Question 1

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

Question 2

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

Question 3

Find the value of the letter in the following and give reasons for the steps involved.

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 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?

Question 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)

Question 14

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