Let's call the number of paperback books "22x", and the number of hardcover books "3x". In the end, we're interested in paperback books, so to achieve sufficiency, we'll need "22x". In other words, knowing "x" will be sufficient.
Statement (1) ----> The total number of books on the shelf is 22x+3x = 25x. Now, we want to be very conscious of our shelf (or...."shelf-conscious", if you prefer), so the total number of books on the shelf has to be some multiple of 25. Here we're told that the total number of books is somewhere between 202 and 247, inclusive. The only number in that range that would be a multiple of 25 is 225.
So 25x = 225, and we'd be able to solve for "x". SUFFICIENT.
Statement (2) ----> If 18 paperbacks were removed from the shelf, our new paperback total would be "22x - 18". If 18 hardcovers were added to the shelf, our new hardcover total would be "3x+18". And then the new ratio of paperback to hardcover would be 4:1, so we'd get this equation:
(22x-18)/(3x+18) = 4/1. With this equation, we can certainly solve for "x", so this statement is SUFFICIENT.
With each statement being sufficient, our answer is (D).
Side note: We don't need to solve, since it's DS, but if you did, you'd get x=9 in either statement.
Remember that not only are the statements always true, but also they'll never directly contradict each other. So whenever you're selecting (D) as an answer, it's not a coincidence that each statement gives you the same answer to the original question.
Side note 2: Sometimes it's OK to judge a book by its cover. For example, if you see a book called "How to Lose Weight Quickly Without Diet or Exercise," you know the book is filled with lies! : )
Gene Suhir
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