You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Input: Consider Input: Points Q, R, and S lie on \(\overline { XZ } \) in such a way that Q is the midpoint of \(\overline { XZ } \), R is the midpoint of \(\overline { XQ } \) and S is the mid point of \(\overline { QZ } \). If QS = 4, what is length of RZ?
(A)8 (B)12 (C)16 (D)20 (E)24

Output: B


Input: Consider Input: \begin{gather} nA = 360 \end{gather} The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 50 degrees, what is the greatest number of sides it can have?
(A)5 (B)6 (C)7 (D)8

Output: C


Input: Consider Input: If the graph of the function g in the xy-plane contains the points (0,4), (-2,0), and (2,0), which of the following could be true? I. The graph of g is a parabola. II. The graph of g has a maximum value. III. The graph of g is a line.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III


Output: D