Sample Problem #1:

The following equation has roots in the form (x-a) (x-b) (x-c) (x-d) (x-e) = 0
where e > d > c > b > a

Find (e*d + c*b – a)

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Sample Problem #2:

A. In a river with a constant current, a man can row “2x” miles upstream in 5 hours, while he can row “x” miles downstream in 2 hours. Assume that the man rows at a constant rate in still water. Let a = the ratio of the man’s rowing rate in still water to the rate of the current. Find a.

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B. The sides of a triangle are (16a), (2a-1), and (17a-8), where a is the correct answer from part A. The area of the triangle is 136b², where b is positive. Find b.

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C.

Circle O has radius b, where b is the correct answer from part B. Angle ROA is 75 degrees.
Find the exact area of the segment formed by angle ROA.

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Sample Problem #3:

W, X, Y, and Z are four different positive integers that satisfy the equation

Let (W, X, Y, Z) be a set of integers that satisfies this equation. Find the minimum value of the product W*X*Y*Z.

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