Well-designed AP 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise 3.2 offers step-by-step explanations to help students understand problem-solving strategies.
Playing with Numbers Class 6 Exercise 3.2 Solutions – 6th Class Maths 3.2 Exercise Solutions
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 even.
b) The sum of any two even numbers is even.
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 [∵ 1 + 3 + 5 = 9 (odd) ]
b) True [∵ 3 + 5 + 6 = 14 (even) ]
c) True [∵ 1 × 3 × 5 = 15 (odd) ]
d) False [∵ 8 ÷ 2 = 4 (even) ]
e) False [∵ 2 is a prime number but it is even]
f) False [∵ 3 is a prime number having 1 and 3 as its factors]
g) False [∵ 2 + 3 = 5 (odd)]
h) True
i) False [∵ 2 is even but not composite number]
i) True [∵ 4 × 6 = 24 (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 upto 100.
Solution:
Pair of prime numbers having same digits upto 100 are :
(13 and 31), (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 ?
Solutuion:
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
44 = 7 + 37
44 = 13 + 31
b) 36 = 5 + 31
36 = 7 + 29
36 = 13 + 23
36 = 17 + 19
c) 24 = 5 + 19
24 = 7 + 17
24 = 11 + 13
d) 18 = 5 + 13
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)
[Note : Two prime numbers whose difference is 2 are called twin primes. Some other pair of twin primes are (17 and 19), (29 and 31). (41 and 43). (59 and 61), (71 and 73)]
Question 8.
Which of the following numbers are prime ?
a) 23
b) 51
c) 37
d) 26
Solution:
a) 23 is a prime number (∵ 23 = 1 × 23)
b) 51 is not a prime number (∵ 51 = 1 × 51; 51 = 3 × 17)
c) 37 is a prime number (∵ 37 = 1 × 37)
d) 26 is not a prime number (∵ 26 = 1 × 26; 26 = 2 × 13)
Question 9.
Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
Solution:
Required 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 + 5 + 13
21 = 3 + 7 + 11
b) 31 = 3 + 5 + 23
31 = 5 + 7 + 19
31 = 7 + 11 + 13
c) 53 = 3 + 7 + 43
53 = 3 + 19 + 31
53 = 5 + 7 + 41
d) 61 = 3 + 5 + 53
61 = 3 + 11 + 47
61 = 3 + 17 + 41
Question 11.
Write five pairs of prime numbers less than 20 whose sum is divisible by 5 . (Hint : 3 + 7 = 10)
Solution:
Five pairs of prime numbers less than 20 whose sum is divisible by 5 are
i) 2 + 3 = 5
ii) 2 + 13 = 15
iii) 3 + 7 = 10
iv) 3 + 17 = 20
v) 7 + 13 = 20
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, composite
d) 2
e) 4
f) 2