If x² - 2x - 15 = 0 and x > 0, which of the following must be equal to 0 ?

I. x² - 6x + 9

II. x² - 7x + 10

III. x² - 10x + 25

Of the goose eggs laid at a certain pond, ~$2 \over 3$~ hatched, and ~$3 \over 4$~ of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, ~$3 \over 5$~ did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?

What is the larger of the 2 solutions of the equation x² - 4x = 96 ?

In the figure above, what is the area of triangular region BCD ?

List S consists of 10 consecutive odd integers, and list T consists of 5 consecutive even integers. If the least integer in S is 7 more than the least integer in T, how much greater is the average (arithmetic mean) of the integers in S than the average of the integers in T ?

When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 35 ?

A total of 5 liters of gasoline is to be poured into two empty containers with capacities of 2 liters and 6 liters, respectively, such that both containers will be filled to the same percent of their respective capacities. What amount of gasoline, in liters, must be poured into the 6-liter container?

The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 11 percent, what was the annual interest rate last year?

If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S ?

A certain bridge is 4,024 feet long. Approximately how many minutes does it take to cross this bridge at a constant speed of 20 miles per hour? (1 mile = 5,280 feet)