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Julian owns only hardcover books and paperback books. If Julian buys 18 additional hardcover books, he will then have exactly 3 times as many hardcover books as paperback books. Does Julian currently have more hardcover books than paperback books?
(1) Julian currently has fewer than 12 paperback books.
(2) Julian currently has more than 9 paperback books.
(1) Julian currently has fewer than 12 paperback books.
(2) Julian currently has more than 9 paperback books.
30 May 2026, 08:26
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Official Solution:
Julian owns only hardcover books and paperback books. If Julian buys 18 additional hardcover books, he will then have exactly 3 times as many hardcover books as paperback books. Does Julian currently have more hardcover books than paperback books?
Let \(p\) be the number of paperback books and \(h\) be the number of hardcover books Julian has now. From the stem, \(h + 18 = 3p\), so \(h = 3p - 18\).
We need to know whether \(h > p\), which is equivalent to:
Is \(3p - 18 > p\)?
Is \(2p > 18\)?
Is \(p > 9\)?
(1) Julian currently has fewer than 12 paperback books.
If \(p = 9\), then \(h = 9\), so the answer is No, but if \(p = 10\), then \(h = 12\), so the answer is Yes. Not sufficient.
(2) Julian currently has more than 9 paperback books.
This directly gives a Yes answer to the question. Sufficient.
Answer: B
Julian owns only hardcover books and paperback books. If Julian buys 18 additional hardcover books, he will then have exactly 3 times as many hardcover books as paperback books. Does Julian currently have more hardcover books than paperback books?
Let \(p\) be the number of paperback books and \(h\) be the number of hardcover books Julian has now. From the stem, \(h + 18 = 3p\), so \(h = 3p - 18\).
We need to know whether \(h > p\), which is equivalent to:
Is \(3p - 18 > p\)?
Is \(2p > 18\)?
Is \(p > 9\)?
(1) Julian currently has fewer than 12 paperback books.
If \(p = 9\), then \(h = 9\), so the answer is No, but if \(p = 10\), then \(h = 12\), so the answer is Yes. Not sufficient.
(2) Julian currently has more than 9 paperback books.
This directly gives a Yes answer to the question. Sufficient.
Answer: B
