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 the sum of all the positive even integers less than 1000 is A, what is the sum of all the positive odd integers less than 1000?
(A)\(A - 998\) (B)\(A - 499\) (C)\(A + 1\) (D)\(A + 500\) (E)\(\frac { A } { 2 } + 999\)

SOLUTION: D

PROBLEM: If the ratio of \(a\) to \(b\) is 2 to 5, and the ratio of \(b\) to \(c\) is 1 to 4, what is the ratio of \(a\) to \(c\) ?
(A)1 : 2 (B)1 : 10 (C)5 : 8 (D)5 : 4 (E)5 : 2

SOLUTION: B

PROBLEM: The members of set A are the single digit prime numbers. Two numbers are selected at random from set A. What is the probability that the sum of the two selected numbers is even?
(A)0 (B)\(\frac { 1 } { 6 } \) (C)\(\frac { 1 } { 3 } \) (D)\(\frac { 1 } { 2 } \) (E)1

SOLUTION:
D