How many hours does it take 12 machines with identical production rate

D


Machines are running at identical rate

(a) Sufficient. 1 Machine take 60 hours to fill order.... so rate = 1/60... so it would take 5 hours to complete the order by 12 machines
(b) Sufficient ... 10 machines take 6 hrs... so rate =1/60... so it would take 5 hrs to complete

Answer is D

St 1 Let rate of each machine be R then Time taken by 12 machines will be (12*R) *Time= Work

St1 1 machine takes 60 hrs so we have 1*R*60=W=12R*T or Time taken by 12 machines =5 hrs

St2 says 10*R*6=12R*T or T=5 hrs...Sufficient

Ans D

1 machine takes 60 hrs so 12 machines take 60/12=5 hrs A suff.
10 machines take 6 hrs so 12 machines will take 10*6/12 =5 hrs. B suff
Hence D

Statement 1: It takes each machine alone, running continuously, 60 hours to fill the production order
60/12 = 5hrs -- Sufficient

Statement 2: It takes 10 of these machines, running simultaneously without stopping, 6 hours to fill the production order
h*12=6*10 --> h=5hrs -- Sufficient

Each Statement alone is sufficient, Answer D

I would like to point out that every post on this thread so far has figured out the exact time it will take the 12 machines to complete this order. Data sufficiency is not about finding the exact time it takes. Data sufficiency is about knowing that you will get one definite answer. For many questions, finding out the exact number is a waste of time.

For this problem, you have 3 variables: Output, rate, and time. (Output = rate * time)
You know that you need 2 of the 3 variables in order to get one definite answer.

The question stem gives you almost enough for rate, but not quite enough. It does let you know that all of the rates are the same. So if you get the rate for one machine, you have the rate for all the machines.

The first stimulus gives you the rate and the time for one machine. This will be the same for all the machines. Since it gives you 2 of the 3 variables, the first stimulus is sufficient.

The second stimulus gives you the rate and time for ten machines. You know that you can get the information for the individual machines because the rates are the same for all. Since it gives you 2 of the 3 variables, the second stimulus is sufficient.

The answer is D.

Notice that you don't have to calculate anything for this problem to get the answer. You just have to recognize what information you need, and know when that information is provided. Calculating the exact time it takes for the 12 machines is a waste of time for this problem.

Again, I just want to point out that data sufficiency is, much of the time, not about calculating the exact answer. Data sufficiency is about knowing that you have enough information to get one definite answer.

Hope this helps!

The correct answer is D. Good job everyone!

hi Bunuel

One doubt...

If the question stem states different rates for machines then B is not sufficient right??????

Yes, in that case B would be insufficient.

From (1)


So, let total work be 60 units
Thus 12 machines will take \(\frac{60}{12} = 5\ hours\)

From (2)


So, let total work be 60 units
Thus 12 machines will take \(\frac{60}{12} = 5\ hours\)

Thus EACH statement ALONE is sufficient to answer the question asked, answer will be (D)

Asked: How many hours does it take 12 machines with identical production rates, running simultaneously without stopping, to fill a certain production order ?

(1) It takes each machine alone, running continuously, 60 hours to fill the production order.
12 machines will take = 60/12 =5 hours to fill the production order
SUFFICIENT

(2) It takes 10 of these machines, running simultaneously without stopping, 6 hours to fill the production order.
12 machines will take = 6*10/12 =5 hours to fill the production order
SUFFICIENT

IMO D

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