Difference between revisions of "2014 AMC 8 Problems/Problem 13"

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If <math>n</math> and <math>m</math> are integers and <math>n^2+m^2</math> is even, which of the following is impossible?
 
If <math>n</math> and <math>m</math> are integers and <math>n^2+m^2</math> is even, which of the following is impossible?
  
<math>\textbf{(A) }n and m are even \qquad\textbf{(B) }n and m are odd \qquad\textbf{(C) }n+m is even \qquad\textbf{(D) }n+m is odd \qquad \textbf{(E) } none of these are impossible</math>
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<math>\textbf{(A) }</math><math>n</math> and <math>m</math> are even <math>\qquad\textbf{(B) }</math><math>n</math> and <math>m</math> are odd <math>\qquad\textbf{(C) }</math><math>n+m</math> is even <math>\qquad\textbf{(D) }</math><math>n+m</math> is odd <math>\qquad \textbf{(E) }</math> none of these are impossible
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2014|num-b=12|num-a=14}}
 
{{AMC8 box|year=2014|num-b=12|num-a=14}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 18:39, 26 November 2014

If $n$ and $m$ are integers and $n^2+m^2$ is even, which of the following is impossible?

$\textbf{(A) }$$n$ and $m$ are even $\qquad\textbf{(B) }$$n$ and $m$ are odd $\qquad\textbf{(C) }$$n+m$ is even $\qquad\textbf{(D) }$$n+m$ is odd $\qquad \textbf{(E) }$ none of these are impossible

See Also

2014 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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