Manhattan GMAT advanced quant

[cumulonimbus]

Hi,
I have a question regarding this MGMAT's advanced guide example on page 79.

If x is not equal to 0, Is xy>0
1) x>0
2) 1/x<y

I marked the answer as B, because if xy>1 then xy has to greater that 0,
i.e. xy>0.

Please clarify.

[tim]

What makes you say that xy > 1? It looks like you multiplied both sides by x, which we cannot do unless we know that x is positive ahead of time.