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Is 1/x-y<y-x?

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Is 1/x-y<y-x?  [#permalink]

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New post 07 Mar 2019, 09:50
1
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  35% (medium)

Question Stats:

76% (01:22) correct 24% (01:50) wrong based on 29 sessions

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Is \(\frac{1}{x-y}\)< \((y-x)\)?
1) \(x>0\)
2) \(y<0\)

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Is 1/x-y<y-x?  [#permalink]

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New post 07 Mar 2019, 19:29
Is \(\frac{1}{x-y}\)< \((y-x)\)?
1) \(x>0\)...x=2, y=1, Ans is NO, but X=2 and y=3, the answer will be yes..
2) \(y<0\)...x=2, y=-1, answer is NO, but x=-3 and y=-1, the answer will be yes..

Combined..
X>0 and y<0, so x-y>0 and \(\frac{1}{x-y}\) will always be positive..
On the other hand y-x will be negative.. so \(\frac{1}{(x-y)}>y-x\)
Answer will always be NO
Sufficient

C

SECOND way..
We can modify the original condition...
\(\frac{1}{x-y}\)< \((y-x)\).....\(\frac{1}{x-y}\)- \((y-x)<0\)....\(\frac{1+(x-y)^2}{x-y}<0\)
The numerator is always positive, so basically question becomes .." Is x-y<0?" or Is x<y?
1) \(x>0\)...x=2, y=1, Ans is NO, but X=2 and y=3, the answer will be yes..
2) \(y<0\)...x=2, y=-1, answer is NO, but x=-3 and y=-1, the answer will be yes..
Combined x>0 and y<0.....so y<0<x, that is x>y
sufficient
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Re: Is 1/x-y<y-x?  [#permalink]

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New post 07 Mar 2019, 22:23
chetan2u wrote:
Is \(\frac{1}{x-y}\)< \((y-x)\)?
1) \(x>0\)...x=2, y=1, Ans is NO, but X=2 and y=-1, the answer will be yes..

Hi chetan2u,
If x=2, and y=-1
\(\frac{1}{2-(-1)}\)<\((-1-2)\)?
\(\frac{1}{2+1}\)<\(-3\)?
\(\frac{1}{3}\)<\(-3\)?
Is it possible in real life?
Did you miss anything or am I?
Thanks__
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Re: Is 1/x-y<y-x?  [#permalink]

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New post 07 Mar 2019, 23:09
AsadAbu wrote:
chetan2u wrote:
Is \(\frac{1}{x-y}\)< \((y-x)\)?
1) \(x>0\)...x=2, y=1, Ans is NO, but X=2 and y=-1, the answer will be yes..

Hi chetan2u,
If x=2, and y=-1
\(\frac{1}{2-(-1)}\)<\((-1-2)\)?
\(\frac{1}{2+1}\)<\(-3\)?
\(\frac{1}{3}\)<\(-3\)?
Is it possible in real life?
Did you miss anything or am I?
Thanks__


It was a typo .. was meant to be 3 and not -1.. Thanks
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Re: Is 1/x-y<y-x?   [#permalink] 07 Mar 2019, 23:09
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