Number Theory (Primes & Divisibility)
What is the smallest prime number greater than 50?
53
Simplify: 2^3 + 3^2
17 (8 + 9)
Solve for x: 3x + 7 = 22
x = 5
What is the sum of the interior angles of a pentagon?
540 degrees (180 x (5-2))
A shirt is 20% off. If the sale price is $24, what was the original price?
$30
A number is divisible by 9 if the sum of its digits is divisible by 9. Is the number 12,345,678 divisible by 9?
Yes (Sum = 36, which is $9 \times 4$).
What is the value of (-1)^2026
1
Solve for y: 5(y - 2) = 30
y = 8
A triangle has a base of 10 and an area of 35. What is its height?
7
If 3 cats can catch 3 mice in 3 minutes, how many cats are needed to catch 10 mice in 10 minutes?
3 cats (The rate is 1 cat per mouse per 3 minutes).
Find the Greatest Common Divisor (GCD) of 48 and 72.
24
Simplify: 5 x (4 - 7)^2
45 (5 x (-3)^2 = 5 x 9)
Solve for z: 4z - 10 = 2z + 8
z = 9
Find the perimeter of a square whose area is 81 square units.
36 units
The ratio of boys to girls in a class is 3:4. If there are 28 students total, how many are boys?
12 boys.
How many total divisors does the number 36 have?
9 divisors (1, 2, 3, 4, 6, 9, 12, 18, 36).
Express 2^10 / 2^4 as a power of 2
2^6
If 2/3 of a number is 12, what is the number?
18
In a right triangle, if the legs are 6 and 8, what is the hypotenuse?
10 (Pythagorean Triple: 6-8-10)
Bob travels 60 miles at 30 mph and returns at 60 mph. What is his average speed for the whole trip?
40 mph (Total distance / Total time: 120 / 3).
Find the Least Common Multiple (LCM) of 12, 15, and 20.
60
What is the square root of 2^6 x 3^2
24 (sqrt{64 x 9} = 8 x 3)
Solve the inequality: -3x + 5 < 11
x > -2 (Remember to flip the sign!)
If the radius of a circle is doubled, by what factor does the area increase?
4 (2^2)
Find the sum of all integers from 1 to 100.
5050