A circular medallion is made of a circular piece of colored

[guest2]

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.

[GMAT 2007]

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

[dbernst]

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

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)

[siobhan]

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.

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.

[RonPurewal]

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.

[capntangen]

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.

[RonPurewal]

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.

[theboombody]

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.

There's a ton of ambiguity in this problem. It's horribly worded. Otherwise half the people that tried it wouldn't have made the same exact mistake. When you see the words "SURROUNDED BY A FRAME" you think that the frame is not part of the medallion and that the frame surrounds the medallion itself. I saw answer E differed by mine by one sign, but it was enough to throw me off and have me select another answer in a panic due to time constrictions. I assumed, like many others apparently, that the radius did not include the frame, which was not a bad assumption based on the wording of the problem. I had to assume that the radius included the frame or it didn't include the frame. I thought I picked the more logical of the two assumptions, and I stand by that thought. The question should be reworded so that it's CLEAR the frame be included. It could say, "The combined total radius of the shaded and unshaded areas is such and such." Then the person that started the original post here would have gotten the answer right. True, a VERY skilled quantitative person probably could have known to restructure the problem for the radius to include the frame after noticing no answers corresponded to his solution, but still, give us a break. This test is freakin' hard enough.

[RonPurewal]

theboombody, i understand why you are frustrated, but the problem clearly states that "the medallion consists of..." both parts.

on top of that, there's the actual, real-world meaning of the word -- i.e., what a "medallion" actually is in everyday parlance. a medallion is not just the glass/gem/centerpiece/whatever in the middle of the thing; the medallion is the whole thing hanging from a chain.