instruction:
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.
question:
In the equation \(S = 4\pi r^2h\), if the value of \(S\) is doubled, and the value of \(r\) is doubled, then the value of \(h\) is multiplied by...
(A)\(\frac { 1 } { 4 } \) (B)\(\frac { 1 } { 2 } \) (C)2 (D)4 (E)8
answer:
B


question:
If \(k^6 = m^ { -2 } n^4\), where \(k\), \(m\), and \(n\) are positive numbers, which of the following is the value of \(m\)?
(A)\(k^3n^2\) (B)\(\frac { k^3 } { n^2 } \) (C)\(\frac { 1 } { k^3n^2 } \) (D)\(\frac { k^6 } { n^3 } \) (E)\(\frac { n^2 } { k^3 } \)
answer:
E


question:
The first term of a sequence is \(a\). Every term after the first is equal to \(d\) plus the preceding term. If the seventh term is 20 and the fourth term is 11, what is the value of \(a + d\)?
(A)5 (B)6 (C)7 (D)8 (E)9
answer:

A


