In a class of 30 students, 2 students did not borrow any : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 19:18

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# 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

Director
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: 997
Location: Singapore
Followers: 22

Kudos [?]: 747 [2] , given: 36

In a class of 30 students, 2 students did not borrow any [#permalink]

### Show Tags

30 Sep 2010, 10:17
2
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:41) correct 32% (01:51) wrong based on 265 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
[Reveal] Spoiler: OA

_________________

Please press kudos if you like my post.

Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7067

Kudos [?]: 92926 [0], given: 10528

Re: max books [#permalink]

### Show Tags

30 Sep 2010, 10:22
Expert's post
7
This post was
BOOKMARKED
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.

Hope it's clear.
_________________
Manager
Joined: 06 Aug 2010
Posts: 225
Location: Boston
Followers: 3

Kudos [?]: 183 [2] , given: 5

Re: max books [#permalink]

### Show Tags

30 Sep 2010, 10:28
2
KUDOS
(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.
Retired Moderator
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 105

Kudos [?]: 956 [0], given: 25

Re: max books [#permalink]

### Show Tags

30 Sep 2010, 10:55
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.

_________________
Senior Manager
Joined: 20 Dec 2013
Posts: 273
Location: India
Followers: 0

Kudos [?]: 81 [0], given: 29

Re: In a class of 30 students, 2 students did not borrow any [#permalink]

### Show Tags

17 Feb 2014, 07:32
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
Current Student
Joined: 03 Oct 2014
Posts: 145
Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
WE: Engineering (Aerospace and Defense)
Followers: 2

Kudos [?]: 29 [0], given: 89

Re: In a class of 30 students, 2 students did not borrow any [#permalink]

### Show Tags

26 Jan 2015, 11:06
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
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 47

Kudos [?]: 1928 [1] , given: 193

Re: In a class of 30 students, 2 students did not borrow any [#permalink]

### Show Tags

02 Feb 2015, 21:51
1
KUDOS
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

_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13419
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: In a class of 30 students, 2 students did not borrow any [#permalink]

### Show Tags

11 Feb 2016, 22:12
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.
_________________
Senior Manager
Status: Exam scheduled!!
Joined: 05 Sep 2016
Posts: 411
Location: United States (WI)
Concentration: Marketing, Technology
WE: Other (Law)
Followers: 3

Kudos [?]: 13 [0], given: 236

Re: In a class of 30 students, 2 students did not borrow any [#permalink]

### Show Tags

31 Oct 2016, 10:02
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
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 54
Followers: 4

Kudos [?]: 24 [0], given: 15

Re: In a class of 30 students, 2 students did not borrow any [#permalink]

### Show Tags

31 Oct 2016, 11:09
here is the solution of this problem,

Hope it is clear
Attachments

IMAG0321.jpg [ 774.63 KiB | Viewed 277 times ]

_________________
Re: In a class of 30 students, 2 students did not borrow any   [#permalink] 31 Oct 2016, 11:09
Similar topics Replies Last post
Similar
Topics:
5 In a class of 50 students, 10 did not opt for math. 15 did not opt for 4 19 Aug 2015, 21:51
18 60% of all students in a class commute by public transportation. If 30 10 13 May 2015, 06:31
9 In a class of 30 students, 2 students did not borrow any 6 25 Mar 2012, 10:30
2 There are n new students in a class. Among any three of them, there 5 08 Sep 2010, 17:55
4 In a class of 30 students, 2 students did not borrow any boo 4 06 Oct 2009, 11:32
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 and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.