2012 AMC 8 Problem 22
Attempt Problem 22 of the 2012 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
Let be a set of nine distinct integers. Six of the elements of the set are and What is the number of possible values of the median of
Answer: D
Small hint:
The median is the fifth number after sorting the nine integers.
Big hint:
Test which integers from through can occupy the fifth position.
Video solution:
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Written solution:
In a sorted set of nine distinct integers, the median is the fifth number.
The median cannot be below , since then , , , , and would already give at least five larger elements. It cannot be above , since , , , , and would already give at least five smaller elements.
Each integer from through can be made the median by choosing the three missing integers appropriately. Therefore there are possible medians. Thus, the answer is D .
Problem 22 in other years
- 1985 AMC 8
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