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IMAS 2023–2024 — Middle Primary — Round 2 Question 2

IMAS · IMAS 2023–2024 — Middle Primary — Round 2

Question 2

Each of Alex, Ben and Carl writes down 120 numbers from 1 to 500. If a number appears on more than one list, it is erased from all the lists. In the end, Alex’s list has 81 numbers left and Ben’s list has 70 numbers left. What is the positive difference between the maximum and the minimum possible number of numbers that are left on Carl’s list?
  1. $31$
  2. $78$
  3. $81$
  4. $92$
  5. $109$