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Is (x – 2)^2 > x^2?

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Is (x – 2)^2 > x^2? [#permalink]

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New post 27 Jan 2018, 05:07
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

38% (01:34) correct 63% (01:23) wrong based on 48 sessions

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Is (x – 2)^2 > x^2?

(1) x^2 > x
(2) 1/x > 0
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jan 2018, 06:29, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Is (x – 2)^2 > x^2? [#permalink]

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New post 27 Jan 2018, 05:46
Why not A?

In 1, if x^2>x, then wouldn't x>1?

Last edited by urvashis09 on 27 Jan 2018, 06:57, edited 1 time in total.
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Is (x – 2)^2 > x^2? [#permalink]

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New post 27 Jan 2018, 06:33
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tamal99 wrote:
Is (x – 2)^2 > x^2?

(1) x^2 > x
(2) 1/x > 0


\((x – 2)^2 > x^2.....x^2-4x+4>x^2....4x<4....x<1\)
So Q basically asks us - Is x<1?

(1) \(x^2 > x\)..
\(x^2 > x....x^2-x>0...x(x-1)>0\)..
so if x>0, x-1>0 or x>1...NO
if x<0, x-1<0 or x<1...YES
insuff

(2) \(\frac{1}{x} > 0\)..
\(\frac{1}{x} > 0\)..
this tells us that x >0
insuff

combined
x>0, so x>1
ans is NO
suff
C
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Re: Is (x – 2)^2 > x^2? [#permalink]

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New post 27 Jan 2018, 06:40
opted D. But later learnt it is C. Thanks for the explanation chetan2u
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Re: Is (x – 2)^2 > x^2? [#permalink]

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New post 27 Jan 2018, 07:30
tamal99 wrote:
Is (x – 2)^2 > x^2?

(1) x^2 > x
(2) 1/x > 0



Question can be simplified as

x^2 +4 -4x > x^2
4 - 4x > 0
x < 1
so we need to find if x < 1

Statement 1 says x^2 > x

so x^2 - x > 0
x(x-1)>0

so this inequality is true for X <0 & x > 1. So we cannot say that x is always < 1 so not sufficient

Statement 2 says

1/x > 0 so x is not 0 and x is not negative. But x can be 1 and greater than 1 so we cannot always say that question is < 1 so not sufficient

Combining both we get X is always greater than 1 so we answer the question so answer C
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Re: Is (x – 2)^2 > x^2? [#permalink]

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New post 28 Jan 2018, 23:11
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urvashis09 wrote:
Why not A?

In 1, if x^2>x, then wouldn't x>1?


Hi Urvashi

If x^2 > x , then it could mean two things:
Either x > 1 Or
x < 0 (x can take any negative value which would make its square positive, positive is always greater than negative).
Thats why first statement alone is NOT sufficient.
Re: Is (x – 2)^2 > x^2?   [#permalink] 28 Jan 2018, 23:11
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