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 0.05 percent of n is 5, what is 5 percent of n?
(A)900 (B)700 (C)500 (D)0.007 (E)0.005
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 \(a = 9c^2 + 4\) and \(b = 7 + 3c\), what is a in terms of b?
(A)\(2b^2 - 7b + 49\) (B)\(b^2 - 14b + 49\) (C)\(b^2 + 14b + 49\) (D)\(b^2 - 14b + 53\) (E)\(b^2 + 14b + 53\)
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: The average (arithmetic mean) of three consecutive even integers \(a\), \(b\), and \(c\) is 8. What is the median of a, b, c, and 20 ?
(A)8 (B)9 (C)10 (D)11 (E)12
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: The integer 90 can be expressed as the sum of \(z\) consecutive integers. The value of z could be any of the following EXCEPT
(A)3 (B)4 (C)5 (D)6 (E)9
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: Let the function \(g(x)\) be defined by \(g(x) = 2f(x) + k\) , where \(f(x)\) is a linear function. If \(g(2) = 10\) and \(g(5) = 18\), what is the slope of function \(f\)?
(A)\(\frac { 2 } { 3 } \) (B)\(\frac { 4 } { 3 } \) (C)2 (D)3 (E)\(\frac { 9 } { 2 } \)
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: If \(X = \frac { ab^2 } { c } \), what is the result on X of doubling a, tripling b, and quadrupling c?
(A)X is multiplied by 1.5. (B)X is multiplied by 3. (C)X is multiplied 4.5. (D)X is multiplied by 6. (E)X is multiplied by 9.
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: The nth term of a sequence is defined to be \(5n + 2\). The 35th term is how much greater than the 30th term?
(A)5 (B)18 (C)25 (D)36 (E)40
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 \(\frac{\sqrt{x} + n}{\sqrt{x} + 9} = 1\), then \(n =\)
(A)1 (B)3 (C)5 (D)8 (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: The average (arithmetic mean) of the numbers in set A is 8. If a second set of numbers, B, is created by dividing each of the numbers in set A by two, then what is the average of the numbers in set B?
(A)\(\frac { 1 } { 2 } \) (B)4 (C)8 (D)12 (E)16
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 \(\sqrt { a^2 + b^2 } = a + b\), which of the following must be true?
(A)\(a = 0\) and \(b = 0\) (B)\(a + b = 0\) (C)\(ab = 0\) (D)\(ab \neq 0\) (E)\(a^2 - b^2 = 0\)
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: Let \(f(x) = \frac { \sqrt { x - \pi } } { x - 4 } \). What is the smallest integer for which \(f(x)\) is defined?
(A)0 (B)1 (C)3 (D)4 (E)5
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 positive four-digit integer JKLM contains the digits J, K, L and M, what is the decimal equivalent of \(JKLM \times 10^ { -3 } \)
(A)0.JKLM (B)J.KLM (C)JK.LM (D)JK,LM0 (E)J,KLM,000
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 x is a positive integer, all of the following are equal to \((4^3)^x\) EXCEPT
(A)\(4^ { 3x } \) (B)\(2^ { 4x } (4^x)\) (C)\(4^x (4^3x)\) (D)\(4^x (4^2x)\) (E)\(8^2x\)
Output: 


Answer: C