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# If x^3 < x^2, is x < 0 ?

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Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 106
If x^3 < x^2, is x < 0 ?  [#permalink]

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31 Oct 2018, 00:45
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:10) correct 46% (01:27) wrong based on 39 sessions

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If $$x^3 < x^2$$, is $$x < 0$$ ?

A) $$|x| > x^2$$
B) $$x > x^2$$

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2726
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
If x^3 < x^2, is x < 0 ?  [#permalink]

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31 Oct 2018, 07:03
AnisMURR wrote:
If $$x^3 < x^2$$, is $$x < 0$$ ?

A) $$|x| > x^2$$
B) $$x > x^2$$

Given: $$x^3 < x^2$$
i.e. $$x^3 - x^2 < 0$$
i.e. $$x^2(x - 1) < 0$$
But $$x^2$$ can NOT be negative as being square of a number
i.e. $$x-1 < 0$$
i.e. $$x < 1$$

Question: is $$x < 0$$ ?

Statement 1: $$|x| > x^2$$
i.e. $$-1 < x < 1$$
NOT SUFFICIENT

Statement 2: $$x > x^2$$

i.e. $$0 < x < 1$$

SUFFICIENT

P.S. I don't rate this question appropriate for GMAT practice as the GMAT question do NOT include any redundant information like $$x^3 < x^2$$ given in this question
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Intern
Joined: 19 Aug 2018
Posts: 28
Re: If x^3 < x^2, is x < 0 ?  [#permalink]

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31 Oct 2018, 09:07
GMATinsight wrote:
AnisMURR wrote:
If $$x^3 < x^2$$, is $$x < 0$$ ?

A) $$|x| > x^2$$
B) $$x > x^2$$

Given: $$x^3 < x^2$$
i.e. $$x^3 - x^2 < 0$$
i.e. $$x^2(x - 1) < 0$$
But $$x^2$$ can NOT be negative as being square of a number
i.e. $$x-1 < 0$$
i.e. $$x < 1$$

Question: is $$x < 0$$ ?

Statement 1: $$|x| > x^2$$
i.e. $$-1 < x < 1$$
NOT SUFFICIENT

Statement 2: $$x > x^2$$

i.e. $$0 < x < 1$$

SUFFICIENT

P.S. I don't rate this question appropriate for GMAT practice as the GMAT question do NOT include any redundant information like $$x^3 < x^2$$ given in this question

Excuse me, how do you solve the first equation?
$$|x| > x^2$$
Thank you.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2726
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If x^3 < x^2, is x < 0 ?  [#permalink]

### Show Tags

31 Oct 2018, 19:24
jorgetomas9 wrote:
GMATinsight wrote:
AnisMURR wrote:
If $$x^3 < x^2$$, is $$x < 0$$ ?

A) $$|x| > x^2$$
B) $$x > x^2$$

Given: $$x^3 < x^2$$
i.e. $$x^3 - x^2 < 0$$
i.e. $$x^2(x - 1) < 0$$
But $$x^2$$ can NOT be negative as being square of a number
i.e. $$x-1 < 0$$
i.e. $$x < 1$$

Question: is $$x < 0$$ ?

Statement 1: $$|x| > x^2$$
i.e. $$-1 < x < 1$$
NOT SUFFICIENT

Statement 2: $$x > x^2$$

i.e. $$0 < x < 1$$

SUFFICIENT

P.S. I don't rate this question appropriate for GMAT practice as the GMAT question do NOT include any redundant information like $$x^3 < x^2$$ given in this question

Excuse me, how do you solve the first equation?
$$|x| > x^2$$
Thank you.

jorgetomas9

I prefer to avoid mathematically solving such expressions.

There are 4 critical ranges which are
0 to 1
greater than 1
0 to -1 and
Less than -1

I always prefer to test the given expression in these ranges to test the validity.

Here I see that $$|x| > x^2$$

so point to be noted is $$|x|$$ as well as $$x^2$$ will always be positive for all values of x except zero.
also the absolute value of the number should become a smaller number when squared which happened in range 0 to 1

i.e. the expression will be valid in ranges 0 to 1 and 0 to -1

I HOPE THIS HELPS!!!
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e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

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Re: If x^3 < x^2, is x < 0 ? &nbs [#permalink] 31 Oct 2018, 19:24
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