Problem:
A data set containing 20 numbers, some of which are 6 , has mean 45 . When all the 6 s are removed, the data set has mean 66 . How many 6 s were in the original data set?
Answer Choices:
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Solution:
Let the number of 6 s in the original data set be . Numbers in the original data set have sum , and the data set with the 6 s removed has sum . Thus
Solving this equation for yields . For example, the data set could consist of 7 copies of 6 and 13 copies of 66.
The problems on this page are the property of the MAA's American Mathematics Competitions