In which quadrant of the coordinate plane does the point : GMAT Data Sufficiency (DS)
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# In which quadrant of the coordinate plane does the point

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14 Jul 2009, 06:22
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55% (hard)

Question Stats:

62% (01:57) correct 38% (01:43) wrong based on 73 sessions

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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|

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-which-quadrant-of-the-coordinate-plane-does-the-point-86767.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Jun 2012, 00:14, edited 1 time in total.
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Re: DS question - Help [#permalink]

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14 Jul 2009, 07:25
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Wengen wrote:
Hi Guys,

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|

I chose ans B but the right answer seems to be D - Each stmt alone is sufficient.

since you understood B works i will help on A(1).
I just used basic POE assuming XY,X(-Y),(-X)Y, (-X)(-Y) representing the 4 quadrants.
XY: XY +XY+XY+XY >0 TRUE
X(-Y): XY+XY-XY-XY >0 FALSE
(-X)Y: XY-XY+XY-XY>0 FALSE
(-X)(-Y): XY-XY-XY+XY>0 FALSE

hope it helps kudos
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Re: DS question - Help [#permalink]

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14 Jul 2009, 10:14
Trying to learn !

When ever I see a |mod| I do one iteration by keeping all positives and next iteration by removing the |mod|

so when keep the |mod| in the first option I get..

4xy > 0 then xy >0 , which shows either its in Quadrant 1 or Q4

then coming to removing mod symbol, i get
-xy-xy-xy+xy = -2xy >0 which is xy < 0 which contradicts the result that I got above, so I stopped there... what is wrong with my approach ?

I solved the B in the same lines...

-x < -y <|y|
1) -x <-y --> x > y
2) -y < |y|
so -y < y or -y < -y
y > 0 or 0 > 0

second 0>0 is wrong so concluded y > 0 , when y >0 and x > y (x,y) lies in Q1. thats how I concluded B

Guys I am in serious trouble I just dont understnad how to proceed with modulus, I get freezed looking at them
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Re: In which quadrant of the coordinate plane does the point [#permalink]

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18 Jun 2012, 00:09
Wengen wrote:
Hi Guys,

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|

I chose ans B but the right answer seems to be D - Each stmt alone is sufficient.

I know this is late but I had to give my crack on it and, of course, so other people might be able to learn from this very great DS question.

Anyway,

The rephrase of the question asks us for the signs of x and y. If we know the signs of x and y then we'll be able to determine which quadrant does (x,y) lie.

On to the statements:
Statement (1) |xy| + x|y| + |x|y + xy > 0

There are two ways of attacking this:
1. By algebra (conceptual method)
We can test four cases:

(A) x < 0 and y < 0:
xy + (-x)(y) + xy + (-x)(y) > 0
xy - xy + xy - xy > 0
0 = 0
So this doesn't satisfy the equation

(B) x > 0 and y < 0:
xy + xy + (x)(-y) + (x)(-y) > 0
xy + xy - xy - xy > 0
0 = 0
So this doesn't satisfy the equation

(C) x < 0 and y > 0:
xy + (-x)(y) + xy + (-x)(y) > 0
xy - xy + xy - xy > 0
0 = 0
So this doesn't satisfy the equation

(D) x > 0 and y > 0:
xy + xy + xy + xy > 0
4xy > 0
This satisfies the equation. We conclude that x > 0 and y > 0 or x = + and y = +, which means that point (x,y) lies in quadrant I.
Statement (1) is sufficient.

2. By plugging in numbers:
x = + 3
x = - 3
y = + 3
y = -3

(A) x = -3 and y = -3

|(-3)(-3)| + (-3)|-3| + |-3|(-3) + (-3)(-3) > 0
9 - 9 - 9 + 9 > 0
0 = 0
Doesn't satisfy the equation.

This is the same as the above method. This helps if someone is having a hard time dealing with the "theoretical" side of modulus.

Statement (2) -x < -y < |y|

We break down the equation into two
(A) -y < |y| -> for this to be true, y should be +
(B) -x < -y multiplying both sides by negative 1 we have: x > y (since we know that y is positive, for this to be true x should be true)
Therefore, we know that x and y are positive. Statement (2) is sufficient.

Hope other people could chime in on this, especially statement (2). I am not convinced with myself. HAHA!
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Re: In which quadrant of the coordinate plane does the point [#permalink]

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18 Jun 2012, 00:14
OPEN DISCUSSION OF THIS QUESTION IS HERE: in-which-quadrant-of-the-coordinate-plane-does-the-point-86767.html
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Re: In which quadrant of the coordinate plane does the point   [#permalink] 18 Jun 2012, 00:14
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