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.

Example Input: In a list of four positive even numbers, the mean, median, and mode are all equal. Which of the following CANNOT be done to the list if the mean, median, and mode are to remain equal?
(A)Add one number to the list. (B)Add one number to the list that is greater than the mean. (C)Add two distinct numbers to the list. (D)Add 2 to each number in the list. (E)Remove the first and fast numbers from the list.
Example Output: B

Example Input: If \(8a < 3b\) and \(3b < 10c\), which of the following is true?
(A)\(8a < 10c\) (B)\(10c < 8a\) (C)\(c < a\) (D)\(8a = 10c\) (E)\(8a + 1 = 10c\)
Example Output: A

Example Input: \begin { gather* } 1, 2, 2, 2, 3, 3, 4, 5, 8, 10 \end { gather* } For the list of 10 numbers above, which of the following must be true?
(A)mode < mean < median (B)median < mode < mean (C)median < mean < mode (D)mean < median < mean (E)mode < median < mean
Example Output:
E