Chapter 3 Playing With Numbers Ex 3.2 Solutions
Question - 1 : - What is the sum of any two (a) Odd numbers? (b) Even numbers?
Answer - 1 : -
(a) The sum of two odd numbers is even.
e.g., 1 + 5 = 6
13 + 11 = 24
(b) The sum of two even numbers is even.
e.g., 4 + 8 = 12
12 + 16 = 28
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.
Answer - 2 : -
(a) False 3 + 5 + 7 = 15, i.e., odd
(b) True 3 + 5 + 6 = 14, i.e., even
(c) True 3 × 5 × 7 = 105, i.e., odd
(d) False 4 ÷ 2 = 2, i.e., even
(e) False 2 is a prime number and it is also even
(f) False 1 and the number itself are factors of the number
(g) False 2 + 3 = 5, i.e., odd
(h) True
(i) False 2 is a prime number
(j) 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 up to 100.
Answer - 3 : -
17, 71
37, 73
79, 97
Question - 4 : - Write down separately the prime and composite numbers less than 20.
Answer - 4 : -
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?
Answer - 5 : -
Prime numbers between 1 and 10 are 2, 3, 5, and 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
Answer - 6 : -
(a) 44 = 37 + 7
(b) 36 = 31 + 5
(c) 24 = 19 + 5
(d) 18 = 11 + 7
Question - 7 : - Give three pairs of prime numbers whose difference is 2.
Answer - 7 : -
3, 5
41, 43
71, 73
Question - 8 : - Which of the following numbers are prime?
(a) 23 (b) 51 (c) 37 (d) 26
Answer - 8 : -
(a) 23 23 = 1 × 23 23 = 23 × 1
23 has only two factors, 1 and 23. Therefore, it is a prime number.
(b) 51 51 = 1 × 51 51 = 3 × 17
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. Therefore, 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.
Answer - 9 : -
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
Answer - 10 : -
(a) 21 = 3 + 7 + 11
(b) 31 = 5 + 7 + 19
(c) 53 = 3 + 19 + 31
(d) 61 = 11 + 19 + 31