Difference between revisions of "2022 AMC 8 Problems"

Revision as of 10:10, 28 January 2022

IMPORTANT: When copied a problem, replace the X's for answer choices.

Problem 1

The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches?

usepackage("mathptmx");
defaultpen(linewidth(0.5));
size(5cm);
defaultpen(fontsize(14pt));
label("$\textbf{Math}$", (2.1,3.7)--(3.9,3.7));
label("$\textbf{Team}$", (2.1,3)--(3.9,3));
filldraw((1,2)--(2,1)--(3,2)--(4,1)--(5,2)--(4,3)--(5,4)--(4,5)--(3,4)--(2,5)--(1,4)--(2,3)--(1,2)--cycle, mediumgray*0.5 + lightgray*0.5);

draw((0,0)--(6,0), gray);
draw((0,1)--(6,1), gray);
draw((0,2)--(6,2), gray);
draw((0,3)--(6,3), gray);
draw((0,4)--(6,4), gray);
draw((0,5)--(6,5), gray);
draw((0,6)--(6,6), gray);

draw((0,0)--(0,6), gray);
draw((1,0)--(1,6), gray);
draw((2,0)--(2,6), gray);
draw((3,0)--(3,6), gray);
draw((4,0)--(4,6), gray);
draw((5,0)--(5,6), gray);
draw((6,0)--(6,6), gray);
 (Error making remote request. Unexpected URL sent back)

$\textbf{(A) } 10 \qquad \textbf{(B) } 12 \qquad \textbf{(C) } 13 \qquad \textbf{(D) } 14 \qquad \textbf{(E) } 15$

Solution

Problem 2

Consider these two operations: $\begin{align*} a \, \blacklozenge \, b &= a^2 - b^2\\ a \, \bigstar \, b &= (a - b)^2 \end{align*}$ What is the value of $(5 \, \blacklozenge \, 3) \, \bigstar \, 6?$

$\textbf{(A) } {-}20 \qquad \textbf{(B) } 4 \qquad \textbf{(C) } 16 \qquad \textbf{(D) } 100 \qquad \textbf{(E) } 220$

Solution

Problem 3

When three positive integers $a$ , $b$ , and $c$ are multiplied together, their product is $100$ . Suppose $a < b < c$ . In how many ways can the numbers be chosen?

$\textbf{(A) } 0 \qquad \textbf{(B) } 1\qquad\textbf{(C) } 2\qquad\textbf{(D) } 3\qquad\textbf{(E) } 4$

Solution

Problem 4

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 5

Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned $6$ years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is $30$ years. How many years older than Bella is Anna?

$\textbf{(A)} ~1\qquad\textbf{(B)} ~2\qquad\textbf{(C)} ~3\qquad\textbf{(D)} ~4\qquad\textbf{(E)} ~5$

Solution

Problem 6

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 7

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 8

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 9

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 10

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 11

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 12

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 13

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 14

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 15

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 16

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 17

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 18

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 19

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 20

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 21

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 22

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 23

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 24

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Problem 25

$\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X$

Solution

Page

Toolbox

Search

Difference between revisions of "2022 AMC 8 Problems"

Revision as of 10:10, 28 January 2022

Contents

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

@@ Line 1: / Line 1: @@
-IMPORTANT: THESE ARE NOT THE 2022 AMC 8 PROBLEMS. THIS IS COPY PASTED FROM THE 2020 AMC 8 PROBLEMS WIKI PAGE.
+IMPORTANT: When copied a problem, replace the X's for answer choices.
 ==Problem 1==
@@ Line 44: / Line 44: @@
 What is the value of <math>(5 \, \blacklozenge \, 3) \, \bigstar \, 6?</math>
-<math>\textbf{(A) } {-}20\qquad\textbf{(B) } 4\qquad\textbf{(C) } 16\qquad\textbf{(D) } 100\qquad\textbf{(E) } 220</math>
+<math>\textbf{(A) } {-}20 \qquad \textbf{(B) } 4 \qquad \textbf{(C) } 16 \qquad \textbf{(D) } 100 \qquad \textbf{(E) } 220</math>
 [[2022 AMC 8 Problems/Problem 2|Solution]]
@@ Line 52: / Line 52: @@
 When three positive integers <math>a</math>, <math>b</math>, and <math>c</math> are multiplied together, their product is <math>100</math>. Suppose <math>a < b < c</math>. In how many ways can the numbers be chosen?
-<math>\textbf{(A)} ~0\qquad\textbf{(B)} ~1\qquad\textbf{(C)} ~2\qquad\textbf{(D)} ~3\qquad\textbf{(E)} ~4</math>
+<math>\textbf{(A) } 0 \qquad \textbf{(B) } 1\qquad\textbf{(C) } 2\qquad\textbf{(D) } 3\qquad\textbf{(E) } 4</math>
 [[2022 AMC 8 Problems/Problem 3|Solution]]
@@ Line 58: / Line 58: @@
 ==Problem 4==
-[[2020 AMC 8 Problems/Problem 4|Solution]]
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
+[[2022 AMC 8 Problems/Problem 4|Solution]]
 ==Problem 5==
@@ Line 66: / Line 68: @@
 <math>\textbf{(A)} ~1\qquad\textbf{(B)} ~2\qquad\textbf{(C)} ~3\qquad\textbf{(D)} ~4\qquad\textbf{(E)} ~5</math>
-[[2020 AMC 8 Problems/Problem 5|Solution]]
+[[2022 AMC 8 Problems/Problem 5|Solution]]
 ==Problem 6==
-[[2020 AMC 8 Problems/Problem 6|Solution]]
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
+[[2022 AMC 8 Problems/Problem 6|Solution]]
 ==Problem 7==
-[[2020 AMC 8 Problems/Problem 7|Solution]]
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
+[[2022 AMC 8 Problems/Problem 7|Solution]]
 ==Problem 8==
-[[2020 AMC 8 Problems/Problem 8|Solution]]
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
+[[2022 AMC 8 Problems/Problem 8|Solution]]
 ==Problem 9==
-[[2020 AMC 8 Problems/Problem 9|Solution]]
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
+[[2022 AMC 8 Problems/Problem 9|Solution]]
 ==Problem 10==
-[[2020 AMC 8 Problems/Problem 10|Solution]]
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
+[[2022 AMC 8 Problems/Problem 10|Solution]]
 ==Problem 11==
-[[2020 AMC 8 Problems/Problem 11|Solution]]
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
+[[2022 AMC 8 Problems/Problem 11|Solution]]
 ==Problem 12==
-[[2020 AMC 8 Problems/Problem 12|Solution]]
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
+[[2022 AMC 8 Problems/Problem 12|Solution]]
 ==Problem 13==
-[[2020 AMC 8 Problems/Problem 13|Solution]]
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
+[[2022 AMC 8 Problems/Problem 13|Solution]]
 ==Problem 14==
-In how many ways can the letters in BEEKEEPER be rearranged so that two or more Es do not appear together?
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-<math>\textbf{(A)} ~1\qquad\textbf{(B)} ~4\qquad\textbf{(C)} ~12\qquad\textbf{(D)} ~24\qquad\textbf{(E)} ~120\qquad</math>
