Problem Solving

Victor's job requires him to complete a series of identical jobs. If vitor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish 36 jobs. How long would it take Victor to complete 10 jobs without any supervision?

can we set up the following equation? When i do it this way though, i can't get the right answer so i imagine you cant, but i cant figure out why the equation i set up wont work.

72r + 72(r-3) =36

rt = d

so 72 days at the regular rate plus 72 days at the rate shortened by 3 days should give us 36 jobs. apparently ..not?

say speed when supervised is 'S' and speed when not supervised is "US':

S(t-3) = 1W --A
US(t) = 1W --B

thus, from A and B, t = W/US

=> S = 4US {insert value of t in equation (A)}

also given that, 72S + 72US = 36W => 2S + 2US = W

=> 8US + 2US = W => US = W/10

thus, for finishing 10 jobs: US X T = 10W

or T = 10W/(W/10) = 100 days.

Answer is indeed 60! My fault!!

Neo Anderson wrote:say speed when supervised is 'S' and speed when not supervised is "US':

S(t-3) = 1W --A
US(t) = 1W --B

thus, from A and B, t = W/US => S = 4US {insert value of t in equation (A)}

also given that, 72S + 72US = 36W => 2S + 2US = W

=> 8US + 2US = W => US = W/10

thus, for finishing 10 jobs: US X T = 10W

or T = 10W/(W/10) = 100 days.

the answer is 60.

fangtray wrote:Victor's job requires him to complete a series of identical jobs. If vitor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish 36 jobs. How long would it take Victor to complete 10 jobs without any supervision?

can we set up the following equation? When i do it this way though, i can't get the right answer so i imagine you cant, but i cant figure out why the equation i set up wont work.

72r + 72(r-3) =36

rt = d

so 72 days at the regular rate plus 72 days at the rate shortened by 3 days should give us 36 jobs. apparently ..not?

1. Let d denote the number of days required to finish a job when supervised
2. d+3, therefore, is the number of days required to finish a job when unsupervised

To convert days per job to jobs per day, we simply take the inverse...

3. Let 1/d denote the rate per job while supervised
4. Let 1/(d+3) denote the rate per job while unsupervised

So, we have...

72/d + 72/(d+3) = 36

72(d+3) + 72d = 36*d*(d+3)
2(d+3) + 2d = d*(d+3)
d^2 - d - 6 = 0
(d - 3)*(d + 2) = 0
d = 3 days to complete one job while supervised

Therefore, it takes 6 days while not supervised

10 jobs * 6 days per job = 60 days

Victor's job is to complete series of identical jobs. If victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long would it take Victor to complete 10 jobs without any supervision?

A. 34
B. 52
C. 60
D. 70
E. 92

The posted question should have included the answer choices shown above.

We can plug in the answers, which represent the time for Victor to complete 10 jobs unsupervised.
Given the values in the problem -- 144, 36, and 10 -- the correct answer is likely to be a multiple of 6 and 10.

Answer choice C: 60 days
Since 10 jobs are produced, the time for each unsupervised job = 60/10 = 6 days.
Since the supervised rate is 3 days faster, the time for each supervised job = 3 days.
When Victor works for 144 days-- supervised for half the time -- he must produce 36 jobs.
The number of jobs produced in 72 supervised days = (total days)/(days per job) = 72/3 = 24.
The number of jobs produced in 72 unsupervised days = (total days)/(days per job) = 72/6 = 12.
Total number of jobs produced = 24+12 = 36.
Success!

The correct answer is C.

Because we assessed the viability of the answer choices BEFORE we plugged them in, we had to try ONLY ONE -- a very efficient way to solve the problem.

So everyone that got 60 is correct, and there are clearly several different methods to get the correct answer. Below is a snapshot of how I got to the answer using the rate box.

The first step, like all wordy math problems with too much information, is to organize it as clearly as possible. We know that R X T = D so we set it up in such a way that it's clear what information they are telling us in order to figure out what we need to figure out in order to spit back the correct answer.

So we know that when he's unsupervised he goes at a certain rate, we'll call that "X", and when he is supervised, like most employees, they work faster, in this case 3 times as fast (as X), so we call this rate 3X.

We know that if he works for 1/2 of 144 (their great more complicated way of saying 72) days at this rate he produces 36 of the jobs. This means we can figure out what X is by setting up our formula. They gave us the number of jobs (work), they gave us the time, and we know that the speed is 3X, and we have to figure out what X is. So if 3X x 72 = 36, then it must be true that 3X = 36/72. 36/72 is the same as 1/2. So 3X = 1/2. (I like to reduce fractions wherever possible to avoid big numbers. Helps me reduce mistakes.) So "what" multiplied by 3 gives us 1/2? We have to make 3X equal one half. Well, we can do that by sticking a 6 under the 3. And we can do that by multiplying the 3 by 1/6. So this means that X = 1/6.

So, now that we know what X is, we can plug it in to the rate box and now we can put together the equation we need to get the final answer. We know that at rate X, which is 1/6, he completes 10 jobs - how long does it take him? So 1/6 x SOMETHING = 10. So the left side has to equal 10. What can we multiply 1/6 by in order to get 10? The answer is 60. 1/6 x 60/1 = 10. So this means, that the time is 60.

Sorry if the explanation is too wordy, but I find the best explanations I get when I have problems are the ones that are wordy and explain everything (idiot proof, as it were since I can be an idiot late at night when my brain is overcooked with GMAT.

Hope this helped!

GMATGuruNY wrote:

Victor's job is to complete series of identical jobs. If victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long would it take Victor to complete 10 jobs without any supervision?

A. 34
B. 52
C. 60
D. 70
E. 92

The posted question should have included the answer choices shown above.

We can plug in the answers, which represent the time for Victor to complete 10 jobs unsupervised.
Given the values in the problem -- 144, 36, and 10 -- the correct answer is likely to be a multiple of 6 and 10.

Answer choice C: 60 days
Since 10 jobs are produced, the time for each unsupervised job = 60/10 = 6 days.
Since the supervised rate is 3 days faster, the time for each supervised job = 3 days.
When Victor works for 144 days-- supervised for half the time -- he must produce 36 jobs.
The number of jobs produced in 72 supervised days = (total days)/(days per job) = 72/3 = 24.
The number of jobs produced in 72 unsupervised days = (total days)/(days per job) = 72/6 = 12.
Total number of jobs produced = 24+12 = 36.
Success!

The correct answer is C.

Because we assessed the viability of the answer choices BEFORE we plugged them in, we had to try ONLY ONE -- a very efficient way to solve the problem.

Hey Mitch,
Can you please elaborate how you assessed the answer to likely be a multiple of 6 & 10 given the numbers 144, 36 and 10?
Thanks
-Prasoon