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# A shelf contains hardcover and paperback books, of either fiction or n

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Math Expert
Joined: 02 Sep 2009
Posts: 48041
A shelf contains hardcover and paperback books, of either fiction or n  [#permalink]

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16 Feb 2015, 06:45
1
5
00:00

Difficulty:

95% (hard)

Question Stats:

53% (02:03) correct 47% (03:12) wrong based on 154 sessions

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A shelf contains hardcover and paperback books, of either fiction or nonfiction. How many books are on the shelf?

(1) 2/3 of the books are fiction and 1/4 of the books are hardcover
(2) Fewer than 30 books are paperback and more than 10 are nonfiction

Kudos for a correct solution.

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Concentration: Technology, Other
Schools: Berkeley Haas
GMAT Date: 01-14-2015
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Re: A shelf contains hardcover and paperback books, of either fiction or n  [#permalink]

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16 Feb 2015, 10:42
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Statement 1 : Not sufficient , we do know the value of X

Statement 2 : Not sufficient we do know the number of books still

Attachment:

Stmnt.PNG [ 9.85 KiB | Viewed 3044 times ]

When combined $$\frac{X}{3} >10$$ = $$X > 30$$
$$\frac{3*X}{4} < 30$$ = $$X < 40$$

Values can be 30 < X < 40 . Only 36 seems to satisfy the equation .

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A shelf contains hardcover and paperback books, of either fiction or n  [#permalink]

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17 Feb 2015, 08:32
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Bunuel wrote:
A shelf contains hardcover and paperback books, of either fiction or nonfiction. How many books are on the shelf?

(1) 2/3 of the books are fiction and 1/4 of the books are hardcover
(2) Fewer than 30 books are paperback and more than 10 are nonfiction

Kudos for a correct solution.

ans C..

1) statement tells us ' 2/3 of the books are fiction and 1/4 of the books are hardcover'... it basically tells us that the total books have to be a multiple of 3 and 4 or 12..
so total books = 12,24,36,48,60..... insufficient
2) say total books are x...two informations-
a) as 1/4 are hardcover, 3/4 are paperback..
x*3/4<30.. or x<40
b) 2/3 are fiction, so 1/3 are nonfiction...
x*1/3>10...x>30..
insufficient..

combined with (a), the values can be 12,24,36.. and with (b), the values can be 36,48..
however only 36 is common... so sufficient
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Math Expert
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Posts: 48041
Re: A shelf contains hardcover and paperback books, of either fiction or n  [#permalink]

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22 Feb 2015, 11:02
Bunuel wrote:
A shelf contains hardcover and paperback books, of either fiction or nonfiction. How many books are on the shelf?

(1) 2/3 of the books are fiction and 1/4 of the books are hardcover
(2) Fewer than 30 books are paperback and more than 10 are nonfiction

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Solution: C.

Statement 1 indicates that the total number of books is a multiple of 12, as the number must be able to be broken into both thirds and fourths. But without any actual numbers, the statement is not sufficient. Similarly statement 2 is not sufficient, as it offers no insight into proportions. But together, the statements guarantee that there are either 24, 36 or 48 total books (multiples of 12 that are in the range of the statement 2 numbers). 48 is out of the question, as if 3/4 of the books are paperback, that would mean that 3/4 of 48 = 36 books are paperback, and statement 2 limits that number to under 30. And 24 is not enough - 1/3 of the books are nonfiction, meaning that only 8 out of 24 books would be nonfiction, and the statement requires that at least 10 be nonfiction. With 36 total books: 2/3 are fiction = 24. 1/3 are nonfiction = 12. 1/4 are hardcover = 9, and 3/4 are paperback = 27.
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Re: A shelf contains hardcover and paperback books, of either fiction or n  [#permalink]

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31 Jul 2018, 12:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A shelf contains hardcover and paperback books, of either fiction or n &nbs [#permalink] 31 Jul 2018, 12:48
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