Math Study Pack for Sainik School Entrance Exam - Class 6

Presentation on Number System

Find the difference between face value and place value of 8 in 35829.

• 834

• 729

• 792

• None of these

Find the difference between greatest and the smallest 5-digit numbers formed by the digits 9 ,4, 8, 2, 7 (using all the digits once)

• 73853

• 24789

• 98742

• 73953

Unit digit of product of first ten prime number is

• 6

• 4

• 2

• 0

Five digits’ greatest odd number to be formed with the help of 3, 5, 7, 9 and 0 is

• 90573

• 97530

• 97503

• 97053

Five digits’ smallest number, which is completely divisible by 75 is

• 10025

• 10050

• 10075

• 9975

Find out the unit's digit in the product of (3207 x 12 x 17 x 13).

• 0

• 3

• 4

• 7

Highest two digits prime number is

• 125

• 115

• 135

• 105

How many 4 digit numbers, in all are there?

• 9999

• 9990

• 9000

• 8999

In a number 36490, when the digits 6 and 9 are interchanged, then the difference between the original and the new number is

• 2870

• 2960

• 2970

• 3970

Find the greatest 5-digit number divisible by 14

• 99989

• 99888

• 99988

• 10000

Eighty thousand nine hundred and five is represented in number form as

• 8095

• 80905

• 809005

• 80090005

What will be the sum of the numbers from 1 to 25?

• 322

• 325

• 340

• 285

The sum of greatest and the smallest four digits even number is

• 8998

• 9998

• 10998

• 10888

In number 4 x 104 + 3 x 103 + 6 x 100 + 9 x 10 + 8, when the digit at hundred’s and one’s place interchanged, then the difference between the original and new number is ________

• 199

• 148

• 198

• 178

1000000 is obtained, when a number is subtracted from the sum of 893645 and 635489, find that number.

• 106355

• 364511

• 51329

• 529134

The sum of two numbers is 234560. If one number is more than the other number by ten thousand ten. Find the greatest number.

• 112275

• 122285

• 132285

• 117280

How many times will the digit 9 occur in writing numbers from 1 to 100?

• 9

• 10

• 20

• 21

If Divisor = 132, Quotient=29, Remainder = 12, Find the dividend.

• 3480

• 3840

• 3540

• 3380

How many prime numbers are there between 80 and 100?

• 6

• 7

• 8

• 9

  
  

Sum of prime numbers between 1 and 20 is

• 77

• 67

• 87

• 76

The sum of the face value of 3 in 6231, 6321 and 3621 is

• 3033

• 9

• 3330

• 3333

What will be the sum of the even numbers from 1 to 24?

• 146

• 156

• 186

• 166

What will be the sum of the odd numbers from 1 to 20?

• 100

• 90

• 110

• 120

What must be added to 2910 so that the quotient is 243 on dividing by 12.

• 4

• 8

• 10

• 6

Dividend = 100400, Quotient = 392, Remainder = 48, Divisor = ?

• 126

• 226

• 256

• 258

Introduction to Operations on Whole Numbers

Introduction to Divisibility Test

If 9587 – A = 7429 – 4358, then what is value of A?

6516

5616

6156

6616

976 x 237 + 976 x 763 = ?

9760

7600

976000

237000

3251 + 587 + 369 - A = 3007

1250

1300

1375

1200

The product of Two numbers is 18432. If one of the number is twice the other, then find the smaller number.

48

96

192

82

The smallest number greater than 9320 which is divisible by 8 is

9330

9328

9350

9382

What number multiplied by 18 gives a product of 846?

51

48

47

57

A bus can take 57 passengers from place A to B. How many buses are required to take 3660 passengers?

64

65

63

70

If the unit digit in the product (529) x (16*) x (324) be 2, the smallest digit in place of * will be

7

0

2

5

What least number must be subtracted from 543 to get a number exactly divisible by 8?

9

1

5

7

What least number must be added to 2010 to obtain a number which is completely divisible by 19?

