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og math # 130
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rajeshsinghgmat
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Printing rate of x = 1/12resilient wrote:working alone, printers x,y, and z can do a certain printing job, consisitning of a large number of pages, 12, 15, and 18 hours, respectively. 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, working together at their individual rates?
a. 4/11
b.1/2
c. 15/22
d.22/15
e.11/4
qa is d. I dont see why C is wrong. I dont see why the solution flips the combined rate of y and z working together. help stuart?
Printing rate of y and z combined = 1/15 + 1/18 = 6/90 + 5/90 = 11/90
So printer x takes 12 hours while printers y and z combined take 90/11 hours to do the job.
Ratio = 12/(90/11) = 12*11/90 = 22/15
Hence d
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The answer is choice D.
I divide the workload into 180 widgets.
In one hour:
- Printer x can finish: 180/12 = 15 widgets.
- Printer y can finish: 180/15 = 12 widgets.
- Printer z can finish: 180/18 = 10 widgets.
So in one hour y and z can finish: 22 widgets. Therefore it takes them 190/22 = 90/11 hours to finish the work.
So the ratio is: 12/(90/11) = 22/15
I divide the workload into 180 widgets.
In one hour:
- Printer x can finish: 180/12 = 15 widgets.
- Printer y can finish: 180/15 = 12 widgets.
- Printer z can finish: 180/18 = 10 widgets.
So in one hour y and z can finish: 22 widgets. Therefore it takes them 190/22 = 90/11 hours to finish the work.
So the ratio is: 12/(90/11) = 22/15
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sansulee
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Could you explain why the answer is D?GMATGuruNY wrote:I think that the easiest approach is to plug in a value for the job in order to determine everyone's respective rates.resilient wrote:working alone, printers x,y, and z can do a certain printing job, consisitning of a large number of pages, 12, 15, and 18 hours, respectively. 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, working together at their individual rates?
a. 4/11
b.1/2
c. 15/22
d.22/15
e.11/4
qa is d. I dont see why C is wrong. I dont see why the solution flips the combined rate of y and z working together. help stuart?
Plug in job = 180.
Rate for x = w/t = 180/12 = 15/hour.
Rate for y = w/t = 180/15 = 12/hour.
Rate for z = w/t = 180/18 = 10/hour.
Combined rate of y+z = 12+10 = 22/hour.
Time for y+z = w/r = 180/22 = 90/11.
Ratio of (time x):(time y+z) = 12/(90/11) = 22/15.
The correct answer is D.
Aren't we supposed to take the ratio of the "rates" of these individual entities? (considering x as one and the combo of y-z as another entity)?
In that case, shouldn't the calculation go as:
1/12 / 33/15*18 = 15*18 / 33*12 ; eventually yielding 15/22 ?
Please correct me if I am wrong, so that I do not repeat the mistake.
Thanks!
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kshitijhbti
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Answer is D.
Time taken by x = 12
Time taken y and z to work together = (18*15)/(18+15) = 270/33 = 90/11
Ratio= x/(y+z)= 12/(90/11) = 12*11/ 90 = 22/15
Time taken by x = 12
Time taken y and z to work together = (18*15)/(18+15) = 270/33 = 90/11
Ratio= x/(y+z)= 12/(90/11) = 12*11/ 90 = 22/15
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Joseph_Alexander
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Hi resilent!resilient wrote:hmm still not seeing the picture. What I am trying to grasp is why the flip of the combined rates. It doesnt make sense to me and goes against what is taught with mahattan gmat. confused
thank you
I got the same answer as yours. Noticed that 12, 15 and 18 is the time they take to complete a job and it is not their speed. So assuming that the work is 180, their speed would be 15, 12 and 10. Now if you use 15, 12 and 10, you won't have to flip!
Dont jump and solve this problem straight away.
You can straight away eliminate choices a, b and c as those choices dosen't make any sense. ( time for A to complete the job will always be greater than time for B & C working together)
Now we are left with D and E.
pick a comfortable number which divides 12, 15 and 18. I chose 180. time taken for printing 180 units will be,
A - 15
B - 12
C - 10
180/15 by 180/(12 +10) = 22/15
Answer: D
You can straight away eliminate choices a, b and c as those choices dosen't make any sense. ( time for A to complete the job will always be greater than time for B & C working together)
Now we are left with D and E.
pick a comfortable number which divides 12, 15 and 18. I chose 180. time taken for printing 180 units will be,
A - 15
B - 12
C - 10
180/15 by 180/(12 +10) = 22/15
Answer: D
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GMATinsight
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resilient wrote:
working alone, printers x,y, and z can do a certain printing job, consistning of a large number of pages, 12, 15, and 18 hours, respectively. 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, working together at their individual rates?
a. 4/11
b.1/2
c. 15/22
d.22/15
e.11/4
Let's assume the Total work in terms of "Work units" by assuming it a number which is a Common multiple (not essentially the LCM) of 12, 15 and 18. This exercise is specially beneficial in order to avoid the calculation of fraction.
A common multiple of 12, 15 and 18 = 180 (One can also assume this number as 360, 540 etc. however the least is the best]
Since the 180 units is done by X in 12 Hours, Y in 15 hours and X in 18 hours therefore
- One hour of Printer X : 180/12 = 15 Units.
- One hour of Printer Y : 180/15 = 12 Units.
- One hour of Printer Z : 180/18 = 10 Units.
- One hour of Printer Y and Z together : 12+10 = 22 Units.
Total time taken by Y and Z to finish the work together = 180/22 = 90/11 hours
So the Required ratio is: 12/(90/11) = 22/15
Answer: Option D
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