BTGmoderatorLU wrote: ↑

Sun Feb 21, 2021 5:20 am

Source: Veritas Prep

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

The OA is D

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

BTGmoderatorLU wrote: ↑

Sun Feb 21, 2021 5:20 am

Source: Veritas Prep

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

The OA is D

Solution:

The worst case scenario is 34 fantasy, 34 science fiction, 32 historical fiction and 28 nonfiction books are removed and Christie still has not had at least 35 books of the same type removed. However, if she removes 1 more book (regardless of whether it’s a fantasy or a science fiction book), she will have at least 35 books of the same type removed. Therefore, the number of books she must remove to guarantee that is 34 + 34 + 32 + 28 + 1 = 129.

Answer: D