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R d sharma mathematics solutions class 6 Solutions for Chapter 2 playing with numbers

Exercises in Chapter 2 playing with numbers Grade 6
Playing with numbers Exercise 2.1
Playing with numbers Exercise 2.10
Playing with numbers Exercise 2.11
Playing with numbers Exercise 2.2
Playing with numbers Exercise 2.3
Playing with numbers Exercise 2.4
Playing with numbers Exercise 2.5
Playing with numbers Exercise 2.6
Playing with numbers Exercise 2.7
Playing with numbers Exercise 2.8
Playing with numbers Exercise 2.9
Questions in Playing with numbers Exercise 2.10

What is the smallest number which when divided by 24, 36 and 54 gives a remainder of 5 each time?

What is the smallest number that both 33 and 39 divide leaving remainders of 5?

Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).

What is the smallest number that, when divided by 35, 56 and 91 leaves remainders of 7 in each case?

In a school there are two sections – section A and section B of Class VI. There are 32 students in sectionA and 36 in section B. Determine the minimum number of books required for their class library so thatthey can be distributed equally among students of section A or section B.

In a morning walk three persons step off together. Their steps measure 80cm, 85cm and 90cmrespectively. What is the minimum distance each should walk so that he can cover the distance in completesteps?

Determine the number nearest to 100000 but greater than 100000 which is exactly divisible by each of 8,15 and 21.

A school bus picking up children in a colony of flats stops at every sixth block of flats. Another schoolbus starting from the same place stops at every eighth blocks of flats. Which is the first bus stop at whichboth of them will stop?

Telegraph poles occur at equal distances of 220m along a road and heaps of stones are put at equaldistances of 300m along the same road. The first heap is at the foot of the first pole. How far from it alongthe road is the next heap which lies at the foot of a pole?

Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.
Questions in Playing with numbers Exercise 2.3

What are prime numbers? List all primes between 1 and 30.

Write all prime numbers between:

(i)10 and 50

(ii)70 and 90

(iii)40 and 85

(iv)60 and 100

What is the smallest prime number? Is it an even number?

What is the smallest odd prime? Is every odd number a prime number? If not, give an example of an oddnumber which is not prime.

What are composite numbers? Can a composite number be odd? If yes, write the smallest odd compositenumber.

What are twin-primes? Write all pairs of twin-primes between 50 and 100.

What are co-primes? Give examples of five pairs of co-primes. Are co-primes always prime? If no,illustrate your answer by an example.

Which of the following pairs are always co-prime?

(i)two prime numbers

(ii)one prime and one composite number

(iii)two composite numbers

Express each of the following as a sum of two or more primes:

(i)13

(ii)130

(iii)180

Express each of the following numbers as the sum of two odd primes:

(i)36

(ii)42

(iii)84

Express each of the following numbers as the sum of three odd prime numbers:

(i)31

(ii)35

(iii)49

Express each of the following numbers as the sum of twin primes:

(i)36

(ii)84

(iii)120

Find the possible missing twins for the following numbers so that they become twin primes:

(i)29

(ii)89

(iii)101

A list consists of the following pairs of numbers:

(i)51, 53; 55, 57; 59, 61; 63, 65; 67, 69; 71, 73

Categorize them as pairs of

(i)co-primes

(ii)primes

(iii)composites

For a number, greater than 10, to be prime what may be the possible digit in the units place?

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

State true (T) or false (F):

(i)The sum of primes cannot be a prime.

(ii)The product of primes cannot be a prime.

(iii)An even number is composite.

(iv)Two consecutive numbers cannot be both primes.

(v)Odd numbers cannot be composite.

(vi)Odd numbers cannot be written as sum of primes.

(vii)A number and its successor are always co-primes.

Fill in the blanks in the following:

(i) A number having only two factors is called a ……….

(ii) A number having more than two factors is called a …………

(iii) 1 is neither ………. Nor ………

(iv) The smallest prime number is ………..

