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

It is currently 18 Jan 2019, 22:47

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
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 21 Sep 2006
Posts: 42
In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post Updated on: 02 Oct 2006, 13:34
1
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:26) correct 37% (01:08) wrong based on 121 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-class-of-30-students-2-students-did-not-borrow-any-101980.html

Originally posted by $uckafr33 on 02 Oct 2006, 10:39.
Last edited by $uckafr33 on 02 Oct 2006, 13:34, edited 1 time in total.
Director
Director
avatar
Joined: 17 Jul 2006
Posts: 631
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 02 Oct 2006, 11:57
I think answer is 15
Intern
Intern
avatar
Joined: 21 Sep 2006
Posts: 42
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 02 Oct 2006, 12:01
baski6 wrote:
I think answer is 15


Nope. Answer is 13.
GMAT Instructor
avatar
B
Joined: 04 Jul 2006
Posts: 1251
Location: Madrid
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 02 Oct 2006, 12:03
$uckafr33 wrote:
In a class of 30 students, 2 students did not borrow any books from the library, 12 students 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 student could have borrowed?

a) 3 b) 5 c) 8 d) 13 e) 15


Let's minimize the number of books that the 30 could borrow, according to the guidelines: 2(0)+12(1)+10(2)+6(3)=12+20+18=50. But we know that the sum is 30*2=60, so there are 10 books unaccounted for- give them to a GMAT student who has already borrowed 3 ==>3+10=13
SVP
SVP
User avatar
Joined: 01 May 2006
Posts: 1775
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 02 Oct 2006, 12:05
(D) for me..... and I think that there is typo problem ;)

As we look for the max x of books that a student can borrow, we can write

av(students) = 2 = (2*0 + 12*1 + 10*2 + (30-(2+12+10+1))*3 + 1*x) / 30
<=> 60 = 12 + 20 + 15 + x
<=> x = 13
Retired Moderator
User avatar
B
Joined: 05 Jul 2006
Posts: 1722
GMAT ToolKit User Premium Member
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 02 Oct 2006, 13:28
10 people each borrowed 12 books..........this is wrong

i think it is a typo....please check
Intern
Intern
avatar
Joined: 21 Sep 2006
Posts: 42
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 02 Oct 2006, 13:33
yezz wrote:
10 people each borrowed 12 books..........this is wrong

i think it is a typo....please check


My apologies...there is a typo. 10 students each borrowed 2 books.

But thanks understand how to solve this now.
Senior Manager
Senior Manager
avatar
Joined: 13 Sep 2006
Posts: 254
Location: New York
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 03 Oct 2006, 12:21
1
One more for 13...

2 students borrowed 0 books (TOTAL 0 books)
12 students borrowed 1 book each (TOTAL 12 Books)
10 students borrowed 2 books each (TOTAL 20 Books)

32 books so far for 24 students hence 6 students left unaccounted for.

Here is where I picked numbers. Say one student picks 13 then total number of books borroed is 45 and 5 students remain borrowing at lease 3 a piece (3*15 = 15). 15 +45 = 60 and 60 divided by 30 equals the mean of 2.
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1809
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 03 Jul 2011, 09:02
5
1
$uckafr33 wrote:
In a class of 30 students, 2 students did not borrow any books from the library, 12 students 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 student could have borrowed?

a) 3 b) 5 c) 8 d) 13 e) 15


Total-> 30 students
0 book-> 2 students
1 book-> 12 students
2 books-> 10 students

Remaining 6 students:
To maximize the number of books taken by any 1 student, let's give the rest of the students exactly the minimum possible i.e. 3 AND give the rest "x" to the one student who is going to take the maximum.

\(\frac{2*0+1*12+2*10+3*5+x*1}{30}=2\)

\(\frac{47+x}{30}=2\)

\(x=60-47=13\)

Ans: "D"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
User avatar
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 194
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 04 Jul 2011, 09:59
kevincan wrote:

Let's minimize the number of books that the 30 could borrow, according to the guidelines: 2(0)+12(1)+10(2)+6(3)=12+20+18=50. But we know that the sum is 30*2=60, so there are 10 books unaccounted for- give them to a GMAT student who has already borrowed 3 ==>3+10=13


Even i will go with the same approach and hence the same answer.... :) :)
_________________

WarLocK
_____________________________________________________________________________
The War is oNNNNNNNNNNNNN for 720+
see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html
do not hesitate me giving kudos if you like my post. :)

Manager
Manager
User avatar
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 194
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 04 Jul 2011, 10:00
fluke wrote:

Total-> 30 students
0 book-> 2 students
1 book-> 12 students
2 books-> 10 students

Remaining 6 students:
To maximize the number of books taken by any 1 student, let's give the rest of the students exactly the minimum possible i.e. 3 AND give the rest "x" to the one student who is going to take the maximum.

\(\frac{2*0+1*12+2*10+3*5+x*1}{30}=2\)

\(\frac{47+x}{30}=2\)

\(x=60-47=13\)

Ans: "D"


That was quite smart fluke
kudos given already :beer :beer
_________________

WarLocK
_____________________________________________________________________________
The War is oNNNNNNNNNNNNN for 720+
see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html
do not hesitate me giving kudos if you like my post. :)

Intern
Intern
User avatar
Joined: 03 Mar 2011
Posts: 16
GMAT 1: 620 Q46 V29
WE: Sales (Hospitality and Tourism)
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 08 Jul 2011, 18:29
Thanks Fluke for the explanation. one more kudo
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52285
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 22 Jan 2015, 03:35
$uckafr33 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-class-of-30-students-2-students-did-not-borrow-any-101980.html


"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.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9434
Premium Member
Re: In a class of 30 students, 2 students did not borrow any  [#permalink]

Show Tags

New post 08 Jan 2019, 00:17
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: In a class of 30 students, 2 students did not borrow any &nbs [#permalink] 08 Jan 2019, 00:17
Display posts from previous: Sort by

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

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®.