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# Quantitative review 2nd edition : DS 76. Is x between 0 and

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Quantitative review 2nd edition : DS 76. Is x between 0 and [#permalink]

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17 Jun 2011, 11:41
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Difficulty:

25% (medium)

Question Stats:

81% (01:37) correct 19% (01:19) wrong based on 36 sessions

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Quantitative review 2nd edition : DS 76.
Is x between 0 and 1?
(1) x^2 is less than x.
(2) x^3 is positive

For (1) "OG explanation says that X^2 is positive so x positive."
But a negative x, x^2 is also positive. What is my wrong?
[Reveal] Spoiler: OA

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

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17 Jun 2011, 12:09
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Baten80 wrote:
Quantitative review 2nd edition : DS 76.
Is x between 0 and 1?
(1) x^2 is less than x.
(2) x^3 is positive

For (1) "OG explanation says that X^2 is positive so x positive."
But a negative x, x^2 is also positive. What is my wrong?

If x^2 is less than x, then x must be +ve. Because, if x is -ve, x^2 will always be greater than x, not less.

Then comes the question whether x is between 0 and 1.
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Re: Is x between 0 and 1? [#permalink]

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17 Jun 2011, 13:32
Baten80 wrote:
Quantitative review 2nd edition : DS 76.
Is x between 0 and 1?
(1) x^2 is less than x.
(2) x^3 is positive

Is x between 0 and 1? ---> is x a + fraction

(1) x^2 is less than x --> means x is a fraction because when fractions are squared, they are less then their original value

now if x was a (-) fraction, it would become greater than its original because its being squared. therefore x = (+) fraction

Suff.

(2) completely meaningless. just tells you that x is a positive. don't know if its a fraction or an integer

hence (a)
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Re: Is x between 0 and 1? [#permalink]

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17 Jun 2011, 14:20
A

x cannot be more than 1 because x^2>x then..same would be the case with x<0....but x^2<x holda true for all values between 0 and 1
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Re: Is x between 0 and 1? [#permalink]

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17 Jun 2011, 17:27
is 0<x<1?

1. x^2<x

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

solutions are x<0 & x>1 or x>0 & x<1

x<0 & x>1 is not possible. So only possible solution is x>0 & x<1. So sufficient

2. x^3>0

all we can say x>0

Not sufficient.

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

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17 Jun 2011, 17:35
think this way

if x^2>0 , x can be positive or negative
but here we were told x^2<x. this will never be true for negative numbers as x^2 is always positive and will not
be less than a negative number.

=> x is positive. Now again x2<x will be true in the range of 0<x<1 .

Hence 0<x<1 . Hope its clear now.

Baten80 wrote:
Quantitative review 2nd edition : DS 76.
Is x between 0 and 1?
(1) x^2 is less than x.
(2) x^3 is positive

For (1) "OG explanation says that X^2 is positive so x positive."
But a negative x, x^2 is also positive. What is my wrong?
Re: Is x between 0 and 1?   [#permalink] 17 Jun 2011, 17:35
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