1988 AMC 8 Problem 21
Attempt Problem 21 of the 1988 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1988 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
A fifth number, is added to the set of numbers to make the mean of the set of five numbers equal to its median. The number of possible values for is
more than
Answer: C
Small hint:
The mean of the five numbers is the median depends on where lands in the sorted order
Big hint:
Split into cases: the median is is itself, or is and solve the equation mean median in each
Solution:
The five numbers have sum and mean The median is the middle value when sorted, which is or depending on the size of
If the median is : gives which is indeed less than If the median is : gives which is between and If the median is : gives which is indeed greater than
Each case yields a valid value, so can be or — three possible values.
Thus, the correct answer is C .
Problem 21 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1989 AMC 8
- 1990 AMC 8
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