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A circular medallion is made of a circular piece of colored

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guest2
 Post subject: A circular medallion is made of a circular piece of colored
 Post Posted: Thu Aug 02, 2007 7:31 pm 
From GMATPrep Quant:

A circular medallion is made of a circular piece of colored glass surrounded by a circular metal frame. If the radius of the medallion is r centimeters and the width of the metal frame is S centimeters, then in terms of S and r, what is the area of the metal frame in square centimeters?

A) Pi(r - s)^2
B) Pi(r^2 - s^2)
C) 2Pi(r - s)
D) rPi(2r - s)
E) sPi(2r - s)

I have re-done this problem several times and always end up with sPi(2r + s), which is close to the answer E, but not quite there. Your help is greatly appreciated.
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GMAT 2007
 Post subject:
 Post Posted: Thu Aug 02, 2007 8:09 pm 
Area of metal frame = Area of medallion - Area of the inner circular area of the medallion (except frame)

= Pi(r^2) - Pi(r-s)^2
= Pi(r^2) - Pi(r^2 + s^2 - 2rs)
= Pi(r^2) - Pi*r^2 - Pi*s^2 + Pi*2rs
= Pi*2rs - Pi*s^2
= Pi*s(2r-s)
Answer is (E)

Hope it helps

GMAT 2007
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dbernst
 Post subject:
 Post Posted: Fri Aug 03, 2007 12:32 am 
Offline
ManhattanGMAT Staff


Posts: 304
You variable guys live in a different world from us lowly numbers folk. As my intellect is slightly less evolved than that of Forrest Gump, I'm going with the plugging in numbers approach on this VIC (Variables In the answer Choices). Also, don't forget to draw the problem. If you don't draw, Stupid is as stupid does, just like Mama says.

If r = 6, the area of the entire medallion is 36pi
If s = 2, the area of the colored class is 16 pi (since the radius of glass = 4)
Thus, the area of the metal frame is 36pi - 16pi = 20pi

Now, just plug r = 6 and s = 2 into the answer choices, and choose the one that equals 20pi.

A) Pi(r - s)^2 = 16pi
B) Pi(r^2 - s^2) = 32 pi
C) 2Pi(r - s) = 8pi
D) rPi(2r - s) = 60pi
E) sPi(2r - s) = 20pi

The correct answer is E, and that's all I have to say about that.

-dan



Quote:
A circular medallion is made of a circular piece of colored glass surrounded by a circular metal frame. If the radius of the medallion is r centimeters and the width of the metal frame is S centimeters, then in terms of S and r, what is the area of the metal frame in square centimeters?

A) Pi(r - s)^2
B) Pi(r^2 - s^2)
C) 2Pi(r - s)
D) rPi(2r - s)
E) sPi(2r - s)


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siobhan
 Post subject: Re: A circular medallion is made of a circular piece of colored
 Post Posted: Fri Oct 23, 2009 1:30 am 
Offline
Course Students


Posts: 7
This question stumped me too. I think it's poorly worded.

The medallion is made up of both the glass piece AND the frame. So the r is the radius of the entire object. The radius of just the inner glass piece is (r-s). Very annoying.

guest2 wrote:
From GMATPrep Quant:

A circular medallion is made of a circular piece of colored glass surrounded by a circular metal frame. If the radius of the medallion is r centimeters and the width of the metal frame is S centimeters, then in terms of S and r, what is the area of the metal frame in square centimeters?

A) Pi(r - s)^2
B) Pi(r^2 - s^2)
C) 2Pi(r - s)
D) rPi(2r - s)
E) sPi(2r - s)

I have re-done this problem several times and always end up with sPi(2r + s), which is close to the answer E, but not quite there. Your help is greatly appreciated.
Top 
RonPurewal
 Post subject: Re: A circular medallion is made of a circular piece of colored
 Post Posted: Sat Oct 24, 2009 8:25 am 
Offline
ManhattanGMAT Staff


Posts: 7146
yeah, see the post above by dbernst. this is a problem that is made WAY easier by plugging in numbers.

for anyone reading this who's not american, he is making movie references in his post. feel free to ignore them.
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capntangen
 Post subject: Re: A circular medallion is made of a circular piece of colored
 Post Posted: Mon Jul 25, 2011 9:22 pm 
Offline
Students


Posts: 2
FYI, plugging in doesn't help if you didn't understand (like I didn't) that the radius referred to both the medallion and the frame. Thanks for the explanation.
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RonPurewal
 Post subject: Re: A circular medallion is made of a circular piece of colored
 Post Posted: Sat Jul 30, 2011 3:16 am 
Offline
ManhattanGMAT Staff


Posts: 7146
capntangen wrote:
FYI, plugging in doesn't help if you didn't understand (like I didn't) that the radius referred to both the medallion and the frame. Thanks for the explanation.


there is no ambiguity in the problem statement; the term “radius” refers only to the radius of an actual circle. therefore, “the radius of the medallion” must refer to the radius of the entire circular area enclosed by the medallion, even if there's a hole in the middle of the medallion.
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