2011 AMC 8 Problem 22
Attempt Problem 22 of the 2011 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
What is the tens digit of
Answer: D
Small hint:
The last two digits of powers of repeat every powers.
Big hint:
Work modulo , since the tens digit depends on the last two digits.
Solution:
To find the tens digit, it is enough to track powers of modulo . Since , the last two digits repeat every four powers.
Because , we have Thus the tens digit is .
Thus, D is the correct answer.
Problem 22 in other years
- 1985 AMC 8
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