NCERT Solutions for Class 6 Maths Chapter 3: Playing with Numbers - Exercise 3.2

Exercise 3.2

1. What is the sum of any two:

a) Odd numbers.

Ans: 

Let us take an example \[1+3=4\]. Thus, we can say that the sum of any two 

odd numbers is an even number.

b) Even numbers.

Ans: 

Let us take an example \[2+4=6\]. Thus, we can say that the sum of any two 

even numbers is an even number.

2. State whether the following statements are true or false:

a) The sum of three odd numbers is even.

Ans: 

Let us check by taking an example: \[1+3+5=9\]. So, the given statement is 

false.

b) The sum of two odd numbers and one even number is even.

Ans:

Let us check by taking an example: \[1+3+2=6\]. So, the given statement is 

true.

c) The product of three odd numbers is odd.

Ans:

Let us check by taking an example: \[1\times 3\times 5=15\]. So, the given 

statement is true.

d) If an even number is divided by \[\mathrm{2}\], the quotient is always odd.

Ans:

Let us check by taking an example: \[\frac{4}{2}=2\]. So, the given statement 

is false.

e) All prime numbers are odd.

Ans:

\[\text{2}\] is prime and even. So the given statement is false.

f) Prime numbers do not have any factors.

Ans:

\[2\times 1=2\], here \[2\] is prime and having \[1,2\] but having \[2,1\] as 

factors. So, the given statement is false.

g) The Sum of two prime numbers is always even.

Ans:

Let us check by taking an example: \[2+6=8\]. So, the given statement is true.

h) \[\mathrm{2}\] is the only even prime number.

Ans:

The given statement is true.

i) All even numbers are composite numbers.

Ans:

Given statement is false because \[\text{2}\] is an even prime number.

j) The product of two even numbers is always even. 

Ans:

Let us check by taking an example: \[2\times 6=12\]. So, the given statement 

is true.

k)  The numbers \[\mathrm{13}\] and \[\mathrm{31}\] are primenumbers.Both these numbers have the same digits \[\mathrm{1}\] and \[\mathrm{3}\]. Find such pairs of prime numbers up to \[\mathrm{100}\].

Ans: \[\text{17}\] and \[\text{71}\]; \[37\] and \[73\]; \[79\] and \[97\].

3. Write down separately the prime and composite numbers less than \[\mathrm{20}\].

Ans:

Prime numbers less than \[\text{20}\] are \[\text{2,3,5,7,11,13,17,19}\].

Composite numbers less than \[\text{20}\] are \[\text{4,6,8,9,10,12,14,15,16,18}\].

4. What is the greatest prime number between \[\mathrm{1}\] and \[\mathrm{10}\]?

Ans: The greatest prime number below \[\text{10}\] is \[\text{7}\].

5. Express the following as the sum of two odd numbers:

a) \[\mathrm{44}\]

Ans: 

We can write \[\text{44}\] as \[\text{3+41}\] which is the sum of two odd 

numbers.

b) \[\mathrm{36}\]

Ans:

We can write \[36\] as \[\text{3+33}\] which is the sum of two odd numbers.

c) \[\mathrm{24}\]

Ans:

We can write \[24\] as \[\text{1+23}\] which is the sum of two odd numbers.

d) \[\mathrm{18}\]

Ans:

We can write \[18\] as \[\text{1+17}\] which is the sum of two odd numbers.

6. Give three pairs of prime numbers whose difference is \[\mathrm{2}\]. (Remark: Two prime numbers whose difference is \[\mathrm{2}\) are called twin primes.]

Ans:

\[\text{1,3}\],\[\text{3,5}\] and \[\text{5,7}\] are twin primes because their respective differences are \[\text{2}\].

7. Which of the following numbers are prime:

a) \[\mathrm{23}\]

Ans:

\[\text{23}\] is a prime number because it has no factors rather than 

\[\text{1,23}\].

b) \[\mathrm{51}\]

Ans:

\[51\] is a prime number because it has no factors rather than \[\text{1,51}\].

c) \[\mathrm{37}\]

Ans:

\[37\] is a prime number because it has no factors rather than \[\text{1,37}\].

d) \[\mathrm{26}\]

Ans:

\[26\] is not a prime number because it has factors more than \[\text{1,26}\].

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

Ans:

\[90,91,92,93,94,95,96\] are the only seven consecutive numbers less than \[100\].

9. Express each of the following numbers as the sum of three odd primes:

a) \[\mathrm{21}\]

Ans: 

\[\text{17+3+1}\] is the sum for \[\text{21}\] expressed in sum of \[\text{3}\] 

odd numbers.

b) \[\mathrm{31}\]

Ans: 

\[\text{27+3+1}\] is the sum for \[31\] expressed in sum of \[\text{3}\] odd 

numbers.

c) \[\mathrm{53}\]

Ans: 

\[\text{49+3+1}\] is the sum for \[53\] expressed in sum of \[\text{3}\] odd 

numbers.

d) \[\mathrm{61}\]

Ans: 

\[\text{57+3+1}\] is the sum for \[61\] expressed in sum of \[\text{3}\] odd 

numbers.

10. Write five pairs of prime numbers less than \[\mathrm{20}\] whose sum is divisible by \[\mathrm{5}\].

Ans:

\[\text{3+7=10}\],\[7+13=20\],\[2+3=5\],\[3+17=20\] and \[5+5=10\].

Thus, \[3,7\]; \[7,13\]; \[2,3\]; \[3,17\]; \[5,5\] are the five pairs of numbers less than \[20\] whose sum is divisible by \[5\].

11. Fill in the blanks:

a) A number that has only two factors is called a ………..

Ans: Prime number.

b) A number that has more than two factors is called a ……….

Ans: Composite number.

c) \[\mathrm{1}\] neither ………. nor …………….

Ans: Prime nor a composite number.

d) The smallest prime number is …………….

Ans: \[\text{2}\] is the smallest prime number.

e) The smallest composite number is …………...

Ans: \[4\] is the smallest composite number.

f) The smallest even number is …………...

Ans: \[2\] is the smallest even number.

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise 3.2

Opting for the NCERT solutions for Ex 3.2 Class 6 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 3.2 Class 6 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 6 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 6 Maths Chapter 3 Exercise 3.2 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 6 Maths Chapter 3 Exercise 3.2, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it. 

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