Question

Question 2
If 31z5 is a multiple of 9, where z is a digit, what is the value of z?
You will find that there are two answers for the last problem. Why is this so?

Answer 1

Since, 31z5 is a multiple of 9.
Therefore according to the divisibility rule of 9, the sum of all the digits should be a multiple of 9.

$\therefore 3+1+z+5=9+z\Rightarrow 9+z=9,18,\mathrm{27.......}\Rightarrow z=0orz=9$
Hence 0 and 9 are two possible answers.
Hence 3105 and 3195 both are multiple of 9