Problem Solving & Analysis
Data set A: 72, 73, 73, 76, 76
Data set B: 61, 64, 74, 85, x
Data set A and data set B each contain 5 numbers. If the mean of data set A is equal to the mean of data set B, what is the value of x?
86
The function g is defied by g(x) = -x + 8. What is the value of g(0)?
8
6x - 9y > 12
Which of the following inequalities is equivalent to the inequality above?
A. x - y > 2 B. 2x - 3y > 4
C. 3x - 2y > 4 D. 3y - 2x > 2
B. 2x - 3y > 4
A cube has an edge length of 41 inches. What is the value, in cubic inches, of the cube?
68,921
If a is an odd integer and b is an even integer, which of the following is an odd integer?
(A) 3b (B) a + 3 (C) 2(a + b)
(D) a + 2b (E) 2a + b
(D) a + 2b
For a person m miles from a flash of lightning, the length of the time interval from the moment the person sees the lightning to the moment the person hears the thunder is k seconds. The ratio of m to k can be estimated to be 1 to 5. According to this estimate, the person is how many miles from a flash of lightning if the time interval is 25 seconds?
5 miles
A total of 364 paper straws of equal length were used to construct two types of polygons: triangles and rectangles. The triangles and rectangles were constructed so that no two polygons had a common side. The equation 3x + 4y = 364 represents this situation, where x is the number of triangles constructed and y is the number of rectangles constructed. What is the best interpretation of (x, y) = (24, 73) in this context?
If 24 triangles were constructed, then 73 rectangles were constructed.
y = x^2 + x
If (x, y) is a solution to the system of equations above, which of the following could be a value of x?
1 or -1
A right circular cylinder has a volume of 45(pi). If the height of the cylinder is 5, what is the radium of the cylinder?
3
The football team has jerseys numbered from 10 to 30. Everyone gets a jersey and there are three leftover. How many people are on the football team?
18
The population density of Iceland, in people per square kilometer of land area, increased from 2.5 in 1990 to 3.3 in 2014. During this time period, the land area of Iceland was 100,250 square kilometers. By how many people did Iceland's population increase from 1990 to 2014?
80,200 people
2x + 16 = a(x + 8)
In the given equation, a is a constant. If the equation has infinitely many solutions, what is the value of a?
2
4a^2 + 20ab + 25b^2
What is the factored form of the polynomial above?
(2a + 5b)^2
What is the length of one side of a square that has the same area as a circle with radius 2?
2(sqrt(pi))
Derek is the 11th tallest person in the room and the 9th shortest. How many people are in the room?
19
2012 sold 5,600 subscriptions
2013 sold 5,880 subscriptions
The manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?
6,027
Line p is defined by 4y + 8x = 6. Line r is perpendicular to line p in the xy-plane. What is the slope of line r?
.5 or 1/2
f(x) = x^2 - 48x + 2,304
What is the minimum value of the given function?
1,728
Two nearby trees are perpendicular to the ground, which is flat. One of these trees is 10 feet tall and has a shadow that is 5 feet long. At the same time, the shadow of the other tree is 2 feet long. How tall, in feet, is the other tree?
4
It takes 12 minutes to saw a log into four pieces. Given that each cut takes an equal amount of time, how many minutes would it take to saw the log into 6 pieces instead?
20
Data set A consists of 10 positive integers less than 60. The list shown gives 9 of the integers from data set A.
43, 45, 44, 43, 38, 39, 40, 46, 40
The mean of these 9 integers is 42. If the mean of data set A is an integer that is greater than 42, what is the value of the largest integer from data set A?
52
A local transit company sells a monthly pass for $95 that allows an unlimited number of trips of any length. Tickets for individual trips cost $1.50, $2.50, or $3.50, depending on the length of the trip. What is the minimum number of trips per month for which a monthly pass could cost less than purchasing individual tickets for trips?
28
The product of two positive integers is 426. If the first integer is 5 greater than twice the second integer, what is the smaller of the two integers?
14
A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container A. What is the volume, in cubic centimeters, of container B?
20,000(pi)
The length of a rectangle is increased by 50% and the width is decreased by 50%. How does the area of the rectangle change?
Decreases by 25%