Question

In an examination, the maximum marks a student can score is 20 and the minimum is 12. The students score an average of 16 marks. 3 students score 18 or more. If the sum of the scores of all the students is 240, what is the maximum number of students who can score exactly 16 marks?

• A. 9
• B. 11
• C. 10
• D. 8

Answer 1

The correct option is C 10

There are totally 15 students $\frac{240}{16}$

3 students score 18 or more marks.

We need to maximize the number of students scoring 16, hence, assume that 3 students have scored 18 marks.

The average is 16, to balance the +6 surplus, there is one student who scores 14 and one student who scores 12.

All the remaining students score exactly 16. Maximum = 15-3-2 =10