BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

How many books we could borrow

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 70
Joined: Mon May 12, 2008 12:26 pm
Thanked: 3 times
by adam15 » Sun Dec 06, 2009 2:47 pm
In class of 30 students, 2 did not borrow any books from the liberary, 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 ( arithemtic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?
3
5
8
13
15
Last edited by adam15 on Sun Dec 06, 2009 5:29 pm, edited 1 time in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Sun Dec 06, 2009 5:03 pm
adam15 wrote:In class of 30 students, 2 did not borrow any books from the liberary, 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 ( arithemtic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?
3
5
8
13
15
, my answer:

28 is the sum of books borrowed by the 6 students, the maximum book that each could have is
5*5+3; thus 5 of 6 will have 5, and one will have 3.
the number of books a single student could borrow will be:
5+3+2+1=11+2=13 (because the 2 students who did not borrow any book.
Assuming your math is correct to this point, here's where you made your mistake.

We want "the maximum number of books that any single student could have borrowed?"

Whenever you're asked to maximize one thing, you want to minimize everything else.

So, those 6 students must borrow 28 books and each one must borrow at least 3 books. To maximize a single student, we minimize the other 5 at 3 each, giving us:

28 - 5*3 = 28 - 15 = 13 books
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 70
Joined: Mon May 12, 2008 12:26 pm
Thanked: 3 times

by adam15 » Sun Dec 06, 2009 5:28 pm
Hy Stuart,
you totally right. I was think about my solution, and it seems weird. and I tried backsolving here is my backsolution and by the way thank you again or you solution.

let's start with the first choice. between parethensis the number of students left
60-3(28)=57-12(15)=45-20 (5)=25=5*5 and max(3,5)=5 so wrong.
second choice
60-5=55-12=43-20=23=5*4+3 so we still have tree book left
60-8=52-12=40-20=20=5*4 no book left maybe
60-13=47-12=35-20=15=5*3 no book left and max(13,8)=13.
60-15=45-12=33-20=13=5*2+3 we still have tree book left
then best answer choice will be 13
please correct me if wrong
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 487
Joined: Fri Mar 27, 2009 5:49 am
Thanked: 36 times

by dtweah » Mon Dec 07, 2009 11:04 am
adam15 wrote:In class of 30 students, 2 did not borrow any books from the liberary, 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 ( arithemtic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?
3
5
8
13
15
12(1) + 10(2)=32 books
12 +10 =22 students. 6 to divide remaining 28 books
Each of 6 must have 3 or 6x 3 =18 books. This leaves 10 extra books.
If one student takes all 10 in addition to his 3 he will have 13 books.
Choose D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1