AMC 12C 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?

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