Difference between revisions of "2004 AMC 12A Problems/Problem 25"
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Revision as of 20:19, 3 July 2013
Problem
For each integer , let
denote the base-
number
. The product
can be expressed as
, where
and
are positive integers and
is as small as possible. What is the value of
?
Solution
This is an infinite geometric series with common ratio and initial term
, so
.
Alternatively, we could have used the algebraic manipulation for repeating decimals,
Some factors cancel, (after all, isn't one of the answer choices)
Since the only factor in the numerator that goes into is
,
is minimized. Therefore the answer is
.
See Also
2004 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 24 |
Followed by Final Question |
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 AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.