View source for 2021 AMC 10B Problems

{{AMC10 Problems|year=2021|ab=B}}

==Problem 1==
How many integer values of <math>x</math> satisfy <math>|x| < 3\pi</math>?

<math>\textbf{(A)} ~9 \qquad\textbf{(B)} ~10 \qquad\textbf{(C)} ~18 \qquad\textbf{(D)} ~19 \qquad\textbf{(E)} ~20</math>

==Problem 2==
What is the value if <math>\sqrt{(3-2\sqrt{3})^2}+\sqrt{(3+2\sqrt{3})^2}</math>?

<math>\textbf{(A)} ~0 \qquad\textbf{(B)} ~4\sqrt{3}-6 \qquad\textbf{(C)} ~6 \qquad\textbf{(D)} ~4\sqrt{3} \qquad\textbf{(E)} ~4\sqrt{3} + 6</math>

==Problem 3==

==Problem 4==

==Problem 5==

==Problem 6==

==Problem 7==
In a plane, four circles with radii <math>1,3,5,</math> and <math>7</math> are tangent to line <math>l</math> at the same point <math>A,</math> but they may be on either side of <math>l</math>. Region <math>S</math> consists of all the points that lie inside exactly one of the four circles. What is the maximum possible area of region <math>S</math>?

<math>\textbf{(A) }24\pi \qquad \textbf{(B) }32\pi \qquad \textbf{(C) }64\pi \qquad \textbf{(D) }65\pi \qquad \textbf{(E) }84\pi</math>

==Problem 8==

==Problem 9==

==Problem 10==

==Problem 11==

==Problem 12==

==Problem 13==

==Problem 14==

==Problem 15==

==Problem 16==

==Problem 17==

==Problem 18==
A fair <math>6</math>-sided die is repeatedly rolled until an odd number appears. What is the probability that every even number appears at least once before the first occurrence of an odd number?

<math>\textbf{(A)} ~\frac{1}{120} \qquad\textbf{(B)} ~\frac{1}{32} \qquad\textbf{(C)} ~\frac{1}{20} \qquad\textbf{(D)} ~\frac{3}{20} \qquad\textbf{(E)} ~\frac{1}{6}</math>

==Problem 19==

==Problem 20==

==Problem 21==

==Problem 22==
Ang, Ben, and Jasmin each have <math>5</math> blocks, colored red, blue, yellow, white, and green; and there are <math>5</math> empty boxes. Each of the people randomly and independently of the other two people places one of their blocks into each box. The probability that at least one box receives <math>3</math> blocks all of the same color is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. What is <math>m + n ?</math>

<math>\textbf{(A)} ~47 \qquad\textbf{(B)} ~94 \qquad\textbf{(C)} ~227 \qquad\textbf{(D)} ~471 \qquad\textbf{(E)} ~542</math>

==Problem 23==

==Problem 24==

==Problem 25==

==See also==
{{AMC10 box|year=2021|ab=B|before=[[2021 AMC 10A]]|after=[[2022 AMC 10A]]}}
* [[AMC 10]]
* [[AMC 10 Problems and Solutions]]
* [[Mathematics competitions]]
* [[Mathematics competition resources]]
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