1988 AJHSME Problems/Problem 21
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Problem
A fifth number, , is added to the set to make the mean of the set of five numbers equal to its median. The number of possible values of is
Solution
The possible medians after is added are , , or . Now we use casework.
Case 1: The median is
In this case, and so this case contributes .
Case 2: The median is
We have and so this case also contributes .
Case 3: The median is
We have and so this case adds .
In all there are possible values of .
See Also
1988 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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 AJHSME/AMC 8 Problems and Solutions |
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