2011 AMC 12B Problems/Problem 19
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 |
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All AMC 12 Problems and Solutions |