Algebra
Geometry
Properties of Numbers
Probability
Word Problems
100
What is the hundreds digit of (20!-15!)?
0
100
The sides of a triangle with positive area have lengths 4, 6, and x. The sides of a second triangle with positive area have lengths 4, 6, and y. What is the smallest positive number that is not a possible value of | x - y |?
8
100
The sum of two numbers is S. Suppose 3 is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?
(In terms of S)
2S + 12
100
A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue balls, 11 white balls, and 9 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn
76
100
Sarah pours four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then transfers half the coffee from the first cup to the second and, after stirring thoroughly, transfers half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream?
2/5
200
Supposed that x and y are nonzero real numbers such that 
What is the value of 
?
2
200
A right triangle has a hypotenuse of 13 and an area of 30. What is the perimeter of the triangle?
30
200
The sum of two natural numbers is 17,402 . One of the two numbers is divisible by 10 . If the units digit of that number is erased, the other number is obtained.
What is the difference of these two numbers?
14,238
200
A box contains 5 chips, numbered 1,2,3,4, and 5. Chips are drawn randomly one at a time without replacement until the sum of the values drawn exceeds 4. What is the probability that 3 draws are required?
1/5
200
Ana and Bonita were born on the same date in different years, n years apart. Last year Ana was 5 times as old as Bonita. This year Ana's age is the square of Bonita's age. What is n?
12
300
Suppose a real number x satisfies
What is the value of 
?
8
300
The lines with equations ax-2y=c and 2x+by=-c are perpendicular and intersect at (1,-5). What is c?
13
300
Using the digits 1, 2, 3, 4, 5, 6, 7, and 9, form 4 two-digit prime numbers, using each digit only once. What is the sum of the 4 prime numbers?
190
300
When 7 fair standard 6-sided dice are thrown, the probability that the sum of the numbers on the top faces is 10 can be written as
where n is a positive integer. What is n?
84
300
Chandra pays an on-line service provider a fixed monthly fee plus an hourly charge for connect time. Her December bill was $12.48 , but in January her bill was $17.54 because she used twice as much connect time as in December. What is the fixed monthly fee?
$7.42
400
If 
, and ,
what is the value of 
?
15
400
Rectangle ABCD has AB=6 and BC=3. Point M is chosen on side AB so that angle AMD = angle CMD. What is the degree measure of angle AMD?
75
400
Real numbers x and y satisfy x+y=4 and x*y=-2.
What is the value of x+(x^3)/(y^2)+(y^3)/(x^2)+y?
440
400
If the probability of rain on any given day in City X is 50 percent, what is the probability that it rains on exactly 3 days in a 5-day period?
5/16
400
Every week Roger pays for a movie ticket and a soda out of his allowance. Last week, Roger's allowance was A dollars. The cost of his movie ticket was 20% of the difference between A and the cost of his soda, while the cost of his soda was 5% of the difference between A and the cost of his movie ticket. To the nearest whole percent, what fraction of A did Roger pay for his movie ticket and soda?
23%
500
Let a and b be relatively prime positive integers with 
and 
.
What is a-b ?
3
500
What is the volume of tetrahedron 
with edge lengths 
, 
, 
, 
, 
, and 
?
*simply use the volume of a pyramid to calculate: V=(1/3)bh
4
500
Let P(n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P(23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P(N) + S(N). What is the units digit of N?
9
500
An integer n between 1 and 99, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 3 ?
2/3
500
Henry decides one morning to do a workout, and he walks 3/4 of the way from his home to his gym. The gym is 2 kilometers away from Henry's home. At that point, he changes his mind and walks 3/4 of the way from where he is back toward home. When he reaches that point, he changes his mind again and walks 3/4 of the distance from there back toward the gym. If Henry keeps changing his mind when he has walked 3/4 of the distance toward either the gym or home from the point where he last changed his mind, he will get very close to walking back and forth between a point A kilometers from home and a point B kilometers from home. What is |A-B| ?
6/5