Problem:
What are the sign and units digit of the product of all the odd negative integers strictly greater than ?
Answer Choices:
A. It is a negative number ending with a .
B. It is a positive number ending with a .
C. It is a negative number ending with a .
D. It is a positive number ending with a .
E. It is a negative number ending with a .
Solution:
There are negative integers strictly greater than , and exactly half of them, or , are odd. The product of an odd number of negative numbers is negative. Furthermore, because all factors are odd and some of them are multiples of , this product is an odd multiple of and therefore has units digit .
The problems on this page are the property of the MAA's American Mathematics Competitions