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

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Intern
Joined: 24 Jan 2013
Posts: 37
If x^3 < x, is x > x^2 ?  [#permalink]

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10 Feb 2014, 02:00
6
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:42) correct 37% (01:53) wrong based on 160 sessions

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If x^3 < x, is x > x^2 ?

(1) x > -5
(2) x < -2
Math Expert
Joined: 02 Sep 2009
Posts: 52431
Re: If x^3 < x, is x > x^2 ?  [#permalink]

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10 Feb 2014, 02:13
2
3
If x^3 < x, is x > x^2 ?

Given: $$x^3 < x$$ --> $$(x+1)x(x-1)<0$$ --> $$x<-1$$ (firs range) or $$0<x<1$$ (second range).

Question: $$x>x^2$$? --> $$x(1-x)>0$$? Is $$0<x<1$$? So, the question basically asks whether x is from the second range.
Check the links below to see how the ranges are derived.

(1) x > -5 --> x can be from the first range (for example, if x=-3), but x can be from the second range too (for example, if x=1/2). Not sufficient.

(2) x < -2 --> x cannot be from the second range. Sufficient.

Hope this helps.
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Re: If x^3 < x, is x > x^2 ?  [#permalink]

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10 Feb 2014, 04:29
Make a table...

x | x^3
--------
-2| -8 --- True

1/2| 1/8 ----- True

2 | 8 ---- false

2 conditions

Stm 1- Can be any value.... Not Suff

Stm 2- Less that -2 -- Suff

B
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Joined: 17 Oct 2015
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If x3 < x, is x > x2?  [#permalink]

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Updated on: 17 Oct 2015, 16:20
If $$x^3$$ < x, is x >$$x^2$$?

1. x > -5

2. x < -2

Originally posted by theventurer on 17 Oct 2015, 11:20.
Last edited by theventurer on 17 Oct 2015, 16:20, edited 3 times in total.
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Joined: 13 Nov 2014
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Re: If x3 < x, is x > x2?  [#permalink]

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17 Oct 2015, 11:42
Is the OA really E? I am inclined to say the answer is B. If x is less than -2 then x is negative with an absolute value greater than 1 (where the gmat tries to trick you with decimals being greater than or less than). The square of any number (technically any real number, which is all the gmat is concerned with) is positive. X^2 > X.

Unless I am missing something
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Re: If x^3 < x, is x > x^2 ?  [#permalink]

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18 Oct 2015, 10:01
Merging topics.

Wofford09 wrote:
Is the OA really E? I am inclined to say the answer is B. If x is less than -2 then x is negative with an absolute value greater than 1 (where the gmat tries to trick you with decimals being greater than or less than). The square of any number (technically any real number, which is all the gmat is concerned with) is positive. X^2 > X.

Unless I am missing something

Yes, the correct answer is B.
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If x^3 < x, is x > x^2 ?  [#permalink]

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18 Oct 2015, 13:39
peacewarriors wrote:
If x^3 < x, is x > x^2 ?

(1) x > -5
(2) x < -2

Hi,

as per given statement: x^3 < x will be valid in two conditions:
1) x values will lie between 0 to 1.
2) x values will lie less than -1.
Question asks: x > x^2 ....means....is x lie between -1 to 1?

Stat1:
x > -5 that means x may be -4 which will satisfy the condition( condition 2 mentioned above) and -4 does not lie between -1 to 1. Hence ans for this is NO.
now take x value 0.5 which satisfy the condition( condition 1 mentioned above) and 0.5 lies between -1 to 1. Thus ans for this is Yes.
We can see that for this option there is not any definite answer. Hence this option is insufficient.

Stat2:
x < -2 hence what ever the value we will take will less than -1 (hence satisfies the condition 2 mentioned above) and will never fall in between -1 to 1. Hence ans for this is definite, which is NO. Thus this option suffice the data. Sufficient

+1 kudos if it helped you
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Re: If x^3 < x, is x > x^2 ?  [#permalink]

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19 Oct 2015, 22:29
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x^3 < x, is x > x^2 ?

(1) x > -5
(2) x < -2

For questions regarding inequalities, if the range of the question includes that of the condition, the condition becomes the answer.
If we modify the question, x^3-x<0, x(x^2-1)<0, x(x-1)(x+1)<0 ==> x<-1, 0<x<1, so we want to know whether x^2-x<0? ==> x(x-1)<0? ==> 0<x<1
so, whether 0<x<1 if x<-1, 0<x<1
1) x>-5
2) x<-2
one variable (x), we therefore need one equation. Two equations are given, so there is high chance (D) will be our answer.
1) the question does not include the range of -5<x<-1, 0<x<1, so insufficient.
2) for x<-2, the answer to the question is 'no'; this condition is sufficient, so the answer becomes B.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: If x^3 < x, is x > x^2 ?  [#permalink]

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29 Jul 2018, 09:29
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Re: If x^3 < x, is x > x^2 ? &nbs [#permalink] 29 Jul 2018, 09:29
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# If x^3 < x, is x > x^2 ?

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