help

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