Of all the students in a certain dormitory,  ~$\frac{1}{2}$~ are first-year students and the rest are second-year students.  If  ~$\frac{4}{5}$~  of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?

When n liters of fuel was added to a tank that was already ~$\frac{1}{3}$~  full, the tank was filled to  ~$\frac{7}{9}$~ of its capacity.  In terms of n, what is the capacity of the tank, in liters?

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department.  If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

~$\frac{4.8\left ( 10^{9} \right )}{1.6\left ( 10^{3} \right )}=$~

If the population of a certain country is 120,256,000 and its land area is 2,998,000 square kilometers, then the population per square kilometer is closest to which of the following?

A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated.  If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996.  If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

If ~$\left | d-9 \right |=$~ 2d, then d =

At a certain food stand, the price of each apple is ¢ 40 and the price of each orange is ¢ 60.  Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is ¢ 56.  How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is ¢ 52?

For a certain race, 3 teams were allowed to enter 3 members each.  A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.  There were no ties, disqualifications, or withdrawals.  If no team earned more than 6 points, what is the least possible score a team could have earned?