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Victor's job requires him to complete a series of identical

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Victor's job requires him to complete a series of identical [#permalink] New post 11 Sep 2011, 13:17
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Victor's job requires him to complete a 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Mar 2013, 01:55, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Victor's job [#permalink] New post 11 Sep 2011, 13:33
supervised not supervised

time per job t-3 t


In 144 days when victor was supervised for half of the time , he finished 36 jobs.

=> During 72 days of supervision he finished 36 jobs.

=> 36(t-3) = 72

=> t = 5

=> victor took 5 days to finish a each unsupervised job.

time taken by victor to finish 10 jobs with out supervision = 10t = 50
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Re: Victor's job [#permalink] New post 11 Sep 2011, 13:39
Spidy001 wrote:
supervised not supervised

time per job t-3 t


In 144 days when victor was supervised for half of the time , he finished 36 jobs.

=> During 72 days of supervision he finished 36 jobs.

=> 36(t-3) = 72

=> t = 5

=> victor took 5 days to finish a each unsupervised job.

time taken by victor to finish 10 jobs with out supervision = 10t = 50



OA is 60 but.... there is some mistake with your solution
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Re: Victor's job [#permalink] New post 11 Sep 2011, 13:57
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my bad. ignore the previous post. i thought the question said 36 jobs in 72 days of supervision.


Where as Questions says it took 36 jobs in 144 days out of which he worked halftime supervised.


Supervised not supervised
time per job t-3 days t days


=> jobs in 72 days of supervision + jobs in 72 days when not supervised = 36

=> 72/(t-3) + 72/t = 36

solving we get t = 1 or 6

=> t=6 ( t = 1 is not possible as t-3 would be negative)

=> time taken by victor each unsupervised job = 6 days.

=> time taken by victor to finish 10 unsupervised jobs = 10t = 60 days.
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Re: Victor's job [#permalink] New post 12 Sep 2011, 01:34
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60 days it is

72/ (x-3) + 72/x = 36

=> x^2 -7x+6 =0 => x= 1 or 6

X = 1 is omitted coz x-3 = -2 if x=1

so x=6 and time taken for 10 jobs under no supervision = 10x6 = 60
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Re: Victor's job [#permalink] New post 15 Nov 2012, 23:21
Guys,

I've made th same error as Spidy001. This advanced RTW problem is otherwise not that hard, but I wonder what strategies you apply in order to fully grasp the right meaning of the problem. At first, I also thought the 5 days per job scenario was right. Based on this problem, do you have any tips on that?

Thanks in advance!
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Re: Victor's job [#permalink] New post 15 Nov 2012, 23:57
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bgpower wrote:
Guys,

I've made th same error as Spidy001. This advanced RTW problem is otherwise not that hard, but I wonder what strategies you apply in order to fully grasp the right meaning of the problem. At first, I also thought the 5 days per job scenario was right. Based on this problem, do you have any tips on that?

Thanks in advance!


bgpower,

I can imagine why Spidy001 made that mistake. The question says that he was supervised for half that time, but it doesn't say that Victor did not work during the time he was unsupervised.
So, what the question intended to say was, Victor worked under supervision for 72 days and without supervision for the remaining 72. What Spidy001 has done is, he hasn't taken into account the 72 days that Victor worked without supervision.

Secondly, as data given to us was in the form of (days/job) and not (jobs/day), you should divide 72 by (t-3) and (t) rather than multiplying it.

This sort of an error can be avoided by simply taking a step back to understand what the question says and writing the facts down, rather than trying to hold them in your head.
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Re: Victor's job requires him to complete a series of identical [#permalink] New post 23 Mar 2013, 22:00
siddhans wrote:
Victor's job requires him to complete a 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?


