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 \(y < O\) and \(z \neq O\), each of the following could be true EXCEPT
(A)\(y^2z^2 < 0\) (B)\(yz^2 < 0\) (C)\(y^2 z < 0\) (D)\(yz < 0\) (E)\(y^3z < 0\)
answer:
A


question:
If the average (arithmetic mean) of 9 different positive integers is 15 and the median is 20, what is a possible value of the greatest of the 9 integers?
(A)99 (B)75 (C)39 (D)30 (E)28
answer:
C


question:
Set C consists of all of the positive integer multiples of 5 that are less than 20. Set D consists of all of the factors of 20. Which of the following is the union of Set C and Set D ?
(A)\(\lbrace 1, 2, 4, 5, 10, 15, 20\rbrace\) (B)\(\lbrace 2, 4, 5, 10, 15\rbrace\) (C)\(\lbrace 5, 10\rbrace\) (D)\(\lbrace 5, 10, 15, 20\rbrace\) (E)\(\lbrace 2, 4, 5, 10\rbrace\)
answer:

A


