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## If x persons take y days to complete z similar jobs,

This topic has 4 expert replies and 0 member replies

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NandishSS Master | Next Rank: 500 Posts
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#### If x persons take y days to complete z similar jobs,

Thu Nov 10, 2016 6:54 am
If x persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?

A. z
B. x
C. x/y
D. z/x
E. x/z

OA:E

How to use number plugging?

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DavidG@VeritasPrep Legendary Member
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Thu Nov 10, 2016 7:17 am
NandishSS wrote:
If x persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?

A. z
B. x
C. x/y
D. z/x
E. x/z

OA:E

How to use number plugging?
Let's say it takes 1 person 2 days to complete 4 jobs.
(so x = 1, y =2, and z = 4.)

If this person takes 2 days to do 4 jobs, it would take 2/4 or 1/2 a day to complete a single job.

If one person can do a job in 1/2 a day, 2 people (we said y = 2) would do the job twice as fast, so they'd only need 1/4 of a day.

So 1/4 is our target. Plugging in 1 for x and 4 for z, only E works.

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GMATGuruNY GMAT Instructor
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Thu Nov 10, 2016 8:19 am
NandishSS wrote:
If x persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?

A. z
B. x
C. x/y
D. z/x
E. x/z
An alternate approach is to use the following equation:
(workers)(time)/(output) = (workers)(time)/(output)

Since x people take y days to produce z jobs, and we want to determine the number of days for y people to produce 1 job, we get:
(x people)(y days)/(z jobs) = (y people)(t days)/(1 job)
xy/z = yt/1
x/z = t.

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Matt@VeritasPrep GMAT Instructor
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Fri Nov 11, 2016 2:59 pm
I think it's easiest to put it in words first.

Work = Rate * Time

z jobs = x people * (each person's rate) * y days

z/xy = each person's rate

From there, go to the equation we want:

1 job = y people * (each person's rate) * time

1 = y * z/xy * time

x/z = time

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Jeff@TargetTestPrep GMAT Instructor
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Thu Dec 07, 2017 7:54 am
NandishSS wrote:
If x persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?

A. z
B. x
C. x/y
D. z/x
E. x/z
We are given that x people take y days to complete z similar jobs. Since rate = work/time, we can determine the rate of x people:

rate of x people = z/y

To determine the rate for y people to complete 1 job, we can use a proportion to determine the rate of y people, in which n = the rate of y people. Our proportion read as:

“x people is to a rate of z/y as y people is to a rate of n”

x/(z/y) =y/n

xn = y(z/y)

xn = z

n = z/x

Since we have the rate of y people, we now can determine the time it takes for y people to complete 1 job.

time = work/rate

time = 1/(z/x) = x/z

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