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Difference between revisions of "AMC 12C 2020 Problems"

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<math>\mathrm{(A) \ } -12\qquad \mathrm{(B) \ } 0\qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) \ } 16\qquad \mathrm{(E) \ } 24</math>
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<math>\textbf{(A)}\ 10 \qquad\textbf{(B)}\ 16 \qquad\textbf{(C)}\ 18 \qquad\textbf{(D)}\ 21 \qquad\textbf{(E)}\ 24</math>

Revision as of 14:19, 21 April 2020

Problem 1

What is the sum of the solutions of the equation $(x + 4)(x - 5)(x + 6)(x - 8) = 0$?


$\textbf{(A)}\ 3 \qquad\textbf{(B)}\ 5 \qquad\textbf{(C)}\ 8 \qquad\textbf{(D)}\ 11 \qquad\textbf{(E)}\ 15$


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 $6$ units. $2$ wolves are tied with ropes of length $6$ as well, both of them being at points $(6, 6)$, and $(-6, -6)$. What is the area that the lamb can run around without being in the range of the wolves?


$\textbf{(A)}\ 70 \qquad\textbf{(B)}\ 71 \qquad\textbf{(C)}\ 72 \qquad\textbf{(D)}\ 100 \qquad\textbf{(E)}\ 110$


Problem 6

In how many ways can $10$ candy canes and $9$ lollipops be split between $8$ children if each child must receive atleast $1$ candy but no child receives both types?


Problem 7

Let $T(n)$ denote the sum of the factors of a positive integer $n$. What is the sum of the $3$ least possible values of $x$ such that $T(x) + T(2x) = 8$?


Problem 8

The real value of $n$ that satisfies the equation $ln(n) + ln(n^{2} - 34) = ln(72)$ can be written in the form \[a + \sqrt{b}\] where $a$ and $b$ are integers. What is $a + b$?


$\textbf{(A)}\ 10 \qquad\textbf{(B)}\ 16 \qquad\textbf{(C)}\ 18 \qquad\textbf{(D)}\ 21 \qquad\textbf{(E)}\ 24$

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