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14 Jul 2022, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
71% (02:30) correct
29%
(02:52)
wrong
based on 243
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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 together in 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
Are You Up For the Challenge: 700 Level Questions
A. 14
B. 13
C. 11
D. 9
E. 7
Are You Up For the Challenge: 700 Level Questions
14 Jul 2022, 02:30
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Machine A can do a certain job in 12 days working 2 full shifts: \(12*2=24\) total shifts required for Machine A, or \(\frac{1}{24}\) of the job is completed per shift.
Machine B can do the same job in 15 days working 2 full shifts: \(15*2=30\) total shifts required for Machine B, or \(\frac{1}{30}\) of the job is completed per shift.
As Machine A and Machine B work individually and together on the same job, it is best to that they have a common denominator.
Machine A: \(\frac{5}{120}\)
Machine B: \(\frac{4}{120}\)
Working together: \(\frac{5}{120}+\frac{4}{120} = \frac{9}{120}\)
So the total fraction of the job done per day is: \(\frac{5}{120}+\frac{4}{120}+\frac{9}{120} = \frac{18}{120}\)
Which means that it will take \(120÷18≈7\) days to complete the job with the current work schedule.
Answer E
Machine B can do the same job in 15 days working 2 full shifts: \(15*2=30\) total shifts required for Machine B, or \(\frac{1}{30}\) of the job is completed per shift.
As Machine A and Machine B work individually and together on the same job, it is best to that they have a common denominator.
Machine A: \(\frac{5}{120}\)
Machine B: \(\frac{4}{120}\)
Working together: \(\frac{5}{120}+\frac{4}{120} = \frac{9}{120}\)
So the total fraction of the job done per day is: \(\frac{5}{120}+\frac{4}{120}+\frac{9}{120} = \frac{18}{120}\)
Which means that it will take \(120÷18≈7\) days to complete the job with the current work schedule.
Answer E
25 Jul 2022, 19:07
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Bunuel
Two ways.
First, Ballpark!! This is exactly what I would do on the actual test; it is faster, easier, leaves no chance for a silly calculation error, and is 100% right (not a guess).
In our final scenario, we have A + B + AandBtogether, which is really just 2 shifts for A and 2 shifts for B.
Machine B can do the job in 15 days working two shifts. If we had two machine B's, they would finish in 7.5 days. Machine A is faster than machine B, so we need to be faster than 7.5. Only one answer choice fits.
Answer choice E.
Second, fine, let's do the math. I hate fractional jobs, so I treat these as "Hidden Plug In" questions and make up something to define the size of the job. Let's make the job solving 60 GMAT questions.
Machine A takes 12 days, so solves 5 per day, which is 2.5 per shift.
Machine B takes 15 days, so solves 4 per day, which is 2 per shift.
In the final scenario, we have 2.5 + 2 + (2.5+2) = 9 per day.
60/9 = 20/3 = 6.6667
Answer choice E.
ThatDudeKnowsBallparking
ThatDudeKnowsHiddenPlugIn