2

3

4

5

On dividing a certain number by 342, we get 47 as remainder. If the same number is divided by 18, what will be the remainder.

8

9

10

11

Problem No.12

143865 is divisible by

3, 4 and 8

5, 2 and 9

2, 3 and 5

3, 5 and 9

The product of two numbers is 8192. One of the number is two times the second number, the smaller number is

8

16

32

64

The number 13013 is divisible by 13. The smallest 5 digit number beginning with 14 and exactly divisible by 13 is

14040

14001

14014

14027

A shopkeeper charges Rs. 10 for every bottle of coke or Rs. 240 for every carat of 30 bottles . If Vandana wants to buy 185 bottle of coke, what amount she will have to pay?

1480

1490

1600

1850

Sarala opened an account in a bank with Rs. 35000. She deposited 10000 in her account after 1 month and withdrew Rs.7000 from her account after 2 months and again deposited Rs.8000 in her account after 3 months. What is the balance in her account after last transaction?

43000

46000

56000

36000

Rajesh’s weight is 5 kg less than Ram’s weight and Neha’s weight is 3 kg more than Ram’s weight. If the weight of three is 103 kg, then the weight of Ram is

34 kg

38 kg

33 kg

35 kg

Which one of the following numbers is exactly divisible by 11?

1552

1331

1882

1902

How many of the following numbers are divisible by 3 but not by 9?

2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276

5

6

7

None of these

When 20.2 is multiplied by 18.01, the result rounded to complete numbers without decimal is

360

362

364

365

Which smallest number must be subtracted from 52792, so that it is divisible by 15?

7

8

5

6

In an examination Karan got 10 marks more than Bhavana. Isha got 5 marks less than Bhavana. If trio get a total of 170, then what is the marks obtained by Isha?

65

55

50

45

If the number 517*324 is completely divisible by 3, then the smallest whole number in place of * will be

0

1

2

None of these

Which one is greatest?

The sum of 7985 and largest 4-digit number.

The sum of largest 6-digit number and the least 4-digit number.

8 x 873 + 987

21035 x 2893 – 1893 x 21035

The total numbers from 1 to 400 which are divisible either 3 or 7 are

195

171

133

190

Introduction to Square and Square Root

The square root of 6561 by means of factors is

81

64

96

24

If √529=x, then find the value of x.

23

25

27

13

If √81 + √64 = x , then find the value of x

17

18

9

8

Square root of 289 is

15

16

17

18

What is the square root of 2ˆ8 ?

64

48

32

16

Simplify √169 + √144 - √196 .

11

12

13

14

The least number which must be subtracted to 4931 to make it a perfect square, is

100

31

140

110

The smallest number by which 9408 must be divided so that it becomes a perfect square. Also, the square root of the perfect square so obtained, is

3,56

4,56

21,56

42,56

The least number which must be subtracted from 2361 to make it a perfect square, is

48

88

57

40

Find the least number from which multiplication of 2352 gives a perfect square number

2

3

6

8

Which of the numbers will multiply 27 to make it a complete square?

4

3

5

7

The square root of 400/169

2023

1713

1013

207

The value of (√64 + √36)/(√64 - √36).

2

7

14/6

6

The square root of 1 15/49 is

1/7

1 1/7

9/7

4/7

The value of √0.01 + √0.81 + √1.21 + √ 0.0009 is

2.03

2.1

2.11

2.13

The square root of the fraction 23 26/11 is

4 9/11

5 9/11

3 9/11

2 9/11

(√28 x √24) / (√42 x √8) is equal to

2

21

√2

1/√2

By what least number, 720 be multiplied so that the resulting number is a perfect square?

3

4

5

6

5929 Students are sitting in an auditorium in such a manner that there are as many students in a row as there are rows in auditorium. How many rows are there in the auditorium?

