Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2025 AMC 8 Problems"

(2025 AMC 8 Problem 9)
(→‎Problem 10)
Line 41: Line 41:
 
==Problem 10==
 
==Problem 10==
  
−
The 2025 AMC 8 is not held yet. '''Please do not post false problems.'''
+
There are fifty \$1, \$2, and \$5 notes. There are two more \$1 notes than \$2 notes. Given that the total value of the notes is \$116, find the number of \$5 notes.
 +
 
 +
<math>\textbf{(A) } 9\qquad\textbf{(B) } 10\qquad\textbf{(C) } 11\qquad\textbf{(D) } 12\qquad\textbf{(E) } 13</math>
  
 
==Problem 11==
 
==Problem 11==

Revision as of 08:40, 23 February 2024

Problem 1

Let $m$ and $n$ be $2$ integers such that $m>n$. Suppose $m+n=20$, $m^2+n^2=328$, find $m^2-n^2$.

$\textbf{(A)}\ 280 \qquad \textbf{(B)}\ 292 \qquad \textbf{(C)}\ 300 \qquad \textbf{(D)}\ 320 \qquad \textbf{(E)}\ 340$

Problem 2

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 3

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 4

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 5

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 6

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 7

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 8

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 9

There are $10$ matchsticks on the table. Percy takes $1$, $2$ or $3$ matchsticks each time. How many ways are there for him to take all the matchsticks?

$\textbf{(A)}\ 274 \qquad \textbf{(B)}\ 275 \qquad \textbf{(C)}\ 276 \qquad \textbf{(D)}\ 280 \qquad \textbf{(E)}\ 295$

Problem 10

There are fifty $1, $2, and $5 notes. There are two more $1 notes than $2 notes. Given that the total value of the notes is $116, find the number of $5 notes.

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

Problem 11

Find the smallest positive integer $k$ such that $(2^{91}+k)$ is divisible by $127$.

$\textbf{(A)}\ 122 \qquad \textbf{(B)}\ 123 \qquad \textbf{(C)}\ 124 \qquad \textbf{(D)}\ 125 \qquad \textbf{(E)}\ 126$

Problem 12

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 13

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 14

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 15

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 16

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 17

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 18

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 19

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 20

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 21

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 22

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 23

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 24

The 2025 AMC 8 is not held yet. Please do not post false problems.

Problem 25

The 2025 AMC 8 is not held yet. Please do not post false problems.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2025_AMC_8_Problems&oldid=216117"