In this numerical odd-man-out question, four numbers are given: 10, 20, 15 and 30. Three of these numbers are exact multiples of 10, while one number is not divisible by 10. Which number is the odd one out on the basis of divisibility by 10?

Introduction / Context:
This question is a simple odd-man-out problem involving basic divisibility rules from arithmetic. The numbers 10, 20, 15 and 30 are given, and you are expected to identify which one does not share a common property with the others. In many aptitude tests, divisibility by 2, 5, 10 and similar small numbers is frequently tested. Here, the most relevant concept is divisibility by 10 and recognizing multiples of 10 at a glance based on their last digit.

Given Data / Assumptions:
The given numbers are 10, 20, 15 and 30.
Three of these numbers are exact multiples of 10.
One number is not a multiple of 10 and is therefore the odd one out.
No advanced operations like squares or cubes are needed; simple divisibility checks are sufficient.

Concept / Approach:
A number is divisible by 10 if and only if its last digit is 0. Any integer that ends in 0 can be written as 10 * n for some integer n. The strategy in odd-man-out questions is to look for a clear common feature shared by most of the options. Once you spot that three numbers end in 0 and one does not, the decision becomes straightforward. This approach is quick and reliable in competitive exams, where time management is very important.

Step-by-Step Solution:
Step 1: Check 10. It ends in 0, so 10 is equal to 10 * 1 and is a multiple of 10. Step 2: Check 20. It also ends in 0, so 20 is equal to 10 * 2 and is a multiple of 10. Step 3: Check 30. This number ends in 0 as well, so 30 is equal to 10 * 3 and is a multiple of 10. Step 4: Check 15. The last digit is 5, so the number is not divisible by 10. While 15 is a multiple of 5, it is not a multiple of 10. Step 5: Conclude that three numbers (10, 20 and 30) are multiples of 10, but 15 is not. Therefore, 15 is the odd number.
Verification / Alternative check:
You can also express the numbers as products: 10 = 10 * 1, 20 = 10 * 2 and 30 = 10 * 3, which clearly shows the relationship with 10. When trying to express 15 in the same way, you get 15 = 10 * 1.5, which is not an integer product and therefore shows that 15 is not an exact multiple of 10. This alternative check confirms your earlier conclusion based on the last digit rule.

Why Other Options Are Wrong:
10 is a standard multiple of 10 and perfectly fits the main pattern of numbers ending in 0, so it is not the odd one out.
20 also ends in 0 and is clearly divisible by 10, so it belongs to the majority group rather than being odd.
30 is another multiple of 10 because it ends in 0, so it shares the same property as 10 and 20 and cannot be the odd option.
15 is the only number that ends in 5 and is not divisible by 10, which makes it different from the others.

Common Pitfalls:
Some students may get distracted by the fact that 15 is an odd number, while 10, 20 and 30 are even. Although this is true, the more striking and intended pattern here is divisibility by 10. Another mistake is to overthink the problem and look for complicated relationships, when a simple divisibility rule is enough. In time-bound exams, always look for the simplest and most common property that groups most of the options together.

Final Answer:
The number that is not a multiple of 10 and is therefore the odd one out is 15.