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:
\begin { gather* } 10, 15, 5, 10 \end { gather* } In the sequence above, the first term is 10, the second term is 15 and each term after the second is the nonnegative difference between the two previous terms. If \(a_n\) is defined as the nth term, what is the value of \(a_124\)?
(A)0 (B)5 (C)10 (D)15 (E)30
answer:
A


question:
If\( a^\frac { 1 } { 2 } = b^2\) and \(a\) and \(b\) are both greater than 1, then what is the value of \(a^2\) in terms of \(b\) ?
(A)\(\frac { b^1 } { 4 } \) (B)\(\frac { b^1 } { 2 } \) (C)\(b\) (D)\(b^4\) (E)\(b^8\)
answer:
E


question:
1. Choose a number between 0.5 and 0.99. 2. Multiply the number from the previous step by 20. 3. Determine the largest integer less than or equal to the number obtained from the previous step. 4. Subtract 4 from the number obtained from the previous step. 5. Write down the resulting number. Which, if any, of the following changes could be made to the sequence of steps without changing the number written in step 5?
(A)Remove step 2. (B)Remove step 3. (C)Replace step 3 with step 4 and vice versa. (D)Replace step 2 with step 4 and vice versa. (E)None of the above
answer:

C


