Of the science books in a certain supply room, 50 are on botany, 65 are

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:17 am

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

Answer: e
Source: official guide

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

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:17 am

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

Answer: e
Source: official guide

Solution:

We could remove all 50 of the botany books, all 65 of the zoology books, all 50 geology books, PLUS 79 of the physics books, and 79 of the chemistry books, for a total of 323 books, and we still have not removed 80 books of the same science. However, the very next book chosen must be either a physics book or a chemistry book, which would then yield 80 books of the same science being chosen. Therefore, we must draw 323 + 1 = 324 books to ensure that 80 books removed are on the same science.

Answer: E