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# Is X between 0 & 1? 1) X^2 is less than X 2) X^3 is

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Manager
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Is X between 0 & 1? 1) X^2 is less than X 2) X^3 is [#permalink]

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04 Mar 2010, 17:53
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50% (00:00) correct 50% (00:47) wrong based on 1 sessions

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Is X between 0 & 1?

1) X^2 is less than X
2) X^3 is positive

the right answer is A, but I think it should be E

here is my explanation: 1) as x^2 is less than x, so x is a decimal (positive or negative) - insufficient
2) x^3 is positive, so x is positive as well...insufficient

from 1 & 2, we know that x is positive and between 0 &1.

so how come 1 alone is sufficient according to the book?
Senior Manager
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Re: OG - Quantitative #76 [#permalink]

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04 Mar 2010, 18:13
A is right in this case.
Let me explain why.
For X^2 to be less than X we can have X only between 0 and 1.
eg.
X = 1/2
(1/2)^2 = 1/4 < 1/2 (true)

However in the other case: (the negative decimal between -1 and 0)
X = -1/2
(-1/2)^2 = 1/4 > -1/2 (not true)

So in this case 1.A is sufficient to say that X is between 0 and 1.
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Manager
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Posts: 176
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Re: OG - Quantitative #76 [#permalink]

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04 Mar 2010, 19:40
sidhu4u wrote:
A is right in this case.
Let me explain why.
For X^2 to be less than X we can have X only between 0 and 1.
eg.
X = 1/2
(1/2)^2 = 1/4 < 1/2 (true)

However in the other case: (the negative decimal between -1 and 0)
X = -1/2
(-1/2)^2 = 1/4 > -1/2 (not true)

So in this case 1.A is sufficient to say that X is between 0 and 1.

makes sense
thanks you
Re: OG - Quantitative #76   [#permalink] 04 Mar 2010, 19:40
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