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 \(a^x = 4\) and \(a^c = 64\), what is the value of \(a^ { x - c } \) ?
(A)-60 (B)-16 (C)\(\frac { 1 } { 16 } \) (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 \(3^ { x^2 + y^2 } = \frac { 1 } { 9^xy } \), what is the value of \(x + y\) ?
(A)-2 (B)-1 (C)0 (D)1 (E)2
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: \begin { gather* } 1, 2, 2, 2, 3, 3, 4, 5, 8, 10 \end { gather* } For the list of 10 numbers above, which of the following must be true?
(A)mode < mean < median (B)median < mode < mean (C)median < mean < mode (D)mean < median < mean (E)mode < median < mean
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: Which of the following expressions represents \(b - 3a\) subtracted from twice the sum of \(2a\) and \(5b\) ?
(A)\(-9b - 7a\) (B)\(-4b - a\) (C)\(4b + a\) (D)\(7b + 3a\) (E)\(9b + 7a\)
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 \(2^{2x - 3} = 8\), then what is the value of x?
(A)0 (B)1 (C)2 (D)3 (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 \(\frac{4}{\sqrt{r + 4}} = 2\), what is the value of r?
(A)\(-4\) (B)\(-2\) (C)0 (D)2 (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: If \(\sqrt { x } = \frac { x } { 10 } \) and \(x > 0\), what is the value of \(x\) ?
(A)-1 (B)1 (C)10 (D)100 (E)1,000
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 \((x + y)^2 - (x - y)^2 = 72\), where \(x\) and \(y\) are positive integers, which of the following could be a value of \(x + y\)?
(A)10 (B)11 (C)12 (D)13 (E)14
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: S = 1 + 2 + 3 + 4 + ... + 49 + 50 T = 51 + 52 + 53 + ... + 99 + 100 If the sum of the positive integers from 1 to 50 is \(S\), and the sum of the positive integers from 51 to 100 is \(T\), what is \(T\) in terms of \(S\)?
(A)\(2S\) (B)\(S + 50\) (C)\(S + 100\) (D)\(S + 2500\) (E)\(S + 10000\)
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 \(a > b\) and \(k < 0\), which of the following must be true? I. \(ak > bk\) II. \(a^2 > b^2\) III. \(\frac { a + k } { k } < \frac { b + k } { k } \)
(A)I only (B)II only (C)III only (D)II and III only (E)I, II and III
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 what value of \(x\) does \((x-1)^3 = x^3 - 1\) ?
(A)x = 1 only (B)x = -1 only (C)x = 0 or x = 1 (D)x = 1 or x = -1 (E)x = O or x = -1
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 \(\frac { 1 } { p } + \frac { 1 } { q } = t\), and \(pq = w\), then \(p + q = \)
(A)\(\frac { w } { t } \) (B)\(\frac { t } { w } \) (C)\(tw\) (D)\(\frac { tw } { 2 } \) (E)\(t(t + w)\)
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 \(x + 2y = a\) and \(x - 2y = b\), which of the following is an expression for \(xy\)?
(A)\(ab\) (B)\(\frac { a + b } { 2 } \) (C)\(\frac { a - b } { 2 } \) (D)\(\frac { a^2 - b^2 } { 4 } \) (E)\(\frac { a^2 - b^2 } { 8 } \)
Output: 


Answer: E