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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]

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05 Mar 2014, 02:16
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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

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

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[Reveal] Spoiler: OA

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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.

Thus required ratio 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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05 Mar 2014, 20:39
3
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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)

= $$12 * \frac{11}{90} = \frac{22}{15}$$

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Last edited by PareshGmat on 06 Mar 2014, 00:57, edited 3 times in total.
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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

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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.

Thus required ratio 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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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)

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

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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
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Expert's post
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

[Reveal] Spoiler:
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
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
Expert's post
[quote="Bunuel"]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

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..
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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 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

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:
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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11 May 2016, 10:17
D it is ... great explanations above
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Re: Working alone, Printers X, Y, and Z can do a certain printin   [#permalink] 11 May 2016, 10:17
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