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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