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, the denominator of <math>m</math> must be greater than <math>100</math>. We see that the nearest fraction bigger than <math>\frac{1}{2}</math> that does not have its denominator over <math>100</math> is <math>\boxed{\textbf{(B)}\frac{50}{99}}</math>. | + | We see that for the graph of <math>y=mx+2</math> to not pass through any lattice points, the denominator of <math>m</math> must be greater than <math>100</math>, or else it would be canceled by some <math>0<x\le100</math>. We see that the nearest fraction bigger than <math>\frac{1}{2}</math> that does not have its denominator over <math>100</math> is <math>\boxed{\textbf{(B)}\frac{50}{99}}</math>. |
==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}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 14:24, 31 January 2016
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, the denominator of must be greater than 
, or else it would be canceled by some 
. We see that the nearest fraction bigger than 
that does not have its denominator over is 
.
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 | ||
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