2016 AMC 10B Problems/Problem 8
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Problem
What is the tens digit of
Solution 1
Notice that, for ,
is congruent to
when
is even and
when
is odd. (Check for yourself). Since
is even,
and
.
So the answer is .
Solution 2
In a very similar fashion, we find that , which equals
. Next, since every power (greater than
) of every number ending in
will end in
(which can easily be verified), we get
. (In this way, we don't have to worry about the exponent very much.) Finally,
, and thus
, as above.
Video Solution
~savannahsolver
See Also
2016 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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All AMC 10 Problems and Solutions |
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