Difference between revisions of "2019 AMC 12B Problems/Problem 7"
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Now let the mean=8 | Now let the mean=8 | ||
− | <math>\frac{35+x}{5}= | + | <math>\frac{35+x}{5}=8</math> when <math>x=5</math> and the sequence is 4, 5, 6, 8, 17 which has median 6 so no go. |
Finally we let the mean=x | Finally we let the mean=x |
Revision as of 12:49, 14 February 2019
Problem
4, 6, 8, 17, x
What is the sum of all values of x such that the mean is equal to the median?
Solution
The mean is .
There are 3 possibilities: either the median is 6, 8, or x.
Let's start with 6.
when and the sequence is -5, 4, 6, 8, 17 which has 6 as the median so we're good.
Now let the mean=8
when and the sequence is 4, 5, 6, 8, 17 which has median 6 so no go.
Finally we let the mean=x
and the sequence is 4, 6, 8, 8.75, 17 which has median 8 so no go.
So the only option for x is
--mguempel
See Also
2019 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 6 |
Followed by Problem 8 |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.