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# Working together, A and B can do a job in 6 days. B and C

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Current Student
Joined: 29 Jan 2005
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Working together, A and B can do a job in 6 days. B and C [#permalink]  29 Oct 2005, 09:21
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(N/A)

Question Stats:

80% (01:02) correct 20% (00:00) wrong based on 1 sessions
Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?

(1) 8 days
(2) 5 days
(3) 3 days
(4) 7 days
(5) 6 days

How long will it take for A alone to complete the job?

(1) 8 days
(2) 6 days
(3) 10 days
(4) 20 days
(5) 5 days
Director
Joined: 27 Jun 2005
Posts: 515
Location: MS
Followers: 2

Kudos [?]: 26 [0], given: 0

A B and C together will do the Job in 5 days .

A alone in 10 Days......?

what is OA ..?
RK
Manager
Joined: 01 Aug 2005
Posts: 68
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I get 5 for number one and 10 for A alone as well, but the calculations took me quite a while, around 3-5 min! Is there some simple way of doing this one? What is OE
SVP
Joined: 24 Sep 2005
Posts: 1895
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Re: PS Work Ascent 4/02 [#permalink]  29 Oct 2005, 18:30
GMATT73 wrote:
Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?

(1) 8 days
(2) 5 days
(3) 3 days
(4) 7 days
(5) 6 days

How long will it take for A alone to complete the job?

(1) 8 days
(2) 6 days
(3) 10 days
(4) 20 days
(5) 5 days

Q.1: Using the productivity to solve:
Let x,y,z be the work A,B and C can do in one day.
We have:
x+y=1/6
y+z=1/10
x+z=1/7.5
---> 2(x+y+z)= 1/6+1/10+1/7.5= 24/60=2/5 ---> x+y+z=1/5 -----> if they work together, they'll finish the work in 5 days

Q.2 (x+y)+(x+z)-(y+z)= 2x= 1/6+1/7.5 -1/10= 12/60=1/5---> x=1/10
----> A alone can finish the work in 10 days.
Senior Manager
Joined: 11 May 2004
Posts: 458
Location: New York
Followers: 1

Kudos [?]: 14 [0], given: 0

Great explanations laxie...

for the first question, why do u multiply (x+y+z) by 2? Is it because of the double-counting?
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5079
Location: Singapore
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Question 1
A and B can do 1/6 job in 1 day
B and C can do 1/10 job in 1 day
C and A can do 2/15 job in 1 day

1/A + 1/B = 1/6 ----(1)
1/B + 1/C = 1/10 ---(2)
1/C + 1/A = 2/15 --(3)

Adding (1), (2) and (3), we get:

2/A + 2/C + 2/B = 2/5
1/A + 1/C + 2/B = 1/5 job in 1 day
So A + B + C willl finishi 1 job in 5 days

Question 2
(1) - (2) --> 1/A - 1/C = 1/15 --(4)
(4) + (3) --> 2/A = 1/5
So A alone finish 1/10 job in 1 day = 10 days for 1 job
Current Student
Joined: 29 Jan 2005
Posts: 5244
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Kudos [?]: 175 [0], given: 0

Re: PS Work Ascent 4/02 [#permalink]  31 Oct 2005, 23:35
laxieqv wrote:
GMATT73 wrote:
Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?

(1) 8 days
(2) 5 days
(3) 3 days
(4) 7 days
(5) 6 days

How long will it take for A alone to complete the job?

(1) 8 days
(2) 6 days
(3) 10 days
(4) 20 days
(5) 5 days

Q.1: Using the productivity to solve:
Let x,y,z be the work A,B and C can do in one day.
We have:
x+y=1/6
y+z=1/10
x+z=1/7.5
---> 2(x+y+z)= 1/6+1/10+1/7.5= 24/60=2/5 ---> x+y+z=1/5 -----> if they work together, they'll finish the work in 5 days

Q.2 (x+y)+(x+z)-(y+z)= 2x= 1/6+1/7.5 -1/10= 12/60=1/5---> x=1/10
----> A alone can finish the work in 10 days.

Got it Laxie! Thanx for the explanation. Is there any reason why you are so fond of using the variables x, y, and z?
Re: PS Work Ascent 4/02   [#permalink] 31 Oct 2005, 23:35
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