Arithmetic Mean

In a class of 30 students, 2 did not borrow any books, 12 borrowed 1 book, 10 borrowed 2 books and the rest borrowed at least 3 books. The average (arithmetic mean) number of book borrowed per student was 2. What is the maximum number of books that any single student could have borrowed?

1. 3
2. 5
3. 8
4. 13
5. 15

Total number of books borrowed = (average)*(number of students) = 2*30 = 60.
Since 2 students do not borrow any books, the number of students borrowing = 30-2 = 28.

From here we can plug in the answer choices, which represent the maximum number of books that any single student could have borrowed.

Answer choice E: 15
60-15 = 45 books left.
10 students borrowed 2 books each = 10*2 = 20 books.
45-20 = 25 books left.
12 students borrowed 1 book each = 12*1 = 12 books.
25-12 = 13 books left.
Number of students left = 28-1-10-12 = 5.
These remaining students must borrow at least 3 books each:
5*3 = 15 books.
Doesn't work, since only 13 books remain.

Since 2 MORE BOOKS are required for the 5 remaining students, the maximum number of books that a student can borrow must DECREASE BY 2.

The correct answer is D.

but in the GMAT prep it is 13.pLEASE HELP