Difference between revisions of "2006 Alabama ARML TST Problems/Problem 1"
(New page: ==Problem== How many integers <math>x</math> satisfy the inequality <center><math>(x-2006)(x-2004)(x-2002)\cdots (x-4)<0?</math></center> ==Solution== {{solution}} ==See also==) |
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==Solution== | ==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 <math>\boxed{501}</math> numbers in that list. |
==See also== | ==See also== | ||
| + | {{ARML box|year=2006|state=Alabama|before=First Question|num-a=2}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
Latest revision as of 09:28, 1 August 2024
Problem
How many integers 
satisfy the inequality
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 | ||
