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 r is a multiple of both 12 and 18, which of the following must be a factor of r ?
(A)8 (B)24 (C)27 (D)30 (E)36

SOLUTION: E

PROBLEM: 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)\(y^3z < 0\)

SOLUTION: A

PROBLEM: For which of the following lists of numbers is the mode equal to the average (arithmetic mean) ?
(A)10, 10, 10, 50, 70 (B)10, 20, 25, 30, 40 (C)15, 35, 35, 35, 55 (D)10, 20, 25, 35, 45 (E)5, 15, 25, 25, 50

SOLUTION:
C

