RBSE Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.2

Rajasthan Board RBSE Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.2 Textbook Exercise Questions and Answers.

RBSE Class 6 Maths Solutions Chapter 3 Playing With Numbers Ex 3.2

Question 1.
What is the sum of any two:
(a) Odd numbers?.
(b) Even numbers?
Answer:
(a) The sum of any two odd numbers is an even number.
Example :3 + 5 = 8; 1 + 9 = 10

(b) The sum of any two even umbers is also
an even number.
Example: 2 + 6 = 8
6 + 10 = 16

Question 2.
State whether the following statements are True or False :
(a) The sum of three odd numbers is even.
Answer:
False

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

(c) The product of three odd numbers is odd.
Answer:
True

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

(e) All prime numbers are odd.
Answer:
False

(f) Prime numbers do not have any factors.
Answer:
False

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

(h) 2 is the only even prime number.
Answer:
True

(i) All even numbers are composite numbers.
Answer:
False

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

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.
Answer:
(i) 17 and 71
(ii) 37 and 73
(iii) 79 and 97

Question 4.
Write down separately the prime and composite numbers less than 20.
Answer:
Prime numbers : 2, 3, 5, 7, 11, 13, 17,19.
Composite numbers : 4, 6, 8, 9, 10,12, 14, 15,16,18.

Question 5.
What is the greatest prime number between 1 and 10?
Answer:
The greatest prime number between 1 and 10 is 7.

Question 6.
Express the following as the sum of two odd primes :
(a) 44
Answer:
44 = 41 + 3 or 7 + 37 or 1

(b) 36
Answer:
36 = 5 + 31 or 13 + 23 or 17 + 19

(c) 24
Answer:
24 = 7 + 17 or 11 + 13 or 5 + 19

(d) 18
Answer:
18 = 5 + 13 or 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.]
Answer:
(i) 3 and 5 (ii) 5 and 7 (iii) 11 and 13

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

Question 9.
Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
Answer:
90,91,92, 93,94, 95, 96.

Question 10.
Express each of the following numbers as the sum of three odd primes:
(a) 21
Answer:
21 = 3 + 7 + 11

(b) 31
Answer:
31 = 3 + 11 + 17

(c) 53
Answer:
53 = 13 + 17+ 23

(d) 61
Answer:
61 = 19 + 29 + 13

Question 11.
Write five pairs of prime numbers less than 20 whose sum is divisible by 5. (Hint: 3 + 7 = 10)
Answer:
3 + 2 = 5
5 + 5 = 10
2 + 13 = 15
7 + 13 = 20
3 + 17 = 20

Question 12.
Fill in the blanks:
(a) A number which has only two factors is called a.....
Answer:
prime number

(b) A number which has more than two factors is called a ..........
Answer:
composite number

(c) 1 is neither..... nor 
Answer:
prime number, composite number

(d) The smallest prime number is ..........
Answer:
2

(e) The smallest composite number is .......
Answer:
4

(f) The smallest even number is ...........
Answer:
2