2022 AMC 10A Problems/Problem 8
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Problem
A data set consists of not distinct) positive integers:
,
,
,
,
, and
. The
average (arithmetic mean) of the
numbers equals a value in the data set. What is
the sum of all positive values of
?
Solution
Case 1: the mean is
.
Case 2: the mean is
.
Case 3: the mean is
.
Hence, adding up the cases, the answer is .
~MrThinker
See Also
2022 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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 10 Problems and Solutions |
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