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Intern  Status: Learning
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Five men started working on a job that was to be finished in hundred d  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 53% (03:02) correct 47% (03:31) wrong based on 144 sessions

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Five men started working on a job that was to be finished in hundred days. After ten percent of the work was completed, “x” number of men were added to the taskforce and it was found that the whole work was completed in a total of “y” days. Select the values of x and y that are consistent with the given data.

A) X= 16 Y= 20

B) X= 20 Y= 24

C) X= 24 Y= 28

D) X= 28 Y= 32

E) X= 20 Y= 28

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Re: Five men started working on a job that was to be finished in hundred d  [#permalink]

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arindamsur wrote:
Five men started working on a job that was to be finished in hundred days. After ten percent of the work was completed, “x” number of men were added to the taskforce and it was found that the whole work was completed in a total of “y” days. Select the values of x and y that are consistent with the given data.

A) X= 16 Y= 20

B) X= 20 Y= 24

C) X= 24 Y= 28

D) X= 28 Y= 32

E) X= 20 Y= 28

10% of the work = 10 days of work for the 5 men

(5+x) men work for (y-10) days to complete 90% of work.

5 men do 1/100th of the work in one day
1 man does 1/500th of the work in one day

Therefore (5+X) (Y-10)/500 = 9/10

X = 20 & Y = 28 satisfies this equation.

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Posts: 73
Re: Five men started working on a job that was to be finished in hundred d  [#permalink]

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arindamsur wrote:
Five men started working on a job that was to be finished in hundred days. After ten percent of the work was completed, “x” number of men were added to the taskforce and it was found that the whole work was completed in a total of “y” days. Select the values of x and y that are consistent with the given data.

A) X= 16 Y= 20

B) X= 20 Y= 24

C) X= 24 Y= 28

D) X= 28 Y= 32

E) X= 20 Y= 28

IMO -
None of these.

My equation -> (5+x)(y-10)= (500)*9/10 ->
one possible solution is - x=10, y=13.
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Re: Five men started working on a job that was to be finished in hundred d  [#permalink]

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I saw the solution (5 + x) × (y – 10) = 450 Its is not clear to me (y - 10)

From there they jump to solution x = 20 and y = 28

MKS wrote:
arindamsur wrote:
Five men started working on a job that was to be finished in hundred days. After ten percent of the work was completed, “x” number of men were added to the taskforce and it was found that the whole work was completed in a total of “y” days. Select the values of x and y that are consistent with the given data.

A) X= 16 Y= 20

B) X= 20 Y= 24

C) X= 24 Y= 28

D) X= 28 Y= 32

E) X= 20 Y= 28

IMO -
None of these.

My equation -> (5+x)(y-10)= (500)*9/10 ->
one possible solution is - x=10, y=13.

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Arindam Sur
Manager  Joined: 12 Sep 2014
Posts: 142
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Re: Five men started working on a job that was to be finished in hundred d  [#permalink]

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I got E and here's how I got there.

At the beginning, we know it takes 100 days for 5 people working together to complete. This means each will take 500 days to complete working solo. But, 10% of the work is already done, so it will take another 90 days for the 5 people to complete. This means, the remaining work takes 450 days to complete solo.

To get this, I just did 5*(1/person) = 1/100 and 1/90, respectively to get 500 and 450 days, respectively, when solving for "person."

Next, you need to calculate (5+x)/450 = 1/(y-10) to form an analogy with the work/rate problem. This is only possible when x=20 and y=28, which means an additional 18 days is needed after 10% work is done. Hope that makes sense.
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Re: Five men started working on a job that was to be finished in hundred d  [#permalink]

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five men started working on a job that was to be finished in hundred days. After ten percent of the work was completed, “x” number of men were added to the taskforce and it was found that the whole work was completed in a total of “y” days. Select the values of x and y that are consistent with the given data.

From question i understand that if 5 men worked together they would have completed 1 task n 100 day mean seach person will take 20 days to complete a task.

Than how come below mention predication(500 )days are possible ???????????????????????????????????????

At the beginning, we know it takes 100 days for 5 people working together to complete. This means each will take 500 days to complete working solo. But, 10% of the work is already done, so it will take another 90 days for the 5 people to complete. This means, the remaining work takes 450 days to complete solo.

To get this, I just did 5*(1/person) = 1/100 and 1/90, respectively to get 500 and 450 days, respectively, when solving for "person."

Next, you need to calculate (5+x)/450 = 1/(y-10) to form an analogy with the work/rate problem. This is only possible when x=20 and y=28, which means an additional 18 days is needed after 10% work is done. Hope that makes.

Intern  Joined: 18 Jul 2013
Posts: 31
Re: Five men started working on a job that was to be finished in hundred d  [#permalink]

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five men started working on a job that was to be finished in hundred days. After ten percent of the work was completed, “x” number of men were added to the taskforce and it was found that the whole work was completed in a total of “y” days. Select the values of x and y that are consistent with the given data.

From question i understand that if 5 men worked together they would have completed 1 task n 100 day mean seach person will take 20 days to complete a task.

Than how come below mention predication(500 )days are possible ???????????????????????????????????????

At the beginning, we know it takes 100 days for 5 people working together to complete. This means each will take 500 days to complete working solo. But, 10% of the work is already done, so it will take another 90 days for the 5 people to complete. This means, the remaining work takes 450 days to complete solo.

