Difference between revisions of "AMC 12C 2020"

(Problem 4)
(Problem 5)
Line 29: Line 29:
  
 
<math>10</math> cows can consume <math>20</math> kilograms of grass in <math>5</math> days. How many more cows are required such that it takes all of the cows to consume <math>80</math> kilograms of grass in <math>8</math> days?
 
<math>10</math> cows can consume <math>20</math> kilograms of grass in <math>5</math> days. How many more cows are required such that it takes all of the cows to consume <math>80</math> kilograms of grass in <math>8</math> days?
 +
 +
 +
 +
==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?

Revision as of 12:25, 20 April 2020


Problem 1

What is the sum of the solutions to the equation $(x + 5)(x + 4) - (x + 5)(x - 6) = 100$?


$\mathrm{(A) \ } -10\qquad \mathrm{(B) \ } -3\qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) \ } 10\qquad \mathrm{(E) \ } 15$

Problem 2

How many increasing subsets of ${{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}}$ contain no $2$ consecutive prime numbers?


Problem 3

A field is on the real $xy$ plane in the shape of a circle, centered at $(5, 6)$ with a a radius of $8$. The area that is in the field but above the line $y = x$ is planted. What fraction of the field is planted?


Problem 4

What is the numerical value of $1^{3} + 2^{3} + 3^{3} + … + 11^{3}$?


Problem 5

$10$ cows can consume $20$ kilograms of grass in $5$ days. How many more cows are required such that it takes all of the cows to consume $80$ kilograms of grass in $8$ days?


Problem 6

$10$ candy canes and $9$ lollipops are to be distributed among $8$ children such that each child gets atleast $1$ candy. What is the probability that once the candies are distributed, no child has both types of candies?