question_answer 3)

                If \[24x\] is a multiple of 3, where \[x\] is a digit, what is the value of \[x\]? (Since \[24x\] is a multiple of 3, its sum of digits \[6+x\] is a multiple of 3; so \[6+x\] is one of these numbers: 0, 3, 6, 9, 12, 15, 18, ... .But since \[x\] is a digit, it can only be that \[6+x=6\] or 9 or 12 or 15. Therefore, \[x=0\] or 3 or 6 or 9. Thus, \[x\] can have any of four different values.)

Answer:

                Solution given with question.                 If \[31z5\] is a multiple of 3, where z is a digit, what might be the values of z?                 Since \[31z5\] is a multiple of 3, its sum of digits \[3+1+z+5=9+z\] is a multiple of 3; so \[9+z\] is one of these numbers: 0, 3, 6, 9, 12, 15, 18, ... . But since z is a digit, it can only be that \[9+z=9\] or 12 or 15 or 18. Therefore, z = 0 or 3 or 6 or 9.