If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?

If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?

I.    ~$\frac{1}{8}$~
II.    ~$\frac{1}{9}$~
III.    ~$\frac{1}{10}$~

A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office.  In how many ways can the company assign 3 employees to 2 different offices?

A wire that weighs 24 kilograms is cut into two pieces so that one of the pieces weighs 16 kilograms and is 34 meters long.  If the weight of each piece is proportional to its length, how many meters long is the other piece of wire?

Of the mutual funds on a “select list,” ~$\frac{1}{3}$~  have 5-star ratings, and  ~$\frac{2}{5}$~ of the remaining funds have 4-star ratings.  If the remaining 300 funds on the list have 3-star ratings, how many funds are on the list?

If x, y, and k are positive numbers such that ~$10\left ( \frac{x}{x+y} \right )+20\left ( \frac{y}{x+y} \right )=k$~ and if x < y, which of the following could be the value of k?

If the volume of a small container is 14,520 cubic millimeters, what is the volume of the container in cubic centimeters? (1 millimeter = 0.1 centimeter)

In the xy-plane, the vertices of a triangle have coordinates (0, 0), (3, 3), and (7, 0).  What is the perimeter of the triangle?

For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form  ~$\frac{1}{t}$~ , where t is an integer between 1 and k, inclusive.  What is the value of ~$\frac{5^{\ast }}{4^{\ast }}$~ ?

In a certain English class, ~$\frac{1}{4}$~ of the number of girls is equal to  ~$\frac{1}{6}$~ of the total number of students.  What is the ratio of the number of boys to the number of girls in the class?