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) such that < | + | 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>. |
[[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
.
Solution
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10