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Difference between revisions of "2022 AMC 12B Problems"

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==Problem 1 ==
 
==Problem 1 ==
  
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Define <math>x\diamond y</math> to be <math>|x-y|</math> for all real numbers <math>x</math> and <math>y</math>. What is the value of<cmath>(1\diamond(2\diamond3))-((1\diamond2)\diamond3)?</cmath>
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<math> \textbf{(A)}\ -2 \qquad
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\textbf{(B)}\ -1 \qquad
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\textbf{(C)}\ 0 \qquad
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\textbf{(D)}\ 1 \qquad
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\textbf{(E)}\ 2</math>
  
 
[[2022 AMC 12B Problems/Problem 1|Solution]]
 
[[2022 AMC 12B Problems/Problem 1|Solution]]

Revision as of 15:33, 17 November 2022

2022 AMC 12B (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 6 points for each correct answer, 2.5 points for each problem left unanswered if the year is before 2006, 1.5 points for each problem left unanswered if the year is after 2006, and 0 points for each incorrect answer.
  3. No aids are permitted other than scratch paper, graph paper, ruler, compass, protractor and erasers (and calculators that are accepted for use on the test if before 2006. No problems on the test will require the use of a calculator).
  4. Figures are not necessarily drawn to scale.
  5. You will have 75 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

Define $x\diamond y$ to be $|x-y|$ for all real numbers $x$ and $y$. What is the value of\[(1\diamond(2\diamond3))-((1\diamond2)\diamond3)?\] $\textbf{(A)}\ -2 \qquad \textbf{(B)}\ -1 \qquad \textbf{(C)}\ 0 \qquad \textbf{(D)}\ 1 \qquad \textbf{(E)}\ 2$

Solution

Problem 2

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Solution

Problem 3

How many of the first ten numbers of the sequence $121$, $11211$, $1112111$, ... are prime numbers?

$\text{(A) } 0 \qquad \text{(B) }1 \qquad \text{(C) }2 \qquad \text{(D) }3 \qquad \text{(E) }4$

Solution

Problem 4

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Solution

Problem 5

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Solution

Problem 6

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Solution

Problem 7

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Solution

Problem 8

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Solution

Problem 9

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Solution

Problem 10

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Solution


Problem 11

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Solution

Problem 12

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Solution

Problem 13

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Solution

Problem 14

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Solution

Problem 15

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Solution

Problem 16

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Solution

Problem 17

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Solution

Problem 18

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Solution

Problem 19

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Solution

Problem 20

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Solution


Problem 21

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Solution

Problem 22

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Solution

Problem 23

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Solution

Problem 24

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Solution

Problem 25

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Solution

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