niks18 wrote:

If \(x>2\) and \(y>-1\), then which of the following statements must be true?

A. \(xy>-2\)

B. \(-x<2y\)

C. \(xy<-2\)

D. \(-x>2y\)

E. \(x<-2y\)

OE\(x>2\) this implies \(-x<-2\) ----------------\((1)\)

\(y>-1\), multiplying both side of the inequality by \(2\), we get \(2y>-2\) ---------------\((2)\)

Combining equations \((1)\) & \((2)\), it is clear that

\(-x<2y\)

Hence Option

B---------------------------------

Another method could be to test some values of \(x\) & \(y\) as per the given condition but that might take more than a minute to arrive at the final answer