**Playing With Numbers Class 6 Ex. 3.2**

**Ncert Class 6 Math Free Solution.**

**Exercise 3.2**

**Question 1 :- What is the sum of any two :-**

**(a) Odd numbers ?**

**(b) Even numbers ?**

**Solution 1:-**

(a) Sum of any 2 odd numbers is an even number.

For Example:- 1 + 3 = 4, 3 + 5 = 8

(b) Sum of any 2 even numbers is also an even number.

For Example:- 2 + 4 = 6, 6 + 8 = 14

**Question 2 :- State whether the following statements are True or False :-**

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

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

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

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

**(e) All prime numbers are odd.**

**(f) Prime numbers do not have any factors.**

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

**(h) 2 is only the even prime number.**

**(i) All even numbers are composite numbers.**

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

**Solution 2:- **

(а) False [For example:- 3 + 5 + 7 = 15 (odd)]

(b) True [For example:- 3 + 5 + 6 = 14 (even)]

(c) True [For example:- 5 x 7 x 9 = 315 (odd)]

(d) False [For example:- 12 + 2 = 6 (even)]

(e) False [For example:- 2 is a prime number but it is even]

(f) False [For example:- 3 is a prime number having 1 and 3 as its factors]

(g) False [For example:- 7 + 2 = 9 (odd)]

(h) True [For example:- 2 is even and the lowest prime number]

(i) False [For example:- 2 is even number but not composite number]

(j) True [For example:- 4 x 6 = 24 (even)]

**Question 3 :-The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to 100.**

**Solution 3:-**

The necessary pair of prime numbers with the same digits is as follows:

(17, 71); (37, 73); and (79, 97).

**Question 4 :- Write down separately the prime and composite numbers less than 20.**

**Solution 4:-**

Prime numbers less than 20 are:

2, 3, 5, 7, 11, 13, 17 , 19.

Composite numbers less than 20 are:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

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

**Solution 5:-**

Seven is the largest prime number between one and ten.

**Question 6 :- Express the following as the sum of two odd primes.**

**(a) 44**

**(b) 36**

**(c) 24**

**(d) 18**

**Solution 6:-**

(a) 44 = 3 + 41

(b) 36 = 5 + 31

(c) 24 = 5 + 19

(d) 18 = 5 + 13

[This could be one of the ways. There can other ways also]

**Question 7 :- Give three pairs of prime numbers whose difference is 2.**

**{Remark: Two prime numbers whose difference is 2 are called twin primes}**

**Solution 7:-**

three pairs of prime numbers whose difference 2 are: (3 and 5); (5 and 7); and (11 and 13).

**Question 8 :- Which of the following numbers are prime?**

**(a) 23**

**(b) 51**

**(c) 37**

**(d) 26**

**Solution 8:-**

(a) 23 is a prime number [ because of 23 = 1 x 23]

(b) 51 is not a prime number [because of 51 = 1 x 3 x 17]

(c) 37 is a prime number [because of 37 = 1 x 37]

(d) 26 is not a prime number [because of 26 = 1 x 2 x 13]

So, clearly (a) and (c) are prime numbers.

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

**Solution 9:-**

The numbers which is required are:

90, 91, 92, 93, 94, 95 and 96

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

**(a) 21**

**(b) 31**

**(c) 53**

**(d) 61**

**Solution 10:-**

(a) 21 can be expressed as 3 + 5 + 13

(b) 31 can be expressed as 5 + 7 + 19

(c) 53 can be expressed as 13 + 17 + 23

(d) 61 can be expressed as 11 + 13 + 37

**Question 11 :- Write five pairs of prime numbers less than 20 whose sum is divisible by 5.**

**(Hint: 3 + 7 = 10)**

**Solution 11:-**

The required pairs of prime numbers less than 20 are:

(i) 2 + 3 = 5

(ii) 2 + 13 = 15

(iii) 11 + 9 = 20

(iv) 17 + 3 = 20

(v) 7 + 13 = 20

**Question 12 :-Fill in the blanks.**

**(a) A number which has only two factors is called a ………… .**

**(b) A number which has more than two factors is called a ………… .**

**(c) 1 is neither ………… nor ………… .**

**(d) The smallest prime number is ………… .**

**(e) The smallest composite number is ………… .**

**(f) The smallest even number is ………… .**

**Solution 12:-**

(a) prime number

(b) composite number

(c) prime number, composite number

(d) 2

(e) 4

(f) 2

**Playing With Numbers Class 6 Exercise. 3.2 for Free**