AMC 12C 2020

Revision as of 11:21, 20 April 2020 by Shiamk (talk | contribs) (Problem 3)


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 $1^{3} + 2^{3} + 3^{3} + … + 11^{3}$?