In this number classification question on perfect squares, select the odd number from the given alternatives.

Introduction / Context:
This quantitative aptitude question focuses on perfect squares and requires you to identify the odd number in the list. Perfect power recognition, especially for square numbers, is a common theme in competitive exams. Here, you must decide which number does not belong to the group when the others share the property of being perfect squares of integers.

Given Data / Assumptions:
- The given numbers are 1600, 2500, 3600, and 4000.- All are four digit positive integers.- The likely pattern is whether each number can be written as n^2 for some integer n.

Concept / Approach:
A perfect square is any number that can be expressed as n^2 where n is an integer. Many exam questions use round figures like 40^2, 50^2, and 60^2 because they are easy to recognize. The strategy is to test each number to see whether its square root is an integer. The number that fails this test is the odd one out.

Step-by-Step Solution:
Step 1: 1600 can be written as 40^2, so it is a perfect square.Step 2: 2500 can be written as 50^2, so it is also a perfect square.Step 3: 3600 can be written as 60^2, again a perfect square.Step 4: 4000 has a square root between 63 and 64 but not equal to any integer, so it is not a perfect square.Step 5: Therefore, three numbers are perfect squares of whole numbers, and one is not.

Verification / Alternative check:
You can factor 4000 as 4000 = 400 * 10 = 20^2 * 10. Because there is an extra factor of 10 that does not form a complete square, 4000 cannot be expressed as n^2 for an integer n. This confirms that it is not a perfect square.

Why Other Options Are Wrong:
1600: Equal to 40^2 and so it fits the pattern.2500: Equal to 50^2 and belongs with the others.3600: Equal to 60^2 and also a perfect square.

Common Pitfalls:
Students sometimes guess based on the visual size of the number rather than checking square roots or factorization. Always confirm whether the square root is an integer before deciding if a number is a perfect square.

Final Answer:
The odd number is 4000 because it is not a perfect square, while 1600, 2500, and 3600 are perfect squares.