NUMBER THEORY
Find the greatest common divisor of 42 and 60.
6
How many ways can you arrange the letters in CAT?
6
A rectangle has length 5 and width 2. Find the perimeter.
14
Two coins are flipped. A player wins if exactly one coin shows heads. What is the probability the player wins twice in a row?
1/4
Pipe A can fill a tank in 6 hours. Pipe B can fill the same tank in 3 hours. If both pipes are opened together, how long will it take to fill the tank?
2 hours
Number of positive divisors of 72
12
How many subsets does a set with 6 elements have?
64
A cone has radius 3 and slant height 5. Find the lateral surface area.
15 pi
A box contains 4 red, 3 blue, and 5 green marbles. Two marbles are drawn without replacement. What is the probability that both are red?
1/11
Pipe A can fill a tank in 6 hours, and Pipe B can fill the same tank in 8 hours. Pipe C empties the tank at a rate of 1 tank per 12 hours. If all three pipes are open together, how long will it take to fill the tank?
4h 48min
Find the remainder when 7^15 is divided by 8.
7
How many 3-digit numbers have all distinct digits?
648
A cylinder has radius 5 and height 12. Find the surface area.
170 pi
A fair six-sided die is rolled twice. What is the probability that the sum of the numbers is 7 or 11?
2/9
A faucet fills a sink in 12 minutes. Another faucet fills the same sink in 18 minutes. If both faucets are opened for 5 minutes and then the first faucet is turned off, how long will it take the second faucet to finish filling the sink?
5.5 min
A positive integer n leaves a remainder of 1 when divided by 4, a remainder of 2 when divided by 5, and a remainder of 3 when divided by 6. What is the smallest positive n?
n = 57
From 10 students, how many 4-person committees can be formed?
210
A triangular prism has a triangular base with sides 6, 8, 10 and height 12. Find the volume of the prism.
288
A standard deck of 52 cards is shuffled. Two cards are drawn without replacement. What is the probability that both are face cards (Jack, Queen, King) and of different suits?
8/221
Two pipes, A and B, fill a tank. Pipe A alone can fill it in 3 hours, but pipe B alone can fill it in 5 hours. However, after opening both pipes together, a valve is accidentally opened that empties the tank at a constant rate of 1 tank per 15 hours. How long does it take to fill the tank now?
2h 8.5min
A positive integer n leaves remainder 2 when divided by 3, remainder 3 when divided by 5, and remainder 2 when divided by 7. Find the smallest positive n.
n = 23
How many outcomes of 7 coin flips contain exactly 3 heads?
35
A right triangle has legs of lengths 7 and 24. A circle is inscribed inside the triangle. Find the radius of the inscribed circle.
3
A box contains 5 red, 4 blue, and 3 green balls. You draw three balls one by one without replacement. What is the probability that:
The first ball is red,
The second ball is not blue,
The third ball is green?
3/44
Pipe A fills a tank in 7 hours, Pipe B fills it in 5 hours, and Pipe C empties it in 10 hours.
Pipe A is opened at 8:00 AM.
Pipe B is opened at 9:00 AM.
Pipe C is opened at 10:00 AM.
How long from 8:00 AM will it take to fill the tank completely?
4h 7min