Difference between revisions of "2001 AIME I Problems/Problem 2"
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== Solution == | == Solution == | ||
| − | {{ | + | Let x be the mean of S. Let a be the number of elements in S. |
| + | Then, | ||
| + | <cmath>\FRAC{ax+1}{a+1}=x-13</cmath> | ||
| + | <cmath>\FRAC{ax+2001}{a+1}=x+27</cmath> | ||
== See Also == | == See Also == | ||
{{AIME box|year=2001|n=I|num-b=1|num-a=3}} | {{AIME box|year=2001|n=I|num-b=1|num-a=3}} | ||
Revision as of 22:54, 21 December 2007
Problem
A finite set 
of distinct real numbers has the following properties: the mean of 
is 
less than the mean of , and the mean of 
is 
more than the mean of . Find the mean of .
Solution
Let x be the mean of S. Let a be the number of elements in S. Then,
\[\FRAC{ax+1}{a+1}=x-13\] (Error compiling LaTeX. Unknown error_msg)
\[\FRAC{ax+2001}{a+1}=x+27\] (Error compiling LaTeX. Unknown error_msg)
See Also
| 2001 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
