Difference between revisions of "2006 Alabama ARML TST Problems/Problem 1"
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− | { | + | 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 <math>\boxed{501}</math> numbers in that list. |
==See also== | ==See also== | ||
{{ARML box|year=2006|state=Alabama|before=First Question|num-a=2}} | {{ARML box|year=2006|state=Alabama|before=First Question|num-a=2}} | ||
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+ | [[Category:Introductory Algebra Problems]] |
Latest revision as of 10:28, 1 August 2024
Problem
How many integers satisfy the inequality
![$(x-2006)(x-2004)(x-2002)\cdots (x-4)<0?$](http://latex.artofproblemsolving.com/0/e/3/0e3dd1ad272fd8a547d857b5700f6a79e0edd918.png)
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 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 |