Problem Solving

Answer D : 22/15

rate ratio
1/12*(15)(18)/33
=15/22
as
rate*time= work
to get the time to complete 1 job
t=22/15

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

Printer Rate Time Work Done
X 1/12 12 1
Y 1/15 15 1
Z 1/18 18 1
Y+Z 11/90 *90/11 1

*Y+Z = 1/15 +1/18 =11/90
Ratio:
12: 90/11
=132:90
=22:15

Answer is 22/15
Simple calculation already explained...

Answer is e 22/15

D is correct

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


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
==> in case of power questions, we use the inverse numbers once we see 'together and alone'. In other words, since y and z worked together and took t hours, (1/15)=(1/18)=1/t, (6+5)/90=1/t, t=90/11 therefore 12:(90/11)=2:(15/11). multiplying 11 to both sides gives us 22:15, therefore D is the answer.

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Two important things in time and work :

if X completes work is x hrs, X RATE of work = 1/x
Y completes work is y hrs,Y RATE of work= 1/y

and they work together

1/x + 1/y = 1/h will give the total 'TIME' taken to complete the work (usually days)

where as 'h' gives total 'RATE' of combined x and y

that's why the flip happens

Hello all,

so far I have only understood the answer from "GMATinsight" which makes totally sense.

I have a different approach and want to know why I can't proceed as followed:

the medium time of Printer y and z to finish the certain Job is 16,5 hours.

I divided the 16,5 by two because I assume that with the average time the two Printers will print twice as many as one Printer. The result should be proportioned to the result of the time Printer x Needs for this certain printing Job.

Thanks for your help in advance and Kind regards,
Max

maxmayr93 wrote:Hello all,

so far I have only understood the answer from "GMATinsight" which makes totally sense.

I have a different approach and want to know why I can't proceed as followed:

the medium time of Printer y and z to finish the certain Job is 16,5 hours.

I divided the 16,5 by two because I assume that with the average time the two Printers will print twice as many as one Printer. The result should be proportioned to the result of the time Printer x Needs for this certain printing Job.

Thanks for your help in advance and Kind regards,
Max

This is where intuition fails.

The time it takes for both Y and Z working together is as follows:

1 = T(1/18 + 1/15) . Solving for T yields 90/11 hours, or 8 2/11 hours.

So each of them working 8 2/11 hours will finish the job. This differs from a simple average you mention above of 8 1/4 hours.

2/11 = 8/44 versus 1/4 = 11/44 > your method has them working 3/44 longer as necessary.

The 15 and 18 hours can be viewed as a form of rate, which is a ratio, and you have to be very careful averaging ratios and how you interpret them

x can do work by 12 hours
y and z together can do the work by 15.18 / (15+18)

x : y+z = 12 : 15 . 18 / 33 = 2 : 15 / 11 = 22 : 15

Rates are measured in inverse time. So the total rate of x and y together = 1/15 + 1/18 = 1/3(1/5 + 1/6) = 1/3(11/30) = 11/90
The total time is the reciprocal of this, namely 90/11.
The ratio required is x:(x and y) = 12: 90/11 = 12 x 11 /90 = 22/15 (D)

D