Question 24
Some students sat for a test. The first group of students scored an average of $91$ marks and were given Grade A. The second group of students scored an average of $80$ marks and were given Grade B. The last group of students scored an average of $70$ marks and were given Grade C. The numbers of students in all three groups are prime numbers and the total score of all the students is $1785$. Determine the total number of students.