BTGmoderatorDC wrote:Working alone, three persons P, Q, and R can do a certain job in 10, 12, and 15 hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least 1 person must work?
A. 1:3
B. 1:2
C. 1:1
D. 3:1
E. 15:4
Let the job = the LCM of the 3 times = 60 widgets.
Maximum time:
The maximum time is yielded when the slowest person -- R -- works alone.
Since R takes 15 hours to complete the 60-widget job, the maximum time = 15 hours.
Minimum time:
The minimum time is yielded when all 3 people work together.
Since P takes 10 hours to complete the 60-widget job, P's rate = 60/10 = 6 widgets per hour.
since Q takes 12 hours to complete the 60-widget job, Q's rate = 60/12 = 5 widgets per hour.
Since R takes 15 hours to complete the 60-widget job, R's rate = 60/15 = 4 widgets per hour.
Since the combined rate for P+Q+R = 6+5+4 = 15 widgets per hour, the time for P+Q+R to complete the 60-widget job = 60/15 = 4 hours.
Resulting ratio:
(max time) : (min time) = 15:4.
The correct answer is
E.
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
