If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x + y is divided by 11?
- (a) 1
- (b) 3
- (c) 5
- (d) 7 ✓ UPSC's answer
Why the answer is (d)
• The number is 4x5y790, which has 7 digits with positions 1 to 7 from left to right.
• For divisibility by 11, the difference between the sum of digits at odd positions and the sum of digits at even positions must be a multiple of 11 (including 0).
• Odd positions (1, 3, 5, 7) contain digits 4, 5, 7, 0. Their sum is 4 + 5 + 7 + 0 = 16.
• Even positions (2, 4, 6) contain digits x, y, 9. Their sum is x + y + 9.
• The condition is (16) - (x + y + 9) = 0 or ±11, ±22, etc. Simplifying gives 7 - (x + y) = 0 or ±11, etc.
• Since x and y are digits (0-9), x + y ranges from 0 to 18. The only valid solution for 7 - (x + y) being a multiple of 11 is 0, which implies x + y = 7.
• The question asks for the remainder when x + y is divided by 11. Since x + y = 7, the remainder is 7.
Why the other options are wrong
- (a) 1
- Option (a) is incorrect because x + y equals 7, not 12 or 1, so the remainder is not 1.
- (b) 3
- Option (b) is incorrect because x + y equals 7, not 14 or 3, so the remainder is not 3.
- (c) 5
- Option (c) is incorrect because x + y equals 7, not 16 or 5, so the remainder is not 5.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.