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enfinity
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Circle: Area triples, what happends to the radius (MGMAT) 20 Sep 2009, 07:03
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Hi there,

I found a very useful document on the MGMAT website. However, I think they made a mistake in one of their sample problem so I just want some confirmation that this is indeed a mistake...

Here the link: https://www.manhattangmat.com/strategy- ... oncept.cfm

Here the problem:
Quote:
At a certain barn, the horses exercise in one of two circular arenas using what is called a lunge rope. A trainer stands in the center of the circular arena holding a rope attached to the horse, and the horse runs in a circular path along the perimeter of the arena. Assuming negligible distance between the horse's path of motion and the edge of the arena, approximately how many times as much rope is needed to lunge a horse in the larger arena if the larger arena has an area three times that of the smaller one?

(A) 1.5
(B) 1.7
(C) 2
(D) 3
(E) 6


MGMAT SOLUTION:
The formula for the area of a circle is A=pi*r^2. Mathematically, this means that the area of a circle is proportionate to the square of the radius. If the radius of a circle is doubled, the area of the circle will be quadrupled. If the radius of a circle is tripled, the area of the circle will multiply by a factor of 9. We can represent this relationship in a proportion:

A1/A2=r1^2/r2^2

Let's call circle 1 the smaller circle. We know that the ratio of the areas in this question is 1:3. Since it is simply the ratio of the radii that we are concerned with in this question, we can assign a random value of 1 as the radius of the smaller circle and solve for x, the radius of the larger circle.
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I marked the part that I do not agree with. They simply say that 1=pi*1^2 (this equation is never true). Did I miss something or is this indeed a mistake.



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Circle: Area triples, what happends to the radius (MGMAT) 20 Sep 2009, 07:04
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Ok, I think I got it (they're just comparing the ratios on the right side). So it should be correct.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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