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# Is x > y ?

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Intern
Joined: 26 Jun 2012
Posts: 9
Is x > y ?  [#permalink]

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29 Jul 2012, 11:21
5
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Difficulty:

55% (hard)

Question Stats:

52% (01:15) correct 48% (00:58) wrong based on 110 sessions

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Is x > y?

(1) x/4 = y^2

(2) x > 1
Manager
Joined: 28 Sep 2011
Posts: 62
Location: United States
GMAT 1: 520 Q34 V27
GMAT 3: 690 Q47 V38
GPA: 3.01
WE: Information Technology (Commercial Banking)
Re: Is X > Y ?  [#permalink]

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29 Jul 2012, 13:13
Simplify 1:
$$X = 4Y^2$$

The squared tells us the right side will always be positive and for integers X will always be greater then Y irrespective if Y is positive or negative.

Y = 1/4 --> X = 1/4.

So now we know we need B to filter the values.
Math Expert
Joined: 02 Sep 2009
Posts: 49271
Re: Is x > y ?  [#permalink]

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29 Jul 2012, 15:06
2
1
jayoptimist wrote:
Is x > y?

(1) x/4 = y^2

(2) x > 1

Is x > y ?

(1) x/4 = y^2 --> $$x = 4y^2$$. If $$x=y=0$$ then the answer is NO but if $$x=4$$ and $$y=1$$ then the answer is YES. Not sufficient.

(2) x > 1. Not sufficient.

(1)+(2) $$\frac{x}{4} = y^2$$ --> $$y=\frac{\sqrt{x}}{2}$$ (or $$y=-\frac{\sqrt{x}}{2}$$). Now, since $$x>1$$ then $$x>\sqrt{x}$$, so $$x>\frac{\sqrt{x}}{2}=y$$. Sufficient.

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Intern
Joined: 02 Aug 2012
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Re: Is x > y ?  [#permalink]

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03 Aug 2012, 07:51
Why do you need to know that x>1 to find out that y= sq.root x/2? couldn't you have found that in A?
Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)
Re: Is x > y ?  [#permalink]

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03 Aug 2012, 08:23
jayoptimist wrote:
Is x > y?

(1) x/4 = y^2

(2) x > 1

(1) Since $$x=4y^2$$, the question becomes whether $$4y^2>y$$, or $$y(4y-1)>0.$$
We don't know anything about y, so not sufficient. Check for example $$y = 0$$ and $$y = 1$$.

(2) Obviously not sufficient, as we don't know anything about $$y$$.

(1) and (2): Since $$x > 1$$, $$x=4y^2>1$$, from which $$y>1/2$$ or $$y<-1/2$$. Then $$x=4y^2>y$$, because $$y(4y-1)>0$$ holds for either $$y > 1/2$$ or $$y < -1/2$$.
Sufficient.

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PhD in Applied Mathematics
Love GMAT Quant questions and running.

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Re: Is x > y ?  [#permalink]

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05 Jul 2018, 13:16
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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 x > y ? &nbs [#permalink] 05 Jul 2018, 13:16
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