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# Is x between 0 and 1?

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Is x between 0 and 1? [#permalink]

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06 Feb 2014, 01:16
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is x between 0 and 1?

(1) x^2 is less than x.
(2) x^3 is positive.

Data Sufficiency
Question: 76
Category: Arithmetic Arithmetic operations
Page: 158
Difficulty: 600

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Re: Is x between 0 and 1? [#permalink]

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06 Feb 2014, 01:16
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SOLUTION

Is x between 0 and 1?

(1) x^2 is less than x --> $$x^2<x$$ --> $$x(x-1)<0$$:

Multiples must have opposite signs:
$$x<0$$ and $$x-1>0$$, or $$x>1$$ --> no solution ($$x$$ cannot be simultaneously less than zero and more than 1);
$$x>0$$ and $$x-1<0$$, or $$x<1$$ --> $$0<x<1$$;

So $$x(x-1)<0$$ holds true when $$0<x<1$$. Sufficient.

For alternate approach check "How to solve quadratic inequalities": x2-4x-94661.html#p731476

(2) x^3 is positive --> $$x^3>0$$ just tells us that x is positive. Not sufficient.

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Re: Is x between 0 and 1? [#permalink]

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06 Feb 2014, 11:58
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Is x between 0 and 1?

(1) x^2 is less than x.
(2) x^3 is positive.

St1: x>x^2-----> x(1-x)>0
So either x>0 and 1-x>0 or 1>x and thus 0<x<1 or
x<0 or 1-x<0 or x>1...this is not possible cause we said x<0 so st1 alone is sufficent

St2: x^3 is positive...well there are many options like x=2 and x^3=8 or x=1/2 and x^3=1/8

So ans is A

Difficulty level 600 is okay

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Re: Is x between 0 and 1? [#permalink]

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07 Feb 2014, 19:12
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Is x between 0 and 1? -> is 0 < x < 1?

(1) x^2 is less than x -> only possible for values between 0 and 1. (if x < 0, x^2 always > x; if x > 1, x^2 always > x).
(2) x^3 is positive -> example: x = 2 or 1/2, Not sufficient.

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Re: Is x between 0 and 1? [#permalink]

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08 Feb 2014, 05:55
SOLUTION

Is x between 0 and 1?

(1) x^2 is less than x --> $$x^2<x$$ --> $$x(x-1)<0$$:

Multiples must have opposite signs:
$$x<0$$ and $$x-1>0$$, or $$x>1$$ --> no solution ($$x$$ cannot be simultaneously less than zero and more than 1);
$$x>0$$ and $$x-1<0$$, or $$x<1$$ --> $$0<x<1$$;

So $$x(x-1)<0$$ holds true when $$0<x<1$$. Sufficient.

For alternate approach check "How to solve quadratic inequalities": x2-4x-94661.html#p731476

(2) x^3 is positive --> $$x^3>0$$ just tells us that x is positive. Not sufficient.

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Re: Is x between 0 and 1? [#permalink]

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23 May 2014, 07:45
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Hi Bunuel, Just a small typo here. This is question number 76 on page#189 in OG Quant Review and not 71 as you mention here. thanks
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Re: Is x between 0 and 1? [#permalink]

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23 May 2014, 10:11
MensaNumber wrote:
Hi Bunuel, Just a small typo here. This is question number 76 on page#189 in OG Quant Review and not 71 as you mention here. thanks

Edited. Thank you. BTW, the question IS on page 158, the solution is on 189.
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Re: Is x between 0 and 1? [#permalink]

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23 May 2014, 10:29
Great! yup youre right about the page no.
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Re: Is x between 0 and 1? [#permalink]

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03 May 2015, 13:01
No need to talk why B is wrong. A) If X^2 < X it means that 0<X<1, X can not be negative -> -2^2 isalways > -2, so X is positive. And a positive X^2 can ONLY be smaller than X if its range is between 0 and 1.

It's actually a property of a normal fraction that X^2 < X (see MGMAT)
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Re: Is x between 0 and 1? [#permalink]

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06 May 2015, 02:28
Hi All,

We can also solve this question using the Wavy Line method.

Given:
We are asked if $$0< x <1$$. For finding the range of $$x$$, we need to solve the inequality given in the statements.

Statement-I:
St-I tells us that $$x^2 < x$$ i.e. $$x(x -1) < 0$$. Let's find the range of this inequality using the Wavy Line method.

The zero points of this inequality are {1,0}.

Plotting them on the number line using the Wavy Line method we see that the inequality is negative for the range $$0 < x < 1$$.

Hence, statement-I is sufficient to answer the question.

Statement-II:
St-II tells us that $$x^3 > 0$$. Let's draw a Wavy line for this inequality. The zero point of the inequality is {0}

Plotting it on the number line we see that the inequality is positive for the range $$x > 0$$. Thus, we can't say for sure if $$0 < x < 1$$.

Hence, statement-II is not sufficient to answer the question.

For more reading on the Wavy Line method try out inequalities-trick-91482-80.html#p1465609

Hope its clear!

Regards
Harsh
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Re: Is x between 0 and 1? [#permalink]

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15 Aug 2016, 23:50
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Re: Is x between 0 and 1?   [#permalink] 15 Aug 2016, 23:50
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