SOLUTION: In library system with 6 branches, 60 workers are employed. If no library has fewer than 7 workers and no more than 11, what is the minimum number of workers in any 2 of the branch

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Question 252892: In library system with 6 branches, 60 workers are employed. If no library has fewer than 7 workers and no more than 11, what is the minimum number of workers in any 2 of the branches?
(A) 10 (B) 14 (C) 16 (D) 19 (E) 22
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You know at least one branch has 7 people in it.
You know that some number of the remaining 5 branches 'could have' 11 people each.
So let's grind this problem out using the givens noted above.
Assume the first branch has 7 workers. There are now 5 branches with 60-7+=+53 people left to be accounted for
Assume as many remaining branches as possible have 11 workers in them. You can see that there could be 4 branches will 11 each. 4%2A11=44
53-44+=+9
So the remaining branch must have 9 workers. If any of the other branches had fewer than 11 workers, then the last branch would have even more than 9.
You were asked for the 'minimum' in two branches. That would be 7+%2B9+=+16
Make sense?