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: 872
Location: Singapore
Concentration: General Management, Finance
Schools: Chicago Booth  Class of 2015

In a class of 30 students, 2 students did not borrow any [#permalink]
Show Tags
30 Sep 2010, 11:17
Question Stats:
68% (01:36) correct 32% (01:57) wrong based on 460 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
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 46307

Re: max books [#permalink]
Show Tags
30 Sep 2010, 11:22
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 6032=28 books are left to distribute among 3024=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 2815=13 books. Answer: D. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 06 Aug 2010
Posts: 192
Location: Boston

Re: max books [#permalink]
Show Tags
30 Sep 2010, 11:28
(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: 775
Location: London

Re: max books [#permalink]
Show Tags
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)
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 30 Nov 2011
Posts: 29
Location: United States
GPA: 3.54

In a class of 30 students, 2 students did not borrow any [#permalink]
Show Tags
25 Mar 2012, 11:30
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



Math Expert
Joined: 02 Sep 2009
Posts: 46307

Re: Word problems [#permalink]
Show Tags
25 Mar 2012, 11:33
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 6032=28 books are left to distribute among 3024=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 2815=13 books. Answer: D. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 30 Nov 2011
Posts: 29
Location: United States
GPA: 3.54

Re: In a class of 30 students, 2 students did not borrow any [#permalink]
Show Tags
26 Mar 2012, 01:05
thanks Bunuel, explanation very clear.



Math Expert
Joined: 02 Sep 2009
Posts: 46307

Re: In a class of 30 students, 2 students did not borrow any [#permalink]
Show Tags
14 Jun 2013, 05:27



Senior Manager
Joined: 20 Dec 2013
Posts: 250
Location: India

Re: In a class of 30 students, 2 students did not borrow any [#permalink]
Show Tags
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,2818=10 have been borrowed by one person only. Max total becomes=3+10=13
Posted from my mobile device



Manager
Joined: 03 Oct 2014
Posts: 138
Location: India
Concentration: Operations, Technology
WE: Engineering (Aerospace and Defense)

Re: In a class of 30 students, 2 students did not borrow any [#permalink]
Show Tags
26 Jan 2015, 12:06
D  13.....Distribute 3 books to remaining 6....total will come 50....but our total should be 60......so 6050 = 10....add original 3....10+3 = 13



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
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
02 Feb 2015, 22:51
Average for 30 students = 2, so total books = 60 Unallocated 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
Status: DONE!
Joined: 05 Sep 2016
Posts: 398

Re: In a class of 30 students, 2 students did not borrow any [#permalink]
Show Tags
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
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 65

Re: In a class of 30 students, 2 students did not borrow any [#permalink]
Show Tags
31 Oct 2016, 12:09
here is the solution of this problem, Hope it is clear
Attachments
IMAG0321.jpg [ 774.63 KiB  Viewed 2175 times ]
_________________
Cours particuliers de GMAT



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154

Re: In a class of 30 students, 2 students did not borrow any [#permalink]
Show Tags
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 6032 = 28 books Now the least books borrows by them => 3 So for the maximum number => 3,3,3,3,3,3,x => x= 2815 = 13
Hence D
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2779
Location: United States (CA)

Re: In a class of 30 students, 2 students did not borrow any [#permalink]
Show Tags
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 WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: In a class of 30 students, 2 students did not borrow any
[#permalink]
11 Apr 2018, 16:25






