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A furniture manufacturer has two machines, but only one can

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Re: PS: Furniture Manufacturer (m06q21) [#permalink] New post 12 May 2013, 05:40
Bunuel wrote:
priyankur_saha@ml.com wrote:
A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?

(A) 14
(B) 13
(C) 11
(D) 9
(E) 7

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

Kindly explain it.


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 (3/2 shifts), and together, in one day, they are doing (3/2)/24+(3/2)/30=9/80 th of the whole, thus with the current work schedule they'll need 80/9=~9 days to do the whole job.

Answer: D.



I am still a little confused with this question . I came across this on GMAT club test today.
How can we say that in one day , there are three shifts i.e first shift , second shift and third shift ? Cos it first says that , machine A takes 12 days to complete the job working 2 whole shifts . Here , you take it to mean that two shifts comprise of one day. But when the question stem says "Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift" , you are assuming , one day to comprise of - first shift , second shift and half of third shift .
I do not know what is it that I am missing out here . Appreciate if you can revert on this.

Thanks,
Jyothi
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Re: A furniture manufacturer has two machines, but only one can [#permalink] New post 05 Jun 2013, 09:15
Machine A can complete the job in 24 days working one shift
Rate = 1/24 per shift

Machine B can complete the job in 30 days working one shift
Rate = 1/30 per shift

The question says they each work 1.5 shifts per day. I thought of it as them working together for 1.5 shifts.
Rate A + Rate B = 5/120 + 4/120 = 9/120
Rate A+B*1.5 shifts per day = 9/120 * 3/2 = 9/80 of the job is completed per day

Therefore, the job is completed on the 9th day.
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Re: PS: Furniture Manufacturer (m06q21) [#permalink] New post 22 May 2014, 06:28
That's elegant. Nice.

isst80 wrote:
Alternative method.
If we rewrite the RTD question in terms of "shifts" it is easier to understand.

In terms of Shifts where there are 2 shifts/day:
Rate x Shifts = Work
1/24 x 24 shifts = 1
1/30 x 30 shifts = 1

Now rewrite the eqs in terms of days, assuming one machine works the ENTIRE day:
Rate x Days = Work
1/8 x 8 = 1
1/10 x 10 = 1

Since the shifts during a day is shared between A and B equally we know that the rate must be somewhere between 8 days and 10 days. Therefore the answer is 9.
Re: PS: Furniture Manufacturer (m06q21)   [#permalink] 22 May 2014, 06:28
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