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.

Ex Input:
If a, b, and c are positive and \(a^ { -2 } b^2c^2 > a^ { -3 } b^3c^2\), which of the following must be true? I. \(a > b\) II. \(a > c\) III. \(b > c\)
(A)I only (B)II only (C)III only (D)I and III only (E)I, II and III

Ex Output:
A


Ex Input:
Sequence Y: 5, 10, 15, ... Sequence Z: 3, 6, 12, ... The first term in Sequence Y is 5, and each term after the first is 5 more than the preceding term. The first term in sequence Z is 3, and each term after the first is 2 times the preceding term. What is the least value of x such that the xth term of Sequence Z is more than three times the xth term of Sequence Y?
(A)5 (B)6 (C)7 (D)8 (E)9

Ex Output:
B


Ex Input:
The average (arithmetic mean) of two numbers is equal to twice the positive difference between the two numbers. If the larger number is 35, what is the smaller number?
(A)3 (B)9 (C)15 (D)21 (E)27

Ex Output:

D