150 workers were engaged to finish a piece of work in a certain number

Question

150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped the second day, 4 more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is:

A. 10
B. 17
C. 20
D. 25
E. 30

A. 10
B. 17
C. 20
D. 25
E. 30

gmatophobia · Answer

I think there could be a better way of solving this. I could think of this. We have to equate work lost = work gained Option D https://gmatclub.com/forum/download/file.php?id=81758 GMAT-Club-Forum-cchtz1wh.png

playthegame · Answer

Yes right the answer is 25 days. The other way of doing this is to equate the man-days needed to do the work as the effort does not change to do the same work. So then if 150 people work for x days man days is 150 x. And then if we lose 4 people every day work gets dones in x+8 days. Now day 1 150 people work, day 2 146 people work, day 3 142 people work this goes on for x+8 days. This is an AP so we can use the to n terms AP formula with x+8 terms to get an expression. Then you equate 150 x with this expression and it give you a quadratic to solve. Not an easy question at all. GMAT-Club-Forum-7ojrd3oq.png

shoshonte · Answer

Can we get a source for this question? Took me around 36 minutes to solve, I think it would take an actual genius to solve this in the provided 2min 13 seconds that we have to pace on average to finish the exam.

playthegame · Answer

Hi this is a very hard problem for the GMAT, I think the source for this is the CAT exam in India. The additional complexity comes from the fact that you have to solve a qudratic. Some of the higher difficulty problems on the GMAT could come close to this but no where near.

On the GMAT bail when you see a problem like this and you cannot solve within 3 mins.

Thanks and good luck.

DannyR24 · Answer

This can be solved quicker by thinking about it as a work/rate problem, and the decreasing amount of workers as an average instead of a series. Set "D" as the desired solution (# of days to finish work) and set "W" as amount of work done: Equation #1: 150 * (D-8) = W 150D - 1200 = W Equation #2: (Average Amount of Workers during Days) * (D) = W ((150 + 150 - 4 * (D-1)) /2) * (D) = W (152 - 2D) * (D) = W 152D - 2D^2 = W Substitute 150D - 1200 = 152D - 2D^2 0 = D^2 - D - 600 0 = (D - 25) * (D + 24) D=25 GMAT-Club-Forum-800yk6s2.png

AD21 · Answer

I used the proportion method to solve it and it was short.

150 workers/1/x = n workers/1/x+8

x= no. of days to complete the job and (x+8) is the no.of days to complete the job with every 4 workers leaving.

hence n= 150x/(x+8)

for n to be an integer, (x+8) has to be a factor of 150.
out of all the answer choices only if x=17, we will get (x+8) divide 150 evenly. 
Hence the no of days to finish the job will be 25. Answer choice:D

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=84367 I have used the fact that -> Total Work = 150 x (work done per worker per day) x (number of days) Total Work is also = Sum of work done on each day --- Harsha GMAT-Club-Forum-940at7pg.png

150 workers were engaged to finish a piece of work in a certain number

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

150 workers were engaged to finish a piece of work in a certain number

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards