1997 AMC 8 Problem 25
Attempt Problem 25 of the 1997 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 1997 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
All of the even numbers from to inclusive, excluding those ending in are multiplied together. What is the rightmost digit (the units digit) of the product?
Answer: D
Small hint:
Group the factors by their units digit pattern
Big hint:
Only the units digits matter
Solution:
We only care about the units digit, which means that the tens digits don’t matter.
Then we have groups of
The units digit of each group is We now need to find the units digit of
The units digit of is This means we only need to find the units digit of
Note that every power of always ends in a (e.g. ).
Thus, D is the correct answer.
Problem 25 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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