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 \(x^2 + y^2 = (x - y)^2\), which of the following statements must also be true? I. \(x = 0\) II. \(y = 0\) III. \(xy = 0\)
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III only

SOLUTION: C

PROBLEM: \(A = \{ 2, 4, 6 \}\) \(B = \{ 1, 2, 3, 4 \}\) Set \(A\) and \(B\) are shown above. If a is \(a\) member of set \(A\) and \(b\) is a member of set \(B\), how many different values are possible for \(ab\)? If the statement above is true, which of the following must also be true?
(A)6 (B)8 (C)10 (D)12 (E)14

SOLUTION: B

PROBLEM: If \(k\) is a positive integer, what is the smallest value of k for which \((12k)^\frac { 1 } { 3 } \) is an integer?
(A)144 (B)72 (C)36 (D)18 (E)12

SOLUTION:
D