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Ben is driving on the highway at x miles per hour. (One mile

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Ben is driving on the highway at x miles per hour. (One mile

by swerve » Mon Aug 13, 2018 10:42 am

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Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?

A. 5,280(x/y)
B. 5,280(y/x)
C. 5,280(xy)
D. 5,280/(xy)
E. (xy)/5,280

The OA is A.

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by GMATGuruNY » Tue Aug 14, 2018 2:27 am
swerve wrote:Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?

A. 5,280(x/y)
B. 5,280(y/x)
C. 5,280(xy)
D. 5,280/(xy)
E. (xy)/5,280
Note:
One revolution = one CIRCUMFERENCE.

Let x = 2 miles per hour, implying that the distance traveled in 1 hour = 2*5280 = 10560 feet.
Let y = 10 feet.
Since the total distance traveled in 1 hour = 10560 feet, and each circumference = 10 feet, the number of revolutions in 1 hour = 10560/10 = 1056.
Thus, the correct answer must yield 1056 when x=2 and y=10.
Only A works:
(5280)(2/10) = 1056.

The correct answer is A.
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by Brent@GMATPrepNow » Tue Aug 14, 2018 4:33 am
swerve wrote:Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?

A. 5,280(x/y)
B. 5,280(y/x)
C. 5,280(xy)
D. 5,280/(xy)
E. (xy)/5,280

The OA is A.

Source: Manhattan GMAT
Here's an algebraic approach:

Each tire has a circumference of y feet.
So, there will be 1 revolution every time the car travels y feet.
5280/y = the number of times y divides into 5280.
So, if the car travels 5280 feet (aka 1 mile) in one hour, then there will be 5280/y revolutions.
If the car travels (x)(5280) feet (aka x miles) in one hour, then there will be (x)(5280/y) revolutions.
(x)(5280/y) = 5280x/y = 5280(x/y

Answer: A

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by Jeff@TargetTestPrep » Sat Aug 18, 2018 6:39 pm
swerve wrote:Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?

A. 5,280(x/y)
B. 5,280(y/x)
C. 5,280(xy)
D. 5,280/(xy)
E. (xy)/5,280
We are given that Ben is driving at an average rate of x mph, and we need to determine how many revolutions each wheel turns in one hour.

Since 1 mile = 5,280 feet, Ben drives 5280x feet in one hour.

Thus, the number of revolutions is distance/circumference = (5,280x)/y = 5,280(x/y).

Answer: A

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