Data Sufficiency

Usually I get them right AFTER the practice test but this one continues to stump me. Can someone please explain why the answer is what it is?

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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 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.

Data sufficiency... A, B, C, D, E?
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Where is the question from? MGMAT guides? which one?

From GMATPrep Practice Test 2.

I think the answer to avssrs ques is E.

Q stem says
Cost : PBack: 8, HC: 25
Nos.: PBack >10 , HC =?

Stmt I:
Cost of HC > 150
or No. of HC > 6. As it can be any no. >6, no answer.
Insufficient

Stmt II
Cost of all books <260
so, 8*PB + 25 * HC < 260

If we assume PB=11.
HC<7, it can be any number
Similarly, if PB=12, HC <6 and so on..
Insufficient

Lets combine both:
If HC > 6, and 8*PB + 25 * HC < 260
and PB>10, then there are no values for HC which we can get.
coz : 8*11 + 25* HC < 260
or 25*HC < 172
but I says 25 *HC >150

There is no integer value which satisfies it.

So, answer is E

Cheers

avssrs wrote:Usually I get them right AFTER the practice test but this one continues to stump me. Can someone please explain why the answer is what it is?

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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 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.

Data sufficiency... A, B, C, D, E?
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The answer is C,

Let P be the number of Paperbacks and H the number of Hardcovers.

The question reads as "Find the Value of H?"

Statement I:
Cost of Hardcovers is atleast $150.

Please pay attention to phrases like at least, at most, no greater than , no less than etc. on the GMAT. They are used by the test maker for a reason.

So, ($25) (H) >= $150
Or, .......... H >= 6 Books

Since we need a UNIQUE value for Data Suffciency answers, this is insufficient.

Statement II:
Total cost of ALL books is less than $260

So,
($8) ( P) + ($25) (H) < $260

Since P needs to be more than 10 (those phrases again...)....the abolute least number of Paperbacks bought is 11. Lets plug that into the equation created above to see what the maximum value of H could be:

($8) ( P= 11) + ($25) (H) < $260
Or, ( $88) + (25H) < 260
Or, 25H < 172
Or, H < 172 / 25

Since H cannot be fractional (number of books)...the largest possible value of H is 6.

But it could be 5 or 4...so on....if the number of paperbacks bought were higher than 11.

No dice...insufficient.

Combining both statements conclusions:
Statement I : H >=6
Statement II: Maximum Value of H = 6,

we can only arrive at only one unique answer (Translate this in your mind to mean sufficiency), as H = 6.

Good question!

I too answered E in prep test, but correct answer is C.

Question stem says P > 10.

(1) tells us that 25H >= 150, meaning H >= 6. Not sufficient.

(2) tells us that 8P + 25H < 260
If P is 11, 12, 13, ... then H could be 1, 2, 3, etc. Not sufficient.

Together, (1) and (2) tell us that Juan bought at least P = 11 and H = 6.
So minimum cost = 88 + 150 = 238.
One more H will increase total cost to 88 + 175 = 263, not possible.
So H = 6 and answer is C.

Did manage to figure it out today (courtesy of a good sleep), but thanks guys (especially Musiq) for helping.

Thanks Ian for clarifying my doubt.