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number theory intermediate
Problem
What are the sign and units digit of the product of all the odd negative integers strictly greater than ?
(A)
It is a negative number ending with a 1.
(B)
It is a positive number ending with a 1.
(C)
It is a negative number ending with a 5.
(D)
It is a positive number ending with a 5.
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.
Final answer
C