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# A circular rim 28 inches in diameter rotates the same number

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Intern
Joined: 09 Oct 2006
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A circular rim 28 inches in diameter rotates the same number [#permalink]

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08 Nov 2006, 16:15
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Difficulty:

65% (hard)

Question Stats:

66% (02:08) correct 34% (02:25) wrong based on 218 sessions

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A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-circular-rim-28-inches-in-diameter-rotates-the-same-number-65106.html
[Reveal] Spoiler: OA

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Intern
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08 Nov 2006, 16:42
A tricky question from GMATPrep.

It's C.

Let's try the explanation. We have two wheels. One with 28pi and the other one with 35pi. They have the same speed. In the smaller wheel it's 28pi*x, which must be equal to the speed of the bigger one (35pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).
Anyway, we have 28pi*x=35pi*a.
(28pi*x)/(35pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 48x.

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Intern
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08 Nov 2006, 17:30
gmahn wrote:
A tricky question from GMATPrep.

It's C.

Let's try the explanation. We have two wheels. One with 28pi and the other one with 35pi. They have the same speed. In the smaller wheel it's 28pi*x, which must be equal to the speed of the bigger one (35pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).
Anyway, we have 28pi*x=35pi*a.
(28pi*x)/(35pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 48x.

Thanks for the explanation. The OA does indicate C.

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08 Nov 2006, 18:08
Circumference of rim A = 28pi
Circumference of rim B = 35pi

Rim A rotates x revolution/second --> 28xpi inches/second

Rim B also rotates 28xpi inches/second. Rim B will then make 28xpi * 1/35pi rev/second = 4x/5 rev/second = 48x rev/min

(Not too hard, the key to this question is to know how to break down to the desired units. For instance, we started off with inches/second, to get the revs/second, we need to have inches/second * revs/inches)

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08 Nov 2006, 22:39
C ......but I was really trapped into this one as I didn't pay attention to 'minutes'..I calculated my answer in seconds

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Re: A circular rim 28 inches in diameter rotates the same number [#permalink]

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17 Jun 2014, 07:07
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Re: A circular rim 28 inches in diameter rotates the same number [#permalink]

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17 Jun 2014, 07:48
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A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. 48pi/x
B. 75x
C. 48x
D. 24x
E. x/75

1 revolution of a circle = circumference of that circle.

1 revolution of a circle with the diameter of 28 inches = $$\pi{d}=28\pi$$ inches. Hence, x revolutions per second = $$28\pi{x}$$ inches per second = $$60*28\pi{x}$$ inches per minute.

Given that $$60*28\pi{x}=35\pi{n}$$ --> $$n=\frac{60*28\pi{x}}{35\pi}=48x$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-circular-rim-28-inches-in-diameter-rotates-the-same-number-65106.html
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Re: A circular rim 28 inches in diameter rotates the same number   [#permalink] 17 Jun 2014, 07:48
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