MathDB

2

Part of 2006 AIME Problems

Problems(2)

Subset Sums

Source: 2006 AIME A Problem 2

3/9/2006
Let set A\mathcal{A} be a 90-element subset of {1,2,3,…,100},\{1,2,3,\ldots,100\}, and let SS be the sum of the elements of A\mathcal{A}. Find the number of possible values of SS.
AMCAIME
Creatively titled geometry

Source: 2006 AIME II 2

3/28/2006
The lengths of the sides of a triangle with positive area are log⁡1012\log_{10} 12, log⁡1075\log_{10} 75, and log⁡10n\log_{10} n, where nn is a positive integer. Find the number of possible values for nn.
geometrylogarithmsAMCtriangle inequality