2022 AMC 8 Problems

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);
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Solution

Problem 2

Consider these two operations: What is the value of

Solution

Problem 3

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

Solution

Problem 4

Solution

Problem 5

Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned 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 years. How many years older than Bella is Anna?

Solution

Problem 6

Solution

Problem 7

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Problem 8

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Problem 9

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Problem 10

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Problem 11

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Problem 12

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Problem 13

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Problem 14

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Problem 15

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Problem 16

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Problem 17

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Problem 18

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Problem 19

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Problem 20

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Problem 21

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Problem 22

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Problem 23

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Problem 24

Solution

Problem 25

Solution