Algebra
Counting
Number Theory
Geometry
100
Halfway through a 100-shot archery tournament, Chelsea leads by 50 points. For each shot a bullseye scores 10 points, with other possible scores being 8, 4, 2, and 0 points. Chelsea always scores at least 4 points on each shot. If Chelsea's next 
shots are bullseyes she will be guaranteed victory. What is the minimum value for ?
42
100
There are 
coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?
C, E, D, A, B
100
Find the remainder when 1919 is divided by 5.
4
100
Two right circular cylinders have the same volume. The radius of the second cylinder is 
more than the radius of the first. What is the relationship between the heights of the two cylinders?
The height of the first is 21% more than the second
200
Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Roger's allowance was 
dollars. The cost of his movie ticket was 
of the difference between and the cost of his soda, while the cost of his soda was 
of the difference between and the cost of his movie ticket. To the nearest whole percent, what fraction of did Roger pay for his movie ticket and soda?
23
200
The eighth grade class at Lincoln Middle School has 
students. Each student takes a math class or a foreign language class or both. There are 
eighth graders taking a math class, and there are 
eighth graders taking a foreign language class. How many eighth graders take only a math class and not a foreign language class?
39
200
Do there exist integers a and b such that a + b = 544 and whose greatest common divisor is 11? If so, find a and b.
No
200
Rectangle 
is inscribed in a semicircle with diameter 
as shown in the figure. Let 
and let 
What is the area of 
240
300
What is the value of
6
300
Alice has 
apples. In how many ways can she share them with Becky and Chris so that each of the three people has at least two apples?
190
300
How many zeros are there at the end of 1000!?
248
300
Two circles of equal radius 
have an overlap area of 
and the total area covered by the circles is 
. What is the value of ?
4
400
If 
, and 
, what is the value of 
?
15
400
Five different awards are to be given to three students. Each student will receive at least one award. In how many different ways can the awards be distributed?
150
400
Find all integers n such that n leaves a remainder of 2 when divided by 3, a remainder of 2 when divided by 4 and a remainder of 1 when divided by 5.
n=26 (mod 60)
400
Sides 
and 
of equilateral triangle 
are tangent to a circle at points 
and 
respectively. What fraction of the area of 
lies outside the circle?
4/3 - (4sqrt(3)pi)/27
500
Two geometric sequences 
and 
have the same common ratio, with 
, 
, and 
. Find 
.
363
500
A set of 
square blocks is arranged into a 
square. How many different combinations of 
blocks can be selected from that set so that no two are in the same row or column?
600
500
Find the last two digits of 77^7
43
500
In with 
point 
lies strictly between and on side 
and point 
lies strictly between and on side such that 
The degree measure of 
is 
where 
and are relatively prime positive integers. Find 
547