Algebra
If 3x - 7 = 23, what is x?
10
How many sides does a heptagon have?
On a fair six-sided die, what is the probability of rolling a 4?
1/6
What is 338 in base 10? (The 8 stands for the base.)
27
How many legs does a spider have?
8
I have a few marbles. If I borrow 3 more from my friend, but give half of my total after that to my brother, I will end up with 5 marbles left. How many marbles did I start with?
7
I take a square with side length 5 and attach an equilateral triangle on each side. What is the perimeter of the resulting figure?
40
I have 4 distinct cards. How many ways are there for me to pick 2 of them?
6
I have a favorite positive integer. If I divide it by 3, I get a remainder of 2. If I divide it by 4, I get a remainder of 3. What is the smallest possible value of my number?
11
An alien species has invaded Earth! They have 7 hands each and pick up 2 humans with each hand. How many humans will 5 of these monstrosities be holding?
70
What are the roots of the equation 6x^2 + 11x - 35 = 0?
-7/2 and 5/3
I have a triangle ABC where B is a right angle, AB = 3, and BC = 4. I then draw another triangle ADC where angle DAC is a right angle, and AD = 12. What is CD?
13
I roll 3 fair 6-sided dice, and I add the results. How many possible results are there?
16
Daily Double!
If we split 1000 into two positive integer factors, neither of which contains a 0, what is their sum?
133
How many characters are in this current sentence?
Note: Spaces are included.
49
If the roots to the equation are 3x^2 + 7x + 2 = 0 can be expressed as r and s, what is r^2 + s^2?
37/9
I have a rectangle, such that it's length is 5 less than 2 times it's width. If it's area is 63, what is it's perimeter?
32
One mathematician asks another mathematician, "Do you have two children, at least one of which is a girl?"
The other person responds, "Yes."
What is the probability that they have two girls?
(Assume that the chances of having a girl is 50%.)
1/3
What is the units digit of 1! + 2! + 3! ... + 100!
3
Daily Double!
If 5 times Jane's marbles equals 4 times Joe's marbles equals 3 times Jack's marbles, and they each have a positive integer number of marbles, what is the smallest possible value all of their marbles added up?
47
Extra Hard:
A cyclist travels 40 miles at a constant speed. On the way back, they increase their speed by 2 mph, which makes the return trip take 1 hour less than the original trip. What was the original speed?
8 mph
A cylinder has a height of 10 cm and a radius of 3 cm. Inside it, there is a heavy metal sphere with a radius of 3 cm resting at the bottom.
If you fill the cylinder with water until it reaches the very top, what is the volume of the water? Express your answer in terms of pi.
54pi
Extra Hard:
A box contains n pens. There are 3 more black pens than red pens. If you take two pens without replacement, the probability of getting a black pen then a red pen is 9/35. What is n?
15
A five-digit number A28B7 is divisible by 9. If A and B are non-zero digits, how many different pairs of (A, B) are possible?
9
Alvin calculates 10 + 20 + 30 ... + 100 - 9 - 18 - 27 ... - 90 + 8 + 16 + 24 ... + 80 - 7 - 14 - 21 ... 70, and he continues this on until 2 + 4 + 6 ... + 20 - 1 - 2 - 3 ... - 10, what is his sum?
275