+[[2022 AMC 8 Problems/Problem 14|Solution]]
-[[2020 AMC 8 Problems/Problem 14|Solution]]
+==Problem 15==
-==Problem 15==
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-[[2020 AMC 8 Problems/Problem 15|Solution]]
+[[2022 AMC 8 Problems/Problem 15|Solution]]
 ==Problem 16==
-[[2020 AMC 8 Problems/Problem 16|Solution]]
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
+[[2022 AMC 8 Problems/Problem 16|Solution]]
 ==Problem 17==
-How many factors of <math>2020</math> have more than <math>3</math> factors? (As an example, <math>12</math> has <math>6</math> factors, namely <math>1, 2, 3, 4, 6,</math> and <math>12.</math>)
-<math>\textbf{(A) }6 \qquad \textbf{(B) }7 \qquad \textbf{(C) }8 \qquad \textbf{(D) }9 \qquad \textbf{(E) }10</math>
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-[[2020 AMC 8 Problems/Problem 17|Solution]]
+[[2022 AMC 8 Problems/Problem 17|Solution]]
 ==Problem 18==
-Rectangle <math>ABCD</math> is inscribed in a semicircle with diameter <math>\overline{FE},</math> as shown in the figure. Let <math>DA=16,</math> and let <math>FD=AE=9.</math> What is the area of <math>ABCD?</math>
-<asy>
-// diagram by SirCalcsALot
-draw(arc((0,0),17,180,0));
-draw((-17,0)--(17,0));
-fill((-8,0)--(-8,15)--(8,15)--(8,0)--cycle, 1.5*grey);
-draw((-8,0)--(-8,15)--(8,15)--(8,0)--cycle);
-dot("$A$",(8,0), 1.25*S);
-dot("$B$",(8,15), 1.25*N);
-dot("$C$",(-8,15), 1.25*N);
-dot("$D$",(-8,0), 1.25*S);
-dot("$E$",(17,0), 1.25*S);
-dot("$F$",(-17,0), 1.25*S);
-label("$16$",(0,0),N);
-label("$9$",(12.5,0),N);
-label("$9$",(-12.5,0),N);
-</asy>
-<math>\textbf{(A) }240 \qquad \textbf{(B) }248 \qquad \textbf{(C) }256 \qquad \textbf{(D) }264 \qquad \textbf{(E) }272</math>
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-[[2020 AMC 8 Problems/Problem 18|Solution]]
+[[2022 AMC 8 Problems/Problem 18|Solution]]
 ==Problem 19==
-A number is called flippy if its digits alternate between two distinct digits. For example, <math>2020</math> and <math>37373</math> are flippy, but <math>3883</math> and <math>123123</math> are not. How many five-digit flippy numbers are divisible by <math>15?</math>
-<math>\textbf{(A) }3 \qquad \textbf{(B) }4 \qquad \textbf{(C) }5 \qquad \textbf{(D) }6 \qquad \textbf{(E) }8</math>
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-[[2020 AMC 8 Problems/Problem 19|Solution]]
+[[2022 AMC 8 Problems/Problem 19|Solution]]
 ==Problem 20==
-A scientist walking through a forest recorded as integers the heights of <math>5</math> trees standing in a row. She observed that each tree was either twice as tall or half as tall as the one to its right. Unfortunately some of her data was lost when rain fell on her notebook. Her notes are shown below, with blanks indicating the missing numbers. Based on her observations, the scientist was able to reconstruct the lost data. What was the average height of the trees, in meters?
-<cmath>
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-\begingroup
-\setlength{\tabcolsep}{10pt}
-\renewcommand{\arraystretch}{1.5}
-\begin{tabular}{|c|c|}
-\hline Tree 1 & \rule{0.4cm}{0.15mm} meters \\
-Tree 2 & 11 meters \\
-Tree 3 & \rule{0.5cm}{0.15mm} meters \\
-Tree 4 & \rule{0.5cm}{0.15mm} meters \\
