Difference between revisions of "2011 AMC 10B Problems/Problem 24"
(Created page with "== Problem 24 == A lattice point in an <math>xy</math>-coordinate system in any point <math>(x, y)</math> where both <math>x</math> and <math>y</math> are integers. The graph of...") |
(formatting fixes) |
||
| Line 1: | Line 1: | ||
| − | == Problem | + | == Problem == |
A lattice point in an <math>xy</math>-coordinate system in any point <math>(x, y)</math> where both <math>x</math> and <math>y</math> are integers. The graph of <math>y = mx +2</math> passes through no lattice point with <math>0 < x \le 100</math> for all <math>m</math> such that <math>1/2 < m < a</math>. What is the maximum possible value of <math>a</math>? | A lattice point in an <math>xy</math>-coordinate system in any point <math>(x, y)</math> where both <math>x</math> and <math>y</math> are integers. The graph of <math>y = mx +2</math> passes through no lattice point with <math>0 < x \le 100</math> for all <math>m</math> such that <math>1/2 < m < a</math>. What is the maximum possible value of <math>a</math>? | ||
| Line 5: | Line 5: | ||
<math> \textbf{(A)}\ \frac{51}{101} \qquad\textbf{(B)}\ \frac{50}{99} \qquad\textbf{(C)}\ \frac{51}{100} \qquad\textbf{(D)}\ \frac{52}{101} \qquad\textbf{(E)}\ \frac{13}{25}</math> | <math> \textbf{(A)}\ \frac{51}{101} \qquad\textbf{(B)}\ \frac{50}{99} \qquad\textbf{(C)}\ \frac{51}{100} \qquad\textbf{(D)}\ \frac{52}{101} \qquad\textbf{(E)}\ \frac{13}{25}</math> | ||
| − | + | ==Solution== | |
| + | {{solution}} | ||
| + | ==See Also== | ||
| + | {{AMC10 box|year=2011|ab=B|num-a=25|num-b=23}} | ||
Revision as of 14:28, 6 June 2011
Problem
A lattice point in an 
-coordinate system in 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
This problem needs a solution. If you have a solution for it, please help us out by adding it.
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 | ||
