Data Sufficiency

Hi fambrini,

This question will require that you 'play around' a bit with the given information to determine what possible answers exist. We're told that each paperback book costs $8 and each hardcover book cost $25. We're also told that Juan bought MORE than 10 paperback books (which means he spent at least 11x$8 = $88 on those books). We're asked how many HARDCOVER books Juan bought.

1) The total cost of the hardcover books that Juan bought was at least $150

Since hardcover books cost $25 each, and Juan bought AT LEAST $150 worth of these books, then Juan bought AT LEAST 6 hardcover books. However, we don't know the exact number of those books he bought.
Fact 1 is INSUFFICIENT.

2) The total cost of all the books that Juan bought was LESS than $260

We know 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...

Juan COULD have bought...
11 paperbacks and 1 hardcover
11 paperbacks and 2 hardcovers
11 paperbacks and 3 hardcovers
...among many other options.
Fact 2 is INSUFFICIENT.

Combined, we know...
-AT LEAST 11 paperbacks were bought
-AT LEAST 6 hardcovers were bought
-The total spent was LESS than $260

At the minimum, Juan would have spent... (11)($8) + (6)($25) = $238

Since the total was LESS than $260, Juan could not have bought any additional hardcover books (since that would have pushed the total ABOVE $260), so he had to have bought exactly 6 hardcovers.
Combined, SUFFICIENT.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

fambrini wrote:Juan bought some paperback books that cost $8 each and some hardcover book that cost $25 each. If Juan bought more than 10 paperback books, how many hardcover books did he buy?

1) The total cost of 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

We are given that Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each, and that he bought more than 10 paperback books. If we let p = the number of paperback books Juan bought and h = the number of hardcover books, the total cost of the paperback books is 8p, the total cost of the hardcover books is 25h, and the total cost of all books is 8p + 25h.

We need to determine the value of h, the number of hardcover books purchased by Juan.

Statement One Alone:

The total cost of the hardcover books that Juan bought was at least $150.

Using the information in statement one, we can create the following inequality:

25h ≥ 150

h ≥ 6

Thus, at least 6 hardcover books were purchased. However, we cannot determine the exact number of hardcover books purchased by Juan. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The total cost of all the books that Juan bought was less than $260.

Using the information in statement two, we can create the following inequality:

8p + 25h ≤ 260

We still do not have enough information to determine how many hardcover books were purchased by Juan.

Statements One and Two Together:

From the given information as well as our two statements, we know that p > 10, h ≥ 6, and that 8p + 25h ≤ 260.

Since p > 10, Juan, at minimum, purchased 11 paperback books. If we use 11 for p in the inequality 8p + 25h ≤ 260, then we have:

88 + 25h ≤ 260

25h ≤ 172

h ≤ 6 22/25

Recall that h ≥ 6, and since h has to be a whole number, Juan must have purchased 6 hardcover books.

Answer:C

fambrini wrote:Juan bought some paperback books that cost $8 each and some hardcover book that cost $25 each. If Juan bought more than 10 paperback books, how many hardcover books did he buy?

1) The total cost of 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

OA: C

I can't find a quick way to test values using statements 1 and 2.

Thanks,
Fambrini

The challenge with testing values, in case you calculated the number of paperback books is depicted below.

As per statement 1, the minimum amount spent on hardcover books = $150, ensuring 6 hardcover books. The amount left for paperback books = 260-150=110. Thus, one can buy 110/8 = 13.75 number of paperback books. Since we are given that Juan bought more than 10 paperback books, thus he bought 11, 12, or 13 numbers of paperback books.

On the basis of above, had you concluded that even after combining both the statements, we cannot get the unique value, you are mistaken.

The question asks, "how many hardcover books Juan bought and not how many paperback books he bought."

Let us consider that Juan bought one more hardcover book (7), thus the amount left for paperback books = 260-150-25=$85.

He can buy less than 85/8=10.6 books or 10 paperback books. However, this is not possible since he bought more than 10 paperback books. Thus, he must have bought 6 hardcover books.

Hope this helps!

-Jay
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