Question

If sum of the digits of any imteger in between 100 and 1000 is subtracted from that integer , then result is always divisible by

Answer 1

It would always be the number 9.

Lets assume the number is xyz where x, y and z are the three digits of the number.

Lets represent this as 100x + 10y + z (Since x is the 100′s unit and y is the 10′s unit).

We now subtract x+y+z from this.

So we get 100x + 10y + z - (x + y + z) which is 99x + 9y or 9 (11x + y).

Since the expression is always multiplied by 9, it has to be divisible by 9.