In the following sequence of numbers 1, 4, 9, 16, 22 and 36, which number is the odd one out that does not follow the same pattern?

Introduction / Context:
This aptitude question tests your ability to recognize number patterns, specifically perfect squares, and identify the term that breaks the pattern. Odd man out questions like this are common in competitive exams because they quickly reveal how comfortable you are with basic number properties and mental observation skills.

Given Data / Assumptions:

• The given sequence is: 1, 4, 9, 16, 22, 36.
• We assume that there is exactly one term in the list that does not follow the main rule that governs the other terms.
• All numbers are positive integers.

Concept / Approach:
The natural approach is to check whether the numbers follow a well known pattern such as squares, cubes, arithmetic progression, or geometric progression. On quick inspection, several of these numbers look like perfect squares of integers. Therefore, the central idea here is to check which numbers are perfect squares and see if one of them does not fit this pattern.

Step-by-Step Solution:
Check 1: 1 = 1 * 1, so 1 is a perfect square (1^2).Check 2: 4 = 2 * 2, so 4 is a perfect square (2^2).Check 3: 9 = 3 * 3, so 9 is a perfect square (3^2).Check 4: 16 = 4 * 4, so 16 is a perfect square (4^2).Check 5: 36 = 6 * 6, so 36 is a perfect square (6^2).Check 6: 22 cannot be written as n * n for any integer n, so it is not a perfect square.

Verification / Alternative check:
Another way to verify is to list nearby perfect squares around 22. We know that 4^2 = 16 and 5^2 = 25. Since 22 lies strictly between 16 and 25 and is not equal to either of them, it cannot be a perfect square. All other numbers in the list exactly match the square of an integer, so our conclusion is consistent from multiple viewpoints.

Why Other Options Are Wrong:
1 is 1^2 and hence a perfect square, so it follows the pattern and cannot be the odd one out.
4 is 2^2, a perfect square, so it belongs to the pattern.
9 is 3^2, also a perfect square, so it fits the pattern.
16 and 36 are 4^2 and 6^2 respectively, both perfect squares and therefore consistent with the rule of the series.

Common Pitfalls:
Students sometimes focus only on the increasing differences between terms (for example, 3, 5, 7, 6, 14) and try to find a pattern there, which becomes messy and misleading. The key is to step back and notice familiar shapes like 1, 4, 9, 16, and 36 as squares of 1, 2, 3, 4, and 6. Missing such standard number patterns is a frequent error in time pressured exams.

Final Answer:
The only number that is not a perfect square in the list is 22, so 22 is the odd man out.