66

7

11

77

A General arranges his soldiers in rows to from a perfect square. He finds that in doing so 60 soldiers are left out. If the total number of soldiers be 8160. The number of soldiers in each row, are

90

80

70

40

Concept on LCM ( Least Common Multiple )

Concept on HCF ( Highest Common Factor )

Introduction to LCM and HCF of Fraction with Examples

Introduction to Relationship between two numbers and their LCM and HCF with examples

LCM of 6, 8,10 and 12 is

120

60

240

130

LCM of 42, 70, 98 and 126 is

126

2205

4410

8820

The smallest number exactly divisible by 3, 4, 6 and 8 is

26

24

28

32

Find the smallest number divided by 42, 98 and 70

1470

1740

1070

980

Find the HCF of 45, 75 and 165

15

45

75

2475

Find the HCF of 420, 315 and 462

24

27

28

21

The smallest three-digit number completely divisible by 12,18,24 will be

72

144

180

224

What is the least number which when reduced by 5 is divisible by each one of 21, 28, 36, 45?

425

1259

1260

1265

What is the least number which when increased by 7, is divisible by each one of 24,32,36, 54?

867

871

857

4318

What is the least multiple of 8 which when divided by each one of 6, 9 , 15, 18 gives remainder 4 in each case?

196

184

208

124

What is the least number which when divided by 3,6,8,12 and 15 gives remainder 5 in each case and is completely divisible by 18?

365

185

275

175

The largest three-digit number, when divided by 6,9 and 12 leaves 1 as remainder in each case, will be

887

987

973

730

The difference between LCM and HCF of the numbers 30, 36 and 90 is

366

354

186

174

Find the LCM of (2^2 x 3^2 x 5^3 x 7), (2^2 x 3 x 5^3 x 7^4), and (2^2 x 3^2 x 7^2 x 11^2)

2^3 x 3^2 x 5^3 x 11^2

2^3 x 3^2 x 5^3 x 7^4 x 11^2

2^3 x 3^2 x 5^3 x 7^3 x 11^2

2^3 x 3^2 x 5^2 x 7^3 x 11^3

Find the smallest number of four digits which is divisible by 2, 3, 4, 5, 6 and 7

1260

420

840

2100

The greatest number of 5 digits, which is divisible by 16, 25, 40 and 80 is

99999

99600

99000

99500

The HCF of two numbers is 38 and their LCM is 98154. If one of the number is 1558. The other number is

1197

2394

4932

2384

The LCM and the HCF of the numbers 28 and 42 are in the ratio.

6:1

2:3

3:2

7:2

Two numbers are in the ratio 3:4 and the product of their LCM and HCF is 10800. Find the sum of the numbers

190

70

210

200

Find the LCM of 3/8, 4/13,6/15 and 10/27

60

1/60

936

1/936

Find the HCF of 1/9, 3/26, 4/13, 5/72

60

13/60

12/60

1/60

Three pieces of wood 35 m, 75 m, 120 m long have to be divided into planks of the same length. What is the greatest possible length of plank?

8 m

7 m

5 m

3 m

There are two electrical wires, one is 9 m 60 cm long aluminium wire and the other is 5 m 12 cm long copper wire. Find the maximum length that can be equally cut from each wire in such a way that the total length of each wire is exactly divisible by it.

40 cm

46 cm

64 cm

60 cm

Five bells begin to toll together and toll at intervals of 24, 40, 64, 72 and 120 seconds. After what interval to time will they toll again together.

42 min

36 min

48 min

54 min

The Traffic lights at three different road crossing changes after every 48, 72 and 108 seconds respectively. If they change simultaneously at 9 am, at what time will they change again simultaneously?

10 minutes 10 seconds

7 minutes 12 seconds

7 minutes 10 seconds

12 minutes 10 seconds

Three bells ring at intervals of 12, 15 and 18 minutes respectively. They started ringing simultaneously at 9:00 AM. What will be the next time when they ring simultaneously?

10:00 AM

11:00 AM

12:00 PM

1:00 PM

The greatest number which will divide 1277 and 1368 leaving 3 as the remainder in each case is

68

77

91

97

Greatest number, which is to be divided by 280 and 1245 leaves the remainder 4 and 3 respectively, is

138

148

145

178

Concept of Factors and Multiples with examples

The total number of the prime factor of 24 is

8

7

4

9

The number of common factors between 18 and 24 is

1

8

6

4

Which of the following is a not a factor of 316?

1

8

79

158

What is the prime factorization of 37800?

2 x 2 x 3 x 3 x 5 x 5 x 7 x 7

2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 7

8 x 27 x 25 x 7

2 x 4 x 25 x 27 x 7

The sum of all the prime factors of m is 10. Find the number m.

15

20

28

63

Factors of 30 are

2, 3, 5

1,2,3,5,10

1,2,3,10,15

1,2,3,5,6,10,15,30

The prime factors of 80 is

2 x 2 x 2 x 2 x 5

2 x 2 x 2 x 5 x 5

2 x 2 x 2 x 5

2 x 2 x 5 x 5

The number of multiples of 3 which are less than 25 is

6

7

8

9

The sum of the factors of 81 is

141

121

110

114

What will be the sum of prime numbers in the following numbers?

17, 8, 21, 13, 41, 2, 27, 31, 51

104

102

155

125

Among the following numbers, which are common multiples of 18 and 54

32 and 48

54 and 72

48 and 72

54 and 108

Find the sum of factors of 48 that are multiples of 4

112

118

96

106

The product of all the factors of 24 is

331774

331775

317736

331776

The multiple of 7 between 14 and 77 is

10

9

8

7

What are the numbers of multiples of 5, which are less than 45?

9

8

7

10

What is the number which is a factor and multiple both of 32?

8

16

32

64

Which of the following is a prime factor?

48 = 2 x 2 x 2 x 6

63 = 3 x 3 x7

81 = 3 x 3 x 9

54 = 2 x 3 x 9

The number x, x – 2 and x – 6 are all prime numbers, so find the value of x.

15

17

19

21

2 and 5 are the prime factors of 70. Another prime factor is_________.

3

7

10

12

Multiply the second multiple of 8 by 12, we get____________.

176

182

192

196

What is the sum of the 2nd and 9th multiple of 6?

66

76

56

60

Find the difference between the fourth multiple of 12 and third multiple of 25.

75

27

48

28

Divide the fifth multiple 12 by the third multiple of 5.

4

12

10

8

4 is a common factor of 16, 24, ? , 96. What is the largest possible whole number which is less than 70, that can be placed at the place of (?).

56

60

64

84

Number x is a factor of 88. If number x is a two-digit number and the sum of digits is 8, what is the number?

80

62

44

17

Concept of Decimals with examples

1.11 + 11.11 + 111.111 is equal to

123.331

133.331

122.331

123.311

The product of 1.2 x 0.6 x 3.12 x 0.03 is equal to

0.067392

0.063568

0.4812

0.00392

The product of 0.2, 0.02, 0.002, 0.0002 is ______________.

When 61/4 is multiplied by 0.25, then 0.75 is added in result, then 0.3125 is subtracted from result, we get______________.

2

4

0

1

Which of the following is equal to 12 ?

0.15 x 0.800

0.20 x 0.600

0.15 x 800

0.20 x 60

Difference between the place value of 7's in 187.978 is_______.

0.707

7.7

7.07

6.93

Ram bought a book for ₹ 178.50, some medicines for ₹ 248.25 and gave a ₹ 500 note to the shopkeeper. The remaining amount is

₹ 126.50

₹ 70.50

₹ 75.50

₹ 73.25

How many digits will be there to the right of the decimal point in the product of 95.75 and .02554?

5

6

7

3

Which one of the following has the same value as 4+2/25 + 1/5

4.21

4.28

42.1

421.0

The decimal equivalent to [ 3/4+ 4/5+ 8/25 ]

1.870

18.70

187

1870

What is the decimal equivalent of 1 5/8 ?

