2006 Alabama ARML TST Problems/Problem 1

Problem

How many integers $x$ satisfy the inequality

$(x-2006)(x-2004)(x-2002)\cdots (x-4)<0?$

Solution

There are 1002 terms in that polynomial, and the product is less than 0 when an odd number of them are less than 0, and that happens when x is 2005, 2001, 1997, .... , or 5. There are $\boxed{501}$ numbers in that list.

See also

2006 Alabama ARML TST (Problems)
Preceded by:
First Question
Followed by:
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15