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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? 
  1. 10
  2. 12
  3. 8
  4. 11
  5. 9


Solution

The correct option is A 10

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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