Mar 20 07:00 AM PDT  09:00 AM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Mar 19 08:00 AM PDT  09:00 AM PDT Beat the GMAT with a customized study plan based on your needs! Learn how to create your preparation timeline, what makes a good study plan and which tools you need to use to build the perfect plan. Register today! Mar 20 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Wednesday, March 20th at 9 PM EDT Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 12 Oct 2009
Posts: 99

Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
03 Nov 2009, 12:21
Question Stats:
59% (02:51) correct 41% (03:08) wrong based on 580 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? A. 6 B. 7 C. 8 D. 9 E. 10
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 53709

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
03 Nov 2013, 12:37
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 the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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? Extrahard Quant Tests with Brilliant Analytics




Director
Joined: 03 Aug 2012
Posts: 703
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
18 Mar 2014, 07:30
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= (t3)/12 Since C worked for full number of days = t/15
Adding them gives total work which is 1 unit.
2/10 + (t3)/12 + t/15 = 1
Hence t=7




VP
Joined: 05 Mar 2008
Posts: 1398

Re: Word problemwork rate
[#permalink]
Show Tags
03 Nov 2009, 12:27
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  15/6015/60 = 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) 21/609/60 = 12/60 (4 days total; and coincidentally a multiple of 4) so assume carla works alone after this 12/604/60 = 8/60 (5 days) 8/60  4/60 = 4/60 (6 days) 4/604/60 = 0 (7 days)



Director
Joined: 01 Apr 2008
Posts: 760
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

Re: Word problemwork rate
[#permalink]
Show Tags
03 Nov 2009, 22:27
(1/A + 1/B + 1/C)*2 + (1/B + 1/C) ( N23 ) + (1/C)*3 = 1
Solve for N, we get N = 7



Economist GMAT Tutor Instructor
Joined: 01 Oct 2013
Posts: 69

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
19 Oct 2013, 09:35
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), (83)/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) 2920660



SVP
Joined: 06 Sep 2013
Posts: 1677
Concentration: Finance

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
08 May 2014, 14:49
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



Current Student
Joined: 23 May 2013
Posts: 186
Location: United States
Concentration: Technology, Healthcare
GPA: 3.5

Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
06 Apr 2015, 07:53
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8988
Location: Pune, India

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
06 Apr 2015, 21:07
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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Director
Joined: 07 Aug 2011
Posts: 523
Concentration: International Business, Technology

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
06 Apr 2015, 21:43
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



Manager
Joined: 10 Mar 2013
Posts: 189
GMAT 1: 620 Q44 V31 GMAT 2: 690 Q47 V37 GMAT 3: 610 Q47 V28 GMAT 4: 700 Q50 V34 GMAT 5: 700 Q49 V36 GMAT 6: 690 Q48 V35 GMAT 7: 750 Q49 V42 GMAT 8: 730 Q50 V39

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
19 Nov 2015, 07:17
Amount of work Carla completed + Amount of work Abel completed + Amount of work Ben completed = Total amount of work completed t/15 + 2/10 + (t3)/12 = 1 t = 7
The hardest part of this problem (at least for me) was interpreting the amount of time Ben spent working.



VP
Joined: 07 Dec 2014
Posts: 1158

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
19 Nov 2015, 14:47
let d=total days 2(15/60)+(d5)(9/60)+3(4/60)=1 d=7



Senior Manager
Joined: 03 Apr 2013
Posts: 274
Location: India
Concentration: Marketing, Finance
GPA: 3

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
19 Jul 2016, 05:15
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)
_________________
Spread some love..Like = +1 Kudos



Intern
Joined: 29 Dec 2015
Posts: 8

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
12 Aug 2016, 13:09
easy way to solve the problem:
Assume T : time taken for all the three to complete the work
GENERAL CONCEPT: abel's rate will be T/10 (Abel's rate T/10  total time taken by all the three (T)/abel's time to complete(10))
Ben's rate will be :T/12
Carla's rate will be : T/15
Given in problem:
But because Abel leaves in 2 days after the start of work ,his rate will be : 2/10
Ben leaves 3 days before the completion of work so his rate will be :(T3)/12
carla stays till the end of completion so her rate will be : T/15
all of them complete 1 task
so equation is 2/10 + (T3)/12 + T/15 = 1
Hence T = 7



