M07-06

Question

A contractor estimated that his 10-person crew could complete a construction project in 110 days if there were no rain delays. (Assume the crew does not work on rainy days and that rain is the only factor preventing the crew from working). However, on day 61, after having experienced a total of 5 days of rain in the previous days, the contractor hired 6 additional workers and managed to finish the project early. If the project was completed in 100 days, how many rainy days occurred after day 60?

A. 4
B. 5
C. 6
D. 7
E. 8

Show Answer

Official Answer

B

A. 4
B. 5
C. 6
D. 7
E. 8

Bunuel · Accepted Answer

Official Solution:

A contractor estimated that his 10-person crew could complete a construction project in 110 days if there were no rain delays. (Assume the crew does not work on rainy days and that rain is the only factor preventing the crew from working). However, on day 61, after having experienced a total of 5 days of rain in the previous days, the contractor hired 6 additional workers and managed to finish the project early. If the project was completed in 100 days, how many rainy days occurred after day 60?

A. 4
B. 5
C. 6
D. 7
E. 8

Show Answer

Official Answer

B

A. 4
B. 5
C. 6
D. 7
E. 8

Given: A 10-person crew requires 110 days to complete the construction project.
 
"On day 61, after experiencing 5 days of rain...": Since there were 5 days of rain out of the first 60 days, the crew must have been working for 55 days, thus completing half of the job, with the other half remaining (55 days of work for the 10-person crew).
 
Subsequently, the contractor hired "6 additional workers": This increased the construction speed by 1.6 times. Therefore, the new 16-person crew would require  \frac{55}{1.6} \approx 34.4  days to complete the construction. However, after the additional workers were hired, the project was completed in  100-60=40  days. As a result, there must have been 5 rainy days during this period. (The crew needed MORE than 34 days to finish the job, so if there had been 6 rainy days, they wouldn't have been able to complete the project within 100 (40) days.)

Answer: B

aabougabal · Answer

Total Estimate for total Man days = 110 days x 10 Men = 1,100 Man days
Total Actual = 55 days x 10 Men = 550 Man days
Total remaining Man days = Total Est. - Total actual = 1,100 - 550 = 550 remaining Man days

Total days needed to complete the job = Remaining Man days / Total workers = 550/16 = 35 days (However, question stated that they took 40 days instead)
Rain days = 40 (Given)- 35 = 5 days

Hope this helped.

A&N

FightToSurvive · Answer

Hi Bunnuel,

Kindly check my approach to this problem and pls comment on it:

Total Work = 10 persons X 110 days = 1100 person-days
Work completed till it rained for 5 days = 10 person X 55 days = 550 person-days.

Pending Work = 1100 - 550 = 550 person-days.
Ideally, from 61st day to 100th day, the manpower rose to 16, which means they can do a work of = 16 person X 40 days = 640 person-days.

But remaining work is only 550 person-days, so the difference is 640-550 = 90 person-days.
Therefore it rained for = 90/16 = 5.625 person-days.
Hence Work happened = 40-5.6 = 34.4 days

Hence it rained for 5 more days.

If u liked my detailed solution, a kudos will help

gracie · Answer

one man completes 1/1100 of total job in one day
(10)(55)/1100=1/2 of job
d=days to complete remaining 1/2 of job, 
16d/1100=1/2
d=34.4 working days
40 total days taken-34.4 working days=5.6 rain days
can't round rain days up to 6 without exceeding 100 total days for job
answer is 5 days

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation.

nickimonckom · Answer

Hi,

It may sound idiot and I apologies first for it,

How do you quickly calculate that  \frac{550}{16} = 34,4  ?

In GMAT there are lot of intermediate calculus like this one that makes me lose lot of time and I do not know how to go fast on them

Many thanks in advance for your kind help,

Bunuel · Answer

\frac{550}{16}

Reduce by 2:  \frac{275}{8} . Next you should simply divide 275 by 8.

BillyZ · Answer

Dear  Bunuel , How could we relate the people hired to the speed of construction?

Rate = \frac{1}{Time}

Bunuel · Answer

Let me ask you: say 1 man can do a certain job in 10 hours. In how many hours can the job be done by 2 men? In 5 hours, right. So, increasing the number of men twice we reduce the time need by the same rate.

Manoraaju · Answer

I did it this way and i derived at the right answer as well.

Total work done 110x10=1110

55 days work= 55x10=550.

5 days rain=zero work done

61st day 16 works are working. Work is completed in 100 days. So remaining work done in days is 550/16 is approximaterly 34.xx and round off to the next largest integer 35. So 100-55-5-35=5 days.

VAKRATUNDA · Answer

Short and logical Approach:

(10 man-crew X 110 Days) = 1100 Man-days
Less: (10 man-crew X 55 days (On 61st day, 5 rainy days are already passed.)) = 550 Man-days
Balance Work = 550 Mandays

Total man-crew from 61st day=10+6=16
Hence, Balance work after 60 days will be divided by 16 man-crew to arrive at no of days worked after 60th day. 
=550/16 = Appx. 35 days worked appx. (Remember we need to consider part of the day as full day)
Hence, 100 days-60 days = 40 days
40 days-35 days worked=5 rainy days after 60th day.

tirthshah2013 · Answer

The answer for this question will be 5.

We know that 10 man can complete the work in 110 days, so total work done would be 1100. We know that no one works on days in which it rains. After 55 days the work completed would be 550.

So the remaining work = 1100-550= 550.

After 55th day, there was 5 day rain and from 61st day the workers increased from 10 to 16.

New number of workers = 16.

The question says the work was completed in 100 days after the 61st day.

Therefore, total number of days the 16 workers worked for including the rainy days = 40.

We are told work is completed in 100 days, and total work remaining was 550. Therefore they completed the work in 550/16=34.4 days.

Normally in 40 days the 16 workers should have completed 640 work. But only 550 was remaining hence the extra 90 work will be the days when they didn't work.

Therefore total number of days it rained after 61st day = 90/16 = 5.625 but since days cannot be in decimal we select 5 as if we select 6, the work will be completed in 34 days but the work was completed in more than 34 days, so we round down 5.625 to 5

Posted from my mobile device

adewale223 · Answer

From the question 10 men have done work for 55 days.

To calculate how much of work done within that period

55/110 which is 1/2. That means1/2 of work left.

If it took 55 days for 10 men to do half of the work then 16 men will take 10/16 x 55 = 34 days.

Since they started work on day 61, 34 + 61 = 95.

Since work was completed within 100 days that means it rained for 5 days.

Posted from my mobile device

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

ShaunakSawant · Answer

I calculated the number of days when it rained, and thus the answer came down to 5.6, which is approximately 6 days. This is why I chose 6 days/ option C

Can some expert help me why option B is right answer and why we need to round down the count to 5?

Bunuel · Answer

The crew needed MORE than 34 days to finish the job, so if there had been 6 rainy days, they wouldn't have been able to complete the project within 100 (40) days.

A_ · Answer

I like the solution - it’s helpful.

Sushi_545 · Answer

Hi @gracie/@Bunuel

i followed similar approach got 5.6 days as answer so rounded to 6 why we have rounded to 5?

Bunuel · Answer

I addressed this doubt here: https://gmatclub.com/forum/m07-183740.html#p3201553 Hope it helps.

M07-06

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