The figure shown above consists of three identical circles that are tangent to each other.

If the area of the shaded region is 64~$\sqrt{3}$~-32π , what is the radius of each circle?

Two numbers differ by 2 and sum to S. Which of the following is the greater of the numbers in terms of S ?

A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip?

(Assume that the driver did not make any stops during the 40-mile trip.)

Andrew started saving at the beginning of the year and had saved $240 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?

A certain manufacturer sells its product to stores in 113 different regions worldwide, with an average (arithmetic mean) of 181 stores per region. If last year these stores sold an average of 51,752 units of the manufacturer's product per store, which of the following is closest to the total number of units of the manufacturer's product sold worldwide last year?

Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a production lot in 5 hours, and Machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job.

What is the value of x ?

In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS ?

If x ≠ 2, then~$3x^2(x-2)-x+2 \over x-2$~ =

In the sequence x₀, x₁, x₂, ..., x_n, each term from x₁ to x_k is 3 greater than the previous term, and each term from x_k + ₁ to x_n is 3 less than the previous term, where n and k

are positive integers and k < n. If x₀ = x_n = 0 and if x_k =15, what is the value of n?

Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?