BTGmoderatorDC wrote:R and S can complete a certain job in 6 and 4 days respectively, while they work individually. What will be the least number of days they will take to complete the same job, if they work on alternate days?
A. 2.2 days
B. 2.67 days
C. 4.4 days
D. 4.67 days
E. 5 days
OA D
Source: e-GMAT
We see that the rate of R is 1/6 and the rate of S is 1/4. Since we want to determine the least number of days, and since the rate of S is greater than that of R, we should begin with S first.
If S works the first day, then 1 - 1/4 = 3/4 of the job is left to be done after the first day.
If R works the second day, then 3/4 - 1/6 = 9/12 - 2/12 = 7/12 of the job is left to be done after the second day.
If S works the third day, then 7/12 - 1/4 = 7/12 - 3/12 = 4/12 = 1/3 of the job is left to be done after the third day.
If R works the fourth day, then 1/3 - 1/6 = 2/6 - 1/6 = 1/6 of the job is left to be done after the fourth day.
Since we have â…™ of the job remaining at the beginning of the fifth day and the rate of S is 1/4, then it only takes (1/6)/(1/4) = 4/6 = 2/3 of a day to finish the job. Therefore, in total, it takes 4 + 2/3 = 4.67 days to complete the job.
Alternate Solution:
Since S does 1/4 of the job in one day and R does 1/6 of the job in one day, when they work on alternate days, 1/4 + 1/6 = 5/12 of the job is done on two days. Thus, in four days, 5/12 + 5/12 = 10/12 = 5/6 of the job is done no matter in what order they work.
If R started the job on the first day, then R will need to complete 1/6 of the job on the fifth day, which will take R exactly one day. In this scenario, it will take 5 days to complete the job.
If, on the other hand, S started the job on the first day, then S will need to complete 1/6 of the job on the fifth day. Since it takes 4 days for S to complete the whole job, it will take only 4 x 1/6 = 2/3 = 0.67 days to complete the job. Thus, the minimum required time to complete the job when R and S alternate is 4 + 0.67 = 4.67 days.
Answer: D
