Mock AIME 6 2006-2007 Problems

Revision as of 14:16, 30 November 2014 by JoetheFixer (talk | contribs) (Problem 2)

Problem 1

Let $T$ be the sum of all positive integers of the form $2^r\cdot3^s$, where $r$ and $s$ are nonnegative integers that do not exceed $4$. Find the remainder when $T$ is divided by $1000$.

Solution

Problem 2

Draw in the diagonals of a regular octagon. What is the sum of all distinct angle measures, in degrees, formed by the intersections of the diagonals in the interior of the octagon? Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution