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:

Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]

Show Tags

03 Nov 2009, 11:21

2

This post received KUDOS

13

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

53% (03:34) correct
47% (02:49) wrong based on 515 sessions

HideShow timer Statistics

Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6 B. 7 C. 8 D. 9 E. 10

B. 7

1/10 + 1/12 + 15 = 15/60 of the work done each day.

60 - 15/60-15/60 = 30/60 (abel then leaves)

Ben and carla working together finish 9/60 each day. Carla alone finished 4/60 each day so I figured the amount carla finishes alone will be a multiple of 4

30/60 - 9/60 = 21/60 (3 days total) 21/60-9/60 = 12/60 (4 days total; and coincidentally a multiple of 4) so assume carla works alone after this 12/60-4/60 = 8/60 (5 days) 8/60 - 4/60 = 4/60 (6 days) 4/60-4/60 = 0 (7 days)

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6 B. 7 C. 8 D. 9 E. 10

Not to sound like a broken record from some of my earlier posts, but, worst case, you could always plug in answer choices for this problem.

Start with C and you get 2/10 of a job from Abel (which, notice, will always be the case), (8-3)/12 from Ben, and 8/15 from Carla.

LCM and add these up, and you get 12/60+25/60+32/60. Too much!

Do the same with B. Abel stays at 2/10, Ben is now 4/12, and Carla is 7/15. So, 12/60+20/60+28/60 = 60/60.

This approach could take longer in some circumstances, but it's always a default strategy where you have answer choices like these and no idea how to proceed.
_________________

Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6 B. 7 C. 8 D. 9 E. 10

Responding to a pm.

First 2 days all three of them worked together, thus they did 2*(1/10 + 1/12 + 1/15) = 1/2 of the work.

Last 3 days only Carla worked, thus she did 3/15 = 1/5 of the work.

1 - 1/2 - 1/5 = 3/10 of the work was done by Ben and Carla: (time)*(combined rate)=(job done) --> t*(1/12 + 1/15) = 3/10 --> t = 2 days. So, we have that Ben and Carla worked together for 2 days.

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]

Show Tags

18 Mar 2014, 06:30

3

This post received KUDOS

Let the work be completed in 't'.

Then again "Rate * Time = Work"

Rate(A)) = 1/10 Rate(B)=1/12 Rate(C)=1/15

Since A worked for 2 Days Work done by A= 2/10 Since B worked for 3 Days before work was completed work done B= (t-3)/12 Since C worked for full number of days = t/15

Adding them gives total work which is 1 unit.

2/10 + (t-3)/12 + t/15 = 1

Hence t=7
_________________

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

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]

Show Tags

08 May 2014, 13:49

asterixmatrix wrote:

Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6 B. 7 C. 8 D. 9 E. 10

Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains Then if Ben had to leave 3 days before the completion, this means that Carla had to work alone for these 3 days in which she completed 1/5 of the job.

Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 3/5

3/20 (t) = 3/5 ---> t = 4

Therefore, these 4 days worked plus the 3 days that Carla had to work by herself add to 7 days

Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]

Show Tags

06 Apr 2015, 06:53

Bunuel wrote:

asterixmatrix wrote:

Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6 B. 7 C. 8 D. 9 E. 10

Responding to a pm.

First 2 days all three of them worked together, thus they did 2*(1/10 + 1/12 + 1/15) = 1/2 of the work.

Last 3 days only Carla worked, thus she did 3/15 = 1/5 of the work.

1 - 1/2 - 1/5 = 3/10 of the work was done by Ben and Carla: (time)*(combined rate)=(job done) --> t*(1/12 + 1/15) = 3/10 --> t = 2 days. So, we have that Ben and Carla worked together for 2 days.

Total days = 2 + 3 + 2 = 7.

Answer: B.

Hope it's clear.

Bunuel's answer is the quickest way to think about the structure of the solution. Just want to add a small tip: Because right off the bat, you notice you're adding 3 fractions. Instead of doing the usual cross multiply trick to add fractions, I would find the LCM immediately by sketching out a quick venn diagram:

10 = 2*5 12 = 2*2*3 15 = 3*5

2 is common, 3 is common, and 5 is common - leftover is just one 2. Therefore, the LCM is 2*3*5*2 = 60. Rewrite all of the fractions with a denominator of 60 and this problem can be solved in under 2 minutes.

All working together = 6/60 + 5/60 + 4/60 = 15/60 for 2 days = 30/60. B and C working together = 5/60 + 4/60 = 9/60 for (x) days. C working alone = 4/60 for 3 days = 12/60.

Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6 B. 7 C. 8 D. 9 E. 10

Another option is to convert it to units of work if you don't want to work with fractions.

Say, the work involves 60 units (LCM of 10, 12 and 15). So Abel does 60/10 = 6 units a day, Ben does 60/12 = 5 units a day and Carla does 60/15 = 4 units a day. Together, they do 6+5+4 = 15 units a day.

In 2 days, they complete 15*2 = 30 units and are left with 30 units. Then only Ben and Carla are working and doing 5+4 = 9 units a day. The last 3 days Carla works alone and does 4*3 = 12 units of the 30 units so Ben and Carla together do 30 - 12 = 18 units. Hence Ben and Carla work together in the middle at the rate of 9 units per day for 18/9 = 2 days.

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]

Show Tags

06 Apr 2015, 20:43

asterixmatrix wrote:

Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6 B. 7 C. 8 D. 9 E. 10

speed of A=1.2B =1.5C .

combined speed of B and C = \(\frac{1}{B} +\frac{1}{C} = \frac{B+C}{BC} = \frac{3}{20}\) \(1-(\frac{1}{5} +\frac{1}{6}+ \frac{2}{15} + \frac{3}{15} )\) = work done together by B and C= \(\frac{9}{30}.\)

so time take by B and C together (in A's absence) = 2 days

answer 2+2+3=7 days
_________________

Thanks, Lucky

_______________________________________________________ Kindly press the to appreciate my post !!

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]

Show Tags

19 Nov 2015, 06:17

Amount of work Carla completed + Amount of work Abel completed + Amount of work Ben completed = Total amount of work completed t/15 + 2/10 + (t-3)/12 = 1 t = 7

The hardest part of this problem (at least for me) was interpreting the amount of time Ben spent working.

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink]

Show Tags

19 Jul 2016, 04:15

asterixmatrix wrote:

Abel can complete a work in 10 days, Ben in 12 days and Carla in 15 days. All of them began the work together, but Abel had to leave after 2 days and Ben 3 days before the completion of the work. How long did the work last?

A. 6 B. 7 C. 8 D. 9 E. 10

Let the complete work be 60 units.. Per day.. A does = 60/10 = 6 units B = 5 units C = 4 units

The timeline of the work is

ABC for the first 2 days Work done = 2(6+5+4) = 30 units

BC for some days..let it be x Work done = x(5+4) = 9x

C alone for last three days Work done = 3(4) = 12 units

So..

30 + 9x + 12 = 60..

x = 2 days.. and total days = 2 + 2 + 3 = 7 days(B) _________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...