Lots-of-LoRAs/task119_semeval_2019_task10_geometric_mathematical_answer_generation huggingface dataset:
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: Let the lengths of the sides of a triangle be represented by \(x + 3\), \(2x - 3\), and \(3x - 5\). If the perimeter of the triangle is 25, what is the length of the shortest side?
(A)5 (B)7 (C)8 (D)10 (E)It cannot be determined from the information given
Output: 


Answer: B
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: In square \(ABCD\), vertex \(A\) is at (-1, -1) and vertex \(C\) is at (4, 2). What is the area of square \(ABCD\)?
(A)9 (B)15 (C)17 (D)25 (E)34
Output: 


Answer: C
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: \begin{gather} nA = 360 \end{gather} The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 50 degrees, what is the greatest number of sides it can have?
(A)5 (B)6 (C)7 (D)8
Output: 


Answer: C
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: A rectangular box is constructed from ten square tiles, each of which has a perimeter of 24 centimeters. If the box is formed so that the tiles do not overlap, what is the volume of the box in cubic centimeters?
(A)432 (B)288 (C)240 (D)216 (E)36
Output: 


Answer: A
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: Jim has identical drinking glasses each in the shape of a right circular cylinder with internal diameter of 3 inches. He pours milk from a gallon jug into each glass until it is full. If the height of milk in each glass is about 6 inches, what is the largest number of full milk glasses that he can pour from one gallon of milk? (Note: There are 231 cubic inches in 1 gallon.)
(A)2 (B)4 (C)5 (D)6
Output: 


Answer: C
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: Square ABCD in the coordinate plane has points A(1,3), B(5,7) and C(9,3). Which of the following could be the coordinates of point D?
(A)(3,1) (B)(3,-3) (C)(5,-1) (D)(5,3) (E)(7,-5)
Output: 


Answer: C
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: The length of a line segment with endpoints L and P is a positive integer less than 24. N is the midpoint of \(\overline { LP } \), M is the midpoint of \(\overline { LN } \) and O is the midpoint of \(\overline { NP } \). Which of the following could be the distance between M and P?
(A)18 (B)17 (C)16 (D)15 (E)14
Output: 


Answer: D
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: Points Q, R, and S lie on \(\overline { XZ } \) in such a way that Q is the midpoint of \(\overline { XZ } \), R is the midpoint of \(\overline { XQ } \) and S is the mid point of \(\overline { QZ } \). If QS = 4, what is length of RZ?
(A)8 (B)12 (C)16 (D)20 (E)24
Output: 


Answer: B
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: Points L, M, and N lie in a plane. If the distance between L and M is 4, and the distance between M and N is 9, which of the following could be the distance between L and N? I. 5 II. 8 III. 13
(A)I only (B)II only (C)III only (D)I and III (E)I, II and III
Output: 


Answer: E
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: If a rectangular rug measures 72 inches by 96 inches, what is its area in square feet? (1 foot = 12 inches)
(A)864 (B)576 (C)336 (D)144 (E)48
Output: 


Answer: E
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: In a coordinate plane, if points C\((2, 5)\), D\((-1, 2)\), and E\((x, y)\) lie on line l, which of the following could be the coordinates of point E?
(A)\((0, 1)\) (B)\((1, 1)\) (C)\((0, 2)\) (D)\((1, 3)\) (E)\((1, 4)\)
Output: 


Answer: E
Definition: You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric 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.

Positive Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: B

Positive Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: C

Negative Example 1 -
Input: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Output: I dont know.

Negative Example 2 -
Input: The diameter of a basketball is 4 times the diameter of a racquetball. What is the ratio of the radius of the basketball to that of the racquetball?
(A)1 : 2 (B)3 : 2 (C)4 : 1 (D)4 : 3 (E)8 : 1
Output: B,D

Now complete the following example -
Input: If m is an integer and m, m + 1, and m + 2 are the lengths of the sides of a triangle, which of the following could be the value of m? I. 1 II. 10 III. 100
(A)I only (B)II only (C)III only (D)II and III only (E)I, II, and III
Output: 


Answer: D