Difference between revisions of "2016 AMC 10B Problems/Problem 8"
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~savannahsolver | ~savannahsolver | ||
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| + | == Video Solution == | ||
| + | https://youtu.be/zfChnbMGLVQ?t=2683 | ||
| + | |||
| + | ~ pi_is_3.14 | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2016|ab=B|num-b=7|num-a=9}} | {{AMC10 box|year=2016|ab=B|num-b=7|num-a=9}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 01:18, 17 January 2021
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
Video Solution
https://youtu.be/zfChnbMGLVQ?t=2683
~ pi_is_3.14
See Also
| 2016 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