I have a query

R T D
S (1/t) 72 (72/t)
U (1/(t+3) 72 (72/(t+3))

Total jobs = 36

(72/t) + [(72/(t+3)] = 36

=> 2/t + 2/(t+3) = 1
=> 2t + 6 + 2t = t^2 + 3t
=> t^2 - t - 6 = 0

t = 3 or t =-2 (can't be negative)
Hence , 3

So answer is 30

Plz advice where I am wrong as I took the other way around by taking (t+3)

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Re: Victor's job requires him to complete a series of identical [#permalink] New post 24 Mar 2013, 02:07
Expert's post
targetgmatchotu wrote:
siddhans wrote:
Victor's job requires him to complete a 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?


I have a query

R T D
S (1/t) 72 (72/t)
U (1/(t+3) 72 (72/(t+3))

Total jobs = 36

(72/t) + [(72/(t+3)] = 36

=> 2/t + 2/(t+3) = 1
=> 2t + 6 + 2t = t^2 + 3t
=> t^2 - t - 6 = 0

t = 3 or t =-2 (can't be negative)
Hence , 3

So answer is 30

Plz advice where I am wrong as I took the other way around by taking (t+3)

Rgds,
TGC


We are told that if Victor is supervised at work, he finishes each job three days faster than if he is unsupervised.

Supervised = t days;
Unsupervised = (t + 3) days.

Victor to complete 10 jobs without any supervision will need 10(t + 3) = 60.

Hope it helps.
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Re: Victor's job requires him to complete a series of identical [#permalink] New post 24 Mar 2013, 02:25
Bunuel wrote:
targetgmatchotu wrote:
siddhans wrote:
Victor's job requires him to complete a 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?


I have a query

R T D
S (1/t) 72 (72/t)
U (1/(t+3) 72 (72/(t+3))

Total jobs = 36

(72/t) + [(72/(t+3)] = 36

=> 2/t + 2/(t+3) = 1
=> 2t + 6 + 2t = t^2 + 3t
=> t^2 - t - 6 = 0

t = 3 or t =-2 (can't be negative)
Hence , 3

So answer is 30

Plz advice where I am wrong as I took the other way around by taking (t+3)

Rgds,
TGC


We are told that if Victor is supervised at work, he finishes each job three days faster than if he is unsupervised.

Supervised = t days;
Unsupervised = (t + 3) days.

Victor to complete 10 jobs without any supervision will need 10(t + 3) = 60.

Hope it helps.



Hi Bunuel

As I would follow the same method of RTW chart for any problem in TNW, it would be really helpful if you can QUOTE the error in my method .

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Re: Victor's job requires him to complete a series of identical [#permalink] New post 24 Mar 2013, 02:30
Expert's post
targetgmatchotu wrote:
Bunuel wrote:
targetgmatchotu wrote:
I have a query

R T D
S (1/t) 72 (72/t)
U (1/(t+3) 72 (72/(t+3))

Total jobs = 36

(72/t) + [(72/(t+3)] = 36

=> 2/t + 2/(t+3) = 1
=> 2t + 6 + 2t = t^2 + 3t
=> t^2 - t - 6 = 0

t = 3 or t =-2 (can't be negative)
Hence , 3

So answer is 30

Plz advice where I am wrong as I took the other way around by taking (t+3)

Rgds,
TGC


We are told that if Victor is supervised at work, he finishes each job three days faster than if he is unsupervised.

Supervised = t days;
Unsupervised = (t + 3) days.

Victor to complete 10 jobs without any supervision will need 10(t + 3) = 60.

Hope it helps.



Hi Bunuel

As I would follow the same method of RTW chart for any problem in TNW, it would be really helpful if you can QUOTE the error in my method .

Rgds,
TGC


Actually I already did.

You calculated the time needed to complete 10 jobs WITH supervision (10t, less time) but we are asked to find the time needed to complete 10 jobs WITHOUT any supervision (10(t+3), more time).

Hope it's clear.
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Re: Victor's job requires him to complete a series of identical [#permalink] New post 27 Sep 2013, 22:31
Nice Question !

