Difference between revisions of "2023 AMC 10A Problems"
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==Problem 5== | ==Problem 5== | ||
| − | How many digits are in the base-ten representation of <math>8^5 \cdot 5^ | + | How many digits are in the base-ten representation of <math>8^5 \cdot 5^{10} \cdot 15^5</math>? |
<cmath>\qquad\textbf{(A) } 14 \qquad\textbf{(B) }15 \qquad\textbf{(C) }16 \qquad\textbf{(D) }17 \qquad\textbf{(E) } 18</cmath> | <cmath>\qquad\textbf{(A) } 14 \qquad\textbf{(B) }15 \qquad\textbf{(C) }16 \qquad\textbf{(D) }17 \qquad\textbf{(E) } 18</cmath> | ||
Revision as of 19:44, 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)
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. 
