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: Container A and container B are right circular cylinders. Container A has a radius of 4 inches and a height of 5 inches while container B has a radius of 2 inches and a height of 10 inches. Sarah pours equal amounts of oil into both containers and finds that the height of the oil in container A is 2 inches. What is the height of the oil in container B ?
(A)8 inches (B)8.5 inches (C)9 inches (D)9.5 inches (E)10 inches
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: What is the volume, in cubic inches, of a cube whose total surface area is 216 square inches?
(A)6 (B)18 (C)36 (D)216 (E)1296
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: A line passes through the points (0, a) and (b, O). Which of the following is the slope of the line?
(A)\(-\frac { a } { b } \) (B)\(-\frac { b } { a } \) (C)\(\frac { a } { b } \) (D)\(\frac { b } { a } \) (E)\(\frac { a } { ab } \)
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: In \(\triangle { ABC } \), \(\overline { AB } = \overline { BC } \) and \(\overline { AB } \perp \overline { BC } \). If \(\overline { BC } = 10\), what is the area of the triangle?
(A)\(10 \sqrt { 2 } \) (B)25 (C)50 (D)\(50 \sqrt { 2 } \) (E)100
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: What is the equation of the line that passes through the points \((3,4)\) and \((-1,5)\)?
(A)\(x + 4y = 19\) (B)\(3x + 4y = 19\) (C)\(3x + 4y = 20\) (D)\(4x + y = 19\) (E)\(4x + y = 20\)
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: In \(\triangle { ABC } \) two sides, AB and BC are equal. Side AC has a length of 5, and the perimeter of \(\triangle { ABC } \) is 13. If the measure of angle ABC is \(x\), which of the following must be true about \(x\)?
(A)\(x < 60\) (B)\(60 < x < 90\) (C)\(x = 90\) (D)\(x > 90\) (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: \begin{gather} x^2 + y^2 + 4x - 2y = -1 \end{gather} The equation of a circle in the xy-plane is shown above. What is the radius of the circle?
(A)2 (B)3 (C)4 (D)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: The length and width of a certain rectangle are both decreased by 50 percent. If the length and width of the new rectangle are then increased by 40 percent, the area of resulting rectangle is what percent less than the area of the original rectangle?
(A)10\% (B)45\% (C)49\% (D)51\% (E)90\%
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: A line segment joining two points on the circumference of a circle is 1 inch from the center of the circle at its closest point. If the circle has a 2-inch radius, what is the length of the line segment?
(A)1 (B)\(\sqrt{3}\) (C)2 (D)\(2\sqrt{3}\) (E)\(4\sqrt{3}\)
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: If the surface area of a cube is \(150x^2\), what is the volume of the cube?
(A)\(8x^3\) (B)\(27x^3\) (C)\(64x^3\) (D)\(125x^3\) (E)\(150x^3\)
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: If the lengths of the sides of a certain triangle are a, b, and c, which of the following statements could be true?
(A)\(c = b + a\) (B)\(c = b - a\) (C)\(c = 2a + b\) (D)\(c + 2 = a + b + 3\) (E)\(c + 3 = a + b + 2\)
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: Some clay is shaped into a sphere with a radius of 2 inches. If more clay is added to the original sphere so that the radius is increased by 4 inches, then the volume of the new sphere is how many times greater than the volume of the original sphere?
(A)3 (B)8 (C)27 (D)64 (E)208
Output: 


Answer: C