King School has an enrollment of 900 students. The school day consists of 6 class periods during which each class is taught by one teacher. There are 30 students per class. Each teacher teaches a class during 5 of the 6 class periods and has one class period free. No students have a free class period. How many teachers does the school have?

Ben and Ann are among 7 contestants from which 4 semifinalists are to be selected. Of the different possible selections, how many contain neither Ben nor Ann?

On a scale drawing, a rectangle 1 inch by 1~$\frac{1}{3}$~ inches represents the floor of a room and the indicated scale is 1 inch equals 15 feet. How many square tiles 6 inches on a side will be needed to cover this floor? (1 foot= 12 inches)

In the floor plan of an executive's beach house above, the north and south walls of the living room are parallel. what is the floor area, in square feet, of the bedroom?

Three-fourths of the area of a rectangular lawn 30 feet wide by 4o feet long is to be enclosed by a rectangular fence. If the enclosure has full width and reduced length rather than full length and reduced width, how much less fence will be needed?

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

The closing price of Stock ~$X$~ changed on each trading day last month. The percent change in the closing price of Stock ~$X$~ from the first trading day last month to each of the other trading days last month was less than 50 percent. If the closing price on the second trading day last month was $10.00, which of the following CANNOT be the closing price on the last trading day last month?

On a certain day, a bakery produced a batch of rolls at a total production cost of $300. On that day, ~$\frac{4}{5}$~ of the rolls in the batch were sold, each at a price that was 50 percent greater than the average (arithmetic mean) production cost per roll. The remaining rolls in the batch were sold the next day, each at a price that was 20 percent less than the price of the day before. What was the bakery’s profit on this batch of rolls?

The number ~$\sqrt{63-36~\sqrt{3}~}$~ can be expressed as ~$x+y \sqrt{3}$~for some integers ~$x$~ and ~$y$~. What is the valueof ~$xy$~?

 If ~$S$~ is the sum of the reciprocals of the 10 consecutive integers from 21 to 30, then ~$S$~ is between which of the following two fractions?