In the list of numbers 253, 136, 352, 324, 631 and 244, which one is the odd man out because it does not share the same digit-sum property as the others?

Introduction / Context:
This is a classic odd-man-out problem involving three-digit numbers. The idea is that most of the numbers in the list share a hidden property related to their digits, while one number does not. Recognizing this hidden property is essential in many reasoning and aptitude examinations.

Given Data / Assumptions:
The given numbers are: 253, 136, 352, 324, 631 and 244. We are told that exactly one of these numbers does not belong to the same group as the others. We look only at the digits themselves and simple properties like sums of digits, reversals, and similar relationships.

Concept / Approach:
When you see three-digit numbers with no obvious arithmetic progression or multiplication pattern, a very common strategy is to examine the sum of their digits. Sometimes all numbers except one have the same digit sum or share a property such as being equal to 10, 12, or another special value. That is the clue here as well.

Step-by-Step Solution:
Step 1: Compute the sum of digits for each number.253 → 2 + 5 + 3 = 10.136 → 1 + 3 + 6 = 10.352 → 3 + 5 + 2 = 10.631 → 6 + 3 + 1 = 10.244 → 2 + 4 + 4 = 10.324 → 3 + 2 + 4 = 9.Step 2: Observe the pattern. For every number except one, the sum of its digits is equal to 10.Step 3: Only 324 has a digit sum equal to 9, which is different from the common digit sum of 10 shared by all the others.

Verification / Alternative check:
We can quickly re-check the digit sums to avoid mistakes. All of 253, 136, 352, 631 and 244 give 10 when adding their digits. Only 324 gives a different total. There is no need to look for more complicated patterns, because a very neat and unique property (digit sum equal to 10) already groups five of the numbers together, leaving 324 alone.

Why Other Options Are Wrong:
136, 352 and 631 may look different at first glance, but each of them still has a digit sum of 10, so they fit the same pattern as 253 and 244. Choosing any of them as the odd one out would ignore this clear and simple property. Therefore, none of these can be the unique odd number in the set.

Common Pitfalls:
Students may waste time searching for more complex relationships such as prime factors, squares, or cubic relationships, or may focus on the order of digits rather than their sum. In many odd-man-out questions, the key is a very simple digit property like parity, divisibility or digit sums, so it is important to check those first.

Final Answer:
The only number whose digits do not sum to 10 is 324, so it is the odd man out.