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2024 AMC 12A Problem 5

Problem 5 of 25EasierAlgebraProbability & Statistics

A data set containing 2020 numbers, some of which are 6,6, has mean 45.45. When all the 66s are removed, the data set has mean 66.66. How many 66s were in the original data set?

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Solution

The full set sums to 20⋅45=900.20\cdot45=900. Removing kk sixes leaves 20−k20-k numbers summing to 900−6k,900-6k, with mean 66,66, so 900−6k=66(20−k)900-6k=66(20-k) =1320−66k.=1320-66k. Then 60k=420,60k=420, giving k=7.k=7. Thus, the correct answer is D.
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Tagged: mean · linear equation

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