# Playing with Numbers| Worksheet Solutions| Class 8

Worksheet solutions for chapter: Playing with Numbers for class 8 are provided below.

(1) 12, 16, 18, 20, 22 can be divisible from 2.

Ans-

Yes, these numbers will be divided by 2 as they have 2, 6, 8 and 0 at their ones place.

(2) 15, 20, 25, 30… can be divisible from 5?

Ans-

Yes, these numbers will be divided by 5 as they have 5and 0 at their ones place alternatively.

(3) If 31z3 is a multiple of 9, where z is a digit, what is the value of z?

Ans-

Sum of digit = 3 + 1 + z + 3 should be divisible by 9[ 31z3 is a multiple of 9]

7 + z should be divisible by 9.

It can be possible when 7 + z = 9 or18, …

But, z is a single digit, therefore,

If 7 + z = 9

z = 9 – 7

z = 2 required digit

If 7 + z = 18

z = 18 – 7

z = 11 not required digit, ie, double digit number

Hence, value of z is 2.

Find the values of the letters in each of the following and give reasons for the steps involved.

(4) 2  5

+  1 A

3  7

Ans-

Condition for ones place: If we add A + 5, we get 7 at ones place.

Therefore, we have to add 5 and 2.

A + 5 = *7

5 + 2 =*7

Therefore, puzzle is solved as presented below:-

2 5

+1 2

3 7

Hence, A = 2

(5)  3 4

× 2

6  A

Ans-

Condition for ones place: 4 2 = 8

Therefore, puzzle is solved as presented below:-

3 4

× 2

6 8

Hence, A = 8

(6) 3 5 A

+ A 2 B

5  7  5

Ans-

Condition for ones place: A  + B = 5

Therefore, we have to add 2 with 3.

2 + 3 = 5, ie, 5 comes at ones place.

Condition for hundreds place: 3 + A = 5

Therefore,

3 + 2 = 5

Therefore, puzzle is solved as presented below:-

3 5 2

+2 2 3

5 7 5

Hence, A = 2 and B = 3

(7) If 32z is a multiple of 3, where z is a digit, what is the value of z? Ramesh calculated value of z 1 while another student Radha calculated value of z 4. Find which answer is correct?

Ans-

Sum of digit = 3 + 2 + z should be divisible by 3[ 31z3 is a multiple of 3]

5 + z should be divisible by 3.

It can be possible when 5 + z = 6 or 9, …

But, z is a single digit, therefore,

If 5 + z = 6

z = 6 – 5

z = 1 required digit

If 5 + z = 9

z = 9 – 5

z = 4 required digit, ie, double digit number

Hence, value of z is 1 and 4. Therefore, Ramesh and Radha both calculated correct values.

(8) If 3 4 A

+1 A 1

4  9 6  Value of A is

(i) 5

(ii) 0

(iii) 4

Ans-

(i) 5

(9) 34268 can be divided by

(i) 2

(ii) 3

(iii) 5

Ans-

(i) 2

(10) 5623 can be divided by

(i) 9

(ii) 5

(iii) none of the above

Ans-

(iii) none of the above

Helping Topics

Playing with Numbers

NCERT Solutions Class 8