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# After running 3,000 meters on a circular path, a runner is

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Eternal Intern
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After running 3,000 meters on a circular path, a runner is [#permalink]  29 Jul 2003, 09:15
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After running 3,000 meters on a circular path, a runner is at her starting point. The radius of the circular path could be which of the following?

I. 1,500/ pi
II. 750 / pi
III. 250/ pi

Is the trick she could be anywhere on her circular path?

VT
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Ride em cowboy

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Joined: 07 Jul 2003
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Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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Curly05 wrote:
After running 3,000 meters on a circular path, a runner is at her starting point. The radius of the circular path could be which of the following?

I. 1,500/ pi
II. 750 / pi
III. 250/ pi

Is the trick she could be anywhere on her circular path?

VT

Strictly speaking, the path could be ANY size because the problem doesn't state that the runner is runner only in one direction (clockwise or counterclockwise). HOWEVER, assuming that the runner IS traveling one way only, the "trick" is picking those radii which would yield a circumference that is exactly divisible into 3000 so that the runner could end up back at the starting point.

In either case, it looks like all of them would work.
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AkamaiBrah
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MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Eternal Intern
Joined: 07 Jun 2003
Posts: 468
Location: Lone Star State
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So it is the first case, right? Akami, your second case would be 1,500/ pi?
Victor
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Ride em cowboy

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Joined: 22 Jul 2003
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That's only partially correct guys. As AkamaiBrah mentioned, all three of the choices are possible.

You are assuming that it will take one full circle around to run 3000 meters. If that is the case then radius=1,500/ pi

If it takes 2 full circles to run the 3000 meters, then radius is= 750 / pi

If it takes 6 full circles to run the 3000 meters, then radius is= 250 / pi

That's why all three of the choices are possible.
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