Algebra
Geometry
Properties of Numbers
Probability
Word Problems
100
What is the value of ((2^2)-2)-((3^2)-3)+((4^2)-4)?
8
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
What is the sum of all real numbers x for which
|x^2 - 12x +34| = 2?
18
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
Alice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, "We are at least 6 miles away," Bob replied, "We are at most 5 miles away." Charlie then remarked, "Actually the nearest town is at most 4 miles away." It turned out that none of the three statements were true. Let d be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of d?
(5,6)
300
A cart rolls down a hill, travelling 5 inches the first second and accelerating so that during each successive 1 -second time interval, it travels inches more than during the previous 1 -second interval.
The cart takes 30 seconds to reach the bottom of the hill. How far, in inches, does it travel?
3195 in
300
A 45 degree arc of circle A is equal in length to a 30 degree arc of circle B. What is the ratio of circle A's area and circle B's area?
4/9
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
Each piece of candy in a store costs a whole number of cents. Casper has exactly enough money to buy either 12 pieces of red candy, 14 pieces of green candy, 15 pieces of blue candy, or n pieces of purple candy. A piece of purple candy costs 20 cents. What is the smallest possible value of n?
21
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 x, y, and z are positive with xy=24, xz=48, and yz=72, then x+y+z is
22
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
Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how many school days from today will they next be together tutoring in the lab?
84 days
500
What is the remainder when 2^202 + 202 is divided by 2^101 + 2^51 + 1 ?
201
500
Two right circular cones with vertices facing down as shown in the figure below contains the same amount of liquid. The radii of the tops of the liquid surfaces are 3 cm and 6 cm.
Into each cone is dropped a spherical marble of radius 1 cm, which sinks to the bottom and is completely submerged without spilling any liquid.
What is the ratio of the rise of the liquid level in the narrow cone to the rise of the liquid level in the wide cone?
Hint: V= (1/3)pi * r^2 * h
12-4sqrt(3)
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
Jamal wants to store 30 computer files on floppy disks, each of which has a capacity of 1.44 megabytes (MB). Three of his files require 0.8 MB of memory each, 12 more require 0.7 MB each, and the remaining 15 require 0.4 MB each. No file can be split between floppy disks. What is the minimal number of floppy disks that will hold all the files?
13 disks