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Difference between revisions of "2013 AMC 8 Problems"

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==Problem 1==
 
==Problem 1==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 2==
 
==Problem 2==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 3==
 
==Problem 3==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 4==
 
==Problem 4==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 5==
 
==Problem 5==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 6==
 
==Problem 6==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 7==
 
==Problem 7==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 8==
 
==Problem 8==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 9==
 
==Problem 9==
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p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 10==
 
==Problem 10==
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p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 11==
 
==Problem 11==
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p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 12==
 
==Problem 12==
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p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 13==
 
==Problem 13==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 14==
 
==Problem 14==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 15==
 
==Problem 15==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 16==
 
==Problem 16==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 17==
 
==Problem 17==
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 18==
 
==Problem 18==
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p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 19==
 
==Problem 19==
−
p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 20==
 
==Problem 20==
−
p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 21==
 
==Problem 21==
−
p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 22==
 
==Problem 22==
−
p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
  
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==Problem 23==
 
==Problem 23==
−
p
 
  
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 24==
 
==Problem 24==
−
p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
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==Problem 25==
 
==Problem 25==
−
p
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<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>
 
<math> \textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in} </math>

Revision as of 18:47, 20 November 2013

Problem 1

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 2

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 3

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 4

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 5

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 6

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 7

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 8

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 9

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 10

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 11

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 12

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 13

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 14

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 15

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 16

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 17

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 18

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 19

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 20

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 21

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 22

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 23

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 24

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution

Problem 25

$\textbf{(A)}\hspace{.05in}\qquad\textbf{(B)}\hspace{.05in}\qquad\textbf{(C)}\hspace{.05in}\qquad\textbf{(D)}\hspace{.05in}\qquad\textbf{(E)}\hspace{.05in}$

Solution The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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