## MP Board Class 6th 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?

Solution:

(a) The sum of any two odd numbers is an even number.

As like, 1 + 3 = 4, 3 + 5 = 8

(b) The sum of any two even numbers is an even number.

As like, 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 the only even prime number.

(i) All even numbers are composite numbers.

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

Solution:

(a) False

Since, sum of two odd numbers is even and sum of one odd number and one even number is always odd.

(b) True

Since, sum of two odd numbers is even and sum of two even numbers is always even.

(c) True

(d) False

If an even number is divided by 2, then the quotient is either odd or even.

(e) False

Since, prime number 2 is even.

(f) False

Factors of prime numbers are 1 and the number itself.

(g) False

Sum of two prime numbers is either even or odd.

(h) True

(i) False

Since, even number 2 is prime i.e., not composite.

(j) 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.

Solution:

Pairs of prime numbers having same digits upto 100 are 17 and 71; 37 and 73; 79 and 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:

The greatest prime number between 1 and 10 is 7.

Question 6.

Express the following as the sum of two odd primes.

(a) 44

(b) 36

(c) 24

(d) 18

Solution:

(a) 44 = 3 + 41

(b) 36 = 5 + 31

(c) 24 = 7 + 17

(d) 18 = 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:

Three pairs of prime numbers whose difference is 2 are 3 and 5; 5 and 7; 11 and 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 and 51 and 26 are composite numbers.

Thus, numbers in option (a) and (c) are prime.

Question 9.

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

Solution:

Seven consecutive composite numbers less than 100 are 90, 91, 92, 93, 94, 95, 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 = 3 + 11 + 17

(c) 53 = 13 + 17 + 23

(d) 61 = 13 + 19 + 29

Question 11.

Write five pairs of prime numbers less than 20 whose sum is divisible by 5.

(Hint :3 + 7 = 10)

Solution:

Since, 2 + 3 = 5; 7 + 13 = 20; 3 + 17 = 20; 2 + 13 = 15; 5 + 5 = 10 and 5, 10, 15, 20 all are

divisible by 5.

So, five pairs of prime numbers less than 20 whose sum is divisible by 5 are 2, 3; 2, 13; 3, 17; 7, 13; 5, 5.

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:

(a) Prime number

(b) Composite number

(c) Prime number, composite number

(d) 2

(e) 4

(f) 2