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Try This- a good puzzle

by imhimanshu » Mon Aug 17, 2009 6:20 am
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
OA to follow. Plz post reasoning for the same
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Re: Try This- a good puzzle

by yezz » Mon Aug 17, 2009 8:06 am
imhimanshu 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

first we have to assume that these books are all wuts there

b = 50, z=65,p = 90,g = 50,c = 110

to make sure 80 from the same science they must be either p or c

1st theortitcally remove all the b,z,g = 165

now if we remove another 160 ( 80 0f each p,c) we are secured as we would have 165+160 = 325 among which 80 are surely from the same sign

however if we looked at 79 from each of p,c ie: total of 158 we would only need to remove one more book and we are sure that we have 80 of eiher p or c then we need only to remove 159+165 = 324

E
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by imhimanshu » Mon Aug 17, 2009 7:09 pm
Thanks..got it.
OA ie E only
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by imhimanshu » Mon Aug 17, 2009 7:10 pm
Thanks..got it.
OA ie E only
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by GambitOS » Thu Aug 20, 2009 2:04 am
Thanks! It's clear now!
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by arbiter » Sun Aug 23, 2009 1:13 am
i didnt get the explaination ...can anyone of u plz explain it again...
arbiter
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by Nermal » Wed Sep 02, 2009 5:11 am
The only way to get 80 books on the same science is either physics or chemistry, of the others there are not even 80 books in the room.

On the whole we have 365 books in the room.
We now look for the most unfavourable situation:

We could pick 50 biology books first.
Then we pick 65 zoology books
and then 50 geology books.
So now we removed 165 books from the room and still do not have 80 books of one kind.

This leaves us with 365-165=200 books in the room.

Now we have only physics and chemistry books left, both of which can sum up to 80 books.

It could now happen that we pick 79 physics books for example (the same applies to the chemistry books as well)
We then have picked 244 books out of those 365 books, which leaves us with 121 books.
Now, we are still looking at the most adverse situation!, we only pick chemistry books. We have to do this until we have picked 80 books.
So, 121 books left - 80 books = 41 books.

Therefore, of those original 365 books we have 41 left which we did not pick.
Thus, we had to pick 324 (365-41) books in order to make sure that we will definitively have 80 books that cover one special science field.

Hope I could help.
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