Difference between revisions of "AMC 12C 2020 Problems"

Revision as of 13:01, 21 April 2020

Problem 1

What is the sum of the solutions of the equation $(x + 4)(x - 5)(x + 6) = 0$ ?

$\textbf{(A)}\ -5 \qquad\textbf{(B)}\ 0 \qquad\textbf{(C)}\ 5 \qquad\textbf{(D)}\ 12 \qquad\textbf{(E)}\ 14$

Problem 2

What is the numerical value of the sum $\sum_{k = 1}^{11}(i^{3} + i^{2})$

$\textbf{(A)}\ 4000 \qquad\textbf{(B)}\ 4608 \qquad\textbf{(C)}\ 4862 \qquad\textbf{(D)}\ 5792 \qquad\textbf{(E)}\ 6100$

Problem 3

In a bag are $7$ marbles consisting of $3$ blue marbles and $4$ red marbles. If each marble is pulled out $1$ at a time, what is the probability that the $6th$ marble pulled out red?

$\textbf{(A)}\ 0 \qquad\textbf{(B)}\ \frac{1}{8} \qquad\textbf{(C)}\ \frac{1}{2} \qquad\textbf{(D)}\ \frac{4}{7} \qquad\textbf{(E)}\ 1$

Problem 4

A lamb is tied to a post at the origin $(0, 0)$ on the real $xy$ plane with a rope that measures $5$ units. $2$ wolves are tied with ropes of length $5$ as well, both of them being at points $(5, 5)$ , and $(-5, -5)$ . What is the area that the lamb can run around without being in the range of the wolves?

@@ Line 23: / Line 23: @@
 <math>\textbf{(A)}\ 0 \qquad\textbf{(B)}\ \frac{1}{8} \qquad\textbf{(C)}\ \frac{1}{2} \qquad\textbf{(D)}\ \frac{4}{7} \qquad\textbf{(E)}\ 1</math>
 ==Problem 4==
 A lamb is tied to a post at the origin <math>(0, 0)</math> on the real <math>xy</math> plane with a rope that measures <math>5</math> units. <math>2</math> wolves are tied with ropes of length <math>5</math> as well, both of them being at points <math>(5, 5)</math>, and <math>(-5, -5)</math>. What is the area that the lamb can run around without being in the range of the wolves?

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