Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In a home library consisting of 108 books, some hardcover an [#permalink]
16 Nov 2013, 05:23

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

57% (03:25) correct
43% (02:37) wrong based on 166 sessions

In a home library consisting of 108 books, some hardcover and some softcover, exactly 2/3 of the hard cover and exactly 1/4 of the softcover books are nonfiction. What is the greatest possible number of nonfiction books in this home library?

Re: In a home library consisting of 108 books, some hardcover an [#permalink]
16 Nov 2013, 05:46

6

This post received KUDOS

Expert's post

registerincog wrote:

In a home library consisting of 108 books, some hardcover and some softcover, exactly \(2/3\) of the hard cover and exactly \(1/4\) of the softcover books are nonfiction. What is the greatest possible number of nonfiction books in this home library?

A) 18 B) 40 C) 67 D) 72 E) 96

Method I: # of hardcover books : 12x ; # of softcover : 108-12x

Thus, 8x+(27-3x) = # of non-fiction books(n)

or 5x = n-27

\(12x = \frac{n-27}{5}*12\) As No of hardcover books is an integral quantity, thus, (n-27) has to be a multiple of 5.

Only option C makes that.

Method II: As a greater fraction of hardcover books is NF, we must maximize that in no. Also, the remaining no of books(which are softcover) must be a multiple of 4.

As lcm of both 3 and 4 is 12, thus the maximum # of hardcover books = 108-12 = 96 and # of softcover = 12.

Thus, # of non-fiction :\(\frac{2}{3}*96+\frac{1}{4}*12 = 64+3 = 67.\)

Re: In a home library consisting of 108 books, some hardcover an [#permalink]
02 Apr 2014, 10:18

4

This post received KUDOS

The ratio of hardcove and softcover is not given. To maximize the # of books I choose 105xhardcover and 3xsoftcover. 2/3 of 105 = 70 and 1/3 of 3 = 1 70+1 = 71 F) should be the answer

registerincog wrote:

What is the greatest possible number of nonfiction books in this home library? A) 18 B) 40 C) 67 D) 72 E) 96

Re: In a home library consisting of 108 books, some hardcover an [#permalink]
06 Apr 2014, 06:24

Expert's post

boonoobo wrote:

The ratio of hardcove and softcover is not given. To maximize the # of books I choose 105xhardcover and 3xsoftcover. 2/3 of 105 = 70 and 1/3 of 3 = 1 70+1 = 71 F) should be the answer

registerincog wrote:

What is the greatest possible number of nonfiction books in this home library? A) 18 B) 40 C) 67 D) 72 E) 96

F) 71

It is \(\frac{1}{4}\) not \(\frac{1}{3}\) _________________

Re: In a home library consisting of 108 books, some hardcover an [#permalink]
04 Sep 2014, 20:21

2

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

registerincog wrote:

In a home library consisting of 108 books, some hardcover and some softcover, exactly 2/3 of the hard cover and exactly 1/4 of the softcover books are nonfiction. What is the greatest possible number of nonfiction books in this home library?

A) 18 B) 40 C) 67 D) 72 E) 96

Hardcover + Softcover = 108

(2/3)*Hardcover + (1/4)*Softcover = Non fiction

We want to maximize the Non fiction books. Note that if more books are Hardcover, more books will be Non Fiction since a higher proportion (2/3 as compared with 1/4 of softcover) of Hardcover books are Non Fiction. Since there must be Softcover books too, we must have at least 4 Softcover books (so that (1/4)*4 = 1 - an integer) So the rest 104 can be Hardcover but note that (2/3)*104 is not an integer since 104 is not divisible by 3.

If there are 8 softcover books, 100 is again not divisible by 3. If there are 12 softcover books, 96 is divisible by 3. So number of hardcover books much be 96.

(2/3)*96 + (1/4)*12 = Non fiction 64 + 3 = 67 = No of non fiction books

Re: In a home library consisting of 108 books, some hardcover an [#permalink]
24 Sep 2014, 21:43

VeritasPrepKarishma wrote:

registerincog wrote:

In a home library consisting of 108 books, some hardcover and some softcover, exactly 2/3 of the hard cover and exactly 1/4 of the softcover books are nonfiction. What is the greatest possible number of nonfiction books in this home library?

A) 18 B) 40 C) 67 D) 72 E) 96

Hardcover + Softcover = 108

(2/3)*Hardcover + (1/4)*Softcover = Non fiction

We want to maximize the Non fiction books. Note that if more books are Hardcover, more books will be Non Fiction since a higher proportion (2/3 as compared with 1/4 of softcover) of Hardcover books are Non Fiction. Since there must be Softcover books too, we must have at least 4 Softcover books (so that (1/4)*4 = 1 - an integer) So the rest 104 can be Hardcover but note that (2/3)*104 is not an integer since 104 is not divisible by 3.

If there are 8 softcover books, 100 is again not divisible by 3. If there are 12 softcover books, 96 is divisible by 3. So number of hardcover books much be 96.

(2/3)*96 + (1/4)*12 = Non fiction 64 + 3 = 67 = No of non fiction books

Re: In a home library consisting of 108 books, some hardcover an [#permalink]
12 Oct 2014, 05:24

mau5 wrote:

registerincog wrote:

In a home library consisting of 108 books, some hardcover and some softcover, exactly \(2/3\) of the hard cover and exactly \(1/4\) of the softcover books are nonfiction. What is the greatest possible number of nonfiction books in this home library?

A) 18 B) 40 C) 67 D) 72 E) 96

Method I: # of hardcover books : 12x ; # of softcover : 108-12x

Thus, 8x+(27-3x) = # of non-fiction books(n)

or 5x = n-27

\(12x = \frac{n-27}{5}*12\) As No of hardcover books is an integral quantity, thus, (n-27) has to be a multiple of 5.

Only option C makes that.

Method II: As a greater fraction of hardcover books is NF, we must maximize that in no. Also, the remaining no of books(which are softcover) must be a multiple of 4.

As lcm of both 3 and 4 is 12, thus the maximum # of hardcover books = 108-12 = 96 and # of softcover = 12.

Thus, # of non-fiction :\(\frac{2}{3}*96+\frac{1}{4}*12 = 64+3 = 67.\)

C.

hey, i wanna ask you about the method 1, how about 72 which is also a multiple of 5. (72-27)=45 i can't get it...thanks

In a home library consisting of 108 books, some hardcover an [#permalink]
09 Nov 2014, 12:46

1

This post received KUDOS

I tried applying the concept I learnt here somewhere: So I got 2/3 HC + 1/4 SC. and we have to maximize this.

Let's take a common LCM o12.

8/12 HC + 3/12SC.

3/12 (HC+SC)+ 5/12 HC

3/12 (108) + 5/12 * HC

27 + 5/12 * HC...But I don't understand what to do now...

I do understand the plug in way, but would like to understand this one as well please.

EDIT: I figured it out. So now plug in the greatest possible value of HC under 108 which is divisible by 12. that would be 96. That gives us 5/12 * 96 = 40.

Therefore non fiction books are 40+27=67

gmatclubot

In a home library consisting of 108 books, some hardcover an
[#permalink]
09 Nov 2014, 12:46

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

McCombs Acceptance Rate Analysis McCombs School of Business is a top MBA program and part of University of Texas Austin. The full-time program is small; the class of 2017...