1997 AJHSME Problems/Problem 25
Problem
All of the even numbers from 2 to 98 inclusive, excluding those ending in 0, are multiplied together. What is the rightmost digit (the units digit) of the product?
Solution
All the tens digits of the product will be irrelevant to finding the units digit. Thus, we are searching for the units digit of
There will be groups of numbers. The number now can be rewritten as
Simplifiying the ins384)^{10}3844^{10}$.
Now, we try to find a pattern to the units digit of$ (Error compiling LaTeX. Unknown error_msg)4^n4^1 = 44^2 = 4\cdot 4 = 1\underline{6}14^3 = 1 \cdot 4 = \underline{4}$$ (Error compiling LaTeX. Unknown error_msg)4^4 = 4 \cdot 4 = 1\underline{6}14^5 = 1 \cdot 4 = \underline{4}\mod {10}$.
Thus, the pattern of the units digits is$ (Error compiling LaTeX. Unknown error_msg)\{4, 6, 4, 6, 4, 6, 4, 6, 4, 6\}nn+26\boxed{D}$
See Also
1997 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Question | |
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All AJHSME/AMC 8 Problems and Solutions |
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