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: A triangle has vertices at points A, B, and C, which are located at (1, 0), (-3, 0), and (0, 5) respectively. What is the distance from the midpoint of \(\overline { AB } \) to point C ?
(A)3 (B)5 (C)\(\sqrt { 26 } \) (D)\(\sqrt { 29 } \) (E)\(\frac { \sqrt { 26 } + \sqrt { 34 } } { 2 } \)
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 playground is 3 feet more than its width. If the length of the playground is 13 feet, what is the area of the playground in square feet?
(A)93 (B)130 (C)145 (D)153 (E)160
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 PQRS, point T is the midpoint of side \(\overline { QR } \). If the area of PQRS is 3, what is the area of quadrilateral PQTS ?
(A)\(\frac { 3 } { 2 } \) (B)2 (C)\(\frac { 9 } { 4 } \) (D)\(\frac { 3 \sqrt { 3 } } { 2 } \) (E)\(2 \sqrt { 3 } \)
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: If A is point (-4, 1) and B is point (2, 1) what is the area of the circle that has \(\overline { AB } \) as a diameter?
(A)\(3\pi\) (B)\(6\pi\) (C)\(9\pi\) (D)\(12\pi\) (E)\(36\pi\)
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: If lines \(\overline { BC } \) and \(\overline { BD } \) are each perpendicular to line \(\overline { AB } \), which of the following must be true?
(A)\(\overline { AB } \perp \overline { CD } \) (B)\(\overline { AB } \perp \overline { AC } \) (C)\(\overline { AC } \perp \overline { AD } \) (D)\(\overline { AB } \parallel \overline { CD } \) (E)\(\overline { BC } \perp \overline { BD } \)
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: A rectangle has a perimeter equal to the circumference of a circle of radius 3. If the width of the rectangle is 3, what is its length?
(A)\(3\pi - 3\) (B)\(4.5\pi - 3\) (C)\(6\pi - 6\) (D)\(9\pi - 3\) (E)\(9\pi - 6\)
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: If the legs of right triangle \(PQR\) have lengths 5 and 12, what is the perimeter of a right triangle with each side twice the length of its corresponding side in \(\triangle { PQR } \) ?
(A)12 (B)20 (C)30 (D)42 (E)60
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: In rectangle EFGH, \(\overline { EF } \perp \overline { EH } \) and GH = 4. Which of the following could be the length of \(\overline { EG } \)?
(A)1 (B)2 (C)3 (D)4 (E)5
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 the length of one side of a triangle is 6 and the length of another side is 2, which of the following CANNOT be the length of the third side of the triangle?
(A)5 (B)6 (C)7 (D)7.5 (E)8
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: Points A, B, C, and D lie on the line in that order. If \(AB = 2BC = 3CD = k\) and \(CD = 6\), what is the distance from A to C?
(A)27 (B)33 (C)38 (D)42 (E)54
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: If point \(M(a,b)\) is the midpoint of the line segment connecting point \(A(5,10)\) and point \(B(15,4)\), what is the value of \(a + b\)?
(A)5 (B)6 (C)7 (D)8 (E)9
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: How many lines can be drawn from one vertex of a cube to the other vertices of the cube, such that the lines are not parallel to any edge of the cube?
(A)4 (B)6 (C)7 (D)24 (E)42
Output: 


Answer: A