A school library contains 200 hardcover and 300 paperback books.

[BTGModeratorVI]

A school library contains 200 hardcover and 300 paperback books. 30% of the hardcover books and 70% of the paperbacks are fiction. If a book is selected at random from the 500 books at the library, what is the probability that the book is either paperback or fiction?

A. 72%
B. 76%
C. 80%
D. 82%
E. 84%

Answer: A
Source: Veritas Prep

[Scott@TargetTestPrep]

A school library contains 200 hardcover and 300 paperback books. 30% of the hardcover books and 70% of the paperbacks are fiction. If a book is selected at random from the 500 books at the library, what is the probability that the book is either paperback or fiction?

A. 72%
B. 76%
C. 80%
D. 82%
E. 84%

Answer: A

Solution:

We are given that 30% of the 200 hardcover books are fiction, and thus 200 x 0.3 = 60 hardcover books are fiction. We are also given that 70% of the 300 paperback books are fiction, and thus 0.7 x 300 = 210 paperback books are fiction. We see that there are a total of 60 + 210 = 270 fiction books.

Recall that P(A or B) = P(A) + P(B) - P(A and B). If we let B be paperback and F be fiction, we have:

P(B or F) = P(B) + P(F) - P(B and F)

P(B or F) = 300/500 + 270/500 - 210/500

P(B or F) = 360/500 = 72/100 = 72%

Alternate Solution:

The group of books referred to as “either paperback or fiction” consists of all of the paperback books plus the hardcover books that are fiction. Since there are 300 paperback books and 200 x 0.3 = 60 hardcover fiction books, there are 300 + 60 = 360 books that are either paperback or fiction, out of a total of 500. Thus, the probability is 360/500 = 72/100 = 72%.

Answer: A

[Brent@GMATPrepNow]

A school library contains 200 hardcover and 300 paperback books. 30% of the hardcover books and 70% of the paperbacks are fiction. If a book is selected at random from the 500 books at the library, what is the probability that the book is either paperback or fiction?

A. 72%
B. 76%
C. 80%
D. 82%
E. 84%

Answer: A
Source: Veritas Prep

Another approach is to use the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).

Here, we have a population of books, and the two characteristics are:
- hardcover or paperback
- fiction or nonfiction

With the given information, we can complete our matrix as follows (I've skipped a few steps. So, if you're unfamiliar with this approach, watch the video (below) to see how to set things up).


We want, P(selected book is either paperback or fiction)
The boxes representing books that are either paperback or fiction are shaded below.

So, the number of books that satisfy this condition = 60 + 210 + 140 = 360
Total number of books = 500

So, P(selected book is either paperback or fiction) = 360/500
= 72%

Answer: A

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent