Problem Solving

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

IMO 324
The only science books that have 80 are chemistry and physics. So to make sure we remove 80 from the same science we have to add all of the others and add 79*2....

Can you be bit clear Shibal...

arghya05 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

IMO 324
so we need to maximize the number of books. To do so, we need to remove the max number of books and be sure the not 80 of the same science books are removed
we can safely remove the 50 botany books,65 zoology books, and 50 geology books.
now we remove 79 physics books and then 79 chemistry books. after this we are not left with any option. we must chose either a physics books or chemistry book and we will get 80 books of same science
so total is 50+65+50+79+79+1=324

I am still unclear on the question. Can someone explain the question?

What is the source of the question?

I think the wording is really bad.........

rajbirdadhiyala wrote:I am still unclear on the question. Can someone explain the question?

The questions asks "after removing how many books can you be sure that 80 books of same subject have been removed" answer is after removing 324 books, you can be sure.
for ex lets say you removed 200 books. Now you cannot be sure that you removed 80 books of same science. say you removed 50 of botany, 50 of zoology, 50 are on physics. 50 are on geology.
now you read my answer explanation again.

arghya05 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

ok u have to consider the extreme case that is max. number of books to ensure that 80 of the books removed are on the same science.

now only chemistry and physics books are more than 80 so
here we go:
take 50 books of botany. u cannot have 80 books of similar subject.
take 50 books of geology, still can't have 80 books for same subject.
take 65 zoology books, still can't have 80 books for same subject.
Now here comes the tricky part.. take 79 more books(these could be chemistry or physics books) coz it might be
possible that these are from the same subject but in worst case, the next book that we are gonna select could not be of the same subject as that of 79 books.. so after u take 79 books take another 80 books now(as the books from all the subjects are taken care of and only the books of this last subject are left) and now u have all the 80 books of the same subject. So this way we have taken care of all the possibilities and hence calculated the book for the worst case as well.
So add the book we've taken till now: 50 + 50 +65 + 79 + 80 = 324
So, withdrawal of these many books will make sure that now u get 80 books of the same subject in any case..
hence 324..
HTH