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Q:

# The product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is

 A) 101 B) 107 C) 111 D) 185

Answer:   C) 111

Explanation:

Let the numbers be 37a and 37b. Then , 37a x 37b =4107  $\inline&space;\fn_jvn&space;\Rightarrow$ ab = 3.

Now co-primes with product 3 are (1,3)

So, the required numbers are (37 x 1, 37 x 3) i.e, (37,111).

$\inline&space;\fn_jvn&space;\therefore$  Greater number = 111.

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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4 54
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 = $\inline \fn_jvn \small 2^{2}x3^{3}x5^{5}$ ;

8 x 9 x 25 x 7 = $\inline \fn_jvn \small 2^{3}x3^{2}x5^{2}x7$

16 x 81 x 5 x 11 x 49 = $\inline \fn_jvn \small 2^{4}x3^{4}x5x7^{2}x11$

H.C.F = $\inline \fn_jvn \small 2^{2}x3^{2}x5$ = 180.

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1 68
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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3 227
Q:

If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to ?

 A) 13/125 B) 14/57 C) 11/120 D) 16/41

Answer & Explanation Answer: C) 11/120

Explanation:

Let the numbers be a and b.
We know that product of two numbers = Product of their HCF and LCM
Then, a + b = 55 and ab = 5 x 120 = 600.
=> The required sum = (1/a) + (1/b) = (a+b)/ab
=55/600 = 11/120

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3 198
Q:

The largest measuring cylinder that can accurately fill 3 tanks of capacity 98, 182 and 266 litres each, is of capacity ?

 A) 7 lts B) 14 lts C) 98 lts D) 42 lts

Answer & Explanation Answer: B) 14 lts

Explanation:

To know the the measuring cylinder that can fill all the given capacities , they must be divisible by the required number.

98,182,266 all are divisible by 14
So  14 litres  is the largest cylinder that can fill all the given cylinders.

(or)

The other method is take HCF of all given capacities i.e 98, 182 and 266.

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