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

Hard

Solution

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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