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

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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

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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

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

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New post 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
\(\frac{(x-4)(x-6)}{x}=\frac{(5-4)(5-6)}{5}=\frac{-1}{5}\)

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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

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

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New post 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

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

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New post 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
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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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