List of practice Questions

A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If \(\frac{1}{9}\) of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x?
The lengths of the line segments are a, b, and ab, respectively. The line segments are drawn to scale.
Column A: a
Column B: 1
The average (arithmetic mean) number of students in 3 economics classes at a certain college is 24. If the total number of students in 2 of the classes combined is 38, how many students are in the remaining class?
If the cube of n is 180 greater than the square of n, then n =
The circular clock above shows a time of exactly 3:30. What is the value of x?
What percent of the integers between 200 and 999, inclusive, end with the digits "03"?
Which of the lines in the figure above contains only points (x,y) with x = y?
Column A: (109)(87-14)
Column B: (109)(87)-(109)(14)
Carol's age, in years, can be expressed by reversing the digits in her father's age, in years. The sum of the digits in each age is 10.
Column A: The positive difference between Carol's age, in years, and her father's age, in years
Column B: 36
\(3 - 2x^2 - [-x(1+2x)] = -5\)
Column A: x
Column B: -8
a and b are positive integers.
Column A: \(\frac{a}{b}\)
Column B: \(\frac{a+3}{b+3}\)
A solid cubical block of wood has dimensions as shown in the figure (3ft side), and the block is to be cut in half as indicated by the shaded region.
Column A: The total surface area of one of the resulting halves of the block
Column B: 36 square feet
PS = SR
Column A: \(x\)
Column B: \(y\)
Column A: \(\frac{24}{23} + \frac{101}{100}\)
Column B: 2
The points P(2,0), Q(0,2), R(4,2) and S(2,4) are in the rectangular coordinate system. :
Column A: The distance from P to Q
Column B: The distance from R to S
The probability that events E and F will both occur is 0.42. The probability that event E will occur is 0.58.
Column A: The probability that event F will occur
Column B: 0.58
Column A: a
Column B: b
Column A: \((1+\sqrt{2})^2\)
Column B: 3
To protect beachfront buildings from ocean storms, ocean resorts have built massive seawalls between beaches and the buildings. Not only do the seawalls block off some buildings' ocean view, but the beaches themselves become ever narrower, because sand can no longer creep inland as storms erode it at the water's edge.
If the information is correct, which of the following conclusions is most strongly supported on the basis of it?
A study found that 70 percent of children surveyed in 1970 had at one time had cavities, whereas only 50 percent of those surveyed in 1985 had ever had cavities. The researchers concluded that the level of dental disease in children had declined between 1970 and 1985.
Which of the following, if true, would most seriously undermine the researchers' conclusion presented above?
David: Since attempting to preserve every species that is currently endangered is prohibitively expensive, the endangered species whose value to humanity is the greatest should be accorded the highest priority for preservation.
Karen: Such a policy would be unsound because it is impossible to predict the future value of a species, nor is it always possible to assess the present value of species whose contributions to humanity, though significant, are indirect.
Which of the following is the main point of Karen's reply to David?
\(x=y=z\)
Column A: \(x^3\)
Column B: \(xyz\)
Mayor: Four years ago when we reorganized the city police department in order to save money, critics claimed that the reorganization would make the police less responsive to citizens and would thus lead to more crime. The police have compiled theft statistics from the years following the reorganization that show that the critics were wrong. There was an overall decrease in reports of thefts of all kinds, including small thefts.
Which of the following, if true, most seriously challenges the mayor's argument?
It takes a particular talent to be a successful business manager. Business courses can help people to solve management problems, but such courses can do so only for those people with managerial talent. Such people should take business courses to acquire ideas that they can subsequently use to good advantage if management problems happen to arise.
If the statements above are true, which of the following must also be true on the basis of them?
When a driver is suspected of having had too much to drink, testing the driver's ability to walk a straight line gives a more reliable indication of fitness to drive than does testing the driver's blood-alcohol level.
Which of the following, if true, best supports the claim made in the statement above?