L.C.M & H.C.F

L.C.M & H.C.F ,

1. The H.C.F of two numbers is 12 and their L.C.M is 360. If one of the numbers is 36. Find the other number?

a) 80 b) 90 c) 100 d) none 120

2. Four bells ring at 24, 30, 40 & 48 seconds respectively. If all of them ring it at 12.30 pm. The immediate next time was

a) 12.43p.m b) 12.34p.m c) 1.00p.m d) none

3. The least square number which is exactly divisible by 8, 12, 20, 48 & 75.

a) 1200 b) 900 c) 3600 d) none

4. Find the smallest number which when divided by 6, 9, 12 & 15 leaves 5 as remainder in each case

a) 185 b) 158 c) 365 d) none

5. Find the least number which when increased by 6 is exactly divided by 12, 21 & 35

a) 441 b) 144 c) 414 d) none

6. What is the greatest number of 4 digits exactly divisible by 2, 3, 4, 5 & 6.

a) 1160 b) 9960 c) 9906 d) none

7. What is least number of 4 digits exactly divisible by 2, 3, 4, 5, 6 & 7.

a) 1160 b) 1260 c) 1620 d) none

8. Find the smallest number which when divided by 32, 40, 56 leaves 12, 20, 36 as remainders respectively

a) 1140 b) 1120 c) 1410 d) none

9. Find the least number which when divided by 3, 5, 9 & 15 leaves 1 as remainder when divided by 34 leaves no remainder

a) 163 b) 316 c) 136 d) none

10. What is the minimum number of square slabs required for laying the floor of room 4m37c.m long and 1m71cm broad?

a) 270 b) 277 c) 200 d) none

11. A trader has three kinds of oil. The first is 28kgs.,the second is 70kgs. And the third is 84kgs. Find the minimum number of packets to store the oil with out mixing?

a) 24 b) 48 c) 12 d) none

12. The L.C.M. of two numbers is 15 times its H.C.F. If the product of those number’s is 14415. Find H.C.F

a) 30 b) 13 c) 31 d) none

13. In finding H.C.F. of two numbers by division method, the quotients are 2, 4, 6 respectively and the last divisor is 17. Find those numbers.

a) 425, 952 b) 452, 952 c) 425, 925 d) none

14. Find the length of the largest square brick, which can be used for paving the floor of 5.89mts X 3.99mts.

a) 91cm. B) 19cm. c) 65cm. d) none

15. Find the second smallest multiple of 36 which when divided by 30, 45, 75 and 135 leaves 18 as remainder in each case

a) 1368 b) 2718 c) 4068 d) none

16. Ratio of two numbers is 5:7 and their L.C.M. is 350, Find the smaller number

a) 50 b) 60 c) 70 d) none

17. A number when divided by a certain divisor leaves remainder 50 when double of that number is divided by the same divisor, the remainder is 8. Find the divisor

a) 42 b) 58 c) 92 d) none

18. Two numbers when separately divided by a certain divisor leave remainders 53 and 46 respectively. When sum of the numbers is divided by the same divisor the remainder is 34. Find the divisor.

a) 35 b) 42 c) 65 d) none

19. Two bills one of Rs.27.50 and the other of Rs.13 are to be paid in coins of the same kind. Find the largest coin that can be used.

a) 50pice b) 25pice c) Rs.1 d) none

20. In a school 391 boys and 323 girls have seen divided into the largest possible equal classes, so that there are equal number of boys and girls in each case. What is the number of classes?

a) 23 girl’s classes and 19 boy’s classes b) 17boy’s classes, 23 girl’s classes

c) 23 boy’s classes and 19 girl’s classes d) None

21. A boy has three kinds of marbles, the first kind 143, the second 182 & the third 208. Find the least number of heaps into which he can keep them separately.

(1) 13 (2) 21 (3) 31 (4) none these

22. LCM of , , & is

(1) 20/1 (2) 30/1 (3) 40/3 (4) none these

23). The HCF & LCM of two numbers are 44 & 264 respectively. If 2 divide the first number, the quotient is 44. Find the other number.

1. 88 (2) 132 (3) 124 (4) none these

24) On dividing a number by 5, 6 & 7, if we get 2 as remainder always, find that smallest number.

(a) 210 (b) 212 (c) 420

(d) 422

25) A number after adding 7 is divisible by 10, 11 & 12. The number is ______.

(a) 660 (b) 653 (c) 453

(d) 473

26). Four bells ring at intervals of 10 min, 12 min, 15 min, & 20 min respectively. If they ring together at 8 am, find after what interval of time do they ring together again?

