neeti2711 wrote:Of the science books in a certain supply room, 50 are 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
Determine the WORST-CASE-SCENARIO -- for each type of book, the MAXIMUM number that can be removed WITHOUT removing 80 of the same science:
50 botany
65 zoology
79 physics
50 geology
79 chemistry
Sum = 50+65+79+50+79 = 323.
Thus, it is possible to remove 323 books without selecting 80 of the same science.
Thus, to GUARANTEE that 80 of the same science are removed, we must remove ONE MORE book:
323+1 = 324.
The correct answer is
E.
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