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In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: a voltage will influence current only if the circuit is :
Options: ['a ) 2', 'b ) 7', 'c ) 6', 'd ) 889', 'e ) 1']
b
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 180 m , its area is ?
Options: a ) 90 , b ) 882 , c ) 277 , d ) 261 , e ) 281
a
Problem: the mass of 1 cubic meter of a substance is 300 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 3.33 , b ) 3.34 , c ) 3.53 , d ) 5.32 , e ) 3.92
|
a
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: if the radius of the sphere is 14 m . then its total surface area is
Options: ['a ) 2644', 'b ) 2446', 'c ) 2464', 'd ) 6442', 'e ) 6424']
SOLUTION: c
PROBLEM: Problem: what is the perimeter , in meters , of a rectangular garden 12 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
Options: a ) 48 , b ) 56 , c ) 60 , d ) 56 , e ) 192
SOLUTION: d
PROBLEM: Problem: an oil cylinder was 3 / 4 th full . when 4 bottles of oil is poured into it , it is 4 / 5 th full . how many bottles of oil can the full cylinder hold ?
Options: a ) 90 , b ) 75 , c ) 70 , d ) 80 , e ) 85
SOLUTION:
|
d
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example input: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Example output: d
Example explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Q: Problem: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 10 % ?
Options: a ) 25 % , b ) 28 % , c ) 21 % , d ) 30 % , e ) 32 %
A:
|
c
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
instruction:
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
question:
Problem: a math teacher has 25 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles .
Options: a ) 8 , b ) 10 , c ) 11 , d ) 12 , e ) 13
answer:
a
question:
Problem: the mass of 1 cubic meter of a substance is 400 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 0.8 , b ) 1.25 , c ) 8.0 , d ) 2.5 , e ) 80.0
answer:
d
question:
Problem: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 2 per metre approximately
Options: a ) 2972 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 4675
answer:
|
a
| 9
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Input: Consider Input: Problem: the sum of two numbers is 16 and the sum of their squares is 113 . find the numbers .
Options: a ) 1 and 2 , b ) 4 and 5 , c ) 7 and 8 , d ) 2 and 3 , e ) 6 and 7
Output: c
Input: Consider Input: Problem: how many 4 x 4 x 4 cubes could fit in a 9 x 13 x 16 box ?
Options: a ) 22 , b ) 28 , c ) 29 , d ) 31 , e ) 32
Output: c
Input: Consider Input: Problem: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 10 % ?
Options: a ) 25 % , b ) 28 % , c ) 21 % , d ) 30 % , e ) 32 %
|
Output: c
| 2
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Example solution: d
Example explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Problem: Problem: a semicircle has a radius of 10 . what is the approximate perimeter of the semicircle ?
Options: a ) 27 , b ) 33 , c ) 39 , d ) 45 , e ) 51
|
Solution: e
| 5
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example Input: Problem: the side of a rhombus is 24 m and length of one of its diagonals is 18 m . the area of the rhombus is ?
Options: a ) 410.47 , b ) 403.47 , c ) 420.47 , d ) 400.47 , e ) 300.47
Example Output: d
Example Input: Problem: if the sides of a triangle are 28 cm , 26 cm and 10 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 130 cm 2 , e ) 886 cm 2
Example Output: d
Example Input: Problem: a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 1 , - 4 ) . what is the smallest possible area of that circle ?
Options: a ) 13 π , b ) 26 π , c ) 262 √ π , d ) 5 π , e ) 64 π
Example Output:
|
d
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of 4 walls , the volume of the hall is :
Options: a ) 3348 , b ) 3898 , c ) 1200 , d ) 2881 , e ) 7881
c
Problem: find the area of a parallelogram with base 15 cm and height 40 cm ?
Options: a ) 200 cm 2 , b ) 100 cm 2 , c ) 42 cm 2 , d ) 600 cm 2 , e ) 230 cm 2
d
Problem: 2 minute is taken to travel the diagonal of square field at 3 km / hour . calculate the area of field ?
Options: ['a ) 25 are', 'b ) 30 are', 'c ) 50 are', 'd ) 60 are', 'e ) 45 are']
|
c
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
One example is below.
Q: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
A: d
Rationale: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Q: Problem: a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 1 , - 4 ) . what is the smallest possible area of that circle ?
Options: a ) 13 π , b ) 26 π , c ) 262 √ π , d ) 5 π , e ) 64 π
A:
|
d
| 9
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Teacher: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Teacher: Now, understand the problem? If you are still confused, see the following example:
Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution: d
Reason: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Now, solve this instance: Problem: juan and his five friends will sit on six fixed seats around a circular table . if juan must sit on the seat closest to the window and jamal must sit next to juan , in how many can juan and his five friends sit ?
Options: ['a ) 20', 'b ) 24', 'c ) 48', 'd ) 72', 'e ) 120']
Student:
|
c
| 2
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example Input: Problem: the length of a rectangular garden is three times its width . if the area of the rectangular garden is 432 square meters , then what is the width of the rectangular garden ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Example Output: e
Example Input: Problem: in 2 triangle , the ratio of the areas is 4 : 3 and that of their heights is 3 : 4 . find the ratio of their bases ?
Options: a ) 10 : 8 , b ) 11 : 8 , c ) 16 : 9 , d ) 17 : 19 , e ) 17 : 10
Example Output: c
Example Input: Problem: the sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq . m . find the perimeter of rectangle .
Options: a ) 121 , b ) 123 , c ) 125 , d ) 122 , e ) 126
Example Output:
|
a
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Q: Problem: in a certain parallelogram the degree measure of one angle exceeds that of the other by 40 what is the degree measure of the smaller angle ?
Options: a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95
A: a
****
Q: Problem: the length of a rectangular landscape is 3 times its breadth . there is a playground in it whose area is 1600 square mtr & which is 1 / 3 rd of the total landscape . what is the length of the landscape ?
Options: a ) 90 , b ) 160 , c ) 150 , d ) 120 , e ) 140
A: c
****
Q: Problem: if circles x and y have the same area and circle x has a circumference of 14 π , half of the radius of circle y is :
Options: ['a ) 16', 'b ) 8', 'c ) 4', 'd ) 3.5', 'e ) 1']
A:
|
d
****
| 4
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example Input: Problem: the diagonals of two squares are in the ratio of 2 : 5 then find the ratio of its areas ?
