Among the numbers 4267, 2498, 2739 and 5496, identify the odd one out using divisibility by 11.

Introduction / Context:
In many aptitude tests, odd one out number questions use divisibility rules as the underlying pattern, especially rules for 3, 9 or 11. Here we have four seemingly unrelated four digit numbers and must decide which one differs from the others. A useful approach is to check divisibility by specific numbers using known digit based rules, rather than performing full division each time.

Given Data / Assumptions:
The given numbers are 4267, 2498, 2739 and 5496. We apply the standard divisibility rule for 11. Divisibility by 11 can be tested by taking the difference between the sum of digits in odd positions and the sum of digits in even positions. If this difference is 0 or a multiple of 11, the number is divisible by 11.

Concept / Approach:
The divisibility test for 11 is very powerful when dealing with multi digit numbers. For a four digit number abcd, we compute (a + c) minus (b + d). If the result is 0, 11, -11 and so on, then the number is divisible by 11. In this question, when we apply this rule to each of the four numbers, three of them will fail the test and one will satisfy it. The one divisible by 11 will be the odd one out, because it has a special divisibility property that the others lack.

Step-by-Step Solution:
Step 1: For 4267, digits are 4, 2, 6 and 7. Sum of first and third digits = 4 + 6 = 10. Sum of second and fourth digits = 2 + 7 = 9. Difference = 10 - 9 = 1, not a multiple of 11. So 4267 is not divisible by 11. Step 2: For 2498, digits are 2, 4, 9 and 8. Sum of first and third digits = 2 + 9 = 11. Sum of second and fourth digits = 4 + 8 = 12. Difference = 11 - 12 = -1, not a multiple of 11. So 2498 is not divisible by 11. Step 3: For 2739, digits are 2, 7, 3 and 9. Sum of first and third digits = 2 + 3 = 5. Sum of second and fourth digits = 7 + 9 = 16. Difference = 5 - 16 = -11, which is a multiple of 11. So 2739 is divisible by 11. Step 4: For 5496, digits are 5, 4, 9 and 6. Sum of first and third digits = 5 + 9 = 14. Sum of second and fourth digits = 4 + 6 = 10. Difference = 14 - 10 = 4, not a multiple of 11. So 5496 is not divisible by 11. Step 5: Therefore 2739 alone is divisible by 11, making it the odd one out.

Verification / Alternative check:
As an additional check, we can perform short division: 2739 divided by 11 equals 249 exactly, so 11 * 249 = 2739 confirms divisibility. For the other numbers, dividing by 11 does not yield an integer, which reinforces the result from the digit test. No other simple pattern, such as digit sum or parity, produces as clear and unique a distinction as divisibility by 11, so this is the intended logic.

Why Other Options Are Wrong:
4267 is not the odd one out because it fails the divisibility by 11 test, like 2498 and 5496. 2498 is not the odd one out for the same reason; it is not divisible by 11 and shares this property with 4267 and 5496. 5496 also fails the test and so cannot be singled out on this basis. Only 2739 passes the 11 divisibility test, so it is different from all the others.

Common Pitfalls:
A common mistake is to check only divisibility by 2 or 5, which does not create a unique classification in this set. Another pitfall is to try to factor each number fully, which is more time consuming than using the digit rule for 11. Learning and practicing divisibility rules for 3, 9 and 11 is very useful for quickly tackling number based reasoning questions in competitive exams.

Final Answer:
The only number divisible by 11 and therefore the odd one out is 2739.