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Co-ordinate Geometry - DS question

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Co-ordinate Geometry - DS question

by yankee.musk » Sat May 22, 2010 1:45 pm
Got trouble with this question. Any suggestions on the solution? I chose (A) and got it wrong.

Question:
If (ab NOT EQUAL 0) and points (-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in this same quadrant?

(1) xy > 0
(2) ax > 0
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by liferocks » Sat May 22, 2010 9:40 pm
points (-a,b) and (-b,a) are in the same quadrant of the xy-plane a and b are of same sign
if (-x,y) is also in the same quadrant with (-a,b) and (-b,a),x and y has to be of same sign as a and b

From 1
xy>0..so x and y are of same sign.but no information whether x,y are of same sign as a and b...not sufficient

From2
ax>0..a and x are of same sign..no information about sign of y...not sufficient

combining
all of a,x,y and b are of same sign....sufficient
Ans option C
"If you don't know where you are going, any road will get you there."
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by gmatmachoman » Sat May 22, 2010 10:21 pm
Let us assume (a,b) = (1,2) where a>0, b>0

so as per the stem : (-a,b) = (-1,2) & (-b,a) = (-2,1). Both these points are in second quadrant.

St1 : xy > 0

case 1: x<0, y<0

Third quadrant

case 2:

x>0, y>0

First quadrant

Inconsistent/. So Insufficient

St 2: ax > 0

we have a>0 , so x>0. But we dont have any idea about y. Insufficient.

Combining we will have, from st2 that x>0,

Recall case 2 of St 1:

when X>0 , then Y has to be >0

so xy>0 where X>0 & Y>0

.Having said that, (-X,Y) will also reside in secon quadrant as that of (-a,b) or (-b,a).

Pick C
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by Patrick_GMATFix » Sat May 22, 2010 10:36 pm
This question is a bit challenging because it disguises itself as a geometry question when it's really a number properties question.

Two points can be in the same quadrant only if the x coordinates have the same sign and the y coordinates have the same sign. So this question is asking: Is (-x) of the same sign as (-a) and (-b)? Also is y of the same sign as a and b?

For (-x) to have the same sign as (-a) and (-b), x, a and b must have the same sign. Essentially we're asked whether all variables have the same sign.

The correct answer is C.

To better understand, have a look at the video solution. This is GMATPrep question 1043

-Patrick
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by yankee.musk » Mon May 24, 2010 7:26 am
Thank you all. The OA indeed is C.

I'm new to this forum and having trouble using the spoiler feature while posting. Could you help?

Step 1: I start composing a post
Step 2: Click the Spoiler button. The tag [spoiler] gets added.
Step 3: I type a letter corresponding to the answer - such as c or a after [spoiler]
Step 4: I click Submit to submit the post and I see the below text in my posting instead of actual spoiler feature

[spoiler]a[/spoiler]
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by Patrick_GMATFix » Mon May 24, 2010 8:39 am
yankee.musk,

You're welcome :-)

The way I use the spoiler is:

1) just type in the text
2) highlight the spoiler text
3) click the SPOILER button. The text will be automatically wrapped inside SPOILER tags correctly.
4) Hit Preview (instead of submit) to check that the text is hidden correctly.
5) Hit Submit.

[spoiler]It works![/spoiler]
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