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| | [[2018 AMC 12A Problems/Problem 25|Solution]] | | [[2018 AMC 12A Problems/Problem 25|Solution]] |
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| − | ==Problem 2==
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| − | 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?
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| − | <math>\textbf{(A) } 48 \qquad \textbf{(B) } 49 \qquad \textbf{(C) } 50 \qquad \textbf{(D) } 51 \qquad \textbf{(E) } 52 </math>
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| − | [[2018 AMC 12A Problems/Problem 2|Solution]]
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| − | ==Problem 3==
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| − | 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.)
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| − | <math>\textbf{(A) }3\qquad\textbf{(B) }6\qquad\textbf{(C) }12\qquad\textbf{(D) }18\qquad\textbf{(E) }24</math>
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| − | [[2018 AMC 12A Problems/Problem 3|Solution]]
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| − | ==Problem 4==
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| − | [[2018 AMC 12A Problems/Problem 4|Solution]]
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| − | ==Problem 5==
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| − | 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?
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| − | <math>\textbf{(A) }3 \qquad\textbf{(B) }4 \qquad\textbf{(C) }5 \qquad\textbf{(D) }6 \qquad\textbf{(E) }10 \qquad</math>
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| − | [[2018 AMC 12A Problems/Problem 5|Solution]]
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| − | ==Problem 6==
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| − | 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>?
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| − | <math>\textbf{(A)}20\qquad\textbf{(B)}21\qquad\textbf{(C)}22\qquad\textbf{(D)}23\qquad\textbf{(E)}24</math>
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| − | [[2018 AMC 12A Problems/Problem 6|Solution]]
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| − | ==Problem 7==
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| − | [[2018 AMC 12A Problems/Problem 17|Solution]]
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| − | ==Problem 8==
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| − | [[2018 AMC 12A Problems/Problem 8|Solution]]
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| − | ==Problem 9==
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| − | [[2018 AMC 12A Problems/Problem 9|Solution]]
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| − | ==Problem 10==
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| − | [[2018 AMC 12A Problems/Problem 10|Solution]]
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| − | ==Problem 11==
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| − | [[2018 AMC 12A Problems/Problem 11|Solution]]
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| − | ==Problem 12==
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| − | [[2018 AMC 12A Problems/Problem 12|Solution]]
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| − | ==Problem 13==
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| − | [[2018 AMC 12A Problems/Problem 13|Solution]]
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| − | ==Problem 14==
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| − | [[2018 AMC 12A Problems/Problem 14|Solution]]
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| − | ==Problem 15==
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| − | [[2018 AMC 12A Problems/Problem 15|Solution]]
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| − | ==Problem 16==
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| − | [[2018 AMC 12A Problems/Problem 16|Solution]]
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| − | ==Problem 17==
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| − | [[2018 AMC 12A Problems/Problem 17|Solution]]
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| − | ==Problem 18==
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| − | [[2018 AMC 12A Problems/Problem 18|Solution]]
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| − | ==Problem 19==
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| − | [[2018 AMC 12A Problems/Problem 19|Solution]]
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| − | ==Problem 20==
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| − | [[2018 AMC 12A Problems/Problem 20|Solution]]
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| − | ==Problem 21==
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| − | [[2018 AMC 12A Problems/Problem 21|Solution]]
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| − | ==Problem 22==
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| − | [[2018 AMC 12A Problems/Problem 22|Solution]]
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| − | ==Problem 23==
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| − | [[2018 AMC 12A Problems/Problem 23|Solution]]
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| − | ==Problem 24==
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| − | [[2018 AMC 12A Problems/Problem 24|Solution]]
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| − | ==Problem 25==
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| − | [[2018 AMC 12A Problems/Problem 25|Solution]]
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| − | ==Problem 2==
