M02 Q#7

Andy, George and Sally are a team of consultants working on Project Alpha. They have an eight hour deadline to complete the project. The team members work at constant rates throughout the eight hour period. If the team of three has to begin work now and no one else can work on this project, will Project Alpha be completed by the deadline?

1. Sally can finish the project alone in \(4k+7\) hours, where \(k\) is a positive integer with a minimum value of 1 and a maximum value of 5.
2. Working alone, George will take \(2k+1\) hours and Andy will take \(3+2k\) hours, where \(k\) is a positive integer with a minimum value of 1 and a maximum value of 5

a. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
b. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
d. EACH statement ALONE is sufficient
e. Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is not sufficient. From S1, we know Sally can finish the project in \(4k+7\) hours, but we know nothing about George's or Andy's time. Check if Sally can finish the work by herself. If \(k\) is the smallest value (1), Sally will need 11 hours to finish the project. We need to know George's and/or Andy's rate.

Statement (2) by itself is sufficient. From S2, we know that George will take \(2k+1\) hours and Andy will take \(2k+3\) hours.

Check whether George and Andy can finish the project by themselves. Check to see if the maximum value of \(k\) is sufficient for these two together to finish the project. If the maximum value of \(k = 5\) , then George needs 11 hours and Andy needs 13 hours to finish the project alone.

Working together for one hour, George and Andy will finish:
1/11 + 1/13 > 1/8

of the work. Thus, working together, George and Andy finish a greater portion of work per hour than the required . As a result, they will easily finish the project by themselves. It is not necessary to know Sally's time to answer the question.

Hence answer is B.


My question:
How can you assume the maximum value for K when the question clearly specifies a range for K and doesnt talk about any condition to choose the maximum value. The answer would be E, if one were to not assume the max value for K.
Please clarify.