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.

Ex Input:
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)\(6z^2 = z^2 + 6^2\)

Ex Output:
D


Ex Input:
\(r = 4c - d\) \(t = (c +1)r\) If r and t are defined by the equations above, what is the value of \(t\) when \(c = 3\) and \(d = 2\) ?
(A)10 (B)12 (C)30 (D)40 (E)80

Ex Output:
D


Ex Input:
If \(|5x + 15| = 10\), then x could equal
(A)1 and 5 (B)-1 and 5 (C)-1 and -5 (D)-1 (E)-5

Ex Output:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
C


