If it is assumed that each of the n/4 production workers in a factory

Question

If it is assumed that each of the n/4 production workers in a factory assembles one instrument every t minutes and the rest of the workers is 50% faster. How many instruments does the factory assemble in 8.5 hours of production?

A)  \frac{2805n}{4t}

B)  \frac{2805t}{4n}

C)  2805nt

D)  \frac{8.5t}{60} * (\frac{n}{4} + \frac{3n}{4})

E)  \frac{8.5n}{60t} * (\frac{11}{4})

MrGMAT624 · Answer

Hi! Can somebody help me with this question? Struggling to do it

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Victor19 · Answer

The answer is A.

n/4 workers make 1 instrument every 't' minutes. So, they make  n/4t instruments every 1 minute .

The remaining 3n/4 work 50% faster. This means  together they make 3*1*1.5 instruments every 't' minutes , which is 4.5 instruments in 't' minutes.
Thus, the remaining workers make  4.5n/4t instruments every 1 minute .

Total number of instruments made  per minute  = n/4t + 4.5n/4t = 5.5n/4t.

Total number of instruments made  per hour  = 5.5n/4t * 60.

Total number of instruments  made in 8.5 hours  = 5.5n/4t * 60 * 8.5 =  2805n/4t  = Option A.

Victor19 · Answer

Hi MrGMAT624. I have posted the solution above. Hope it helps. If you're still not satisfied with the explanation kindly reply here.

RitwikAgrawal · Answer

I did it in guesswork way sing the options had drastically different structures.

TO calculate work done we would have to multiple Rate * time.

And as per the question the rate will always be (something)/  t

This eliminated choices B C D. We are left with A and E.

E has 8.5n/60t. Since we have been given that "t" is Minutes. It would be a nonsensical value derived from  8.5 hours / 60 minutes * t minutes

So eliminated E. And got left with A.

This was my strategy to get the right answer. Although I did spent some making sure with a Rate-Time-Work table setup.

Regor60 · Answer

This question is poorly written, in my opinion.

I would interpret 50% faster as meaning producing 1 unit in 50% of the time.

The answer depends on the interpretation as producing 50% more product in the same time.

The question should be written as "50% more productive"

Posted from my mobile device

JeffTargetTestPrep · Answer

We have to assume that the total number of workers in the factory is n, because, otherwise, the problem would be unsolvable.

In the  slow subgroup  (which consists of n/4 workers), we have:

rate of 1 worker = work/time = 1/t items per minute
rate of n/4 workers = (n/4)(1/t) = n/4t items per minute

time = 8.5 hours = 510 minutes
total work = rate × time = (n/4t)(510) = 510n/4t items

In the  fast subgroup  (which consists of 3n/4 workers), we have:

rate of 1 worker = (3/2)(1/t) = 3/2t items per minute
rate of 3n/4 workers = (3n/4)(3/2t) = 9n/8t items per minute

time = 8.5 hours = 510 minutes
total work = rate × time = (9n/8t)(510) = 2295n/4t items

So, the total work done by the two subgroups in 8.5 hours is:

510n/4t + 2295n/4t = 2805n/4t items

Answer: A

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If it is assumed that each of the n/4 production workers in a factory

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If it is assumed that each of the n/4 production workers in a factory

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