Algebra
If 3(x − 2) = 2x + 4, what is x?
10
Two supplementary angles have measures in ratio 2:3. What is the smaller angle?
72°
How many positive integers less than 100 are divisible by 3 or 5?
46
A standard die is rolled twice. What is the probability the sum is 7?
1/6
Two trains 300 miles apart travel toward each other at 40 and 60 mph. After how many hours do they meet?
3 hours
If x + 1/x = 5, what is x² + 1/x²?
23
A square is inscribed in a circle of radius 5. What is the area of the square?
50
What is the smallest positive integer with exactly 6 positive divisors?
12
How many distinct ways can the letters of "LEVEL" be arranged?
30
The average of 5 numbers is 20. If one number is removed, the average of the remaining 4 is 18. What was the removed number?
28
The product of two consecutive positive integers is 156. What is their sum?
25
Points A(1,2) and B(7,10) are endpoints of a diameter. What is the area of the circle?
25pi
How many trailing zeros does 15! have?
3
A fair coin is flipped 5 times. What is the probability of getting at least 4 heads?
3/16
Working alone, Alex can paint a fence in 6 hours and Blair in 4 hours. Working together, how many hours will it take them?
12/5 hours = 2.4 hours
If f(x) = x² − 3x + 2, for how many integer values of x is f(x) negative?
0
A regular hexagon has a perimeter of 36. What is its area, in simplest radical form?
54sqrt(3)
What is the units digit of 7^2026?
9
A committee of 3 is chosen from 4 men and 3 women. What is the probability it has at least one woman?
31/35
A merchant marks up an item 25%, then offers a 20% discount off the marked price. What is the net percent change from the original price?
0%
The equation x² − 6x + k = 0 has two positive integer roots. What is the sum of all possible values of k?
22
A right triangle has legs 9 and 12. What is the radius of its inscribed circle?
3
What is the remainder when 2^100 is divided by 7?
Five people are seated randomly around a round table. What is the probability that two specific people sit next to each other?
1/2
A boat travels 10 mph in still water. It goes 12 miles downstream and then 12 miles back upstream, taking 2.5 hours total. What is the speed of the current?
2mph