206374282 exercise 1 problems on number system lcm and hcf

8/17/2019 206374282 Exercise 1 Problems on Number System Lcm and Hcf

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NareshEXERCISE-1

NARESH ADAPA APTITUDE TRAINER

1. Find the number of prime factors of 720.

a) 3 b) 5

c) 4 d) 6

2. How many factors of 720 are even?a) 15 b) 36

c) 8 d) 24

3. Find the sum of the even factors of 300.

a) 728 b) 625

c) 744 d) 600

4. How many factors of 600 are divisible by 5

but not divisible by 25?

a) 24 b) 15

c) 12

d) 8

5. If A, B and C are prime numbers such

that A < B < C and their sum is 80, what

is the value of A?

a) 3 b) 5

c) Cannot be determined d) None of these

6. When the digits of a two digit number are

reversed, the value of the number increases

by 27. How many such two digit numbers

are possible?

a) 3 b) 4

c) 5 d) 6

7. In the first 500 natural numbers, how many

numbers have only three factors? a) 4 b) 5

c) 6 d) None of these

8. In a three digit number, how many numbers

have 6 as atleast one of its digits?

a) 252 b) 256

c) 189 d) 216

9. How many three digit numbers are not

divisible by 3?

a) 333 b) 267

c) 300 d) 600

10. If a 100 digit number consisting of all 7’s

is divided by 8, what is the remainder?

a) 5 b) 1

c) 3 d) 4

11. Find the last non –zero digit in 100!

a) 3 b) 4

c) 2 d) 5

12. How many consecutive zeroes are at the end

of 100!?

a) 20 b) 12

c) 22 d) 24

13. How many natural numbers less than 101 are

divisible by either 2 or 3?

a) 33 b) 50

c) 83 d) 67

14. Find the unit digit of the number 172003

.a) 7 b) 9

c) 3

d) 1

15. What is the unit digit in the expansion of

8^2^4^8^16^.....?

a) 8 b) 4

c) 2 d) 6

16. Find the unit digit of 1! + 2! + 3! + 4! + 5! + 6!

+ …..+ 100!?

a) 3 b) 9

c) 4 d) 0

17. If 1715 + 1315 is divided by 15, what isthe remainder?a) 3 b) 9

c) 0 d) 1

18. If 18201

is divided by 7, what is the remainder?

a) 0 b) 1

c) 3 d) 9

19. If N! has 26 zeroes at the end, what is

the maximum value of N?

a) 105 b) 134 c) 114 d) 125

20. If a person wants to type numbers from 0 to

200, find the number of times he needs to

press the number key on the typewriter?a) 200 b) 480

c) 692 d) 492


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EXERCISE - 2

1. Find the sum of natural numbers up to 100

that are divisible by both 2 and 3.

a) 816 b) 1024

c) 1280 d) 2036

2. How many natural numbers up to 200 are

not divisible by either 2 or 5?a) 60 b) 70

c) 140 d) 80

3. What is the minimum number that can be

added to ‘12345’, to make it a perfect

square?a) 142 b) 199

c) 182 d) 162

4. Ajay purchased a box of sweets and gave

half the number of sweets to his wife, threesweets to his first son, one-third of the

remaining to his second son and two to his

third son. Find the number of sweets he

purchased, if he is finally left with 4 sweets. a) 12 b) 14

c) 16 d) 24

5. When a number is divided by 34, the

remainder is 13. If thrice the same number

is divided by 17, the remainder is

a) 5 b) 3 c) 7 d) 2

6. Find the least possible number which when

divided by 7 and 5, leaves a remainder of 2

and 1 respectively. a) 16 b) 9

c) 23 d) 37

7. When two numbers are divided by 21, they

leave a remainder of 4 and 3. What will be

the remainder, when the product of these two

numbers is divided by 7? a) 5 b) 7

c) 12 d) 1

8. How many three digit numbers, have the

digits in numerical order and are in

Arithmetic Progression?a) 16 b) 32

c) 20 d) 36

9. Find the 130th

term in the given

series A, B, B, C, C, C, D, D, D, D,….

a) R b) T

c) P d) Q

10. A bus started with a full capacity of

passengers. At every stop 50% of the

passengers got down. The number of

passengers boarding the bus is 50% of thenumber of passengers who alighted at every

stop. If the number of passengers in the bus

after the 3rd

stop was 54, find the total number

of passengers who got down in all the three

stops. a) 100 b) 64

c) 128 d) 256

11. What is the relation between Arithmetic Mean

(AM), Geometric Mean (GM) & Harmonic Mean

(HM) for ‘n’ different non-zero integers?a) AM = GM = HM

b) AM => GM => HM

c) HM => AM => GM

d) Cannot be determined

12. Find the approximate value of the sum of

the first 15 terms in the given series.

-729, -243, -81, -27, -9, …. a) 0 b) -729

c) -1093.5 d) -8748

13. A ball is dropped from the top of a building.

Each time it hits the ground it bounces back

to 3/4th

of its previous height. If it bounces

back to a height of 486 inches after the 5th

bounce, find the height of the building. a) 972 inches b) 1024 inches

c) 729 inches d) 2048 inches

14. The speed of a train is 80 kmph and for

every bogie added, the speed decreases by

10%. How many minimum number of bogies

should be added to reduce the speed of the

train to less than 50 kmph? a) 3 b) 4

c) 5 d) 6

15. If 100! is divisible by 12n

, what is themaximum value of n? a) 97 b) 24

c) 48 d) 12

16. If n! is divisible by 1532

, the

minimum value of n is


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a) 134 b) 130

c) 140 d) 144

17. If a, b and c are in Geometric Progression,

then log a, log b, log c, are in

a) Arithmetic Progression

b) Harmonic Progression

c) Geometric Progression

d) None of these

18. Find the sum of 8+88+888+…..up to n terms.

a) 8 10n 9n

8 10n 1 10 9n

b) 81

c) 8 10

n

1

10

‘ d) 8 10 n 1 10

19. Find the approximate value of

2 2 2 .......

a) -1

b) 2

c) 1d) Cannot be determined

20. If x and y are integers, for how many

pairs of (x, y), the value of |x| + |y| = 4?

a) 16 b) 20

c) 12 d) 8


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2. LCM & HCF

Multiples

If a = b x c, then b and c are called the factors of

a, and a is called the multiple of b and c, where a,

b and c are positive integers.

