Data Sufficiency

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

[email protected] wrote: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 and Jack complete an equal amount of work.
In other words, each produces 1/2 the job.
Since Mac works for a total of T days with Jack, Mac's time to produce 1/2 the job = T.
Since Jack works for T days with Mac and for R days alone, Jack's time to produce 1/2 the job = T + R.
Thus, Jack's time to produce the whole job = 2(T+R).

Question stem rephrased: What is the value of 2(T+R)?

Statement 1: M=20
Since Mac takes 20 days to produce the whole job, he takes 10 days to produce 1/2 the job.
Since he produces 1/2 the job in the T days that he works with Jack, T = 10 days.
No way to determine the value of R.
INSUFFICIENT.

Statement 2: R=10
No way to determine the value of T.
INSUFFICIENT.

Statements combined:
Jack's time to produce the whole job = 2(T+R) = 2(10+10) = 40 days.
SUFFICIENT.

The correct answer is C.

[email protected] wrote: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's 1 day Work = 1/M
Jack's 1 day Work = 1/J
1 day's work of both Mac and Jack = 1/M + 1/J

Mac's T Day's work = T/M
Jack's T Day's work = T/J
Jack's R Day's work = R/J

Mac's work = Jack's work

T/M = (T/J)+(R/J)
T/M = (T+R)/J
TJ = M(T+R)

Question: How many days would have it taken Jack to complete the entire job working alone?

i.e. J = ?

Since TJ = M(T+R) therefore, To answer the question, we need the values of R,T and M

But...
Statement(1) M=20 days
i.e. Mac takes 20 days to finish the entire job
therefore, he takes 10 days to produce 1/2 the job.
Since he produces 1/2 the job in the T days therefore T = 10 days.
R is still unknown therefore NOT Sufficient

Statement(2) R=10 days
M and T are Unknown therefore NOT Sufficient

Combining the two statement only will be sufficient as we get all M, T and R.

Answer Option C

GMATGuruNY wrote:

[email protected] wrote: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 and Jack complete an equal amount of work.
In other words, each produces 1/2 the job.
Since Mac works for a total of T days with Jack, Mac's time to produce 1/2 the job = T.
Since Jack works for T days with Mac and for R days alone, Jack's time to produce 1/2 the job = T + R.
Thus, Jack's time to produce the whole job = 2(T+R).

Question stem rephrased: What is the value of 2(T+R)?

Statement 1: M=20
Since Mac takes 20 days to produce the whole job, he takes 10 days to produce 1/2 the job.
Since he produces 1/2 the job in the T days that he works with Jack, T = 10 days.
No way to determine the value of R.
INSUFFICIENT.

Statement 2: R=10
No way to determine the value of T.
INSUFFICIENT.

Statements combined:
Jack's time to produce the whole job = 2(T+R) = 2(10+10) = 40 days.
SUFFICIENT.

The correct answer is 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