Home » Aptitude » Odd Man Out and Series

Number series — identify the odd term (differences should be consecutive squares): 1, 2, 6, 15, 31, 56, 91

Difficulty: Medium

Correct Answer: 91

Explanation:

Introduction / Context:
Some series grow by adding consecutive square numbers. If one term deviates from those differences, it becomes the odd one out. We will inspect first differences to uncover the rule.

Given Data / Assumptions:

Series: 1, 2, 6, 15, 31, 56, 91
One term does not follow the pattern.

Concept / Approach:
Compute term-to-term differences and compare them to 1^2, 2^2, 3^2, 4^2, 5^2, 6^2… A clean match should appear if the rule is "add consecutive squares".

Step-by-Step Solution:

2 − 1 = 1 = 1^26 − 2 = 4 = 2^215 − 6 = 9 = 3^231 − 15 = 16 = 4^256 − 31 = 25 = 5^291 − 56 = 35 (should be 36 = 6^2)The last step is off by 1. The correct next term would be 56 + 36 = 92.

Verification / Alternative check:

If 91 were replaced by 92, the differences would be 1, 4, 9, 16, 25, 36 — perfect consecutive squares.

Why Other Options Are Wrong:

31, 56, and 15 all participate in correct differences matching 4^2 and 5^2 steps; they are consistent.

Common Pitfalls:

Assuming arithmetic progression; instead, the progression is in the differences (squares), not the terms themselves.

Number series — identify the odd term (differences should be consecutive squares): 1, 2, 6, 15, 31, 56, 91

More Questions from Odd Man Out and Series

Discussion & Comments