# Ncert Class 6 Math Playing With Numbers Exercise 3.2

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