A point on the adge of a fan blade that is rotating in a

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

A point on the adge of a fan blade that is rotating in a

by BTGmoderatorLU » Mon May 07, 2018 2:02 pm

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A point on the edge of a fan blade that is rotating in a plane is 10 centimeters from the center of the fan. What is the distance traveled, in centimeters, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per minutes?

$$A.\ 750\pi$$
$$B.\ 1500\pi$$
$$C.\ 1875\pi$$
$$D.\ 3000\pi$$
$$E.\ 7500\pi$$

The OA is B.

Please, can anyone assist me with this PS question? I need help to solve it. Thanks in advance!

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Source: Beat The GMAT — Problem Solving | Mon May 07, 2018 2:02 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon May 07, 2018 7:49 pm

BTGmoderatorLU wrote:A point on the edge of a fan blade that is rotating in a plane is 10 centimeters from the center of the fan. What is the distance traveled, in centimeters, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per minutes?

$$A.\ 750\pi$$
$$B.\ 1500\pi$$
$$C.\ 1875\pi$$
$$D.\ 3000\pi$$
$$E.\ 7500\pi$$

The OA is B.

Please, can anyone assist me with this PS question? I need help to solve it. Thanks in advance!

The information, "A point on the edge of a fan blade that is rotating in a plane is 10 centimeters from the center of the fan" means that the radius of the fan is 10cm.

In one revolution, the point on the edge of the fan would rotate by 2Ï€r = 2*Ï€*10 = 20Ï€ cm.

The number of revolutions done in 15 seconds = [300 revolutions/minutes]*15 seconds = [300 revolutions/60 seconds]*15 seconds = 75 revolutions

The distance traveled, in centimeters, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per minutes = 20Ï€*75 cm = 1500Ï€ cm.

The correct answer: B

Hope this helps!

-Jay
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by [email protected] » Tue May 08, 2018 8:48 pm

Hi All,

We're told that a fan blade is 10cm from the center of the fan (which means we have a radius of 10). We're then told that the fan blade spins for 15 seconds (which means that we're dealing with the circumference of a circle). We're asked how far the point "travels" if the fan makes 300 revolutions per minute. The 'math' involved in this question can be done in a couple of different ways, but here's a step-by-step method that should be easy to follow:

Since radius = 10
Circumference = 2(pi)(R) = 2(pi)(10) = 20pi

So every revolution = 20pi cm traveled

15 seconds = 1/4 of a minute
(300 revolutions/minute)(1/4 of a minute) = 75 revolutions in 15 seconds

(20pi cm)(75) = 1500pi cm

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu May 10, 2018 4:53 pm

BTGmoderatorLU wrote:A point on the edge of a fan blade that is rotating in a plane is 10 centimeters from the center of the fan. What is the distance traveled, in centimeters, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per minutes?

$$A.\ 750\pi$$
$$B.\ 1500\pi$$
$$C.\ 1875\pi$$
$$D.\ 3000\pi$$
$$E.\ 7500\pi$$

One entire revolution is equal to the circumference of the circle, which is 2 x Ï€ x 10 = 20Ï€.

We must convert 300 revolutions per minute to revolutions per second: 300/60 = 5 revolutions per second. So in 15 seconds the number of revolutions is 5 x 15 = 75 revolutions.

So the total distance traveled is 20Ï€ x 75 = 1500Ï€.

Answer: B

Scott Woodbury-Stewart
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