Problem Solving

This was a real GMAT question, but I only have the correct answer, no explanation: I got C, but the correct answer is D. Can anyone explain to me why?

Question: Working alone, printers X,Y, Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?

A) 4/11

B) 1/2

C) 15/22

D) 22/15

E) 11/4

You probably don't know this already, but you can get in serious trouble, or get this site in serious trouble, by posting real GMAT questions.

Just curious: How do you know the right answer if you don't know how to get to it? Real GMAT Qs don't provide answers.


-Patrick

I bought GMAT Test Papers (old GMAT exams) through mba.com. Each exam provides only correct answers, but no explanations. I was just wondering if anyone can get D, since each time I resolve it, I get C.

To solve this quickly, 2 concepts are important to understand:

1) The combined rates of multiple agents is the sum of their individual rates.
2) The rate and the time it takes to do a job are always inverses of one another.

In this case, we already know that it takes X 12hrs to do the job, so in askng for the ratio of timeX to combined_timeYZ, we're really only asked for the combined time of Y & Z.

The good news is that because of concept #2 above, if we knew the combined rate, we could find the combined time by just inverting it.

The other piece of good news is that the combined rate can be easily found using concept #1 above. Combined rate is the sum of rateY and rateZ.

What are the rates? That's simple enough. Thanks to concept #2, we can determine that since timeY and timeZ are 15 and 18hrs, rateY and rateZ must be 1/15 and 1/18. Thus the combined rate is the sum of the two, or 6/90 + 5/90 = 11/90.

Thanks to concept 2, we can determine that the combined time of Y & Z is 90/11.

Now we know: time X = 12hrs. combined_time YZ=90/11 hrs. This is a ratio of (12/1)/(90/11), or(12/1)*(11/90) = 22/15.

The correct answer is D

-Patrick

PS. Note that concept #2 applies only if we're talking about the time it takes to complete one job.

wcheng57 wrote:This was a real GMAT question, but I only have the correct answer, no explanation: I got C, but the correct answer is D. Can anyone explain to me why?

Question: Working alone, printers X,Y, Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?

A) 4/11

B) 1/2

C) 15/22

D) 22/15

E) 11/4

I deem that even if the previous REAL GMAT questions can be procured from the souk, we should still not furnish its orientation if we just can't skirt posting the same on this site. This could still protect the site from a possible trouble, if any.

Well, it's already open that printer x alone can do the job in 12 hours. We just need to find how long it takes the unit y and z to do the job, working together at their individual rates.

Please remember that if A can do a job in x unit of time and B can do the same job in y unit of time, then the time taken by the unit A and B to do the job can be given by the formula

x y/ (x + y) unit of time.

Therefore, the time it takes printers y and z to do the job, working together at their individual rates = (15 × 18)/ (15 + 18) = 90/11 hours; hence the required ratio is

12: (90/11)

= [spoiler]22/15.

D[/spoiler]

x -12 hours
y+z -15*18/(15+18)=15*18/33

12*33/15*18=22/15

This question is also in the OG with the explanation if you wanted to look there