Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to of capacity in 3 hours and a second inlet pipe fills the same empty tank to of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?

Consider two circles A and B for which the following is true: the diameter of circle A is 8 times the radius of circle B in centimeters.

In the table below, select the values for the areas of circle A and circle B that are consistent with the information above. Make only two selections, one in each column.

A hotel arranged cars to transport its guests to a venue. If 4 guests were assigned to each car, the number of guests left over would be evenly divisible by both 6 and 9. When the hotel instead sent 5 guests in each car, the remaining guests had to take a taxi. If the total number of guests was between 40 and 60, what is the minimum number of guests who took a taxi?

Many health experts have recently suggested that plastic water bottles begin to break down over time, releasing a chemical called bisphenol A that can cause heightened risks of diabetes and cancer. The experts found that this breakdown usually begins a year into the bottle’s use. Thus, people should stop using plastic water bottles after a year.

Which of the following, if true, would most weaken the conclusion above?

The difference in average annual income in favor of employees who have college degrees, compared with those who do not have such degrees, doubled between 1980 and 1990. Some analysts have hypothesized that increased competition between employers for employees with college degrees drove up income for such employees.

Which of the following, if true, most seriously undermines the explanation described above?

When a certain drug was administered to a group of patients, some patients showed improvement and some patients experienced side effects. If at least 10 patients experienced side effects and 60 percent of the patients who showed improvements also experienced side effects, did more patients in the group show improvement than experience side effects?

(1) 90 percent of the patients in the group showed improvement.

(2) 90 percent of the patients in the group who experienced side effects also showed improvement.

To combat forest fires in Country X, the forestry ministry has been clearing susceptible areas of small trees; but this is expensive, and the resulting small logs often go to waste because there is little demand for them. The ministry therefore plans to encourage local businesses to invest in processes to convert the logs into potentially valuable products, such as flooring or wood chips for heating, and to subsidize the businesses in the purchase of new equipment. The hope is that if these businesses become viable, sales of the small logs will consistently help offset the ministry's costs.

Which of the following would, if true, most increase the plan's chances of success?

In 1999, Company X's gross profit was what percent of its revenue?

(1) In 1999 Company X's gross profit was of its expenses

(2) In 1999 Company X's expenses were of its revenue.

Country X's recent stock-trading scandal should not diminish investors' confidence in the country's stock market. For one thing, the discovery of the scandal confirms that Country X has a strong regulatory system, as the following considerations show. In any stock market, some fraudulent activity is inevitable. If a stock market is well regulated, any significant stock-trading fraud in it will very likely be discovered. This deters potential perpetrators and facilitates improvement in regulatory processes.

In the argument, the portion in boldface plays which of the following roles?