Classification – Number pairs (square-difference test): in three pairs the difference (first − second) is a perfect square; one pair has a non-square difference. Find the odd one out. Options: 61 - 12, 34 - 30, 44 - 31, 25 - 21.

Introduction / Context:Pair-difference classification often checks whether differences land on special sets (e.g., perfect squares). A single miss identifies the outlier.

Given Data / Assumptions:

• 61 − 12 = 49 = 7^2 → square.
• 34 − 30 = 4 = 2^2 → square.
• 25 − 21 = 4 = 2^2 → square.
• 44 − 31 = 13 → not a perfect square.

Concept / Approach:Compute the difference of each pair and test for perfect-square status.

Step-by-Step Solution:Calculate each difference.Mark square vs non-square results.Identify the pair whose difference is not square.

Verification / Alternative check:Nearest squares around 13 are 9 and 16; 13 is not square, confirming the exception.

Why Other Options Are Wrong:61−12, 34−30, 25−21: Each yields a perfect square difference and thus belongs together.

Common Pitfalls:Miscomputing 61−12 as 51; the correct result is 49.

Final Answer:44 - 31