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Arithmetic
Algebra and Functions
Geometry
Word Problems
Probability, Mean, Median and Mode
100
If 3x + n = x + 1, what is n interms of x?
What is 1-2x
100
If x + y = y - 3, what is the value of x-2 in terms of y?
What is y - 9
100
The perimeter of equilateral triangle ABC is 3 times the perimeter of equilateral triangle DEF. If the perimeter of ∆DEF is 10, what is the length of one side of ∆ABC?
What is 10.
100
The Smith Metal Company's old machine makes 300 bolts per hour. Its new machine makes 450 bolts per hour. If both machines begin running at the same time, how many minutes will it take the two machines to make a total of 900 bolts?
What is 72 minutes.
100
A box contains wood beads, red glass beads, and blue glass beads. The number of glass beads is 4 times the number of wood beads. If one bead is to be chosen at random from the box, the probability that a red glass bead will be chosen is 3 times the probability that a blue glass bead will be chosen. If there are 12 glass beads in the box, what is the total number of beads in the box
What is 20
200
If the average (arithmetic mean) of x and 3x is 12, what is the value of x?
What is 6
200
If (2x - 5)(2x + 5) = 5, what is the value of 4x^2?
What is 30
200
Point P lies on the line with equation y - 4 = 3(x - 2). If the x-coordinate of P is 4, what is the y-coordinate of P?
What is 10
200
Flying at a constant speed, a bird traveled 62 miles in 4 hours. At this rate, how many miles did the bird travel in 3 hours?
What is 93/2 or 46.5
200
A die with 20 identically shaped sides has 5 faces painted red, 8 faces painted white, and 7 faces painted blue. What is the probability of rolling either a red or blue face?
What is 3/5 or 12/20
300
When the positive integer v is divided by 5, the remainder is 2. What is the remainder when v-3 is divided by 5.
What is 4
300
If a + 2b is equal to 125 percent of 4b, what is the value of a/b?
What is 3
300
If the volume of a cube is 8, what is the shortest distance from the center of the cube to the base of the cube?
What is 1
300
Car A traveled 60 miles and averaged 20 miles per gallon of gasoline. If car B traveled 15 miles for each gallon of gasoline it used, how many miles had car B traveled when it used the same amount of gasoline that car A used to travel 60 miles?
What is 45 miles.
300
The median of a set of 9 consecutive integers is 42. What is the greatest of these 9 integers?
What is 46
400
The first term of a sequence is 20 and the second term is 8. The third term an each term thereafter is the average (arithmetic mean) of the two terms preceding it. What is the value of the first term in the sequence that is NOT an integer?
What is 12.5
400
If k is a constant and 2x + 5 =3kx + 5 for all values of x, what is the value of k?
What is 2/3
400
In the xy-coordinate system (p,0) is one of the points of intersection of the graphs y = -x^2 + 9 and y = x^2 - 9. If p is positive, what is the value of p?
What is 3
400
In a mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is 5 to 2. How many pounds of cashews will there be in 4 pounds of this mixture?
What is 8/7
400
Tim wrote a seven-digit phone number on a piece of paper. He later tore the paper accidentally and the last two digits were lost. What is the maximum number of arrangements of two digits, using the digits 0 through 9, that he could use in attempting to reconstruct the correct phone number?
What is 100
500
If k is a positive integer, which of the following must represent an even integer that is twice the value of an odd integer? A) 2k B) 2k + 3 C) 2k + 4 D) 4k + 1 E) 4k + 2
What is E
500
When the nunmber w is multiplied by 4, the result is the same as when 4 is added to w? What is the value of 3w?
What is 4
500
A cube with a volume of 8 cubic centimeters is inscribed in a sphere so that each vertex of the cube touches the sphere. What is the length of the diameter, in centimeters of the sphere?
What is 2√3 (approximately 3.46)
500
If the length of a rectangle is increased by 30% and the width of the same rectangle is decreased by 30% what is the effect on the are of the rectangle? A) It is increased by 60% B) It is increased by 30% C) It is unchanged D) It is decreased by 15% E) It is decreased by 9%
E) It is decreased by 9%
500
One adult and 10 children are in an elevator. If the adult's weight is 4 times the average weight of the children, then the adult's weight is what fraction of the total weight of the 11 people in the elevator?
What is 2/7