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Difference between revisions of "2023 AMC 10A Problems"

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{{AMC10 Problems|year=2023|ab=A}}
  
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==Problem 1==
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Cities <math>A</math> and <math>B</math> are <math>45</math> miles apart. Alicia lives in <math>A</math> and Beth lives in <math>B</math>. Alicia bikes towards <math>B</math> at 18 miles per hour. Leaving at the same time, Beth bikes toward <math>A</math> at 12 miles per hour. How many miles from City <math>A</math> will they be when they meet?
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<math>\textbf{(A) }20\qquad\textbf{(B) }24\qquad\textbf{(C) }25\qquad\textbf{(D) }26\qquad\textbf{(E) }27</math>
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[[2023 AMC 10A Problems/Problem 1|Solution]]
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==Problem 2==
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The weight of <math>\frac{1}{3}</math> of a large pizza together with <math>3 \frac{1}{2}</math> cups of orange slices is the same weight of <math>\frac{3}{4}</math> of a large pizza together with <math>\frac{1}{2}</math> cups of orange slices. A cup of orange slices weight <math>\frac{1}{4}</math> of a pound. What is the weight, in pounds, of a large pizza?
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[[2023 AMC 10A Problems/Problem 2|Solution]]
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==Problem 3==
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How many positive perfect squares less than <math>2023</math> are divisible by <math>5</math>?
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<cmath>\textbf{(A) } 8 \qquad\textbf{(B) }9 \qquad\textbf{(C) }10 \qquad\textbf{(D) }11 \qquad\textbf{(E) } 12</cmath>
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[[2023 AMC 10A Problems/Problem 3|Solution]]
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==Problem 4==
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A quadrilateral has all side lengths, a perimeter of <math>26</math>, and one side of length <math>4</math>. What is the greatest possible length of one side of this quadrilateral?
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<cmath>\textbf{(A) } 9 \qquad\textbf{(B) }10 \qquad\textbf{(C) }11 \qquad\textbf{(D) }12 \qquad\textbf{(E) } 13</cmath>
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==See also==
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{{AMC10 box|year=2023|ab=A|before=[[2022 Fall AMC 10B Problems]]|after=[[2023 AMC 10B Problems]]}}
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{{MAA Notice}}

Revision as of 19:25, 9 November 2023

2023 AMC 10A (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 SAT 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

Cities $A$ and $B$ are $45$ miles apart. Alicia lives in $A$ and Beth lives in $B$. Alicia bikes towards $B$ at 18 miles per hour. Leaving at the same time, Beth bikes toward $A$ at 12 miles per hour. How many miles from City $A$ will they be when they meet? $\textbf{(A) }20\qquad\textbf{(B) }24\qquad\textbf{(C) }25\qquad\textbf{(D) }26\qquad\textbf{(E) }27$

Solution

Problem 2

The weight of $\frac{1}{3}$ of a large pizza together with $3 \frac{1}{2}$ cups of orange slices is the same weight of $\frac{3}{4}$ of a large pizza together with $\frac{1}{2}$ cups of orange slices. A cup of orange slices weight $\frac{1}{4}$ of a pound. What is the weight, in pounds, of a large pizza?

Solution

Problem 3

How many positive perfect squares less than $2023$ are divisible by $5$?

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

Solution

Problem 4

A quadrilateral has all side lengths, a perimeter of $26$, and one side of length $4$. What is the greatest possible length of one side of this quadrilateral?

\[\textbf{(A) } 9 \qquad\textbf{(B) }10 \qquad\textbf{(C) }11 \qquad\textbf{(D) }12 \qquad\textbf{(E) } 13\]

See also

2023 AMC 10A (Problems • Answer Key • Resources)
Preceded by
2022 Fall AMC 10B Problems 		Followed by
2023 AMC 10B Problems
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 AMC 10 Problems and Solutions

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