AMC 10 2021 (Mock) Problems

Problem 1

Given that $A + B - C = 2020, B + C - A = 2021,$ and $A + C - B = 2022,$ what is the value of $A + B + C - 2020 - 2021 - 2022$ ?

$\mathrm{(A) \ } 0\qquad \mathrm{(B) \ } 2020\qquad \mathrm{(C) \ } 2021\qquad \mathrm{(D) \ } 2022\qquad \mathrm{(E) \ } 6063$

Problem 2

A bag of marbles consists of $4$ red marbles and $3$ blue marbles. Each of these $7$ marbles are pulled out one at a time. What is the probability that the $5th$ marble pulled out is red?

$\mathrm{(A) \ } \frac{1}{5}\qquad \mathrm{(B) \ } \frac{3}{7}\qquad \mathrm{(C) \ } \frac{1}{2}\qquad \mathrm{(D) \ } \frac{4}{7}\qquad \mathrm{(E) \ } \frac{4}{5}$

Problem 3

Meena has $11$ snakes, $6$ are purple and the rest are green. Some of the snakes are poisonous. She knows that $2$ of the poisonous snakes are green and the number of poisonous snakes which are purple is double the amount of poisonous snakes that are green. How many snakes are not poisonous?

$\mathrm{(A) \ } 3 \qquad \mathrm{(B) \ } 4 \qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) \ }6\qquad \mathrm{(E) \ }7$

Problem 4

At a birthday celebration consisting of $K$ kids, each of the $K$ kids purchase $S$ soda cans except for the birthday kid, who purchases $2S$ soda cans. $S$ soda cans cost $Q$ quarters. How many dollars were spent total on the soda cans?

$\mathrm{(A) \ } \frac{(K - 1)Q}{6}\qquad \mathrm{(B) \ } \frac{(K - 1)Q}{4}\qquad \mathrm{(C) \ } \frac{KQ}{4}\qquad \mathrm{(D) \ } \frac{(K + 1)Q}{4}\qquad \mathrm{(E) \ } \frac{(K + 1)Q}{2}$

Problem 5

Let a quadratic $Ax^2 + Bx + C$ , where $A, B$ and $C$ are nonzero, have two distinct, real roots $a$ and $b$ . Given that $\frac{1}{a}$ $+$ $\frac{1}{b}$ $=$ $\frac{1}{6}$ , which of the following conditions must be true?

$\mathrm{(A) \ } B^2 - 4A = 0 \qquad \mathrm{(B) \ } B - 24A \le 0 \qquad \mathrm{(C) \ } B^3 - A^2 \le 24 \qquad \mathrm{(D) \ } A + B = 6 \qquad \mathrm{(E) \ } B + 24A - C = 24$

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