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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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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]

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New post 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.

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

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New post Updated on: 06 Mar 2014, 00:57
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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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Originally posted by PareshGmat on 05 Mar 2014, 20:39.
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Re: Working alone, Printers X, Y, and Z can do a certain printin  [#permalink]

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New post 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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New post 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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New post 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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New post 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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New post 20 May 2015, 20:11
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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

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

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New post 21 May 2015, 22:31
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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


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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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New post 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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New post 17 Feb 2016, 18:44
[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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New post 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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New post 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

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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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New post 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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New post 08 Jun 2017, 17:06
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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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New post 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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Re: Working alone, Printers X, Y, and Z can do a certain printin  [#permalink]

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New post 10 May 2018, 09:54
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:
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!



Rate \(\frac{x}{12}\)

Rate y and z = \(\frac{y}{15}\)+\(\frac{z}{18}\) =\(\frac{6y+5z}{90}\)

Ratio of \(x\) to \(z\) and \(y\) ( x/12 ) / (6y+5z)/90 --->

\(\frac{x}{12}\) * \(\frac{90}{6y+5z}\) =\(\frac{30x}{4(6y+5z)}\) = \(\frac{30x}{(24y+20z)}\)

\(\frac{30x}{(44)}\) reduce by 2 \(\frac{15x}{(22)}\)


pushpitkc why isnt it a correct answer :? \(\frac{15x}{(22)}\)

why correct answer is \(22/15\) ? any idea ? :)
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Re: Working alone, Printers X, Y, and Z can do a certain printin  [#permalink]

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New post 10 May 2018, 11:22
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Hi dave13

Since X takes 12 hours to complete the work, X does \(\frac{1}{12}\) of the work in an hour.
Since Y takes 15 hours to complete the work, Y does \(\frac{1}{15}\) of the work in an hour.
Since Z takes 18 hours to complete the work, Z does \(\frac{1}{18}\) of the work in an hour.

Together in an hour, Y and Z do \(\frac{1}{15} + \frac{1}{18}\) or \(\frac{11}{90}\) of the work.
So, the time taken for these machines to do the work is \(\frac{1}{\frac{11}{90}} = \frac{90}{11}\) hours

We know that the time it takes machine X to do the work is 12 hours.

So, the ratio of time taken for X to do the work to time taken for X and Y to do the work is \(\frac{12}{\frac{90}{11}} = 12*\frac{11}{90} = \frac{22}{15}\)

Hope this helps you!
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