IT-CESENATICO 2010 Problem 1

In a mathematics test number of participants is $N < 40$ . The passmark is fixed at $65$ . The test results are the following: The average of all participants is $66$ , that of the promoted $71$ and that of the repeaters $56$ . However, due to an error in the wording of a question, all scores are increased by $5$ . At this point the average of the promoted participants becomes $75$ and that of the non-promoted $59$ . (a) Find all possible values of $N$ . (b) Find all possible values of $N$ in the case where, after the increase, the average of the promoted had become $79$ and that of non-promoted $47$ .