Difference between revisions of "2011 AMC 10B Problems/Problem 24"
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==Solution== | ==Solution== | ||
| − | + | We see that for the graph of <math>y=mx+2</math> to not pass through any lattice points its denominator must be greater the than 100. We see that the nearest fraction bigger than <math>1/2</math> that does not have its denominator over 100 is 50/99. | |
==See Also== | ==See Also== | ||
{{AMC10 box|year=2011|ab=B|num-a=25|num-b=23}} | {{AMC10 box|year=2011|ab=B|num-a=25|num-b=23}} | ||
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Revision as of 17:32, 12 July 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
We see that for the graph of 
to not pass through any lattice points its denominator must be greater the than 100. We see that the nearest fraction bigger than 
that does not have its denominator over 100 is 50/99.
See Also
| 2011 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 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 10 Problems and Solutions | ||
