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.
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Question: If the length of one side of a triangle is 6 and the length of another side is 2, which of the following CANNOT be the length of the third side of the triangle?
(A)5 (B)6 (C)7 (D)7.5 (E)8

Answer: E


Question: If a, b, and x are positive integers and \(\triangle(a,x,b)\) is defined as the number of possible different triangles with sides of lengths a, b, and x, what is the value of \(\triangle(2,x,7)\)?
(A)2 (B)3 (C)4 (D)5 (E)6

Answer: B


Question: C, D, and E are points on a line, in that order. If the length of segment CE is 30, and the length of segment CD is twice the length of DE, what is the length of segment CD?
(A)10 (B)15 (C)20 (D)25 (E)30

Answer:
C