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: If x is directly proportional to \(\sqrt { y } \), then y is inversely proportional to
(A)\(x^2\) (B)\(\sqrt { x } \) (C)\(\frac { 1 } { \sqrt { x } } \) (D)\(\frac { 1 } { x } \) (E)\(\frac { 1 } { x^2 } \)

SOLUTION: E

PROBLEM: If the sum of two negative integers is -15 and the product of two integers is less than 40, then which of the following could be one of the two integers?
(A)-8 (B)-7 (C)-5 (D)-4 (E)-3

SOLUTION: E

PROBLEM: If a, b, and c are distinct positive odd integers less than 6, how many different values of \(a(b^c)\) are possible?
(A)Two (B)Three (C)Four (D)Five (E)Six

SOLUTION:
D