12
Q:

Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:

A) 40 B) 80
C) 120 D) 200

Answer:   A) 40

Explanation:

Let the numbers be 3x, 4x and 5x.

Then, their L.C.M. = 60x.

So, 60x = 2400 or x = 40.

{\color{Blue} \therefore } The numbers are (3 x 40), (4 x 40) and (5 x 40).

Hence, required H.C.F. = 40.

Q:

A drink vendor has 80 liters of Mazza, 144 liters of Pepsi, and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?

A) 35 B) 36
C) 37 D) 38
 
Answer & Explanation Answer: C) 37

Explanation:

If we want to pack the drinks in the least number of cans possible, then each can should contain the maximum numbers of liters possible.As each can contains the same number liters of a drink, the number of liters in each can is a comman factor for 80,144 and 368; and it is also the highest such factor, as we need to store the maximum number of liters in each can.

So, the number of liters in each can  = HCF of 80,144 and 368 = 16 liters.

Now, number of cans of Maaza = 80/16 = 5

Number of cans of Pepsi = 144/16 = 9

Number of cans of Sprite = 368/16 = 23

Thus, the total number of cans required = 5 + 9 + 23 = 37 

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12 686
Q:

A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.

A) 107 B) 117
C) 127 D) 137
 
Answer & Explanation Answer: B) 117

Explanation:

Let us calculate both the length and width of the room in centimeters.

Length = 6 meters and 24 centimeters = 624 cm

width = 4 meters and 32 centimeters = 432 cm

As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.

Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 624 and 432 = 48

Thus, the number of square tiles required = (624 x 432 ) / (48 x 48) = 13 x 9 = 117

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8 620
Q:

The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is

A) 1677 B) 1683
C) 2523 D) 3363
 
Answer & Explanation Answer: B) 1683

Explanation:

 L.C.M of 5, 6, 7, 8 = 840

\inline \fn_jvn \therefore Required Number is of the form 840k+3.

Least value of k for which (840k+3) is divisible by 9 is k = 2 

\inline \fn_jvn \therefore  Required  Number = (840 x 2+3)=1683

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29 1023
Q:

The smallest number which when diminished by 7,  is divisible by  12, 16, 18, 21 and 28 is

A) 1008 B) 1015
C) 1022 D) 1032
 
Answer & Explanation Answer: B) 1015

Explanation:

Required Number = (L.C.M  of 12, 16, 18,21,28)+7

= 1008 + 7

= 1015

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39 3829
Q:

Find the Greatest Number that will devide 43, 91  and 183  so as to leave the same remainder in each case

A) 4 B) 7
C) 9 D) 13
 
Answer & Explanation Answer: A) 4

Explanation:

Required Number = H.C.F  of  (91- 43), (183- 91) and (183-43)

                          = H.C.F of 48, 92, and 140 = 4

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14 1635