Which of the following has the most number of divisors?

Correct Answer: 548

Explanation:

Required number = (L.C.M. of 12, 15, 20, 54) + 8

   = 540 + 8

   = 548.

Correct Answer: ⁷⁄₈

Explanation:

L.C.M. of 8, 16, 40 and 80 = 80.

7	=	70	;	13	=	65	;	31	=	62
8		80		16		80		40		80

Since,	70	>	65	>	63	>	62	, so	7	>	13	>	63	>	31
	80		80		80		80		8		16		80		40

So,	7	is the largest.
	8

Correct Answer: 85

Explanation:

Since the numbers are co-prime, they contain only 1 as the common factor.

Also, the given two products have the middle number in common.

So, middle number = H.C.F. of 551 and 1073 = 29;

First number =	❨	551	❩	= 19;    Third number =	❨	1073	❩	= 37.
		29				29

∴ Required sum = (19 + 29 + 37) = 85.

Correct Answer: 111

Explanation:

Let the numbers be 37 a and 37 b

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).

∴ Greater number = 111.

Correct Answer: ¹¹⁄₁₂₀

Explanation:

Let the numbers be a and b

Then, a + b = 55 and ab = 5 x 120 = 600.

∴ The required sum =	1	+	1	=	a + b	=	55	=	11
	a		b		ab		600		120

Correct Answer: 322

Explanation:

Clearly, the numbers are (23 x 13) and (23 x 14).

∴ Larger number = (23 x 14) = 322.

Correct Answer: 127

Explanation:

Required number = H.C.F. of (1657 - 6) and (2037 - 5)

  = H.C.F. of 1651 and 2032 = 127.

Correct Answer: 308

Explanation:

Other number =	❨	11 x 7700	❩	= 308.
		275

Correct Answer: 4

Explanation:

Given exp. =	(a + b)2 - (a - b)2
	ab

=	4ab
	ab

   = 4 (where a = 469, b = 174.)

Correct Answer: 90

Explanation:

Let number of notes of each denomination be x

Then x + 5x + 10x = 480

⟹ 16x = 480

∴ x = 30.

Hence, total number of notes = 3x = 90.