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
Let the rate for each worker = 1 widget per day, implying that the rate for 10 workers = 10 widgets per day.
Since the job can be finished in 110 days, the total job = (rate for 10 workers)(total number of days) = 10*110 = 1100 widgets.
Since the first 60 days include 5 days of rain, work is produced on 55 of the first 60 days.
Thus, the number of widgets produced in the first 60 days = (rate for 10 workers)(number of work-days) = 10*55 = 550.
Remaining number of widgets = (total job) - (work produced in the first 60 days) = 1110-550 = 550 widgets.
Since the job is completed in 100 days, the remaining number of days = (total number of days) - (first 60 days) = 100-60 = 40 days.
After 6 workers are hired, the rate increases to 16 widgets per day.
Time for 16 workers to produce the remaining 550 widgets = w/r = 550/16 =
34 3/8 days.
The value in blue indicates that -- for the job to be completed -- widgets must be produced on 35 of the remaining 40 days.
Thus, the number of rainy days after the first 60 days = (total number of remaining days) - (total number of remaining work-days) = 40-35 = 5.
The correct answer is
B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
