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 the product of 3 positive integers is even, which of the following must be true?
(A)All of the integers are odd. (B)All of the integers are even. (C)Two of the integers are even and one is odd. (D)At least one of the integers is odd. (E)At least one of the integers is even.
answer:
E


question:
If \(f(x) = x^2 - 1\) and \(g(x) = 1 - x^2\), then for which of the following values of a does \(f(2a) - 7 = g(2a) + 7\)?
(A)0 (B)1 (C)\(\sqrt { 2 } \) (D)\(\sqrt { 7 } \) (E)7
answer:
C


question:
\((-3a^2 b^6)^3 =\)
(A)\(9a^5 b^9\) (B)\(-9a^5 b^9\) (C)\(9a^6 b^{18}\) (D)\(27a^6 b^{18}\) (E)\(-27a^6 b^{18}\)
answer:

E