UPSC Prelims 2026 CSAT, question 60

Topic: Number system

Q60

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?

Solution.

Answer: (d) 7

By the divisibility rule of $11$ for $4x5y790$ , the alternating sum of digits $(0 + 7 + 5 + 4) - (9 + y + x) = 16 - 9 - (x + y) = 7 - (x + y)$ must be a multiple of $11$ .
Therefore, $x + y \equiv 7 \pmod{11}$ , so the remainder when $x + y$ is divided by $11$ is $7$ .