In this divisibility based number classification question, select the odd number from the given alternatives.

Introduction / Context:
This quantitative aptitude question asks you to select the odd number from a group based on divisibility properties. These types of questions are very common in exams because they can be solved quickly using basic arithmetic and knowledge of multiples. The key is to identify a shared property among most numbers and then find the one that does not share that property.

Given Data / Assumptions:
- The options are 15, 20, 40, and 60.- All are positive integers of small size, which allows mental calculations.- We are looking for a number that does not fit a simple multiplicative pattern that the others share.

Concept / Approach:
A natural approach is to look for a common factor that divides three of the numbers. The numbers 20, 40, and 60 immediately suggest a pattern with 20 because 20 multiplied by 1, 2, and 3 gives 20, 40, and 60. If three numbers are multiples of 20 and one is not, that non multiple is the odd one out. We will confirm this pattern step by step.

Step-by-Step Solution:
Step 1: Check 20. It is clearly 1 * 20, so a multiple of 20.Step 2: Check 40. It is 2 * 20, again a multiple of 20.Step 3: Check 60. It is 3 * 20, so it also fits the multiples of 20 pattern, even though it has other factors as well.Step 4: Check 15. When you divide 15 by 20, you do not get a whole number, so 15 is not a multiple of 20.Step 5: Thus, three numbers can be expressed as k * 20 for integer k, and one cannot.

Verification / Alternative check:
You can list the first few multiples of 20: 20, 40, 60, 80, and so on. On that list you will see 20, 40, and 60 but never 15. This confirms that 15 is the only number that does not belong to the multiples of 20 group.

Why Other Options Are Wrong:
20: Exactly equal to 1 * 20.40: Exactly equal to 2 * 20.60: Exactly equal to 3 * 20.

Common Pitfalls:
Many learners first check whether numbers are odd or even. Here, however, both 15 and 45 style numbers could be odd, but that is not the intended pattern. The cleaner rule is to look at a shared multiple, which naturally highlights 15 as different.

Final Answer:
The odd number is 15 because it is not a multiple of 20, whereas 20, 40, and 60 are multiples of 20.