In this number pair reasoning question, four pairs are given: 15 – 225, 25 – 625, 35 – 1225 and 45 – 2525. In each valid pair, the second number should follow a simple rule based on the first number. Select the odd pair that does not follow the same rule.

Introduction / Context:
This question focuses on recognizing the relationship between two numbers in a pair. You are given four number pairs: 15 – 225, 25 – 625, 35 – 1225 and 45 – 2525. In three of these pairs, the second number is directly related to the first number by a simple and familiar rule. One pair breaks that rule and is therefore the odd one out. Such questions are common in bank exams, SSC exams and general aptitude tests.

Given Data / Assumptions:

• Number pairs: 15 – 225, 25 – 625, 35 – 1225 and 45 – 2525.
• We expect a basic arithmetic or algebraic relationship like squaring or multiplication.
• Exactly one pair does not satisfy the common relationship used in the other three pairs.
• Only basic knowledge of squares of two digit numbers is required.

Concept / Approach:
Whenever you see a pair such as 15 – 225, a natural guess is that 225 might be 15^2. We can test this idea for all pairs. If in three pairs the second number equals the square of the first, and in one pair this does not hold, the exceptional pair becomes the odd one out. So we will compute the square of each first number and compare it with the corresponding second number.

Step-by-Step Solution:
Step 1: Check 15 – 225.Compute 15^2 = 15 * 15 = 225. So this pair follows the pattern second number = first number squared.Step 2: Check 25 – 625.Compute 25^2 = 25 * 25 = 625. This also fits the same pattern.Step 3: Check 35 – 1225.Compute 35^2 = 35 * 35 = 1225. Again the second number matches the square of the first.Step 4: Check 45 – 2525.Compute 45^2 = 45 * 45 = 2025, not 2525. The given second number 2525 does not equal 45^2 and does not match the pattern.Step 5: Identify the odd pair.The first three pairs all follow the rule second = first^2, but the pair 45 – 2525 does not. Hence 45 – 2525 is the odd one out.

Verification / Alternative check:
You can also perform a quick reverse check by taking the square root of each second number. The square root of 225 is 15, of 625 is 25 and of 1225 is 35. These are exact integers and match the first numbers in the corresponding pairs. However, the square root of 2525 is not an integer and clearly not equal to 45. This alternative viewpoint confirms that the last pair fails the simple square relationship followed by the others.

Why Other Options Are Wrong:
15 – 225: Perfectly follows second = first^2, so it is consistent with the intended rule.
25 – 625: Also satisfies the exact same square relationship.
35 – 1225: Again matches the rule, with 1225 equal to 35^2.

Common Pitfalls:
Sometimes students may miscalculate squares, especially of numbers ending in 5. A quick trick is to use the pattern for numbers of the form 10k + 5. For example, 35^2 = 3 * 4 followed by 25, which gives 1225. Similarly, 45^2 = 4 * 5 followed by 25, giving 2025. Knowing such shortcuts not only helps here but also speeds up many arithmetic problems in competitive exams.

Final Answer:
The odd pair is 45 – 2525, because in this pair the second number is not equal to the square of the first number, unlike the other three pairs.