2012 AMC 10B Problem 9
Below is the professionally curated solution for Problem 9 of the 2012 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 10B solutions, or check the answer key.
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Difficulty rating: 960
9.
Two integers have a sum of When two more integers are added to the first two integers the sum is Finally when two more integers are added to the sum of the previous four integers the sum is What is the minimum number of even integers among the integers?
Solution:
The first two integers have even sum , so they can both be odd. The next two integers have sum , which is odd, so one of them must be even and one odd.
The last two integers have sum , so they can both be odd. Therefore at least one integer must be even, and one is attainable.
Thus, A is the correct answer.
Problem 9 in Other Years
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