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.

If \(7d < 4r\) and \(4r < 8p\), which of the following must be true?
(A)\(7d < 8p\) (B)\(8p < 7d\) (C)\(p < d\) (D)\(r = 2p\) (E)\(2r = p\)
A

If a is a nonzero integer and b is not an integer, which of the following could be an integer?
(A)\(a + b\) (B)\(a - b\) (C)ab (D)\(2a - b\) (E)\(\frac{b}{a}\)
C

If X is the set of positive multiples of 2 and Y is the set of positive multiples of 3, then the intersection of X and Y is
(A)the set of all positive integers (B)the set of all positive real numbers (C)the set of positive multiples of 3 (D)the set of positive multiples of 5 (E)the set of positive multiples of 6

E

