At least 6 identical printers must be used to produce 25,000

Question

At least 6 identical printers must be used to produce 25,000 copies in no more than one hour. What is the minimum number of printers that may be able to produce 50,000 copies in 40 minutes or less?

(A) 14
(B) 15
(C) 16
(D) 17
(E) 18

SS990 · Answer

I think the answer for the question is programmed wrong.

We are given that at least 6 printers are needed to produce 25k copies in 60 minutes (1 hour). Let r be the rate of one printer in copies per minute. The total number of copies produced by printers in minutes is given by the inequality:
6*r*60>=25k
r>=25k/360...

The minimum number of printers required to produce 50k copies in 40 or less minutes is P

(P*25k*40/360) >= 50k so P>=18 option E

kevincan · Answer

At least 6 identical printers must be used to produce 25,000 copies  in no more than  one hour.

SkyNoYume · Answer

Hello, do you have the answer for this question ? Because I don't understand how to get 16. Thank you

malfoy · Answer

6 Printers can print 25K prints in less than 1hr - got it 
=> 12 Printers can print 50K in less than 1hr

Th fact of the matter remains that we don't know how much time less than an hour all the printers can print 50K pages.
But what we do know if 12 printers will print 50K pages < 1hr .
So to be determine how many more printers we need to ensure we print all pages in less than 40 mins we have to multiply 12 by 3/2 which gives is 18.

Not sure what I am missing to get to 16.

Aman1993 · Answer

I got Gemini to answer this question and he too got E as the right option. Can you provide the solution to this Q?

kevincan · Answer

Let  r  = rate of one printer (copies per hour).

Step 1: Interpret the key condition

“At least 6 printers must be used” ⇒ 5 printers are not enough:

5r < 25000

r < 5000

⸻

Step 2: New requirement

40 minutes =  	frac{2}{3}  hour

Required rate:
 \frac{50000}{2/3} = 75000

⸻

Step 3: Find minimum number of printers

Nr \ge 75000

To minimize  N , use the largest possible  r :

r 	o 5000

N > \frac{75000}{5000} = 15

So:
 N = 16

Adit_ · Answer

The wording is tricky but finally figured it out. Quite a fascinating problem and definitely hard.

The thing is like most of you all solved. Most of you took 1 hr and got 18 computers in total. Here the rate = 25000/360 per minute.

Now there is another lower bound actually which is disguised in a nice manner and that is the key to the answer.

It says "atleast 6 must be used". Which means our upper bound cannot be some really high value that could result in fewer printers being needed.
We for sure need atleast 6 and nothing below it.

So if we see carefully, taking the critical point which is 5, which it is no longer valid, we see that rate = 5000/60 here.

Now all we need to do is to substitute this upper bound and lower bounds in the question asked, which is 50,000 copies.
We thus see that the number of printers are between 15 to 18 included.

Thus the minimum required printers that satisfies =  16.

Answer:  Option C

atharvadixit · Answer

Absolute rage-baiter of a question

VibhuAnurag · Answer

Let each printer’s rate be r copies/hour.
“At least 6 printers are needed” means 5 printers cannot do the job in 1 hour.
So:
5r < 25,000 --> r < 5,000
Now we need 50,000 copies in 40 minutes --> 40 minutes = 2/3 hour
Let the required number of printers be n.
Maximum possible output in 40 minutes:
n × r × 2/3
Since r<5,000r, n × 5,000 × 2/3 must be greater than 50,000.
So:
n × 10,000/3 > 50,000
n > 15
Therefore, the minimum integer value of n is 16.

The answer is C.

At least 6 identical printers must be used to produce 25,000

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At least 6 identical printers must be used to produce 25,000

Prep Toolkit

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