sairamGmat 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
OA is E . Can any one throw some light on this?
The sciences videlicet botany, zoology, and geology do not have enough books to ensure that 80 of the books removed are on the same science. Physics 90 and chemistry 110 are the true contenders left.
Hence, if all books of the sciences videlicet botany, zoology, and geology were removed from the supply room, and then we can still say that we are not sure even after removing 165 books, that 80 of the books removed are on the same science. We still need to remove minimum of the remaining 200 books to meet the said condition.
But, how many more books after removing 165 books would allow us meet the said condition?
Well, we can contentedly eliminate choices A through C now.
D is 120 in excess to 165. Just think, does the removal of 120 meet the said condition, if yes, it's D, otherwise E.
Think of the worst case with D, it's possible that 60 books of each science were have been removed so far. Now go for E without checking it.
Why E?
E is 159 in excess to 165. Just think, does the removal of 159 meet the said condition? The worst case could be when 79 books of each science were have been removed, that's a total of 158 books were have been removed and we are still not sure, just 1 more book of any of the two sciences, and we can bet.
