# 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?

**Solution:**

We know that, according to divisibility rules, if the sum of all the digits of a number is equal to 9 or its multiples, then the number is a multiple of 9.

- If a number is a multiple of 9, then the sum of its digits will be divisible by 9.
- Sum of digits of 31z5 = 3 + 1 + z + 5 = 9 + z
- Hence, 9 + z should be a multiple of 9.
- This is possible when 9 + z is any one of these numbers 0, 9, 18, 27,... and so on.

However, since z is a single-digit number, this sum can be either 9 or 18.

Therefore, 9 + z = 9 or 9 + z = 18

If 9 + z = 9 ⇒ z = 0

If 9 + z = 18 ⇒ z = 9

There are two answers to this problem because for z to be a single digit number, the sum of the digits can either be 9 or 18.

Therefore, z can take two values, either 0 or 9.

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 16

**Video Solution:**

## 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?

Class 8 Maths NCERT Solutions Chapter 16 Exercise 16.2 Question 2

**Summary:**

If 31z5 is a multiple of 9, where z is a digit, the value of z should be either 0 or 9. There are two answers to this problem because for z to be a single digit number, the sum of the digits can either be 9 or 18.

**☛ Related Questions:**

- 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.)
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