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In which quadrant of the coordinate plane does the point

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Re: In which quadrant of the coordinate plane does the point [#permalink]

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New post 28 Aug 2014, 01:56
1. |xy| + x|y| + |x|y + xy > 0

|x||y|+ x|y| + |x|y + xy > 0 ; |x|(|y|+y)+x(|y|+y)>0 ; (|y|+y)(|x|+x)>0

if y <= 0 then |y|+y=-y+y=0 =>(|y|+y)(|x|+x)=0 then y is absolutely positive. same for x. => sufficient

2. -x < -y < |y|

-y<|y| ; if y < 0 then |y|=-y which is not the case then y > 0.

y>0 then -y<0, and -x < -y then -x < 0 and x > 0.

=> sufficient

Answer: D
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Re: In which quadrant of the coordinate plane does the point [#permalink]

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New post 08 Dec 2014, 01:47
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!

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Re: In which quadrant of the coordinate plane does the point [#permalink]

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New post 17 Nov 2016, 20:48
Bunuel wrote:
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|



Please check the solution as attached

Answer: option D
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Re: In which quadrant of the coordinate plane does the point [#permalink]

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New post 19 Nov 2017, 03:29
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Re: In which quadrant of the coordinate plane does the point   [#permalink] 19 Nov 2017, 03:29

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