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A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

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

Given: 10-man crew needs 110 days to complete the construction.

"On the 61-st day, after 5 days of rain ...": as it was raining for 5 days then they must have been working for 55 days thus completed 1/2 of the job, 1/2 is left (55 days of work for 10 men).

Then contractor "hired 6 more people": speed of construction increased 1.6 times, so the new 16-men crew needed \(\frac{55}{1.6} \approx 34.4\) days to complete the construction, but after they were hired job was done in \(100-60=40\) days. Therefore it rained for 5 days. (They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100 (40) days.)

A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

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

Given: 10-man crew needs 110 days to complete the construction.

"On the 61-st day, after 5 days of rain ...": as it was raining for 5 days then they must have been working for 55 days thus completed 1/2 of the job, 1/2 is left (55 days of work for 10 men).

Then contractor "hired 6 more people": speed of construction increased 1.6 times, so the new 16-men crew needed \(\frac{55}{1.6} \approx 34.4\) days to complete the construction, but after they were hired job was done in \(100-60=40\) days. Therefore it rained for 5 days. (They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100 (40) days.)

Answer: B

I was just curious, going by the complexity of the question as well as the explanation, is it really GMAT level? I mean i think it is way beyond it but i guess i might be missing something here.

so 16x(40-k) = 10x*55 which gives us 640x- 16Kx = 550x==> 16kx= 90x ==> K= 90/16 ==> 5.6 days.

Now I was confused whether to choose 5 or 6 since 5.6 is closer to 6.

But is my logic correct?

Regards, Arun

earnit wrote:

Bunuel wrote:

Official Solution:

A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

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

Given: 10-man crew needs 110 days to complete the construction.

"On the 61-st day, after 5 days of rain ...": as it was raining for 5 days then they must have been working for 55 days thus completed 1/2 of the job, 1/2 is left (55 days of work for 10 men).

Then contractor "hired 6 more people": speed of construction increased 1.6 times, so the new 16-men crew needed \(\frac{55}{1.6} \approx 34.4\) days to complete the construction, but after they were hired job was done in \(100-60=40\) days. Therefore it rained for 5 days. (They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100 (40) days.)

Answer: B

I was just curious, going by the complexity of the question as well as the explanation, is it really GMAT level? I mean i think it is way beyond it but i guess i might be missing something here.

so 16x(40-k) = 10x*55 which gives us 640x- 16Kx = 550x==> 16kx= 90x ==> K= 90/16 ==> 5.6 days.

Now I was confused whether to choose 5 or 6 since 5.6 is closer to 6.

But is my logic correct?

Regards, Arun

earnit wrote:

Bunuel wrote:

Official Solution:

A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

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

Given: 10-man crew needs 110 days to complete the construction.

"On the 61-st day, after 5 days of rain ...": as it was raining for 5 days then they must have been working for 55 days thus completed 1/2 of the job, 1/2 is left (55 days of work for 10 men).

Then contractor "hired 6 more people": speed of construction increased 1.6 times, so the new 16-men crew needed \(\frac{55}{1.6} \approx 34.4\) days to complete the construction, but after they were hired job was done in \(100-60=40\) days. Therefore it rained for 5 days. (They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100 (40) days.)

Answer: B

I was just curious, going by the complexity of the question as well as the explanation, is it really GMAT level? I mean i think it is way beyond it but i guess i might be missing something here.

Rain = 5.6 and Work = 34.4.

They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100 (40) days, which means that it rained for 5 days.
_________________

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
_________________

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

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

A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

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

Given: 10-man crew needs 110 days to complete the construction.

"On the 61-st day, after 5 days of rain ...": as it was raining for 5 days then they must have been working for 55 days thus completed \(\frac{1}{2}\) of the job, \(\frac{1}{2}\) is left (55 days of work for 10 men).

Then contractor "hired 6 more people": speed of construction increased 1.6 times, so the new 16-men crew needed \(\frac{55}{1.6} \approx 34.4\) days to complete the construction, but after they were hired job was done in \(100-60=40\) days. Therefore it rained for 5 days. (They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100 (40) days.)

Answer: B

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

\(Rate = \frac{1}{Time}\)
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?

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

Given: 10-man crew needs 110 days to complete the construction.

"On the 61-st day, after 5 days of rain ...": as it was raining for 5 days then they must have been working for 55 days thus completed \(\frac{1}{2}\) of the job, \(\frac{1}{2}\) is left (55 days of work for 10 men).

Then contractor "hired 6 more people": speed of construction increased 1.6 times, so the new 16-men crew needed \(\frac{55}{1.6} \approx 34.4\) days to complete the construction, but after they were hired job was done in \(100-60=40\) days. Therefore it rained for 5 days. (They needed MORE than 34 days to finish the job, so if it rained for 6 days they wouldn't be able to finish the job in 100 (40) days.)

Answer: B

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

\(Rate = \frac{1}{Time}\)

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.
_________________

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.

I think this is a good question, but one thing needs to be clarified. Semantically, it is unclear from the question stem whether the job was completed 100 days from when it was started (regardless of how many days the workers did or did not work), or it was completed in 100 working days (instead of 110).

Personally, that confused me for long enough to make me guess and move on.