2022 AMC 8
Complete problem set with solutions and individual problem pages
Problem 17 Hard
If is an even positive integer, the double factorial notation represents the product of all the even integers from to . For example, . What is the units digit of the following sum?
- A.
- B.
- C.
- D.
- E.
Answer:B
Solution 1
Notice that once the units digit of will be because there will be a factor of Thus, we only need to calculate the units digit of
We only care about units digits, so we have which has the same units digit as The answer is
Solution 2 (Solution 1 worded differently)
We can see that after in the sequence, the units digit is always (every value after is a multiple of ). Therefore, our answer is the sum of the units digits of and respectively. This sum is equal to , or
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