2005 AMC 12A Problem 11
Below is the professionally curated solution for Problem 11 of the 2005 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 12A solutions, or check the answer key.
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Difficulty rating: 1620
11.
How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits?
Solution:
The middle digit is an integer only when the first and last digits are both odd or both even. Each such pair determines the middle digit uniquely.
There are odd-odd choices for the first and last digits. For even-even, the first digit cannot be giving choices.
The total is
Thus, the correct answer is E.
Problem 11 in Other Years
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