Difference between revisions of "AMC 10 2021 (Mock) Problems"

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<math>\mathrm{(A) \ } 3 \qquad \mathrm{(B) \ } 4 \qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) \ }6\qquad \mathrm{(E) \ }7</math>
 
<math>\mathrm{(A) \ } 3 \qquad \mathrm{(B) \ } 4 \qquad \mathrm{(C) \ } 5\qquad \mathrm{(D) \ }6\qquad \mathrm{(E) \ }7</math>
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==Problem 4==
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How many ways are there to arrange <math>3</math> blue tiles, <math>4</math> yellow tiles, <math>5</math> pink tiles, and <math>6</math> black tiles in a row such that all tiles of the same color are adjacent and no pink tile is adjacent to a black tile?
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<math>\mathrm{(A) \ } 6 \qquad \mathrm{(B) \ } 8 \qquad \mathrm{(C) \ } 10\qquad \mathrm{(D) \ }12\qquad \mathrm{(E) \ }15</math>

Revision as of 11:41, 29 November 2021

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

How many ways are there to arrange $3$ blue tiles, $4$ yellow tiles, $5$ pink tiles, and $6$ black tiles in a row such that all tiles of the same color are adjacent and no pink tile is adjacent to a black tile?

$\mathrm{(A) \ } 6 \qquad \mathrm{(B) \ } 8 \qquad \mathrm{(C) \ } 10\qquad \mathrm{(D) \ }12\qquad \mathrm{(E) \ }15$