Vincen wrote: ↑

Thu Oct 01, 2020 1:11 am

In her extensive library, Christie has 42 fantasy books, 35 science fiction books, 32 historical fiction books, and 28 nonfiction books. If she removes books at random, how many must she remove to guarantee that she has removed at least 35 books of the same type?

A. 77
B. 105
C. 128
D. 129
E. 144

Answer: D

Source: Veritas Prep

To answer this question, let's first determine the MAXIMUM number of books that can be removed WITHOUT having 35 books of the same type.

To start, we can remove all 32 historical fiction books, and 28 nonfiction books WITHOUT having 35 books of the same type.
From there, we can remove 34 fantasy books and 34 science fiction books WITHOUT having 35 books of the same type.
So far we have removed 128 books (32 + 28 + 34 + 34 = 128) and we do not have 35 books of the same type.

At this point, all that remains are 8 fantasy books, 1 science fiction book.
So, once we choose the next book, we will be GUARANTEED to have at least 35 books of the same type.
128 + 1 = 129
So, once we select 129 books, we will be GUARANTEED to have at least 35 books of the same type.

Answer: D

Cheers,
Brent