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Difference between revisions of "2023 AMC 8 Problems"

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==Problem 1==
 
==Problem 1==
  
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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>
  
 
[[2023 AMC 8 Problems/Problem 1|Solution]]
 
[[2023 AMC 8 Problems/Problem 1|Solution]]
  
 
==Problem 2==
 
==Problem 2==
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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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[[2023 AMC 8 Problems/Problem 2|Solution]]
 
[[2023 AMC 8 Problems/Problem 2|Solution]]
  
 
==Problem 3==
 
==Problem 3==
 +
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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>
 +
 
[[2023 AMC 8 Problems/Problem 3|Solution]]
 
[[2023 AMC 8 Problems/Problem 3|Solution]]
  
 
==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>
 +
 
[[2023 AMC 8 Problems/Problem 4|Solution]]
 
[[2023 AMC 8 Problems/Problem 4|Solution]]
  
 
==Problem 5==
 
==Problem 5==
 +
 +
<math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math>
 +
 
[[2023 AMC 8 Problems/Problem 5|Solution]]
 
[[2023 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>
 +
 
[[2023 AMC 8 Problems/Problem 6|Solution]]
 
[[2023 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>
 +
 
[[2023 AMC 8 Problems/Problem 7|Solution]]
 
[[2023 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>
 +
 
[[2023 AMC 8 Problems/Problem 8|Solution]]
 
[[2023 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>
 +
 
[[2023 AMC 8 Problems/Problem 9|Solution]]
 
[[2023 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>
 +
 
[[2023 AMC 8 Problems/Problem 10|Solution]]
 
[[2023 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>
 +
 
[[2023 AMC 8 Problems/Problem 11|Solution]]
 
[[2023 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>
 +
 
[[2023 AMC 8 Problems/Problem 12|Solution]]
 
[[2023 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>
 +
 
[[2023 AMC 8 Problems/Problem 13|Solution]]
 
[[2023 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>
 +
 
[[2023 AMC 8 Problems/Problem 14|Solution]]
 
[[2023 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>
 +
 
[[2023 AMC 8 Problems/Problem 15|Solution]]
 
[[2023 AMC 8 Problems/Problem 15|Solution]]
  
 
==Problem 16==
 
==Problem 16==
 +
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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>
 +
 
[[2023 AMC 8 Problems/Problem 16|Solution]]
 
[[2023 AMC 8 Problems/Problem 16|Solution]]
  
 
==Problem 17==
 
==Problem 17==
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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>
 +
 
[[2023 AMC 8 Problems/Problem 17|Solution]]
 
[[2023 AMC 8 Problems/Problem 17|Solution]]
  
 
==Problem 18==
 
==Problem 18==
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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>
 +
 
[[2023 AMC 8 Problems/Problem 18|Solution]]
 
[[2023 AMC 8 Problems/Problem 18|Solution]]
  
 
==Problem 19==
 
==Problem 19==
 +
 +
<math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math>
 +
 
[[2023 AMC 8 Problems/Problem 19|Solution]]
 
[[2023 AMC 8 Problems/Problem 19|Solution]]
  
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==Problem 21==
 
==Problem 21==
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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>
 +
 
[[2023 AMC 8 Problems/Problem 21|Solution]]
 
[[2023 AMC 8 Problems/Problem 21|Solution]]
  
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[insert asy]
 
[insert asy]
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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>
  
 
[[2023 AMC 8 Problems/Problem 23|Solution]]
 
[[2023 AMC 8 Problems/Problem 23|Solution]]
  
 
==Problem 24==
 
==Problem 24==
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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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[[2023 AMC 8 Problems/Problem 24|Solution]]
 
[[2023 AMC 8 Problems/Problem 24|Solution]]
  
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What is the sum of digits of <math>a_{14}</math>?
 
What is the sum of digits of <math>a_{14}</math>?
  
−
<math>\textbf{(A)}~8\qquad\textbf{(B)}~9\qquad\textbf{(C)}~10\qquad\textbf{(D)}~11\qquad\textbf{(E)}~12</math>
+
<math>\textbf{(A)}\ 8 \qquad \textbf{(B)}\ 9 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 11 \qquad \textbf{(E)}\ 12</math>
  
 
[[2023 AMC 8 Problems/Problem 25|Solution]]
 
[[2023 AMC 8 Problems/Problem 25|Solution]]

Revision as of 18:28, 24 January 2023

2023 AMC 8 (Answer Key)
Printable versions: Wiki • AoPS Resources • PDF

Instructions

  1. This is a 25-question, multiple choice test. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct.
  2. You will receive 1 point for each correct answer. There is no penalty for wrong answers.
  3. No aids are permitted other than plain scratch paper, writing utensils, ruler, and erasers. In particular, graph paper, compass, protractor, calculators, computers, smartwatches, and smartphones are not permitted. Rules
  4. Figures are not necessarily drawn to scale.
  5. You will have 40 minutes working time to complete the test.
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

Problem 1

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

Solution

Problem 2

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

Solution

Problem 3

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

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

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

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

Two integers are inserted into the list $3,3,8,11,28$ to double it's range. The mode and median remain unchanged. What is the maximum possible sum of two additional numbers?

$\textbf{(A)}\ 56 \qquad \textbf{(B)}\ 57 \qquad \textbf{(C)}\ 58 \qquad \textbf{(D)}\ 60 \qquad \textbf{(E)}\ 61$

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

In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term is $4000$. What is the first term?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 10$

Solution

Problem 23

Each square in a 3x3 grid is randomly filled with one of the 4 gray-and-white tiles as shown below.

[insert asy]

What is the probability that the tiling will contain a large gray diamond in one of the smaller 2x2 grids? Below is such a tiling

[insert asy]

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

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

Fifteen integers $a_1, a_2, a_3, \dots, a_{15}$ are arranged in order on a number line. The integers are equally spaced and have the property that \[1 \le a_1 \le 10, \thickspace 13 \le a_2 \le 20, \thickspace 241 \le a_{15}\le 250.\] What is the sum of digits of $a_{14}$?

$\textbf{(A)}\ 8 \qquad \textbf{(B)}\ 9 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 11 \qquad \textbf{(E)}\ 12$

Solution

See Also

2023 AMC 8 (Problems • Answer Key • Resources)
Preceded by
2022 AMC 8 		Followed by
2024 AMC 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions
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