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

Question

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

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

Bunuel · Accepted Answer

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.

raghavakumar85 · Answer

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

TGC · Answer

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) +   = 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

Bunuel · Answer

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.

TGC · Answer

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

Bunuel · Answer

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.

TGC · Answer

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

TooLong150 · Answer

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: "https://gmatclub.com/forum/running-at-their-respective-constant-rates-machine-x-takes-98599.html"?

himgkp1989 · Answer

KarishmaB  Hi Karishma, Is it possible to calculate the days without the quadratic equation

ThatDudeKnows · Answer

himgkp1989

Before we get all bogged down in algebra, let's just take a second to see if we can plug in and get to the finish line. My full scratch paper for this question is attached...sure looks easier than the algebra!

We are told that he works for 144 days and is supervised for half the time, so supervised for 72 days and unsupervised for 72 days. And in that time, he completes 36 jobs.
Unsupervised takes three days longer.

Let's try supervised takes 1 day and unsupervised takes 4 days. He would finish 72 jobs supervised and 72/4=18 jobs unsupervised. That's 90 jobs. Too many.
Let's try supervised takes 2 days and unsupervised takes 5 days. Oh, wait, 72 isn't divisible by 5. Let's move on.
Let's try supervised takes 3 days and unsupervised takes 6 days. He would finish 72/3=24 supervised and 72/6=12 unsupervised. That's 36. Yay!
It takes 6 days to finish a job unsupervised. So how long does it take to finish 10 jobs unsupervised? 60 days.

Answer choice C.

ThatDudeKnowsPluggingIn

KarishmaB · Answer

himgkp1989 We need to take a variable (we cannot use ratios here because there is a subtraction given, not multiplication or division) but we can avoid actually solving the quadratic. Say he completes one job unsupervised in d days. Then supervised, he takes d - 3 days. Since he was supervised for 72 days and unsupervised for d days, total number of jobs he completed is given by \frac{72}{d} + \frac{72}{(d - 3)} = 36 All numbers are multiples of 12 and 3.. 36 could be 12 + 24 so try d = 6 (so that d - 3 is also 3 which will divide 72 evenly) It works. So d = 6. To complete 10 jobs unsupervised, he needs 6*10 = 60 days Also, check this blog post: https://anaprep.com/data-sufficiency-ca ... culations/

finisher009 · Answer

Solution
 1. Best to go for answer choice testing.
 2. Pick the middle & clean answer: 60 days for 10 unsupervised jobs, so 1 job unsupervised takes 6 days, supervised takes 3 days (since each job is 3 days faster supervised).
 3. In 72 unsupervised days: 72/6 = 12 jobs. In 72 supervised days: 72/3 = 24 jobs. Total = 12 + 24 = 36 jobs.
 4. This fits the information perfectly. No need for algebra or equations, so 60 is the answer.

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

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