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?
og math # 130

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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 xtime taken for x to do the work alone
ytime for y to do the work alone
htime taken for the work to be done when both x and y work together.
now for your problem.........
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........
1/x+1/y=1/h
where xtime taken for x to do the work alone
ytime for y to do the work alone
htime taken for the work to be done when both x and y work together.
now for your problem.........
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........

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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?
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?
Correct me If I am wrong
Regards,
Amitava
Regards,
Amitava

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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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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
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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Lets say total no. of pages that each printer prints are 180.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?
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
Regards,
Farooq Farooqui.
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Answer: D
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.
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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Was going to do the problem with this method , but farooq has already posted it. I support his method and answer completely.farooq wrote:Lets say total no. of pages that each printer prints are 180.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?
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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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
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

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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
so answer = D
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
so answer = D
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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.
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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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.
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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.
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.