-Tree 5 & \rule{0.5cm}{0.15mm} meters \\ \hline
-Average height & \rule{0.5cm}{0.15mm}\text{ .}2 meters \\
-\hline
-\end{tabular}
-\endgroup</cmath>
-<math>\newline \textbf{(A) }22.2 \qquad \textbf{(B) }24.2 \qquad \textbf{(C) }33.2 \qquad \textbf{(D) }35.2 \qquad \textbf{(E) }37.2</math>
-[[2020 AMC 8 Problems/Problem 20|Solution]]
+[[2022 AMC 8 Problems/Problem 20|Solution]]
 ==Problem 21==
-A game board consists of <math>64</math> squares that alternate in color between black and white. The figure below shows square <math>P</math> in the bottom row and square <math>Q</math> in the top row. A marker is placed at <math>P.</math> A step consists of moving the marker onto one of the adjoining white squares in the row above. How many <math>7</math>-step paths are there from <math>P</math> to <math>Q?</math> (The figure shows a sample path.)
-<asy>
-// diagram by SirCalcsALot
-size(200);
-int[] x = {6, 5, 4, 5, 6, 5, 6};
-int[] y = {1, 2, 3, 4, 5, 6, 7};
-int N = 7;
-for (int i = 0; i < 8; ++i) {
-for (int j = 0; j < 8; ++j) {
-draw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--(i,j));
-if ((i+j) % 2 == 0) {
-filldraw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--(i,j)--cycle,black);
-}
-}
-}
-for (int i = 0; i < N; ++i) {
-draw(circle((x[i],y[i])+(0.5,0.5),0.35),grey);
-}
-label("$P$", (5.5, 0.5));
-label("$Q$", (6.5, 7.5));
-</asy>
-<math>\textbf{(A) }28 \qquad \textbf{(B) }30 \qquad \textbf{(C) }32 \qquad \textbf{(D) }33 \qquad \textbf{(E) }35</math>
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-[[2020 AMC 8 Problems/Problem 21|Solution]]
+[[2022 AMC 8 Problems/Problem 21|Solution]]
 ==Problem 22==
-When a positive integer <math>N</math> is fed into a machine, the output is a number calculated according to the rule shown below.
-<asy>
-size(300);
-defaultpen(linewidth(0.8)+fontsize(13));
-real r = 0.05;
-draw((0.9,0)--(3.5,0),EndArrow(size=7));
-filldraw((4,2.5)--(7,2.5)--(7,-2.5)--(4,-2.5)--cycle,gray(0.65));
-fill(circle((5.5,1.25),0.8),white);
-fill(circle((5.5,1.25),0.5),gray(0.65));
-fill((4.3,-r)--(6.7,-r)--(6.7,-1-r)--(4.3,-1-r)--cycle,white);
-fill((4.3,-1.25+r)--(6.7,-1.25+r)--(6.7,-2.25+r)--(4.3,-2.25+r)--cycle,white);
-fill((4.6,-0.25-r)--(6.4,-0.25-r)--(6.4,-0.75-r)--(4.6,-0.75-r)--cycle,gray(0.65));
-fill((4.6,-1.5+r)--(6.4,-1.5+r)--(6.4,-2+r)--(4.6,-2+r)--cycle,gray(0.65));
-label("$N$",(0.45,0));
-draw((7.5,1.25)--(11.25,1.25),EndArrow(size=7));
-draw((7.5,-1.25)--(11.25,-1.25),EndArrow(size=7));
-label("if $N$ is even",(9.25,1.25),N);
-label("if $N$ is odd",(9.25,-1.25),N);
-label("$\frac N2$",(12,1.25));
-label("$3N+1$",(12.6,-1.25));
-</asy>
-For example, starting with an input of <math>N=7,</math> the machine will output <math>3 \cdot 7 +1 = 22.</math> Then if the output is repeatedly inserted into the machine five more times, the final output is <math>26.</math>
-<cmath>7 \to 22 \to 11 \to 34 \to 17 \to 52 \to 26</cmath>When the same <math>6</math>-step process is applied to a different starting value of <math>N,</math> the final output is <math>1.</math> What is the sum of all such integers <math>N?</math>
-<cmath>N \to \rule{0.5cm}{0.15mm} \to \rule{0.5cm}{0.15mm} \to \rule{0.5cm}{0.15mm} \to \rule{0.5cm}{0.15mm} \to \rule{0.5cm}{0.15mm} \to 1</cmath>
