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# Is x between 0 and 1?

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Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
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Is x between 0 and 1?  [#permalink]

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06 Mar 2012, 16:03
1
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65% (hard)

Question Stats:

55% (01:33) correct 45% (01:52) wrong based on 121 sessions

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Is x between 0 and 1?

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

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E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
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Posts: 54544
Re: Is x between 0 & 1?  [#permalink]

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06 Mar 2012, 16:08
4
2
enigma123 wrote:
Is x between 0 and 1?

(1) $$-x < x^3$$
(2) $$x < x^2$$

How come statement 1 is not sufficient to answer the question guys?

Is $$0<x<1$$?

(1) -x<x^3 --> $$x^3+x>0$$ --> $$x(x^2+1)>0$$ --> $$x>0$$ (as x^2+1 is always positive). Not sufficient.

(2) x<x^2 --> $$x^2-x>0$$ --> $$x(x-1)>0$$ --> either $$x>1$$ or $$x<0$$, so the answer is NO. Sufficient.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
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##### General Discussion
Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 465
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: Is x between 0 & 1?  [#permalink]

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06 Mar 2012, 16:13
$$x<0$$

Shouldn't be x>0 because x(x-1) > 0?
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
Joined: 02 Sep 2009
Posts: 54544
Re: Is x between 0 & 1?  [#permalink]

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06 Mar 2012, 16:19
enigma123 wrote:
$$x<0$$

Shouldn't be x>0 because x(x-1) > 0?

x(x-1) > 0 --> roots are 0 and 1 --> ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: x<0 or x>1.

Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
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Re: Is x between 0 and 1 ?  [#permalink]

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10 May 2012, 20:42
St1:
-x<-x^3
or x>-x^3 =>holds true for x=2 and holds true for 1/2....not suff.
st2:
x<x^2=>x(x-1)>0 =>x<0 OR x>1.....therefore x is DEFINITELY NOT between 0 and 1...suffecient

Manager
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Concentration: Finance, Economics
Re: Is x between 0 & 1?  [#permalink]

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10 Jun 2012, 07:16
Bunuel wrote:
enigma123 wrote:
$$x<0$$

Shouldn't be x>0 because x(x-1) > 0?

x(x-1) > 0 --> roots are 0 and 1 --> ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: x<0 or x>1.

Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.

I don't understand this either. Is there some rule that explains this?
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Re: Is x between 0 & 1?  [#permalink]

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10 Jun 2012, 08:47
Stiv wrote:
Bunuel wrote:
enigma123 wrote:
$$x<0$$

Shouldn't be x>0 because x(x-1) > 0?

x(x-1) > 0 --> roots are 0 and 1 --> ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: x<0 or x>1.

Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.

I don't understand this either. Is there some rule that explains this?

There is indeed Stiv. That is why I gave the links to the threads explaining solution provided.

Once more, solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
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Re: Is x between 0 & 1?  [#permalink]

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10 Jun 2012, 11:36
Hi Stiv,

This is for your reference, might come handy:
Quote:
Hi,

A better approach is to check the sign of expression on a number line.

for example: (x-1)(x-2)(x-3)(x-7) < 0

To check the intervals in which this inequality holds true, we need to pick only one value from the number line.
Lets say x = 10, then (9)(8)(7)(3) > 0, in every alternate interval the sign would be + for the above expression

---(+)-----1--(-)--2---(+)--3----(-)-------7----(+)------

Thus, inequality would hold true in the intervals:
1 < x < 2
3 < x < 7

This is the general approach which can be used when you see multiplications in inequalities.

Regards,

Stiv wrote:
Bunuel wrote:
enigma123 wrote:
$$x<0$$

Shouldn't be x>0 because x(x-1) > 0?

x(x-1) > 0 --> roots are 0 and 1 --> ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: x<0 or x>1.

Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.

I don't understand this either. Is there some rule that explains this?
Manager
Joined: 02 Nov 2009
Posts: 102
Re: Is x between 0 & 1?  [#permalink]

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17 Jul 2012, 08:10
Bunuel

I did not understand this part

Statement 2 hovv did they both get opposite signs

Bunuel wrote:
enigma123 wrote:
Is x between 0 and 1?

(1) $$-x < x^3$$
(2) $$x < x^2$$

How come statement 1 is not sufficient to answer the question guys?

Is $$0<x<1$$?

(1) -x<x^3 --> $$x^3+x>0$$ --> $$x(x^2+1)>0$$ --> $$x>0$$ (as x^2+1 is always positive). Not sufficient.

(2) x<x^2 --> $$x^2-x>0$$ --> $$x(x-1)>0$$ --> either $$x>1$$ or $$x<0$$, so the answer is NO. Sufficient.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.
Math Expert
Joined: 02 Sep 2009
Posts: 54544
Re: Is x between 0 & 1?  [#permalink]

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17 Jul 2012, 08:16
venmic wrote:
Bunuel

I did not understand this part

Statement 2 hovv did they both get opposite signs

Bunuel wrote:
enigma123 wrote:
Is x between 0 and 1?

(1) $$-x < x^3$$
(2) $$x < x^2$$

How come statement 1 is not sufficient to answer the question guys?

Is $$0<x<1$$?

(1) -x<x^3 --> $$x^3+x>0$$ --> $$x(x^2+1)>0$$ --> $$x>0$$ (as x^2+1 is always positive). Not sufficient.

(2) x<x^2 --> $$x^2-x>0$$ --> $$x(x-1)>0$$ --> either $$x>1$$ or $$x<0$$, so the answer is NO. Sufficient.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Hope it helps.

Explained here:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
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Is x between 0 and 1?  [#permalink]

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21 Oct 2015, 03:42
enigma123 wrote:
Is x between 0 and 1?

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

Required: Is 0 < x < 1

Statement 1: $$-x < x^3$$
On rearranging, we have
$$x^3 + x > 0$$
$$x(x^2 + 1) > 0$$
Since a perfect square is always positive, hence adding 1 to a square will also be positive
Hence we have w > 0
From this information, w can be between 0 and 1 and can be greater than 1

INSUFFICIENT

Statement 2: $$x < x^2$$
$$x^2 - x >0$$
$$x(x - 1) > 0$$

Hence the possible values of x are x < 0 or x >1
We can safely say that x does not lie between 0 and 1

SUFFICIENT

Option B
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Is x between 0 and 1?  [#permalink]

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25 Oct 2015, 12:09
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.

Is x between 0 and 1?

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

There is only 1 variable (x), and 2 equations are given so there is high chance (D) will be our answer.
If the range of the question includes that of the condition, the condition is sufficient. We can use this to solve questions quickly and accurately.
From condition 1, x^3+x>0, x(x^2+1)>0 (as x^2+1>0). From this we get x>0. This is insufficient as the range of the question does not include this range.
From condition 2, x^2-x>0 x(x-1)>0, --> x<0 or 1<x. The condition answers the question 'no', so this is sufficient.

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: Is x between 0 and 1?  [#permalink]

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26 Mar 2019, 19:57
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Re: Is x between 0 and 1?   [#permalink] 26 Mar 2019, 19:57
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