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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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Answer : [D]
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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Answer : [C]
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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Answer : [D]
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  
  • Answer & Explanation
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Answer : [A]
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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Answer : [B]
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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