Difference between revisions of "2001 AIME I Problems/Problem 2"

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== Problem ==
 
== Problem ==
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A finite set <math>\mathcal{S}</math> of distinct real numbers has the following properties: the mean of <math>\mathcal{S}\cup\{1\}</math> is <math>13</math> less than the mean of <math>\mathcal{S}</math>, and the mean of <math>\mathcal{S}\cup\{2001\}</math> is <math>27</math> more than the mean of <math>\mathcal{S}</math>. Find the mean of <math>\mathcal{S}</math>.
  
 
== Solution ==
 
== Solution ==
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{{solution}}
  
{{AIME box|year=2001|num-b=1|num-a=3}}
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== See Also ==
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{{AIME box|year=2001|n=I|num-b=1|num-a=3}}

Revision as of 00:19, 20 November 2007

Problem

A finite set $\mathcal{S}$ of distinct real numbers has the following properties: the mean of $\mathcal{S}\cup\{1\}$ is $13$ less than the mean of $\mathcal{S}$, and the mean of $\mathcal{S}\cup\{2001\}$ is $27$ more than the mean of $\mathcal{S}$. Find the mean of $\mathcal{S}$.

Solution

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See Also

2001 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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All AIME Problems and Solutions
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