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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