2008 AMC 12A Problem 5
Below is the professionally curated solution for Problem 5 of the 2008 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 12A solutions, or check the answer key.
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Difficulty rating: 1100
5.
Suppose that is an integer. Which of the following statements must be true about
It is negative.
It is even, but not necessarily a multiple of
It is a multiple of but not necessarily even.
It is a multiple of but not necessarily a multiple of
It is a multiple of
Solution:
Combining the fractions,
This is an integer exactly when is even. The example is even but not a multiple of which rules out every other statement.
Thus, B is the correct answer.
Problem 5 in Other Years
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