To find the minimum number of students with more than 3 points, we should try to accommodate as much students as possible at 3 points each And after we have accommodated enough students affective points each, remaining students will be accommodated at more than 3 points. In case of elective A, maximum number of students who can get 3 points = 3. Hence, remaining 3 students are getting a total of 12 points. And in no way these 3 students are getting 3 points or less than 3 points to satisfy the conditions given In case of elective C, the minimum number of students that can be accommodated at 3 points each = 3. Hence, total points = 9. Now, remaining 19 points are to accommodated among4 students and none of these to year students can get 3 points or less than 3 points [Otherwise then 16 points will be required to be accommodated among 3 students and in that case atleast one student will get more than 5 points and that is a contradiction). We can further see that each of these students will get more than 3 points now to satisfy the given conditions. Hence, minimum number of the students who have scored more than 3 points in atleast one elective = 4.