Difference between revisions of "Mock AIME 1 2013 Problems"
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== Problem 2 == | == Problem 2 == | ||
Find the number of ordered positive integer pairs <math>(a,b,c)</math> such that <math>a</math> evenly divides <math>b</math>, <math>b+1</math> evenly divides <math>c</math>, and <math>c-a=10</math>. | Find the number of ordered positive integer pairs <math>(a,b,c)</math> such that <math>a</math> evenly divides <math>b</math>, <math>b+1</math> evenly divides <math>c</math>, and <math>c-a=10</math>. | ||
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[[2013 Mock AIME I Problems/Problem 2|Solution]] | [[2013 Mock AIME I Problems/Problem 2|Solution]] | ||
Revision as of 18:51, 6 May 2013
Contents
Problem 1
Two circles and , each of unit radius, have centers and such that . Let be the midpoint of and let $C_#$ (Error compiling LaTeX. Unknown error_msg) be a circle externally tangent to both and . and have a common tangent that passes through . If this tangent is also a common tangent to and , find the radius of circle .
Problem 2
Find the number of ordered positive integer pairs such that evenly divides , evenly divides , and .
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10