The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly 1/2 centimeter thick. A closed canister in the shape of a right circular cylinder is to be placed inside the box so that it stands upright when the box rests on one of its sides. Of all such canisters that would fit, what is the outer radius, in centimeters, of the canister that occupies the maximum volume?

November 16, 2001, was a Friday. If each of the years 2004, 2008, and 2012 had 366 days, and the remaining years from 2001 through 2014 had 365 days, what day of the week was November 16, 2014 ?

If the length of a diagonal of a square is 2~$\sqrt{x}$~ , what is the area of the square in terms of x?

If k and n are positive integers such that n > k, then k! + (n - k) • (k - 1)! is equivalent to which of the following?

Last year Brand X shoes were sold by dealers in 403 different regions worldwide, with an average（arithmetic mean) of 98 dealers per region.  If last year these dealers sold an average of 2,488 pairs of Brand X shoes per dealer, which following is closest to the total number of pairs of Brand X shoes sold last year by the dealers worldwide?

Carol purchased one basket of fruit consisting of 4 apples and 2 oranges and another basket of fruit consisting of 3 apples and 5 oranges. Carol is to select one piece of fruit at random from each of the two baskets. What is the probability that one of the two pieces of fruit selected will be an apple and the other will be an orange?

The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The

least possible value of the actual area of the square region is

One inch represents 20 miles on Map K and one inch represents 30 miles on Map L. An area of 3 square inches represents how many more square miles on Map L than on Map K?

Exchange Rates in a Particular Year

$1 = 5.3 francs

$1 = 1.6 marks

An American dealer bought a table in Germany for 480 marks and sold the same table in France for 2,385 francs. What was the dealer's gross profit on the two transactions in dollars?

In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?