help

This topic has expert replies
Legendary Member
Posts: 512
Joined: Mon Jun 18, 2012 11:31 pm
Thanked: 42 times
Followed by:20 members

help

by sana.noor » Wed Jul 31, 2013 3:15 am
3. 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

OA is D
Last edited by sana.noor on Wed Jul 31, 2013 7:04 am, edited 1 time in total.
Work hard in Silence, Let Success make the noise.

If you found my Post really helpful, then don't forget to click the Thank/follow me button. :)
Source: — Problem Solving |

Master | Next Rank: 500 Posts
Posts: 145
Joined: Fri Jan 18, 2013 8:27 am
Thanked: 7 times

by sparkles3144 » Wed Jul 31, 2013 5:28 am
Mean = 2 books/student
Total students = 30
Total number of books = 30*2 = 60

2 students borrowed 0 books = 2* 0 = 0
12 students borrowed 1 book = 12* 1 = 12
10 students borrowed 2 books = 10* 2 = 20

Total books borrowed by (2+12+10 = 24) students is 0+12+20 = 32 books

24 students borrowed 32 books

Remaning students = 30-24 = 6
Remaning students = 60-32 = 28

6 remaining students borrowed 28 book total

Each of the six students borrowed at least 3.

Lets just say 5 students borrowed the minimum, i.e., three books each.

Out of 6 students,

5*3 = 15

28-15 = 13 books left for the last person to borrow

Hope it makes sense!

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Jul 31, 2013 6:14 am
sana.noor wrote:3. 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
Please note: When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

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
Image