-<math>\textbf{(A) }73 \qquad \textbf{(B) }74 \qquad \textbf{(C) }75 \qquad \textbf{(D) }82 \qquad \textbf{(E) }83</math>
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-[[2020 AMC 8 Problems/Problem 22|Solution]]
+[[2022 AMC 8 Problems/Problem 22|Solution]]
 ==Problem 23==
-A <math>\triangle</math> or <math>\bigcirc</math> is placed in each of the nine squares in a 3-by-3 grid. Shown below is a sample configuration with three <math>\triangle</math>s in a line.
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-[center][img]https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvZC8wL2ZjMDdkOGRlMzVjNWZlOWE3NTI5MjkwODIxODQ0YWRkYmQxZmJiLnBuZw==&rn=dGljX3RhY190b2VfdHJpYW5nbGVzLnBuZw==[/img][/center]
+[[2022 AMC 8 Problems/Problem 23|Solution]]
-How many configurations will have three <math>\triangle</math>s in a line and three <math>\bigcirc</math>s in a line?
-<math>\textbf{(A) } 39 \qquad \textbf{(B) } 42 \qquad \textbf{(C) } 78 \qquad \textbf{(D) } 84 \qquad \textbf{(E) } 96</math>
-[[2020 AMC 8 Problems/Problem 23|Solution]]
 ==Problem 24==
-A large square region is paved with <math>n^2</math> gray square tiles, each measuring <math>s</math> inches on a side. A border <math>d</math> inches wide surrounds each tile. The figure below shows the case for <math>n=3</math>. When <math>n=24</math>
-, the <math>576</math> gray tiles cover <math>64\%</math> of the area of the large square region. What is the ratio <math>\frac{d}{s}</math> for this larger value of <math>n?</math>
-<asy>
-draw((0,0)--(13,0)--(13,13)--(0,13)--cycle);
-filldraw((1,1)--(4,1)--(4,4)--(1,4)--cycle, mediumgray);
-filldraw((1,5)--(4,5)--(4,8)--(1,8)--cycle, mediumgray);
-filldraw((1,9)--(4,9)--(4,12)--(1,12)--cycle, mediumgray);
-filldraw((5,1)--(8,1)--(8,4)--(5,4)--cycle, mediumgray);
-filldraw((5,5)--(8,5)--(8,8)--(5,8)--cycle, mediumgray);
-filldraw((5,9)--(8,9)--(8,12)--(5,12)--cycle, mediumgray);
-filldraw((9,1)--(12,1)--(12,4)--(9,4)--cycle, mediumgray);
-filldraw((9,5)--(12,5)--(12,8)--(9,8)--cycle, mediumgray);
-filldraw((9,9)--(12,9)--(12,12)--(9,12)--cycle, mediumgray);
-</asy>
-<math>\textbf{(A) }\frac6{25} \qquad \textbf{(B) }\frac14 \qquad \textbf{(C) }\frac9{25} \qquad \textbf{(D) }\frac7{16} \qquad \textbf{(E) }\frac9{16}</math>
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-[[2020 AMC 8 Problems/Problem 24|Solution]]
+[[2022 AMC 8 Problems/Problem 24|Solution]]
 ==Problem 25==
-Rectangles <math>R_1</math> and <math>R_2,</math> and squares <math>S_1,\,S_2,\,</math> and <math>S_3,</math> shown below, combine to form a rectangle that is 3322 units wide and 2020 units high. What is the side length of <math>S_2</math> in units?
-<asy>
-draw((0,0)--(5,0)--(5,3)--(0,3)--(0,0));
-draw((3,0)--(3,1)--(0,1));
-draw((3,1)--(3,2)--(5,2));
-draw((3,2)--(2,2)--(2,1)--(2,3));
-label("$R_1$",(3/2,1/2));
-label("$S_3$",(4,1));
-label("$S_2$",(5/2,3/2));
-label("$S_1$",(1,2));
-label("$R_2$",(7/2,5/2));
-</asy>
-<math>\textbf{(A) }651 \qquad \textbf{(B) }655 \qquad \textbf{(C) }656 \qquad \textbf{(D) }662 \qquad \textbf{(E) }666</math>
+<math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math>
-[[2020 AMC 8 Problems/Problem 25|Solution]]
+[[2022 AMC 8 Problems/Problem 25|Solution]]