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

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Manager
Joined: 27 Jul 2011
Posts: 53
If x > 0, is x^2 < x ?  [#permalink]

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15 Oct 2016, 09:14
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:12) correct 18% (01:44) wrong based on 142 sessions

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If x > 0, is x^2 < x ?

(1) 0.1 < x < 0.4
(2) x^3 < x^2

Dear experts, I know that this question has been discuss before but I still find it difficult to accept the official answer. Please help.
Manager
Joined: 27 Jul 2011
Posts: 53
Re: If x > 0, is x^2 < x ?  [#permalink]

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15 Oct 2016, 09:19
My confusion is on statement 2.

x^3 < x^2
x^3 - x^2 < 0
x (x + 1) (x - 1) < 0

Therefore
x< -1 or 0<x<1

So, how can the answer be D?
Manager
Joined: 28 Jun 2016
Posts: 207
Concentration: Operations, Entrepreneurship
Re: If x > 0, is x^2 < x ?  [#permalink]

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15 Oct 2016, 11:14
Statement 2:

x^3 < x^2

x^3 - x^2 < 0

x^2(x-1) < 0

x < 1 (since x^2 will always be positive)

From question stem we have to find whether 0<x<1.

Question stem says x>0.

So x lies between 0 and 1.

0<x<1

Sent from my iPhone using GMAT Club Forum mobile app
CEO
Joined: 11 Sep 2015
Posts: 3357
Re: If x > 0, is x^2 < x ?  [#permalink]

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15 Oct 2016, 11:59
1
Top Contributor
smartyman wrote:
If x ＞ 0, is x² ＜ x ?

(1) 0.1 ＜ x ＜ 0.4
(2) x³ ＜ x²

Target question: Is x² ＜ x ?

This is a great candidate for rephrasing the target question.
Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Given: x ＞ 0
Since we're told that x is POSITIVE, we can safely take x² ＜ x and divide both sides by x to get: x ＜ 1
REPHRASED target question: Is x ＜ 1 ?

Statement 1: 0.1 ＜ x ＜ 0.4
If x is BETWEEN 0.1 and 0.4, then we can be certain that x ＜ 1
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x³ ＜ x²
If x is POSITIVE, then we know that x² is also POSITIVE
This means we can safely take x³ ＜ x² and divide both sides by x² to get x ＜ 1
Aha! This is exactly what our REPHRASED target question is asking!
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

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Director
Joined: 14 Nov 2014
Posts: 632
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: If x > 0, is x^2 < x ?  [#permalink]

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15 Oct 2016, 22:07
[quote="smartyman"]If x ＞ 0, is x^2 ＜ x ?
(1) 0.1 ＜ x ＜ 0.4
(2) x^3 ＜ x^2

lets take x^2-x <0 --We can rewrite it as: x(x-1)<0, if we plot it on number line , we will get a range between {0-1}(0 and 1 not included) that will satisfy x^2-x <0.
so any solution having range 0-1 will satisfy the given equation.

A. Suff.

B.x^2(x-1)<0---if plot in a number line , x can only have value between {0-1}(excluding 0 and 1) and can have x<0 as solution..as in the question stem it is given as x can take only positive value.only possible range is {0-1}.this range satisfy x^2-x <0 also .so suff.

Intern
Joined: 14 Oct 2014
Posts: 17
Re: If x > 0, is x^2 < x ?  [#permalink]

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20 Feb 2017, 04:12
smartyman wrote:
My confusion is on statement 2.

x^3 < x^2
x^3 - x^2 < 0
x (x + 1) (x - 1) < 0

Therefore
x< -1 or 0
So, how can the answer be D?

You did the factorisation wrong.
x^3x^3-x^2<0
x^2(x-1)<0
Since x^2 is always >0 so x-1<0 and which leads to x<1
Hope it helps

Posted from my mobile device
Intern
Joined: 18 Jan 2017
Posts: 36
Re: If x > 0, is x^2 < x ?  [#permalink]

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10 Mar 2017, 02:47
1
This is strange. The original post says: (2) x^3 > x^2

However, it seems that all the solutions have used (2) x^3 < x^2

What's the actual question?
Math Expert
Joined: 02 Sep 2009
Posts: 52390
Re: If x > 0, is x^2 < x ?  [#permalink]

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10 Mar 2017, 02:52
malavika1 wrote:
This is strange. The original post says: (2) x^3 > x^2

However, it seems that all the solutions have used (2) x^3 < x^2

What's the actual question?

Edited. It's (2) x^3 < x^2
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Intern
Joined: 18 Jan 2017
Posts: 36
Re: If x > 0, is x^2 < x ?  [#permalink]

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10 Mar 2017, 06:30
Thanks Bunuel. This is good to know.
Re: If x > 0, is x^2 < x ? &nbs [#permalink] 10 Mar 2017, 06:30
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