Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number ?
- (a) 64
- (b) 80
- (c) 81 ✓ UPSC's answer
- (d) 100
Why the answer is (c)
• The number is 111111111 (nine 1s).
• 111111111 × 111111111 = 12345678987654321.
• Its digits rise 1 to 9 and fall back to 1, so the digit sum is 2 × (1 + 2 + … + 8) + 9 = 2 × 36 + 9 = 81.
• Hence option (c).
Why the other options are wrong
- (a) 64
- The sum of the digits is 81, not 64.
- (b) 80
- The sum of the digits is 81, not 80.
- (d) 100
- The sum of the digits is 81, not 100.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.