Difference between revisions of "2016 AMC 10B Problems/Problem 8"
(→Solution) |
(→Solution) |
||
Line 11: | Line 11: | ||
==Solution== | ==Solution== | ||
− | We notice that <math>2015^{n}</math> is 25 (mod 100) when n is even and 75 (mod 100) when n is odd. ( | + | We notice that <math>2015^{n}</math> is <math>25 (mod 100)</math> when <math>n is even</math> and <math>75 (mod 100)</math> when <math>n is odd.</math> (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> | So the answer is <math>\textbf{(A)}\ 0 \qquad</math> | ||
solution by Wwang | solution by Wwang |
Revision as of 10:22, 21 February 2016
Problem
What is the tens digit of
Solution
We notice that is when and when (Check for yourself). Since 2016 is even, is 25 (mod 100) and
So the answer is
solution by Wwang