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Difference between revisions of "AMC 12C 2020 Problems"

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<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>
 
<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>
  
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==Problem 4==
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<math>10</math> cows can consume <math>40</math> kilograms of grass in <math>20</math> days. How many more cows are required such that all the cows together can consume <math>60</math> kilograms of grass in <math>10</math> days?
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<math>\textbf{(A)}\ 20 \qquad\textbf{(B)}\ \ 21 \qquad\textbf{(C)}\ \ 22 \qquad\textbf{(D)}\ \ 23 \qquad\textbf{(E)}\ 24</math>
  
 
==Problem 5==
 
==Problem 5==
  
 
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?
 
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?

Revision as of 13:44, 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

$10$ cows can consume $40$ kilograms of grass in $20$ days. How many more cows are required such that all the cows together can consume $60$ kilograms of grass in $10$ days?


$\textbf{(A)}\ 20 \qquad\textbf{(B)}\ \ 21 \qquad\textbf{(C)}\ \ 22 \qquad\textbf{(D)}\ \ 23 \qquad\textbf{(E)}\ 24$

Problem 5

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?

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