NCERT Class 6 Mathematics Third Chapter Playing with Numbers Exercise 3.2 Solutions
EXERCISE 3.2
(1) What is the sum of any two
(a) Odd numbers? = Even numbers
(b) Even numbers? = Even numbers
(2) State whether the following statements are True or False:
(a) The sum of three odd numbers is even. = F
(b) The sum of two odd numbers and one even number is even. = T
(c) The product of three odd numbers is odd. = T
(d) If an even number is divided by 2, the quotient is always odd. = F
(e) All prime numbers are odd. = F
(f) Prime numbers do not have any factors. = F
(g) Sum of two prime numbers is always even. = F
(h) 2 is the only even prime number. = T
(i) All even numbers are composite numbers. = F
(j) The product of two even numbers is always even. = T
(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.
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: 2, 3, 5, 7, 11, 13, 17, 19
Composite numbers: 4, 6, 8, 10, 12, 14, 15, 16, 18
(5) What is the greatest prime number between 1 and 10?
Solution: 7
(6) Express the following as the sum of two odd primes.
(a) 44 = (41 + 3)
(b) 36 = (31 + 5)
(c) 24 = (19 +5)
(d) 18 = (13 + 5)
(7) Give three pairs of prime numbers whose difference is 2. [Remark: Two prime numbers whose difference is 2 are called twin primes].
Solution: 3, 5; 5, 7; 11, 13
(8) Which of the following numbers are prime?
(a) 23 = Prime
(c) 37 = Prime
(9) Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
Solution: 90, 91, 92, 93, 94, 95, 96
(10) Express each of the following numbers as the sum of three odd primes:
(a) 21 = 3 + 5 + 13
(b) 31 = 3 + 5 + 23
(c) 53 = 13 + 17 + 23
(d) 61 = 7 + 13 + 41
(11) Write five pairs of prime numbers less than 20 whose sum is divisible by 5.
Ans: 2, 3; 2, 13; 3, 17; 7, 13, 11, 19
(12) Fill in the blanks:
(a) A number which has only two factors is called a prime number.
(b) A number which has more than two factors is called a composite number.
(c) 1 is neither prime number nor composite number.
(d) The smallest prime number is 2.
(e) The smallest composite number is 4.
(f) The smallest even number is 2.
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