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 500,000 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]

Show Tags

16 Nov 2013, 06:23

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

58% (03:23) correct
42% (03:11) wrong based on 189 sessions

HideShow timer Statictics

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]

Show Tags

16 Nov 2013, 06:46

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]

Show Tags

02 Apr 2014, 11:18

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]

Show Tags

06 Apr 2014, 07:24

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]

Show Tags

04 Sep 2014, 21:21

3

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]

Show Tags

24 Sep 2014, 22:43

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]

Show Tags

12 Oct 2014, 06:24

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]

Show Tags

09 Nov 2014, 13:46

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.

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

Show Tags

03 Apr 2016, 11:09

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

to get the greatest number of non-fiction books, hardcover needs to be maximized while softcover minimized. S=12 H=96 1/4 * S = 3 2/3 * H = 64 3+64=67

In a home library consisting of 108 books, some hardcover an [#permalink]

Show Tags

03 Apr 2016, 12:39

1. note higher proportion of hardcover nonfiction to softcover nonfiction--2/3:1/4 2. working downward from 108, identify the highest possible ratio of hardcovers to softcovers, where hardcovers are a multiple of 3 and softcovers are a multiple of 4, with a lcm of 12 3. highest possible ratio is 108-12=96 hardcover:12 softcover 4. (2/3)(96)+(1/4)(12)=64+3=67 maximum nonfiction books in library

gmatclubot

In a home library consisting of 108 books, some hardcover an
[#permalink]
03 Apr 2016, 12:39

So, my final tally is in. I applied to three b schools in total this season: INSEAD – admitted MIT Sloan – admitted Wharton – waitlisted and dinged No...

A few weeks ago, the following tweet popped up in my timeline. thanks @Uber_Mumbai for showing me what #daylightrobbery means!I know I have a choice not to use it...

“This elective will be most relevant to learn innovative methodologies in digital marketing in a place which is the origin for major marketing companies.” This was the crux...