Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 Sep 2015, 13:27
GMAT Club Tests

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Abel can complete a work in 10 days, Ben in 12 days and Carl

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
avatar
Joined: 12 Oct 2009
Posts: 115
Followers: 2

Kudos [?]: 35 [1] , given: 3

Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 03 Nov 2009, 11:21
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

51% (03:43) correct 49% (02:45) wrong based on 316 sessions
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
[Reveal] Spoiler: OA
3 KUDOS received
VP
VP
avatar
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 224 [3] , given: 31

Re: Word problem-work rate [#permalink] New post 03 Nov 2009, 11:27
3
This post received
KUDOS
1
This post was
BOOKMARKED
jade3 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


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)
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 903
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 18

Kudos [?]: 362 [0], given: 18

Re: Word problem-work rate [#permalink] New post 03 Nov 2009, 21:27
(1/A + 1/B + 1/C)*2 + (1/B + 1/C) ( N-2-3 ) + (1/C)*3 = 1

Solve for N, we get N = 7
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6162
Followers: 344

Kudos [?]: 70 [0], given: 0

Premium Member
Re: Word problem-work rate [#permalink] New post 17 Oct 2013, 22:21
Hello from the GMAT Club BumpBot!

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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
2 KUDOS received
Economist GMAT Tutor Instructor
User avatar
Joined: 01 Oct 2013
Posts: 69
Followers: 6

Kudos [?]: 27 [2] , given: 7

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 19 Oct 2013, 08:35
2
This post received
KUDOS
Expert's post
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


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.
_________________

Economist GMAT Tutor
http://econgm.at/econgmat
(866) 292-0660

Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50038 [4] , given: 7519

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 03 Nov 2013, 11:37
4
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

2 KUDOS received
Current Student
avatar
Joined: 03 Aug 2012
Posts: 920
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 17

Kudos [?]: 386 [2] , given: 322

Premium Member
Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 18 Mar 2014, 06:30
2
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
_____________________________________________________________________________

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 2046
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 32

Kudos [?]: 344 [0], given: 355

GMAT ToolKit User
Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 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

Answer: B
Manager
Manager
avatar
Joined: 23 May 2013
Posts: 106
Concentration: Strategy, Social Entrepreneurship
GMAT Date: 08-05-2015
Followers: 1

Kudos [?]: 50 [0], given: 29

GMAT ToolKit User
Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 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.

30 + 9x+12 = 60; 42 + 9x = 60; 9x = 18; x =2.

Therefore, total number of days = x+2+3 = 7 days.

Answer: B
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5863
Location: Pune, India
Followers: 1481

Kudos [?]: 7972 [1] , given: 190

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 06 Apr 2015, 20:07
1
This post received
KUDOS
Expert's post
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


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.

The work lasts for 2 + 2 + 3 = 7 days.

Answer (B)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 588
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Followers: 2

Kudos [?]: 238 [0], given: 75

GMAT ToolKit User
Re: Abel can complete a work in 10 days, Ben in 12 days and Carl [#permalink] New post 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 Image to appreciate my post !! :-)

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl   [#permalink] 06 Apr 2015, 20:43
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic A person x working alone can complete a work in 10 days. A person Y .. anurag356 3 18 Jun 2015, 17:16
3 Experts publish their posts in the topic A can complete a certain job in 12 days. B is 60% b2bt 4 02 Jun 2014, 06:09
1 P,Q and R can do a piece of work in 4,6 and 12 days working abhishekkhosla 1 23 Oct 2013, 10:50
17 Experts publish their posts in the topic A can complete a project in 20 days and B can complete the 154238 9 21 Sep 2012, 04:16
6 A can complete a project in 20 days and B can complete the Titleist 68 02 Nov 2005, 12:37
Display posts from previous: Sort by

Abel can complete a work in 10 days, Ben in 12 days and Carl

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.