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.

The least integer of a set of consecutive even integers is \(-30\). If the sum of these integers is 66, how many integers are in the set?
(A)12 (B)14 (C)30 (D)33 (E)35
D
The least integer of a set of consecutive even integers is \(-30\), so the integers are \(-30, -28, -26, ...\). The sum of these integers is 66, so we have \(\sum_{i=1}^{n}(-30+2i) = 66 \implies n(-15+n) = 33 \implies n^2 - 15n + 33 = 0\). Solving this quadratic equation gives us that \(n\) must be either 3 or 11. Since there cannot be fewer than 3 consecutive even integers in the set (for then their sum would not be equal to 66), the answer is (D) 33..