Mock AIME 2 Pre 2005 Problems
Contents
[hide]Problem 1
Compute the largest integer such that
divides
.
Problem 2
is a real number with the property that
. Let
. Determine the value of
.
Problem 3
In a box, there are green balls,
blue balls,
red balls, a brown ball, a white ball, and a black ball. These balls are randomly drawn out of the box one at a time (without replacement) until two of the same color have been removed. This process requires that at most
balls be removed. The probability that
balls are drawn can be expressed as
, where
and
are relatively prime positive integers. Compute
.
Problem 4
Let . Given that
has
digits, how many elements of
begin with the digit
?
Problem 5
Let be the set of integers
for which
, an infinite decimal that has the property that
for all positive integers
. Given that
is prime, how many positive integers are in
? (The
are digits.)