Odd One Out — From the pairs (25, 36), (9, 64), (100, 121), (144, 169), pick the pair that is not a consecutive-squares pair.

Introduction / Context:Square recognition and adjacency (n^2 and (n+1)^2) provide a clean basis for classification. Three pairs are consecutive squares; one is not.

Given Data / Assumptions:

• 25 = 5^2, 36 = 6^2 → consecutive squares.
• 100 = 10^2, 121 = 11^2 → consecutive squares.
• 144 = 12^2, 169 = 13^2 → consecutive squares.
• 9 = 3^2, 64 = 8^2 → not consecutive.

Concept / Approach:Express each number as an integer square and check whether the exponents differ by 1.

Step-by-Step Solution:(25, 36) → (5^2, 6^2) ✓(100, 121) → (10^2, 11^2) ✓(144, 169) → (12^2, 13^2) ✓(9, 64) → (3^2, 8^2) ✗ (gap of 5 in the bases)

Verification / Alternative check:Compute differences: (n+1)^2 − n^2 = 2n + 1; for (5,6) that is 11; for (10,11) that is 21; for (12,13) that is 25. The non-consecutive pair will not fit this form consistently.

Why Other Options Are Wrong:

• (25, 36): consecutive squares.
• (100, 121): consecutive squares.
• (144, 169): consecutive squares.

Common Pitfalls:Assuming any two squares constitute a valid pair. Here, adjacency of bases is the key.

Final Answer:9, 64