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

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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