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 to the last problem. Why is this so?

Dear Student

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.
3 + 1 + z + 5 = 9 + z
Therefore, 9 + z is a multiple of 9.
This is only possible when 9 + z is any one of these numbers: 0, 9, 18, 27, and so on.
This implies, 9 + 0 = 9 and 9 + 9 = 18
Hence 0 and 9 are two possible answers.

Thanks