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# How many divisions of the company are overfunded?

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How many divisions of the company are overfunded? [#permalink]  05 Mar 2012, 17:12
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Question Stats:

8% (00:00) correct 92% (01:48) wrong based on 13 sessions
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 Tough [Reveal] Spoiler: OA _________________ Moderator Joined: 01 Sep 2010 Posts: 2605 Followers: 441 Kudos [?]: 3475 [0], given: 720 Re: How many divisions of the company are overfunded? [#permalink] 06 Mar 2012, 09:26 Expert's post No one knows how to handle this problem. ??? _________________ Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 17 Kudos [?]: 267 [0], given: 11 Re: How many divisions of the company are overfunded? [#permalink] 01 Dec 2012, 22:28 I am praying that this is no GMAT question. I'm guessing E because we don't know the the actual distribution of the budget over the division. _________________ Impossible is nothing to God. Moderator Joined: 02 Jul 2012 Posts: 1228 Location: India Concentration: Strategy GMAT 1: 740 Q49 V42 GPA: 3.8 WE: Engineering (Energy and Utilities) Followers: 80 Kudos [?]: 867 [0], given: 116 Re: How many divisions of the company are overfunded? [#permalink] 02 Dec 2012, 03:18 carcass wrote: 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 Tough

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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Re: How many divisions of the company are overfunded?   [#permalink] 02 Dec 2012, 03:18
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