M17-20

Question

It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

Bunuel · Accepted Answer

Official Solution:

It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

A. 12
B. 18
C. 20
D. 24
E. 30

Let's denote the time taken by printer A to print 40 pages as  a  minutes. By the given information, printer B can accomplish the same task in  a-4  minutes.
 
The printing rate of A can be calculated as  rate = \frac{job}{time} = \frac{40}{a}  pages per minute, and for B it would be  rate = \frac{job}{time} = \frac{40}{a-4}  pages per minute.
 
The combined printing rate of A and B together is therefore  \frac{40}{a}+\frac{40}{a-4}  pages per minute. From the stem we also know that both printers together can print 50 pages in 6 minutes, which means that the combined printing rate of A and B together is  rate = \frac{job}{time} = \frac{50}{6} . Hence,  \frac{40}{a}+\frac{40}{a-4} = \frac{50}{6} . 
 
Dividing this equation by 40, we obtain  \frac{1}{a}+\frac{1}{a-4}=\frac{5}{24} . At this point, we can either substitute values from answer choices or solve the resulting quadratic equation. It's crucial to remember that we're asked for the time printer A would take to print 80 pages. Therefore, our answer should be  2a  (since  a  is the time required to print 40 pages).
 
Answer D fits the equation:
 
If  2a=24 , then  a=12 .
 
Substituting  a  into the equation gives  \frac{1}{12}+\frac{1}{8}=\frac{5}{24} , which holds true. Hence, the solution is  2a = 24 .

Answer: D

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation.

gmatzpractice · Answer

Rates: 40/x
40/(x+4)

40/x*6+40/(x+4)*6=50
240/x+240/(x+4)=50
240(x+4)+240x=50x(x+4)
240x+960+240x=50x^2+200x
0=50x^2-280x-960
0=5x^2-28x-96
0=(5x+12)(x-8)
x=8

40/12 t = 80
t=24 min
Answer D

Gmatprep550 · Answer

Tried to find correct answer through POE and solved in less than 2 mins and you can also reach to correct ans if you don't have superb knowledge which required to use above described method, Following are the steps which I followed.

1) Try to plugin value of option C(medium value) 80/20 = 4 PPM (Pages Per Min), hence in 6 min A will print 24 pages hence B will print 26 pages hence B will print 26/6 PPM but calculation will get difficult if you try to prove 1st condition and GMAT never give difficult calculations as it tests your logic skills and not calculation skills.

2) Try with option B 80/18 = 40/9 PPM, hence in 6 Min A will print 40/9 * 6 = 26 pages which is not possible as A can not print more than 50% of pages in total contribution of 50 pages as it works slow than B.

3) Now You can also eliminate option A as Printer A can not take less than 18 Min. Hence Option A, B, and C is canceled and left with D and E.

4) Try with option D 80/24 = 10/3 PPM, hence in 6 min Printer A will print 10/3 * 6 = 20 pages and B will print 50-20 = 30 Pages. Hence B can print 30/6 = 5 PPM
Now plug in this value for 1st condition and you will find that A will print 40 pages in 12 min and B will print 40 pages in 8 min. Got your ans.
  
 This looks like time consuming but it is not if you perform most of the steps in Brain and not Paper.

Hi  chetan2u ,  Bunuel ,

Could you please advise if I have followed any incorrect steps to reach right answer.

leonardBe · Answer

Hi  Bunuel  do you have links to similar questions please?

Bunuel · Answer

17. Work/Rate Problems 
     Theory   
 Work Rate Problems - All in One Topic! 
 Work Word Problems Made Easy 
 How to Solve Relative Rate of Work Questions on the GMAT 
     Questions   
 DS Questions 
 PS Questions

On other subjects:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Vikramaditya00 · Answer

I think this is a  high-quality  question and I agree with explanation. Was able to solve little bit but later got stuck loved the divide by 40 step really makes all the calulations easy

Stmraj · Answer

I have an easy way.

40 page difference is 4 min,
 50 page difference will be 5 min

let B takes x min so A will take x+5 min.

now x(x+5) whole divided by x+(x+5) should be equal to 6 solve for x

x=10

So B takes 10 min for 50 page and A takes 15 min for 50 page, now use linear eqn to get A time for 80 page which will be 24 mins

ADhanjal · Answer

Hi  Bunuel ,
Why did you decide to solve the question with respect to printer A, i.e. taking the time to print 40 pages to be 'a', and for B it becomes'a-4'? How did you know that solving this way will save time? At the end everything fell in place and you did not had to solve for 'a'. The way I solved it was a mess at the end, started with time for printer B to print 40 pages = t mins, time for printer A = t+4 mins.
Was stuck solving this:
5/24 = 1/(t+4) + 1/t
Can't plug in the answers for 't'.

Bunuel · Answer

The question specifically asks about printer A’s time, so it’s natural to assign the variable to A first. That way, whatever you solve or back‐solve directly answers the question without extra conversion. If you start with B, you just create an extra step for yourself.

ADhanjal · Answer

So, would you suggest solving questions like these with respect to the reference point in the question? I find it very difficult sometimes to solve for the variable especially in work/rate problems and distance/speed problems.

Bunuel · Answer

Ir depends on a question but generally yes.

Amrinder12 · Answer

I like the solution - it’s helpful. What happens if you use a for B and a+4 for A?

Bunuel · Answer

First of all, you mentioned a and a+4, but it should be b and b+4. Next, the question specifically asks about printer A’s time, so it’s more natural to assign the variable to A first. That way, once you solve the equation or back-solve, you directly get A’s time without any extra conversion. If you start with B and write A as b+4, you’ll still reach the same solution, but you’ll need extra steps at the end to translate B’s value into A’s. So it would be possible to reach the answer, but it would be less convenient than the approach shown in the solution.

agrasan · Answer

I like the solution - it’s helpful.

agrasan · Answer

I like the solution - it’s helpful.

Dream009 · Answer

ANother way to look at this is A has to print 80 pages that will be twice the time for 40 pages so options for 40 pages are

A. 12/2 = 6 So B is 2 => 1/ 6 + 1/2 = 
B. 18/2 = 9 , B is 5 => 1/ 9 + 1/5
C. 20/2 = 10, B is 6 => 1/10+ 1/6 = 16/60
D. 24/2 = 12, B is 8 => 1/12 + 1/8 = 5/24
E. 30/2 = 15, B is 11 = > 1/ 15 + 1/11
Now we know that how much portion of 40 pages work in happening in 1 min

If both can print 50 pages in 6 mins
So they can together print 40 pages in 6*4/5 24/5 mins. So we need above values to be 5/24 work in 1 min . Answer is D

Vivek1707 · Answer

This is a great question that’s helpful for learning.

M17-20

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