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by dreamv » Tue Feb 28, 2012 4:46 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 of the students each borrowed at least 3 books. If the average number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowe?

A. 3
B. 5
C. 8
D. 13
E. 15
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by GMATGuruNY » Tue Feb 28, 2012 7:19 pm
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by Anurag@Gurome » Tue Feb 28, 2012 9:04 pm
dreamv wrote: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 number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowe?

A. 3
B. 5
C. 8
D. 13
E. 15
Total number of books borrowed = 2 * 30 = 60
Number of students who borrowed books = 2 + 12 + 10 = 24
Number of books borrowed by 24 students = (2 * 0) + (12 * 1) + (10 * 2) = 32
Number of books left = 60 - 32 = 28
Number of students left among whom 28 books are to be distributed = 30 - 24 = 6
It is given that "the rest of the students each borrowed at least 3 books".
Now if 5 of the remaining students borrow 5 books per student, then total books borrowed by 5 students = 3 * 5 = 15
Hence, maximum books that can be borrowed by the 6th student = 28 - 15 = 13

The correct answer is D.
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by [email protected] » Wed Feb 29, 2012 8:57 am
Let us assume that the maximum number of books borrowed is by a student (from group 4: 6 students)is X:

Hence: (2*0+12*1+10*2+((6*3)+X))/30 = 2 (AVERAGE)

X=10:

Hence maximum books a person can borrow: 3 +10 = 13

Option D
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