In this aptitude number reasoning question, find the odd number out from the sequence: 100, 101, 97, 105, 90.

Introduction / Context:
This question presents a set of numbers clustered around 100: 100, 101, 97, 105 and 90. You are asked to choose the odd number out from the given alternatives 90, 105, 97 and 101. Instead of looking for a typical arithmetic or geometric sequence, the pattern here is based on how far each number is from 100 and the nature of that difference.

Given Data / Assumptions:

• Central reference number: 100.
• Other numbers in the group: 101, 97, 105, 90.
• We measure each number by its difference from 100.
• Exactly one option should stand out based on the parity of this difference.

Concept / Approach:
The key observation is that 100 is a nice round base. All other numbers are either slightly above or slightly below 100. If we treat 100 as the central point and compute the differences, we can classify each number by how far and in what direction it lies from this base. The parity (odd or even) of these differences provides a simple way to find the odd one out.

Step-by-Step Solution:
Step 1: Find the difference between each number and 100.101: 101 - 100 = +1.97: 100 - 97 = 3 (that is, -3 from 100).105: 105 - 100 = +5.90: 100 - 90 = 10 (that is, -10 from 100).Step 2: Classify the differences as odd or even.For 101 the difference is 1 (odd).For 97 the difference is 3 (odd).For 105 the difference is 5 (odd).For 90 the difference is 10 (even).Step 3: Identify the odd one out.Three numbers (101, 97 and 105) differ from 100 by an odd number; only 90 differs by an even number (10).

Verification / Alternative check:
We can also visualize the numbers around 100 on a number line. The points 97, 101 and 105 lie at distances 3, 1 and 5 respectively from 100, all of which are odd. The point 90 is ten units away, which makes it the only number at an even distance. Since the question asks for the number that does not follow the same pattern as the others, 90 stands out naturally.

Why Other Options Are Wrong:
105: Lies 5 units above 100, with an odd difference that matches the pattern.
97: Lies 3 units below 100, again an odd difference consistent with the others.
101: Lies 1 unit above 100, also an odd difference and therefore part of the main group.

Common Pitfalls:
Candidates often attempt to find a direct series pattern using consecutive terms, which can be confusing here because the order is not central to the logic. Another mistake is to focus on properties like primality or divisibility by 5, which do not yield a unique odd term among the options. Instead, focusing on how far each number lies from 100 provides a much clearer and more elegant solution.

Final Answer:
The odd number out in the sequence is 90, because it is the only number whose distance from 100 is an even number rather than an odd number.