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Q:

The L.C.M of two numbers is 495 and their H.C.F is 5. If the sum of the numbers is 100, then their difference is

A) 10	B) 46
C) 70	D) 90

Answer & Explanation Answer: A) 10

Explanation:

Let the numbers be x and (100-x).

Then, $x (100 - x) = 5 * 495$

=> $x^{2} - 100 x + 2475 = 0$

=> (x-55) (x-45) = 0

=> x = 55 or x = 45

The numbers are 45 and 55

Required difference = (55-45) = 10

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Q:

The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is

A) 12	B) 48
C) 84	D) 108

Answer & Explanation Answer: C) 84

Explanation:

Let the numbers be x and 4x. Then, $x \times 4 x = 84 \times 21 \Leftrightarrow x^{2} = \frac{84 \times 21}{4} \Leftrightarrow x = 21$

Hence Larger Number = 4x = 84

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Q:

The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275 , then the other is

A) 279	B) 283
C) 308	D) 318

Answer & Explanation Answer: C) 308

Explanation:

Other number = $(\frac{11 \times 7700}{275})$ = 308

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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 & Explanation Answer: C) 111

Explanation:

Let the numbers be 37a and 37b. Then , 37a x 37b =4107 => 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).

Therefore, Greater number = 111.

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Q:

The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above condition is

A) 4	B) 6
C) 8	D) 12

Answer & Explanation Answer: A) 4

Explanation:

Let the required numbers be 33a and 33b.

Then 33a +33b= 528 => a+b = 16.

Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).

Therefore, Required numbers are ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)

The number of such pairs is 4

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Q:

The ratio of two numbers is 3 : 4 and their H.C.F is 4. Their L.C.M is

A) 12	B) 16
C) 24	D) 48

Answer & Explanation Answer: D) 48

Explanation:

Let the numbers be 3x and 4x . Then their H.C.F = x. So, x=4

Therefore, The numbers are 12 and 16

L.C.M of 12 and 16 = 48

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Q:

Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are

A) 4, 8, 12	B) 5, 10, 15
C) 10, 20, 30	D) 12, 24, 36

Answer & Explanation Answer: D) 12, 24, 36

Explanation:

Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 12

Therefore, The numbers are 12, 24, 36

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Q:

The G.C.D of 1.08, 0.36 and 0.9 is

A) 0.03	B) 0.9
C) 0.18	D) 0.108

Answer & Explanation Answer: C) 0.18

Explanation:

Given numbers are 1.08 , 0.36 and 0.90

H.C.F of 108, 36 and 90 is 18 [ $∵$ G.C.D is nothing but H.C.F]

Therefore, H.C.F of given numbers = 0.18

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