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Math Expert V
Joined: 02 Sep 2009
Posts: 55618

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Difficulty:   55% (hard)

Question Stats: 64% (01:55) correct 36% (02:01) wrong based on 152 sessions

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Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. If each day machine A is working during the first shift, machine B is working during the second shift and both machines A and B are working half of the third shift, approximately how many days will it take machines A and B to do the job with the current work schedule?

A. 14
B. 13
C. 11
D. 9
E. 7

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Math Expert V
Joined: 02 Sep 2009
Posts: 55618

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Official Solution:

Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. If each day machine A is working during the first shift, machine B is working during the second shift and both machines A and B are working half of the third shift, approximately how many days will it take machines A and B to do the job with the current work schedule?

A. 14
B. 13
C. 11
D. 9
E. 7

Machine A needs 12 days * 2 shifts = 24 shifts to do the whole job;

Machine B needs 15 days * 2 shifts = 30 shifts to do the whole job;

In one day each machine works 1.5 shifts ($$\frac{3}{2}$$ shifts), and together, in one day, they are doing $$\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}$$th of the whole, thus with the current work schedule they'll need $$\frac{80}{9} \approx 9$$ days to do the whole job.

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Intern  Joined: 30 Jul 2014
Posts: 4
Location: United States
Concentration: Strategy, Finance
GMAT 1: 640 Q39 V38 Show Tags

I think this question is poor and not helpful.
Where does it say in this question what the length of one shift is? 1 Shift could equal 4 days for instance....
Intern  Joined: 23 Oct 2014
Posts: 15
Schools: Zicklin'18

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Hi,

I had a different approach to solve this problem that was incorrect, but I'm having a hard time understanding why my approach was wrong, and why the official solution works the way it does.

What I did:

Added the rates (1 job/24 shifts and 1 job/30 shifts) 1/24+1/30 = 5/120 +4/120 = 9/120 combined rate. I used the reciprocal (120 shifts/9 jobs) as the time and converted this to days using the logic that together both machines complete three shifts/day. With this logic I got the answer ~4 days, which is obviously wrong, but I am having difficulty wrapping my head around why. If someone could help me understand this, I would be super grateful.
Intern  Joined: 08 Mar 2014
Posts: 46
Location: United States
GMAT Date: 12-30-2014
GPA: 3.3

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Bunuel wrote:
Official Solution:

Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. If each day machine A is working during the first shift, machine B is working during the second shift and both machines A and B are working half of the third shift, approximately how many days will it take machines A and B to do the job with the current work schedule?

A. 14
B. 13
C. 11
D. 9
E. 7

Machine A needs 12 days * 2 shifts = 24 shifts to do the whole job;

Machine B needs 15 days * 2 shifts = 30 shifts to do the whole job;

In one day each machine works 1.5 shifts ($$\frac{3}{2}$$ shifts), and together, in one day, they are doing $$\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}$$th of the whole, thus with the current work schedule they'll need $$\frac{80}{9} \approx 9$$ days to do the whole job.

Hello
I understand your point up to the point that each machine will work 1.5 shifts in a day as per the question. But I am unable to grasp the last point that you made in the equation $$\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}$$th of the whole. Can you please explain that how you arrive at this equation.

Thanks Math Expert V
Joined: 02 Sep 2009
Posts: 55618

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1
vik09 wrote:
Bunuel wrote:
Official Solution:

Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. If each day machine A is working during the first shift, machine B is working during the second shift and both machines A and B are working half of the third shift, approximately how many days will it take machines A and B to do the job with the current work schedule?

A. 14
B. 13
C. 11
D. 9
E. 7

Machine A needs 12 days * 2 shifts = 24 shifts to do the whole job;

Machine B needs 15 days * 2 shifts = 30 shifts to do the whole job;

In one day each machine works 1.5 shifts ($$\frac{3}{2}$$ shifts), and together, in one day, they are doing $$\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}$$th of the whole, thus with the current work schedule they'll need $$\frac{80}{9} \approx 9$$ days to do the whole job.

Hello
I understand your point up to the point that each machine will work 1.5 shifts in a day as per the question. But I am unable to grasp the last point that you made in the equation $$\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}$$th of the whole. Can you please explain that how you arrive at this equation.

Thanks Sure.

In one day Machine A works of $$\frac{3}{2}$$ shifts, and since Machine A needs 24 shifts to do the whole job, then in one day Machine A does (3/2)/24th of the whole job.

In one day Machine B works of $$\frac{3}{2}$$ shifts, and since Machine B needs 30 shifts to do the whole job, then in one day Machine B does (3/2)/30th of the whole job.

