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?

NCERT - Mathematics

Book: NCERT - Mathematics

Chapter: 16. Playing with Numbers

Subject: Maths - Class 8^th

Q. No. 2 of Exercises 16.2

Listen NCERT Audio Books - Kitabein Ab Bolengi

2

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?

We know that 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 …

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

Therefore, z should be either 0 or 9

2

Chapter Exercises

Exercises 16.1

Exercises 16.2

1

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

2

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?

3

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)

4

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