2011 AMC 12A Problems/Problem 20
Problem
Let , where
,
, and
are integers. Suppose that
,
,
,
for some integer
. What is
?
Solution
From , we know that
. From the first inequality:
Since must be an integer, it follows that
. Similarly, from the second inequality:
And it follows that . We now have a system of three equations. Solving it gives us
. From this, we find that
And since , we find that
See also
2011 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 19 |
Followed by Problem 21 |
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All AMC 12 Problems and Solutions |