Difference between revisions of "AMC 12C 2020"
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How many increasing subsets of <math>{{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}}</math> contain no <math>2</math> consecutive prime numbers? | How many increasing subsets of <math>{{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}}</math> contain no <math>2</math> consecutive prime numbers? | ||
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==Problem 3== | ==Problem 3== |
Revision as of 15:47, 20 April 2020
Contents
Problem 1
What is the sum of the solutions to the equation ?
Problem 2
How many increasing subsets of contain no
consecutive prime numbers?
Problem 3
A field is on the real plane in the shape of a circle, centered at
with a a radius of
. The area that is in the field but above the line
is planted. What fraction of the field is planted?
Problem 4
What is the numerical value of ?
Problem 5
cows can consume
kilograms of grass in
days. How many more cows are required such that it takes all of the cows to consume
kilograms of grass in
days?
Problem 6
candy canes and
lollipops are to be distributed among
children such that each child gets atleast
candy. What is the probability that once the candies are distributed, no child has both types of candies?
Problem 7
Persons and
can plough a field in
days, persons
and
can plough the same field in
days, and persons
and
can plough the same field in
days. In how many days can all of them plough the field together?
Problem 8
The real value of that satisfies the equation
can be written in the form
where
and
are integers. What is
?
Problem 9
On a summer evening stargazing, the probability of seeing a shooting star in any given hour
on a sunny day is and the probability of seeing a shooting star on a rainy
day is
. Both rainy and sunny days happen with equal chances. What is the
probability of seeing a shooting star in the second
minutes of an hour stargazing on a
random night?
Problem 10
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
?