The number of passengers on a certain bus to Houston at any given time is given by the equation $P=−2(S−4)²+32$, where $P$ is the number of passengers and $S$ is the number of stops that the bus has made since the beginning of its route. If the bus begins its route without any passenger, how many passengers will be on the bus two stops after the stop where it has its greatest number of passengers?

An auditorium contains n seats arranged in 6 rows, each containing equal number of seats. The last row seats are pulled out and are divided equally among the remaining 5 rows such that each row appears identical after this whole transaction and no seat is left out. What is the minimum value of n?

Andy has 6 Canadian dollars and $y$ Australian dollars. If more than $$ of the total dollars are Australian, then what is the minimum number of dollars that Andy has?

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?

16 cylindrical cans, each having radius of one inch, are placed inside a rectangular box in a single column. If all the cans are placed in the upright position and fit exactly inside the box, what is the area of the base of the box?

A + L =130, where A is the area of a rectangle and L is the length of one side of the same rectangle. If the length of other side of the rectangle is 6, what is the value of A?

The sides of a right-angled triangle are n,2n–1,2n+1. What is the length of the hypotenuse, if n is a positive integer?

In triangle ABC, AB = AC and angle A = 60°. A semicircle with diameter along the side BC is drawn. If length of the arc of the semi-circle is 50π, what is the perimeter of the triangle?

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.