2012 AMC 8 Problem 22
Below is the video solution and professionally curated solution for Problem 22 of the 2012 AMC 8, 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.
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Difficulty rating: 1720
22.
Let be a set of nine distinct integers. Six of the elements are and What is the number of possible values of the median of
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 would already give at least five larger elements. It cannot be above , since 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
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