
One straightforward method is to check for perfect squares, cubes, and basic divisibility patterns. Perfect squares are numbers that can be written as n^2, where n is an integer. If exactly one number in the set is a perfect square and the others are not, that number will be the odd one out.

Step-by-Step Solution:
Step 1: Test each number to see if it is a perfect square.61: Square root is between 7 and 8, so it is not a perfect square.66: Square root is between 8 and 9, not a perfect square.83: Square root is between 9 and 10, not a perfect square.121: Square root is exactly 11, so 121 = 11^2, a perfect square.185: Square root is between 13 and 14, not a perfect square.Step 2: Summarize the observation.121 alone is a perfect square. The other four numbers are not perfect squares.

Verification / Alternative check:
We can confirm by listing nearby perfect squares: 10^2 = 100, 11^2 = 121, 12^2 = 144. Only 121 from the given set appears in this list. No similar unique property like primality or divisibility by a small fixed number isolates any of the other values alone, making the perfect square property the cleanest discriminator.

Why Other Options Are Wrong:
61: Not a perfect square, and several other numbers share this non-square property.
66: Also not a perfect square and does not have a unique easy-to-use property in this group.
83: Again not a perfect square and shares this trait with most of the other numbers.
185: Not a perfect square and not uniquely different from the rest in any simple way.

Common Pitfalls:
Students sometimes focus too much on primes versus composites here. While 61 and 83 are prime, there are two such primes, so neither alone can be selected as the odd one out. The principle is that the odd term should be unique based on the chosen property. The perfect square property singles out exactly 121, so it is the correct answer.

Final Answer:
The odd number out in the given list is 121.