geometry
algebra
combinatorics
number theory
100
If a 12-hour analog clock reads 8:00, what is the degree measure of the smaller angle formed by the minute and hour hands?
120
100
Two negative integers differ by 6 and their product is 135. What is the larger integer?
-9
100
How many perfect cubes are between 100 and 900 (exclusive)?
5
100
What is the remainder when the product of the 5 smallest prime numbers is divided by 42?
0
200
What is the measure of an angle, in degrees, if its supplement is six times its complement?
72
200
What is the smallest value of x that satisfies the equation 4(x^2) - 5x - 54 = 0?
-9/4
200
How many different two-person sub-committees can be selected from a committee of six people (the order of choosing the people does not matter)?
15
200
97 is the largest prime less than 100. What is the largest prime factor of (97!) (97 factorial)?
97!-1
300
We have a right triangle {ABC} where the legs {AB} and {BC} have lengths 6 and (3sqrt{3}) respectively. Medians AM and CN meet at point P. What is the length of CP?
4
300
The midpoint of a line segment is located at (3, -2). If one of the endpoints is (1, 6), the other endpoint is P, which is the vertex of the graph of the quadratic polynomial y=x^2+2x+c. Determine the value of c.
15
300
A {convex} polygon is a polygon in which every interior angle is less than 180 degrees. A {diagonal} of a convex polygon is a line segment that connects two non-adjacent vertices. How many diagonals does a convex polygon with 20 sides have?
70
300
The greatest common divisor of positive integers m and n is 6. The least common multiple of m and n is 126. What is the least possible value of m+n?
60
400
An antacid tablet is in the shape of a right circular cylinder. The diameter of the base is 3/4 inches and the tablet is 3/16 inches thick. How many cubic inches are in the volume of the tablet? Express your answer as a common fraction in terms of pi
27pi/1024
400
Suppose P(x) is a polynomial of smallest possible degree such that: P(x) has rational coefficients P(-3) = P(sqrt 7) = P(1-sqrt 6) = 0 P(-1) = 8 Determine the value of P(0)
35
400
4 students sit in 13 distinctive chairs. If you have 6 lessons a week and there are 52 weeks in a year, how many years does it take to get trough all different possibilities of sitting? (suppose they never graduate)
55
400
A whole number is said to be ''9-heavy'' if the remainder when the number is divided by 9 is greater than 5. What is the smallest three-digit 9-heavy whole number?
105
500
In right triangle ABC, AB=9, BC=13, and AB, BC are altitudes of the triangle. Points D and E are midpoints of AB and AC respectively; CD and BE intersect at point X. Compute the ratio of the area of quadrilateral AEXD to the area of triangle BXC.
1
500
Let p(x) be a polynomial of the form: p(x) = 2(x^3)+a(x^2)+38x+c, such that 4 and 6 are roots of p(x). Compute a*c
-456
500
2 diagonals of a regular heptagon (a 7-sided polygon) are chosen. What is the probability that they intersect inside the heptagon?
5/13
500
How many digits does the decimal equal to 54317/80000 have to the right of the decimal point?
7
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