A list of measurements, in increasing order, is 5, 8, 13, 14, 16, 21, 28, and . If the median of the measurements is times the mean, what is the value of ?

Mixture contains 25% alcohol, Mixture contains 10% alcohol, and Mixture contains 15% alcohol. If liters of Mixture , liters of Mixture , and liters of Mixture are mixed to give liters of mixture that contain 20% alcohol, what is in terms of and ?

A collection of DVDs includes comedies, dramas, and action movies. If DVDs are to be selected at random and without replacement, what is the probability that both DVDs will be action movies?

An art exhibit has 30 landscape paintings, 25 watercolor paintings, and 20 portrait paintings. If 2 different paintings are selected at random to be displayed in a catalog, what is the probability that both paintings will be watercolors?

A hotel manager will select 1 of 10 eligible families to receive a free night’s stay and 2 of 15 eligible families to receive a free dinner in the hotel’s restaurant. If none of the families is eligible to receive both free services, how many different ways are are there of selecting 3 families to receive a free service?

A company will select 1 of 8 eligible employees to work its second shift and 2 of 12 eligible employees to work its third shift. If none of the employees is eligible to work both shifts, how many different sets of 3 employees are there to work these shifts?

Lines and lie in the -plane. Is the slope of line greater than the slope of line ?

(1) The -intercept of line is negative and the -intercept of line is positive.

(2) Lines and intersect at the point .

Lines and lie in the -plane. Is the slope of line less than the slope of line ?

(1) The -intercept of line is greater that the -intercept of line .

(2) Line contains the point and line contains the point .

Five friends donated a total of books to a library, and no two friends donated the same number of books. Of the five friends, if Marlon donated the second greatest number of books, did Marlon donate at least books?

(1) One of the five friends donated books to the library.

(2) Marlon donated fewer than books to the library.

A restaurant delivered a total of 55 pizzas to six different customers one night, and no two customers had the same number of pizzas delivered. Of the six customers, if Customer A had the second greatest number of pizzas delivered, did Customer A have fewer than 9 pizzas delivered?

(1) One of the six customers had 20 pizzas delivered.

(2) Customer A had more than 5 pizzas delivered.

What is the thousandths digit of the decimal ?

(1) The units digit of is .

(2) The hundredths digit of is .

Car dealerships in the state of Fairview have prospered over the term of the current governor: sales are up by 10 percent relative to four years ago. Nevertheless, car manufacturers have found that the proportion of credit they have extended to dealerships that was paid off on time, despite rising over the first two years of this period, has fallen sharply in the latter two years of the governor's term.

Which of the following, if true, most helps to explain the change between the first two and the second two years of the governor's term in the proportion of credit paid off on time?

The country of Olmantia has generally relied on growing soybeans as an export. Recently, the ministry of agriculture has implemented a system to reduce dependence on this single crop by encouraging farmers to grow other legumes. Olmantia currently grows more non-soy legumes each year than it consumes, and exports of soybeans are in decline, due to competition from suppliers in other nations. If these trends continue, Olmantia's ability to export other legumes is likely to grow in the near future.

Which of the following would it be most useful to establish in evaluating the argument?

Last year, Company X reconfigured its direct sales team to include more experienced sales people. The company spent less time and money training the experienced sales hires than they had found necessary to do with the previous, less experienced new hires, and both groups obtained equal direct sales results. The more experienced sales staff, however, received higher financial compensation, and what Company X saved on training costs was less than the additional expenditure of financial compensation. Company X concluded that the reconfiguration strategy would not increase profits in the future.

Which of the following would it be most useful to know in order to evaluate the argument?

Although computers can improve hand-eye coordination and spatial reasoning, computer games are a cause of poor literacy in children. After-school hours spent playing computer games are hours not spent reading. Therefore, children who spend most of their spare time playing these games have less experience reading than other children have.

The argument depends on which of the following assumptions?

Utility Corp, a company with a specific level of cash in its budget, has been clearing uninhabited land near a national park for the construction of a coal plant. This practice continues even though greater annual profits can be made from a nuclear plant, which will not damage the nearby park, than from a coal plant, which will injure the habitat.

Which of the following, if true, most helps to explain why Utility Corp has been pursuing the less profitable of the two economic activities mentioned above?

Seattle's osprey population has been declining in recent years, primarily because of hunting, both legal and illegal. Osprey prey heavily on salmon, yet the naturally occurring population of salmon has also declined, even though the annual number caught for human consumption has not increased.

Which of the following, if true, most helps to explain the decline in the population of the salmon?

Recently, scientists determined that great white sharks can live over 70 years, much longer than had been previously thought. They made the discovery by examining the layers of different colors that accumulated on the shark's teeth over the years. In the 1950s, atomic bomb testing produced unusually large amounts of carbon-14, which fell from the atmosphere into the ocean and accumulated as a distinctive layer on the shark's teeth corresponding to a known period in time. Perplexingly, even though great white sharks live longer than had been expected, some parties maintain that based on the new findings, the great white sharks must be protected from overfishing.

Which of the following, if true, best resolves the discrepancy identified above?

Wappo, a company that manufactures turbine blades for hydroelectric dams, has designed a new model of blade with a superior hydrodynamic form that will save energy and hence cost in implementation. Wappo is willing to sell these blades to a particular hydroelectric dam at no initial cost. The only payment will be the difference between, first, a percentage of the dam's improved profits, as measured by the percentage improvement of the hydroelectric dam efficiency times the value of energy sold by the plant over an 18-month period, and, second, the additional cost of installation and maintenance of the new turbines. On installation, the dam will make an estimated payment, which will be adjusted after eighteen months to equal the proper amount.

Which of the following, if it occurred, would constitute a disadvantage for Wappo of the plan described above?

Because they can craft objects of a new design without having extrusion fittings custom-designed for that purpose, 3D printers have an application in building prototypes of new models of objects long before those new models are on production lines, and it was on this basis that they first captured the interest of the market. However, suitability for prototyping does not limit 3D printers to prototyping, and in fact their capability to craft items without specialized fittings for each design can allow them, in essence, to be the production line. 3D printers have this natural application to mass-production in part because they can produce items at a cost competitive with that of production lines.

In the argument given, the two portions in boldface play which of the following roles?