A bookshelf holds both paperback and hardcover books. The

BTGmoderatorLU wrote:Source: 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.

The OA is D

Say there are p paperback and h hardcover books. Thus, there are a total of p + h books.

We are given that p/h = 22/3.

We have to get the value of p.

Let's take each statement one by one.

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

Given that p/h = 22/3, say p= 22x and h = 3x. Thus, p + h = 25x; where x is a positive integer

Thus, 202 < 25x < 247

The only integer value of x that satisfies above inequality is 9. Thus, there are 22x = 22*9 = 198 paperback books. 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.

Again, given that p/h = 22/3, say p= 22x and h = 3x.

Thus, we have (22x – 18) / (3x + 18) = 4/1 => x = 9. Thus, Thus, there are 22x = 22*9 = 198 paperback books. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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