Problem Solving

Vincen wrote: ↑

Sat Dec 04, 2021 1:58 pm

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 student 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

Answer: D

Source: GMAT Prep

GIVEN: The average number of books per student was 2
There are 30 students in total.
We can write: (total number of books borrowed)/30 = 2
Multiply both sides by 30 to get: total number of books borrowed = 60

2 students borrowed 0 books. (2)(0) = 0 books borrowed
12 students borrowed 1 book. (12)(1) = 12 books borrowed
10 students borrowed 2 books. (10)(2) = 20 books borrowed
6 students borrowed 3 or more books. We'll leave this one for now

0 + 12 + 20 = 32

60 - 32 = 28
So there are 28 borrowed books that are unaccounted for

This means the six students who borrowed three or more books must have borrowed a total of 28 books.
Our goal is to MAXIMIZE the number of books a single student borrowed.

To do this, we will MINIMIZE the number of books five of those students borrowed, which will leave all of the remaining books for the sixth student.
Since the six students borrowed three or more books, 3 is the minimum number of books one can borrow.
So, if five of the students borrowed 3 books each, this will account for 15 books.

28 - 15 = 13
So the remaining (the 6th) student must have borrowed 13 books

Answer: D