|
|
Line 101: |
Line 101: |
| | | |
| [[2018 AMC 12A Problems/Problem 25|Solution]] | | [[2018 AMC 12A Problems/Problem 25|Solution]] |
− |
| |
− | ==Problem 2==
| |
− |
| |
− | While exploring a cave, Carl comes across a collection of <math>5</math>-pound rocks worth <math>$14</math> each, <math>4</math>-pound rocks worth <math>$11</math> each, and <math>1</math>-pound rocks worth <math>$2</math> each. There are at least <math>20</math> of each size. He can carry at most <math>18</math> pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?
| |
− |
| |
− | <math>\textbf{(A) } 48 \qquad \textbf{(B) } 49 \qquad \textbf{(C) } 50 \qquad \textbf{(D) } 51 \qquad \textbf{(E) } 52 </math>
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 2|Solution]]
| |
− |
| |
− | ==Problem 3==
| |
− |
| |
− | How many ways can a student schedule 3 mathematics courses -- algebra, geometry, and number theory -- in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)
| |
− |
| |
− | <math>\textbf{(A) }3\qquad\textbf{(B) }6\qquad\textbf{(C) }12\qquad\textbf{(D) }18\qquad\textbf{(E) }24</math>
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 3|Solution]]
| |
− |
| |
− | ==Problem 4==
| |
− |
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 4|Solution]]
| |
− |
| |
− | ==Problem 5==
| |
− |
| |
− | What is the sum of all possible values of <math>k</math> for which the polynomials <math>x^2 - 3x + 2</math> and <math>x^2 - 5x + k</math> have a root in common?
| |
− |
| |
− | <math>\textbf{(A) }3 \qquad\textbf{(B) }4 \qquad\textbf{(C) }5 \qquad\textbf{(D) }6 \qquad\textbf{(E) }10 \qquad</math>
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 5|Solution]]
| |
− | ==Problem 6==
| |
− |
| |
− | For positive integers <math>m</math> and <math>n</math> such that <math>m+10<n+1</math>, both the mean and the median of the set <math>\{m, m+4, m+10, n+1, n+2, 2n\}</math> are equal to <math>n</math>. What is <math>m+n</math>?
| |
− |
| |
− | <math>\textbf{(A)}20\qquad\textbf{(B)}21\qquad\textbf{(C)}22\qquad\textbf{(D)}23\qquad\textbf{(E)}24</math>
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 6|Solution]]
| |
− | ==Problem 7==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 17|Solution]]
| |
− | ==Problem 8==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 8|Solution]]
| |
− | ==Problem 9==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 9|Solution]]
| |
− | ==Problem 10==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 10|Solution]]
| |
− | ==Problem 11==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 11|Solution]]
| |
− | ==Problem 12==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 12|Solution]]
| |
− | ==Problem 13==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 13|Solution]]
| |
− | ==Problem 14==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 14|Solution]]
| |
− | ==Problem 15==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 15|Solution]]
| |
− | ==Problem 16==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 16|Solution]]
| |
− | ==Problem 17==
| |
− | [[2018 AMC 12A Problems/Problem 17|Solution]]
| |
− |
| |
− | ==Problem 18==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 18|Solution]]
| |
− | ==Problem 19==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 19|Solution]]
| |
− | ==Problem 20==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 20|Solution]]
| |
− | ==Problem 21==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 21|Solution]]
| |
− | ==Problem 22==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 22|Solution]]
| |
− | ==Problem 23==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 23|Solution]]
| |
− | ==Problem 24==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 24|Solution]]
| |
− | ==Problem 25==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 25|Solution]]
| |
− |
| |
− | ==Problem 2==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 2|Solution]]
| |
− | ==Problem 3==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 3|Solution]]
| |
− | ==Problem 4==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 4|Solution]]
| |
− | ==Problem 5==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 5|Solution]]
| |
− | ==Problem 6==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 6|Solution]]
| |
− | ==Problem 7==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 17|Solution]]
| |
− | ==Problem 8==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 8|Solution]]
| |
− | ==Problem 9==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 9|Solution]]
| |
− | ==Problem 10==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 10|Solution]]
| |
− | ==Problem 11==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 11|Solution]]
| |
− | ==Problem 12==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 12|Solution]]
| |
− | ==Problem 13==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 13|Solution]]
| |
− | ==Problem 14==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 14|Solution]]
| |
− | ==Problem 15==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 15|Solution]]
| |
− | ==Problem 16==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 16|Solution]]
| |
− | ==Problem 17==
| |
− | [[2018 AMC 12A Problems/Problem 17|Solution]]
| |
− |
| |
− | ==Problem 18==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 18|Solution]]
| |
− | ==Problem 19==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 19|Solution]]
| |
− | ==Problem 20==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 20|Solution]]
| |
− | ==Problem 21==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 21|Solution]]
| |
− | ==Problem 22==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 22|Solution]]
| |
− | ==Problem 23==
| |
− |
| |
− | [[2018 AMC 12A Problems/Problem 23|Solution]]
| |