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 operation 'a * b' is defined as the square root of the sum of the squares of the two numbers, i.e., $\sqrt{a^2 + b^2}$.
• For the first example, $7^2 + 24^2 = 49 + 576 = 625$, and $\sqrt{625} = 25$.
• For the second example, $12^2 + 16^2 = 144 + 256 = 400$, and $\sqrt{400} = 20$.
• Applying this rule to $16 * 63$, calculate $16^2 + 63^2 = 256 + 3969 = 4225$.
• The square root of 4225 is 65.
• Therefore, the value of $16 * 63$ is 65, which corresponds to option (c).
Why the other options are wrong
- (a) 70
- 70 is incorrect because $\sqrt{16^2 + 63^2}$ equals 65, not 70.
- (b) 66
- 66 is incorrect because the square root of 4225 is exactly 65, not 66.
- (d) 64
- 64 is incorrect because 64 squared is 4096, which is not equal to 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.