M06-21

Question

Machine A can complete a certain job in 12 days, working 2 full shifts per day, while Machine B can complete the same job in 15 days, also working 2 full shifts per day. If Machine A works during the first shift each day, Machine B works during the second shift, and both machines work half of the third shift, approximately how many days will it take for Machines A and B to complete the job under this work schedule?

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

Show Answer

Official Answer

D

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

Bunuel · Accepted Answer

Official Solution:

Machine A can complete a certain job in 12 days, working 2 full shifts per day, while Machine B can complete the same job in 15 days, also working 2 full shifts per day. If Machine A works during the first shift each day, Machine B works during the second shift, and both machines work half of the third shift, approximately how many days will it take for Machines A and B to complete the job under this work schedule?

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

Show Answer

Official Answer

D

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

Machine A requires 12 days * 2 shifts = 24 shifts to complete the entire job;
 
Machine B requires 15 days * 2 shifts = 30 shifts to complete the entire job;
 
Each day, both machines work 1.5 shifts ( \frac{3}{2}  shifts). Together, in one day, they complete  \frac{(\frac{3}{2})}{24}+\frac{(\frac{3}{2})}{30}=\frac{9}{80}  of the whole job. Therefore, under the current work schedule, they will need approximately  \frac{80}{9} \approx 9  days to finish the entire job.

Answer: D

naumyuk · Answer

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

vik09 · Answer

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

Bunuel · Answer

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.

ppac · Answer

Hi,

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

Bunuel · Answer

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.

frapoz95 · Answer

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

HimanshuW11 · Answer

kabirdash · Answer

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.

arun8sharma · Answer

Hey,

Please help me out.

A 12 d for 2 shifts so for 1.5 shifts, it is 9 d
B 15 d for 2 shifts so for 1.5 shifts it is 15/4 d

How to move from here? I am stuck and unable to understand how to move forward?

Desertchampion · Answer

Hi, you must first calculate how many days it takes each machine working just ONE shift:

Machine A: If it takes 12 days working 2 shifts per day, then it takes 24 days working 1 shift per day.
Machine B: If it takes 15 days working 2 shifts per day, then it takes 30 days working 1 shift per day.

We are told that each machine is going to be working 1.5 shifts each day, which is 3/2 as a fraction, therefore:

Rate of Machine A + Rate of Machine B =   +  
The least common denominator of 24 & 30 is 120

{ x(5/5)} + { x(4/4)} =   + (6/120) =  /120

Let's solve the numerator:
(15/2) + (6/1) = (15/2) + (12/2) = 27/2

Plug the numerator back into the equation:
(27/2)/120 = (27/2)/(120/1) = (27/2)x(1/120) = (9/2)x(1/40) = 9/80

Therefore, each machine working 1.5 shifts would complete 9 jobs in 80 days
But we want to know how many days it would take to complete just 1 job at this rate, so we need to divide 80 by 9

80/9 = 8.88 which is roughly 9 days

The correct answer is choice (D)

TheNightKing · Answer

A takes 24 shifts to complete the job.
B takes 30 shifts to complete the job.

Let's say the work is 240.

A is doing 10 units per shift.
B is doing 8 units per shift.

Now they are doing 10 in the first shift, 8 in the second and (10+8)/2=9 in the third shifts.

Which means total is 27 in a day.

We have work of 240. Days taken will be 240/27 = 8.8888888 Or you just know it is less than 10 and around 9.

sankarsh · Answer

My way:
machine A: 12 days to complete a job with 2 shifts/day - a total of 24 days with 1 shift per day to complete 1 job.
machine B: 15 days to complete a job with 2 shifts/day - a total of 30 days with 1 shift per day to complete 1 job.

RATE * TIME = W
A 1/24 24 days 1
B 1/30 30 days 1
A+B=1/24+1/30 13.3days 1

13.3 days = 2 shifts per day -- to complete the job by both machines working together with a total of 2 shifts /day.question asks us for 3 shifts/day
x days= 3 shifts per day

13.3*2=x*3
x=26.6/3
x~9days

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Aakash7 · Answer

I think this is a  poor-quality  question and I agree with explanation. Even though the question asks about approximation, but here were are talking about finishing a work. 
The work can not be finished in 9 days with the current schedule. 
Finishing the work is priority. If 1% of the work is left still it is unfinished.

Good question for understanding concept. But does not seem like a GMAT quality question

Bunuel · Answer

The job is finished in  \frac{80}{9} = 8.\overline{8}  days, which is approximated to 9 days. So, everything is fine with the question. Even if the job were to be finished in 9.1 days, approximating it to 9 days would still be acceptable. We are approximating a number, after all. Therefore, there's nothing wrong with saying that a job needing 9.1 days to be finished needs approximately 9 days to be finished.

Mohnish2702 · Answer

I like the solution - it’s helpful.

M06-21

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