2023 AMC 8 Problems

2023 AMC 8 (Answer Key) Printable versions: Wiki • AoPS Resources • PDF
Instructions 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. You will receive 1 point for each correct answer. There is no penalty for wrong answers. 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 Figures are not necessarily drawn to scale. You will have 40 minutes working time to complete the test.
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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 its 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

2023 AMC 8 (Problems • Answer Key • Resources)
Preceded by 2022 AMC 8	Followed by 2024 AMC 8
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All AJHSME/AMC 8 Problems and Solutions

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2023 AMC 8 Problems

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

See Also