**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 21*y*5 is a multiple of 9, where *y* is a digit, what is the value of *y*?

**Question 12**

If 31*z*5 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 24*x* is a multiple of 3, where *x* is a digit, what is the value of *x*?

(Since 24*x* 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 31*z*5 is a multiple of 3, where *z* is a digit, what might be the values of *z*?

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