A certain company has 500 employees split among three divisions, such that there are at least 100 employees in each division. An $8,000,000 benefits budget is to be distributed among the three divisions, and a division will be considered underfunded if it receives no more than $10,000 per employee, and overfunded if it receives at least $40,000 per employee. How many divisions of the company are overfunded?
1) If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is underfunded.
2) If the amounts assigned to each division are rearranged such that each division receives an amount that had been assigned to another division, there is no possible rearrangement in which any division is overfunded.
Really really tough. Would be best to just guess on these types of questions and move on. Anyway, my explanation AFTER seeing the answer is
1) After shuffling, we know each division was given more than 1,000,000. The maximum number of people possible in a group is 300. So this group must have got more than 3,000,000. If one another group got just more than 1,000,000, then the 3rd group would have got more than 3,000,000 (Since there are no arrangements to make the first group underfunded) and less than 4,000,000.
Let groups be A,B & C and amounts initially assigned be a,b & c. So, after shuffling, I should be able to assign both b & c to A such that A is not underfunded. That is after shuffling, other than the amount assigned to A, there should be one more amount as well which if assigned to A does not make it underfunded.
So none of the groups were overfunded.
Took me a good 10 minutes to work this out even after seeing the answer and I still am not sure if I'm right.
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