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?
:
C
solution: option (c)
there are totally 15 students (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
Approach 2-Reverse Gear
Go from answer options.
option (c)
If 11 students score 16, then 176 marks are distributed. We next need to distribute 18x3 =54 marks. Total
= 230. Only 10 marks are left. Since minimum possible score is 12 for a student, 11 cannot be the answer
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