id stringlengths 25 25 | question stringlengths 45 1.01k | chain stringlengths 75 4.11k | result stringclasses 5 values | result_float float64 -4,212 100B | question_without_options stringlengths 6 962 | options dict | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | rationale stringlengths 1 2.74k | category stringclasses 6 values |
|---|---|---|---|---|---|---|---|---|---|---|
math_qa__b6khjBkX4mAMtC43 | Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.120. How much was lent at 5%? Pick.
A) 2333 B) 2777 C) 3000 D) 1000 E) 2871 | <gadget id="calculator">6 * 2_500</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 / 100</gadget>
<output>150</output>
<gadget id="calculator">120 - 150</gadget>
<output>-30</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(1/20) - (3/50)</gadget>
<output>-1/100 = around -0.01</output>
<gadget id="calculator">(-30) / (-1/100)</gadget>
<output>3_000</output>
<result>C</result> | C | 3,000 | Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.120. How much was lent at 5%? | {
"A": "2333",
"B": "2777",
"C": "3000",
"D": "1000",
"E": "2871"
} | divide(subtract(120, divide(multiply(6, 2500), const_100)), subtract(divide(5, const_100), divide(6, const_100))) | divide(n1,const_100)|divide(n2,const_100)|multiply(n0,n2)|divide(#2,const_100)|subtract(#0,#1)|subtract(n3,#3)|divide(#5,#4) | ( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 120 x = 3000 answer : c | gain |
math_qa__gURyL6siVkTQZptO | The average age of a class of 23 students is 22 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher? Choose the correct answer:
A) 40 B) 41 C) 46 D) 42 E) 49 | <gadget id="calculator">23 + 1</gadget>
<output>24</output>
<gadget id="calculator">22 + 1</gadget>
<output>23</output>
<gadget id="calculator">24 * 23</gadget>
<output>552</output>
<gadget id="calculator">23 * 22</gadget>
<output>506</output>
<gadget id="calculator">552 - 506</gadget>
<output>46</output>
<result>C</result> | C | 46 | The average age of a class of 23 students is 22 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher? | {
"A": "40",
"B": "41",
"C": "46",
"D": "42",
"E": "49"
} | subtract(multiply(add(23, 1), add(22, 1)), multiply(23, 22)) | add(n0,n2)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | "total age of all students = 23 ã — 22 total age of all students + age of the teacher = 24 ã — 23 age of the teacher = 24 ã — 23 â ˆ ’ 23 ã — 22 = 23 ( 24 â ˆ ’ 22 ) = 23 ã — 2 = 46 answer is c ." | general |
math_qa__eyuJeBt6KkEkW6Is | The length of a rectangle hall is 5 m more than its breadth. The area of the hall is 750 m2. The length of the hall is : Choose the correct choice from the following.
A) 15 m B) 22.5 m C) 25 m D) 30 m E) none of these | <gadget id="calculator">750 / 5</gadget>
<output>150</output>
<gadget id="calculator">150 / 5</gadget>
<output>30</output>
<result>D</result> | D | 30 | The length of a rectangle hall is 5 m more than its breadth. The area of the hall is 750 m2. The length of the hall is : | {
"A": "15 m",
"B": "22.5 m",
"C": "25 m",
"D": "30 m",
"E": "none of these"
} | divide(divide(750, 5), 5) | divide(n1,n0)|divide(#0,n0) | solution let breadth = x metres . then , length = ( x + 5 ) metres . then x ( x + 5 ) = 750 ⇔ x 2 + 5 x − 750 = 0 ⇔ ( x + 30 ) ( x + 25 ) = 0 ⇔ x = 25 . ∴ length = ( x + 5 ) = 30 m . answer d | geometry |
math_qa__3UYi92AELndIXiu9 | 65 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? Choose the correct option:
A) 64 B) 128 C) 151 D) 216 E) 256 | <gadget id="calculator">65 ** (1/3)</gadget>
<output>65**(1/3) = around 4.020726</output>
<gadget id="calculator">(65**(1/3)) + 2</gadget>
<output>2 + 65**(1/3) = around 6.020726</output>
<gadget id="calculator">(2 + 65**(1/3)) ** 3</gadget>
<output>(2 + 65**(1/3))**3 = around 218.246123</output>
<gadget id="calculator">((2 + 65**(1/3))**3) - 65</gadget>
<output>-65 + (2 + 65**(1/3))**3 = around 153.246123</output>
<result>C</result> | C | 151 | 65 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? | {
"A": "64",
"B": "128",
"C": "151",
"D": "216",
"E": "256"
} | subtract(volume_cube(add(cube_edge_by_volume(65), const_2)), 65) | cube_edge_by_volume(n0)|add(#0,const_2)|volume_cube(#1)|subtract(#2,n0) | 65 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 65 = 151 hence , c is the answer . | geometry |
math_qa__iyaCALqix61NxACZ | A student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there? Choose one.
