• Board contributors include instructors with "800" GMAT scores.
  • 95% of posts have replies within 24 hours.
  • Join for discounts with 800score, VeritasPrep and ManhattanGMAT


FAQ  - Register  - Search - Login 

All times are UTC - 7 hours




Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: GMAT Rate
PostPosted: Wed Apr 10, 2013 10:25 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 477
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. 1 hour, 15 minutes
B. 2 hours, 30 minutes
C. 3 hours
D. 7 hours, 30 minutes
E. 10 hours

(E) 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 (E).
-------------

For 5 snow plows to take 12 hours, would each take 5/12 or 2.4 hours and then you combine them?


Top
 Profile  
 
 Post subject: Re: GMAT Rate
PostPosted: Wed Apr 10, 2013 10:26 am 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 453
No, when 5 snow plows clear the iced parking lot in 12 hours, they work simultaneously. So each snow plow works 12 hours.


Top
 Profile  
 
 Post subject: Re: GMAT Rate
PostPosted: Wed Apr 10, 2013 10:28 am 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 453
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.
Image

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.
Image

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.
Image

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

-----------
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
Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

All times are UTC - 7 hours


Who is online

Users browsing this forum: No registered users and 1 guest


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
Template made by DEVPPL -
phpBB SEO
 
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.