UPSC Prelims 2026 · CSAT
Question 60: Basic Numeracy
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?
AnswerUPSC’s answer is (d).
A number is divisible by 11 if the sums of its digits in odd and even places differ by a multiple of 11. For 4x5y790, counting from the right, odd places hold 0, 7, 5, 4 (sum 16) and even places hold 9, y, x (sum 9 + x + y). The difference 7 − (x + y) must be a multiple of 11, so x + y = 7 or 18 (the largest possible). Both leave remainder 7 on division by 11.
Why each option is right or wrong
- (a) Wrong: the remainder is 7, not 1.
- (b) Wrong: the remainder is 7, not 3.
- (c) Wrong: the remainder is 7, not 5.
- (d) Right: x + y is 7 or 18, remainder 7.
Only the provisional key (27 May 2026) was found; the final key replaces it when found.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.