Among the numbers 13981, 93172, 47542 and 67325, identify the odd one out based on the sum of digits.

Introduction / Context:
Odd one out questions with large numbers often hide a pattern in the digits rather than in the overall magnitude of the number. A very common and exam friendly idea is to look at the sum of the digits, sometimes called the digit sum, and see whether it satisfies a particular property such as being equal in several options or being a multiple of a fixed value. In this problem, we have four five digit numbers and need to decide which one is different when we look at the sum of its digits.

Given Data / Assumptions:
The numbers given are 13981, 93172, 47542 and 67325. We compute the sum of the digits of each number separately. We compare these sums to see whether three of them share a common value and one does not. All calculations use simple addition of individual digits.

Concept / Approach:
The approach is to compute the digit sum of each number and then compare them. If three numbers have the same digit sum and one number has a different digit sum, then the number with the different sum is the odd one out. This method is straightforward to implement and generates small results that are easy to compare mentally, which is why exam setters frequently use it as the hidden logic behind such questions.

Step-by-Step Solution:
Step 1: For 13981, the digits are 1, 3, 9, 8 and 1. The sum of digits is 1 + 3 + 9 + 8 + 1 = 22. Step 2: For 93172, the digits are 9, 3, 1, 7 and 2. The sum of digits is 9 + 3 + 1 + 7 + 2 = 22. Step 3: For 47542, the digits are 4, 7, 5, 4 and 2. The sum of digits is 4 + 7 + 5 + 4 + 2 = 22. Step 4: For 67325, the digits are 6, 7, 3, 2 and 5. The sum of digits is 6 + 7 + 3 + 2 + 5 = 23. Step 5: We observe that 13981, 93172 and 47542 all have a digit sum of 22, while 67325 has a digit sum of 23. Step 6: Therefore 67325 is the number that does not match the common digit sum and is the odd one out.

Verification / Alternative check:
We can quickly recompute each sum to avoid any addition mistakes, especially with five digit numbers. Seeing the same value 22 for three different numbers strongly suggests that the examiner intentionally chose these values to form a group. Since only 67325 breaks this otherwise perfect match, and there is no other simple pattern that separates three numbers from one, the digit sum property is clearly the intended logic.

Why Other Options Are Wrong:
13981 is not the odd one out because its digit sum is 22, which matches the sums of 93172 and 47542. 93172 is not the odd one out because it also has a digit sum of 22 and belongs to the same group. 47542 is not the odd one out because its digit sum again equals 22, continuing the pattern. Only 67325 has a digit sum of 23, which is different from 22 and sets it apart from the others.

Common Pitfalls:
A common mistake is to try complex divisibility tests or factorization on these large numbers, which is time consuming and usually not necessary in exam conditions. Another pitfall is to miscalculate the digit sum of one of the numbers under time pressure and then draw a wrong conclusion. To avoid such issues, it is wise to double check simple additions and to always consider digit sums as a first idea when dealing with odd one out questions involving multi digit numbers.

Final Answer:
The number whose digit sum is different from the others and is therefore the odd one out is 67325.