Find all possible digits x, y, z such that the number 13xy45z is divisible
by 792.
I agree with Math Man's answer, but slightly simpler (I think) is the following:
If 13xy456 is divisible by 99, then it is divisible by 9 and by 11.
In order to be divisible by 9, x + y = 8 or 17
In order to be divisible by 11, x - y = -3 or 8
By inspection,
If x + y = 17, then x - y cannot be -3 or 8
If x + y = 8, then x - y cannot be -8
So, x+y = 8 = x-y
The only solution is x = 8, y = 0
Improved method?
