If 2 @ 3 = 13, 3 @ 4 = 25, then what is 4 @ 5?

Question

If 2 @ 3 = 13, 3 @ 4 = 25, then what is 4 @ 5?

1. A. 36
2. B. 39
3. C. 41 (Correct answer)
4. D. 33

Correct Answer

Option C — 41

Detailed Solution & Explanation

The correct answer is 41.

Key Points

• Test the squares rule on the given pairs: 2 @ 3 = 2² + 3² = 4 + 9 = 13 ✓; 3 @ 4 = 9 + 16 = 25 ✓.
• The operation is the sum of squares.
• So 4 @ 5 = 4² + 5² = 16 + 25 = 41.
• When outputs grow faster than the inputs but not explosively, sums of squares/cubes are the first rules to try; verify on both examples before committing.