Options: a ) 2 : 12 , b ) 4 : 25 , c ) 5 : 31 , d ) 2 : 19 , e ) 3 : 17
Example Output: b
Example Input: Problem: the ratio of the volumes of two cubes is 8 : 27 what is the ratio of their total surface areas ?
Options: a ) 2 : 4 , b ) 3 : 6 , c ) 4 : 12 , d ) 4 : 9 , e ) 1 : 3
Example Output: d
Example Input: Problem: a rectangular circuit board is designed to have a width of w inches , a length of l inches , a perimeter of p inches , and an area of c square inches . which of the following equations must be true ?
Options: ['a ) 2 w ^ 2 + pw + 2 c = 0', 'b ) 2 w ^ 2 − pw + 2 c = 0', 'c ) 2 w ^ 2 − pw − 2 c = 0', 'd ) w ^ 2 + pw + c = 0', 'e ) w ^ 2 − pw + 2 c = 0']
Example Output:
|
b
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
[EX Q]: Problem: the water level in a rectangular swimming pool measuring 60 feet by 20 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 4500 , d ) 1200 , e ) 5625
[EX A]: c
[EX Q]: Problem: if the height of a cone is increased by 140 % then its volume is increased by ?
Options: ['a ) 100', 'b ) 140', 'c ) 998', 'd ) 729', 'e ) 2879']
[EX A]: b
[EX Q]: Problem: mr . loyd wants to fence his square shaped land of 60 sqft each side . if a pole is laid every 12 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
[EX A]:
|
a
| 6
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Part 1. Definition
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Part 2. Example
Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Answer: d
Explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Part 3. Exercise
Problem: a rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size . which of the following could be a length of a side of the squares ?
Options: ['a ) a ) 4 inches', 'b ) b ) 6 inches', 'c ) c ) 5 inches', 'd ) d ) 8 inches', 'e ) e ) 10 inches']
Answer:
|
c
| 7
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Given the task definition, example input & output, solve the new input case.
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Output: d
"Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
New input case for you: Problem: if anangletis defined as 1 percent of 1 degree , then how many anglets are there in one half circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 360 , d ) 18,000 , e ) 36,000
Output:
|
d
| 1
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Example solution: d
Example explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Problem: Problem: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 11 , 0 ) , ( 0 , - 3.5 ) , ( - 11 , 0 ) ?
Options: a ) 56 , b ) 77 , c ) 112 , d ) 116 , e ) 120
|
Solution: b
| 5
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: a cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm . the percentage of the wood wasted is :
Options: ['a ) 45 %', 'b ) 56 %', 'c ) 67 %', 'd ) 75 %', 'e ) none of these']
SOLUTION: d
PROBLEM: Problem: find the perimeter of a triangle with sides measuring 7 centimeters , 10 centimeters and 15 centimeters .
Options: ['a ) 10 cm', 'b ) 15 cm', 'c ) 32 cm', 'd ) 35 cm', 'e ) 20 cm']
SOLUTION: c
PROBLEM: Problem: find the perimeter and area of a square of side 19 cm .
Options: a ) 324 , b ) 361 , c ) 400 , d ) 441 , e ) 484
SOLUTION:
|
b
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example input: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Example output: d
Example explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Q: Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 2 : 40 : 70 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 500 , b ) 600 , c ) 650 , d ) 700 , e ) 720
A:
|
d
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Ex Input:
Problem: a lady builds 7 cm length , 18 cm width , and 3 cm height box using 9 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: ['a ) 42', 'b ) 45', 'c ) 47', 'd ) 49', 'e ) 56']
Ex Output:
a
Ex Input:
Problem: a 1.5 by 2 rectangle is inscribed in circle . what is the circumference of the circle ?
Options: ['a ) 2.5 π', 'b ) 3 π', 'c ) 3.5 π', 'd ) 4 π', 'e ) 5.5 π']
Ex Output:
a
Ex Input:
Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 2 : 40 : 70 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 500 , b ) 600 , c ) 650 , d ) 700 , e ) 720
Ex Output:
|
d
| 1
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Ex Input:
Problem: the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 square feet , how much will it cost to paint outside of a cube having 8 feet each side .
Options: a ) rs . 850 , b ) rs . 860 , c ) rs . 876 , d ) rs . 886 , e ) none of these
Ex Output:
c
Ex Input:
Problem: a rectangular cube has sides measuring 3 inches long by 2 inches wide by 0.5 inches high . if the surface area of the rectangle is the same as a cube , what do the sides / walls of the cube measure ? round to the nearest whole number .
Options: ['a ) 4', 'b ) 5', 'c ) 6', 'd ) 7', 'e ) 2']
Ex Output:
e
Ex Input:
Problem: three interviewers , x , y , and z are interviewing 40 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer x admitted 15 applicants , y admitted 17 applicants , and z admitted 20 applicants , at least how many applicants get the admission ?
Options: ['a ) 0', 'b ) 2', 'c ) 6', 'd ) 8', 'e ) 12']
Ex Output:
|
a
| 1
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Input: Consider Input: Problem: abcd is a square . e and f are the midpoints of sides cd and bc , respectively . what is the ratio of the shaded region area to the unshaded region ?
Options: ['a ) 1 : 1', 'b ) 2 : 1', 'c ) 3 : 1', 'd ) 5 : 3', 'e ) 8 : 3']
Output: d
Input: Consider Input: Problem: a rectangular garden is 12 m by 5 m , what is its area ?
Options: ['a ) 12 square meters', 'b ) 5 square meters', 'c ) 44 square meters', 'd ) 60 square meters', 'e ) 22 square meters']
Output: d
Input: Consider Input: Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 50 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 80
|
Output: e
| 2
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Input: Consider Input: Problem: if radius of a circle is reduced by 10 % , then how much % of its area will be reduced ?
