instruction:
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.
question:
If \(2a = 3b\), \(\frac { 1 } { 3 } c = 6b^2 + 2\), and \(b > 0\), what is \(c\) in terms of \(a\) ?
(A)\(8a^2 + 6\) (B)\(8a^2 + 12\) (C)\(12a^2 + 6\) (D)\(18a^2 + 6\) (E)\(18a^2 + 12\)
answer:
A


question:
If \(m\) and \(n\) are integers and \((x + m)(x + n) = x^2 + 11x + c\), what is the greatest possible value of \(c\) ?
(A)22 (B)24 (C)28 (D)30 (E)33
answer:
D


question:
The members of set R are the integer solutions of |y| < 10, and the members of set S are the even integer solutions of |x| >5. Which of the following includes all the members common to both set R and set S ?
(A)\(\lbrace -8, -6, 6, 8\rbrace\) (B)\(\lbrace -9, -8, -7, -6, -5, 5, 6, 7, 8, 9\rbrace\) (C)\(\lbrace -9, -8, -7, -6, 6, 7, 8, 9\rbrace\) (D)\(\lbrace 6, 8\rbrace\) (E)\(\lbrace 6, 7, 8, 9\rbrace\)
answer:

A