Question: Juan Bought Some Paperback Books that Cost $8 Each and Some hardcover books that cost $25 each. If Juan bought more than 10 paperback books, how many hardcover books did he buy?
(1) The total cost of hardcover books that Juan bought was at least $150
(2) The total cost of all books that Juan bought was less than $260
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
“Juan Bought Some Paperback Books that Cost $8”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.
Solution and Explanation:
Approach Solution 1:
The given situation is that each paperback book costs $8 and each hardcover book costs $25. Accordingly, Juan bought MORE than 10 paperback books which means he spent at least 11 * $8 that equals $88 on those books. We're asked how many HARDCOVER books Juan bought.
Based on the first given statement- the total cost of the hardcover books that Juan bought was at least $150
Since the cost of the hardcover books was $25 each, and Juan bought at least $150 worth of these books, then Juan bought at least 6 hardcover books. However, since it is not known how many or the number of books in hardcover he bought, the first given statement is insufficient.
Now, considering the second statement given in the question, the total cost of all the books that Juan bought was LESS than $260
It is known from the prompt that Juan spent at least $88 on paperback books, so we have to think about how he could have gotten to a total that is less than $260...
Accordingly, the following situations could have been possible for Juan:
Juan could have bought his books in the following ways-
- 11 paperbacks and 1 hardcover
- 11 paperbacks and 2 hardcovers
- 11 paperbacks and 3 hardcovers
The above options can be considered among many other options. Accordingly, the statement 2 given is insufficient.
Combining both the conditions
- At least 11 paperbacks were bought
- At least 6 hardcovers were bought
- The total spent was less than $260
At the minimum, Juan must have spent around the following-
(11)($8) + (6)($25) = $238
Since the total was less than $260, Juan could not have bought any additional hardcover books. This can be stated considering that hardcover books cost more and would have pushed the total to more than $260. So he had to have bought exactly 6 hardcovers.
Correct Answer: C
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