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MathNet 2021 — Part 09 Question 90

Math Olympiad Vault · MathNet 2021 — Part 09

Question 90

A school has 100 students and 5 teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are 50, 20, 20, 5, and 5. Let $t$ be the average value obtained if a teacher is picked at random and the number of students in their class is noted. Let $s$ be the average value obtained if a student is picked at random and the number of students in their class, including that student, is noted. What is $t-s$?
  1. $-18.5$
  2. $-13.5$
  3. $0$
  4. $13.5$
  5. $18.5$