Difference between revisions of "AMC 12C 2020"
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==Problem 6== | ==Problem 6== | ||
<math>10</math> candy canes and <math>9</math> lollipops are to be distributed among <math>8</math> children such that each child gets atleast <math>1</math> candy. What is the probability that once the candies are distributed, no child has both types of candies? | <math>10</math> candy canes and <math>9</math> lollipops are to be distributed among <math>8</math> children such that each child gets atleast <math>1</math> candy. What is the probability that once the candies are distributed, no child has both types of candies? | ||
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| + | ==Problem 7== | ||
| + | In what ratio should a <math>70%</math> water and <math>30%</math> alcohol solution be mixed with a <math>40%</math> water and <math>60%</math> alcohol solution such that the resulting solution consists of <math>45%</math> alcohol and <math>55%</math> water? | ||
Revision as of 12:30, 20 April 2020
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
In what ratio should a $70%$ (Error compiling LaTeX. Unknown error_msg) water and $30%$ (Error compiling LaTeX. Unknown error_msg) alcohol solution be mixed with a $40%$ (Error compiling LaTeX. Unknown error_msg) water and $60%$ (Error compiling LaTeX. Unknown error_msg) alcohol solution such that the resulting solution consists of $45%$ (Error compiling LaTeX. Unknown error_msg) alcohol and $55%$ (Error compiling LaTeX. Unknown error_msg) water?
