• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

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

This topic has 3 expert replies and 0 member replies

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

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Source: GMAT Prep

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 students 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 OA is D

  • +1 Upvote Post
  • Quote
  • Flag
Post
BTGmoderatorLU wrote:
Source: GMAT Prep

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 students 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 OA is D
Total number of books borrowed = T = 30*2 = 60;

Total number of books borrowed by 12 students = A = 1*12 = 12;

Total number of books borrowed by 10 students = B = 2*10 = 20;

Thus, the number of students who borrowed at least 3 books = 30 - 2 - 12 - 10 = 6;

Since we need to maximize the number of books any single student can borrow, let's assume that out of the remaining 6 students, barring ONE student, 5 borrowed the minimum number of books, i.e., 3 each.

Thus, the total number of books borrowed by 5 students = C = 3*5 = 15;

Say, the single student borrowed D number of books; thus, we have

T = A + B + C + D

60 = 12 + 20 + 15 + D

=> D = 13

The correct answer: D

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Classes Singapore | GMAT Tutoring Zurich | GRE Prep Hyderabad | TOEFL Prep Classes Manhattan | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
BTGmoderatorLU wrote:
Source: GMAT Prep

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 students 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 OA is D
The average (arithmetic mean) number of book borrowed per student was 2.
Since there are 30 students altogether, the total number of borrowed books = (2)(30) = 60

2 students borrowed 0 books: total of 0 books
12 students borrowed 1 book each: total of 12 books
10 students borrowed 2 books each: total of 20 books
6 students borrowed 3 or more books each: total of 28 books (since the total borrowed books must equal 60)

Now we'll focus on the 6 students who borrowed a total of 28 books.
In order to MAXIMIZE the number of books that one students borrowed, we need to MINIMIZE the number of books that the other 5 students borrowed.
Each student must borrow at least 3 books, so let's say that those 5 students borrowed 3 books each.
This accounts for 15 books, which means the last remaining student borrowed 13 books.

Answer: D

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Post
BTGmoderatorLU wrote:
Source: GMAT Prep

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 students 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 OA is D
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



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Top First Responders*

1 Ian Stewart 53 first replies
2 Brent@GMATPrepNow 36 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 25 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

76 posts
4 image description Ian Stewart

GMATiX Teacher

62 posts
5 image description GMATGuruNY

The Princeton Review Teacher

44 posts
See More Top Beat The GMAT Experts