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 \(p\), \(q\), and \(r\) are positive, which of the following represents \(p\) percent of \(q\) percent of \(r\)?
(A)\(0.0001pqr\) (B)\(0.001pqr\) (C)\(0.1pqr\) (D)\(100pqr\) (E)\(10000pqr\)
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 \(4(x + y) - 2(x + y) = 12\), then \(x + y =\)
(A)2 (B)4 (C)6 (D)8 (E)10
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 \(2 - 3 \sqrt { x } = 8\), what is the value of \(x\)?
(A)0 (B)2 (C)4 (D)9 (E)There is no value of x that satisfies the equation
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: For any positive integer [n] represents the sum of the integers from 1 to n. For example, [5] = 1 + 2 + 3 + 4 + 5 = 15. Which of the following is equal to [10] - [9] ?
(A)[1] (B)[2] (C)[3] (D)[4] (E)[5]
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: After the first term, each term in a sequence is 4 greater than \(\frac{1}{4}\) of the preceding term. If n is the first term of the sequence and \(n \neq 0\), what is the ratio of the second term to the first term?
(A)\(\frac{n + 16}{4}\) (B)\(\frac{n + 4}{4}\) (C)\(\frac{n + 16}{4n}\) (D)\(\frac{n + 4}{4n}\) (E)\(\frac{16 - n}{4}\)
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: If \(\frac { a + 3 } { 3 } \) is an integer, what is the remainder when \(a\) is divided by 5 ?
(A)1 (B)2 (C)3 (D)4 (E)It cannot be determined from the information given
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 a positive number a is 150 percent of \(4p\), and if \(p\) is 25 percent of \(8b\), then what is the value of \(\frac { a } { b } \)?
(A)4 (B)8 (C)12 (D)16 (E)32
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 \(\frac { 1 } { a } + \frac { 1 } { a } + \frac { 1 } { a } = 12\), then \(a\) =
(A)\(\frac { 1 } { 12 } \) (B)\(\frac { 1 } { 4 } \) (C)\(\frac { 1 } { 3 } \) (D)3 (E)4
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: Given a sequence of integers where, starting from the first term, every third term is a multiple of 3 and every second term is a multiple of 2, which of the following could be the value of the 144th term in the sequence?
(A)15 (B)44 (C)81 (D)114 (E)206
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: Which of the following is the equivalent of the statement that three-fourths of the cube of a plus b divided by the square of c equals a ?
(A)\((-a)^3 + b - c^2 = a\) (B)\(\frac{3}{4}a^2 + \frac{b}{c} = a\) (C)\(\frac{3a^3}{4} + \frac{b}{c^2} = a\) (D)\(\frac{3}{4}a^3 + \frac{b}{c} = a\) (E)\(\frac{3}{4}a^3 + bc^2 = a\)
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 any positive integer [n] represents the sum of the integers from 1 to n. For example, [5] = 1 + 2 + 3 + 4 + 5 = 15. If \([1000] = a\) and \([10] = b\), what is the value of [1010]?
(A)\(a + b\) (B)\(a + l0b\) (C)\(a + b + 1000\) (D)\(a + b + 10,000\) (E)\(a + 1000b\)
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 \(|x - 10| = -5\), for how many values of \(x\) is the equation true?
(A)None (B)One (C)Two (D)Four (E)More than four
Output: 


Answer: A