If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2ⁱ3^k5^m7^p, then i + k + m + p =

On a map Town G is 10 centimeters due east of Town H and 8 centimeters due south of Town J.  Which of the following is closest to the straight-line distance, in centimeters, between Town H and Town J on the map?

The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively.  If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?

I. 3
II. 7
III. 12

If 5^x – 5^{x - 3} = (124)(5^y), what is y in terms of x?

A certain machine produces 1,000 units of product P per hour.  Working continuously at this constant rate, this machine will produce how many units of product P in 7 days?

Company S produces two kinds of stereos:  basic and deluxe.  Of the stereos produced by Company S last month,  ~$\frac{2}{3}$~ were basic and the rest were deluxe.  If it takes  ~$\frac{7}{5}$~ as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

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 ~$\frac{5^{*}}{4^{*}}$~ ?

Which of the following fractions has a decimal equivalent that is a terminating decimal?

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 x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y?