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# In which quadrant of the coordinate plane does the point

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Intern
Joined: 09 May 2013
Posts: 33
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.28
Re: In which quadrant of the coordinate plane does the point  [#permalink]

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08 Dec 2014, 02:47
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

Hope it helps!
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Re: In which quadrant of the coordinate plane does the point  [#permalink]

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17 Nov 2016, 21:48
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

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21 Apr 2018, 01:30
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|

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.

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Joined: 02 Sep 2009
Posts: 49916
Re: In which quadrant of the coordinate plane does the point  [#permalink]

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21 Apr 2018, 01:39
Shivikaa wrote:
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|

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.

-x < -y < |y| is true for ONLY positive values of x and y (which means that the point (x,y) lies in the first quadrant) but it's not true for ALL positive values of x and y.
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08 May 2018, 06:44
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.
In which quadrant of the coordinate plane does the point &nbs [#permalink] 08 May 2018, 06:44

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