2024 AMC 12A Problems/Problem 5
Contents
[hide]Problem
A data set containing numbers, some of which are , has mean . When all the 6s are removed, the data set has mean . How many 6s were in the original data set?
Solution
Because the set has numbers and mean , the sum of the terms in the set is .
Let there be sixes in the set.
Then, the mean of the set without the sixes is . Equating this expression to and solving yields , so we choose answer choice .
Solution 2
Let be the sum of the data set without the sixes and be the number of sixes. We are given that and ; the former equation becomes and the latter . Since we want , we equate the two equations and see that .
~Technodoggo
Solution 3
Suppose there are sixes. Then the sum of all the numbers can be written as
Then, the mean of this set is . Solving this, we get
See Also
2024 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 4 |
Followed by Problem 6 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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