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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.
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27 Mar 2026, 02:15
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GMAT Club 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, or 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, or 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.
General Discussion
18 Mar 2026, 23:21
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The key is translating the stem into algebra first before touching the statements.
Let h = hardcover books Julian currently has, p = paperback books he currently has.
Stem tells us: h + 18 = 3p, so h = 3p - 18.
The question "does Julian currently have more hardcover than paperback" becomes: is h > p?
Substitute: is 3p - 18 > p? Simplify: is 2p > 18? Which is just: is p > 9?
That's the rephrased question. Now the statements are easy.
Also worth noting: since h can't be negative, 3p - 18 >= 0 means p >= 6. So valid values of p start at 6.
1. Statement (1): p < 12. So p could be 6, 7, 8, 9, 10, or 11.
If p = 10, then h = 12, and yes h > p.
If p = 9, then h = 9, and no h = p (not strictly greater).
If p = 8, then h = 6, and no h < p.
Not sufficient, because we get both yes and no answers.
2. Statement (2): p > 9. This directly answers our rephrased question "is p > 9?" with a definitive YES. So h > p in every case. Sufficient.
Answer: B.
The trap here is picking C. Most people instinctively feel like they need both statements to "nail down" the value of p. But DS doesn't ask you to find the exact value, just to answer yes or no. Statement (2) alone tells you everything you need.
Let h = hardcover books Julian currently has, p = paperback books he currently has.
Stem tells us: h + 18 = 3p, so h = 3p - 18.
The question "does Julian currently have more hardcover than paperback" becomes: is h > p?
Substitute: is 3p - 18 > p? Simplify: is 2p > 18? Which is just: is p > 9?
That's the rephrased question. Now the statements are easy.
Also worth noting: since h can't be negative, 3p - 18 >= 0 means p >= 6. So valid values of p start at 6.
1. Statement (1): p < 12. So p could be 6, 7, 8, 9, 10, or 11.
If p = 10, then h = 12, and yes h > p.
If p = 9, then h = 9, and no h = p (not strictly greater).
If p = 8, then h = 6, and no h < p.
Not sufficient, because we get both yes and no answers.
2. Statement (2): p > 9. This directly answers our rephrased question "is p > 9?" with a definitive YES. So h > p in every case. Sufficient.
Answer: B.
The trap here is picking C. Most people instinctively feel like they need both statements to "nail down" the value of p. But DS doesn't ask you to find the exact value, just to answer yes or no. Statement (2) alone tells you everything you need.