Took me a good amount of time !

Rate(Supervised) = 1/(t-3)
Rate(Unsupervised) = 1/(t)

72/(t-3) + 72 /(t) = 36

t=6 or t=1

Cannot be 1 as 't-3' would be negative then => t=6

Rate (UN) = 1/6

Rate * Time = work

1/6 * time = 10

Time = 10*6 = 60
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Re: Victor's job requires him to complete a series of identical [#permalink] New post 13 Oct 2013, 11:10
siddhans wrote:
Victor's job requires him to complete a 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



My approach:
Since we are asked Unsupervised time, i make that as t (variable in question). This way i do not have to worry about other stuff.

S => 1/(t-3)
U => 1/t

72days Job S + 72days job U = 36job
72/t + 72/(t-3) = 36

now pick a number to that LHS = RHS
t=6 => 72\6 + 72\3 = 36

now asked is 10t=6*10 = 60.
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Re: Victor's job [#permalink] New post 17 Oct 2013, 11:14
raghavakumar85 wrote:
60 days it is

72/ (x-3) + 72/x = 36

=> x^2 -7x+6 =0 => x= 1 or 6

X = 1 is omitted coz x-3 = -2 if x=1

so x=6 and time taken for 10 jobs under no supervision = 10x6 = 60



edit: nevermind, had a mistake in my work
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Re: Victor's job requires him to complete a series of identical [#permalink] New post 23 Oct 2013, 18:47
Why multiply the following by 72 instead of 144 seeing that Victor worked for 144 days?
Unsupervised rate + Supervised rate = Combined Rate
1/u + 1/(u-3) = 1/c
144*(1/c)=36
c = 4
c = (u^2-3u)/(2u-3) = 4

Isn't this the same logic that was done here: "http://gmatclub.com/forum/running-at-their-respective-constant-rates-machine-x-takes-98599.html"?
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Re: Victor's job requires him to complete a series of identical [#permalink] New post 23 Oct 2013, 23:42
Expert's post
TooLong150 wrote:
Why multiply the following by 72 instead of 144 seeing that Victor worked for 144 days?
Unsupervised rate + Supervised rate = Combined Rate
1/u + 1/(u-3) = 1/c
144*(1/c)=36
c = 4
c = (u^2-3u)/(2u-3) = 4

Isn't this the same logic that was done here: "http://gmatclub.com/forum/running-at-their-respective-constant-rates-machine-x-takes-98599.html"?


Victor's job requires him to complete a 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

Rate when supervised = (job)/(time) = 1/t.
Rate when unsupervised = (job)/(time) = 1/(t+3).

For 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs:
72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days.

Victor to complete 10 jobs without any supervision will need 10(t + 3) = 60 days.

Answer: C.

Hope it's clear.
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Re: Victor's job requires him to complete a series of identical [#permalink] New post 24 Oct 2013, 05:33
i tried to do with 72/x + 72/x+3=36 but it requires huge amount of time with use quadratic equation. Better to backsolve the answers with start from 60 (choice C). 60/10=6 and x=3, it wins
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Re: Victor's job requires him to complete a series of identical [#permalink] New post 13 Jan 2014, 08:16
Temurkhon wrote:
i tried to do with 72/x + 72/x+3=36 but it requires huge amount of time with use quadratic equation. Better to backsolve the answers with start from 60 (choice C). 60/10=6 and x=3, it wins


Simplifying \frac{72}{{x}} + \frac{72}{{x+3}}=36 to \frac{2}{{x}}+\frac{2}{{x+3}}=1 may make it easier to solve the resultant quadratic equation.

We then have
x^2+3x=4x+6
x^2-x-6=0
(x-3)(x+2)=0 => x=3 (Supervised time). so 6 is unsupervised time per job. Therefore 6*10 = 60 hrs
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Re: Victor's job requires him to complete a series of identical   [#permalink] 13 Jan 2014, 08:16
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