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imc

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