Geometry
Algebra
Number Theory
Combinatorics
Misc
100
A quadrilateral has all integer side lengths, a perimeter of 
, and one side of length 
. What is the greatest possible length of one side of this quadrilateral?
D) 12
100
What is the value of 9901 * 101 - 99 * 10101?
A) 2 B) 20 C) 200 D) 202 E) 2020
A) 2
100
How many positive perfect squares less than 
are divisible by 
?
A) 8
100
In a long line of people arranged left to right, the 1013th person from the left is also the 1010th person from the right. How many people are in the line?
B) 2022
100
Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely but runs out of juice when the fourth glass is only 
full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into the fourth glass so that all four glasses will have the same amount of juice?
A) 1/12 B) 1/4 C) 1/6 D) 1/8 E) 2/9
C) 1/6
200
A 
right triangle is inscribed in circle 
, and a 
right triangle is inscribed in circle 
. What is the ratio of the area of circle to the area of circle ?
D) 25/169
200
The weight of of a large pizza together with 
cups of orange slices is the same weight of 
of a large pizza together with 
cups of orange slices. A cup of orange slices weigh 
of a pound. What is the weight, in pounds, of a large pizza?
A) 1 4/5
200
How many digits are in the base-ten representation of 
?
E) 18
200
What is the minimum number of successive swaps of adjacent letters in the string 
that are needed to change the string to 
(For example, 
swaps are required to change 
to 
one such sequence of swaps is 
)
D) 15
200
Let 
, 
, and 
for 
. How many terms in the sequence 
are even?
E) 274
300
A square of area 
is inscribed in a square of area , creating four congruent triangles, as shown below. What is the ratio of the shorter leg to the longer leg in the shaded right triangle?
C) 2 - sqrt(3)
300
How many ordered pairs of integers 
satisfy 
?
D) 4
300
The product of three integers is 
. What is the least possible positive sum of the three integers?
B) 3
300
In how many ways can 
juniors and seniors form disjoint teams of people so that each team has juniors and seniors?
B) 1350
300
Abdul and Chiang are standing 
feet apart in a field. Bharat is standing in the same field as far from Abdul as possible so that the angle formed by his lines of sight to Abdul and Chiang measures 
. What is the square of the distance (in feet) between Abdul and Bharat?
C) 3072