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2001 AIME Problems
2
Averages.
Averages.
Source:
December 6, 2005
Problem Statement
A finite set
S
\mathcal{S}
S
of distinct real numbers has the following properties: the mean of
S
∪
{
1
}
\mathcal{S}\cup\{1\}
S
∪
{
1
}
is 13 less than the mean of
S
\mathcal{S}
S
, and the mean of
S
∪
{
2001
}
\mathcal{S}\cup\{2001\}
S
∪
{
2001
}
is 27 more than the mean of
S
.
\mathcal{S}.
S
.
Find the mean of
S
.
\mathcal{S}.
S
.
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