16.
The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8, is:
• A.
504
• C.
544
• B.
536
• D.
548
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Explanation :

Required number = (L.C.M. of 12, 15, 20, 54) + 8

 = 540 + 8

 = 548

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17.
The H.C.F. and L.C.M. of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is:
• A.
12
• C.
84
• B.
48
• D.
108
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Explanation :

Let the numbers be x and 4x,

Then, x x 4x = 84 x 21   x2 =   84 x 21       x = 21
4

Hence, larger number = 4x = 84

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18.
Find the least number which when divided by 16, 18, 20 and 25 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
• A.
17004
• C.
18002
• B.
18000
• D.
18004
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Explanation :

L.C.M. of 16, 18, 20, 25 = 3600.

Required number is of the form 3600k + 4

Least value of k for which (3600k + 4) is divisible by 7 is k = 5.

 Required number = (3600 x 5 + 4) = 18004

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19.
Which of the following fractions is the largest?
•  A. 7 8
•  C. 31 40
•  B. 13 16
•  D. 63 80
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Explanation :

L.C.M. of 8, 16, 40 and 80 = 80

 7 = 70 ; 13 = 65 ; 31 = 62 8 80 16 80 40 80

 Since, 70 > 63 > 65 > 62 , so 7 > 63 > 13 > 31 80 80 80 80 8 80 16 40

 so, 7 is the largest. 8

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20.
Find the least multiple of 23, which when divided by 18, 21 and 24 leaves remainders 7, 10 and 13 respectively.
• A.
3002
• C.
3024
• B.
3013
• D.
3036
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Explanation :

Here (18 - 7) = 11, (21 - 10) = 11 and (24 - 13) = 11.

L.C.M. of 18, 21 and 24 is 504.

Let required number be 504k – 11.

Least value of k for which (504k - 11) is divisible by 23 is k = 6

 Required number = 504 x 6 - 11

 = 3024 - 11

 = 3013

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