If 7 * 24 = 25 and 12 * 16 = 20, then what is 16 * 63 equal to ?
- (a) 70
- (b) 66
- (c) 65 ✓ UPSC's answer
- (d) 64
Why the answer is (c)
• The rule is a * b = √(a² + b²).
• Check: 7² + 24² = 49 + 576 = 625 and √625 = 25; 12² + 16² = 144 + 256 = 400 and √400 = 20.
• For 16 * 63: 16² + 63² = 256 + 3969 = 4225, and √4225 = 65.
• So 16 * 63 = 65, option (c).
Why the other options are wrong
- (a) 70
- 70 is incorrect because √(16² + 63²) = √4225 = 65, while 70² = 4900.
- (b) 66
- 66 is incorrect because the square root of 4225 is exactly 65, not 66 (66² = 4356).
- (d) 64
- 64 is incorrect because 64² = 4096, which is not the sum of squares 4225.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.