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# Is x^2 greater than x ? (1) x^2 is greater than 1. (2) x is

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VP
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Is x^2 greater than x ? (1) x^2 is greater than 1. (2) x is [#permalink]

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15 May 2008, 18:16
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8. Is x^2 greater than x ?
(1) x^2 is greater than 1.
(2) x is greater than –1

Kudos [?]: 844 [0], given: 10

Senior Manager
Joined: 20 Feb 2008
Posts: 295

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Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross

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15 May 2008, 18:24
I would say the answer is E
From the queston we have is x^2>x, this is true if x>1 and for x<0

From 1
x^2>1
x>1 or x>-1, this is insufficient

From 2
x>-1,
if x>-1 then we have a MAYBE situation where x^2>1 or x^2<1
so insufficient

Together 1 and 2
x>-1, this is insufficient

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Intern
Joined: 04 May 2008
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15 May 2008, 18:42
goalsnr wrote:
8. Is x^2 greater than x ?
(1) x^2 is greater than 1.
(2) x is greater than –1

I use the decision tree to solve DS questions as followed:
- Is statement (1) alone is sufficient?
Yes, ie. if x = 2 then x^2=4 > 2=x
Then we eliminate answer choices: B, C, E.
- Is statement (2) alone is sufficient?
No, it isn't sufficient. Because if x>-1 then x^2 may be greater than x (-1<x<0 or x>1) or smaller than x (0<x<1).
Then we eliminate D. The answer is A.

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VP
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15 May 2008, 20:11
nvhungtct wrote:
goalsnr wrote:
8. Is x^2 greater than x ?
(1) x^2 is greater than 1.
(2) x is greater than –1

I use the decision tree to solve DS questions as followed:
- Is statement (1) alone is sufficient?
Yes, ie. if x = 2 then x^2=4 > 2=x
Then we eliminate answer choices: B, C, E.
- Is statement (2) alone is sufficient?
No, it isn't sufficient. Because if x>-1 then x^2 may be greater than x (-1<x<0 or x>1) or smaller than x (0<x<1).
Then we eliminate D. The answer is A.

Yes, ie. if x = 2 then x^2=4 > 2=x
>>> x can be 2 or -2. -> suff 1 insuff

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Intern
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15 May 2008, 20:34
goalsnr wrote:

Yes, ie. if x = 2 then x^2=4 > 2=x
>>> x can be 2 or -2. -> suff 1 insuff

I mean: the statement (1): x^2 > 1, so x <-1 or x>1
then we always have: x^2 > x.
So (1) alone is sufficent.

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SVP
Joined: 28 Dec 2005
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16 May 2008, 04:38
i agree, i get A as well.

from stat 1, if x^2>1, then either x>1 or x<-1 ... in either case, x^2 will always be greater than x (pick some numbers to see this)

from stat 2, if x=0, then statement isnt true, but if x>1, it is ... so insuff.

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VP
Joined: 03 Apr 2007
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16 May 2008, 05:56
nvhungtct wrote:
goalsnr wrote:

Yes, ie. if x = 2 then x^2=4 > 2=x
>>> x can be 2 or -2. -> suff 1 insuff

I mean: the statement (1): x^2 > 1, so x <-1 or x>1
then we always have: x^2 > x.
So (1) alone is sufficent.

Ok .Now I get it. The OA is A

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Manager
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16 May 2008, 06:20
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goalsnr wrote:
8. Is x^2 greater than x ?
(1) x^2 is greater than 1.
(2) x is greater than –1

I feel that in such questions, plugging values directly is an easier option than solving/simplifying the equations.
Just identify the boundary conditions and plug both sides.

Eg.
For Stt1: Plug -2 and +1 => since it works for both. This is most probably sufficient. (You cannot be definite by plugging just 2 values. But a statement like this might be easy to visualise after 2 values have been plugged)
For Stt2: Plug +0.5 and -0.5 => since it fails for one and works for the other, thus it is definitely insufficient.

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16 May 2008, 07:30
i get A for this..

x^2>x?

in other words |x|>1?

1) x^2>1... yes.. x=-2 x^2=4..x=2 x^2=4..

2) insuff x could be a fraction .025 for example..

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Re: DS -x square   [#permalink] 16 May 2008, 07:30
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