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
• Answer & Explanation
• Report
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
• Report
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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