Help needed on a problem from the downloaded question set

[biswajits]

Hi,

Can anybody please solve this below question. I thought first of all the question was wrongly worded. Then replacing 80 with 80 %, I thought the answer is 159.

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

Thanks in Advance

[Ian Stewart]

Hi,

Can anybody please solve this below question. I thought first of all the question was wrongly worded. Then replacing 80 with 80 %, I thought the answer is 159.

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

Thanks in Advance

Imagine the worst possible case: how many books could you remove without getting 80 on a single one of the topics? You could remove all 50 botany books, all 65 zoology books, all 50 geology books, 79 physics books and 79 chemistry books and still not have 80 books on any single topic. That's the worst case, but as soon as you remove one more book after that, you're assured of having 80 books on a single topic. Add those numbers and you get 324.

[Brent@GMATPrepNow]

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

Let's see what happens when the following books are removed:
50 on botany
65 on zoology
79 on physics
50 on geology
79 on chemistry
TOTAL = 323

At this point, we do NOT have 80 of any one science topic.
However, if we remove one of the remaining books (which are either physics books or chemistry books), we will certainly have 80 books on one science topic.
In other words, if we remove 324 books, we can be certain of having 80 books on one science topic

Answer: E

Cheers,
Brent