Playing with Numbers
Find the values of the letters in each of the following and give reasons for the steps involved.
11. If 21y5 is a multiple of 9, where y is a digit, what is the value of y ?
12. 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?
13. 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.)
14. If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?