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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.

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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]

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05 Mar 2014, 02:17

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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]

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08 Mar 2014, 12:38

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]

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18 Mar 2014, 04:14

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]

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15 Apr 2014, 21:10

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]

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20 May 2015, 15:06

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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)

Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]

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17 Feb 2016, 17:44

Considering the answer choices are distant, we can also use logical approximation to solve this under a minute: Y and Z take 15 and 18 hours each. So when both of them work together, they will take somewhere between 7.5 and 9 hours (7.5 had two Ys had done it and 9 had two Zs had done it). Lets take the combined time as 8 hours. Therefore the ratio of time taken must be approx. 12/8 = 1.5. Looking at answer choices only D comes close.

P.S. This approach also makes sure that we don't mistakenly select choice C as the answer.

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

Hi, you can do it in two ways..

1) standard method

Xs one hour work=1/12.. Ys and Zs combined work= 1/15 + 1/18=11/90..

so the ratio= 12/(90/11)=22/15..

POE

As correctly observed above , the combined time is between 15/2=7.5 and 18/2=9... so the ratio is between 12/7.5 and 12/9.. we can clearly see the ratio will be between 1 and 2.. eliminate all those below 1- A, B and C OUT.. eliminate anything above 2- E out only D left.. D Ofcourse proces of elimination has more to do with the spread of choices.. _________________

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.

Thank you!

Printer y and z together can do the job in 15*18/15+18 = 15*18/33 The required ratio is 12*33/15*18 = 22/15

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