Each of the 45 books on a shelf is written either in English or in Spanish, and

[BTGModeratorVI]

Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback. If a book is to be selected at random from the books on the shelf, is the probability less than 1/2 that the book selected will be a paperback written in Spanish?

(1) Of the books on the shelf, 30 are paperback.
(2) Of the books on the shelf, 15 are written in Spanish.

Answer: B
Source: Official guide

[Brent@GMATPrepNow]

Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback. If a book is to be selected at random from the books on the shelf, is the probability less than 1/2 that the book selected will be a paperback written in Spanish?

(1) Of the books on the shelf, 30 are paperback.
(2) Of the books on the shelf, 15 are written in Spanish.

Answer: B
Source: Official guide

Given: Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback. A book is to be selected at random from the books on the shelf.

Target question: Is the probability less than 1/2 that the book selected will be a paperback written in Spanish?
This is a good candidate for rephrasing the target question

Let's use the Double Matrix Method to solve this question. 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:
- English or Spanish
- Hardcover or paperback

We can set up our diagram like this:


1/2 of 45 = 22.5
So in order for the probability to be less than 1/2, we need 22 or fewer books to be Spanish paperbacks.
In other words, we need 22 or fewer books in the yellow shaded region.
Let's use this information to REPHRASE the target question
REPHRASED target question: Is the number of books in the yellow shaded region 22 or less?



Statement 1: Of the books on the shelf, 30 are paperback
If 30 of the 45 books are paperback, then the remaining 15 books must be hardcover. We'll add this to our diagram


There are many different ways to complete this diagram so that we meet the given conditions.
For example, we could have the following situation:

In this case, the answer to the REPHRASED target question is YES, the number of books in the yellow shaded region IS 22 or less

Alternatively, we could also have this situation:

In this case, the answer to the REPHRASED target question is NO, the number of books in the yellow shaded region is NOT 22 or less

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Of the books on the shelf, 15 are written in Spanish.
When we add this information to our diagram, we get:


IMPORTANT: This tells us that the two boxes in the bottom row, must add to 15.
So it will be impossible for the value in the yellow shaded region to be greater than 22.
In other words, the answer to the REPHRASED target question is YES, the number of books in the yellow shaded region IS 22 or less
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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

[deloitte247]

Total no. of books = 45
Target question: If a book is to be selected at random from the books on the shelf, is the probability less than 1/2 that the book selected will be a paperback written in Spanish?
1/2 of 45 = 22.5
Hence, if the total number of Spanish paperback is less than 22, then the probability of selecting a paperback is less than 1/2
Statement 1: Of the books on the shelf, 30 are paperback.
Paperbacks = 30, hardcovers = 45-30 = 15
Therefore, total no. of paperback = English paperbacks + Spanish paperbacks
30 = (English + Spanish) paperback; their sum could either be 20+5. In this case, Spanish paperback is less than 22 OR it could also be 3+27 in which Spanish paperback > 22.
Therefore, the information available is not enough to arrive at a definite answer. So, statement 1 is NOT SUFFICIENT.

Statement 2: Of the books on the shelf, 15 are written in Spanish.
This means that (Hardcover + Paperback) Spanish = 15
Since the sum of Spanish Hardcover and Spanish Paperback is < 22, then the value of Spanish cannot be greater than > 22. So, the probability that a random book selected will be a paperbook written in Spanish is less than 1/2.
Therefore, statement 2 alone is SUFFICIENT. Hence, option B is the correct answer.