Factor / Divisor

A factor or a divisor of an integer ‘n’ is an integer

which divides ‘n’ leaving a remainder ‘0’.

Common Factors

A common factor of two or more numbers is a

number which divides each of the numbers

leaving a remainder ‘0’.

e.g: 3 is a common factor of 6 and 15.

H.C.F (Highest Common factor)

The highest common factor also called the greatest

common divisor of two or more numbers is the

greatest number that divides each of the numbers

leaving a remainder ‘0’. This is symbolically written

as G. C.D, GCD, G.C.D. or H.C.F

e.g: 3, 4, 6, 12 are the factors of 12 & 36. Among

them the greatest is 12 and hence the H. C. F of

12 and 36 is 12.

L.C.M (Least common multiple)

The least common multiple of two or more given

numbers is the ‘least or lowest number’ which is

exactly divisible by each of the numbers leaving a

remainder ‘0’.

e.g: The L.C.M of 36 and 60 is 180.

Finding the L.C.M and the H.C.F of Fractions

Note: The Product of two numbers = The Product

of their L.C.M and H.C.F

Co-Prime / Relative Prime

Two numbers m and n are said to be co-prime or

relative prime if the G.C.D or H.C.F of m and n is

equal to 1.

EXERCISE

1. Find the greatest number that divides 43,

91 and 183 leaveing the same remainder.

a) 4 b) 7

c) 9 d) 13

2. If the H.C.F. of two numbers is 23, and their

L.C.M is 4186, one of the two numbers is

a) 276 b) 300

c) 322 d) 345

3. If ‘N’ is the greatest number that divides

1305, 4665 and 6905, leaving the same

remainder the sum of the digits in ‘N’ is

a) 4 b) 5

c) 6 d) 8

4. The greatest four digit number divisible by

15, 25, 40 and 75 is

a) 9000 b) 9400

c) 9600 d) 9800

5. The product of two numbers is 4107. If the

H.C.F. of these numbers is 37, the greater

number is a) 101 b) 107

c) 111 d) 185

6. Three numbers are in the ratio 3: 4: 5

and their L.C.M. is 2400. Their H.C.F. is

a) 40 b) 80

c) 120 d) 200

7. The G.C.D. of 1.08, 0.36 and 0.9 is

a) 0.03 b) 0.9

c) 0.18 d) 0.108

8. The product of two numbers is 2028 and their

H.C.F. is 13. The number of such pairs is

a) 1 b) 2 c) 3 d) 4

9. The least multiple of 7, which leaves a

remainder 4, when divided by 6, 9, 15 and

18 isa) 74 b) 94

c) 184 d) 364


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10. The least number which should be added to 18. Three numbers are co-prime to each other. 2497 so that the sum is exactly divisible by The product of the first two numbers is 551

5, 6, 4 and 3 is and the product of the last two numbers is

a) 3 b) 13 1073. The sum of the three numbers is c) 23 d) 33 a) 75 b) 81

c) 85 d) 89 11. Find the least number which is divisible by

9, and leaves a remainder of 3 when divided 19. The length, breadth and height of the room by 5, 6, 7 and 8. are 12 m, 9 m & 6 m respectively. If the room

a) 1677 b) 1683 is filled with cubical boxes, find the minimum c) 2523 d) 3363 number of the maximum size cubical boxes,

that can be filled in the room. 12. A, B and C go around a circular stadium a) 20 b) 22

starting from the same point, at the same c) 24 d) 36

time and in the same direction. A completes a round in 252 seconds, B in 308 seconds 20. Find the smallest number that leaves a

and C in 198 seconds. How long will it take remainder of 8 when divided by 12, 15,20 for A, B and C to meet again at the starting and 54.

point? a) 504 b) 536 a) 24 minutes and 18 seconds c) 544 d) 548 b) 26 minutes and 18 seconds

c) 45 minutes

d) 46 minutes and 12 seconds

13. The H.C.F. of two numbers is 11 and their

L.C.M. is 7700. If one of the numbers is

275, the other number isa) 279 b) 283

c) 308 d) 318

14. Find the least number that will be exactly

divisible by 12, 18, 21 and 30 when doubled.

a) 196 b) 630

c) 1260 d) 2520

15. Find the smallest number that will be exactly

divisible by 12, 16,18, 21 and 28 when

decreased by 7. a) 1008 b) 1015

c) 1022 d) 1032

16. 252 can be expressed as a product ofprimes as:

a) 2 x 2 x 3 x 3 x 7

b) 2 x 2 x 2 x 3 x 7

c) 3 x 3 x 3 x 3 x 7

d) 2 x 3 x 3 x 3 x 7

17. The greatest possible length which can be

used to measure the exact lengths of 7 m,

3 m 85 cm and 12 m 95 cm is

EXERCISE


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a) 15cm b) 25cm

c) 35cm d) 42cm .


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206374282 exercise 1 problems on number system lcm and hcf

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