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!
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