Difference between revisions of "2022 AMC 8 Problems"
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==Problem 1== | ==Problem 1== | ||
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What is the value of <math>(5 \, \blacklozenge \, 3) \, \bigstar \, 6?</math> | 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]] | [[2022 AMC 8 Problems/Problem 2|Solution]] | ||
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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? | 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)} | + | <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]] | [[2022 AMC 8 Problems/Problem 3|Solution]] | ||
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==Problem 4== | ==Problem 4== | ||
− | [[ | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> |
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+ | [[2022 AMC 8 Problems/Problem 4|Solution]] | ||
==Problem 5== | ==Problem 5== | ||
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<math>\textbf{(A)} ~1\qquad\textbf{(B)} ~2\qquad\textbf{(C)} ~3\qquad\textbf{(D)} ~4\qquad\textbf{(E)} ~5</math> | <math>\textbf{(A)} ~1\qquad\textbf{(B)} ~2\qquad\textbf{(C)} ~3\qquad\textbf{(D)} ~4\qquad\textbf{(E)} ~5</math> | ||
− | [[ | + | [[2022 AMC 8 Problems/Problem 5|Solution]] |
==Problem 6== | ==Problem 6== | ||
− | [[ | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> |
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+ | [[2022 AMC 8 Problems/Problem 6|Solution]] | ||
==Problem 7== | ==Problem 7== | ||
− | [[ | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> |
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+ | [[2022 AMC 8 Problems/Problem 7|Solution]] | ||
==Problem 8== | ==Problem 8== | ||
− | [[ | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> |
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+ | [[2022 AMC 8 Problems/Problem 8|Solution]] | ||
==Problem 9== | ==Problem 9== | ||
− | [[ | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> |
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+ | [[2022 AMC 8 Problems/Problem 9|Solution]] | ||
==Problem 10== | ==Problem 10== | ||
− | [[ | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> |
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+ | [[2022 AMC 8 Problems/Problem 10|Solution]] | ||
==Problem 11== | ==Problem 11== | ||
− | [[ | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> |
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+ | [[2022 AMC 8 Problems/Problem 11|Solution]] | ||
==Problem 12== | ==Problem 12== | ||
− | [[ | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> |
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+ | [[2022 AMC 8 Problems/Problem 12|Solution]] | ||
==Problem 13== | ==Problem 13== | ||
− | [[ | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> |
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+ | [[2022 AMC 8 Problems/Problem 13|Solution]] | ||
==Problem 14== | ==Problem 14== | ||
− | + | <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 14|Solution]] | |
− | + | ==Problem 15== | |
− | + | <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 15|Solution]] |
==Problem 16== | ==Problem 16== | ||
− | [[ | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> |
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+ | [[2022 AMC 8 Problems/Problem 16|Solution]] | ||
==Problem 17== | ==Problem 17== | ||
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− | <math>\textbf{(A) } | + | <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 17|Solution]] |
==Problem 18== | ==Problem 18== | ||
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− | <math>\textbf{(A) } | + | <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 18|Solution]] |
==Problem 19== | ==Problem 19== | ||
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− | <math>\textbf{(A) } | + | <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 19|Solution]] |
==Problem 20== | ==Problem 20== | ||
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− | + | <math>\textbf{(A) } X \qquad \textbf{(B) } X \qquad \textbf{(C) } X \qquad \textbf{(D) } X \qquad \textbf{(E) } X</math> | |
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− | [[ | + | [[2022 AMC 8 Problems/Problem 20|Solution]] |
==Problem 21== | ==Problem 21== | ||
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− | <math>\textbf{(A) } | + | <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 21|Solution]] |
==Problem 22== | ==Problem 22== | ||
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− | <math>\textbf{(A) } | + | <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 22|Solution]] |
==Problem 23== | ==Problem 23== | ||
− | + | <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 23|Solution]] |
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==Problem 24== | ==Problem 24== | ||
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− | <math>\textbf{(A) } | + | <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 24|Solution]] |
==Problem 25== | ==Problem 25== | ||
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− | <math>\textbf{(A) } | + | <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 25|Solution]] |
Revision as of 11:10, 28 January 2022
IMPORTANT: When copied a problem, replace the X's for answer choices.
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
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)
Problem 2
Consider these two operations:
What is the value of
Problem 3
When three positive integers ,
, and
are multiplied together, their product is
. Suppose
. In how many ways can the numbers be chosen?
Problem 4
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?
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