• NEW! FREE Beat The GMAT Quizzes  Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A, B and C working alone can complete a work in 24 tagged by: Brent@GMATPrepNow ##### This topic has 2 expert replies and 2 member replies ## A, B and C working alone can complete a work in 24 A, B and C working alone can complete a work in 24, 32, and 48 days respectively. "A" started the work and "B" joined him after 4 days and "C" joined them after 4 more days. If they were paid$10,800 for the work done, how much did "A" get ?

(A) 2800
(B) 3600
(C) 5400
(D) 6400
(E) 7600

OA is D

Thanks & Regards
Vinni

Senior | Next Rank: 100 Posts Joined
12 Nov 2012
Posted:
85 messages
Followed by:
2 members
8
In 4 days, A completes 4/24 part of the whole work. Remaining work is 20/24 after 4 days.
When B joins after 4 days, A and B together do (1/24 + 1/32)*4 = 7/24. So remaining work after 8 days is (20/24 -7/24) =13/24.
When C joins after another 4 days, A, B and C can do (1/24 + 1/32+ 1/48) = 3/32 in 1 day. So, they need (32/3 * 13/24) = 52/9 days to complete the task.
This means, A works for a total of (4+4+52/9) days and in this he completes (4+4+52/9)*(1/24)=31/54 part of the whole task. So, A gets 10,800 * (31/54) = 6200.
I think choice D should be 6200.

### GMAT/MBA Expert

GMAT Instructor Joined
08 Dec 2008
Posted:
13046 messages
Followed by:
1253 members
5254
GMAT Score:
770
vinni.k wrote:
A, B and C working alone can complete a work in 24, 32, and 48 days respectively. "A" started the work and "B" joined him after 4 days and "C" joined them after 4 more days. If they were paid $10,800 for the work done, how much did "A" get ? (A) 2800 (B) 3600 (C) 5400 (D) 6400 (E) 7600 Another approach is to assign the entire job a certain number of units. Since the least common multiple of 24, 32 and 48 is 96, let's say that the entire job consists of 96 work units. So, if A can complete the entire job (i.e., 96 work units) in 24 days, then A's rate is 4 units/day Likewise, if B can complete the entire job (i.e., 96 work units) in 32 days, then B's rate is 3 units/day And if C can complete the entire job in 48 days, then C's rate is 2 units/day A works alone for 4 days. So, during this time, A completes 16 units of work. This leaves us with 80 work units remaining (96 - 16 = 80) A & B work together for 4 days. Their combined rate is 7 units/day (4+3=7). So, during this time, A+B complete 28 units of work. This leaves us with 52 work units remaining (80 - 28 = 52) A, B & C work together to complete job. Their combined rate is 9 units/day (4+3+2=9). Since there are 52 work units remaining in the job, the number of days to complete the job = 52/9 IMPORTANT: 52/9 is not a nice number. However, since the answer choices are somewhat spread apart, I'm going to be somewhat aggressive with my estimation/rounding. So, let's say that 52/9 = 6 (close enough). This means that it takes A,B and C about 6 days to complete the rest of the job. So, in total, A worked for approximately 14 days (4+4+6=14) Since A works at a rate of 4 units/day, A completed a total of 56 work units (since 14x4=56). The ENTIRE job was 96 work units. So, A did 56/96 of the work. This means that A should get 56/96 of the$10,800 payment.
(56/96)(10,800) = (7/12)(10,800)
= $6300 Of course, none of the answer choices match$6300, but that's because we did some estimating/rounding earlier.
The closest answer choice is $6400, so the correct answer must be D Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! Master | Next Rank: 500 Posts Joined 17 Apr 2011 Posted: 421 messages Followed by: 2 members Upvotes: 6 Test Date: 2016 Target GMAT Score: 700+ GMAT Score: 620 Thanks Brent. Your solution is crystal clear, and i also believe that the word "approx" must be mentioned here. Vinni Brent@GMATPrepNow wrote: Another approach is to assign the entire job a certain number of units. Since the least common multiple of 24, 32 and 48 is 96, let's say that the entire job consists of 96 work units. So, if A can complete the entire job (i.e., 96 work units) in 24 days, then A's rate is 4 units/day Likewise, if B can complete the entire job (i.e., 96 work units) in 32 days, then B's rate is 3 units/day And if C can complete the entire job in 48 days, then C's rate is 2 units/day A works alone for 4 days. So, during this time, A completes 16 units of work. This leaves us with 80 work units remaining (96 - 16 = 80) A & B work together for 4 days. Their combined rate is 7 units/day (4+3=7). So, during this time, A+B complete 28 units of work. This leaves us with 52 work units remaining (80 - 28 = 52) A, B & C work together to complete job. Their combined rate is 9 units/day (4+3+2=9). Since there are 52 work units remaining in the job, the number of days to complete the job = 52/9 IMPORTANT: 52/9 is not a nice number. However, since the answer choices are somewhat spread apart, I'm going to be somewhat aggressive with my estimation/rounding. So, let's say that 52/9 = 6 (close enough). This means that it takes A,B and C about 6 days to complete the rest of the job. So, in total, A worked for approximately 14 days (4+4+6=14) Since A works at a rate of 4 units/day, A completed a total of 56 work units (since 14x4=56). The ENTIRE job was 96 work units. So, A did 56/96 of the work. This means that A should get 56/96 of the$10,800 payment.
(56/96)(10,800) = (7/12)(10,800)
= $6300 Of course, none of the answer choices match$6300, but that's because we did some estimating/rounding earlier.
The closest answer choice is $6400, so the correct answer must be D Cheers, Brent ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 The solution below is similar to Brent's, but with one suggestion: To make the math easier, we can divide all of the times by 4: Quote: A, B and C working alone can complete a work in 6, 8, and 12 days respectively. "A" started the work and "B" joined him after 1 day and "C" joined them after 1 more day. If they were paid$10,800 for the work done, how much did "A" get ?

(A) 2800
(B) 3600
(C) 5400
(D) 6200
(E) 7600
Let the job = the LCM of 6, 8 and 12 = 24 units.
Pay per unit = 10800/24 = $450. A's rate = w/t = 24/6 = 4 units per day. B's rate = w/t = 24/8 = 3 units per day. C's rate = w/t = 24/12 = 2 units per day. Work produced by A on the first day = 4 units. Work produced by A on the second day = 4 units. Work produced by B on the second day = 3 units. Remaining work = 24-4-4-3 = 13 units. When A, B and C work together, their combined rate = 4+3+2 = 9 units, of which 4 will be produced by A. Thus, A will produces 4/9 of the remaining 13 units: (4/9) * 13 = 52/9 ≈ 6. Total number of units produced by A ≈ 4+4+6 = 14. Thus: A's pay ≈ 14*450 ≈ 6300. The correct answer is D. Please note that A's exact pay =$6200 (not $6400 as indicated in the problem as posted above): (4 + 4 + 52/9) * 450 = 6200. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 44 first replies
2 Jay@ManhattanReview 35 first replies
3 Brent@GMATPrepNow 34 first replies
4 Scott@TargetTestPrep 31 first replies
5 GMATGuruNY 18 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

129 posts
2 Max@Math Revolution

Math Revolution

89 posts
3 Ian Stewart

GMATiX Teacher

53 posts
4 Brent@GMATPrepNow

GMAT Prep Now Teacher

50 posts
5 Jay@ManhattanReview

Manhattan Review

35 posts
See More Top Beat The GMAT Experts