\(M\) and \(N\) working together, can finish a job in 6 days. With the help of \(P,\) they completed the job in 4 days.

[M7MBA]

\(M\) and \(N\) working together, can finish a job in 6 days. With the help of \(P,\) they completed the job in 4 days. If \(Q\) joined them, all 4 together would have completed the job in \(3\frac13\) days. If all work at their respective constant rate, then in how many days \(Q\) alone can complete the work?

A. 10
B. 12
C. 15
D. 18
E. 20

[spoiler]OA=E[/spoiler]

Source: e-GMAT

[Jay@ManhattanReview]

\(M\) and \(N\) working together, can finish a job in 6 days. With the help of \(P,\) they completed the job in 4 days. If \(Q\) joined them, all 4 together would have completed the job in \(3\frac13\) days. If all work at their respective constant rate, then in how many days \(Q\) alone can complete the work?

A. 10
B. 12
C. 15
D. 18
E. 20

[spoiler]OA=E[/spoiler]

Source: e-GMAT

Given that \(M\) and \(N\) working together, can finish a job in 6 days, let's club M and N and rename them R.

So, we have

R can finish a job in 6 days;
R & P working together can finish a job in 4 days;

Let's club R and P and rename them S.

So, we have

=> S can finish a job in 4 days
S & Q working together can finish a job in \(3\frac13\) days

With these data, we deduce

No. of days required for Q to finish the job = Reciprocal of \(\frac1{3\frac13}) – \frac14 = \frac 3{10} - \frac14=\frac{6-5}{20}=\frac1{20}\)

= 20 days

Correct answer: E

Hope this helps!

-Jay
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