Official Solution:


Mac can finish the job in \(M\) days: the rate of Mac is \(\frac{1}{M}\) job/day;

Jack can finish the job in \(J\) days: the rate of Jack is \(\frac{1}{J}\) job/day;

After working together for \(T\) days, Mac left and Jack alone worked to complete the remaining work in \(R\) days, hence Mac worked for \(T\) days only and did \(\frac{T}{M}\) part of the job while Jack worked for \(T+R\) days and did \(\frac{T+R}{J}\) part of the job;

Since Mac and Jack completed an equal amount of work (so half of the job each) then \(\frac{T}{M}=\frac{1}{2}\) and \(\frac{T+R}{J}=\frac{1}{2}\). So, \(T=\frac{M}{2}\) and \(T=\frac{J}{2}-R\), therefore \(\frac{M}{2}=\frac{J}{2}-R\), which gives \(J=M+2R\).

(1) \(M = 20\) days. Not sufficient, we still need the value of \(R\).

(2) \(R = 10\) days. Not sufficient, we still need the value of \(M\).

(1)+(2) \(J=M+2R=20+2*10=40\). Sufficient.


Answer: C

You made this so easy.

Can you please suggest,what was your line of thinking ..I took a longer approach and got confused at the end...

Here is my approach,

Mac's Work =1/M
Jacks' = 1/J

When both work for T days work done = ((1/M) + (1/J))*T
Remaining work = 1 - {(M+J)/MJ}*T

Now work done by jack= T+R days..
So I would make acomplex equution equation work done by Jack and Mac and this would really confuse me spotting R and T

Mac can finish a job in \(M\) days and Jack can finish the same job in \(J\) days. After working together for \(T\) days, Mac left and Jack alone worked to complete the remaining work in \(R\) days. If Mac and Jack completed an equal amount of work, how many days would have it taken Jack to complete the entire job working alone?


(1) \(M = 20\) days

(2) \(R = 10\) days

Mac can finish a job in \(M\) days and Jack can finish the same job in \(J\) days. After working together for \(T\) days, Mac left and Jack alone worked to complete the remaining work in \(R\) days. If Mac and Jack completed an equal amount of work, how many days would have it taken Jack to complete the entire job working alone?


(1) \(M = 20\) days

(2) \(R = 10\) days

I initially interpreted that since Jack and Mac completed the same amount of work T/M = (T+R)/J

However this yields inconclusive info for Jack. Why is this incorrect Bunuel ?