Four four-digit numbers are given – 8314, 3249, 2518 and 1315. Exactly one of these numbers has a special property that the others lack. Which of the following numbers is the odd one out in this group?

Introduction / Context:
This logical reasoning question involves identifying a special mathematical property among four four-digit numbers. Three numbers are similar in the sense that they do not have this property, while one number stands apart and is therefore the odd one out. These types of questions test familiarity with square numbers and quick mental recognition of perfect squares.

Given Data / Assumptions:
The numbers are 8314, 3249, 2518 and 1315.
We are looking for a simple, well known mathematical property, suitable for an aptitude exam setting.
A common property for such questions is whether a number is a perfect square of some integer.
Exactly one of the numbers is expected to satisfy this property, with the remaining three failing it.

Concept / Approach:
A perfect square is a number that can be expressed as n multiplied by n, where n is an integer. Aptitude questions often hide one perfect square among other non square numbers. Your task is to check whether any of the four numbers is an exact square of an integer. If only one is a perfect square and the others are not, that square number will be the odd one out because it has a special structural property that the others do not share.

Step-by-Step Solution:
Step 1: Recall some nearby perfect squares of two digit numbers: 50 squared is 2500, 55 squared is 3025, 57 squared is 3249, 60 squared is 3600 and so on. Step 2: Compare 3249 with 57 squared. Compute 57 multiplied by 57: 50 multiplied by 57 is 2850, and 7 multiplied by 57 is 399. Adding 2850 and 399 gives 3249. Therefore, 3249 is equal to 57 squared, so it is a perfect square. Step 3: Check 8314. It lies between 91 squared (8281) and 92 squared (8464). Since it does not match either value, 8314 is not a perfect square. Step 4: Check 2518. It lies between 50 squared (2500) and 51 squared (2601), but 2518 does not equal 2500 or 2601, so it is not a perfect square. Step 5: Check 1315. It lies between 36 squared (1296) and 37 squared (1369). Since it does not equal any of these exact squares, it is not a perfect square. Step 6: Conclude that 3249 is the only perfect square among the four given numbers, which makes it the odd one out, as the others are non square numbers.

Verification / Alternative check:
You can also confirm by estimating the square roots of each number. The square root of 3249 is exactly 57. On the other hand, the approximate square roots of 8314, 2518 and 1315 are not integers; they fall between consecutive integers. Since the square root of a perfect square must be an integer, only 3249 qualifies as a perfect square. This independent method confirms that 3249 is different from the other numbers.

Why Other Options Are Wrong:
8314: Not equal to the square of any integer, so it shares the “non square” property with 2518 and 1315.
2518: Lies between consecutive perfect squares but is itself not a square, so it does not have the special property.
1315: Also not equal to any integer squared and therefore similar to 8314 and 2518 in this respect.

Common Pitfalls:
A common error is to check only divisibility rules or parity, such as whether the numbers are odd or even. That does not isolate a single odd one out because more than one number will share each such property. The question is designed so that a more distinctive property, like being a perfect square, is the key. Practice recognising nearby perfect squares to speed up this process in exams.

Final Answer:
The only perfect square among the given numbers is 3249, so it is the odd one out.