TASK DEFINITION: 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.
PROBLEM: If \(d\) is the length of a diagonal of a square, what does \(d^2\) represent?
(A)the area of the square (B)twice the area of the square (C)\(\frac { 1 } { 2 } \) the area of the square (D)4 times the area of the square (E)\(\frac { 1 } { 4 } \) the area of the square

SOLUTION: B

PROBLEM: Some clay is shaped into a sphere with a radius of 2 inches. If more clay is added to the original sphere so that the radius is increased by 4 inches, then the volume of the new sphere is how many times greater than the volume of the original sphere?
(A)3 (B)8 (C)27 (D)64 (E)208

SOLUTION: C

PROBLEM: Points L, M, and N lie in a plane. If the distance between L and M is 4, and the distance between M and N is 9, which of the following could be the distance between L and N? I. 5 II. 8 III. 13
(A)I only (B)II only (C)III only (D)I and III (E)I, II and III

SOLUTION:
E