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 the sum of four numbers is between 53 and 57, then the average (arithmetic mean) of the four numbers could be which of the following?
(A)\(11 \frac{1}{2}\) (B)12 (C)\(12 \frac{1}{2}\) (D)13 (E)14
E

If \(2 \leq p \leq 6\) and \(1 \leq q \leq 12\), what is the smallest value of \((p + q)^2 - (p - q)^2\)?
(A)20 (B)18 (C)8 (D)6 (E)4
C

If \(|x| < 5\) and \(|x| > 2\), how many integers satisfy both of the two inequalities?
(A)1 (B)2 (C)3 (D)4 (E)More than 4

D