HBSE 6th Class Maths Solutions Chapter 3 Playing With Numbers Ex 3.2

Haryana State Board HBSE 6th Class Maths Solutions Chapter 3 Playing With Numbers Ex 3.2 Textbook Exercise Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 3 Playing With Numbers Exercise 3.2

Question 1.
What is the sum of any two (a) odd numbers and (b) even numbers ?
Solution:
(a) The sum of any two odd numbers is even and
(b) Sum of any two even numbers is also even.

Question 2.
State whether the following statements are true of false :
(a) The sum of three odd numbers is even.
(b) The sum of t wo 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 num bers are odd.
(f) Prime numbers do not. have any factors.
(g) Sum of two prime numbers is always even.
(h) 2 is the only even prime number.
(i) All even numbers are composite numbers.
(j) The product of two even numbers is always even.
Solution:
(a) F (b) T (c) T (d) F (e) F (f) F (g) F (h) T (i) F (j) T.

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 upto 100.
Solution:
17 and 71; 37 and 73; 79 and 97 are such pairs of prime numbers upto 100.

Question 4.
Write down separately the prime and composite numbers less that 20.
Solution:

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:

7 is the greatest prime number between 1 and 10.

Question 6.
Express the following as the sum of two odd primes :
(a) 44
(b) 36
(c) 24
(d) 18
Solution:
(a) 44 = 13 + 31 = 3 + 41
(b) 36 = 13 + 23 = 5 + 31
(c) 24 = 11 + 13 = 5 + 19
(d) 18 = 5 + 13 = 7 + 11.

 

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:
(i) (3, 5) (ii) (5, 7) (iii) (11, 13).

Question 8.
Which of the following numbers are prime ?
(a) 23
(b) 51
(c) 37
(d) 26.
Solution:
23 and 37 are prime numbers.

Question 9.
Write seven consecutive com¬posite numbers less than 100- so that there is no prime number between them.
Solution:
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:
(a) 21 = 3 + 5 + 13
(b) 31 = 3 + 5 + 23
(c) 53 = 3 + 7 + 43
(d) 61 = 3 + 5 + 53 = 7 + 13 + 41

Question 11.
Write five pairs of prime numbers below 20 whose sum is divisible by 5.
Solution:
(i) 2 + 3 = 5
(ii) 3 + 7 = 10
(iii) 2 + 13 = 15
(iv) 3 + 17 = 20
(v) 7 + 13 = 20.

Question 12.
Fill in the blanks in the following:
(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:
(a) Prime number
(b) Composite number.
(c) Prime, Composite
(d) 2
(e) 4
(f) 2.