Options: ['a ) 10 %', 'b ) 19 %', 'c ) 20 %', 'd ) 36 %', 'e ) 30 %']
Output: b
Input: Consider Input: Problem: if k and w are the dimensions of a rectangle that has area 20 and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: ['a ) two', 'b ) three', 'c ) four', 'd ) five', 'e ) six']
Output: b
Input: Consider Input: Problem: what is the area of a rectangle whose length is twice its width and whose perimeter is equal to that of a square whose area is 1 ?
Options: ['a ) 1 / 9 sq units .', 'b ) 4 / 9 sq units .', 'c ) 8 / 9 sq units .', 'd ) 7 / 9 sq units .', 'e ) 6 / 9 sq units .']
|
Output: c
| 2
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Given the task definition, example input & output, solve the new input case.
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Output: d
"Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
New input case for you: Problem: a larger cube has 216 cubic inch as a volume and in the cube there are 216 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 216 smaller cubes and the surface area of the larger cube , in square inch ?
Options: a ) 54 , b ) 64 , c ) 81 , d ) 1080 , e ) 120
Output:
|
d
| 1
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
One example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution is here: d
Explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Now, solve this: Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 50 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 80
Solution:
|
e
| 6
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Let me give you an example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
The answer to this example can be: d
Here is why: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
OK. solve this:
Problem: the side of a rhombus is 22 m and length of one of its diagonals is 16 m . the area of the rhombus is ?
Options: a ) 327.9 , b ) 325.9 , c ) 347.7 , d ) 357.9 , e ) 327.9
Answer:
|
a
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field in meter square
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
c
Problem: the edge of a cube is 5 a cm . find its surface ?
Options: a ) 150 a 2 cm 2 , b ) 170 a 2 cm 2 , c ) 125 a 2 cm 2 , d ) 175 a 2 cm 2 , e ) 120 a 2 cm 2
a
Problem: triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 25 , what is the measure of side xy ?
Options: a ) 10 , b ) 4 √ 2 , c ) 8 , d ) 8 √ 2 , e ) can not be determined from the information provided
|
a
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
--------
Question: Problem: a wooden cube whose edge length is 8 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 46.3 % , b ) 50.4 % , c ) 54.2 % , d ) 57.8 % , e ) 61.3 %
Answer: d
Question: Problem: the area of a parallelogram is 72 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 6 , b ) 16 , c ) 8 , d ) 36 , e ) none
Answer: a
Question: Problem: the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 33 , what is the perimeter of the garden in feet ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Answer:
|
e
| 7
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example input: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Example output: d
Example explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Q: Problem: the area of a triangle will be when a = 2 m , b = 4 m , c = 6 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 7 , c ) 5 , d ) 6 , e ) 4
A:
|
d
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: a 1.5 by 2 rectangle is inscribed in circle . what is the circumference of the circle ?
Options: ['a ) 2.5 π', 'b ) 3 π', 'c ) 3.5 π', 'd ) 4 π', 'e ) 5.5 π']
a
Problem: a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 3 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 6 , b ) 2 , c ) 4 , d ) 8 , e ) 16
a
Problem: the area of a triangle will be when a = 2 m , b = 4 m , c = 6 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 7 , c ) 5 , d ) 6 , e ) 4
|
d
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Let me give you an example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
The answer to this example can be: d
Here is why: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
OK. solve this:
Problem: the perimeter of an isosceles right triangle is 10 + 10 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 5 , b ) 6 , c ) 7.07 , d ) 8 , e ) 9
Answer:
|
c
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Let me give you an example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
The answer to this example can be: d
Here is why: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
OK. solve this:
Problem: how many times are the hands of a clock at right angle in 2 weeks ?
Options: a ) 616 , b ) 611 , c ) 661 , d ) 116 , e ) 666
Answer:
|
a
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example Input: Problem: the mass of 1 cubic meter of a substance is 700 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 0.8 , b ) 1.42 , c ) 8.0 , d ) 12.5 , e ) 80.0
Example Output: b
Example Input: Problem: the area of a square is 4624 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 11 : 34
Example Output: e
Example Input: Problem: the perimeter of a square is equal to the perimeter of a rectangle of length 15 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: ['a ) 22.78', 'b ) 23.54', 'c ) 24.5', 'd ) 25.55', 'e ) 23.51']
Example Output:
|
a
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example input: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Example output: d
Example explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Q: Problem: a rectangular grass field is 75 m * 55 m , it has a path of 2.8 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1518.8 , b ) s . 1327 , c ) s . 1328 , d ) s . 1397 , e ) s . 1927
A:
|
a
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
One example is below.
Q: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
A: d
Rationale: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Q: Problem: an 11 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: ['a ) 3 / 7', 'b ) 5 / 8', 'c ) 3 / 10', 'd ) 5 / 11', 'e ) 6 / 11']
A:
|
e
| 9
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Let me give you an example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
The answer to this example can be: d
Here is why: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
OK. solve this:
Problem: what is the area of square field whose side of length 5 m ?
Options: a ) 80 sq m , b ) 26 sq m , c ) 25 sq m , d ) 45 sq m , e ) 96 sq m
Answer:
|
c
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: a wooden cube whose edge length is 8 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 46.3 % , b ) 50.4 % , c ) 54.2 % , d ) 57.8 % , e ) 61.3 %
SOLUTION: d
PROBLEM: Problem: the perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
Options: a ) a ) 72 , b ) b ) 45 , c ) c ) 729 , d ) d ) 34 , e ) e ) 35
SOLUTION: b
PROBLEM: Problem: what is the area of square field whose side of length 5 m ?
Options: a ) 80 sq m , b ) 26 sq m , c ) 25 sq m , d ) 45 sq m , e ) 96 sq m
SOLUTION:
|
c
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Example solution: d
Example explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Problem: Problem: the diagonals of a rhombus are 17 cm and 20 cm . find its area ?
Options: a ) 176 , b ) 186 , c ) 150 , d ) 170 , e ) 172
|
Solution: d
| 5
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: the area of a rectangular plot is 24 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: ['a ) 14 metres', 'b ) 5 metres', 'c ) 7.5 metres', 'd ) data inadequate', 'e ) none of these']
a
Problem: find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 9 cm and 6 cm ?
