In this aptitude number classification question, find the odd number out from the series: 49, 81, 121, 169, 196, 225.

Introduction / Context:
This question comes from the number classification section of aptitude tests. You are given a series of numbers 49, 81, 121, 169, 196 and 225 and asked to find the odd number out. Such questions usually involve properties like perfect squares, cubes, prime numbers or parity. Here, the idea is to look at the square roots of the numbers and then compare the nature of those roots.

Given Data / Assumptions:

• Numbers in the series: 49, 81, 121, 169, 196, 225.
• Each of these numbers is a perfect square.
• Exactly one number must be selected as the odd one out based on a clear and simple property.
• We assume standard school-level knowledge of squares and even or odd integers.

Concept / Approach:
The natural first step is to check whether these numbers are perfect squares, and then to examine the square roots. If all except one share a particular property, then the corresponding number is the odd one out. In this case, the most useful property is whether the square root is an odd integer or an even integer. A neat pattern emerges when we do this check.

Step-by-Step Solution:
Step 1: Write each number as a square of an integer.49 = 7^2, 81 = 9^2, 121 = 11^2, 169 = 13^2, 196 = 14^2, 225 = 15^2.Step 2: Classify the square roots as odd or even.7, 9, 11, 13 and 15 are all odd integers; 14 is the only even integer.Step 3: Connect the property back to the original numbers.The numbers 49, 81, 121, 169 and 225 are squares of odd numbers, while 196 is the only square of an even number.

Verification / Alternative check:
An alternative approach is to list the sequence of square roots explicitly: 7, 9, 11, 13, 14, 15. This almost forms a sequence of consecutive odd numbers except for the inclusion of 14. If we remove 14, we would have a clean run of odd numbers. Therefore 196, which corresponds to 14^2, clearly breaks the otherwise consistent pattern of odd squares.

Why Other Options Are Wrong:
81: Equal to 9^2, and 9 is an odd integer, so it belongs to the main pattern of odd squares.
121: Equal to 11^2, again with an odd square root, so it fits the same structure.
225: Equal to 15^2, and 15 is odd, so it also matches the dominant pattern.

Common Pitfalls:
Students sometimes try to examine only differences between the numbers or check for prime factors, which does not reveal a clear unique element here. Another common mistake is to overlook that all numbers are perfect squares, and hence miss the simpler method of comparing their square roots. Always try to move one level deeper in such problems by considering roots or exponents rather than working only with the surface values.

Final Answer:
The odd number out in the series is 196 because it is the only square of an even integer, while all the others are squares of odd integers.