Algebra
Number Theory
Geometry
Counting and Probability
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100
Evaluate 24-(2x-y) if x=4 and y=3.
19
100
If the pattern shown continues, what is the letter in the 2010th position? MATHLETEMATHLETEMATHLETE...
A
100
A 10-by-12-inch page has margins of 1.5 inches on all sides. What fraction of the area of the page is taken up by the margins? Express your answer as a common fraction.
19/40
100
Compute 
48
100
How many isosceles triangles are there with positive area whose side lengths are all positive integers and whose longest side has length 2025?
3037
200
New York and Denver are in different time zones. When it is noon in New York, it is 10 a.m. in Denver. A train leaves New York at 2 p.m. (New York time) and arrives in Denver 45 hours later. What time is it in Denver when the train arrives?
9 a.m.
200
What is the sum of the proper divisors of 256? (A proper divisor is any positive divisor of a number, excluding the number itself.)
255
200
Chuck the llama is tied to the corner of a 2m by 3m shed on a 3m leash. How much area (in square meters) does Chuck have in which to play if he can go only around the outside of the shed?
7pi
200
What is the sum of all integer values n for which 
?
26
200
Consider the sequence of positive integers
1,2,1,2,3,2,1,2,3,4,3,2,1,2,3,4,5,4,3,2,1,2,3,4,5,6,5,4,3,2,1,2,...
What is the 2025th term in this sequence?
45
300
One root of the equation 5x2 + 4x = k (for some real k) is 2. What is the other?
-14/5
300
How many different prime factors does 20! have? (Reminder: If n is a positive integer, then n! stands for the product 1 * 2 * 3 * ... * (n-1) * n.)
8
300
Rose has a spherical plum of radius 2 and a spherical watermelon of radius 8. She builds a glass sphere around the two fruits to contain them, making the sphere as small as possible. When she has done this, the volume contained within the sphere, but not in the plum or the watermelon, is 
. What is the value of K?
640
300
How many triangles can be formed using the vertices of a regular dodecagon (a 12-sided polygon)?
220
300
Agnes writes the following four statements on a blank piece of paper.
At least one of these statements is true.
At least two of these statements are true.
At least two of these statements are false.
At least one of these statements is false.
Each statement is either true or false. How many false statements did Agnes write on the paper?
1
400
A rectangular block of candy 10 inches by 10 inches by 5 inches is coated on all faces with a very thin layer of chocolate. The block of candy is then cut into cubes measuring 1 inch by 1 inch by 1 inch. What percent of the cubes have no chocolate on them? Express your answer to the nearest tenth.
38.4%
400
Delilah writes down the positive factors of 12 on a piece of paper, which she gives to Ezekiel. Next to each factor, Ezekiel writes all of the positive integers that are less than or equal to that number and that share no divisors with the factor other than 1. (So, for example, Ezekiel will write "1" next to each of the factors Delilah writes.) How many numbers total does Ezekiel write?
12
400
In triangle ABC, AB = AC = 5 and BC = 6. Let O be the circumcenter of triangle ABC. Find the area of triangle OBC.
21/8
400
The three-digit positive integer N has a ones digit of 3. What is the probability that N is divisible by 3? Express your answer as a common fraction.
1/3
400
Two farmers agree that pigs are worth $300 and that goats are worth $210. When one farmer owes the other money, he pays the debt in pigs or goats, with "change'' received in the form of goats or pigs as necessary. (For example, a $390 debt could be paid with two pigs, with one goat received in change.) What is the amount of the smallest positive debt that can be resolved in this way?
$30
500
If the sum of the squares of nonnegative real numbers a,b, and c is 13, and ab + bc + ca = 6, then what is the sum of a,b, and c?
5
500
A palindrome is a number that is the same when read forwards and backwards, such as 43234. Compute the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4.
15
500
Carla rotated point A 420 degrees clockwise about point B and it landed at point C. Devon rotated the original point A x degrees counterclockwise about point B and it also landed at point C. If 0 < x < 360, what is the value of x?
300
500
Twenty switches in an office computer network are to be connected so that each switch has a direct connection to exactly three other switches. How many connections will be necessary?
30
500
In the figure below, 
is a rectangle, 
, 
, 
, and 
. What is the area of 
?
3/8