# Playing with Numbers

**Exercise 1**

Find the values of the letters in each of the following and give reasons for the steps involved.

**Exercise 2**

**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?