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
• Answer & Explanation
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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
• Answer & Explanation
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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
• Answer & Explanation
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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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