1. 9 am (2) 10 am (3) 11 am (4) none these

27) Three alarms ring at intervals of 2,6,12 minutes respectively. If they all ring together at 1 PM when will they ring

all together the next time.

a) 1 AM b) 1.12 PM

100. 1.12 AM d) Next 1 PM

28) On dividing a number by 4, 5 & 6, we Get 3, 4 & 5 as remainder. Find the number.

(a) 59 (b) 60 (c)61 (d) 81

29) LCM of 24, 36 and a third number is 2016 and their GCD is 4. What is the smallest possible value of the third number?

a) 36 b) 224

100. 324 d) 216

30) What is the minimum number of identical square tiles required to floor a room measuring 10.8m × 9m?

a) 64 b) 72

c) 30 d) 48

LOGICAL QUESTIONS ON NUMBER SYSTEM

1) A man wrote all the natural numbers starting from 1 in a series. What will be the 50^th digit of the number?

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

2). The value of 101 + 102 + 103 + …… + 200 is

(a) 15050 (b) 20200 (c) 10909

(d) 16500 (e) None of these

3. A monkey wanted to climb on the smooth vertical pole of height of 35 metre. In the first one minute he climbs up 5 metre in the next one minute he slips down by 2 metre. Further he repeated the same process till he has reached on the top of the pole. How many times it has to go upward to reach the apex of the pole?

(1) 10 (2) 11 (3) 12 (4) none these

4) What least number should be added to 16380 to make it a perfect square?

(1) 1 (2) 2 (3) 3 (4) none these(4)

5). How many numbers between 500 and 1000 are divisible by 13?

(1) 33 (2) 34 (3) 35 (4) none these(38)

6). A bought some chocolates from a shop, he gave to B one less than half of what he had initially. Then be and given 3 chocolates to C and then half of the chocolates which he had then given to D. finally he gave one chocolate to E and one chocolate with him. The number of chocolates he had bought.

(1) 8 (2) 12 (3) 14 (4) none these

7). A typist starts to type the serial numbers of candidates in a list, up to 500. Minimum how many times he has to press the keys of numerals only?

1. 1389 (2) 1392 (3) 1344 (4) none these

8)There are two, 2-digit numbers ab & cd, ba is another 2-digit number prepared by reversing the digits of ab, if

ab  cd = 493 and ba  cd = 2059, what is the value of sum of (ab + cd)?

(a) 43 (b) 45 (c) 47

500. 46 (e) 49

9) Numbers from 1 to 100 are written side by side. What is the 74^th digit?

a) 3 b) 4

100. 1 d) 5

10) What is the number of zeros at the end of 126!?

(a) 26 (b) 12 (c) 13 (d) 31

11). (149)₁₀ = ( )₇

(a) 302 (b) 149 (c) 151

(d) 342

12). The sum of the digits of a two-digit numbers is 10, while when the digits are reversed, the number decrease by 54. The changed number.

(a) 28 (b) 19 (c) 37

(d) 46

13). The sum of two numbers is 15 and their geometrical mean is 20% lower than their arithmetic mean. Find the numbers.

(a) 11, 4 (b) 12, 3 (c) 13, 2

(d) 10, 5

14). If A381 is divisible by 11, find the value of the smallest natural number A?

(a) 5 (b) 6 (c) 7

(d) 9

15. If 146! is divisible by 5ⁿ, then find the maximum value of n.

(a) 34 (b) 35 (c) 36

(d) 37

16. Find the number of divisors of 1420.

(a) 14 (b) 15 (c) 13

500. 12

17). Which of the following is not a perfect square?

(a) 100858 (b) 325137

(c) 945723 (d) All the above

18). Which of the following can never be in the ending of a perfect square?

(a) 6 (b) 00 (c) 000

(d) 5

19)120 apples were present with total of 7 persons. Each person had atleast 13 apples. The number of apples with each is distinct. Which of the following cannot be the total number of apples with any 2 persons.

a) 47 b) 44

100. 27 d) 33

20) 1000! ends with _________ number of consecutive zeros

a) 248 b) 249

c) 312 d) 124

21) What comes in the place of x in the following question? 8^9.4 × 4^12.8 × 64^8.1 = 16^x

a) 41.8 b) 16.2

c) 18.4 d) 25.6

22) If k+2 is a four digit odd number, then which among the following must be a four digit even number

a) k+1 b) k-1

c) k+3 d) More than one of above

23) If x+y+z is a positive number, then which of the following cannot be true?

a) x<0<y<z b) y<0<x<z

c) z<x<y<0 d) x<y<z

UNIT DIGIT VALUE

1) Find the unit digit of 122¹²²  133¹³³.

(a) 2 (b) 4 (c) 6

(d) 8

2) Find the unit digit of the product of all the elements of the set which consists of all the prime numbers greater than 2 but less than 222.

(1) 3 (2) 4 (3) 5 (4) none these

3) .

