In a class of 20 students, 10 boys brought 11 books each and 6 girls brought 13 books each. Remaining students brought atleast on book each and no two students brought the same number of books. If the average number of books brought in the class is a positive integer, then what could be the total number of books brought by the remaining students?

Options

A. 12
B. 16
C. 14
D. 8

Answer

A

Explanation

10 boys brought 11 books each. Therefore, total number of books brought by 10 boys = 110. Six girls brought 13 books eack. Therefore, total number of books brought by 6 girls = 78.
Remaining number of students are 4 and the total number of books brought by student = x.
Given that `(x + 78 + 110)/(20)` is a positive integer.
If x = 12 then the above value is an integer.