Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2 Questions and Answers.

## Gujarat Board Textbook Solutions Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2

Question 1.

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

Solution:

∵ We have 2 + 1 + y + 5 = 8 + y

21y5 is a multiple of 9,

∴ (8 + y) must be divisible by 9.

∴ (8 + y) should be 0, 9, 18, 27, …, etc.

∴ 8 + y = 0 is not required.

Since, y is a digit

8 + y = 9 ⇒ y = 9 – 8 or y = 1

Question 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?

Solution:

We have 3 + 1 + z + 5 = 9 + z

∵ 31z5 is divisible by 9.

∴ (9 + z) must be equal to 0, or 9 or 18 or 27, … But z is a digit.

∴ 9 + z = 0 or 9 + z = 18

If 9 + z = 0, then z = -9 (which is not required since z is a digit) and if 9 + z = 18, then z = 9.

Question 3.

If 24x is a multiple of 3, where x is a digit, what is the value of x?

Solution:

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 4.

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

Solution:

We have 3 + 1 + z + 5 = 9 + z

∵ 31z5 is divisible by 3.

∴ (9 + z) must be divisible by 3.

i.e. (9 + z) = 0 or 3 or 6 or 9 or 15 or 18 since, z is a digit.

∴ If 9 + z = 0, then z = -9.

If 9 + z = 3, then z = -6.

If 9 + z = 6, then z = -3.

If 9 + z = 9, then z = 0.

If 9 + z = 12, then z = 3.

If 9 + z = 15, then z = 6.

If 9 + z = 18, then z = 9.

If 9 + z = 21, then z = 12.

∴ Possible values of z are 0, 3, 6 or 9.