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A shelf contains only books of poetry

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by BTGmoderatorDC » Sun Jan 14, 2018 3:22 am
A shelf contains only books of poetry, short stories, and non-fiction. If Jana draws a book randomly off the shelf, what is the probability that the book will be non-fiction?

(1) There are 15 books on the shelf.
(2) There are 4 books of poetry and 5 books of short stories on the shelf.

Which of the statements is sufficient?

OA C
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by Jay@ManhattanReview » Sun Jan 14, 2018 11:54 pm
lheiannie07 wrote:A shelf contains only books of poetry, short stories, and non-fiction. If Jana draws a book randomly off the shelf, what is the probability that the book will be non-fiction?

(1) There are 15 books on the shelf.
(2) There are 4 books of poetry and 5 books of short stories on the shelf.

Which of the statements is sufficient?

OA C
The probability that the book will be non-fiction = (# of non-fiction) / The total number of books

(1) There are 15 books on the shelf.

=> The total number of books = 15, but we do not know the total number of non-fiction. Insufficient.

(2) There are 4 books of poetry and 5 books of short stories on the shelf.

Neither we know the total number of books nor do we know the number of non-fiction. Insufficient.

(1) and (2) together

From (10, we know that the total number of books = 15, and from (2), we know there are 4 books of poetry and 5 books of short stories on the shelf, thus, the number of non-fiction = 15 - 4 - 5 = 6.

The probability that the book will be non-fiction = (# of non-fiction) / The total number of books = 6/15 = 2/5. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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