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Working alone, Printers X, Y, and 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

Problem Solving Question: 130 Category:Arithmetic Operations on rational numbers Page: 78 Difficulty: 600

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
05 Mar 2014, 01:17

Expert's post

2

This post was BOOKMARKED

SOLUTION

Working alone, Printers X, Y, and 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

The rate of Y and Z are 1/15 and 1/18 job/hour, respectively.

Their combined rate is 1/15 + 1/18 = 1/t. Thus the time it takes Printers Y and Z to do the job is t = 90/11.

Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
08 Mar 2014, 11:38

Expert's post

SOLUTION

Working alone, Printers X, Y, and 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

The rate of Y and Z are 1/15 and 1/18 job/hour, respectively.

Their combined rate is 1/15 + 1/18 = 1/t. Thus the time it takes Printers Y and Z to do the job is t = 90/11.

Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
18 Mar 2014, 03:14

Rate(X)=1/12 Rate(Y)=1/15 Rate(Z)=1/18

Time for X=12

Combined Rate of Y and Z= 1/15 + 1/18 = 33/(18*15)

Since Rate * Time = work

And work =1 then Time for combined Y and Z = (18*15)/33

Ratio of Time for X/Time for combined Y and Z

(12*33)/(18*15)=22/15 _________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
15 Apr 2014, 20:10

Printer X can do Printing Job in 12 hrs. So Printer X completes (1/12)th of the work in 1hr.

Printer Y can do Printing Job in 15 hrs. So Printer Y completes (1/15)th of the work in 1hr.

Printer Z can do Printing Job in 18 hrs. So Printer Z completes (1/18)th of the work in 1hr.

Printer's Y and Z combined rate(working for 1 hr) is 1/15+1/18 = 11/90;

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 is (1/12)/(11/90) = 15/22;

so rate is 15/22; rate is inversly proportional to time. Time is 22/15; Hence D

Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
20 May 2015, 14:06

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Working alone, Printers X, Y, and 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) 11/41

Problem Solving Question: 130 Category:Arithmetic Operations on rational numbers Page: 78 Difficulty: 600

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

If you want to avoid fractions, assume the total number of pages is 180. X does 180/12 = 15 pages/hr Y does 180/15 = 12 pages/hr Z does 180/18 = 10 pages/hr

Y and Z together do 12+10 = 22 pages/hr

Ratio of speed of X : speed of Y and Z combined = 15:22 Ratio of time taken by X : time taken by Y and Z combined = 22:15 (time taken varies inversely with speed)

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