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Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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05 Mar 2014, 02:16
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The Official Guide For GMAT® Quantitative Review, 2ND EditionWorking 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach 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!
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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
SOLUTIONWorking 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. Thus required ratio is 12/(90/11) = 22/15. Answer: D.
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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, 20:39
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Job rate of Printer Y = \(\frac{1}{15}\) Job rate of Printer Z = \(\frac{1}{18}\) Job rate for Y & Z = \(\frac{1}{15} + \frac{1}{18} = \frac{11}{90}\) Time taken by Y & Z \(= \frac{90}{11}\) Ratio of (Time taken by Printer X) to (Combined time taken by Y & Z) = \(12 * \frac{11}{90} = \frac{22}{15}\) Answer = D
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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, 23:35
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Y and Z can do the job in (15*18)/15+18 hours, that is (15*18)/33 hours.
X can do the job in 12 hours.
Ratio = 12/(15*18)/33 = 22/15
Answer (D).



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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
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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



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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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28 Apr 2014, 02:34
Rate X: 1/12 Rate Y: 1/15 Rate Z: 1/18 Combined rate Y and Z ( let's call this ''c''): (1/15)+(1/18)=(6/90)+(5/90)=(11/90) Rate x / Rate c = (1/12)/(11/90) = (1/12)*(90/11) = (90/132) = (15/22) Answer D.
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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20 May 2015, 20:11
Hi All, This question is perfect for the "Work Formula." While there are 3 machines, only 2 of them are actually working together. Work Formula = (AxB)/(A+B) X = 12 hours to do a job Y = 15 hours to do a job Z = 18 hours to do a job Together, Y and Z takes…. (15x18)/(15+18) hours to do the job. 270/33 = 90/11 hours The ratio of X to (YandZ) = 12/(90/11) = 12(11)/90 = 132/90 = 22/15 Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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21 May 2015, 22:31
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionWorking 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach 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) Answer (D)
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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17 Feb 2016, 17:44
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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.



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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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17 Feb 2016, 18:44
[quote="Bunuel"] The Official Guide For GMAT® Quantitative Review, 2ND EditionWorking 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.. DOfcourse proces of elimination has more to do with the spread of choices..
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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14 Mar 2016, 02:59
x takes 12 hours to complete the job. Similarly, let y and z work for B hours together to complete the job. i/e., B/15 + B/18=1 (1 implies work is completed) We get B=90/11 hrs So the answer is 12/ (90/11)= 22/15
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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14 Mar 2016, 04:35
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionWorking 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach 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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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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05 Jun 2017, 17:43
Bunuel wrote: 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
1.Time taken by x is 12 hours 2.Time taken by y and z is 1/ (1/15+1/18)=90/11 3.The ratio of time taken by x to time taken by y and z = 132/90= 22/15
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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08 Jun 2017, 17:06
Bunuel wrote: 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
We are given that 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. Thus, the rate of Printer X is 1/12. The combined rate of Printers Y and Z is 1/15 + 1/18 = 6/90 + 5/90 = 11/90. Since rate = work/time, the time for Y and Z combined to complete the job is 1/(11/90) = 90/11 hours. Since the time for X to complete the job is 12 hours, we can create the following ratio: 12/(90/11) = (11 x 12)/90 = (11 x 2)/15 = 22/15 Answer: D
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
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07 Oct 2017, 07:43
Reduce the units to just a single hour. 1/12 hour = x 1/15 hour = y 1/18 hour = z
y and z are working together: 1/15 + 1/18 the LCM of 15 and 18 is 90 6/90 + 5/90 = 11/90 hours
bring x back into the picture: 11/90 + 1/12 = 22/180 + 15/180 since the question concerns the ratio of yz to x, we have no need for the 180 denominator, and we are left with... 22/15 (D)




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