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 all the hardcover books that Juan bought was at least $150.
(2) The total cost of all the books that Juan bought was less than $260.
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Information given in the question:
Juan bought more than 10 paperbacks. So Juan bought at 11 paperbacks, which means he spent at least $88 on paperbacks.
Statement 1: Juan spent at least $150 on Hardcovers. So that means he bought at least 6 harcovers. We have no upside limit though.
Insufficient.
Statement 2: Juan spent less than $260 total on books. This tells us at most that Juan spent $259 - $88 (minimum amount possible spent on paperbacks) = $171 maximum on hardcovers. 171 divided by 25 is 6 and change. So round down. The maximum number of harcovers that could be purchased is 6. This statement could also be true with any number of hardcovers below six being purchased. For example, 0 hardcovers + 12 paperbacks = $96, which is less than $260.
Insufficient.
Together:
Looking at Statement 1, we know that at least 6 hardcovers had to be purchased. Looking at Statement 2, we know that no more than 6 hardcovers could be purchased. So Juan must have purchased 6 hardcovers.
Juan bought more than 10 paperbacks. So Juan bought at 11 paperbacks, which means he spent at least $88 on paperbacks.
Statement 1: Juan spent at least $150 on Hardcovers. So that means he bought at least 6 harcovers. We have no upside limit though.
Insufficient.
Statement 2: Juan spent less than $260 total on books. This tells us at most that Juan spent $259 - $88 (minimum amount possible spent on paperbacks) = $171 maximum on hardcovers. 171 divided by 25 is 6 and change. So round down. The maximum number of harcovers that could be purchased is 6. This statement could also be true with any number of hardcovers below six being purchased. For example, 0 hardcovers + 12 paperbacks = $96, which is less than $260.
Insufficient.
Together:
Looking at Statement 1, we know that at least 6 hardcovers had to be purchased. Looking at Statement 2, we know that no more than 6 hardcovers could be purchased. So Juan must have purchased 6 hardcovers.
