Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part of the

BTGmoderatorLU wrote: ↑

Mon Jan 18, 2021 3:04 am

Source: Official Guide

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

The OA is B

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

BTGmoderatorLU wrote: ↑

Mon Jan 18, 2021 3:04 am

Source: Official Guide

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

The OA is B

Solution:

We see that the rates of the three machines are 1/4, 1/5, and 1/6, respectively. Thus, if the two machines with the greatest rates work together, then the greatest part of the job that can be done in one hour is 1/4 + 1/5 = 5/20 + 4/20 = 9/20.

Answer: B