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 Post subject: GRE Rate (Select One)
PostPosted: Sun Mar 13, 2011 3:45 am 
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Joined: Sun May 30, 2010 3:15 am
Posts: 424
5 identical snow plows can clear an iced parking lot in 12 hours. How long would it take 6 such snow plows to clear the same parking lot?

A. 10 hours
B. 7 hours, 30 minutes
C. 3 hours
D. 2 hours, 30 minutes
E. 1 hour, 15 minutes

(A) For a problem where a job size remains the same, but the number of workers changes, there is a very intuitive way to get to the answer, without using algebra. For example, if we double the number of workers on a job, it should take half the time. If we triple the number of workers on a job, it should take one-third the time. Similarly, if we use one-half the number of workers on a job, it should take twice the time. There is a nice reciprocal relationship here, so even when the numbers are not as easy to deal with, the relationship still holds.

So, in increasing the number of plows from 5 to 6, we are using 6/5 as many plows. So clearing the lot should take 5/6 the time:
(5/6)(12) = 10 = 10 hours.
The correct answer is choice (A).
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For 5 snow plows to take 12 hours, would each take 5/12 or 2.4 hours and then you combine them?


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 Post subject: Re: math (t.2, q. 16): rate
PostPosted: Sun Mar 13, 2011 4:00 am 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
No, when 5 snow plows clear the iced parking lot in 12 hours, they work simultaneously. So each snow plow works 12 hours.


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 Post subject: Re: math (t.2, q. 16): rate
PostPosted: Fri Jul 22, 2011 3:48 pm 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
1) The common approach for this type of the questions is to calculate the rate of a unit. In other words "how much of the parking lot does a snow plow clear in 1 hour"?
We start with the fact that 5 snow plows clear the parking lot in 12 hours. On the diagram we show a rectangular parking lot, but the shape of the parking does NOT affect the reasoning.
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2) Since 5 snow plows clear the iced parking lot in 12 hours, then each of the snow plows clears 1/5 of the parking lot.
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3) Since a snow plow clears 1/5 of the parking lot in 12 hours, then in 1 hour it clears (1/5)/12 of the parking lot.
(1/5)/12 = 1/(5 × 12) = 1/60
Now we have a rate for one snow plow. That's the key moment to all such questions.
Image

4) Since a snow plow clears 1/(5 × 12) of the parking lot in 1 hour, then 6 snow plows clear 6 × 1/(5 × 12) = 1/10 of the parking lot in 1 hour.
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5) Since 6 snow plows clear 1/10 of the parking lot in 1 hour, then to clean the whole parking lot it will take them 1 / (1/10) = 10 hours. The correct answer is A.
Image

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This is the basic logic that stands behind all of questions of this type. Once you understand it, you can take shortcuts, like using the whole formula at once:

new time = 1 / ([the rate of 1] × 6)
new time = 1 / (1 / (5 × 12) × 6) = 1 / 0.1 = 10


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