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Detailed Solutions for NCERT Class 6th Mathematics Chapter 3 – Playing with Numbers – Exercise 3.2

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Questions and Solutions for NCERT Class 6th Mathematics Chapter 3 – Playing with Numbers – Exercise 3.2

1. What is the sum of any two (a) Odd numbers? (b) Even numbers?

Ans: (a) The sum of any two odd numbers is an even number.

For Example: 1 +3 = 4

5 + 11 = 16

(b) The sum of any two even numbers is an even number.

For Example: 2 + 4 = 6

12 + 8 = 20

2. State whether the following statements are True or False:

(a) The sum of three odd numbers is even.

Ans: False, because sum of three odd numbers is a an odd number.

Example: 5 +1 + 7 = 13

(b) The sum of two odd numbers and one even number is even.

Ans: True

Example: 3 + 1 + 4 = 8

(c) The product of three odd numbers is odd.

Ans: True

Example: 1*3*5 = 15

(d) If an even number is divided by 2, the quotient is always odd.

Ans: False, because the quotient will be even number.

Example: 8/2 = 4

(e) All prime numbers are odd.

Ans: False, because 2 is an even number.

(f) Prime numbers do not have any factors.

Ans: False, because prime numbers have two factors – 1 and the number itself.

(g) Sum of two prime numbers is always even.

Ans: False, because sum of 2 + 3 = 5, is an odd number.

(h) 2 is the only even prime number.

Ans: True

(i) All even numbers are composite numbers.

Ans: False

(j) The product of two even numbers is always even.

Ans: True

For example: 2*6 = 12

3. The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers upto 100.

Ans: 17 and 71, 37 and 73, 79 and 97

4. Write down separately the prime and composite numbers less than 20.

Ans: Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19

Composite Number: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

Imp: 1 is neither prime nor composite.

5. What is the greatest prime number between 1 and 10?

Ans: The greatest prime number between 1 and 10 is 7

6. Express the following as the sum of two odd primes.

(a) 44

Ans: 37 + 7 = 44

(b) 36

Ans: 23 + 13 = 36

(c) 24

Ans: 19 + 5 = 24

(d) 18

Ans: 15 + 3 = 18

7. Give three pairs of prime numbers whose difference is 2. [Remark : Two prime numbers whose difference is 2 are called twin primes].

Ans: 7 and 5, 13 and 11 and 19 and 17

8. Which of the following numbers are prime?

(a) 23

Ans: 23 is a prime number.

(b) 51

Ans: 51 is not a prime number.

(c) 37

Ans: 37 is a prime number.

(d) 26

Ans: 26 is not a prime number.

9. Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

Ans: 90, 91, 92, 93, 94, 95, 96

10. Express each of the following numbers as the sum of three odd primes:

(a) 21

Ans: 3 + 7 + 11 = 21

(b) 31

Ans: 3 + 11 + 17 = 31

(c) 53

Ans: 13 + 17 +23 = 53

(d) 61

Ans: 13 + 19 + 29 = 61

11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5. (Hint : 3+7 = 10)

Ans: 2+3 = 5

3 + 7 = 10

2 + 13 = 15

17 + 3 = 20

5 + 5 = 10

12. Fill in the blanks :

(a) A number which has only two factors is called a Prime Number.
(b) A number which has more than two factors is called a Composite Number.
(c) 1 is neither Prime Number nor Composite Number.
(d) The smallest prime number is 2.
(e) The smallest composite number is 4.
(f) The smallest even number is 2.

You can find the solutions for Class 6 Mathematics previous exercises from here

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