Algebra
If (x+3)/(x-1) = 4, what is x?
7/3
An equilateral triangle has side length 10. What is its area?
25sqrt(3)
How many positive divisors does 72 have?
12
A bag has 4 red and 6 blue marbles. Two are drawn without replacement. What is the probability both are red?
2/15
A merchant marks an item up 50% from cost, then sells at a 10% discount off the marked price, making a $70 profit. What was the cost price?
$200
If x^2 + y^2 = 20 and xy = 8, what is (x+y)^2?
36
A triangle has vertices A(0,0), B(6,0), C(2,4). What is its area?
12
How many ordered pairs of positive integers (x,y) satisfy 1/x+1/y=1/12?
15
How many 3-digit numbers have all distinct digits and are even?
328
A two-digit number has digit sum 11. Reversing its digits gives a number 45 less than the original. What is the original number?
83
The sum of a number and its reciprocal is 13/6. What is the number, given it's greater than 1?
3/2
A square is inscribed in a right triangle with legs 6 and 8, with two sides of the square lying along the two legs. What is the side length of the square?
24/7
What is the sum of all positive divisors of 360?
1170
A committee of 4 is chosen from 6 men and 4 women. What is the probability it has exactly 2 men and 2 women?
3/7
Machines A, B, C alone finish a job in 6, 8, and 12 hours respectively. All three work together for 2 hours, then A stops. How many more hours do B and C need to finish?
6/5 hours = 1.2 hours
If x and y are positive integers satisfying xy + x + y = 17, what is the maximum possible value of x + y?
9
A regular hexagon has area 24sqrt(3). What is the length of its longest diagonal?
8
What is the largest power of 2 that divides 100!?
97
How many ways can 6 people be seated around a round table if two of them refuse to sit next to each other?
72
Two cars start together and travel in opposite directions; Car B is 10 mph faster than Car A. After 3 hours they are 270 miles apart. How far apart are they after 5 total hours?
450
The polynomial x^3 - 6x^2 + 11x - 6 has three roots. What is the sum of the squares of the roots?
14
Three circles of radius 4 are mutually externally tangent. What is the area of the region bounded by all three circles (the small curved triangle between them)?
16sqrt(3)-8pi
How many positive integers less than 1000 are divisible by neither 2, 3, nor 5?
266
In how many ways can 10 identical candies be distributed among 4 children so each child gets at least 1?
84
A two-digit number is 4 times the sum of its digits. Reversing its digits gives a number 27 more than the original. What is the original number?
36