GAUSS7 2023 Problem 25

A school trip offered its participants three activities: hiking, canoeing and swimming. Attendance records show that of all participants

  • 10 students participated in all three activities,
  • 50 \% participated in at least hiking and canoeing,
  • 60 \% participated in at least hiking and swimming,
  • k \% participated in at least canoeing and swimming, and
  • no students participated in fewer than two activities.

If k is a positive integer, what is the sum of all possible values of k?

Answer Choices
A. 191
B. 185
C. 261
D. 95
E. 175