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?
Answer & explanation
Answer: (d) 7
For divisibility by 11, the alternating digit sums must differ by a multiple of 11. Here that gives 7 − (x + y) ≡ 0 (mod 11), so x + y leaves remainder 7 when divided by 11.
- Digits from the right: 0, 9, 7, y, 5, x, 4.
- Odd places (1st, 3rd, 5th, 7th): 0 + 7 + 5 + 4 = 16.
- Even places (2nd, 4th, 6th): 9 + y + x.
- 16 − (9 + x + y) = 7 − (x + y) must be a multiple of 11.
- So x + y = 7 or 18; either way the remainder on division by 11 is 7.
- Check: x = 0, y = 7 gives 4057790 = 11 × 368890.
Remember · Divisibility by 11: (sum of digits in odd places) − (sum in even places) must be 0 or a multiple of 11.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·