question_answer 1)

                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:

                Since \[31z5\] is a multiple of 9, its sum of digits \[3+1+z+5=9+z\] is a multiple of 9; so \[9+z\] is one of these numbers: 0, 9, 18, 27, 36, 45, ... But since z is a digit, it can only be that \[9+z=9\] or 18. Therefore, \[z=0\] or 9.