Data Sufficiency

BTGmoderatorLU wrote:If a group of 5 craftsmen takes 3 hours to finish a job, how long will it take a group of 4 apprentices to do the same job?

1) An apprentice works at 2/3 the rate of a craftsman.
2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job.

The OA is D.

Please, can anyone assist me with this DS question? I need help to solve it. Thanks in advance!

We do not know the rate of the apprentices; if we get this, we can get the answer.

1) An apprentice works at 2/3 the rate of a craftsman.

It means that the job that the 5 craftsmen take to finish in 3 hours will be completed by 5*(3/2) = 15/2 apprentices in the same time (3 hours).

Thus, the time taken by the 4 apprentices = 3*[(15/2)/4] = 45/8 hours. Sufficient.

2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job.

We know the 'rate of 5 craftsmen' and the 'rate of 5 craftsmen and the 4 apprentices working together,' thus, we can get the rate of 4 apprentices. There is no need to calculate. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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