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46.
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
  • A.
    1
  • C.
    3
  • B.
    2
  • D.
    4
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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.
 
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47.
The product of two numbers is 1320 and their H.C.F. is 6. the L.C.M. of the numbers is:
  • A.
    220
  • C.
    1326
  • B.
    1314
  • D.
    7920
  • Answer & Explanation
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Answer : [A]
Explanation :
 
L.C.M. = Product of numbers = 1320  = 220    
H.C.F. 6    
 
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48.
The least number of five digits which is exactly divisible by 12, 15 and 18, is:
  • A.
    10010
  • C.
    10020
  • B.
    10015
  • D.
    10080
  • Answer & Explanation
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Answer : [D]
Explanation :
 
Least number of 5 digits is 10000. L.C.M. of 12, 15 and 18 is 180.
 
On dividing 10000 by 180, the remainder is 100.
 
    Required number = 10000 + (180 100) = 10080  
 
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49.
The H.C.F. and L.C.M. of two numbers are 11 and 385 respectively. If one number lies between 75 and 125, then that number is:
  • A.
    77
  • C.
    99
  • B.
    88
  • D.
    110
  • Answer & Explanation
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Answer : [A]
Explanation :
 
Product of numbers = 11 x 385 = 4235.
 
Let the numbers be 11a and 11b. Then 11a x 11b = 4235    ab = 35  
 
Now, co-primes with product 35 are (1, 35) and (5, 7).
 
So, the numbers are (11 x 1, 11 x 35) and (11 x 5, 11 x 7).
 
Since one number lies between 75 and 125, the suitable pair is (55, 77)
 
Hence, required number = 77
 
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50.
The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case, is:
  • A.
    64
  • C.
    156
  • B.
    124
  • D.
    260
  • Answer & Explanation
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Answer : [A]
Explanation :
 
Required number = H.C.F. of (1356 12), (1868 12) and (2764 12)
 
  = H.C.F. of 1344, 1856 and 2752 = 64  
 
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