TASK DEFINITION: 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.
PROBLEM: \begin{gather*} 3, 8,13,18,23,28, 33, 38 \end{gather*} If from the sequence of numbers above, a new sequence is created by increasing each odd-valued term by 3 and decreasing each even-valued term by 2, the sum of the terms of this new sequence is how much greater than the sum of the terms of the original sequence?
(A)4 (B)6 (C)8 (D)10 (E)12

SOLUTION: A

PROBLEM: If set S has the property that x is in S, and \(x^2 - 2x + 1\) is also in S, which of the following sets could be S?
(A)1,2,3 (B)0,1,2 (C)-1,0,1 (D)0,2 (E)1,2

SOLUTION: B

PROBLEM: Between which two digits of the number 987,654 should a decimal point be placed so that the value of the resulting number is equal to \(9.87654 \times 10^4\)?
(A)9 and 8 (B)8 and 7 (C)7 and 6 (D)6 and 5 (E)5 and 4

SOLUTION:
E