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Working alone, printers X, Y, and Z can do a certain

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Working alone, printers X, Y, and Z can do a certain [#permalink] New post 27 Jan 2007, 15:12
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Question Stats:

62% (02:23) correct 38% (01:27) wrong based on 144 sessions
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
[Reveal] Spoiler: OA
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 [#permalink] New post 27 Jan 2007, 17:39
D

X takes 12 hrs

Y and Z together = (1/15) + (1/18) = 11/90 = 90/11 hrs

ratio = X /( YandZ) = 12 * (11/90) = 22/15
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 [#permalink] New post 01 Feb 2007, 21:23
Indeed D is the correct answer, got 22/15 by the exact same approach
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 [#permalink] New post 02 Feb 2007, 14:53
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Rate(X) = 1/12 job/hour or 12 hour/job
Rate(Y) = 1/15 job/hour
Rate(Z) = 1/18 job/hour

Rate(Y + Z) = 1/15 + 1/18 job/hour = (6 + 5)/90 = 11/90 job/hour

This mean that Machine Y and Z can finish 11/90 job in one hour

So how long will will take for Machine X to finish 11/90 job? Rate(X) = 12 hour/job
Time(x) to do 11/90 job = 11/90 job x 12 hour/job = 11 x 12 /90 = 44/30 = 22/15 hours

(D) is the answer.
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Re: Working alone, printers X, Y, and Z can do a certain [#permalink] New post 23 Jan 2013, 12:12
Hi,

if somebody could help me what I am doing wrong here, it would be great:

1) I am calculating individual rates for all 3 printer and bring them onto the same denominator.
X = 1/12 = 30/360
Y = 1/15 = 24/360
Z = 1/18 = 20/360

2) Comparing the nominators of X with the sum of Y and Z, since they are now comparable.
30/(24+20) = 30/44 = 15/22

The ratio is X to (Y + Z) so it should be fine.
This would be answer (C) and not (D).
Why should I flip the nominator and denominator here? :?:

Thanks for your help in advance
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Re: Working alone, printers X, Y, and Z can do a certain [#permalink] New post 23 Jan 2013, 19:02
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leventg wrote:
Hi,

if somebody could help me what I am doing wrong here, it would be great:

1) I am calculating individual rates for all 3 printer and bring them onto the same denominator.
X = 1/12 = 30/360
Y = 1/15 = 24/360
Z = 1/18 = 20/360

2) Comparing the nominators of X with the sum of Y and Z, since they are now comparable.
30/(24+20) = 30/44 = 15/22

The ratio is X to (Y + Z) so it should be fine.
This would be answer (C) and not (D).
Why should I flip the nominator and denominator here? :?:

Thanks for your help in advance


RATES of X, Y and Z are 30/360, 24/360 and 20/360

Ratio of RATE of X:RATE of Y+Z = 30:44 = 15:22

The question asks for the ratio of TIME TAKEN = 1/15 : 1/22 = 22:15
(Time taken is the inverse of rate)
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Re: Working alone, printers X, Y, and Z can do a certain [#permalink] New post 24 Jan 2013, 03:23
Thanks for your fast reply Karishma, :-D

As this was still difficult for me to understand, I have created an easy example for better understanding.
Let’s assume all printers take 12 hours. So printer Y and Z are doing the same job as printer X twice as fast.

X = 1/12 (job/hours)
Y = 1/12 (job/hours)
Z = 1/12 (job/hours)
Y+Z = 2/12 = 1/6 (job/hours)

X : (Y+Z) = 1 : 2 => This ratio refers to the output.

Regarding Time Taken, X makes in 12 hours 1 job and Y+Z are doing in 6 hours 1 job.
So what you are saying is that we are comparing the hours and not the jobs right?
And therefore the ratio of X : Y is 12 : 6, which is 2 : 1.

Summarizing both steps:
X : (Y+Z) = (1/12) : (2/12) = 1 : 2 => This ratio refers to the output.
X : (Y+Z) = (1/12) : (1/6) = 12: 6 = 2 : 1 => This ratio refers to the time

Referring to my example again:
X = 12 hours
Y+Z = 6 hours
Ratio is not 12 : 6 or 2 : 1 because time taken is inverse to rate?
Instead the Ratio is (1/12) : (1/6) = (6/12) = 1 : 2

Actually this TIME-IS-INVERSE-APPROACH is quite difficult to understand. I can apply it but still it is difficult to understand. May be it is just easier to divide 2 fractions. (Divide Y+Z by X).

Last edited by leventg on 24 Jan 2013, 05:04, edited 1 time in total.
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Re: Working alone, printers X, Y, and Z can do a certain [#permalink] New post 24 Jan 2013, 03:40
Expert's post
leventg wrote:
Thanks for your fast reply Karishma, :-D

As this was still difficult for me to understand, I have created an easy example for better understanding.
Let’s assume all printers take 12 hours. So printer Y and Z are doing the same job as printer X twice as fast.

X = 1/12 (job/hours)
Y = 1/12 (job/hours)
Z = 1/12 (job/hours)
Y+Z = 2/12 = 1/6 (job/hours)

X : (Y+Z) = 1 : 2 => This ratio refers to the output.

Regarding Time Taken, X makes in 12 hours 1 job and Y+Z are doing in 6 hours 1 job.
So what you are saying is that we are comparing the hours and not the jobs right?
And therefore the ratio of X : Y is 12 : 6, which is 2 : 1.

Summarizing both steps:
X : (Y+Z) = (1/12) : (2/12) = 1 : 2 => This ratio refers to the output.
X : (Y+Z) = (1/12) : (1/6) = 2 : 1 => This ratio refers to the time.


Referring to my example again:
X = 12 hours
Y+Z = 6 hours
Ratio is not 12 : 6 or 2 : 1 because time taken is inverse to rate?
Instead the Ratio is (1/12) : (1/6) = (6/12) = 1 : 2

Actually this TIME-IS-INVERSE-APPROACH is quite difficult to understand. I can apply it but still it is difficult to understand. May be it is just easier to divide 2 fractions. (Divide Y+Z by X).


For an intuitive understanding of ratios approach, check out these posts:
http://www.veritasprep.com/blog/2011/03 ... of-ratios/
http://www.veritasprep.com/blog/2011/03 ... os-in-tsd/
http://www.veritasprep.com/blog/2011/03 ... -problems/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: Working alone, printers X, Y, and Z can do a certain   [#permalink] 24 Jan 2013, 03:40
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