Carcass wrote:
Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?
(A) 1/4
(B) 12/47
(C) 1/3
(D) 5/12
(E) 20/47
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math BookOne approach is to assign a "nice" value to the entire job. That is, a value that works well with the given information (3, 4, and 5 hours).
The least common multiple of 3, 4 and 5 is
60.
So, let's say the ENTIRE job consists of making
60 widgets.
If Paul can complete the job (make
60 widgets) in 3 hours, then his RATE of work =
20 widgets PER HOUR
If Abdul can make
60 widgets in 4 hours, then his RATE of work =
15 widgets PER HOUR
If Adam can make
60 widgets in 5 hours, then his RATE of work =
12 widgets PER HOUR
So, if they work TOGETHER, their combined RATE =
20 +
15 +
12 =
47 widgets PER HOUR
So, for every HOUR that passes, the GROUP can make
47 widgets
We also know that, for every HOUR that passes, the Adam can made
12 widgets (since his RATE of work =
12 widgets PER HOUR)
This means that, when the 3 people work together, Adam makes
12/
47 of the widgets
Answer: B
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep