2015 AMC 10B Problems/Problem 10
Contents
Problem
What are the sign and units digit of the product of all the odd negative integers strictly greater than ?
It is a negative number ending with a 1.
It is a positive number ending with a 1.
It is a negative number ending with a 5.
It is a positive number ending with a 5.
It is a negative number ending with a 0.
Solution
Since , the product must end with a .
The multiplicands are the odd negative integers from to . There are of these numbers. Since , the product is negative.
Therefore, the answer must be
Alternatively, we can calculate the units digit of each group of 5 odd numbers using modular arithmetic
Video Solution
~savannahsolver
See Also
2015 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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All AMC 10 Problems and Solutions |
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