Director
Joined: 17 Dec 2012
Posts: 626
Location: India

Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
06 Jun 2017, 19:14
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 1. (time worked by Abel)/(time taken by Abel working alone)+ (time worked by Ben)/(time taken by Ben working alone) + (time worked by Carla)/(time taken by Carla working alone) = 1 2. 2/10 + (x3)/12 + x/15 =1 So x=7.
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



Intern
Joined: 11 Apr 2017
Posts: 38

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
15 Oct 2017, 08:47
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= (t3)/12 Since C worked for full number of days = t/15
Adding them gives total work which is 1 unit.
2/10 + (t3)/12 + t/15 = 1
Hence t=7



Intern
Joined: 09 Aug 2018
Posts: 1

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
09 Aug 2018, 04:35
When Abel Ben and Carla started together, they finished half of the job in 2 days. So the part left is 1/2. This should be done by Ben and Carla only; and they should take 10/3 days to complete the remaining half portion, but Ben left 3 days prior to completion, that means Ben and Carla worked for only 1/3 days. In this 1/3 days Ben and Carla together finished 1/20 part, so the remaining 19/20 part of the work has to be done by the Carla alone. Carla should take 14 and 1/4 days. Hence the total duration of the work = 2+1/3+14 and 1/4 days.
Every answer so far shown here assumed that Carla should finish the job in 3 days after Ben left, but when Abel left, Ben and Carla started together, the time taken to complete the remaining job will be changed, so "T" is not fixed here. Every time "T" changes when some one leaves the job, so the answer 7 days is quite confusing.
Can any body explain with proper logic about the concept of "T" ?



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 966
WE: Supply Chain Management (Energy and Utilities)

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
09 Aug 2018, 05:10
piyali1979g wrote: When Abel Ben and Carla started together, they finished half of the job in 2 days. So the part left is 1/2. This should be done by Ben and Carla only; and they should take 10/3 days to complete the remaining half portion, but Ben left 3 days prior to completion, that means Ben and Carla worked for only 1/3 days. In this 1/3 days Ben and Carla together finished 1/20 part, so the remaining 19/20 part of the work has to be done by the Carla alone. Carla should take 14 and 1/4 days. Hence the total duration of the work = 2+1/3+14 and 1/4 days.
Every answer so far shown here assumed that Carla should finish the job in 3 days after Ben left, but when Abel left, Ben and Carla started together, the time taken to complete the remaining job will be changed, so "T" is not fixed here. Every time "T" changes when some one leaves the job, so the answer 7 days is quite confusing.
Can any body explain with proper logic about the concept of "T" ? Hi piyali1979g , You must know, Work=Rate*Time and Total work =1 Working sequence: Work sequence Who workedTime(in no of days)=How many days?RateWork done 1 A+B+C First 2 days1/10+1/12+1/15=1/42*1/4=1/2 2B+Cx(say)1/12+1/15x*(1/12+1/15) 3CLast 3 days1/153*1/15=1/5 Total work=1 So, \(\frac{1}{2}+x*(\frac{1}{12}+\frac{1}{15})+\frac{1}{5}=1\) Or, \(x*\frac{9}{60}=\frac{1}{2}\frac{1}{5}=\frac{3}{10}\) Or, \(x=\frac{3}{10}*\frac{60}{9}= 2\) So, total no of days taken by ABC to complete the work=\(2+x+3=2+2+3=7\)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4402
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
Show Tags
09 Aug 2018, 09:13
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 total work be 60 units (LCM of 10,12 & 60) Thus, the efficiency of A = 6 units/day ; efficiency of B = 5 units/day & efficiency of C = 4 units/day Let the total time taken for completion of the work be "t" \(2*6 + 5 ( t  3) + 4*t = 60\) Or, \(12 + 5t 15 + 4t = 60\) Or, \(9t = 63\) So, \(t = 7\), Answer must be (B) 7 days.
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )




Re: Abel can complete a work in 10 days, Ben in 12 days and Carl
[#permalink]
09 Aug 2018, 09:13