(v) The smallest composite number is ……….
Questions in Playing with numbers Exercise 2.5

Test the divisibility of the following numbers by 2:

(i)6520

(ii)984325

(iii)367314

Test the divisibility of the following numbers by 3:

(i)70335

(ii)607439

(iii)9082746

Test the divisibility of the following numbers by 6:

(i)7020

(ii)56423

(iii)732510

Test the divisibility of the following numbers by 4:

(i)786532

(ii)1020531

(iii)9801523

Test the divisibility of the following numbers by 8:

(i)8364

(ii)7314

(iii)36712

Test the divisibility of the following numbers by 9:

(i)187245

(ii)3478

(iii)547218

Test the divisibility of the following numbers by 11:

(i)5335

(ii)70169803

(iii)10000001

In each of the following numbers, replace * by the smallest number to make it divisible by 3:

(i)75 * 5

(ii)35 * 64

(iii)18 * 71

In each of the following numbers, replace * by the smallest number to make it divisible by 9:

(i)67 * 19

(ii)66784 *

(iii)538 * 8

In each of the following numbers, replace * by the smallest number to make it divisible by 11:

(i)86 * 72

(ii)467 * 91

(iii)9 * 8071

Given an example of a number which is divisible by

(i)2 but not by 4

(ii)3 but not by 6

(iii)4 but not by 8

(iv)both 4 and 8 but not by 32

Which of the following statements are true?

(i)If a number is divisible by 3, it must be divisible by 9.

(ii)If a number is divisible by 9, it must be divisible by 3.

(iii)If a number is divisible by 4, it must be divisible by 8.

(iv)If a number is divisible by 8, it must be divisible by 4.

(v)A number is divisible by 18, if it is divisible by both 3 and 6.

(vi)If a number is divisible by both 9 and 10, it must be divisible by 90.

(vii)If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.

(viii)If a number divides three numbers exactly, it must divide their sum exactly.

(ix)If two numbers are co-prime, at least one of them must be a prime number.

(x)The sum of two consecutive odd numbers is always divisible by 4.
Questions in Playing with numbers Exercise 2.8

Find the largest number which divides 615 and 963 leaving remainder 6 in each case.

Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.

What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3respectively?

The length, breadth and height of a room are 8m 25cm, 6m 75cm and 4m 50cm, respectively. Determinethe longest rod which can measure the three dimensions of the room exactly.

A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones ofthe same size. Find the least possible number of such stones.

Determine the longest tape which can be used to measure exactly the lengths 7m, 3m 85cm and 12m95cm.

7.105 goats, 140 donkeys and 175 cows have to be taken across a river. There is only one boat which willhave to make many trips in order to do so. The lazy boatman has his own conditions for transporting them.He insists that he will take the same number of animals in every trip and they have to be of the same kind.He will naturally like to take the largest possible number each time. Can you tell how many animals wentin each trip?

Two brands of chocolates are available in packs of 24 and 15 respectively. If I need to buy an equalnumber of chocolates of both kinds, what is the least number of boxes of each kind I would need to buy?

During a sale, colour pencils were being sold in packs of 24 each and crayons in packs of 32 each. If youwant full packs of both and the same number of pencils and crayons, how many of each would you need tobuy?

Reduce each of the following fractions to the lowest terms:

(i)161/ 207

(ii)296/ 481

A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind. Hewants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatestcapacity of such a tin?
Chapters in this book
Knowing your numbers
Playing with numbers
Whole Numbers
Operations on whole numbers
Negative number and integers
Fractions
Decimals
Introduction to Algebra
Ratio, Proportion and Unitary Method
Basic Geometrical Concepts
Angles
Triangles
Circles
Pair of Lines and Transversal
Understanding Three Dimensional Shapes
Symmetry
Basic Geometrical Tools
Geometrical Constructions
Mensuration
Data Handling Presentation Of Data
Data Handling – II
Data Handling Bar Graphs
lido-difference