|
|
| (14 intermediate revisions by 8 users not shown) |
| Line 1: |
Line 1: |
| − | ==Problem 1==
| |
| − |
| |
| − | Let <math>m</math> and <math>n</math> be <math>2</math> integers such that <math>m>n</math>. Suppose <math>m+n=20</math>, <math>m^2+n^2=328</math>, find <math>m^2-n^2</math>.
| |
| − |
| |
| − | <math>\textbf{(A)}\ 280 \qquad \textbf{(B)}\ 292 \qquad \textbf{(C)}\ 300 \qquad \textbf{(D)}\ 320 \qquad \textbf{(E)}\ 340</math>
| |
| − |
| |
| − | ==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==
| |
| − |
| |
| − | ==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.
| |
| − |
| |
| − | <math>\textbf{(A) } 9\qquad\textbf{(B) } 10\qquad\textbf{(C) } 11\qquad\textbf{(D) } 12\qquad\textbf{(E) } 13</math>
| |
| − |
| |
| − | ==Problem 11==
| |
| − |
| |
| − | Find the smallest positive integer <math>k</math> such that <math>(2^{91}+k)</math> is divisible by <math>127</math>.
| |
| − |
| |
| − | <math>\textbf{(A)}\ 122 \qquad \textbf{(B)}\ 123 \qquad \textbf{(C)}\ 124 \qquad \textbf{(D)}\ 125 \qquad \textbf{(E)}\ 126</math>
| |
| − |
| |
| − | ==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.''' | | The 2025 AMC 8 is not held yet. '''Please do not post false problems.''' |
