R2I4D
Andy, George, and Sally are a team of consultants working on Project Alpha. They have an 8 hour deadline to complete the project. The team members work at constant rates throughout the 8 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, Georgia 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.
The wording in this question is really bad, and not at all GMAT-like. For one thing, there is no need to make k a variable in each statement (a real GMAT question would never do that; instead k would have a single fixed value within the range given - they'd say "where 1
< k
< 5"). Then if you choose to combine the statements, because the letters have been turned into variables, it isn't at all clear if the k referred to in Statement 1 must have the same value as the k referred to in Statement 2.
Regardless, one can see why Statement 2 is sufficient fairly quickly. Even in the worst case, Georgia would take 11 hours alone, and Andy 13 hours. Two workers exactly like Andy would take 13/2 = 6.5 hours to do the job. Well, Georgia is faster than Andy, so one worker like Georgia and one worker like Andy must take less time than two workers like Andy, so Andy and Georgia together must take less than 6.5 hours. So even in the worst case, the job is certainly finished in less than 6.5 hours, and the answer is B.