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## og math # 130

tagged by: Brent@GMATPrepNow

This topic has 8 expert replies and 124 member replies
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resilient Legendary Member
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#### og math # 130

Sat Mar 08, 2008 8:24 pm
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?

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Stuart Kovinsky GMAT Instructor
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Sun Mar 09, 2008 3:55 pm
There's another formula you can use when it's exactly 2 workers:

Comb time = (a*b)/(a+b)

In this question, we want the ratio of x working alone to y+z working together.

So:

12 / (15*18)/(15+18)

12 / (270/33)

12*33/270

12*11/90

2*11/15

22/15

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gmatjeet Master | Next Rank: 500 Posts
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Sun Nov 07, 2010 12:44 pm
hrs taken by x = 12
hrs taken by y = 15
hrs taken by z = 18

lets say y and z together = m hrs

1/m = 1/15 + 1/18

m = 90/11

so hrs taken by y and z together = 90/11

rations of hrs taken by x to hrs taken by y and z together = 12/(90/11) = 22/15

siddarthd2919 Junior | Next Rank: 30 Posts
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Sat Mar 08, 2008 9:08 pm
hi engin, i guess u have seen the intro for the math section in o.g...... there is a formula for work done combined when the individual times are given

1/x+1/y=1/h

where x-----time taken for x to do the work alone

y-----time for y to do the work alone

h-----time taken for the work to be done when both x and y work together.

x=12, y=15 z=18

the question is x/h

12/(1/((1/15)+(1/18))

that gives

12/(1/(33/(15*18))

that gives

12*33/(15*18)========22/15........

resilient Legendary Member
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Sun Mar 09, 2008 12:42 am
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

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camitava Legendary Member
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Sun Mar 09, 2008 5:38 am
Enginpasa1,
Look if y and z work together, they can do = (1/15 + 1/18) amount in 1 day = (6 + 5) / 90 = 11/90.
so y and z can complete the work in 90/11 days.

On the other hand, x can do the work in 12 day.
So ratio is = 12 : 90/11 = 22/15.

Look the Qs is asking for - 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? So you can not do the ratio with the amount of work, u got, that x and (y + z) can do in 1 hr.

1/12 -> Amount of work done by X in 1 hr
11/90 -> Amount of work done by Y and Z in 1 hr . So u can not do the ratio of these numbers. Got me, Enginpasa1?

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resilient Legendary Member
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Sun Mar 09, 2008 12:38 pm
Thank you friend. I got it. THe problem was coming from not being able to understand the basic formula. I am approaching the problem the way I was taught from Manhattan gmat. I plug in the values according to a chart. In the end the same operatiosn are done. Thank you very much.

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farooq Master | Next Rank: 500 Posts
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Fri Oct 30, 2009 8:08 am
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?
Lets say total no. of pages that each printer prints are 180.

X prints 180 pages in 12 hours. 15 pages per hour.
Y prints 180 pages in 15 hours. 12 Pages per hour.
Z prints 180 pages in 18 hours. 10 pages per hour.

If Y and Z both work together, they will print 12+10 = 22 pages per hour.

Therefore total no. of hours to print 180 pages by Y and Z will be 180/22.

Time taken by X to print total no. of pages/Time taken by (Y and Z together)to print total no. of pages = 12/(180/22) = 22/15

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AtifS Senior | Next Rank: 100 Posts
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Sun Oct 31, 2010 7:05 am
Explanation:
Time printer x takes to do a certain job = 12 hours
Time printers y & x take to do together a certain job is
Rate of job by both y &z =1/15 + 1/18= (15+18)/(15)(18)= (5+6)/(15)(6)= 11/90 --> Time=90/11 hours

Now, the ratio of time printer x takes to do the job to the time printers y & z take to do = 12 /(90/11)= 12*11/90= 2*11/15= 22/15, which is option D.

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Andijansky Newbie | Next Rank: 10 Posts
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Sun Oct 31, 2010 7:17 pm
seems like D

Abhishek009 Master | Next Rank: 500 Posts
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Thu Nov 04, 2010 1:56 am
farooq wrote:
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?
Lets say total no. of pages that each printer prints are 180.

X prints 180 pages in 12 hours. 15 pages per hour.
Y prints 180 pages in 15 hours. 12 Pages per hour.
Z prints 180 pages in 18 hours. 10 pages per hour.

If Y and Z both work together, they will print 12+10 = 22 pages per hour.

Therefore total no. of hours to print 180 pages by Y and Z will be 180/22.

Time taken by X to print total no. of pages/Time taken by (Y and Z together)to print total no. of pages = 12/(180/22) = 22/15
Was going to do the problem with this method , but farooq has already posted it. I support his method and answer completely.

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thebigkats Senior | Next Rank: 100 Posts
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Sun Nov 07, 2010 1:05 am
fairly straightforward.
Assume total no of pages to be 12*15*18
Speed of X = 12*15*18 / 12 = (15*18) pages per hour
Speed of Y = 12*15*18 / 15 = 12*18 pages per hour
Speed of Z = 12*15*18 / 18 = 12*15 pages per hour

So now to finish the same pages, X will take - (12*15*18) / 15*18 = 12 hours
To finish the same pages both Y and Z will take - (12*15*18) / ((12*18) + (12*15))

Ratio X / (Y+Z) hours = (12*15*18) / (15*18) / ((12*15*18) / ((12*18) + (12*15)))
==> ((12*18) + (12*15) ) / (15*18)
==> 12*33 / 15*18
==> 22/15

g.manukrishna Newbie | Next Rank: 10 Posts
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Thu Nov 18, 2010 2:37 am
work done = rate X time taken

for A alone the equation is:

1 = 1/12 X t1

for B and C together

1 = (1/15)+(1/18) X t2

question is what is the ratio of t1 and t2 which is 22/15. So D is the correct option.

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GMATGuruNY GMAT Instructor
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Thu Nov 18, 2010 3:50 am
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?
I think that the easiest approach is to plug in a value for the job in order to determine everyone's respective rates.

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.

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Swapnil_R Newbie | Next Rank: 10 Posts
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Thu Nov 18, 2010 9:21 am
There is other way to solve such problems.
Printer x alone can do 8.33% (1/12%) work in an hr. Similary y and z can do 6.66% and 5.55% work in an hr respectively.
Together y and z can do 12.22% of work in an hr.

So % work done ratio for x / (y + z) = 8.33/12.22
so time raio = 12.22/8.33 approx 22/15.

Hope this will help to solve such time and speed problems.

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