I have come across this question in CAT 2 and I feel the explanation given is wrong.

I feel 1 is insufficient since we cannot tell which quadrant the point lies if x & y are not positive . And the question do not indicate whether X & Y are positive .

Question & MH Answer :

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|

In essence, this question asks whether the signs of both x and y can be determined.

(1) SUFFICIENT: The key to evaluating this statement is to see which values of x and y actually satisfy it (“crack the code”). To do so, consider all possibilities for the signs of x and y.
• x > 0, y > 0: The left side becomes xy + xy + xy + xy = 4xy, which is a positive number; the statement is satisfied.
• x < 0, y > 0: The left side becomes xy – xy + xy – xy = 0, so the statement is not satisfied.
• x > 0, y < 0: The left side becomes xy + xy – xy – xy = 0, so the statement is not satisfied.
• x < 0, y < 0: The left side becomes xy – xy – xy + xy = 0, so the statement is not satisfied.
• Either x or y (or both) is 0: The left side becomes 0 + 0 + 0 + 0 = 0, so the statement is not satisfied.

Therefore, statement (1) can be rephrased simply as “Both x and y are positive.” The point (x, y) is thus in the first quadrant.

(2) SUFFICIENT: If –y does not equal |y|, then y must be positive (and –y must be negative). Since -x < -y, we know that –x is also negative, so x is also positive. The point (x, y) is therefore in the first quadrant.

The correct answer is D.

Take a look at the explanation you pasted in. All that stuff about statement 1 means is that statement 1 implies that x and y are both positive.

The logic goes like this. There are five possible sets of signs for x and y:

x>0, y>0
x>0, y<0
x<0, y>0
x<0, y<0
at least one of x and y is 0

Only the first of those is consistent with statement 1.
If statement 1 is true, then only the first of those is possible.
Statement 1 just means that x>0 and y>0.

Yes . I apologize . I underlooked that point. Thanks .

Cool.