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: How many primes less than 1000 are divisible by 7?
(A)None (B)1 (C)More than 1 but less than 142 (D)142 (E)More than 142

SOLUTION: B

PROBLEM: \begin{gather*} A + A = CB \\ C + B = 5 \end{gather*} Each correctly worked addition problem above shows the sum of two one-digit numbers. If the digits A, B, and C are nonzero, then \(A =\)
(A)2 (B)4 (C)5 (D)7 (E)9

SOLUTION: D

PROBLEM: If k and s are positive integers and the ratio of 2k to 6s is the same as the ratio of \(6k + 5\) to \(18s + 10\), which of the following must be true? I. \(k = s\) II. \(k = 1.5\) III. \(k = 1.5s\)
(A)None (B)I only (C)II only (D)III only (E)I and II

SOLUTION:
D