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OG - 2nd Edition - Arithmetic

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OG - 2nd Edition - Arithmetic

by shanice » Thu May 17, 2012 11:57 pm
Hi again,

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

Answer is D.

My workings:-

Printer Y and Z working together:-

1/15 + 1/18 = 11/90 and Printer X working alone = 1/12

So, 1/12 / 11/90 = 90/121 ( From my answer, I can know that my workings are wrong)

The workings in the OG book states as below:-

1/15 + 1/18=11/90 which is convert into as 90/11

So, 12/90/11=22/15(D).

Why Printer x is considered as 12/1 instead of 1/12?
Why the sum for Printer X and Y is considered as 90/11 instead of 11/90?

Please help me to clear my doubts.

Thank you.
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by mdavidm_531 » Fri May 18, 2012 1:51 am
shanice wrote:Hi again,

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

Answer is D.

My workings:-

Printer Y and Z working together:-

1/15 + 1/18 = 11/90 and Printer X working alone = 1/12

So, 1/12 / 11/90 = 90/121 ( From my answer, I can know that my workings are wrong)

The workings in the OG book states as below:-

1/15 + 1/18=11/90 which is convert into as 90/11

So, 12/90/11=22/15(D).

Why Printer x is considered as 12/1 instead of 1/12?
Why the sum for Printer X and Y is considered as 90/11 instead of 11/90?

Please help me to clear my doubts.

Thank you.
Remember what you are being asked for: "What is the ratio of the TIME it takes Printer X to to the job (working alone at its rate), to the TIME it takes Printer Y and Z to to do the job?"

As such, by simple formula of (rate)(time) = work , we have: time = work/rate

Printer X:

rate = 1/12 time = ? work = 1 .. as such time = 12 hours

Printer Z and Y:

rate = (1/15 + 1/18) = 11/90 time = ? work = 1 .. as such time = 90/11 hours

Now, remember what you being asked for: ratio of time/ratio of time

As such:

time of x = 12
time of y and z = 90/11

As such: 12/(90/11) = 22/15

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by GMATGuruNY » Fri May 18, 2012 2:02 am
shanice wrote:Hi again,

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
Perhaps the reasoning will be easier to see if we plug in a value for the job.

Let the job = 90 units.
Rate for Y = 90/15 = 6 units per hour.
Rate for Z = 90/18 = 5 units per hour.
Time for Y+Z working together = 90/(6+5) = 90/11 hours.
Ratio of (X's time) to (Y+Z's time) = 12/(90/11) = 12(11/90) = 22/15.

The correct answer is D.
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by shanice » Fri May 18, 2012 5:54 am
Thank you, guys. I understand it clearly now.
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