Difference between revisions of "2021 AMC 12B Problems/Problem 25"
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+ | ==Problem== | ||
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+ | 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> | ||
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+ | <math>\textbf{(A) }31 \qquad \textbf{(B) }47 \qquad \textbf{(C) }62\qquad \textbf{(D) }72 \qquad \textbf{(E) }85</math> | ||
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{{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 02:51, 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
2021 AMC 10B (Problems • Answer Key • Resources) | ||
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All AMC 10 Problems and Solutions |