1. 0 (2) 1 (3) 2 (4) none these

4). The unit digit of the following expression is

(1!)¹ + (2!)² + (3!)³ + (4!)⁴ + (5!)⁵ + (6!)⁶

1. 5 (2) 6 (3) 7 (4) none these

5). Find the unit digit of 222⁸⁸⁸ + 888²²².

1) 0 2) 1 3) 2 4) none these

REMINDER

1). Find the remainder of 15  17  19 when divided by 7.

(a) 5 (b) 3 (c) 1

500. 0

2). A Certain number when divided by 95 leaves a remainder 30. What is the remainder if, the same number be divided by 19?

(1) 8 (2) 9 (3) 10 (4) none these (11)

3). Find the remainder when 11⁸ is divided by 7

(1) 0 (2) 1 (3) 2 (4) none these

4). Find the remainder of

(a) 1 (b) 9 (c) 8

(d) 7

5). Find the remainder of

(a) 4 (b) 3 (c) 7

6) When 51²⁵ is divided by 13, the remainder obtained is

(a) 12 (b) 10

100. 2 (d) 1

7) What is the remainder when N = (1! + 2! + 3! + …… + 1000!)⁴⁰ is divided by 10?

(a) 1 (b) 3 (c) 7 (d) 8

8). When a 4 digit number is divided by 85 it leaves a remainder of 39. If the same number is divided by 17 the remainder would be?

(a) 2 (b) 5 (c) 7 (d) 9

_{NO OF FACTERS}

1). If P & Q are different prime numbers. Find the number of divisors of P × Q.

(a) 2 (b) 4 (c) 6

500. 8

2).A milkman has 3 different qualities of milk. 403 gallons of 1^st quantity, 465 gallons of 2^nd quantity and 496 gallons of 3^rd quantity. Find the least possible number of bottles of equal size in which different milk of different qualities be filled without mixing?

(a) 34 (b) 46 (c) 26

500. 44

PROBLEMS ON DIVISALBLE RULES

1). What is the greatest number of 4 digits that when divided by any of the numbers 6, 9, 12, 17 leaves a remainder of 1?

(a) 9997 (b) 9793 (c) 9895

(d) 9487

2). Which of these has total 24 positive factors?

(a) 21⁵  2³ (b) 2⁷  12³

(c) 2⁶  3⁴ (d) 63  55

3). Find the total number of factors of number N = 12³  13²  14?

(a) 24 (b) 64 (c) 192 (d) 216

4). In a certain base 137 + 254 = 402 then what is the sum of 342 + 562 in that base.

(a) 904 (b) 1014 (c) 1104 (d) 1024

5). How many such numbers are there between 1 & 100 such that each of which is not divisible by 4, and has one digit as 4 in the number?

(a) 5 (b) 12 (c) 6

(d) 15 (e) 7

6). A number is greater than 3 but less than 8. Also, the number is greater than 6 but less than 10. What is the number?

(a) 5 (b) 4 (c) 9

(d) 6 (e) 7

7). 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ is divisible by

(a) 3 (b) 11 (c) 13

(d) 17 (e) None of these

8). The number, one less than 7¹⁹ is divisible by

(a) 49 (b) 7 (c) 16

(d) 18 (e) 6

9). A man reads of a book on a day and of the remainder, on the second day. If the number of pages still unread are 40, how many pages did the book contain?

(a) 320 (b) 420

(c) 160 (d) 240

10). A man spends of his salary on food. of his salary on house rent and of salary on clothes. He still has Rs.1400 left with him. Find his salary.

(a) 7000 (b) 8000

(c) 4500 (d) 6500

11) Find the remainder when 2222⁵⁵⁵⁵+5555²²²² is divided by 7

a) 1 b) 3

c) 0 d) 5

12) What is the difference between the largest and the smallest 4-digit number that can be formed with the digits

0,7,8 and 9 without repetition

a) 5683 b) 2781

c) 3820 d) 5432

13) If N chocolafgtes are divided among 6 boys, each gets an equal number of chocolates. Find W, if it is a perfect cube and is by the first three perfect squares?

a) 216 b) 324

c) 624 d) 625

14) In a division, the quotient and the remainder are two and four less than the divisor respectively. If the number is

178, what are the quotient and the divisor

a) 16,21 b) 12,14

100. 14,12 d) 21,16

15) Which of the following is exactly divisible by all prime numbers between 10 and 20?

a) 75294 b) 46189

c) 35273 d) 48391

16) What is the least number that should be added to 37301 so that it is exactly divisible by 27?

a) 21 b) 6

c) 14 d) 13

17) If n² is perfect cube, then which of the following statements is always true?

a) n is odd b) n is even

c) n³ is perfect square d) n is a perfect cube