Five men started working on a job that was to be finished in hundred d

Question

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

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

Vetrik · Accepted Answer

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.

Hence Answer E.

EMPOWERgmatRichC · Answer

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

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

MKS · Answer

IMO -
None of these.

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

arindamsur · Answer

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

intheend14 · Answer

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.

ssriva2 · Answer

please help
Still not clear to me why y-10 is taken instead of y?
 (5+x) (y-10) = (500)*9/10

gracie · Answer

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

pushpitkc · Answer

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!

Kinshook · Answer

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.

Man-days required to complete the job = 5*100 = 500 man-days

Remaining work after completion of 10% work = 90%*500 = 450 man-days
Time required for completion of 10% work with 5 men = 10 days

Men available = x + 5 men
Time for completion = y - 10

5*10 + (x+5)*(y-10) = 500
(X+5)(Y-10) = 450

A) X= 16 Y= 20; (X+5)(Y-10) = 21*10 = 210; Incorrect

B) X= 20 Y= 24 ; (X+5)(Y-10) = 25*14 = 350; Incorrect

C) X= 24 Y= 28 ; (X+5)(Y-10) = 29*18 = 522; Incorrect

D) X= 28 Y= 32 ; (X+5)(Y-10) = 33*22 = 726; Incorrect

E) X= 20 Y= 28 ; (X+5)(Y-10) = 25*18 = 450; Correct

IMO E

Five men started working on a job that was to be finished in hundred d

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