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)
• Divisibility by 11: the difference between the sums of alternate digits must be a multiple of 11.
• In 4x5y790, counting from the right, the odd places hold 0, 7, 5, 4 (sum 16) and the even places hold 9, y, x (sum 9 + x + y).
• 16 − (9 + x + y) = 7 − (x + y) must be 0 or −11, so x + y = 7 or 18.
• 7 ÷ 11 leaves 7, and 18 ÷ 11 also leaves 7. The remainder is 7: (d).
Why the other options are wrong
- (a) 1
- x + y is 7 or 18, and both leave remainder 7, not 1.
- (b) 3
- x + y is 7 or 18, and both leave remainder 7, not 3.
- (c) 5
- x + y is 7 or 18, and both leave remainder 7, 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.