2018 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 14 Medium

A list of 2018 positive integers has a unique mode, which occurs exactly 10 times. What is the least number of distinct values that can occur in the list? (2018 AMC 10B Problem, Question#14)

  • A.

    202

  • B.

    223

  • C.

    224

  • D.

    225

  • E.

    234

Answer:D

To minimize the number of distinct values, we want to maximize the number of times they appear. So, we could have 223 numbers appear 9 times, 1 number appear once, and the mode appear 10 times, giving us a total of 223+1+1 =\rm (D)~225.

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