naaga wrote:

Is xy > x/y?

(1) xy > 0

(2) y < 0

Is xy > x/y?

Is

xy > \frac{x}{y}? --> is

\frac{xy^2-x}{y}>0? is

\frac{x(y^2-1)}{y}>0? --> is

\frac{x(y+1)(y-1)}{y}>0? This inequality holds true when:

A. x>0 and y>1 or -1<y<0;

B. x<0 and 0<y<1 or y<-1. (1) xy > 0 -->

x and

y have the same sign. Not sufficient.

(2) y < 0. Not sufficient.

(1)+(2) Both

x and

y are negative, so we are in scenario B, though we still need more precise range for

y (if

y<-1 then the answer will be YES but if

-1<y<0 then the answer will be NO). Not sufficient.

Or: we can reduce our expression by x/y (which is positive since

x and

y have the same sign) and the question becomes: is

(y+1)(y-1)>0? and as

y<0 then the question reduces whether

y<-1. But we don't know that and thus even taken together statements are not sufficient.

Answer: E.

Bunuel, how did you deduce A and B above(the range for x and y) from given inequality and how did you appropriately put "and" and "or" to the respective places? I always get confused at this. Could you please show me your way of thinking for that?