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Three machines operating independently, simultaneously,

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Three machines operating independently, simultaneously,

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Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?

A. 6
B. 9
C. 12
D. 27
E. 48

The OA is B.

I made some calculus and I got 27. Experts, may you show me how to solve this PS question? Thanks.

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GMAT/MBA Expert

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Hello Vincen.

Let's take a look at your question.

3 machines ------ 36 hours
4 machines ------- x hours

Then x=3*36/4 = 27 hours.

But the question says "in how many fewer hours..." Now, if 3 machines spend 36 hours and 4 machines spend 27 hours to do the work, then the work could be done in 9 hours less.

So, the correct answer is B.

I hope this explanation may help you.

I'm available if you'd like a follow up.

Regards.

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Hi Vincen,

We're told that 3 machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. We're asked if one additional machine were used under the same operating conditions, in how many FEWER hours of simultaneous operation could the production order be fulfilled.

In these types of Work questions, it helps to determine how much work-time is needed to complete the job. Here, we have 3 machines working 36 hours each...

(3 machines)(36 hours each) = 108 machine-hours of work needed to complete the job.

Adding 1 additional machine creates the following equation:

(4 machines)(X hours each) = 108 machine-hours of work
X = 108/4 = 27 hours for each machine

The question asks for how many FEWER hours are needed... 36 hours - 27 hours = 9 fewer hours

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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