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# Of the science books in a certain supply room, 50 are on

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Director
Joined: 29 Jul 2006
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Of the science books in a certain supply room, 50 are on [#permalink]  04 Nov 2006, 11:37
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Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 81
(B) 159
(C) 166
(D) 285
(E) 324

Manager
Joined: 04 Oct 2006
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You take as many books out as you can without taking out 80 of 1 science.

Take out all the botany, zoology, and geology books = 165

Then take out 79 physics books and 79 chemistry books = 158

You then take out one more and it will have to be either a physics or chemistry book, making 80 of either subject = 1 book

165 + 158 + 1 = 324
Manager
Joined: 03 Nov 2006
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Re: PS-Science [#permalink]  04 Nov 2006, 11:46
vineetgupta wrote:
Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 81
(B) 159
(C) 166
(D) 285
(E) 324

Its E.

To ensure you remove 80 of the same, you need to assume the worst case scenario. That is you first remove the 50 botany, 65 soology, 50 geology. You now have 165 and you don't have 80 of the same.

Then you remove another 79 of one (either physics or chemistry). Lastly you take out another 80 and then you are sure you have 80 of the same.

Add them all up and you get 324.
Senior Manager
Joined: 05 Oct 2006
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Re: PS-Science [#permalink]  05 Nov 2006, 03:12
it's e
i proceeded like hosam which is already explained
Re: PS-Science   [#permalink] 05 Nov 2006, 03:12
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