Math Prize 2014 Problem 15
Source:
September 29, 2014
inequalities
Problem Statement
There are two math exams called A and B. 2014 students took the A exam and/or the B exam. Each student took one or both exams, so the total number of exam papers was between 2014 and 4028, inclusive. The score for each exam is an integer from 0 through 40. The average score of all the exam papers was 20. The grade for a student is the best score from one or both exams that she took. The average grade of all 2014 students was 14. Let be the greatest possible number of students who took both exams. Let be the least possible number of students who took both exams. Compute .