Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND EditionMichael arranged all his books in a bookcase with 10 books on each shelf and no books left over. After Michael acquired 10 additional books, he arranged all his books in a new bookcase with 12 books on each shelf and no books left over. How many books did Michael have before he acquired the 10 additional books?
(1) Before Michael acquired the 10 additional books, he had fewer than 96 books.
(2) Before Michael acquired the 10 additional books, he had more than 24 books.
We are given that Michael arranged all his books in a bookcase with 10 books on each shelf and no books left over, and that after he acquired 10 additional books, he arranged all his books in a new bookcase with 12 books on each shelf and no books left over. We need to determine how many books Michael had before he acquired 10 additional books.
Using the given information we can determine that Michael originally had a total number of books that was a multiple of 10, and after he acquired 10 new books, he had a total number of books that was a multiple of 12.
Statement One Alone:Before Michael acquired the 10 additional books, he had fewer than 96 books.
The information in statement one is sufficient to answer the question. Since we know the original number of books was a multiple of 10, the number of books could have been the following:
10, 20, 30, 40, 50, 60, 70, 80, or 90.
Using the above numbers, he could have had the following number of books after acquiring 10 more:
20, 30, 40, 50, 60, 70, 80, 90, or 100.
Remember, after acquiring the 10 new books, the total number of books was a multiple of 12. Of the numbers above, only 60 is a multiple of 12. Thus, Michael originally had 50 books. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:Before Michael acquired the 10 additional books, he had more than 24 books.
We can analyze statement two in a similar way to how we analyzed statement one. Michael could have originally had any one of the following numbers of books:
30, 40, 50, 60, 70, 80, 90, 100, 110, 120, and so on.
Using the above numbers, he could have had any one of the following numbers of books after acquiring 10 more:
40, 50, 60, 70, 80, 90, 100, 110, 120, 130, and so on.
Once again, remember that after acquiring the 10 new books, the total number of books was a multiple of 12. Of the numbers above, 60 and 120 are both multiples of 12. Thus, Michael could have originally had 50 or 110 books. Statement two is not sufficient to answer the question.
Answer: A
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