kunaljain1701 wrote:

Bunuel , can u pls give one complete solution for this question. It is simplest to learn from your solutions which are short and apt.

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!