Lots-of-LoRAs/task104_semeval_2019_task10_closed_vocabulary_mathematical_answer_generation huggingface dataset:
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: If set A is \{3,5,7,11,19\} and set B consists of all the even numbers between 1 and 11, how many elements are in the union of the two sets?
(A)0 (B)10 (C)11 (D)19 (E)30
Output: 


Answer: B
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: If m and n are positive integers and \(2m + 3n = 15\), what is the sum of all possible values of m ?
(A)2 (B)3 (C)5 (D)6 (E)9
Output: 


Answer: E
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: What is the value of \(b\) if \(1 - \frac { 4 } { b } = \frac { 5 } { 3 } \) ?
(A)-6 (B)-2 (C)\(\frac { 1 } { 4 } \) (D)\(\frac { 2 } { 3 } \) (E)6
Output: 


Answer: A
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: If \(x > 0\), then \((4^x)(8^x) =\)
(A)\(2^{9x}\) (B)\(2^{8x}\) (C)\(2^{6x}\) (D)\(2^{5x}\) (E)\(2^{4x}\)
Output: 


Answer: D
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: If \(x = 5 + y\) and \(x = 5 - y\), what is the value of \(y\) ?
(A)0 (B)\(\frac { 1 } { 2 } \) (C)1 (D)\(\frac { 3 } { 2 } \) (E)5
Output: 


Answer: A
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: The average (arithmetic mean) of \(2a\) and \(b\) is 15 and the average of \(2a\),\(b\), and \(3c\) is 20. What is the value of \(c\)?
(A)5 (B)10 (C)15 (D)20 (E)25
Output: 


Answer: B
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: Let the function \(f\) be defined by \(f(2k) = 2f(k)\) and \(f(5) = 10\). Which of the following functions could be the definition of \(f(x)\)?
(A)\(f(x) = x + 5\) (B)\(f(x) = x - 5\) (C)\(f(x) = 15 - x \) (D)\(f(x) = 2x\) (E)\(f(x) = x\)
Output: 


Answer: D
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: If \(x\) and \(y\) are integers, how many distinct ordered pairs \((x,y)\) satisfy the equation \(2x + 4y = 17\) ?
(A)None (B)One (C)Two (D)Three (E)Four
Output: 


Answer: A
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: If \(3y^4 + xy - x^2 = y^2 - 25\) and \(y = 0\), how many possible values of \(x\) are there?
(A)0 (B)1 (C)2 (D)3 (E)4
Output: 


Answer: C
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: For all positive integers r and q, where \(r > q\), let the operation \& be defined by \(r \& q = \frac{3^{r + q}}{3^{r - q}}\). for how many positive integers r is r \& 1 equal to 9?
(A)0 (B)1 (C)2 (D)4 (E)More than 4
Output: 


Answer: E
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: If the price of a certain product is increased by 15 percent, by approximately what percent must the new price be reduced to obtain the original price?
(A)13 (B)15 (C)17 (D)85 (E)115
Output: 


Answer: A
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: \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
Output: 


Answer: A
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.

Positive Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: B

Positive Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: C

Negative Example 1 -
Input: If k is an integer and \(k = \frac { m } { 3 } \) which of the following must be true? I. m is an even number. II. m is a multiple of 3. III. m is an odd number.
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: I dont know.

Negative Example 2 -
Input: If x = 1 = kx, for which of the following values of k will the equation have NO solution?
(A)-1 (B)0 (C)1 (D)2 (E)3
Output: A,B

Now complete the following example -
Input: If n is an integer, which of the following must be true about \(12n + 3\) ? I. It is even II. It is odd III. It is divisible by 3
(A)I only (B)II only (C)III only (D)II and III only (E)I, II, and III
Output: 


Answer: D