AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 12 Easy

A data set containing 20 numbers, some of which are 6, has mean 45. When all the 6s are removed, the data set has mean 66. How many 6s were in the original data set?

  • A.

    4

  • B.

    5

  • C.

    6

  • D.

    7

  • E.

    8

Answer:D

Let the number of 6s in the original data set be k. Numbers in the original data set have sum 20 \cdot 45 = 900, and the data set with the 6s removed has sum 900 - 6k. Thus

\frac{900 - 6k}{20 - k} = 66.

Solving this equation for k yields k = 7. For example, the data set could consist of 7 copies of 6 and 13 copies of 66.

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