2020 AIME I Problems
2020 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
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Contents
Problem 1
Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule!
Problem 2
Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule!
Problem 3
Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule!
Problem 4
Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule!
Problem 5
Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule!
Problem 6
Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule!
Problem 7
Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule!
Problem 8
Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule!
Problem 9
Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule! Pakistowners rule!
Problem 10
Let and
be positive integers satisfying the conditions
is a multiple of
and
is not a multiple of
Find the least possible value of
Problem 11
For integers and
let
and
Find the number of ordered triples
of integers with absolute values not exceeding
for which there is an integer
such that
Problem 12
Let be the least positive integer for which
is divisible by
Find the number of positive integer divisors of
Problem 13
Point lies on side
of
so that
bisects
The perpendicular bisector of
intersects the bisectors of
and
in points
and
respectively. Given that
and
the area of
can be written as
where
and
are relatively prime positive integers, and
is a positive integer not divisible by the square of any prime. Find
Problem 14
Let be a quadratic polynomial with complex coefficients whose
coefficient is
Suppose the equation
has four distinct solutions,
Find the sum of all possible values of
Problem 15
Let be an acute triangle with circumcircle
and let
be the intersection of the altitudes of
Suppose the tangent to the circumcircle of
at
intersects
at points
and
with
and
The area of
can be written in the form
where
and
are positive integers, and
is not divisible by the square of any prime. Find
2020 AIME I (Problems • Answer Key • Resources) | ||
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