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

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

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

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

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

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

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

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

If 21y5 is a multiple of 9, where y is a digit, what is the value of y?

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?

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 that6 + 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)

If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?