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 1. There are $\boxed{502}$ numbers in that list.

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

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2006 Alabama ARML TST Problems/Problem 1

Problem

Solution

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