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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 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

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, 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

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

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New post 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.

Please explain what I'm missing.
Thanks in advance.
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Re: In which quadrant of the coordinate plane does the point  [#permalink]

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New post 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.

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


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

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New post 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.
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In which quadrant of the coordinate plane does the point &nbs [#permalink] 08 May 2018, 06:44

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