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2002 AMC 12B Problems/Problem 1

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Problem

The arithmetic mean of the nine numbers in the set \{9, 99, 999, 9999, \ldots, 999999999\} is a 9-digit number M, all of whose digits are distinct. The number M does not contain the digit

\mathrm{(A)}\ 0\qquad\mathrm{(B)}\ 2\qquad\mathrm{(C)}\ 4\qquad\mathrm{(D)}\ 6\qquad\mathrm{(E)}\ 8

Solution

The average of the nine numbers is M=\frac{9 + 99 + \cdots + 999999999}{9} = 1 + 11 + \cdots + 111111111 = 123456789

which does not have the digit 0 \Rightarrow \mathrm{(A)}.

See also

2002 AMC 12B (ProblemsResources)
Preceded by
First question
Followed by
Problem 2
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
Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.
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