Problem Solving

grandh01 wrote: ↑

Mon Aug 13, 2012 7:31 pm

Three machines, individually, can do a
certain job in 4, 5, and 6 hours,
respectively. What is the greatest part
of the job that can be done in one hour
by two of the machines working
together at their respective rates?

(A)11/30
(B)9/20
(C)3/5
(D)11/15
(E)5/6

Assign a "nice" value to the job (i.e., a value that works well with the given numbers, 4, 5 and 6)
Since 4, 5 and 6 all divide into 60, let's say that completing the job means making 60 widgets

So, the first machine can make 60 in 4 hours, which means its rate is 15 widgets per hour.
The second machine can make 60 in 5 hours, which means its rate is 12 widgets per hour.
The 3rd machine can make 60 in 6 hours, which means its rate is 10 widgets per hour.

So, the first machine and second machine are the two fastest.
Their combined rate = 15 + 12 = 27 widgets per hour
So, in one hour, those two machines can make 27 widgets, which means they can complete 27/60 of the job.

27/60 simplifies to be 9/20
Answer: B