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## Karnataka State Syllabus Class 6 Maths Chapter 3 Playing with Numbers Ex 3.2

Question 1.

What is the sum of any two

a) odd numbers

b) Even numbers?

Solution:

a) The sum of two odd numbers is even

eg:- 1 + 5 = 6; 16 + 18 = 34

b) The sum of two even numbers is even

eg:- 4 + 2 = 6; 10 + 18 = 28

Question 2.

State whether the following statements are True or False:

Solution:

a) The sum of three odd numbers is even.

False 3 + 5 + 7 = 15. i,e. odd

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

True 3 + 5 + 6 = 14 i,e = even

c) The product of three odd numbers is odd.

True 3 × 5 × 7 = 105 i.e, odd.

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

False 4 ÷ 2 = 2 i.e, even

e) All prime numbers are odd.

False; 2 is even number.

f) Prime numbers do not have any factors.

False; 1 and the numbers itself are factors of the number.

g) Sum of two prime numbers is always even.

False 2 + 3 = 5 i,e odd

h) 2 is the only even prime number.

True

i) All even numbers are composite numbers.

False, 2 is a prime numbers.

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

True; 2 × 4 = 8, i.e 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 upto 100.

Solution:

a) 17, 71

b) 37, 73

c) 79, 97

Question 4.

Write down separately the prime and composite numbers less than 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:

Prime numbers between 1 and 10 are 2, 3, 5, 7 among these numbers 7 is the greatest.

Question 6.

Express the following as the sum of two odd primes,

a) 44

b) 36

c) 24

d) 18

Solution:

a) 44 = 37 + 7 = 13 + 31

b) 36 = 31 + 5 = 17 + 19

c) 24 = 19 + 5 = 11 + 13

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

iv) 17 & 19

v) 29 & 31 etc.

Question 8.

Which of the following numbers are prime?

a) 23

b) 51

c) 37

d) 26

Solution:

a) 23 = 23 × 1 = 23; 23 = 1 × 23

23 has only two factors, 1 and 23 Therefore, it is a prime numbers

b) 5 = 1 × 51 = 51; 51 = 17 × 3

51 has four factors, 1, 3, 17, 51. Therefore, it is not a prime number, it is a composite number.

c) 37 It has only two factors 1 and 37.

It is a prime number

d) 26 26 has four factors (1, 2, 13, 26)

Therefore, it is not a prime number It is a composite number

Question 9.

Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

Solution:

Between 89 and 97, both of which are prime numbers there are 7 composite numbers.

They are 90, 91, 92, 93, 94, 95, 96, numbers factors

90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

91 = 1, 7, 13, 91

92 = 1, 2, 4, 23, 46, 92

93 = 1, 3, 31, 93

94 = 1, 2, 47, 94

95 = 1, 5, 19, 95

96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 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 + 7 + 11

b) 31 = 5 + 7 + 19

c) 53 = 3 + 19 + 31

d) 61 = 11 + 19 + 31

Question 11.

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

Solution:

The five pair of prime numbers less than 20 divisible by 5 are 2 + 3 = 5

2 + 13 = 15

3 + 17 = 20

7 + 13 = 20

19 + 11 = 30

Question 12.

Fill in the blanks:

1. A number which has only two factors is called a prime number

2. A numbers 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