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Difficulty: 605-655 Level,   Work and Rate Problems,                           
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Re: Working alone, Printers X, Y, and Z can do a certain printing job, con [#permalink]
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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 printing job, con [#permalink]
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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 printing job, con [#permalink]
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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:

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

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 printing job, con [#permalink]
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Attached is a visual that should help.
Attachments

Screen Shot 2016-05-05 at 6.16.09 PM.png
Screen Shot 2016-05-05 at 6.16.09 PM.png [ 100.35 KiB | Viewed 68317 times ]

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Re: Working alone, Printers X, Y, and Z can do a certain printing job, con [#permalink]
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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 printing job, con [#permalink]
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prude_sb 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


----ASIDE-----------------------------------
For work questions, there are two useful rules:
Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.
---------------------------------------------------------

Let’s use these rules to solve the question. . . .

Printer Y takes 15 hours to complete a job. So, by rule #1, printer Y’s rate is 1/15 of the job per hour
Printer Z takes 18 hours to complete a job. So, by rule #1, printer Z’s rate is 1/18 of the job per hour
So, their combined rate per hour = 1/15 + 1/18
= 6/90 + 5/90
= 11/90
So, working together, printers Y and Z can complete the 11/90 of the job in one hour.
When we apply rule #2, we can conclude that, working together, printers Y and Z will complete the entire job in 90/11 hours.


What is the ratio of the time it takes printer X to do the job, working at its rate, to time it takes printers y and z to do the job?
So, (time for X to complete)/ (time for Y & Z to complete) = 12/(90/11)
= (12)(11/90)
= 22/15

Answer: D

Originally posted by BrentGMATPrepNow on 25 Apr 2018, 18:06.
Last edited by BrentGMATPrepNow on 02 Apr 2020, 07:54, edited 1 time in total.
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Re: Working alone, Printers X, Y, and Z can do a certain printing job, con [#permalink]
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prude_sb 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


Total work = LCM(12,15,18) = 180 units

Rate of Y = 180/15 = 12 units/hr , and Rate of Z = 180/18 = 10 units/hr. Combined rate of Y+Z = 22 units/hr

Time required to complete the job by Y+Z = 180/22 hr

Required ratio:

= \(\frac{12}{\frac{180}{22}} = \frac{12 \times 22}{180} = \frac{22}{15}\)

Thanks.
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Re: Working alone, Printers X, Y, and Z can do a certain printing job, con [#permalink]
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