In a print shop, 36 identical printers working together can print

Question

In a print shop, 36 identical printers working together can print a batch of flyers in 3 hours. Initially, 24 printers started printing, and after 2.5 hours, 48 identical reserve printers joined them. Will it take more than 1.5 hours for all the printers together to finish printing the batch?

(1) The rate of a reserve printer is 1/4th of the rate of an original printer.

(2) The rate of a reserve printer is lower than the rate of an original printer.

Bunuel · Accepted Answer

Official Solution:

In a print shop, 36 identical printers working together can print a batch of flyers in 3 hours. Initially, 24 printers started printing, and after 2.5 hours, 48 identical reserve printers joined them. Will it take more than 1.5 hours for all the printers together to finish printing the batch? 
 
Assuming each printer completes 1 unit of work in 1 hour, the total work would be 36 * 3 = 108 units. In 2.5 hours, 24 printers would complete 24 * 2.5 = 60 units of work. In the next 1.5 hours, they would complete 24 * 1.5 = 36 units of work, leaving 108 - 60 - 36 = 12 units. So essentially, the question boils down to whether 48 reserve printers can complete these remaining 12 units of work in 1.5 hours.
 
(1) The rate of a reserve printer is 1/4th of the rate of an original printer.
 
From the stem, we know the rate of an original printer, so from this statement we can get the rate of a reserve printer, which was the only missing piece. Now, we know everything, and there is no need to calculate anything for this statement. From the stem, we know the rate and number of original printers involved, and the size of the work to be done. From this statement, we know the rate of the reserve printers. We also know all the relevant time values given in the question. Therefore, we can surely answer any question about this setup. Sufficient.
 
(2) The rate of an original printer is higher than the rate of a reserve printer.
 
48 original printers would complete 48 * 1.5 = 72 units of work in 1.5 hours, which is more than the 12 units remaining. We know that reserve printers would complete less, but we don't know by how much. Depending on how slow they are, the group could either finish the remaining work in less than or more than 1.5 hours. Thus, this statement alone is not sufficient.

Answer: A

YUKESH23 · Answer

Given: 36 printers can do a batch in 3hrs
Required : Time taken by (48+24 =72 printers ) <1.5 hr?

Case-1: Rate of 48 printers < rate of 36 printer, which means the time taken by 48 reserve printers to print a batch is more than 3 hours. And combined with 24 printers the time will be more than 1.5hrs since, 72 printers at original rate can print a batch in exactly in 1.5hrs. If the rate of either 24 printers or 48 printers is decreased than the time will exceed 1.5hrs.

Case-2: Rate of reserve printer (48nos) < rate of original printer (36). Same explanation as in case-1.

Hence both options can able to answer the question in a definite manner. So option D

Bunuel · Answer

Similar tricky question to practice: https://gmatclub.com/forum/in-a-factory ... 44378.html

Bunuel · Answer

Anyone else want to try this question?

Rohit_842 · Answer

Rate for 24 printers is 2/9 and in 2.5 hours they complete 5/9 work, in additional 1.5 hours they complete a total of 8/9 of work. 
Now we need to know if the reserve printers can complete this 1/9 work within the 1.5 hours.

Using Statement 1 we can directly get rate of reserve printers and hence it's sufficient

Statement 2 on the other hand says rate of 1 reserve printer is less than 1 regular printer. However if it was greater we could've said with gurantee that 1/9th of work would've finished within 1.5 hours (24 regular printers finish 3/9 work in 1.5 hours) but since its less we don't know how much exactly less.

Hence option A

ShotaK · Answer

If 36 printers do the job in 3 hours, we have: 36*3*1/x=N, where 1/x is the rate and N is the total amount of newspapers. After simplification, we obtain that the rate = N/108.

If we follow the problem, we have the following equation: 2.5*24*N/108 + t*24*N/108 + 48*t*x = N, where t is the time after 2.5 hours and x is the rate of the reserve printer.

After algebraic manipulations, we will obtain: t = 4N / (2N + 48*x*9).

Now we can see the conditions:

1) If we know how N and x are related, the problem would be a linear one-variable problem. Hence, A on its own is enough.

2) If we know that x is less than N/108, we can substitute the maximum and minimum values into x. Min value would be close to zero and in that case t = 2 that is more than 1.5. However, if we substitute close to N/108 the time would be close to 2/3, which is less than 1.5. Hence, B is not our answer.

In a print shop, 36 identical printers working together can print

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In a print shop, 36 identical printers working together can print

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