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. number theory proposednumber theory