GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Oct 2019, 21:44

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

In a class of 30 students, 2 students did not borrow any

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 26 Nov 2009
Posts: 621
Location: Singapore
Concentration: General Management, Finance
Schools: Chicago Booth - Class of 2015
GMAT ToolKit User
In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 30 Sep 2010, 11:17
3
1
28
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (02:22) correct 33% (02:48) wrong based on 485 sessions

HideShow timer Statistics

In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58409
Re: Word problems  [#permalink]

Show Tags

New post 25 Mar 2012, 11:33
9
11
In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15

"The average number of books per student was 2" means that total of 2*30=60 books were borrowed;
2+12+10=24 students borrowed total of 2*0+12*1+10*2=32 books;
So 60-32=28 books are left to distribute among 30-24=6 students, these 6 are "the rest who borrowed at least 3 books";

To maximize the number of books one student from above 6 could have borrowed we should minimize the number of books other 5 students from 6 could have borrowed. Minimum these 5 students could have borrowed is 3 books per student, so total number of books they could have borrowed is 5*3=15 books. So the 6th student could have borrowed is 28-15=13 books.

Answer: D.

Hope it's clear.
_________________
Most Helpful Community Reply
Manager
Manager
avatar
Joined: 06 Aug 2010
Posts: 153
Location: Boston
Re: max books  [#permalink]

Show Tags

New post 30 Sep 2010, 11:28
5
2
(D), 13

We know that 2 students borrowed 0 books, 12 borrowed 1 book, 10 borrowed 2 books, and 6 borrowed 3 or more books. The average of books per student is 2.

Let a, b, c, d, e, and f be the number of books borrowed by each of the 6 students who borrowed 3 or more.

So we have:

\(\frac{12 + 20 + a + b + c + d + e + f}{30} = 2\)

\(a + b + c + d + e + f = 28\)

Now, to maximize one of these, we need to minimize the other 5. So set them all equal to 3:

\(3 + 3 + 3 + 3 + 3 + f = 28\)

\(f = 28 - 15 = 13\)

So the maximum is 13.
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58409
Re: max books  [#permalink]

Show Tags

New post 30 Sep 2010, 11:22
3
6
In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15

"The average number of books per student was 2" means that total of 2*30=60 books were borrowed;
2+12+10=24 students borrowed total of 2*0+12*1+10*2=32 books;
So 60-32=28 books are left to distribute among 30-24=6 students, these 6 are "the rest who borrowed at least 3 books";

To maximize the number of books one student from above 6 could have borrowed we should minimize the number of books other 5 students from 6 could have borrowed. Minimum these 5 students could have borrowed is 3 books per student, so total number of books they could have borrowed is 5*3=15 books. So the 6th student could have borrowed is 28-15=13 books.

Answer: D.

Hope it's clear.
_________________
Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 726
Location: London
GMAT ToolKit User Reviews Badge
Re: max books  [#permalink]

Show Tags

New post 30 Sep 2010, 11:55
Total book borrowed = 30*2 = 60
2 borrowed 0 books, 12 borrowed 1 book, 10 borrowed 2 books; So that accounts for 32 books, leaving 28 books for the 6 students
And we know that each of these had atleast 3 books

To maximize the highest number of books, give all but one student 3 books (the minimum they must have) and all the rest to the last student
So 5 students get a total of 15 books; leaving 13 for the last student.

Answer = (D)
_________________
Intern
Intern
avatar
Joined: 30 Nov 2011
Posts: 23
Location: United States
GMAT 1: 700 Q47 V38
GPA: 3.54
In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 25 Mar 2012, 11:30
2
1
In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ?

A. 3
B. 5
C. 8
D. 13
E. 15
Intern
Intern
avatar
Joined: 30 Nov 2011
Posts: 23
Location: United States
GMAT 1: 700 Q47 V38
GPA: 3.54
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 26 Mar 2012, 01:05
thanks Bunuel, explanation very clear.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58409
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 14 Jun 2013, 05:27
Manager
Manager
avatar
Joined: 20 Dec 2013
Posts: 224
Location: India
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 17 Feb 2014, 08:32
Option D.
A total of 2(no book)+12(1 book)+10(2 books)=24 students borrowed 32 books.
Total books borrowed=30*2=60
Books left=28
Rest of the students borrowed at least 3 books each=>6*3=18
Now to maximize books borrowed by any one individual we'll suppose,28-18=10 have been borrowed by one person only.
Max total becomes=3+10=13

Posted from my mobile device
Manager
Manager
User avatar
Joined: 03 Oct 2014
Posts: 126
Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
WE: Engineering (Aerospace and Defense)
Reviews Badge
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 26 Jan 2015, 12:06
D - 13.....Distribute 3 books to remaining 6....total will come 50....but our total should be 60......so 60-50 = 10....add original 3....10+3 = 13
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1749
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 02 Feb 2015, 22:51
1
Average for 30 students = 2, so total books = 60

Un-allocated books =

60 - (1*12 + 2*10+3*6) = 60 - 50 = 10

Maximum books per individual possible = 10+3 = 13

Answer = D
_________________
Kindly press "+1 Kudos" to appreciate :)
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 357
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 31 Oct 2016, 11:02
X/30 (total students) = 2 --> x = 60 (# of books checked out)

We have 12+2(10)+6(at least 3), leaving us with 10 to account for, thus one of the students who borrowed at least 3, could add on an additional 10 books, walking out with a total of 13.
Manager
Manager
User avatar
P
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 31 Oct 2016, 12:09
here is the solution of this problem,

Hope it is clear
Attachments

IMAG0321.jpg
IMAG0321.jpg [ 774.63 KiB | Viewed 5145 times ]


_________________
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2568
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 18 Dec 2016, 17:07
Amazing Official Question.
Here is what i did in this Question =>


12*1=> 12
10*2=> 20
So 32 books are borrowed by 22 students
Sum(30)=2*30=60

Hence 6 students borrow 60-32 = 28 books
Now the least books borrows by them => 3
So for the maximum number => 3,3,3,3,3,3,x => x= 28-15 = 13


Hence D

_________________
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8099
Location: United States (CA)
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 11 Apr 2018, 16:25
nusmavrik wrote:
In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?

A. 3
B. 5
C. 8
D. 13
E. 15


Since the average number of books per student was 2, the total number of books borrowed was 2 x 30 = 60 books.

The number of books borrowed by the students who borrowed two or fewer books is 2 x 0 + 12 x 1 + 10 x 2 = 32.

These 32 books were borrowed by 2 + 12 + 10 = 24 students.

So we have 60 - 32 = 28 books left for the remaining 6 students. Since we want to maximize the number of books borrowed by a single student, we must minimize the number of books borrowed by the other 5 students. We see that if 5 of these students borrowed 3 books each, then we have 28 - 15 = 13 books for the last student.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13239
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 15 Oct 2019, 08:51
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: In a class of 30 students, 2 students did not borrow any   [#permalink] 15 Oct 2019, 08:51
Display posts from previous: Sort by

In a class of 30 students, 2 students did not borrow any

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne