**Download NCERT Solutions for Class 8 Maths Chapter 16 Exercise 16.2 – Playing with Numbers**

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

** Sol.:** – For a number to be a multiple of 9, the sum of digit of the number should be divisible by 9.

So, sum of digit of 21y5 = 2 + 1 + y + 5 = (8 + y)

So, to make (8 + y) divisible by 9, we must put y = 1 (since y is a single digit number)

So,

**y = 1**will make 21y5 a multiple of 9.

**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?**

** Sol.:** – For a number to be a multiple of 9, the sum of digit of the number should be divisible by 9.

So, sum of digit of 31z5 = 3 + 1 + z + 5 = (9 + z)

So, to make (9 + z) divisible by 9, we can put z = 0 or 9(since z is a single digit number).

As we can see, we are getting two values of ‘z’ which we can put to make 31z5 a multiple of 9. So,

**z = 0 or 9**will make 31z5 a multiple of 9.

**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 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.)**

** Sol.:** – For a number to be a multiple of 3, the sum of digit of the number should be divisible by 3.

So, Sum of digit of 24x = 2 + 4 + x = 6 + x

So, to make (6 + x) divisible by 3 we can put x = 0 or 3 or 6 or 9. (since x is a single digit number).

So,

**x = 0 or 3 or 6 or 9**will make 24x a multiple of 3.

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

** Sol.:** – For a number to be a multiple of 3, the sum of digit of the number should be divisible by 3.

So, Sum of digit of 31z5 = 3 + 1 + z + 5 = 9 + z

So, to make (9 + z) divisible by 3 we can put z = 0 or 3 or 6 or 9 (since z is a single digit number).

So,

**z = 0 or 3 or 6 or 9**will make 31z5 a multiple of 3.

**Download NCERT Solutions for Class 8 Maths Chapter 16 Exercise 16.2 – Playing with Numbers**

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