## Chapter 3: Playing With Numbers

## Exercise 3.2

**Q1. 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: 1 + 7 = 8, 7 + 5 = 12

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

Example: 2 + 6 = 8, 6 + 4 = 10

**Q2. 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. **

**Answer. **

(a) False

(b) True

(c) True

(d) False

(e) False

(f) False

(g) False

(h) True

(i) False

(j) True

**Q3. The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to 100. **

**Answer.** Pairs are

17 and 71

37 and 73

79 and 97

**Q4. 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

**Q5. What is the greatest prime number between 1 and 10? **

**Answer.** The greatest prime number between 1 and 10 is ‘**7**’.

**Q6. Express the following as the sum of two odd numbers: **

**(a) 44 **

**(b) 36 **

**(c) 24 **

**(d) 18 **

**Answer. **

(a) 3 + 41 = 44

(b) 5 + 31 = 36

(c) 7 + 17 = 24

(d) 7 + 11 = 18

**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. **

3 and 5

5 and 7

11 and 13

**Q8. Which of the following numbers are prime: **

**(a) 23 **

**(b) 51 **

**(c) 37 **

**(d) 26 **

**Answer.**

(a) 23 and (c) 37

**Q9. Write seven consecutive composite numbers less than 100 so that there is no prime number between them. **

**Answer.** Seven consecutive composite numbers: 90, 91, 92, 93, 94, 95, 96

**Q10. 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 + 7 + 11

(b) 31 = 3 + 11 + 17

(c) 53 = 13 + 17 + 23

(d) 61 = 19 + 29 + 13

**Q11. Write five pairs of prime numbers less than 20 whose sum is divisible by 5. **

**[Hint: 3 + 7 = 10] **

**Answer.**

2 + 3 = 5

7 + 13 = 20

3 + 17 = 20

2 + 13 = 15

5 + 5 = 10

**Q12. 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 neither _______________ nor _______________. **

**(d) The smallest prime number is _______________. **

**(e) The smallest composite number is _______________. **

**(f) The smallest even number is _______________.**

**Answer.**

(a) Prime number

(b) Composite number

(c) Prime number and composite number

(d) 2

(e) 4

(f) 2