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# The numerator of a fraction is multiple of two numbers. One of the

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Math Expert
Joined: 02 Aug 2009
Posts: 5229

Kudos [?]: 5882 [0], given: 118

The numerator of a fraction is multiple of two numbers. One of the [#permalink]

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12 Nov 2017, 06:25
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The numerator of a fraction is multiple of two integers. One of the numbers is greater than the other by 2. If the greater number is smaller than the denominator by 4, what will be the minimum value of the fraction ?

(1) -1
(2) $$\frac{-1}{5}$$
(3) 0
(4) $$\frac{1}{5}$$
(5) 1

source - formatting, adding OA and reposting Q from other subforum
[Reveal] Spoiler: OA

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5882 [0], given: 118

Math Expert
Joined: 02 Aug 2009
Posts: 5229

Kudos [?]: 5882 [0], given: 118

Re: The numerator of a fraction is multiple of two numbers. One of the [#permalink]

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12 Nov 2017, 06:26
chetan2u wrote:
The numerator of a fraction is multiple of two numbers. One of the numbers is greater than the other by 2. If the greater number is smaller than the
denominator by 4, what will be the minimum value of the fraction ?
(1) -1
(2) $$\frac{-1}{5}$$
(3) 0
(4) $$\frac{1}{5}$$
(5) 1

source - formatting, adding OA and reposting Q from other subforum

let the denominator be x, therefore the numerator will be (x-4)(x-6)
fraction = $$\frac{(x-4)(x-6)}{x}$$

what does (x-4)(x-6) tell you
1) It tells us that x<4 and x>6, both terms will be negative and the value will be positive.
2) At 4 and 6 it will be 0
3) AND at x as 5, the value will be NEGATIVE
so lowest value will be at x = 5
$$\frac{(x-4)(x-6)}{x}=\frac{(5-4)(5-6)}{5}=\frac{-1}{5}$$

B
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5882 [0], given: 118

Manager
Joined: 17 Mar 2015
Posts: 122

Kudos [?]: 55 [0], given: 4

Re: The numerator of a fraction is multiple of two numbers. One of the [#permalink]

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12 Nov 2017, 07:10
I might be wrong, but I think, provided no info is given about the constraints of the x, value x = $$2*\sqrt{6}$$ gives a smaller number.

Kudos [?]: 55 [0], given: 4

Math Expert
Joined: 02 Aug 2009
Posts: 5229

Kudos [?]: 5882 [0], given: 118

Re: The numerator of a fraction is multiple of two numbers. One of the [#permalink]

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12 Nov 2017, 07:43
Zhenek wrote:
I might be wrong, but I think, provided no info is given about the constraints of the x, value x = $$2*\sqrt{6}$$ gives a smaller number.

Edited for more clarity.
Thanks
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5882 [0], given: 118

Re: The numerator of a fraction is multiple of two numbers. One of the   [#permalink] 12 Nov 2017, 07:43
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# The numerator of a fraction is multiple of two numbers. One of the

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