Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Twelve identical machines, running continuously at the same [#permalink]

Show Tags

31 May 2010, 14:30

2

This post received KUDOS

10

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

68% (01:34) correct
32% (01:31) wrong based on 687 sessions

HideShow timer Statistics

Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?

One way is to think "faster by what ratio?" or "the same job in what fraction of the time?"

We want to reduce the time by 2 days from the original 8 days: 6 days to complete.

6 days is 3/4 of the original 8 days. Since R = W/T, if R is constant, T of 3/4 as much implies W of 4/3 as much. In other words, if each machine doesn't speed up individually, you have to have 4/3 as many machines doing the work.

4/3 of the original number of machines (12) is 16 machines, or 4 additional machines.

Another way is to pick some smart numbers to make the problem more "real."

We have 12 machines working 8 days to make complete one "shipment." Let's say the shipment is 96 widgets (that's just 12*8). So the 12 machines make 12 widgets a day, which means each machine makes 1 widget a day (easiest number to work with!).

To complete the 96 widgets in 6 days, then, you'd need 16 widgets each day, or 16 machines working. 4 additional machines.
_________________

Emily Sledge | Manhattan GMAT Instructor | St. Louis

Now the question is if 1 man can complete a task in 8 days how many men are needed to complete the same task in 6 days.

Simple unitary method:

To complete the work in 8 days - 1 man is needed To complete the work in 1 day - (1X8) men needed To complete the work in 6 days - (1x8)/6

Which means that if I want to complete the same work in 6 days I would need 4/3 times initial effort i.e. if I had 12 machines initially I would now need (4/3)x12=16

we know that w = R*T work is constant here in both the cases. so R = 1/T 12 -----> 1/8 x -----> 1/6 12/x = 6/8 x= 16 (so 16-12 = 4 more machines will be required.)

What number of machines must be multiplied by 1/96 to make it 1/6

16, and knowing that we used 12 machined already the additional machine number is 4. Hence (C)
_________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: Twelve identical machines, running continuously at the same [#permalink]

Show Tags

21 Oct 2013, 04:27

1

This post received KUDOS

Rate = job / time

12 machines do 1 job in 8 days: 12x = 1/8 ==> x = 1/96 Rate of one machine = 1/96

Job reduced by 2 days means the job needs to be completed in 6 days. How many machines can do the job in 6 days? ==> 1/96*x = 1/6 ==> x = 96/6 ==> x = 16

Re: Twelve identical machines, running continuously at the same [#permalink]

Show Tags

20 Jan 2014, 03:27

1

This post received KUDOS

Another way to look at it...

Assume each machine completes 1 unit of work a day. 12 machines complete 12 units of work a day. in 8 days number of units completed is 12*8 = 96 units.

Now number of machines required to complete 96 units in 6 days is 96/6 = 16. Additional number of machines required will be 16-12 = 4.
_________________

Re: Twelve identical machines, running continuously at the same [#permalink]

Show Tags

13 Mar 2016, 03:51

gsaxena26 wrote:

Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?

A. 2 B. 3 C. 4 D. 6 E. 9

12 machines take 8 days to complete the task. We need to find the number of machines to complete the same task in 6 days. Machines and time are in inverse proportion. To increase the number of machines multiply with increasing ratio' 12*8/6 = 16 machines Therefore, 4 additional machines are required.

Re: Twelve identical machines, running continuously at the same [#permalink]

Show Tags

29 Aug 2016, 12:31

I think I have an easier way...

From the question you know that 12R = 1/8. The question asks you (partially) to make the rate from 1/8 to 1/6 (drop from 8 day to 6). So the only thing that you need to do is to find the magic number than can convert 1/8 to 1/6.

So 1/8 * x = 1/6 (1 equation with one unknown). So by solving this you get x = 8/6 or 4/3. Thats it then! Take the magic number 4/3 and multiply BOTH sides of the original equation and you have:

12*(4/3)*R = (4/3) * 1/8

4 * 4 * R = 1/6, Hence 16R = 1/6, therefore 4 more machines!

Re: Twelve identical machines, running continuously at the same [#permalink]

Show Tags

29 Aug 2016, 19:08

gsaxena26 wrote:

Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by two days?

Re: Twelve identical machines, running continuously at the same [#permalink]

Show Tags

17 Sep 2016, 22:28

Since 12 machines take 8 days to complete the task, then in terms of rate 12 (1/X) = 1/8 [1/X is the rate of machine & 1/8 is the work completed by the 12 machines at rate of 1/X].

Solving for X, X=96. If 12 machines take 8 days to complete 96 units of work. Then I would need 4 additional machines to complete the work before 2 days.

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...