When we write a three-digit number in base-ten we are really saying "so many hundreds", "so many tens" and "so many units". If our number is n and the digits are represented by x, y and z (reading from left to right) then we can write:

n = 100x + 10y + z

We are told that

y = x + z

Therefore

n = 100x + 10(x + z) + z

n = 110x + 11z

n = 11(10x + z)

therefore n must be divisible by 11!