Options: a ) 225 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 187 cm 2
a
Problem: cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 26 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 99
|
e
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
[EX Q]: Problem: a rectangular tiled patio is composed of 126 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 126 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: ['a ) 5', 'b ) 6', 'c ) 9', 'd ) 13', 'e ) 28']
[EX A]: c
[EX Q]: Problem: what will be the area of a semi - circle of 14 metres diameter ?
Options: ['a ) 154 sq metres', 'b ) 77 sq metres', 'c ) 308 sq metres', 'd ) 22 sq metres', 'e ) none of these']
[EX A]: b
[EX Q]: Problem: what is the area of an equilateral triangle whose one side length is 70 ?
Options: a ) 825 √ 3 , b ) 925 √ 3 , c ) 1025 √ 3 , d ) 1125 √ 3 , e ) 1225 √ 3
[EX A]:
|
e
| 6
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Input: Consider Input: Problem: the volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is :
Options: ['a ) 89.8 cm ³', 'b ) 92.5 cm ³', 'c ) 132.8 cm ³', 'd ) 144.5 cm ³', 'e ) none']
Output: a
Input: Consider Input: Problem: if the height of a cone is increased by 140 % then its volume is increased by ?
Options: ['a ) 100', 'b ) 140', 'c ) 998', 'd ) 729', 'e ) 2879']
Output: b
Input: Consider Input: Problem: 34 . the side surface of a cylinder is rolled with a rectangular plate . if the perimeter of the circular base is 9 feet , and the diagonal of the rectangular plate was 15 ft . what is height of the of the cylinder ?
Options: ['a ) 12', 'b ) 15', 'c ) 10', 'd ) 8', 'e ) 14']
|
Output: a
| 2
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: in two triangle , the ratio of the areas is 4 : 3 and that of their heights is 3 : 4 the ratio of their bases is
Options: ['a ) 16 : 9', 'b ) 9 : 16', 'c ) 9 : 12', 'd ) 16 : 12', 'e ) 4 : 12']
a
Problem: what is the smallest positive integer nn such that √ 6,480 ∗ n is a perfect cube ?
Options: a ) 5 , b ) 5 ^ 2 , c ) 30 , d ) 30 ^ 2 , e ) 30 ^ 4
e
Problem: two cubes of their volumes in the ratio 8 : 125 . the ratio of their surface area is :
Options: ['a ) 1.5 : 5', 'b ) 2 : 5', 'c ) 3 : 5', 'd ) 1 : 5', 'e ) 4 : 5']
|
b
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Q: Problem: if each edge of a cube is doubled , then its volume :
Options: ['a ) becomes 8 times', 'b ) becomes 9 times', 'c ) is double', 'd ) becomes 6 times', 'e ) none']
A: a
****
Q: Problem: the parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 77.14 cm , b ) 25.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 23.57 cm
A: b
****
Q: Problem: the perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm . find its area ?
Options: a ) 290 , b ) 240 , c ) 2870 , d ) 289 , e ) 292
A:
|
b
****
| 4
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: the water level in a rectangular swimming pool measuring 50 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 1200 , e ) 4687.5
e
Problem: the length of the diagonal of a square is 12 cm . find its area and perimeter .
Options: ['a ) 31.84 cm', 'b ) 33.84 cm', 'c ) 35.84 cm', 'd ) 38.84 cm', 'e ) 38.92 cm']
b
Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 30 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 69 , d ) 125 , e ) 250
|
c
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example Input: Problem: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 14 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276 , b ) 1680 , c ) 2832 , d ) 1299 , e ) 1236
Example Output: b
Example Input: Problem: the length of rectangle is thrice its breadth and its perimeter is 72 m , find the area of the rectangle ?
Options: a ) 432 , b ) 212 , c ) 243 , d ) 992 , e ) 212
Example Output: c
Example Input: Problem: what will be the cost of building a fence around a square plot with area equal to 81 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 2287 , c ) 2977 , d ) 2088 , e ) 1298
Example Output:
|
d
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example input: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Example output: d
Example explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Q: Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 363 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 11 , b ) 17 , c ) 18 , d ) 101 , e ) 1322
A:
|
a
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Input: Consider Input: Problem: the difference of the areas of two squares drawn on two line segments in 32 sq . cm . find the length of the greater line segment if one is longer than the other by 2 cm
Options: ['a ) 9 cm', 'b ) 8 cm', 'c ) 7 cm', 'd ) 6 cm', 'e ) 5 cm']
Output: c
Input: Consider Input: Problem: the ratio of radius of a circle and the side of a square is 2 : 9 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 7 , c ) 8 : 77 , d ) 4 : 81 , e ) none
Output: d
Input: Consider Input: Problem: the number 90 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
|
Output: b
| 2
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Detailed Instructions: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
See one example below:
Problem: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution: d
Explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Problem: Problem: the number 90 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Solution:
|
b
| 4
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Q: Problem: a certain cube floating in a bucket of water has between 70 and 85 percent of its volume below the surface of the water . if between 8 and 20 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9
A: a
****
Q: Problem: an artist wishes to paint a circular region on a square poster that is 3.4 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: ['a ) 1 / pi', 'b ) sqrt ( 2 / pi )', 'c ) 1', 'd ) 2 / sqrt ( pi )', 'e ) sqrt ( 5.78 / pi )']
A: e
****
Q: Problem: when a certain perfect square is increased by 148 , the result is another perfect square . what is the value of the original perfect square ?
Options: ['a ) 1296', 'b ) 1369', 'c ) 1681', 'd ) 1764', 'e ) 2500']
A:
|
a
****
| 4
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Let me give you an example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
The answer to this example can be: d
Here is why: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
OK. solve this:
Problem: in a rectangular coordinate system , what is the area of a triangle whose vertices have the coordinates ( - 1 , 0 ) , ( 7 , 4 ) , and ( 7 , - 4 ) ?
Options: ['a ) 29', 'b ) 30', 'c ) 31', 'd ) 32', 'e ) 33']
Answer:
|
d
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 8 inches on a side and costs $ 10 , and a large pizza that measures 12 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 5 square inches , b ) 10 square inches , c ) 16 square inches , d ) 25 square inches , e ) 350 square inches
c
Problem: rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 4 / 5 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 5 / 4 , b ) 25 / 16 , c ) 4 / 5 , d ) 16 / 25 , e ) 16 / 5
d
Problem: the largest four - digit number which is a perfect cube , is
Options: ['a ) 8000', 'b ) 9261', 'c ) 9999', 'd ) none of these', 'e ) can not be determined']
|
b
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Example solution: d
Example explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Problem: Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 128 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
|
Solution: a
| 5
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: find the perimeter and area of a square of side 19 cm .
Options: a ) 324 , b ) 361 , c ) 400 , d ) 441 , e ) 484
b
Problem: a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 200 square feet , what is the total length of the fence , in feet ?
Options: ['a ) 10', 'b ) 20', 'c ) 30', 'd ) 40', 'e ) 80']
d
Problem: if the length of the sides of two cubes are in the ratio 6 : 1 , what is the ratio of their total surface area ?
Options: a ) 6 : 1 , b ) 12 : 1 , c ) 24 : 1 , d ) 36 : 1 , e ) 72 : 1
|
d
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Q: Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 4 : 20 : 60 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 1200 , b ) 1250 , c ) 1300 , d ) 1400 , e ) 1450
A: a
****
Q: Problem: what will be the cost of building a fence around a square plot with area equal to 81 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 2287 , c ) 2977 , d ) 2088 , e ) 1298
A: d
****
Q: Problem: the size of a flat - screen tablet is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 6 - inch flat - screen tablet than a square 5 - inch flat - screen tablet ?
Options: ['a ) 5.0', 'b ) 6.0', 'c ) 6.8', 'd ) 5.8', 'e ) 5.5']
A:
|
e
****
| 4
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Input: Consider Input: Problem: what is the perimeter of a square field whose diagonal is 4 √ 2 ?
Options: a ) 16 m , b ) 32 m , c ) 27 m , d ) 26 m , e ) 76 m
Output: a
Input: Consider Input: Problem: if a rectangular room measures 9 meters by 5 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 24,000 , b ) 240,000 , c ) 18 , 000,000 , d ) 24 , 000,000 , e ) 240 , 000,000
Output: c
Input: Consider Input: Problem: the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle . the shorter side of the triangle is 7 centimeters less than the longer side . find the length of the hypotenuse .
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
|
Output: a
| 2
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Given the task definition, example input & output, solve the new input case.
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Output: d
"Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
New input case for you: Problem: a circular wire of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6 : 5 . the smaller side of the rectangle is :
Options: ['a ) 30 cm', 'b ) 60 cm', 'c ) 72 cm', 'd ) 132 cm .', 'e ) 142 cm .']
Output:
|
b
| 1
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
[EX Q]: Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of three cubic feet . if a large block has twice the width , twice the depth , and three times the length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: ['a ) 18', 'b ) 6', 'c ) 27', 'd ) 48', 'e ) 36']
[EX A]: e
[EX Q]: Problem: the surface of a cube is 96 sq cm . find its volume ?
Options: ['a ) 8 cc', 'b ) 9 cc', 'c ) 2 cc', 'd ) 4 cc', 'e ) 64 cc']
[EX A]: e
[EX Q]: Problem: in a rectangular coordinate system , what is the area of a triangle whose vertices have the coordinates ( - 1 , 0 ) , ( 7 , 4 ) , and ( 7 , - 4 ) ?
Options: ['a ) 29', 'b ) 30', 'c ) 31', 'd ) 32', 'e ) 33']
[EX A]:
|
d
| 6
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
You will be given a definition of a task first, then an example. Follow the example to solve a new instance of the task.
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution: d
Why? "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
New input: Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 50 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 100 , d ) 125 , e ) 250
Solution:
|
d
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example Input: Problem: a circle is inscribed in a triangle of side 6 cm . and a square is inscribed in the circle . what is the area of square ?
Options: ['a ) 4 cm ^ 2', 'b ) 6 cm ^ 2', 'c ) 5 cm ^ 2', 'd ) 7 cm ^ 2', 'e ) 8 cm ^ 2']
Example Output: b
Example Input: Problem: a circular ground whose diameter is 35 metres , has a 1.4 metre - broad garden around inside of it . what is the area of the garden in square metres ?
Options: a ) 301.5 , b ) 484.12 , c ) 401.84 , d ) 301.0 , e ) 301.84
Example Output: e
Example Input: Problem: a cube of edge 7 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 25 , b ) 1 : 49 , c ) 1 : 52 , d ) 1 : 522 , e ) none
Example Output:
|
b
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
instruction:
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
question:
Problem: how many odd numbers between 10 and 1,200 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
answer:
e
question:
Problem: how many boxes do you need if you have to pack 240 pairs ornamental bangles into boxes that each hold 2 dozens of bangles ?
Options: a ) 40 , b ) 35 , c ) 20 , d ) 25 , e ) 30
answer:
c
question:
Problem: if the sum of a number and its square is 342 , what is the number ?
Options: a ) 16 , b ) 77 , c ) 25 , d ) 87 , e ) 18
answer:
|
e
| 9
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Teacher: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Teacher: Now, understand the problem? If you are still confused, see the following example:
Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution: d
Reason: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Now, solve this instance: Problem: you have 59 cubic blocks . what is the minimum number that needs to be taken away in order to construct a solid cube with none left over ?
Options: ['a ) 27', 'b ) 43', 'c ) 11', 'd ) 32', 'e ) 45']
Student:
|
d
| 2
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Q: Problem: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 40 cm , find the sum of the perimeters of all the triangles .
Options: ['a ) 180 cm', 'b ) 220 cm', 'c ) 240 cm', 'd ) 270 cm', 'e ) 300 cm']
A: c
****
Q: Problem: if g is the smallest positive integer such that 3150 multiplied by g is the square of an integer , then g must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
A: e
****
Q: Problem: how many books each of volume 100 meter cube can be packed into a crate of volume 3000 meter cube ?
Options: a ) 50 , b ) can not be determined , c ) 150 , d ) 300 , e ) 350
A:
|
b
****
| 4
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Example solution: d
Example explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Problem: Problem: if the sides of a rectangle are increased by 35 % , what is the percentage increase in the area ?
Options: a ) 38.25 % , b ) 40.25 % , c ) 82.25 % , d ) 50 % , e ) 65 %
|
Solution: c
| 5
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Part 1. Definition
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Part 2. Example
Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Answer: d
Explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Part 3. Exercise
Problem: the length of a rectangle is three times of its width . if the length of the diagonal is 8 √ 10 then find the perimeter of the rectangle .
Options: ['a ) 77 cm', 'b ) 88 cm', 'c ) 64 cm', 'd ) 11 cm', 'e ) 18 cm']
Answer:
|
c
| 7
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: if the ratio of the areas of two squares is 225 : 256 , then the ratio of their perimeters is :
Options: ['a ) 15 : 12', 'b ) 15 : 14', 'c ) 15 : 16', 'd ) 15 : 22', 'e ) none of these']
SOLUTION: c
PROBLEM: Problem: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 6 inches tall . carmen places her sculpture on a base that is 12 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.83 feet
SOLUTION: e
PROBLEM: Problem: the diagonals of a rhombus are 12 cm and 15 cm . find its area ?
Options: a ) 30 , b ) 45 , c ) 90 , d ) 120 , e ) 180
SOLUTION:
|
c
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.40 per metre .
Options: a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 2888
d
Problem: the ratio of radius of a circle and the side of a square is 2 : 3 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 9 , c ) 8 : 77 , d ) 4 : 121 , e ) none
b
Problem: if y is the smallest positive integer such that 1260 multiplied by y is the square of an integer , then y must be
Options: a ) 25 , b ) 35 , c ) 60 , d ) 75 , e ) 140
|
b
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction d of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
a
Problem: the length of the side of a square is represented by x + 2 . the length of the side of an equilateral triangle is 2 x . if the square and the equilateral triangle have equal perimeter , then the value of x is ?
Options: a ) 5 , b ) 7 , c ) 4 , d ) 8 , e ) 6
c
Problem: george ' s car calls for 8 ounces of oil for each cylinder used . his car ' s engine has 6 cylinders . if 16 ounces of oil has already been put into the engine used , then how many additional ounces of oil are needed ?
Options: ['a ) 16', 'b ) 48', 'c ) 64', 'd ) 32', 'e ) 8']
|
d
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
--------
Question: Problem: a 10 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 1 / 5 , d ) 2 / 5 , e ) 3 / 5
Answer: d
Question: Problem: the perimeter of a triangle is 42 cm and the inradius of the triangle is 5.0 cm . what is the area of the triangle ?
Options: a ) 128 cm 2 , b ) 36.0 cm 2 , c ) 105 cm 2 , d ) 25 cm 2 , e ) 135 cm 2
Answer: c
Question: Problem: the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is ?
Options: a ) 44 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Answer:
|
a
| 7
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Teacher: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Teacher: Now, understand the problem? If you are still confused, see the following example:
Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution: d
Reason: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Now, solve this instance: Problem: the parameter of a square is equal to the perimeter of a rectangle of length 4 cm and breadth 2 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 4.51 , b ) 4.71 , c ) 4.32 , d ) 4.21 , e ) 4.68
Student:
|
b
| 2
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
[Q]: Problem: the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 5 per metre approximately
Options: a ) 4457 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 7429
[A]: e
[Q]: Problem: how many odd numbers between 10 and 1,200 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
[A]: e
[Q]: Problem: a cube has four of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
Options: a ) 1 : 4 , b ) 1 : 3 , c ) 1 : 2 , d ) 2 : 5 , e ) 2 : 11
[A]:
|
c
| 5
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Q: Problem: two identical circles intersect such that their centers and the points at which they intersect form a square of side 4 cm . what is the area of the region where the two circles intersect ?
Options: ['a ) 16 - 4 pi', 'b ) 4 - pi', 'c ) 2 pi - 4', 'd ) 8 pi - 16', 'e ) pi ^ 2 - 4']
A: d
****
Q: Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm .
Options: a ) 370 cm 2 , b ) 365 cm 2 , c ) 380 cm 2 , d ) 384 cm 2 , e ) 394 cm 2
A: d
****
Q: Problem: two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 49 . find the ratio of their corresponding heights .
Options: a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 4 / 7 , e ) 2 / 3
A:
|
d
****
| 4
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
[Q]: Problem: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 14 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276 , b ) 1680 , c ) 2832 , d ) 1299 , e ) 1236
[A]: b
[Q]: Problem: a voltage will influence current only if the circuit is :
Options: ['a ) 2', 'b ) 7', 'c ) 6', 'd ) 889', 'e ) 1']
[A]: b
[Q]: Problem: the perimeter of a square is 48 m . find the area of the square .
Options: ['a ) 161 m â ² .', 'b ) 144 m â ² .', 'c ) 166 m â ² .', 'd ) 169 m â ² .', 'e ) 273 m â ² .']
[A]:
|
b
| 5
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 5 per sq m ?
Options: a ) 675 , rs . 3375 , b ) 575 , rs . 1350 , c ) 1350 , rs . 675 , d ) 1450 , rs . 775 , e ) 1550 , rs . 875
SOLUTION: a
PROBLEM: Problem: what is the smallest positive integer nn such that √ 6,480 ∗ n is a perfect cube ?
Options: a ) 5 , b ) 5 ^ 2 , c ) 30 , d ) 30 ^ 2 , e ) 30 ^ 4
SOLUTION: e
PROBLEM: Problem: if paint costs $ 3.20 per quart , and a quart covers 1200 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?
Options: ['a ) $ 1.60', 'b ) $ 16.00', 'c ) $ 96.00', 'd ) $ 108.00', 'e ) $ 196.00']
SOLUTION:
|
a
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Ex Input:
Problem: the largest four - digit number which is a perfect cube , is
Options: ['a ) 8000', 'b ) 9261', 'c ) 9999', 'd ) none of these', 'e ) can not be determined']
Ex Output:
b
Ex Input:
Problem: the inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters . a cylindrical drum is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces . of all such drums that could be used , what is the volume , in cubic meters , of the one that has maximum volume ?
Options: ['a ) 20 π', 'b ) 24 π', 'c ) 25 π', 'd ) 96 π', 'e ) 100 π']
Ex Output:
c
Ex Input:
Problem: a wooden cube whose edge length is 6 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: ['a ) 54.9 %', 'b ) 58.7 %', 'c ) 62.5 %', 'd ) 66.3 %', 'e ) 70.4 %']
Ex Output:
|
e
| 1
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Given the task definition, example input & output, solve the new input case.
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Output: d
"Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
New input case for you: Problem: the length and breadth of a rectangle is increased by 10 % and 30 % respectively . what is the increase in the area ?
Options: a ) 43.0 , b ) 44.0 , c ) 43.5 , d ) 45.0 , e ) 42.0
Output:
|
a
| 1
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
One example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution is here: d
Explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Now, solve this: Problem: the circumferences of two circles are 528 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 29963 sq m , b ) 28937 sq m , c ) 43162 sq m , d ) 27688 sq m , e ) 17248 sq m
Solution:
|
e
| 6
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Detailed Instructions: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
See one example below:
Problem: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution: d
Explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Problem: Problem: a wooden cube whose edge length is 6 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: ['a ) 54.9 %', 'b ) 58.7 %', 'c ) 62.5 %', 'd ) 66.3 %', 'e ) 70.4 %']
Solution:
|
e
| 4
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Given the task definition, example input & output, solve the new input case.
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Output: d
"Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
New input case for you: Problem: in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 3 , - 1 ) , ( 3 , 8 ) , ( 14 , 2 ) , ( 14 , - 5 ) ?
Options: a ) 76 , b ) 88 , c ) 100 , d ) 112 , e ) 124
Output:
|
b
| 1
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Q: Problem: a certain cube floating in a bucket of water has between 80 and 90 percent of its volume below the surface of the water . if between 6 and 13 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9
A: a
****
Q: Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 27 feet tall and 3 feet in circumference ?
Options: a ) 10 feet , b ) 12 feet , c ) 27 feet , d ) 15 feet , e ) 18 feet
A: c
****
Q: Problem: if the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm , a square with the same area as the original rectangle would result . find the perimeter of the original rectangle ?
Options: a ) 76 , b ) 27 , c ) 19 , d ) 50 , e ) 11
A:
|
d
****
| 4
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
One example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution is here: d
Explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Now, solve this: Problem: in an electric circuit , two resistors with resistances 8 ohms and 9 ohms are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is r value ?
Options: ['a ) 17', 'b ) 45 / 78', 'c ) 72 / 17', 'd ) 17 / 72', 'e ) 72']
Solution:
|
c
| 6
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Given the task definition, example input & output, solve the new input case.
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Output: d
"Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
New input case for you: Problem: the curved surface area of a cylindrical pillar is 264 sq . m and its volume is 924 cub . m . find the ratio of its diameter to its height
Options: ['a ) 7 : 9', 'b ) 7 : 3', 'c ) 7 : 7', 'd ) 7 : 6', 'e ) 7 : 1']
Output:
|
b
| 1
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: the diagonals of a rhombus are 10 cm and 12 cm . find its area ?
Options: a ) 158 , b ) 60 , c ) 150 , d ) 123 , e ) 117
SOLUTION: b
PROBLEM: Problem: the measurement of a rectangular box with lid is 25 cmx 4 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 11.12 , b ) 10.11 , c ) 72 , d ) 10.66 , e ) 9.2
SOLUTION: d
PROBLEM: Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 4 inches wide on each side , the total area would have been ( m + 108 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 34 , b ) 36 , c ) 16 , d ) 40 , e ) 42
SOLUTION:
|
c
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
One example is below.
Q: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
A: d
Rationale: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Q: Problem: if the radius of a circle is decreased 10 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 19 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease
A:
|
b
| 9
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 180 m , its area is ?
Options: a ) 90 , b ) 882 , c ) 277 , d ) 261 , e ) 281
SOLUTION: a
PROBLEM: Problem: the area of a square is equal to five times the area of a rectangle of dimensions 50 cm * 10 cm . what is the perimeter of the square ?
Options: a ) 289 cm , b ) 200 cm , c ) 829 cm , d ) 288 cm , e ) 289 cm
SOLUTION: b
PROBLEM: Problem: the volume of a cube is 1728 cc . find its surface .
Options: a ) 864 , b ) 556 , c ) 255 , d ) 287 , e ) 267
SOLUTION:
|
a
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
One example is below.
Q: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
A: d
Rationale: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Q: Problem: a cube of edge 15 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 14 cm , find the rise in water level ?
Options: a ) 6 cm , b ) 12.05 cm , c ) 11.25 cm , d ) 15.12 cm , e ) 20.62 cm
A:
|
b
| 9
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
--------
Question: Problem: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 6 inches tall . carmen places her sculpture on a base that is 12 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.83 feet
Answer: e
Question: Problem: the area of the house of a hall is 20 m 2 that of a longer wall 10 m 2 and of the shorter wall 8 m 2 , find the edge of the new cube ?
Options: ['a ) 45 m 3', 'b ) 40 m 3', 'c ) 60 m 3', 'd ) 600 m 3', 'e ) 300 m 3']
Answer: b
Question: Problem: the diameter of a cylindrical tin is 8 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 33 , b ) 45 , c ) 66 , d ) 80 , e ) 21
Answer:
|
d
| 7
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
One example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution is here: d
Explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Now, solve this: Problem: the diameter of a cylindrical tin is 8 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 33 , b ) 45 , c ) 66 , d ) 80 , e ) 21
Solution:
|
d
| 6
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: the total surface area of a solid hemisphere of diameter 14 cm , is :
Options: ['a ) 462 cm ²', 'b ) 530 cm ²', 'c ) 1345 cm ²', 'd ) 1788 cm ²', 'e ) none']
a
Problem: the area of a rectangular plot is 18 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 10 metres , b ) 8 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these
b
Problem: the area of sector of a circle whose radius is 18 metro and whose angle at the center is 42 â ° is ?
Options: a ) 52.6 , b ) 52.9 , c ) 52.8 , d ) 118.8 , e ) 52.2
|
d
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
You will be given a definition of a task first, then an example. Follow the example to solve a new instance of the task.
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution: d
Why? "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
New input: Problem: the diagonal of the floor of a rectangular closet is 7 feet . the shorter side of the closet is 4 feet . what is the area of the closet in square feet ?
Options: ['a ) 20 sq . ft', 'b ) 27 sq . ft', 'c ) 37 sq . ft', 'd ) 47 sq . ft', 'e ) 57 sq . ft']
Solution:
|
b
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Detailed Instructions: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
See one example below:
Problem: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution: d
Explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Problem: Problem: the radius of a cylinder is 8 m , height 13 m . the volume of the cylinder is :
Options: a ) 2200 , b ) 2614.9 , c ) 3300 , d ) 1100 , e ) 4400
Solution:
|
b
| 4
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
[Q]: Problem: we need to carve out 125 identical cubes from a cube . what is the minimum number of cuts needed ?
Options: ['a ) 8', 'b ) 9', 'c ) 10', 'd ) 11', 'e ) 12']
[A]: e
[Q]: Problem: a metallic sheet is of rectangular shape with dimensions 50 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :
Options: a ) 5440 , b ) 5120 , c ) 6420 , d ) 7500 , e ) 8960
[A]: a
[Q]: Problem: find the smallest number which should be multiplied with 13225 to make it a perfect square .
Options: a ) 25 , b ) 5 , c ) 1 , d ) 23 , e ) 6
[A]:
|
c
| 5
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
One example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution is here: d
Explanation: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Now, solve this: Problem: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 199 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 10,000 , b ) 11,025 , c ) 14,400 , d ) 12,696 , e ) can not be determined
Solution:
|
a
| 6
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example Input: Problem: the least perfect square , which is divisible by each of 21 , 36 and 66 is
Options: a ) 213414 , b ) 213424 , c ) 213434 , d ) 213444 , e ) none of these
Example Output: d
Example Input: Problem: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 5 , 1 ) , ( 1 , 1 ) , ( 1 , - 4 ) and ( - 5 , - 4 ) ?
Options: ['a ) 20', 'b ) 30', 'c ) 40', 'd ) 55', 'e ) 48']
Example Output: b
Example Input: Problem: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 199 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 10,000 , b ) 11,025 , c ) 14,400 , d ) 12,696 , e ) can not be determined
Example Output:
|
a
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example Input: Problem: the diameter of a cylindrical tin is 14 cm and height is 2 cm . find the volume of the cylinder ?
Options: a ) 33 , b ) 45 , c ) 66 , d ) 77 , e ) 98
Example Output: e
Example Input: Problem: 36 people { a 1 , a 2 , . . . , a 36 } meet and shake hands in a circular fashion . in other words , there are totally 36 handshakes involving the pairs , { a 1 , a 2 } , { a 2 , a 3 } , . . . , { a 35 , a 36 } , { a 36 , a 1 } . then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
Options: ['a ) 11', 'b ) 12', 'c ) 13', 'd ) 15', 'e ) 18']
Example Output: b
Example Input: Problem: obra drove 200 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 % , b ) 12.5 % , c ) 41.66 % , d ) 25 % , e ) 33.3 %
Example Output:
|
c
| 3
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
One example is below.
Q: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
A: d
Rationale: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Q: Problem: triangle atriangle b are similar triangles with areas 2023 units square and 1792 units square respectively . the ratio of there corresponding height would be
Options: a ) 9 : 10 , b ) 17 : 16 , c ) 23 : 27 , d ) 13 : 17 , e ) 15 : 23
A:
|
b
| 9
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
You will be given a definition of a task first, then an example. Follow the example to solve a new instance of the task.
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution: d
Why? "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
New input: Problem: if d is the smallest positive integer such that 3,150 multiplied by d is the square of an integer , then d must be
Options: ['a ) 2', 'b ) 5', 'c ) 6', 'd ) 7', 'e ) 14']
Solution:
|
e
| 0
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Given the task definition, example input & output, solve the new input case.
In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Example: Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Output: d
"Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
New input case for you: Problem: the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 34 - inch flat - screen television than a square 27 - inch flat - screen television ?
Options: a ) 106.75 , b ) 213.5 , c ) 427 , d ) 729 , e ) 1,156
Output:
|
c
| 1
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: a volume of 10936 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: ['a ) 2812', 'b ) 8231', 'c ) 2734', 'd ) 4222', 'e ) 4254']
SOLUTION: c
PROBLEM: Problem: a number when divided by 6 leaves a remainder 3 . when the square of the same number is divided by 6 , the remainder is
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
SOLUTION: d
PROBLEM: Problem: if d is the smallest positive integer such that 3,150 multiplied by d is the square of an integer , then d must be
Options: ['a ) 2', 'b ) 5', 'c ) 6', 'd ) 7', 'e ) 14']
SOLUTION:
|
e
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
Teacher: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Teacher: Now, understand the problem? If you are still confused, see the following example:
Problem: if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?
Options: a ) 70 , b ) 79 , c ) 85 , d ) 96 , e ) 92
Solution: d
Reason: "Based on the pythagorean theorem, the triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm. area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"
Now, solve this instance: Problem: which is the smallest no which divides 2880 and gives a perfect square ?
Options: ['a ) 4', 'b ) 9', 'c ) 3', 'd ) 5', 'e ) 7']
Student:
|
d
| 2
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
TASK DEFINITION: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
PROBLEM: Problem: if the area of a circle is 49 pi square feet , find its circumference .
Options: a ) 14 pi feet , b ) 28 pi feet , c ) 38 pi feet , d ) 48 pi feet , e ) 58 pi feet
SOLUTION: a
PROBLEM: Problem: what is the area of a square field whose sides have a length of 16 meters ?
Options: a ) 225 sq m , b ) 286 sq m , c ) 298 sq m , d ) 256 sq m , e ) 231 sq m
SOLUTION: d
PROBLEM: Problem: one side of a rectangular field is 13 m and one of its diagonal is 17 m . find the area of the field .
Options: a ) 100 , b ) 141.7 , c ) 150 , d ) 180 , e ) none
SOLUTION:
|
b
| 8
|
NIv2
|
task1423_mathqa_geometry
|
fs_opt
|
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