In which quadrant of the coordinate plane does the point

In which quadrant of the coordinate plane does the point (x, y) lie?

(1) |xy| + x|y| + |x|y + xy > 0
(2) -x < -y < |y|

(1) SUFFICIENT:
Set |xy| + x|y| + |x|y + xy = A
There are 4 cases (equivalent to 4 quadrant) which we need to consider:
• x > 0, y > 0: A = xy + xy + xy + xy = 4xy > 0 => (x,y) belongs to the first quadrant
• x < 0, y > 0: xy – xy + xy – xy = 0 ; contradict with the first condition A>0 => (x,y) does not belong to the second quadrant
• x > 0, y < 0: xy + xy – xy – xy = 0 ; contradict with the first condition A>0 => (x,y) does not belong to the third quadrant
• x < 0, y < 0: xy – xy – xy + xy = 0; contradict with the first condition A>0 => (x,y) does not belong to the fourth quadrant
Either x or y must be not equal 0; otherwise A = 0; contradict with the first condition A>0
(2) SUFFICIENT:
|y|> -y => y>0 => x>y>0 => (x,y) belongs to the first quadrant

The correct answer is D.

Hope it helps!