jennysussna wrote:
Is x > 0?
(1) (x^2 - 1)(x^3) > 0
(2) x^2 < 1
OA:C
\((1) \quad (x^2 - 1)(x^3) > 0\)
It leads to two cases
Case 1
\((x^2-1)>0\)
AND \(x^3>0\)
This leads to \(x>1\)
ORCase 2
\((x^2-1)<0\)
AND \(x^3<0\)
This leads to \(-1<x<0\)
So \(x\) can be either \(x>1\)
OR \(-1<x<0\)
Statement \(1\) alone is insufficient
\((2) \quad x^2 < 1\)
This leads to \(-1<x<1\)
Statement \(2\) alone is insufficient
Combining \((1)\) and \((2)\), we get \(-1<x<0\).
After combining \((1)\) and \((2)\), there is a definite answer to the question:
Is x > 0? No
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