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A bookshelf holds both paperback and hardcover books.

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by AAPL » Sat Oct 20, 2018 5:33 am

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Manhattan Prep

A bookshelf holds both paperback and hardcover books. The ratio of paperback books to hardcover books is 22 to 3. How many paperback books are on the shelf?

1. The number of books on the shelf is between 202 and 247, inclusive.
2. If 18 paperback books were removed from the shelf and replaced with 18 hardcover books, the resulting ratio of paperback books to hardcover books on the shelf would be 4 to 1.

OA D.
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by Jay@ManhattanReview » Sun Oct 21, 2018 10:03 pm
AAPL wrote:Manhattan Prep

A bookshelf holds both paperback and hardcover books. The ratio of paperback books to hardcover books is 22 to 3. How many paperback books are on the shelf?

1. The number of books on the shelf is between 202 and 247, inclusive.
2. If 18 paperback books were removed from the shelf and replaced with 18 hardcover books, the resulting ratio of paperback books to hardcover books on the shelf would be 4 to 1.

OA D.
Given: The ratio of paperback books to hardcover books is 22 to 3.

Say x is the common ratio, thus, the number of paperback books = 22x and the number of hardcover books = 3x. Or, the total the number of books = 22x + 3x = 25x.

Question: How many paperback books are on the shelf?

Let's take each statement one by one.

1. The number of books on the shelf is between 202 and 247, inclusive.

=> 202 ≤ 25x ≤ 247

8... ≤ x ≤ 9...

We see that only one integer value qualifies the above inequality, i.e., x = 9. Thus, the number of paperback books = 22x = 22*9 = 225. Sufficient.

2. If 18 paperback books were removed from the shelf and replaced with 18 hardcover books, the resulting ratio of paperback books to hardcover books on the shelf would be 4 to 1.

=> (22x - 18) / (3x + 18) = 4 / 1

22x - 18 = 12x + 72

=> x = 9. Suffcient.

The correct answer: D

Hope this helps!

-Jay
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