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 \(f = 1 + 2 + 4 + 8 + 16\) and \(g = \frac { 1 } { 2 } f + \frac { 1 } { 2 } \), then \(f\) exceeds \(g\) by
(A)2 (B)4 (C)8 (D)15 (E)16
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: For any positive integer \(n > 1\), \(n!\) represents the product of the first \(n\) positive integers. For example, \(3! = 1 \times 2 \times 3 = 6\). Which of the following is (are) equal to \(\frac { 10! } { 8! } \) ? I. \(5! - 4! - 3!\) II. \(\frac { 5! } { 4! } \) III. \(15(3!)\)
(A)I only (B)II only (C)III only (D)I and III only (E)I, II and III
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 \(\frac{5}{d} = \frac{3}{2}\), then \(2d =\)
(A)\(1 \frac{2}{3}\) (B)\(3 \frac{1}{3}\) (C)\(6 \frac{2}{3}\) (D)\(7 \frac{1}{2}\) (E)15
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: If \(2\sqrt{4n^2} + 7 = 39\), what is the value of n?
(A)8 (B)4 (C)\(2\sqrt{2}\) (D)2 (E)\(\sqrt{2}\)
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 the ratio of \(a\) to \(b\) is 2 to 5, and the ratio of \(b\) to \(c\) is 1 to 4, what is the ratio of \(a\) to \(c\) ?
(A)1 : 2 (B)1 : 10 (C)5 : 8 (D)5 : 4 (E)5 : 2
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: \(\frac{1}{3}\) of 60 is equal to what percent of 50?
(A)\(16\frac{2}{3}\%\) (B)20\% (C)\(33\frac{1}{3}\%\) (D)40\% (E)60\%
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 \(|x - 5| = 2x - 1\), which of the following is the value of \(x\)?
(A)-4 (B)-2 (C)0 (D)2 (E)4
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 \((a + b)^2 = (a - b)^2\) , which of the following must be true?
(A)\(a = 0\) (B)\(b < 0\) (C)\(a = b\) (D)\(ab = 0\) (E)\(a + b = 0\)
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 \(a < -1\) and \(-1 < b < 0\), what are all of the possible values of \(ab\) ?
(A)All negative numbers (B)All negative numbers between -1 and O (C)All positive numbers less than 1 (D)All positive numbers greater than 1 (E)All positive numbers
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 \(\frac { z } { 3 } - \frac { 5 } { 6 } = |\frac { z } { 3 } - \frac { 5 } { 6 } |\), what is the least possible integer value of \(z\) ?
(A)-3 (B)0 (C)2 (D)3 (E)6
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 \(a^3 = 4\), what is the value of \(a^6\) ?
(A)8 (B)10 (C)12 (D)16 (E)64
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: \begin { gather* } 8, 10, x, 12, 8, 10, 8, 10, 10 \end { gather* } If the set of numbers above has both a median and a single mode of 10, then each of the number below could be the value of x EXCEPT
(A)4 (B)5 (C)6 (D)7 (E)8
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 \(|p| > 10 \), which of the following must be true? I. \(p > 10\) II. \(p^2 > 10\) III. \(p^3 > 10\)
(A)I only (B)II only (C)III only (D)I and II only (E)I, II, and III
Output: 


Answer: B