CBSE Class 6th ( VI) Mathematics Chapter 3. Playing with Numbers :Exercise 3.2

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. i.e. 1+3=4, 3+5=8, 5+7=12
(a) The sum of any two even numbers is an Even number. i.e. 2+4=6, 4+6=10, 12+8=20

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

1. The sum of three odd numbers is even.
2. The sum of two odd numbers and one even number is even.
3. The product of three odd numbers is odd.
4. If an even number is divided by 2, the quotient is always odd.
5. All prime numbers are odd.
6. Prime numbers do not have any factors.
7. Sum of two prime numbers is always even.
8. 2 is the only even prime number.
9. All even numbers are composite numbers.
10. The product of two even numbers is always even

Answer:

1. The sum of three odd numbers is even.[False] i.e. 1+3+5 = 9 which is odd number
2. The sum of two odd numbers and one even number is even.[True] i.e. 3+5+2=10, 7+9+4=20
3. The product of three odd numbers is odd.[True] i.e. 3×5×7=105
4. If an even number is divided by 2, the quotient is always odd.[False] i.e. 12÷2=6 which is an even
   number
5. All prime numbers are odd.[False] i.e. 2 is a Prime number but at the same time is also a even number
6. Prime numbers do not have any factors.[False] i.e.Prime numbers have always 2 factors - 1 and number itself
7. Sum of two prime numbers is always even.[False] i.e. 2 + 3 = 5 which is not an even number
8. 2 is the only even prime number.[True] Because 2 is divisible by 2 and it has two factors - 1 and 2
9. All even numbers are composite numbers.[False] Because 2 is even number which has two factors only i.e. 1 & 2   where as composite number always has more than two factor
10. The product of two even numbers is always even[True] i.e. 4×6=24 or 6×8=48

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:

1. 17 and 71
2. 37 and 73
3. 79 and 97

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

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

6. Express the following as the sum of two odd primes.
(a) 44 (b) 36 (c) 24 (d) 18
Answer:

(a) 44	= 3 + 41
(b) 36	= 5 + 31
(c) 24	= 7 + 17
(d) 18	= 7 + 11

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	as 3 and 5 are prime number and their difference i.e. 5 −3=2, hence are twin primes
(ii) 5 and 7	as 5 and 7 are prime number and their difference i.e. 7 −5=2 hence are twin primes
(iv) 11 and 13	as 11 and 13 are prime number and their difference i.e. 13 −11=2   hence  twin primes

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

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

10. Express each of the following numbers as the sum of three odd primes:
(a) 21 (b) 31 (c) 53 (d) 61
Answer

(a) 21	= 3 + 5 + 13
(b) 31	= 3 + 5 + 23
(c) 53	= 13 + 17 + 23
(d) 61	= 7 + 13 + 41

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

3+7 = 10 which is divisble by 5 2+13= 15 which is divisble by 5 7+13 = 20 which is divisble by 5 3+17 = 20 which is divisble by 5 1+19 = 20 which is divisble by 5

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 ______.

Answer:

1. A number which has only two factors is called a prime number.
2. A number which has more than two factors is called a composite number.
3. 1 is neither prime number nor composite number.
4. The smallest prime number is 2.
5. The smallest composite number is  4.
6. The smallest even number is  2.