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Difference between revisions of "2023 AMC 8 Problems"

(→‎Problem 25)
(→‎Problem 25)
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==Problem 25==
 
==Problem 25==
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[[2023 AMC 8 Problems/Problem 25|Solution]]
 
  
 
Fifteen integers <math>a_1, a_2, a_3, \dots, a_{15}</math> are arranged in order on a number line. The integers are equally spaced and have the property that
 
Fifteen integers <math>a_1, a_2, a_3, \dots, a_{15}</math> are arranged in order on a number line. The integers are equally spaced and have the property that
 
<cmath>1 \le a_1 \le 10, \thickspace 13 \le a_2 \le 20, \thickspace 241 \le a_{15}\le 250.</cmath>
 
<cmath>1 \le a_1 \le 10, \thickspace 13 \le a_2 \le 20, \thickspace 241 \le a_{15}\le 250.</cmath>
 
What is the sum of digits of <math>a_{14}</math>?
 
What is the sum of digits of <math>a_{14}</math>?
−
<cmath>\textbf{(A)}~8\qquad\textbf{(B)}~9\qquad\textbf{(C)}~10\qquad\textbf{(D)}~11\qquad\textbf{(E)}~12</cmath>
+
 
 +
<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]]
  
 
==See Also==
 
==See Also==

Revision as of 18:02, 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

Solution

Problem 2

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

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

Solution

Problem 24

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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