2011年AIME II 真题:
Problem 1
Gary purchased a large beverage, but only drank of it, where
and
are relatively prime positive integers. If he had purchased half as much and drunk twice as much, he would have wasted only
as much beverage. Find
.
Problem 2
On square , point
lies on side
and point
lies on side
, so that
. Find the area of the square
.
Problem 3
The degree measures of the angles in a convex 18-sided polygon form an increasing arithmetic sequence with integer values. Find the degree measure of the smallest angle.
Problem 4
In triangle ,
and
. The angle bisector of angle
intersects
at point
, and point
is the midpoint of
. Let
be the point of intersection of
and the line
. The ratio of
to
can be expressed in the form
, where
and
are relatively prime positive integers. Find
.
Problem 5
The sum of the first terms of a geometric sequence is
. The sum of the first
terms is
. Find the sum of the first
terms.
Problem 6
Define an ordered quadruple of integers as interesting if
, and
. How many interesting ordered quadruples are there?
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