Algebra
If 6 sillickers are in a billicker and 12 billickers are in 9 trillickers, how many sillickers are in a trillicker?
8 sillickers
A triangle with side lengths 2, 4, 4 is similar but not congruent to a triangle with side lengths 4, x, y. What is the value of x?
8
If the median of a collection of five positive integers is 26, what is the least possible value of the average of these five integers?
16
My passcode has four digits. I know the digits are 2, 6, 8 and 7, but I cannot recall their proper sequence. What is the probability that I will enter the correct passcode on my first try? Express your answer as a common fraction.
1/24
For every sporting event where TJ High School wins, CHS wins 6 games. CHS has won 15 more games than TJ this year. How many games have they won this year, combined?
21 games
I have an average score of 84 points on five tests. If each test has a maximum possible score of 100 points, what is the least possible test score I could have earned on one of these tests?
20 points
In equilateral triangle XYZ, YZ = 2x + 5 and XZ = 6x − 7. If all lengths given are in feet, what is XY?
11 feet
What is the value of 10002 - 9992?
1999
What is the sum of all distinct prime number divisors of 22!/20!
23
Thomas Jefferson Student A showers once every 2 months. Student B showers once every 3 months. Student C showers once every 4 months. How many times per decade do they shower, combined?
130 times
I have twelve coins totaling 85 cents. If I only have dimes and nickels, how many dimes do I have?
5 dimes
The angles of a triangle form an arithmetic progression, and the smallest angle is 35 degrees. What is the degree measure of the largest angle of the triangle?
85 degrees
Mr. Sohn randomly chooses a divisor of 2^10. What is the probability that Mr. Sohn's number is also a divisor of 12^3?
7/11
How many different integers can be written as a sum of an element in the set {1, 2, 3, 4, 5} and an element in the set {6, 7, 8, 9, 10}?
9 integers
Thomas Jefferson High School has an unlimited supply of dimes and quarters. In how many different combinations of these coins can they pay exactly $5.00 in bribes to a math contest administrator?
11 combinations
Let k be a real number such that 2/3 ≥ 5/k . What is the least possible positive value of k? Express your answer as a decimal to the nearest tenth.
7.5
The side lengths of a 45-gon are increased by a factor of 45. By what factor does the area increase?
2025
What is the square root of the greatest two-digit positive integer with exactly three positive integer factors?
7
How many different positive three-digit odd integers with three distinct digits can be formed using only the digits 5, 6, 7 and 8?
12 integers
Thomas Jefferson High School has 8 technology labs, arranged in a regular octagon. Each lab is connected to every other lab with a straight path. How many paths are there?
28 paths
The sum of six consecutive integers is 3. What is their product?
0
A quadrilateral has DISTINCT integer side lengths. If the perimeter of the quadrilateral is 14, what is the maximum possible product of its side lengths?
120
How many zeros appear at the end of the number 20^25 × 25^20 when it is multiplied out (in base ten)?
50 zeros
There are two cards; one is red on both sides and the other is red on one side and blue on the other. The cards have the same probability (1/2) of being chosen, and one is chosen and placed on the table. If the upper side of the card on the table is red, then the probability that the under-side is also red is
2/3
A TJ High School Student drives her Mercedes to an MIT admissions meeting at 10 miles per hour. She so happens to leave the keys with the admissions official, forcing her to walk home at 2 miles per hour. Her total journey took 3 hours. How many miles from her house was the admissions meeting?
5 miles