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C
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Difficulty:
55%
(hard)
Question Stats:
59% (02:02) correct
41%
(02:03)
wrong
based on 119
sessions
History
Date
Time
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Not Attempted Yet
14 Jul 2010, 08:12
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Is \(p<0\)?
(1) \(p^3(1-p^2)<0\), or which is the same \(p(1-p^2)<0\) --> \(p<p^3\) --> either \(p\) is more than 1, \(p>1\) OR \(p\) is negative fraction \(-1<p<0\).
So we have two ranges for \(p\): \(p>1\) or \(-1<p<0\). Not sufficient.
(2) \(p^2-1<0\) --> \(-1<p<1\). Not sufficient.
(1)+(2) Intersection of the ranges from (1) and (2) is the range \(-1<p<0\), so the answer to the question "is \(p<0\)" is YES. Sufficient.
Answer: C.
Hope it's clear.
(1) \(p^3(1-p^2)<0\), or which is the same \(p(1-p^2)<0\) --> \(p<p^3\) --> either \(p\) is more than 1, \(p>1\) OR \(p\) is negative fraction \(-1<p<0\).
So we have two ranges for \(p\): \(p>1\) or \(-1<p<0\). Not sufficient.
(2) \(p^2-1<0\) --> \(-1<p<1\). Not sufficient.
(1)+(2) Intersection of the ranges from (1) and (2) is the range \(-1<p<0\), so the answer to the question "is \(p<0\)" is YES. Sufficient.
Answer: C.
Hope it's clear.
Hussain15
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Concentration: Strategy, General Management
Schools: Stanford '14 (D) Booth '14 (D) Johnson '14 (D)
GMAT 1: 680 Q48 V34
Schools: Stanford '14 (D) Booth '14 (D) Johnson '14 (D)
GMAT 1: 680 Q48 V34
Posts: 1,077
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3,237
14 Jul 2010, 08:18
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I assume that stmt 1 is \(p^2-1<0\) & stmt 2 is \(p^3(1-p^2)\)
Stmt 1.
\(p^3(1-p^2)<0\)
Either p\(^3<0\) or \(1-p^2<0\)
\(p<0\) or \(p^2>1\)
\(p<0\) or \(p>1\) or \(p<-1\) so not sufficient
Stmt 2
\(p^2-1<0\)
\((p-1)(p+1)<0\)
either \(p<1\) or \(p<-1\) Not sufficient again
Combing the two, again multiple answers. So "E" for me. I think Bunuel can clarify better, I can be wrong
Stmt 1.
\(p^3(1-p^2)<0\)
Either p\(^3<0\) or \(1-p^2<0\)
\(p<0\) or \(p^2>1\)
\(p<0\) or \(p>1\) or \(p<-1\) so not sufficient
Stmt 2
\(p^2-1<0\)
\((p-1)(p+1)<0\)
either \(p<1\) or \(p<-1\) Not sufficient again
Combing the two, again multiple answers. So "E" for me. I think Bunuel can clarify better, I can be wrong
I believe that Bunuel will soon show up and help us.
