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.

A right circular cylinder vase with an inner base radius of 6 inches is filled with water to a height of 20 inches. After a smaller solid right circular cylinder with base radius of 4 inches is then completely submerged in the water, the height of water is 24 inches. What is the height, in inches, of smaller cylinder?
(A)8 (B)9 (C)10 (D)11 (E)12
B

R, S and T are points with RT = 2RS. Which of the following could be true? I. R, S and T are the vertices of a right triangle. II. R, S and T are three of the vertices of a square. III. R, S and T all lie on the circumference of a circle.
(A)I only (B)III only (C)I and II only (D)I and III only (E)I, II, and III
D

In \(\triangle { EFG } \), the length of \(\overline { EF } \) is 9 and the length of \(\overline { EG } \) is 12. Each of the following could be the length of side \(\overline { FG } \) EXCEPT
(A)20 (B)16 (C)8 (D)4 (E)2

E