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Shivikaa
Bunuel
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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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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Bunuel
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|

here's what inequality plots of 2 inequalities look like:
Attachments

Inequality plots.jpg
Inequality plots.jpg [ 26.15 KiB | Viewed 1598 times ]

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Hello from the GMAT Club BumpBot!

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