To get this, I just did 5*(1/person) = 1/100 and 1/90, respectively to get 500 and 450 days, respectively, when solving for "person."

Next, you need to calculate (5+x)/450 = 1/(y-10) to form an analogy with the work/rate problem. This is only possible when x=20 and y=28, which means an additional 18 days is needed after 10% work is done. Hope that makes.

Manager  Joined: 22 Aug 2014
Posts: 136
Re: Five men started working on a job that was to be finished in hundred d  [#permalink]

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arindamsur wrote:
I saw the solution (5 + x) × (y – 10) = 450 Its is not clear to me (y - 10)

From there they jump to solution x = 20 and y = 28

MKS wrote:
arindamsur wrote:
Five men started working on a job that was to be finished in hundred days. After ten percent of the work was completed, “x” number of men were added to the taskforce and it was found that the whole work was completed in a total of “y” days. Select the values of x and y that are consistent with the given data.

A) X= 16 Y= 20

B) X= 20 Y= 24

C) X= 24 Y= 28

D) X= 28 Y= 32

E) X= 20 Y= 28

IMO -
None of these.

My equation -> (5+x)(y-10)= (500)*9/10 ->
one possible solution is - x=10, y=13.

Still not clear to me why y-10 is taken instead of y?
(5+x)(y-10)= (500)*9/10
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Five men started working on a job that was to be finished in hundred d  [#permalink]

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HI ssriva2,

This question can be solved in a couple of different ways. Beyond the Algebra that you might do, you can also TEST THE ANSWERS. Depending on the approach that you choose to take, the math involved will vary in difficulty. Staying organized is KEY though, since this prompt includes a LOT of details....

We're told that 5 men start a job that will take 100 days to finish. This means that 5(100) = 500 man-days of work are required to finish the job.

After 10% of the work was done, "X" ADDITIONAL men were added.

10% of 100 days = 10 days
10% of 500 man-days = 50 man-days

So, 10 days have gone by and 450 man-days of work remain.

We're told that AFTER adding those "X" men, the TOTAL number of days required to finish the job became "Y." We're asked to find the answer that gives us an X and Y that "fit" this situation.

Remember those initial 5 workers in the question....they still impact the calculation. Since all of the answer choices include INTEGERS, we'll need a value for X so that (X+5) divides evenly into 450. Considering the values of X that appear in the answers, you'll find that (20+5) divides into 450:

450/25 = 18

So with 25 workers, it would take 18 MORE days to finish the job (after the initial 10 days of work already occurred).

X = 20 and Y = 28

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Re: Five men started working on a job that was to be finished in hundred d  [#permalink]

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Not sure to find the right answer in less than 2 min.
if this is a real Gmat question then it must be of 700+ level
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Re: Five men started working on a job that was to be finished in hundred d  [#permalink]

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I got it wrong took total no of days as 100
But now seeing it gain I got the concept of Man days

Sent from my ONE E1003 using GMAT Club Forum mobile app
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Five men started working on a job that was to be finished in hundred d  [#permalink]

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arindamsur wrote:
Five men started working on a job that was to be finished in hundred days. After ten percent of the work was completed, “x” number of men were added to the taskforce and it was found that the whole work was completed in a total of “y” days. Select the values of x and y that are consistent with the given data.

A) X= 16 Y= 20

B) X= 20 Y= 24

C) X= 24 Y= 28

D) X= 28 Y= 32

E) X= 20 Y= 28

number of men=5+x
rate of 1 man per 1 day=1/500
time to complete work=y-10 days
portion of work to be completed=9/10
hence, (5+x)/500*(y-10)=9/10➡(x+5)(y-10)=450
plugging in choices, only E works:
x=20; y=28
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Five men started working on a job that was to be finished in hundred d  [#permalink]

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arindamsur wrote:
Five men started working on a job that was to be finished in hundred days. After ten percent of the work was completed, “x” number of men were added to the taskforce and it was found that the whole work was completed in a total of “y” days. Select the values of x and y that are consistent with the given data.

A) X= 16 Y= 20
B) X= 20 Y= 24
C) X= 24 Y= 28
D) X= 28 Y= 32
E) X= 20 Y= 28

Consider the total work to be 1000 units. Since 10%(100 units) of the work was completed by 5 men,
each man did about 2 units/day as the work went on for 10 days.

Now that x men join the work force, the work done in a day will be 2(5+x). They will have y-10 days
to complete the work. For the correct combination of x and y, the men must complete 900 units(exactly)

A) X= 16 Y= 20 | Work done = 2(5+16)*(20-10) = 42*10 = 420 units
B) X= 20 Y= 24 | Work done = 2(5+20)*(24-10) = 50*14 = 700 units
C) X= 24 Y= 28 | Work done = 2(5+24)*(28-10) = 58*18 = 1044 units
D) X= 28 Y= 32 | Work done = 2(5+28)*(32-10) = 33*22 = 726 units

E) X= 20 Y= 28 | Work done = 2(5+20)*(28-10) = 50*18 = 900 units

Therefore, Option E(X= 20 Y= 28) has the values that are consistent and is our answer!
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_________________ Re: Five men started working on a job that was to be finished in hundred d   [#permalink] 31 Mar 2019, 04:52
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