Difference between revisions of "2000 AMC 8 Problems/Problem 14"
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<math>\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 9</math> | <math>\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 9</math> | ||
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+ | ==Video Solution== | ||
+ | https://youtu.be/7an5wU9Q5hk?t=1552 | ||
==Solution== | ==Solution== |
Revision as of 20:06, 27 October 2020
Problem
What is the units digit of ?
Video Solution
https://youtu.be/7an5wU9Q5hk?t=1552
Solution
Finding a pattern for each half of the sum, even powers of have a units digit of , and odd powers of have a units digit of . So, has a units digit of .
Powers of have the exact same property, so also has a units digit of . which has a units digit of , so the answer is .
Solution 2
Using modular arithmetic:
Similarly,
We have
-ryjs
Solution 3
Experimentation gives
Using this we have
Both and are odd, so we are left with which has units digit -ryjs
See Also
2000 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.