At a garage sale, all of the prices of the items sold were different.  If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?

In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term.  What is the sum of the 16th, 17th, and 18th terms in the sequence?

In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps.  The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps.  If 5,000 have been vaccinated against both, how many have been vaccinated only against rubella?

A certain list consists of 21 different numbers.  If n is in the list and n is 4 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

A company has assigned a distinct 3-digit code number to each of its 330 employees.  Each code number was formed from the digits

$$2, 3, 4, 5, 6, 7, 8, 9$$

and no digit appears more than once in any one code number.  How many unassigned code numbers are there?

Which of the following is equal to ~$\frac{2^{12}-2^{6}}{2^{6}-2^{3}}$~ ?

A certain liquid leaks out of a container at the rate of k liters for every x hours.  If the liquid costs $6 per liter, what is the cost, in dollars, of the amount of the liquid that will leak out in y hours?

A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly.  Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively.  What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

An equilateral triangle that has an area of ~$9\sqrt{3}$~  is inscribed in a circle.  What is the area of the circle?

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be