2008 AMC 10A Problem 9
Below is the professionally curated solution for Problem 9 of the 2008 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 10A solutions, or check the answer key.
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Difficulty rating: 1170
9.
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 over a common denominator,
For to be an integer, must be even.
The example shows that need not be a multiple of and rules out the other statements.
Thus, the correct answer is B.
Problem 9 in Other Years
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