2021 AMC 12B Problems/Problem 25: Difference between revisions
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==Problem== | |||
Let <math>S</math> be the set of lattice points in the coordinate plane, both of whose coordinates are integers between <math>1</math> and <math>30,</math> inclusive. Exactly <math>300</math> points in <math>S</math> lie on or below a line with equation <math>y=mx.</math> The possible values of <math>m</math> lie in an interval of length <math>\frac ab,</math> where <math>a</math> and <math>b</math> are relatively prime positive integers. What is <math>a+b?</math> | |||
<math>\textbf{(A) }31 \qquad \textbf{(B) }47 \qquad \textbf{(C) }62\qquad \textbf{(D) }72 \qquad \textbf{(E) }85</math> | |||
{{AMC10 box|year=2021|ab=B|num-b=24|after=Last Problem}} | {{AMC10 box|year=2021|ab=B|num-b=24|after=Last Problem}} | ||
Revision as of 01:51, 12 February 2021
Problem
Let 
be the set of lattice points in the coordinate plane, both of whose coordinates are integers between 
and 
inclusive. Exactly 
points in lie on or below a line with equation 
The possible values of 
lie in an interval of length 
where 
and 
are relatively prime positive integers. What is 
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