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!

Hi,
How can Statement 2 be true ?
Let's say x,y is (1,1)
so, the statement becomes -1<-1< |-1|
i.e -1<-1<1
It is not true.

Please explain what I'm missing.
Thanks in advance.

For stmt 1 to be true, both x & y have to be +ve.
For stmt 2, lets deal it in two parts.
for -y<|y|; Y has to be positive.
now since Y is positive,
for -x<-y; x has to be positive and greater that Y.

In both cases X and Y are positive hence D.