Together they do $$\frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}$$th of the whole job.

Hope it's clear.
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Intern  Joined: 31 Jan 2012
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Hi,

Could you please clarify how did you get 1.5 shifts (3/2). Probably I am missing out something really silly.
Math Expert V
Joined: 02 Sep 2009
Posts: 55618

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ppac wrote:
Hi,

Could you please clarify how did you get 1.5 shifts (3/2). Probably I am missing out something really silly.

3/2 = 1.5. Or did you mean something else?
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Intern  Joined: 31 Jan 2012
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Hi,

I understand 3/2=1.5. How did you deduce "In one day each machine works 1.5 shifts (3/2 shifts)"
Math Expert V
Joined: 02 Sep 2009
Posts: 55618

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ppac wrote:
Hi,

I understand 3/2=1.5. How did you deduce "In one day each machine works 1.5 shifts (3/2 shifts)"

Each day machine A is working during the first shift (1 shift), machine B is working during the second shift (1 shift) and both machines A and B are working half of the third shift (0.5 shifts each). Therefore, each work for 1 + 0.5 shifts per day.

Hope it's clear.
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Intern  Joined: 31 Jan 2012
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Thanks heaps! I knew I was missing something!
Current Student Joined: 29 Apr 2015
Posts: 26
Location: Russian Federation
GMAT 1: 710 Q48 V38 GPA: 4

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Bunuel wrote:
Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. If each day machine A is working during the first shift, machine B is working during the second shift and both machines A and B are working half of the third shift, approximately how many days will it take machines A and B to do the job with the current work schedule?

A. 14
B. 13
C. 11
D. 9
E. 7

Alternative approach.
Machine A can do a job in 12 days * 2 shifts = 24 shifts.
Machine B can do a job in 15 days * 2 shifts = 30 shifts.

$$\frac{1}{24} + \frac{1}{30} + (\frac{1}{24} + \frac{1}{30})/2$$;

$$\frac{18}{240} + \frac{9}{240} = \frac{27}{240}$$;

$$\frac{240}{27} ≈ 9$$
Intern  Joined: 12 Feb 2016
Posts: 8

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another straight approach:

rate=============time======work
2Sa=============12=======1 machine A working 2 shifts completes the job in 12 days. => 1/12=2Sa => Sa=1/24
2Sb=============15=======1 machine B working 2 shifts completes the job in 15 days. => 1/15=2Sb => Sb=1/30
Sa+Sb+.5*(Sa+Sb)==x========1

the combined rate will be Sa+Sb (each machine works for 1 shift) + .5Sa+.5Sb (each machine works half of the third shift)

x=240/27=80/9=approx less than 9
Intern  B
Joined: 26 Dec 2016
Posts: 19

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bschool42 wrote:
Hi,

I had a different approach to solve this problem that was incorrect, but I'm having a hard time understanding why my approach was wrong, and why the official solution works the way it does.

What I did:

Added the rates (1 job/24 shifts and 1 job/30 shifts) 1/24+1/30 = 5/120 +4/120 = 9/120 combined rate. I used the reciprocal (120 shifts/9 jobs) as the time and converted this to days using the logic that together both machines complete three shifts/day. With this logic I got the answer ~4 days, which is obviously wrong, but I am having difficulty wrapping my head around why. If someone could help me understand this, I would be super grateful.

Hi, you would calculate the time, if the machines would only work one shift each day.
Furthermore you made a calculation mistake: If the combined Rate is 9/120 it takes 120/9 days to finish one Job, so at about 13.333 Days ...

Hope it helps
Intern  B
Joined: 10 May 2017
Posts: 27

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I did it this way and kinda worked.

12 and 15 common factor is 120.

A=> 12 days x 2 shifts x 5 components=120
b=> 15 days x2 shifts x4 components =120

A and B working together,

1shift x 5n + 1shift x 4n + 1/2(5n+4n)=120

13.5n=120

n is approximately 8.88
Manager  S
Joined: 14 Jul 2014
Posts: 90
Location: India
Concentration: Social Entrepreneurship, Strategy
GMAT 1: 620 Q41 V34 WE: Information Technology (Computer Software)

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Intern  B
Joined: 15 Jan 2018
Posts: 13
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A better way to solve this question is to take LCM of 24 and 30=120.
It means 120 work to be done.
A does 1/24 work each day=>5 work each shift
B does 1/30 work each day=>4 work each shift.
In third shift both work half of the time,so work done=2.5+2=4.5 work
Total work done in a day=13.5 work.For doing 120 work,it will take 9 days approx. Re: M06-21   [#permalink] 06 Nov 2018, 23:17
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