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# A wheel has a diameter of x inches and a second wheel has a diameter

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A wheel has a diameter of x inches and a second wheel has a diameter [#permalink]

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20 Jan 2015, 05:34
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A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: A wheel has a diameter of x inches and a second wheel has a diameter [#permalink]

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20 Jan 2015, 20:05
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[quote="Bunuel"]A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y

First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)

Now,
Revolutions = distance/circumference

So, from equation (1)
100 = d/(x*pi)
d = 100 * x * pi ---------- (3)

From equation (2)
Revolutions = d/(y*pi) = (100 * x * pi) / (y*pi) = 100x/y

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Re: A wheel has a diameter of x inches and a second wheel has a diameter [#permalink]

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20 Jan 2015, 22:41
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d feet = 12d inches = 100 revolutions = 100*circumference = 100*(pi)*x
For same distance # revolutions for second wheel = distance/circumference = 100*pi*x/(pi*y) = 100x/y.

Bunuel wrote:
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y

Kudos for a correct solution.

Kudos [?]: 252 [1], given: 32

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Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A wheel has a diameter of x inches and a second wheel has a diameter [#permalink]

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22 Jan 2015, 20:48
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Answer = E. 100x/y

............................ Wheel A ..................... Wheel B

Diameter .................. x .............................. y

Radius .................... $$\frac{x}{2}$$ ............................ $$\frac{y}{2}$$

Circumference .......... $$\frac{d}{100}$$ ......................... $$2\pi(\frac{y}{2})$$ .............

$$2\pi(\frac{x}{2}) = \frac{d}{100}$$

$$d = 100\pi x$$

Revolutions of Wheel B to achieve distance d$$= \frac{100\pi x}{2\pi(\frac{y}{2})} = 100\frac{x}{y}$$
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Re: A wheel has a diameter of x inches and a second wheel has a diameter [#permalink]

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15 Feb 2016, 08:57
Bunuel wrote:
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y

Kudos for a correct solution.

A very simple Question

Circumference of a circle = pi * D = distance covered in one revolution.
For first circle, one revolution = pi*x
In 100 revolutions, distance covered = 100* pi*x = d feet
Second wheel in one revolution = pi*y
For d feet or for 100*pi*x it will take 100*pi*x / pi*y

or, 100x/y

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Re: A wheel has a diameter of x inches and a second wheel has a diameter [#permalink]

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14 Oct 2017, 06:47
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Re: A wheel has a diameter of x inches and a second wheel has a diameter   [#permalink] 14 Oct 2017, 06:47
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# A wheel has a diameter of x inches and a second wheel has a diameter

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