1.58

1.62

1.622

1.625

If 4015 ÷ 11 = 365, 40.15 ÷ 1.1 is equal to

36.5

3.65

0.365

0.0365

What fraction of ₹ 4 is ₹ 1.50 ?

1/8

3/8

1/4

2/5

5.125 when changed into fraction, becomes

5 1/125

5 1/25

5 1/8

51 1/4

Which of the following is equal to 1?

(0.7×6) / (10×42)

(0.7×6) / (1.0×4.2)

(0.7×0.6) / (10×4.2)

(7.0×6.0) / (1.0×4.2)

Concept of Fractions with Example

Find the value of 1 23 + 4 6/7

6 12/21

6 11/21

6 13/14

6 11/23

The difference of 1 3/16 and its reciprocal is equal to

1 1/8

4/3

15/16

None of these

The sum of the fraction and is 4/3, 5/9 and 6/18 is

2/5

11/18

19/9

20/9

Simplest form of 4 17/25 x 2 36/90 x 125/234 is _________.

54/8

6

54/7

3

1 + 1/2 + 1/4 + 1/7 + 1/14 + 1/28 is equal to:

2

2 1/2

3

3 1/2

The value of (5/7 of 1 6/13 ) ÷ (2 5/7 ÷ 3 1/4) is equal to

20/169

1

5/4

1 119/180

( 3/4) of 144 is how much greater than (2/3 ) of 96?

20

44

54

64

The product of two numbers is 5/4. If one numbers is 5/6, what is the other number?

2

1/2

1/3

2/3

When ( 1/2 - 1/4 - 1/5 - 1/6)  is divided by (2/5 - 5/9 + 3/5 - 7/18) , the result is:

2 1/18

3 1/6

3 3/10

5 1/10

The smallest fraction which should be subtracted from the sum of 1 3/4, 2 1/2, 5 1/12, 3 1/3 and 2 1/4 to make the result a whole number is:

5/12

7/12

1/2

7

The value of (5/7 of 1 6/13) ÷ (2 5/7 ÷ 3 1/4)

20/1639

1

5/4

1 119/180

3/4th of 144 is how much greater than 2/3 of 96?

20

44

54

64

Rohit has ₹ 4500. If he spent and of money on movie and tuition fees respectively, how much money is left with him?

₹ 2200

₹ 2000

₹ 3000

₹ 2500

Mohit competed 1/12 of his project in 4 1/2 days. How long would he take to complete the whole project?

27 days

54 days

48 days

64 days

Select the correct match.

18 1/2 + 8 1/3 + 7 1/7 = 456

4 1/6 + 3 5/12 = 90/12

7/10 - 1/5 = 1/2

-1/2 + 1/2 + = 1

1/5th part of a drum is filled with milk. What is the capacity of drum if it requires 28 L more to fall the drum completely?

30 L

32 L

35 L

140 L

1/3rd of a drum is filled with water. If need another 60 L water to filled whole drum, then what is the capacity of drum?

120 L

90 L

60 L

30 L

Which of the following is the largest fraction?

5/6

9/10

7/9

10/11

Which of the following is the smallest fraction?

1/10

2/15

3/8

4/9

The correct arrangement of the fractional numbers 17/25, 17/13, 17/19 and 17/27 in ascending order is

17/19, 17/13, 17/27, 17/25

17/27, 17/25, 17/19, 17/13

17/27, 17/19, 17/13, 17/25

17/13, 17/25, 17/19, 17/27

Arrange there fractions in ascending order : 3/4, 1/6, 9/8, 10/3

9/8, 1/6, 3/4, 10/3

10/3, 9/8, 1/6, 3/4

3/4, 9/8, 1/6, 10/3

1/6, 3/4, 10/3, 9/8

Arrange there fractions in descending order

5/6, 7/8, 2/3, 1/7

      7/8, 5/6, 2/3, 1/7

      5/6, 1/7, 2/3, 7/8

      5/6, 7/8, 2/3, 1/7

      1/7, 2/3, 5/6, 7/8

The fraction is divided by 8/7, the result is 64/49 the fraction is_________.

