November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat. November 20, 2018 November 20, 2018 06:00 PM EST 07:00 PM EST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50652

A and B together complete a piece of job in 10 days, B and C together
[#permalink]
Show Tags
14 Aug 2017, 21:19
Question Stats:
73% (02:56) correct 27% (02:25) wrong based on 132 sessions
HideShow timer Statistics



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82

A and B together complete a piece of job in 10 days, B and C together
[#permalink]
Show Tags
Updated on: 14 Aug 2017, 22:05
Bunuel wrote: A and B together complete a piece of job in 10 days, B and C together complete the same piece of job in 15 days, whereas A and C together complete it in 8 days. How many days will it take to complete the job if all of them work together?
A. \(3 \frac{3}{7}\)
B. \(6 \frac{6}{7}\)
C. \(7\)
D. \(7 \frac{23}{35}\)
E. \(7 \frac{6}{7}\) (A+B)'s 1 day job = \(\frac{1}{10}\) (B+C)'s 1 day job = \(\frac{1}{15}\) (A+C)'s 1 day job = \(\frac{1}{8}\) Adding the three equations we get  \(2\)(A+B+C)'s 1 day job = \(\frac{1}{10}+\frac{1}{15}+\frac{1}{8} = \frac{35}{120}\) or (A+B+C)'s 1 day job = \(\frac{35}{120}*\frac{1}{2}\) \(=\frac{7}{48}\) Hence time taken by All to complete the job = \(\frac{48}{7}\) = \(6 \frac{6}{7}\) Option B
Originally posted by niks18 on 14 Aug 2017, 21:34.
Last edited by niks18 on 14 Aug 2017, 22:05, edited 1 time in total.



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3307
Location: India
GPA: 3.12

A and B together complete a piece of job in 10 days, B and C together
[#permalink]
Show Tags
14 Aug 2017, 21:58
If A and B can together do the piece of work in \(10(2*5)\) days, B and C do the work in \(15(3*5)\) days , and A and C do the work in \(8(2^3)\) days Let us assume the work to be \(120(2^3 * 3 * 5)\) units. Therefore A & B's combined rate is 12 units, B & C's combined rate is 8 units, and A & C's combined rate is 15 units. Together they would do half of 35(12+8+15) units in a day. So their combined rate is \(\frac{35}{2}\) units per day. In order to finish 120 units at that rate, it would require \(120 * (\frac{2}{35}) = \frac{120*2}{35} = \frac{24*2}{7} = \frac{48}{7} = 6\frac{6}{7}\) days (Option B)
_________________
You've got what it takes, but it will take everything you've got



Manager
Joined: 22 Nov 2016
Posts: 213
Location: United States
Concentration: Leadership, Strategy
GPA: 3.4

A and B together complete a piece of job in 10 days, B and C together
[#permalink]
Show Tags
09 Nov 2017, 21:37
When we are given AB, BC and CA rates, there is a quicker method. Eventually we have to add the rates, hence, the shortcut is 2*(combined rate) = Sum of rates of AB + BC + CA \(2*x= \frac{1}{8}+\frac{1}{10}+\frac{1}{15}\) \(x=\frac{7}{48}\) Flip the rate to get the time. Answer is \(\frac{48}{7}\)
_________________
Kudosity killed the cat but your kudos can save it.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: A and B together complete a piece of job in 10 days, B and C together
[#permalink]
Show Tags
14 Nov 2017, 06:21
Bunuel wrote: A and B together complete a piece of job in 10 days, B and C together complete the same piece of job in 15 days, whereas A and C together complete it in 8 days. How many days will it take to complete the job if all of them work together?
A. \(3 \frac{3}{7}\)
B. \(6 \frac{6}{7}\)
C. \(7\)
D. \(7 \frac{23}{35}\)
E. \(7 \frac{6}{7}\) We can let a = the number of days A will complete the job alone, b = the number of days B will complete the job alone and c = the number of days C will complete the job alone. We can now create the following combined rate equations: 1/a + 1/b = 1/10 and 1/b + 1/c = 1/15 and 1/a + 1/c = 1/8 Adding the equations together, we have: 2/a + 2/b + 2/c = 1/10 + 1/15 + 1/8 2/a + 2/b + 2/c = 12/120 + 8/120 + 15/120 2/a + 2/b + 2/c = 35/120= 7/24 Thus, 1/a + 1/b + 1/c = 7/24 x 1/2 = 7/48. So, the time it would take the machines to work together is 1/(7/48) = 48/7 = 6 6/7. Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4224
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: A and B together complete a piece of job in 10 days, B and C together
[#permalink]
Show Tags
14 Nov 2017, 07:55
Bunuel wrote: A and B together complete a piece of job in 10 days, B and C together complete the same piece of job in 15 days, whereas A and C together complete it in 8 days. How many days will it take to complete the job if all of them work together?
A. \(3 \frac{3}{7}\)
B. \(6 \frac{6}{7}\)
C. \(7\)
D. \(7 \frac{23}{35}\)
E. \(7 \frac{6}{7}\) Let the total work be 120 units So, Efficiency of A and B together is 12 Efficiency of B and C together is 8 Efficiency of A and C together is 15 Combined efficiency is \(\frac{12+8+15}{2} = \frac{35}{2}\) Time required to complete the work is \(120*\frac{2}{35}\) = \(6 \frac{6}{7}\) Answer will be (B) \(6 \frac{6}{7}\)
_________________
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 )



Manager
Joined: 20 Feb 2017
Posts: 166
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)

A and B together complete a piece of job in 10 days, B and C together
[#permalink]
Show Tags
19 Nov 2017, 07:20
Lets solve this using LCM method A+B = 10 days B+C = 15 days C+D = 8 days LCM of 10,15 and 8 is 120. so 120 units of work done (Assume) therefore rate of work A+B = 120/10 = 12 units per day B+C = 120/15 = 8 units per day C+D = 120/8 = 15 units per day. So if all of them work together i.e A+B+C = 35/ 2units ((12+8+15)/2)(we are dividing by 2 because each rate gets repeated twice) hence number of days = 120/ (35/2) = 48/7 (answer B)
_________________
If you feel the post helped you then do send me the kudos (damn theya re more valuable than $)



Intern
Joined: 26 Sep 2016
Posts: 7

Re: A and B together complete a piece of job in 10 days, B and C together
[#permalink]
Show Tags
19 Nov 2017, 09:35
sasyaharry wrote: When we are given AB, BC and CA rates, there is a quicker method. Eventually we have to add the rates, hence, the shortcut is
2*(combined rate) = Sum of rates of AB + BC + CA
\(2*x= \frac{1}{8}+\frac{1}{10}+\frac{1}{15}\)
\(x=\frac{7}{48}\)
Flip the rate to get the time.
Answer is \(\frac{48}{7}\) what is combined rate?



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3307
Location: India
GPA: 3.12

Re: A and B together complete a piece of job in 10 days, B and C together
[#permalink]
Show Tags
19 Nov 2017, 19:57
Combined rate here will refer to the rate at which the three of them(A,B, and C) do the work. I have used a different method to solve this problem. Check if that method is clear
_________________
You've got what it takes, but it will take everything you've got




Re: A and B together complete a piece of job in 10 days, B and C together &nbs
[#permalink]
19 Nov 2017, 19:57






