Difference between revisions of "2011 AMC 12B Problems/Problem 19"
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Revision as of 18:48, 11 March 2011
Problem
A lattice point in an -coordinate system is any point
where both
and
are integers. The graph of
passes through no lattice point with
for all
such that
. What is the maximum possible value of
?
Solution
Answer: (B)
It is very easy to see that the in the graph does not impact whether it passes through lattice.
We need to make sure that cannot be in the form of
for
, otherwise the graph
passes through lattice point at
. We only need to worry about
very close to
,
,
will be the only case we need to worry about and we want the minimum of those, clearly for
, the smallest is
, so answer is (B)
See also
2011 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 18 |
Followed by Problem 20 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |