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: If the circumference of a circle is equal to the perimeter of a square whose sides are \(7t\), what is the radius of the circle?
(A)1 (B)2 (C)4 (D)\(\pi\) (E)\(2\pi\)
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: If A is at (3, -1) and B is at (5, 6) what is the slope of the perpendicular bisector of segment \(\overline { AB } \) ?
(A)\(-\frac { 7 } { 2 } \) (B)\(-\frac { 2 } { 5 } \) (C)\(-\frac { 2 } { 7 } \) (D)\(\frac { 2 } { 7 } \) (E)\(\frac { 2 } { 5 } \)
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: Points E and F lie in the xy-coordinate plane at (0,10) and (6,0), respectively. Which of the following is the midpoint of \(\overline { EF } \) ?
(A)(5,3) (B)(3,5) (C)(3,10) (D)(10,3) (E)(6,10)
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: A square and an equilateral triangle each have sides of length 5. What is the ratio of the area of the square to the area of the triangle?
(A)\(\frac { 4 } { 3 } \) (B)\(\frac { 16 } { 9 } \) (C)\(\frac { \sqrt { 3 } } { 4 } \) (D)\(\frac { 4\sqrt { 3 } } { 3 } \) (E)\(\frac { 16\sqrt { 3 } } { 9 } \)
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: \(A\) (5, 1) lies on a circle whose center is \(O\) (1, 5). If \(AB\) is a diameter, what are the coordinates of \(B\) ?
(A)(3, 3) (B)(6, 6) (C)(-1, 5) (D)(-1, 10) (E)(-3, 9)
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: A circle with radius r is inscribed in a square. If a point within the square is randomly selected, what is the probability that the point will not be within the circle?
(A)\(\frac { \pi } { 4 } \) (B)\(\frac { \pi - 4 } { 4 } \) (C)\(\frac { 4 - \pi } { 4 } \) (D)\(\pi r\) (E)\(4r\)
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 graph of \(y = x - 2\) is drawn on a set of coordinate axes. If the graph of \(y = x + 7\) is then drawn on the same axes, how does the second graph compare to the first?
(A)The second graph will be 9 units above the first. (B)The second graph will be 3 units above the first. (C)The second graph will be 5 units bellow the first. (D)The second graph will be 9 units bellow the first. (E)The second graph will have a greater slope than the first.
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 area of the quadrilateral whose vertices are at (1, 1), (5, 1), (5, 5) and (3, 5)?
(A)8 (B)12 (C)16 (D)24 (E)10 + 2\(\sqrt { 2 } \)
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 A, B and C are three vertices of a triangle. The location of point X is such that AX = BX. Which of the following could be true? I. X is on \(\overline { AB } \) II. X is inside \(\triangle { ABC } \) III. X is outside \(\triangle { ABC } \)
(A)I only (B)III only (C)I and II only (D)II and III only (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: A frame 2 inches wide is placed around a rectangular picture with dimensions 8 inches by 12 inches. What is the area of the frame in square inches?
(A)44 (B)96 (C)128 (D)144 (E)168
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: R, S and T are points with RT = 2RS. Which of the following could be true? I. R, S and T are the vertices of a right triangle. II. R, S and T are three of the vertices of a square. III. R, S and T all lie on the circumference of a circle.
(A)I only (B)III only (C)I and II only (D)I and III only (E)I, II, and III
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(-3,2) B(1,2) C(6,-1) The coordinates of points A, B and C in the xy- plane are given above. What is the area of \(\triangle { ABC } \) ?
(A)6 (B)8 (C)10 (D)12 (E)18
Output: 


Answer: A