EXERCISE 3.2

1.) What is the sum of any two:
a) Odd numbers
Ans.The sum of any two odd numbers is always an even number
eg:  3 + 5 = 8 ,   5 +7 = 12 ,   13 +11 = 24
b) Even numbers
Ans.The sum of any two even numbers is always an even number.
eg:  8 + 6 = 14 ,   12 + 14 = 26 ,   2 + 4 = 6

2). State, whether the following 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.
Ans.
a) False. Eg. 3 + 5 + 7 = 15
b) True. 3 + 5 + 6 = 14
c) True. 3 x 7 x 9 = 189
d) False. Eg. 8 ÷ 2 = 4 which is an even number.
e) False. 2 is a prime number which is even.
f) False. since 1 and the number itself are factors of the number.
g) False. Eg. 2 + 3 = 5 is an odd number.
h) True
i) False. since 2 is even and is a prime number.
j) True. 4 x 6 = 24.

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.
Ans.           17 and 71 , 37 and 73 , 79 and 97

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

5). What is the greatest prime number between 1 and 10?
Ans.           7.

6). Express the following as the sum of two odd primes.
a) 44
Ans.                3 + 41 = 44  , 7+37 = 44 and so on.
b) 36
Ans.                5 + 31 = 36 ,  9+ 27 = 36 and so on.
c) 24
Ans.                5 + 19 = 24 ,  3+21 = 24 and so on.                                                                                         d) 18
Ans.                7 + 11 = 18 ,  5 + 13 = 18 and so on.

7). Give three pairs of prime numbers whose difference is 2.
Ans.    i) 19 – 17 = 2               ii) 7 – 5 = 2                  iii) 13 – 11 = 2

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

a) 23
Ans.
1 x 23 = 23
23 x 1 = 23
Since 23 has only 2 factors 1 and 23, it is a prime number.

b) 51
Ans.
1 x 51 = 51
3 x 17 = 51
Since 51 has four factor 1, 3, 17 and 51 it is a composite number.

c) 37
Ans.
1 x 37 = 37
37 x 1 = 37
Since 37 has only 2 factors 1 and 37, it is a prime number.

d) 26
Ans.
1 x 26 = 26
2 x  13 = 26
Since 26 has four factors 1, 2, 13 and 26 it is a composite number.

9). Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
Ans.Seven consecutive composite numbers less than 100 that lie between 89 and 97 are 90, 91, 92, 93, 94, 95 and 96.
All these numbers have the following factors.

1. 90 ⇒ 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
2. 91 ⇒ 1, 7, 13, 91
3. 92 ⇒ 1, 2, 4, 23, 46, 92
4. 93 ⇒ 1, 3, 31, 93
5. 94 ⇒ 1, 2, 47, 94
6. 95 ⇒ 1, 5, 19, 95
7. 96 ⇒ 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 .Hence  they are called composite numbers                                                                                                                                                                         8.Express each of the following numbers as the sum of three odd primes:

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

11) .Write five pairs of prime numbers below 20 whose sum is divisible by 5.
(Hint : 3 + 7 =10)
Ans.
2 + 3 = 5
2 + 13 = 15
3 + 17 = 20
7 + 13 = 20
19 + 11 = 30
Therefore, the pairs are 2, 3; 2, 13; 3, 17; 7, 13; 19, 11.

12). Fill in the blanks
a) A number which has only two factors is called………………
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……………….

Ans.
a) prime number
b) composite number
c) prime number, composite number                                                                                                              d) 2
e) 4
f) 2