Q 1-Three numbers are in the ratio of 3:4:5 and their L.C.M. is 2400. Their H.C.F. is

A - 40

B - 80

C - 120

D - 200

Answer - A Explanation "Let the numbers be 3x, 4x and 5x. Then ,their L.C.M. = 69x, so 60x = 2400 or x = 40 ∴ The numbers are (3 x 40), (4 x 40) and (5 x 40). Hence, required H.C.F. = 40. "

Q 2-The L.C.M. of two numbers is 48, The numbers are in the ratio 2:3. The sum of the numbers is

A - 28

B - 32

C - 40

D - 64

Answer - C Explanation "Let the numbers be 2x and 3x. Then ,their L.C.M. = 6x. so , 6x = 48 or x = 8 ∴ The numbers are 16 and 24. Hence, required sum = (16 + 24) = 40 "

Q 3-Three numbers which are co-prime to each other are such that the product of the first wo is 551 and that of the last two is 1073. The sum of the three numbers is :

A - 75

B - 81

C - 85

D - 89

Answer - C Explanation "Since the numbers are co-prime. they contain only 1 as the common factor Also, the given two products have the middle number in common so middle number= H.C.F. of 551 and 1073= 29 First number =(551/29) = 19, Third number = (1073/29) = 37 ∴ Required sum = ( 19 + 29 + 37) = 85 "

Q 4-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

Answer - B Explanation "Let the numbers be 13a and 13b. Then , 13a x 13b = 2028 ⇒ ab = 12 Now , co-primes with product 12 are (1,12) and (3, 4). so, the required numbers are (13 x 1, 13 x 12) and ( 13 x 3, 13 x 4). Clearly , there are 2 such pairs."

Q 5-The product of two numbers is 4107. If he H.C.F. of these number is 37 , then the greater number is

A - 101

B - 107

C - 111

D - 185

Answer - C Explanation "Let the number be 37a and 37b. Then , 37a x 37b = 4107 ⇒ ab 3. Now, co-primes with product 3 are (1,3), so, the required numbers are (37 x 1, 37 x 3) i.e. (1, 111) ∴ Greater number = 111 "

Q 6-The H.C.F. of two numbers is 12 and their difference is 12. The numbers are

A - 66, 78

B - 70, 82

C - 94, 106

D - 84, 96

Answer - D Explanation "Out of the given numbers, the two with H.C.F. 12 and difference 12 are 84 and 96. "

Q 7-The number of number-pairs lying between 40 and 100 with their H.C.F.. as 15 is

A - 3

B - 4

C - 5

D - 6

Answer - B Explanation "Numbers with H.C.F. 15 must contain 15 as a factor Now ,multiples of 15 between 10 and 100 are 45,60,75 and 90 ∴ Number-pairs with H.C.F. is are (45, 60),(45, 75), (60,75) and (75, 90) [ ∴ H.C.F. of (60,90) is 30 and that of (45, 90 ) is 45] Clearly , there are 4 such pairs. "

Q 8-The sum of two numbers is 528 and their H.C.F. is 33. The number of pairs of numbers satisfying the above conditions is

A - 4

B - 6

C - 8

D - 12

Answer - A Explanation "Let the required numbers be 33 a and 33b . Then , 33a + 33b = 528 ⇒ a + b = 16 Now ,co-primes with sum 16 are (1, 15) , (3,13), (5, 11) and (7,9) ∴ Required numbers are ( 33 x 1, 33 x 15), (33 x 3, 323 x 13) ,( 33 x 5, 33 x 11),(33 x 7,33 x 9). The number of such pairs is 4. "

Q 9-The sum of two numbers is 216 and their H.C.F. is 27. The number are:

A - 27, 189

B - 81, 189

C - 108, 108

D - 154, 162

Answer - A Explanation "Let the required numbers be 27 a and 27 b . Then , 27a + 27 b = 216 ⇒ a + b = 8 Now, co-primes with sum 8 are ( 1, 7 ) and (3 , 5) ∴ Required numbers are ( 27 x 1, 27 x 7) and (27 x 3 , 27 x 5 ) i.e., (27,189) and (81,135, out of these, the given one in the answer is the pair ( 27,189). "

Q 10-The ratio of two numbers in 3:4 and their H.C.F. is 4. Their L.C.M. is

A - 12

B - 16

C - 24

D - 48

Answer - D Explanation "Let the numbers be 3x3x and 4x. Then, their H.C.F. = x. so x= 4 so, the numbers are 12 and 16 L.C.M. of 12 and 16 = 48 "

Q 11-Three numbers are in the ratio 1:2:3 and their H.C.F. is 12. he numbers are :

A - 4, 8, 12

B - 5, 10, 15

C - 10, 20, 30

D - 12, 24, 36

Answer - D Explanation "Let the required numbers be 2x, and 3x. Then , their H.C.F. = x, so x = 12 ∴ The numbers are 12, 24 and 36 "

Q 12-The L.C.M. of 3,2.7 and 0.09 is

A - 2.7

B - 0.27

C - 0.027

D - 27

Answer - D Explanation "Given numbers are 3.00, 2.70 and 0.09. L.C.M. of 300,270 and 9 is 2700 ∴ L.C.M. of given numbers = 27.00 = 27"

Q 13-The H.C.F. of 0.54, 1.8 and 7.2 is

A - 1.8

B - 0.18

C - 0.018

D - 18

Answer - B Explanation "Given numbers are 0.54,1.80 and 7.20. H.C.F. of 54,180 and 720 is 18. ∴ H.C.F. of given numbers = 0.18 "

Q 14-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

Answer - C Explanation "Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 0.90 = 18. ∴ H.C.F. of given numbers = 0.18"

Q 15-The H.C.F. of 1.75, 5.6 and 7 is

A - 0.07

B - 0.7

C - 3.5

D - 0.35

Answer - D Explanation "Given numbers with two decimal places are : 1.75, 5.60 and 7.00. without decimal places, these numbers are : 175, 560 and 700, whose H.C.F. is 35 ∴ H.C.F. of given numbers = 0.35 "