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| − | [[2018 AMC 12A Problems/Problem 2|Solution]]
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| − | ==Problem 3==
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| − | [[2018 AMC 12A Problems/Problem 3|Solution]]
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| − | ==Problem 4==
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| − | [[2018 AMC 12A Problems/Problem 4|Solution]]
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| − | ==Problem 5==
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| − | [[2018 AMC 12A Problems/Problem 5|Solution]]
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| − | ==Problem 6==
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| − | [[2018 AMC 12A Problems/Problem 6|Solution]]
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| − | ==Problem 7==
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| − | [[2018 AMC 12A Problems/Problem 17|Solution]]
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| − | ==Problem 8==
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| − | [[2018 AMC 12A Problems/Problem 8|Solution]]
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| − | ==Problem 9==
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| − | [[2018 AMC 12A Problems/Problem 9|Solution]]
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| − | ==Problem 10==
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| − | [[2018 AMC 12A Problems/Problem 10|Solution]]
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| − | ==Problem 11==
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| − | [[2018 AMC 12A Problems/Problem 11|Solution]]
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| − | ==Problem 12==
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| − | [[2018 AMC 12A Problems/Problem 12|Solution]]
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| − | ==Problem 13==
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| − | [[2018 AMC 12A Problems/Problem 13|Solution]]
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| − | ==Problem 14==
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| − | [[2018 AMC 12A Problems/Problem 14|Solution]]
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| − | ==Problem 15==
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| − | [[2018 AMC 12A Problems/Problem 15|Solution]]
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| − | ==Problem 16==
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| − | [[2018 AMC 12A Problems/Problem 16|Solution]]
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| − | ==Problem 17==
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| − | [[2018 AMC 12A Problems/Problem 17|Solution]]
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| − | ==Problem 18==
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| − | [[2018 AMC 12A Problems/Problem 18|Solution]]
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| − | ==Problem 19==
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| − | [[2018 AMC 12A Problems/Problem 19|Solution]]
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| − | ==Problem 20==
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| − | [[2018 AMC 12A Problems/Problem 20|Solution]]
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| − | ==Problem 21==
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| − | [[2018 AMC 12A Problems/Problem 21|Solution]]
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| − | ==Problem 22==
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| − | [[2018 AMC 12A Problems/Problem 22|Solution]]
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| − | ==Problem 23==
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| − | [[2018 AMC 12A Problems/Problem 23|Solution]]
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Problem 1
A large urn contains 
balls, of which 
are red and the rest are blue. How many of the blue balls must be removed so that the percentage of red balls in the urn will be 
? (No red balls are to be removed.)
Solution
Problem 2
While exploring a cave, Carl comes across a collection of 
-pound rocks worth 
each, 
-pound rocks worth 
each, and 
-pound rocks worth 
each. There are at least 
of each size. He can carry at most 
pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?
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.)
Solution
Problem 4
Solution
Problem 5
What is the sum of all possible values of 
for which the polynomials 
and 
have a root in common?
Solution
Problem 6
For positive integers 
and 
such that 
, both the mean and the median of the set 
are equal to . What is 
?
Solution
Problem 7
Solution
Problem 8
Solution
Problem 9
Solution
Problem 10
Solution
Problem 11
Solution
Problem 12
Solution
Problem 13
Solution
Problem 14
Solution
Problem 15
Solution
Problem 16
Solution
Problem 17
Solution
Problem 18
Solution
Problem 19
Solution
Problem 20
Solution
Problem 21
Solution
Problem 22
Solution
Problem 23
Solution
Problem 24
Solution
Problem 25
Solution
balls, of which 
are red and the rest are blue. How many of the blue balls must be removed so that the percentage of red balls in the urn will be 
? (No red balls are to be removed.)
-pound rocks worth 
each, 
-pound rocks worth 
each, and 
-pound rocks worth 
each. There are at least 
of each size. He can carry at most 
pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?
for which the polynomials 
and 
have a root in common?
and 
such that 
, both the mean and the median of the set 
are equal to 
?
