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AMO 2027 Grades 8-9 SET 7 - Self-study Question 13

AMO · AMO 2027 Grades 8-9 SET 7 - Self-study

Question 13

When the mean, median, and mode of the list
$$10,2,5,2,4,2,x$$
are arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible real values of $x$?
  1. 3
  2. 6
  3. 9
  4. 17
  5. 20