Counting
A state issues license plates with three letters followed by two digits (e.g., ABC12). The letters can be any of the 26 English alphabet letters, and the digits can be any from 0 to 9. How many different license plates are possible?
1,757,600
A rectangle has a length of 7 cm and a width of 24 cm. What is its diagonal length?
25 cm
What is the smallest prime?
2
Solve for x: 4^(x+1) = 8^(x-1)
x = 5
What is the longest river in the world?
The Nile River
You have 6 different books and want to arrange them on a shelf. However, two of the books must stay together as a single unit. In how many ways can you arrange all 6 books while keeping those two books together?
240
A circle has a radius of 7 cm. What is the area of the sector formed by a central angle of 20°?
49pi/18 cm^2
Find the smallest perfect number (sum of divisors except itself equals the number) >= 6?
The Fibonacci sequence 1,1,2,3,5,8,13,21 starts with two 1s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence?
6
What is the chemical symbol for gold?
Au
How many different ways can the letters of the word "BALLOON" be arranged?
1260
A regular hexagon is inscribed in a circle of radius 10 cm. What is the area of the hexagon?
150*sqrt(3)
How many factors does 24 have?
8
Solve for x*y if x + y = 8, and x^3 + y^3 = 152
15
What is the hardest naturally occurring mineral?
Diamond
A club has 8 members: 5 men and 3 women. A committee of 4 people is to be formed. How many ways can this be done if the committee must include at least one woman?
65
A rhombus has diagonals with lengths 16 and 12. A circle is inscribed in the rhombus. What is the area of the inscribed circle?
576 pi/25 or 23.04 pi
What is the gcd(12, 800) * lcm(12, 800)?
9600
If x + y + z = 12, xy + yz + zx = 41, xyz = 140. Find the sum of the reciprocals of x, y, z.
41/140
What is the largest country by land area?
Russia
Consider a 6×6 grid where you start at (0,0), and end at (6,6), only moving right or up. However, you must pass the point (3,3). How many paths satisfy this condition?
400
What is the area of the red region? (Show Image on Slides)
7 cm^2
How many zeros are at the end of 100!?
24
A function satisfies f(x + y) = f(x)*f(y) for all real numbers x, y. If f(2) = 3, find f(6)
27
What is the tallest animal in the world?
Giraffe