Solutions
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Question
A bookstore that sells used books sells each of its paperback books for a certain price and each of its hardcover books for a certain price. If Joe, Maria, and Paul bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book?
I. Joe bought 2 paperback books and 3 hardcover books for $12.50.
II. Paul bought 4 paperback books and 6 hardcover books for $25.00.
Option A:
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Option B:
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
Option C:
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Option D:
EACH statement ALONE is sufficient to answer the question asked.
Option E:
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Difficulty Level
HardSolution
Option E is the correct answer.
Option Analysis
We should find the value of p+h, where p is the price of one paperback and h is the price of one hardcover book.
Statement I is insufficient: Joe bought 2 paperback books and 3 hardcover books for $12.50 –> 2p + 3h = 12.5. Not sufficient.
Statement II is insufficient: Paul bought 4 paperback books and 6 hardcover books for $25.00 –> 4p + 6h = 25. Not sufficient.
Together I and II, We can get 4p + 6h = 25 by multiplying 2p + 3h = 12.5 by 2, thus even when combining the statements we still have only one equation. Not sufficient.
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