Find the odd pair: Three options are consecutive perfect-square pairs (n^2, (n+1)^2). Identify the pair that is NOT of this form.
Correct Answer: 8 - 15
Introduction / Context:Squares feature heavily in number-classification problems. Here, most options form pairs of consecutive perfect squares, i.e., (n^2, (n+1)^2). The task is to detect the one pair that does not follow this structure.
Given Data / Assumptions:
- Pairs: 8–15, 25–36, 49–64, 81–100.
- Perfect squares to recall: 5^2 = 25, 6^2 = 36; 7^2 = 49, 8^2 = 64; 9^2 = 81, 10^2 = 100.
Concept / Approach:Check whether each pair corresponds to (n^2, (n+1)^2) for some integer n. Non-squares or mismatched pairs will betray the odd one out.
Step-by-Step Solution:
25–36: 25 = 5^2 and 36 = 6^2 → consecutive squares.49–64: 49 = 7^2 and 64 = 8^2 → consecutive squares.81–100: 81 = 9^2 and 100 = 10^2 → consecutive squares.8–15: 8 is not a perfect square and 15 is not a perfect square → not of the form (n^2, (n+1)^2).Verification / Alternative check:Observe that legitimate pairs differ by (n+1)^2 − n^2 = 2n + 1 (an odd number). The listed square pairs differ by 11, 15, and 19 respectively. The pair 8–15 differs by 7 and neither term is a perfect square, confirming it as the odd one out.
Why Other Options Are Wrong:They are correct examples of consecutive square pairs, so they are not the odd item.
Common Pitfalls:Confusing “consecutive integers” with “consecutive squares,” or checking only the difference without confirming each term is a perfect square.
Final Answer:8 - 15 is the odd pair.