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Finesse4eva
Junior Member

USA
6 Posts

Posted - 05/11/2008 :  14:56:49  Show Profile  Reply with Quote
Hey all,

I want to discuss a quantitative circular problem on a GRE General Practice Test but since it's a PDF file, I can't copy and paste the image. I know you can copy and paste an image on a PDF it you have anything but the free version. Can anyone do this?

For those of you who can an image of the problem is available at www.gre.com. On the main page click on click on the tab labeled Test Takers. Then click on the GRE general test. Once you do this there should be a tab that states Download library. Click on the link, and then scroll down to Test Preparation Materials. There should be a PDF file for a Gre General Practice Test. The problem in question is problem 11, section 5, pg. 48 of the PDF file.

If we all have an image that we can reference and is easily accessible I feel a lot of good discussion can come from this math problem. Only 19 of test takers got it right, so it obviously tripped a lot of people up.
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skeeter
Advanced Member

USA
5634 Posts

Posted - 05/11/2008 :  15:35:09  Show Profile  Reply with Quote
http://www.ets.org/Media/Tests/GRE/pdf/gre%20practice%20general%20test.pdf

section 5, problem 11, page 48, quantitative comparison ...

most test takers probably answered with choice "C", the two unshaded regions are equal, however, as with most test problem diagrams that ETS comes up with, one cannot make the assumption that the two lines intersect at the circle's center.
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peppers18
Advanced Member

Canada
124 Posts

Posted - 05/11/2008 :  15:42:38  Show Profile  Reply with Quote
From the picture, it may look like section B is bigger, but from the information given, you can not tell if one is bigger than the other. They just told you that the two shaded regions are the same size. It says nothing about the unshaded regions.
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Finesse4eva
Junior Member

USA
6 Posts

Posted - 05/11/2008 :  16:10:38  Show Profile  Reply with Quote
Exactly skeeter! And thanks for the graphic peppers 18...

I like most test takers answered C because I figured the angels of the shaded region were equal, thus the angels of the unshaded sections were also equal, and hence the areas were also equal. however, this chain of deductions is only valid if the segments constructed by the two lines intersecting represented radii of the circle, essentially what skeeter brought up ... and though they look like they could be radii, it is never explicitly mention and hence i can't assume it

so is the lesson here that you cannot definitively calculate or compare regions of a circle if the problem does not confirm that the lines intersect at the center and/or state that certain segments are indeed radii ... i know it seems like a fairly mundane deduction but the problem seemed fairly innocuous and it turned out to be a monster ... once again, thanks for the help ... my test is on Wednesday : )
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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 05/11/2008 :  22:53:11  Show Profile  Reply with Quote
However, if we assume that the shaded regions were constructed by two intersecting straight lines (instead of four lines out of a point) - then to have equal area - those must intersect at the center.

I guess the critical question is then assumption of two intersecting lines or more (are those even straight-lines).

I hate these questions.
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peppers18
Advanced Member

Canada
124 Posts

Posted - 05/11/2008 :  23:08:13  Show Profile  Reply with Quote
even assuming that they are two intersecting lines, they do not need to intersect at the centre. see my pic (they may not look like equal areas, but it's close enough for me )

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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 05/12/2008 :  14:52:03  Show Profile  Reply with Quote
Pepper,

You are correct - I stand corrected. For equal area, those lines will have to be symmetrical about the diametrical line passintg through the point of intersection.

Still - I hate those questions where the assumptions are not spelled out. Even if they had defined the point of intersection to be the center - there would be questions about whether those are two lines or four lines or three lines.

Edited by - Subhotosh Khan on 05/12/2008 14:53:53
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