In the series 90, 72, 56, 42, 36, 20, which term is the odd one out?

Introduction / Context:
This is an odd man out question in a decreasing number series. The objective is to detect a simple arithmetic rule that most terms satisfy and then identify the term that does not follow that rule.

Given Data / Assumptions:

• Series: 90, 72, 56, 42, 36, 20.
• Exactly one term is incorrect or does not fit the intended pattern.
• The pattern is expected to involve simple subtraction.

Concept / Approach:
For decreasing sequences, it is natural to check the differences between consecutive terms. If most of those differences follow an orderly pattern, such as subtracting even numbers in a consistent fashion, we can then check which term breaks that logic.

Step-by-Step Solution:
Step 1: Compute differences between consecutive terms: 72 − 90 = −18, 56 − 72 = −16, 42 − 56 = −14, 36 − 42 = −6, 20 − 36 = −16. Step 2: Look at the absolute differences: 18, 16, 14, 6, 16. Step 3: A natural pattern to expect is subtracting consecutive even numbers: 18, 16, 14, 12, 10, and so on. Step 4: If we follow this ideal pattern from 90, we get: 90 − 18 = 72, 72 − 16 = 56, 56 − 14 = 42, 42 − 12 = 30, 30 − 10 = 20. Step 5: The corrected series should therefore be 90, 72, 56, 42, 30, 20. Step 6: The term 36 in the given sequence is in place of the expected 30, so 36 breaks the pattern.

Verification / Alternative check:
Once we adjust the fifth term to 30, the consecutive differences are 18, 16, 14, 12, 10 in absolute value. This is a smooth decreasing sequence of even numbers subtracting 2 each time. The intended pattern is therefore clear, and 36 is the only term that does not fit.

Why Other Options Are Wrong:
The terms 20, 42, and 56 fit perfectly into the adjusted series. Removing any of them would destroy the consistent subtraction by 18, 16, 14, 12, and 10. Only 36 prevents that pattern from appearing, which makes it the true odd man out.

Common Pitfalls:
Some learners focus on divisibility or factors instead of differences and may incorrectly pick a term that looks less structured, such as 20. However, the most systematic way to solve such series is to examine differences first. Overlooking the idea of consecutive even subtractions is another typical mistake.

Final Answer:
The term that does not follow the decreasing even difference pattern is 36.