Of the science books in a certain supply room, \(50\) are on botany, \(65\) are on zoology, \(90\) are on physics,

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Wed Jun 07, 2023 12:01 pm

GMAT Paper Tests

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 \(80\) of the books removed are on the same science?

A. \(81\)
B. \(159\)
C. \(166\)
D. \(285\)
E. \(324\)

OA E

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