Algebra
xy = 15 and x^2y = 45. What is y?
y = 5
a square has diagonal length 4. What is its side length?
2sqrt(2)
If I have 3 shirts and 4 pants, how many outfits can I make?
12
What is the 2nd smallest prime number that can be expressed as the sum of two prime numbers
7
What is the probability that after rolling a dice 3 times I get 3 heads in a row?
1/8
3x + 5y + 27z = 58, 5x + 7y + 29z = 74. What is x+y + z.
sum: 3, product: 7
Increase each side length of a cube by a factor of sqrt(2). How much does the volume increase?
2sqrt(2)
If I have 4 blue socks, 5 red socks and 8 yellow socks. How many socks do I need to draw to guarantee I get a matching pair of yellow socks.
11
What is the 2nd smallest positive integer that is both a perfect square and a perfect cube
64
What is the probability that after rolling a dice 3 times I get exactly 2 heads and 1 tail?
3/8
x - y = sqrt(2) and 3y = 6 - 6 * sqrt(3). What is x + y?
4 + sqrt(2) - 4 * sqrt(3)
I have two equilateral triangles with side length 3 which i put together creating a rhombus. What is the length of the longer diagonal of this rhombus.
3sqrt(3)
How many ways are there to rearrange the letters in the word "last"
24
What number less than 10 has the most factors?
6
If I roll a dice until I get an even number, what are the chances that number is 2
1/3
the equation x^2 - 3x + 7 has 2 solutions which are complex. What is the product of these solutions and what is the sum?
sum: 3, product: 7
I have 2 squares of length 6. I put them together creating a rectangle. This rectangle is inscribed in a circle. What is the radius of the circle.
3sqrt(5)
How many ways are there to rearrange the letters in the word "poops"
30
an arithmetic progression is a series of numbers where each consecutive pair is separated by a common difference e.g. 100, 104, 108. What is the smallest arithmetic sequence of 4 primes.
5, 11, 17, 23
1/2
if x + 1/x = 3 then what is x^3 + 1/x^3?
18
a parallelogram has an angle that is 45 degrees and the two sides that create this angle have lengths in the ratio sqrt(2):1. What is the ratio of the length of the long diagonal to the length of the small diagonal.
sqrt(5):1
How many ways are there for Alice, Bob, Charlie, Damian and Edward to sit in 5 seats if Alice and Bob don't want to sit next to each other.
72
m^2 - n^2 = 73, where m and n are positive integers. Find m and n.
m = 37, n = 36.
If I roll a dice twice, what are the chances that the sum I get is prime
15/36 = 5/12