Difference between revisions of "2016 AMC 10B Problems/Problem 8"
(Created page with "==Problem== What is the tens digit of <math>2015^{2016}-2017?</math> <math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 5 \qquad \textb...") |
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\textbf{(D)}\ 5 \qquad | \textbf{(D)}\ 5 \qquad | ||
\textbf{(E)}\ 8</math> | \textbf{(E)}\ 8</math> | ||
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| + | ==Solution== | ||
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| + | We notice that <math>2015^{n}</math> is 25 (mod 100) when n is even and 75 (mod 100) when n is odd. (check for yourself). Since 2016 is even, <math>2015^{2016}</math> is 25 (mod 100) and <math>2015^{2016}-2017 \equiv 25 - 17 /equiv 08 (mod 100)</math> | ||
| + | So the answer is <math>\textbf{(A)}\ 0 \qquad</math> | ||
| + | solution by Wwang | ||
Revision as of 10:49, 21 February 2016
Problem
What is the tens digit of 
Solution
We notice that 
is 25 (mod 100) when n is even and 75 (mod 100) when n is odd. (check for yourself). Since 2016 is even, 
is 25 (mod 100) and 
So the answer is 
solution by Wwang