273/125

64/54

512/343

65/54

A wire 36 1/5 m long was cut into three parts measuring 12 2/5 m, 13 1/2 m and m respectively. If the length of left part of wire is 5 1/6, find the value of.

5 4/15

5 5/13

5 1/15

5 4/13

In a class of 30 students the number of girls is 1/5 the of the number of the boys. How many boys are there in the class?

25

18

20

19

Introduction to Area and Perimeter

Find the area of the rectangle whose length is 15 cm and the width is 4 cm?

90 cm²

60 cm²

70 cm²

30 cm²

If each side of square will be doubled, then its perimeter will be

2 times

3 times

4 times

8 times

The perimeter of a square park is 72 m, then the area of the square is

144 sq m

2376 sq m

1296 sq m

324 sq m

Find the breadth of a room whose floor area is 363 sq m and length is 33 m.

33 m

24 m

11 m

15 m

The breadth of a rectangle is 3/5 of the length. If the length of the rectangle is 25 m, then find the perimeter of the rectangle.

100 m

80 m

75 m

150 m

A rectangle is formed by 100 cm wire. Find out the maximum area of the rectangle.

100 sq cm

400 sq cm

625 sq cm

10000 sq cm

A room floor is 192 sq m in area. If its length is 16 m. Then, its perimeter is

12 m

28 m

56 m

64 m

A rectangular garden is 105 m by 75. How many rounds of this garden will a boy make if he runs 3600 m?

12

20

10

8

The number of 15 cm square tiles required to lay a floor of size 3.6 m x 4.5 m is

720

360

10800

5400

How many rectangular plots of dimensions 40m by 60 m can be made from a rectangular field of dimensions 120 m by 160 m?

2

3

4

8

Introduction to Simplification with examples

1372 ÷ 28 × x - 1653 = 748

49

13

15

18

The value of the expression 2 + 2 ÷ 2 + 2 × 2 + 2 – 2 is

7

14

21

28

[{(6 ÷2) ×3} × 2] is equal to

11

18

13

27

The simplification of 1 + 1/10 + 1/100 + 1/1000 in decimal form gives

1.0001

1.111

1.001

0.111

The simplification of 10 + 4 ÷ 2 – 3 × 2 + 4 ÷ 2 × 2 – 4 gives

0

1

6

8

2 3/5 - 13/7 ÷15/21 + 2/5 × 1/3 = x

1/15

7/15

3/17

2/15

Simplify 10 2/5 × 8 4/5 ÷ 4 2/5 .

20 4/5

5/104

64

21

The value of { 12 (18 - 3) } + 5 (12 – 7) is

5

25

30

55

Simplify 21 × 7 + 25 ÷ 5 – 24 × 1/8 .

150

147

148

149

16 ÷ 4 of 2 – 2 [ 2 – { 2 – 2 ( 2 – 2 – 2 ) } ].

5

-6

6

8

The simplification of 98 - [ 65 + { 32 - ( 12 + 5 ) } ] gives the result

8

18

178

212

Simplify (0.50 + 0.15 ÷ 0.05) × 2/7 .

1

0

3

5

Value of 12 × 8 – 4 ÷ 4 is equal to

12

23

84

95

The simplification of 6 – {5 + 3 – (5 – 2) – 5} gives the result

0

6

12

3

If 178 × 34 = 6052, what is 60.52 ÷ 17.8?

34

3.4

0.34

0.034

By how much does 6/ (7/8) exceed (6/7)/8 ?

6

6

7

7

The Value of expression 7/36 ÷ 5/12 × 25/14 is

7/5

6/5

5/6

7/6

Simplify ( 7/3 × 2/3 ÷ 3/5 ) / ( 2 + 1 2/3 ).

99/70

70/99

33/30

70/27

The Value of 425 – 125 ÷ 25 × 6 + 37 is

39

109

463

432