Difference between revisions of "2023 AMC 10A Problems"
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[[2023 AMC 10A Problems/Problem 5|Solution]] | [[2023 AMC 10A Problems/Problem 5|Solution]] | ||
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| + | ==Problem 6== | ||
| + | An integer is assigned to each vertex of a cube. The value of an edge is defined to be the sum of the values of the two vertices it touches, and the value of a face is defined to be the sum of the values of the four edges surrounding it. The value of the cube is defined as the sum of the values of its six faces. Suppose the sum of the integers assigned to the vertices is 21. What is the value of the cube? | ||
==See also== | ==See also== | ||
{{AMC10 box|year=2023|ab=A|before=[[2022 Fall AMC 10B Problems]]|after=[[2023 AMC 10B Problems]]}} | {{AMC10 box|year=2023|ab=A|before=[[2022 Fall AMC 10B Problems]]|after=[[2023 AMC 10B Problems]]}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 19:51, 9 November 2023
| 2023 AMC 10A (Answer Key) Printable versions: • AoPS Resources • PDF | ||
|
Instructions
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| 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 
and 
are 
miles apart. Alicia lives in and Beth lives in . Alicia bikes towards at 18 miles per hour. Leaving at the same time, Beth bikes toward at 12 miles per hour. How many miles from City will they be when they meet?
Problem 2
The weight of 
of a large pizza together with 
cups of orange slices is the same weight of 
of a large pizza together with 
cups of orange slices. A cup of orange slices weight 
of a pound. What is the weight, in pounds, of a large pizza?
Problem 3
How many positive perfect squares less than 
are divisible by 
?
![\[\textbf{(A) } 8 \qquad\textbf{(B) }9 \qquad\textbf{(C) }10 \qquad\textbf{(D) }11 \qquad\textbf{(E) } 12\]](http://latex.artofproblemsolving.com/9/6/1/961f2de34a3d109d83bde67278c21feff976ac98.png)
Problem 4
A quadrilateral has all side lengths, a perimeter of 
, and one side of length 
. What is the greatest possible length of one side of this quadrilateral?
![\[\textbf{(A) } 9 \qquad\textbf{(B) }10 \qquad\textbf{(C) }11 \qquad\textbf{(D) }12 \qquad\textbf{(E) } 13\]](http://latex.artofproblemsolving.com/5/a/d/5ad471d15f7ac064c50aa53c6b76845b10a5ab3b.png)
Problem 5
How many digits are in the base-ten representation of 
?
![\[\qquad\textbf{(A) } 14 \qquad\textbf{(B) }15 \qquad\textbf{(C) }16 \qquad\textbf{(D) }17 \qquad\textbf{(E) } 18\]](http://latex.artofproblemsolving.com/2/d/8/2d82dc1dc809d244c94ea8ba7d45544ac49647b2.png)
Problem 6
An integer is assigned to each vertex of a cube. The value of an edge is defined to be the sum of the values of the two vertices it touches, and the value of a face is defined to be the sum of the values of the four edges surrounding it. The value of the cube is defined as the sum of the values of its six faces. Suppose the sum of the integers assigned to the vertices is 21. What is the value of the cube?
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
