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

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If x > 0, is x^2 < x ? [#permalink]

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New post 15 Oct 2016, 09:14
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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.
[Reveal] Spoiler: OA
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Re: If x > 0, is x^2 < x ? [#permalink]

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New post 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?
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Re: If x > 0, is x^2 < x ? [#permalink]

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New post 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


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Re: If x > 0, is x^2 < x ? [#permalink]

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New post 15 Oct 2016, 11:59
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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

Answer:
[Reveal] Spoiler:
D


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Re: If x > 0, is x^2 < x ? [#permalink]

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New post 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.

Answer : D
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Re: If x > 0, is x^2 < x ? [#permalink]

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New post 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

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Re: If x > 0, is x^2 < x ? [#permalink]

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New post 10 Mar 2017, 02:47
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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?
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Re: If x > 0, is x^2 < x ? [#permalink]

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New post 10 Mar 2017, 02:52
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Re: If x > 0, is x^2 < x ? [#permalink]

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