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# Is 1/(y - x) > x - y?

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Senior Manager
Joined: 21 Oct 2013
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Is 1/(y - x) > x - y?  [#permalink]

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27 Jun 2014, 23:57
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Difficulty:

45% (medium)

Question Stats:

66% (01:57) correct 34% (02:17) wrong based on 184 sessions

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Is 1/(y - x) > x - y?

(1) y > x

(2) |x - y| > 0
Manhattan Prep Instructor
Joined: 22 Mar 2011
Posts: 1479
Re: Is 1/(y - x) > x - y?  [#permalink]

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28 Jun 2014, 01:19
(1) SUFFICIENT: If y>x, then y-x is positive. Here are a few number cases to demonstrate:

y=5, x=2, 5-2=3
y=0, x=-2, 0-(-2)=2
y=-2, x=-5, -2-(-5)=3

In a related fashion, x-y must be negative. Therefore, the left-hand side of our original inequality is always positive, and the right side is always negative, giving us an answer of Yes.

(2) INSUFFICIENT: This just tells us that neither x-y nor y-x is equal to 0. That allows us to simplify, but not to solve:

Is 1 / (y - x) > x - y?
Is 1 > (x - y) (y - x)?
Is 1 > (x - y) (-1) (x - y)?
Is 1 > (-1) (x - y)^2?
Is 1 > -x^2 + 2xy - y^2?

Fun stuff, but without any information about x or y, I have no way to answer the question.

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Re: Is 1/(y - x) > x - y?  [#permalink]

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28 Jun 2014, 04:24
1
Is 1/(y - x) > x - y?

(1) y > x --> this can be rewritten as y - x > 0 and x - y < 0, thus $$(\frac{1}{y - x} = positive) > (negative=x - y)$$. Sufficient.

(2) |x - y| > 0. This statement just says that $$x\neq{y}$$, which is clearly insufficient to answer the question. Not sufficient.

Hope it's clear.
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Re: Is 1/(y - x) > x - y?  [#permalink]

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03 Jul 2014, 03:45
goodyear2013 wrote:
Is 1 / (y - x) > x - y?

(1) y > x

(2) |x - y| > 0

(1) y > x, which means that x - y is always < 0 AND y - x is always > 0. Hence 1 / (y-x) > x - y , answer YES; Sufficient

(2) |x-y| > 0, basically only tells us that x does not equal y, but it doens't help to solve. IS.

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Re: Is 1/(y - x) > x - y?  [#permalink]

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03 Jul 2014, 10:53
I´m sorry, probably it´s stupid question, but isn´t (-1) (x - y)^2 always negative or 0? Then it will be always less than 1.
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Is 1/(y - x) > x - y?  [#permalink]

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03 Jul 2014, 11:02
tarasovk wrote:
I´m sorry, probably it´s stupid question, but isn´t (-1) (x - y)^2 always negative or 0? Then it will be always less than 1.

You cannot multiply $$\frac{1}{-(x - y)} > x - y$$ by -(x - y) because you don't know it's sign. If it's negative, then you'd have 1 < -(x - y)^2 (flip the sign when multiplying by negative value) and if it's positive, then you'd have 1 > -(x - y)^2 (keep the sign when multiplying by positive value).

Check Tips and hints on inequalities.
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Re: Is 1/(y - x) > x - y?  [#permalink]

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29 Nov 2018, 12:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is 1/(y - x) > x - y?   [#permalink] 29 Nov 2018, 12:06
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