2016 AMC 12B Problems/Problem 22
Problem
For a certain positive integer less than
, the decimal equivalent of
is
, a repeating decimal of period of
, and the decimal equivalent of
is
, a repeating decimal of period
. In which interval does
lie?
Solution
Solution by e_power_pi_times_i
If ,
must be a factor of
. Also, by the same procedure,
must be a factor of
. Checking through all the factors of
and
that are less than
, we see that
is a solution, so the answer is
.
See Also
2016 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 21 |
Followed by Problem 23 |
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