Difference between revisions of "2022 AMC 10A Problems/Problem 8"
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<math>\textbf{(A) } 10 \qquad \textbf{(B) } 26 \qquad \textbf{(C) } 32 \qquad \textbf{(D) } 36 \qquad \textbf{(E) } 40</math> | <math>\textbf{(A) } 10 \qquad \textbf{(B) } 26 \qquad \textbf{(C) } 32 \qquad \textbf{(D) } 36 \qquad \textbf{(E) } 40</math> | ||
| − | ==Solution== | + | ==Solution (Casework)== |
| + | First, note that <math>1+7+5+2+5=20</math>. Then, there are 3 cases. | ||
'''Case 1: the mean is <math>5</math>''' | '''Case 1: the mean is <math>5</math>''' | ||
Revision as of 08:06, 14 November 2022
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 (Casework)
First, note that 
. Then, there are 3 cases.
Case 1: the mean is
.
Case 2: the mean is
.
Case 3: the mean is
.
Hence, adding up the cases, the answer is 
.
~MrThinker
Video Solution 1 (Quick and Simple)
~Education, the Study of Everything
See Also
| 2022 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 | ||
| 2022 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 5 |
Followed by Problem 7 |
| 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. 
