AMC 12C 2020 Problems
Contents
Problem 1
What is the sum of the solutions of the equation ?
Problem 2
What is the numerical value of the sum
Problem 3
In a bag are marbles consisting of
blue marbles and
red marbles. If each marble is pulled out
at a time, what is the probability that the
marble pulled out red?
Problem 4
cows can consume
kilograms of grass in
days. How many more cows are required such that all the cows together can consume
kilograms of grass in
days?
Problem 5
A lamb is tied to a post at the origin on the real
plane with a rope that measures
units.
wolves are tied with ropes of length
as well, both of them being at points
, and
. What is the area that the lamb can run around without being in the range of the wolves?
Problem 6
How many increasing(lower to higher numbered) subsets of contain no
consecutive prime numbers?
Problem 7
Let denote the sum of the factors of a positive integer
. What is the sum of the
least possible values of
such that
?
Problem 8
The real value of that satisfies the equation
can be written in the form
where
and
are integers. What is
?
Problem 9
Let denote the number of trailing
s in the numerical value of the expression
, for example,
since
which has
trailing zero. What is the sum
?
Problem 10
In how many ways can candy canes and
lollipops be split between
children if each child must receive atleast
candy but no child receives both types?