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.

If \(\frac { a } { b } \) is an even number, where \(a\) and \(b\) are integers, which of the following must also be an even number?
(A)\(\frac { b } { a } \) (B)\(a + b\) (C)\(a - b\) (D)\(a\) (E)\(b\)
D

The difference between m and the square of n is equal to the square root of the sum of m and n. Which of the following expressions is the same as the statement above?
(A)\(m - \sqrt{n} = (m + 2)^2\) (B)\(m - n^2 = \sqrt{m + n}\) (C)\(m - n^2 = \sqrt{m} + \sqrt{n}\) (D)\(m - \sqrt{n} = m^2 + n ^2\) (E)\(m^2 - n^2 = \sqrt{m + n}\)
B

Which of the following sets of numbers has the property that the sum of any two numbers in the set is also in the set? I. \(\{ 1,2,3,...\}\) II. \(\{ 1,3,5,...\}\) III. \(\{ 10,20,30,...\}\)
(A)I only (B)II only (C)III only (D)I and III only (E)II and III only

D

