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# Working alone, Printers X, Y, and Z can do a certain printin

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Working alone, Printers X, Y, and Z can do a certain printin [#permalink]  05 Mar 2014, 01:16
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

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

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]  05 Mar 2014, 19:39
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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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Last edited by PareshGmat on 05 Mar 2014, 23:57, edited 3 times in total.
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]  05 Mar 2014, 22:35
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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]  08 Mar 2014, 11:38
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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.

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]  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
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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
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]  28 Apr 2014, 01:34
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]  20 May 2015, 14:06
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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]  20 May 2015, 19:11
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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:
[Reveal] Spoiler:
D

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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]  21 May 2015, 21:31
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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)

Answer (D)
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Re: Working alone, Printers X, Y, and Z can do a certain printin   [#permalink] 21 May 2015, 21:31
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