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If x^3 < x^2, is x < 0 ?

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AnisMURR
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If x^3 < x^2, is x < 0 ? [#permalink] New post   31 Oct 2018, 01:45
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If \(x^3 < x^2\), is \(x < 0\) ?

A) \(|x| > x^2\)
B) \(x > x^2\)
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B
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GMATinsight
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If x^3 < x^2, is x < 0 ? [#permalink] New post   31 Oct 2018, 08:03
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AnisMURR wrote:
If \(x^3 < x^2\), is \(x < 0\) ?

A) \(|x| > x^2\)
B) \(x > x^2\)


Given: \(x^3 < x^2\)
i.e. \(x^3 - x^2 < 0\)
i.e. \(x^2(x - 1) < 0\)
But \(x^2\) can NOT be negative as being square of a number
i.e. \(x-1 < 0\)
i.e. \(x < 1\)

Question: is \(x < 0\) ?

Statement 1: \(|x| > x^2\)
i.e. \(-1 < x < 1\)
NOT SUFFICIENT

Statement 2: \(x > x^2\)

i.e. \(0 < x < 1\)

SUFFICIENT

Answer: Option B

P.S. I don't rate this question appropriate for GMAT practice as the GMAT question do NOT include any redundant information like \(x^3 < x^2\) given in this question
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jorgetomas9
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Re: If x^3 < x^2, is x < 0 ? [#permalink] New post   31 Oct 2018, 10:07
GMATinsight wrote:
AnisMURR wrote:
If \(x^3 < x^2\), is \(x < 0\) ?

A) \(|x| > x^2\)
B) \(x > x^2\)


Given: \(x^3 < x^2\)
i.e. \(x^3 - x^2 < 0\)
i.e. \(x^2(x - 1) < 0\)
But \(x^2\) can NOT be negative as being square of a number
i.e. \(x-1 < 0\)
i.e. \(x < 1\)

Question: is \(x < 0\) ?

Statement 1: \(|x| > x^2\)
i.e. \(-1 < x < 1\)
NOT SUFFICIENT

Statement 2: \(x > x^2\)

i.e. \(0 < x < 1\)

SUFFICIENT

Answer: Option B

P.S. I don't rate this question appropriate for GMAT practice as the GMAT question do NOT include any redundant information like \(x^3 < x^2\) given in this question

Excuse me, how do you solve the first equation?
\(|x| > x^2\)
Thank you.
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GMATinsight
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Re: If x^3 < x^2, is x < 0 ? [#permalink] New post   31 Oct 2018, 20:24
Expert Reply
jorgetomas9 wrote:
GMATinsight wrote:
AnisMURR wrote:
If \(x^3 < x^2\), is \(x < 0\) ?

A) \(|x| > x^2\)
B) \(x > x^2\)


Given: \(x^3 < x^2\)
i.e. \(x^3 - x^2 < 0\)
i.e. \(x^2(x - 1) < 0\)
But \(x^2\) can NOT be negative as being square of a number
i.e. \(x-1 < 0\)
i.e. \(x < 1\)

Question: is \(x < 0\) ?

Statement 1: \(|x| > x^2\)
i.e. \(-1 < x < 1\)
NOT SUFFICIENT

Statement 2: \(x > x^2\)

i.e. \(0 < x < 1\)

SUFFICIENT

Answer: Option B

P.S. I don't rate this question appropriate for GMAT practice as the GMAT question do NOT include any redundant information like \(x^3 < x^2\) given in this question

Excuse me, how do you solve the first equation?
\(|x| > x^2\)
Thank you.


jorgetomas9

I prefer to avoid mathematically solving such expressions.

There are 4 critical ranges which are
0 to 1
greater than 1
0 to -1 and
Less than -1

I always prefer to test the given expression in these ranges to test the validity.

Here I see that \(|x| > x^2\)

so point to be noted is \(|x|\) as well as \(x^2\) will always be positive for all values of x except zero.
also the absolute value of the number should become a smaller number when squared which happened in range 0 to 1

i.e. the expression will be valid in ranges 0 to 1 and 0 to -1

I HOPE THIS HELPS!!!
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Re: If x^3 < x^2, is x < 0 ? [#permalink]
31 Oct 2018, 20:24
Moderator:
Bunuel
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