Among the numbers 5125, 8564, 7343 and 6216, identify the odd one out using the sum of digits property.

Introduction / Context:
In number based odd one out questions, exam setters often hide a pattern in the digits of the numbers rather than in their overall magnitude. A very common and easy to test property is the sum of the digits. Sometimes the sum is prime for most numbers or divisible by a fixed value, and one number breaks that rule. In this question, we are given four four digit numbers and asked to find the one that does not follow the same digit sum pattern as the others.

Given Data / Assumptions:
The four numbers are 5125, 8564, 7343 and 6216. We consider the sum of digits of each number. A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. We assume the intended pattern is based on whether the digit sum is prime or composite.

Concept / Approach:
The approach is to find a property that is shared by three of the numbers and violated by one. Here, when we add the digits of each number, we will see that three sums are prime numbers, while one sum is not prime. The number whose digit sum is not prime will be the odd one out. Using the digit sum is especially convenient because it generates small numbers that are easy to classify as prime or composite.

Step-by-Step Solution:
Step 1: For 5125, compute the digit sum: 5 + 1 + 2 + 5 = 13. The number 13 is a prime number. Step 2: For 8564, compute the digit sum: 8 + 5 + 6 + 4 = 23. The number 23 is also a prime number. Step 3: For 7343, compute the digit sum: 7 + 3 + 4 + 3 = 17. The number 17 is again a prime number. Step 4: For 6216, compute the digit sum: 6 + 2 + 1 + 6 = 15. The number 15 is not prime because 15 = 3 * 5. Step 5: Three numbers have prime digit sums (13, 23 and 17), while 6216 has a composite digit sum (15). Therefore 6216 is the odd one out.

Verification / Alternative check:
After identifying 6216 as the candidate, we can quickly recheck the calculations to avoid arithmetic mistakes. Digit sums 13, 23 and 17 are all well known prime numbers, and 15 is clearly divisible by 3 and 5. No other simple and consistent pattern involving divisibility or parity fits all four numbers as clearly as the digit sum prime versus composite rule, so this logic is very likely the intended one.

Why Other Options Are Wrong:
5125 is not odd because its digit sum 13 is a prime number, fitting the common pattern. 8564 is not odd because its digit sum 23 is also prime and matches the same rule. 7343 is not odd because its digit sum 17 is again prime and belongs to the same group. Only 6216 has a composite digit sum, so it must be the odd one out.

Common Pitfalls:
Students sometimes attempt complex factorization of the full four digit numbers instead of starting with simple digit based checks. Another mistake is to check only divisibility by 2, 3 or 5 on the whole number, which may not reveal any clear pattern here. Remember that for odd one out questions, testing digit sums, parity and small factor patterns often leads to quick and reliable answers.

Final Answer:
The number whose digit sum is not prime and therefore the odd one out is 6216.