~$3,k,2,8,m,3$~

The arithmetic mean of the list of numbers above is 4. If k and m are integers and k≠m ,what is the median of the list?

In pentagon PQRST, PQ = 3, QR = 2, RS = 4, and ST = 5. Which of the lengths 5, 10, and 15 could be the value of PT ?

For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f (12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factor of f(24) ?

If x and k are integers and (12^x)(4^2x + ¹) = (2^k)(3²), what is the value of k ?

On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?

In the figure shown, PQRSTU is a regular polygon with sides of length x. What is the perimeter of triangle PRT in terms of x ?

A window is in the shape of a regular hexagon with each side of length 80 centimeters.If a diagonal through the center of the hexagon is w centimeters long, then w =

The sequence a₁, a₂, . . . , a_n, . . . is such that a_n = 2a_n _ ₁ - x for all positive integers n > 2 and for a certain number x. If a₅ = 99 and a₃ = 27, what is the value of x ?

The infinite sequence a₁, a₂, . . . , a_n, . . . is such that a₁ = 2, a₂ = -3, a₃ = 5, a₄ = -1, and a_n = a_n-4 for n > 4. What is the sum of the first 97 terms of the sequence?

A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28 ?