In the number series 21, 24, 33, 49, 74, one term does not fit a consistent pattern. Identify the odd number out.

Introduction / Context:
This question asks for the odd term out in a numeric sequence. The usual idea is that most of the numbers follow a clear rule, while one of them breaks that rule. Our job is to detect the underlying pattern that links the majority of the terms and then remove the term that does not match it.

Given Data / Assumptions:

• Given series: 21, 24, 33, 49, 74.
• We are to treat exactly one number as inconsistent.
• We look for a pattern that fits at least four numbers strongly, rather than forcing a weak rule through all five.

Concept / Approach:
An effective way to tackle such problems is to consider consecutive differences between terms. If we find that a neat pattern emerges for most of the sequence once one element is removed, that singled out term is usually the odd one out. Here the key is to look at the differences between 24, 33, 49 and 74.

Step-by-Step Solution:
Step 1: Consider the subsequence 24, 33, 49, 74 and compute differences: 33 - 24 = 9, 49 - 33 = 16, 74 - 49 = 25.Step 2: The differences 9, 16 and 25 are perfect squares: 3^2, 4^2 and 5^2.Step 3: This shows a very clean pattern among 24, 33, 49 and 74 with differences following consecutive square numbers.Step 4: The number 21 does not participate in this square difference structure, because 24 - 21 = 3, which is not a perfect square and does not align with the 3^2, 4^2, 5^2 pattern.Step 5: Therefore 21 is the number that breaks the most consistent pattern in the sequence.

Verification / Alternative check:
If we attempt to include 21 in a pattern with perfect square differences, we fail to obtain consistent squares from the beginning. On the other hand, if we simply drop 21, the remaining four terms follow the neat difference pattern of 9, 16 and 25, which strongly supports the conclusion that 21 is the odd one out.

Why Other Options Are Wrong:
Numbers such as 24, 33, 49 and 74 are linked by differences that are perfect squares. Removing any of them would break this clear rule. For example, dropping 24 would give 21, 33, 49, 74, where the differences no longer follow any simple or smooth numeric pattern.

Common Pitfalls:
One common error is to try to fit all five numbers into a single pattern, which can lead to overly complicated reasoning. Another pitfall is ignoring the power and simplicity of square numbers in difference sequences. Many exam setters deliberately hide square difference patterns inside such series questions.

Final Answer:
The number that does not fit the consistent perfect square difference pattern is 21.