I would go wiht E)

Is XY > X/Y

Stmt I

xy>0

x-> positive y->positive or x->negative y->negative

x=2 y=3 YES xy > x/y

x=-2 y=-1/2 NO

INSUFF

Stmt II

y<0

x=2 y= -1/2 YES xy>x/y


x=-2 y=-1/2 NO

INSUFF

Stmt I and II together

y<0 xy>0 so x is negative

x=-2 y=-8 YES xy>x/y

x=-2 y=-1/2 NO


Choose E)


P.S:

For problems like these (if its allowed with the given constraints) always consider values between 0 and 1 or -1 and 0 if needed as they exhibit some unique behaviours.

Hope this helps!

Regards,
CR

xy > x/y?


xy - x/y > 0

Is x( y-1/y) >0?


(2) y < 0

No info for X - INSUF


(1) xy > 0

x+,y+

if y =1 y-1/y=0 so INSUF

x-,y-

for y=-1 the equation is 0

INSUF

1+2) Still it means X and Y are negative

we still can have -1 and make it 0!

so choose E