13
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:   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 

Q:

What is a Common Multiple?

Answer

If the Multiples for two or more numbers which are Common, then those Multiples are said to be Common Multiples. 


 


For Example :


Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,...


Multiples of 5 are 5, 10, 15, 20, 25, 30,...


Here common multiples of 3 & 5 upto 30 are 15, 30.

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16 679
Q:

LCD of 12 and 18

A) 36 B) 42
C) 12 D) 6
 
Answer & Explanation Answer: A) 36

Explanation:

  LCD is nothing but Lowest or Least Common Denominator

 

Here LCD of 12 and 18 means LCD of two fractions with denominators 12 and 18 respectively.

 

Therefore, LCM of 12 & 18 = 6 x 3 x 2 = 36 

 

      •  How to calculate LCD ::


The lowest common denominator or least common denominator (LCD) is the least common multiple (LCM) of the denominators of a set of fractions.

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13 973
Q:

54, 60  LCM is

A) 600 B) 540
C) 60 D) 54
 
Answer & Explanation Answer: B) 540

Explanation:

Here the LCM of 54, 60 is

 

=> 2 x 3 x 3 x 3 x 10

= 6 x 9 x 10

= 54 x 10

540.

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17 1267
Q:

If the HCF of 210 and 55 is expressible in the form of 210 x 5 + 55P, then value of P = ?

A) -23 B) 27
C) 16 D) -19
 
Answer & Explanation Answer: D) -19

Explanation:

HCF of 210 and 55 is 5

Now, 210x5 + 55P = 5

=> 1050 + 55P = 5

=> 55P = -1045

=> P = -1045/55

=> P = -19.

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13 1942
Q:

A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is  ?

A) 63 B) 31
C) 16 D) 27
 
Answer & Explanation Answer: B) 31

Explanation:

To get the least number of coconuts :
LCM = 30 => 30 + 1 = 31

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19 2742
Q:

A drink vendor has 368 liters of Maaza, 80 liters of Pepsi and 144 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) 47 B) 46
C) 37 D) 35
 
Answer & Explanation Answer: C) 37

Explanation:

The number of liters in each can = HCF of 80, 144 and 368 = 16 liters.
Number of cans of Maaza = 368/16 = 23
Number of cans of Pepsi = 80/16 = 5
Number of cans of Sprite = 144/16 = 9
The total number of cans required = 23 + 5 + 9 = 37 cans.

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24 2276
Q:

H.C.F of 4 x 27 x 3125, 8 x 9 x 25 x 7 and 16 x 81 x 5 x 11 x 49 is :

A) 360 B) 180
C) 90 D) 120
 
Answer & Explanation Answer: B) 180

Explanation:

4 x 27 x 3125 = 22 × 33 × 55 ;

 

8 x 9 x 25 x 7 = 23 × 32 × 52 × 7

 

16 x 81 x 5 x 11 x 49 = 24 × 34 × 5 × 11 × 72

 

H.C.F = 22 × 32 × 5 = 180.

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16 1786
Q:

The difference of two numbers is 14. Their LCM and HCF are 441 and 7. Find the two numbers ?

A) 63 and 49 B) 64 and 48
C) 62 and 46 D) 64 and 49
 
Answer & Explanation Answer: A) 63 and 49

Explanation:

Since their HCFs are 7, numbers are divisible by 7 and are of the form 7x and 7y

Difference = 14
=> 7x - 7y = 14
=> x - y = 2

product of numbers = product of their hcf and lcm
=> 7x * 7y = 441 * 7
=> x * y = 63

Now, we have
x * y = 63 , x - y = 2
=> x = 9 , y = 7

The numbers are 7x and 7y
=> 63 and 49

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14 5078