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41.
Which of the following has most number of divisors?
  • A.
    99
  • C.
    176
  • B.
    101
  • D.
    182
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Answer : [C]
Explanation :
 
99 = 1 x 3 x 3 x 11;                101 = 1 x 101;
 
176 = 1 x 2 x 2 x 2 x 2 x 11;    182 = 1 x 2 x 7 x 13
 
So, divisors of 99 are 1, 3, 9, 11, 33 and 99;
 
     divisors of 101 are 1 and 101;
 
     divisiors of 176 are 1, 2, 4, 8, 16, 22, 44, 88 and 176;
 
     divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
 
Hence, 176 has the most number of divisors.
 
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42.
The H.C.F. of 0.54, 1.8 and 7.2 is:
  • A.
    1.8
  • C.
    0.018
  • B.
    0.18
  • D.
    18
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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  
 
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43.
The least number which is a perfect square and is divisible by each of the numbers 16, 20 and 24, is:
  • A.
    1600
  • C.
    6400
  • B.
    3600
  • D.
    14400
  • Answer & Explanation
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Answer : [B]
Explanation :
 
The least number divisible by 16, 20, 24 = L.C.M. of 16, 20, 24 = 240 = 2 x 2 x 2 x 2 x 3 x 5
 
To make it a perfect square, it must be multiplied by 3 x 5
 
    Required number = 240 x 3 x 5 = 3600
 
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44.
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
  • A.
    12
  • C.
    24
  • B.
    16
  • D.
    48
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Answer : [D]
Explanation :
 
Let the numbers be 3x 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
 
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45.
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
  • A.
    9000
  • C.
    9600
  • B.
    9400
  • D.
    9800
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Answer : [C]
Explanation :
 
Greatest number of 4 digits is 9999. L.C.M. of 15, 25, 40 and 75 is 600
 
On dividing 9999 by 600, the remainder is 399
 
    Required number = (9999 399) = 9600
 
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