If x denotes the digit at hundreds place of the number such that the number is divisible by 11. Find all possible values of x.

Question

Philoid · Accepted Answer

Here, given number is .

We know that a number is divisible by 11 if and only if the difference between the sum of odd and even place digits is a multiple of 11.

∴ Sum of even placed digits – Sum of odd placed digits = 0, 11, 22,…

∴ (6 + x + 9) – ( 7+1) = 0, 11, 22,…

∴ x + 7 is a multiple of 11

∴ x + 7 = 11

∴ x = 4