Algebra
Geometry
Number Theory
100
If 4x + 3x = n, for how many positive integers n ≤ 200 is x an integer?
28
100
The faces of a cube are painted with different colors so that no two faces that share an edge will have the same color. What is the minimum number of colors needed?
3
100
The prime factorization of 315 is 3 x 3 × 5 × 7. What is the prime factorization of 3150?
2 x 3 x 3 x 5 x 5 x 7
200
If x − 18 is 40 percent of x, what percent of x is x + 18?
160%
200
If AE = 4, BE = 4 and AC = 12, how long is segment AF?
6
200
How many distinct positive divisors does 180 have?
18
300
If x(6 − x) = 9, then what is the value of x(6 + x)?
27
300
A particular cone has a height of 36 inches. The radius of this original cone is tripled when drawing a new cone. What height does the new cone need to be so that the volume of the new cone is the same as the volume of the original cone? (Volume = 1/3 • B • h)
4
300
If a, b, c and d are positive integers for which a! + b! + c! + d! = 29, what is the value of abcd?
16
400
What is the product of all values of x that satisfy (2x − 7)(3x + 1) = (4x − 5)(2x − 7)?
21
400
A right rectangular prism has edges 12 cm, 15 cm and 16 cm. What is the length of the prism’s diagonal?
25
400
If a, b, c and d are distinct even positive integers such that (abc)^2 = abcd, what is the smallest possible value of d?
48