TASK DEFINITION: You are given a mathematical question described with a circumscribed mathematical vocabulary. Questions in this task usually contain some variables (e.g. X, Y), equations (e.g. X+Y=3) and some relationships (X is greater than Y). Often you need to find the value of the variable using equations and relationships. You are also given 4 or 5 answer options (associated with "A", "B", "C", "D", "E"). Do not generate anything else apart from one of the following characters: 'A', 'B, 'C', 'D', 'E'. LaTeX mathematical format (the standard way to express mathematical expressions in the typesetting software known as LaTeX) is used to express equations. Each question is solvable with high school math knowledge. Give only one answer for each question.
PROBLEM: If \(f(x) = x^2 - 3x\) and \(g(x) = f(3x)\), what is \(g(-10)\)?
(A)210 (B)390 (C)490 (D)810 (E)990

SOLUTION: E

PROBLEM: \begin{gather*} 3, 8,13,18,23,28, 33, 38 \end{gather*} If from the sequence of numbers above, a new sequence is created by increasing each odd-valued term by 3 and decreasing each even-valued term by 2, the sum of the terms of this new sequence is how much greater than the sum of the terms of the original sequence?
(A)4 (B)6 (C)8 (D)10 (E)12

SOLUTION: A

PROBLEM: Squaring the product of z and 6 gives the same result as squaring the difference of z and 6. Which of the following equations could be used to find all the possible values of z?
(A)\(6z^2 = (z + 6)^2\) (B)\((6z)^2 = z^2 + 6^2\) (C)\(6^2 z = z^2 - 6^2\) (D)\((6z)^2 = (z - 6)^2\) (E)\(6z^2 = z^2 + 6^2\)

SOLUTION:
D