A) 7 B) 8 C) 9 D) 10 E) 11 | <gadget id="calculator">4 * 90</gadget>
<output>360</output>
<gadget id="calculator">-1</gadget>
<output>-1</output>
<gadget id="calculator">(-1) ** 2</gadget>
<output>1</output>
<gadget id="calculator">360 + 1</gadget>
<output>361</output>
<gadget id="calculator">361 ** (1/2)</gadget>
<output>19</output>
<gadget id="calculator">1 + 19</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>D</result> | D | 10 | A student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10",
"E": "11"
} | divide(add(const_1, sqrt(add(multiply(const_4, 90), power(negate(const_1), const_2)))), const_2) | multiply(n0,const_4)|negate(const_1)|power(#1,const_2)|add(#0,#2)|sqrt(#3)|add(#4,const_1)|divide(#5,const_2)| | "let the number of people to choose from = n no of people to be chosen = 2 the number of ways 2 people can be chosen from n people = nc 2 now , the two people selected can be arranged in 2 ! ways hence nc 2 * 2 ! = 90 which gives n = 10 answer : d" | other |
math_qa__r2QsKyEImDzlK1nQ | In the coordinate plane, Line A has a slope of -1 and an x-intercept of 2. Line B has a slope of 5 and a y-intercept of -10. If the two lines intersect at the point (a,b), what is the sum a+b? Pick: A) 0 B) 1 C) 2 D) 3 E) 4 | <gadget id="calculator">10 - 5</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<result>C</result> | C | 2 | In the coordinate plane, Line A has a slope of -1 and an x-intercept of 2. Line B has a slope of 5 and a y-intercept of -10. If the two lines intersect at the point (a,b), what is the sum a+b? | {
"A": "0",
"B": "1",
"C": "2",
"D": "3",
"E": "4"
} | divide(subtract(subtract(10, 5), 1), 2) | subtract(n3,n2)|subtract(#0,n0)|divide(#1,n1) | the equation of line a is y = - x + 2 the equation of line b is y = 5 x - 10 5 x - 10 = - x + 2 x = 2 y = 0 the point of intersection is ( 2,0 ) and then a + b = 2 . the answer is c . | general |
math_qa__QnEvpVAJAoHEfpTa | A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 20% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research? Choices.
A) 8 ° B) 10 ° C) 18 ° D) 36 ° E) 52 ° | <gadget id="calculator">14 + 24</gadget>
<output>38</output>
<gadget id="calculator">38 + 20</gadget>
<output>58</output>
<gadget id="calculator">58 + 29</gadget>
<output>87</output>
<gadget id="calculator">87 + 8</gadget>
<output>95</output>
<gadget id="calculator">100 - 95</gadget>
<output>5</output>
<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">5 * 360</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 / 100</gadget>
<output>18</output>
<result>C</result> | C | 18 | A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 20% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research? | {
"A": "8 °",
"B": "10 °",
"C": "18 °",
"D": "36 °",
"E": "52 °"
} | divide(multiply(subtract(const_100, add(add(add(add(14, 24), 20), 29), 8)), divide(const_3600, const_10)), const_100) | add(n0,n1)|divide(const_3600,const_10)|add(n2,#0)|add(n3,#2)|add(n4,#3)|subtract(const_100,#4)|multiply(#1,#5)|divide(#6,const_100)| | "14 % microphotonics ; 24 % home electronics ; 20 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 20 + 29 + 8 ) = 5 % basic astrophysics . 5 % of 360 ° is 18 ° . answer : c ." | gain |
math_qa__HJgY0HCDZ3dN5HPI | By how much does the larger root of the equation 2q^2+5q = 12 exceed the smaller root? Select:
A) 5 / 2 B) 10 / 3 C) 7 / 2 D) 14 / 3 E) 11 / 2 | <gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">2 * 12</gadget>
<output>24</output>
<gadget id="calculator">24 * 4</gadget>
<output>96</output>
<gadget id="calculator">25 + 96</gadget>
<output>121</output>
<gadget id="calculator">121 ** (1/2)</gadget>
<output>11</output>
<gadget id="calculator">5 + 11</gadget>
<output>16</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<gadget id="calculator">5 - 11</gadget>
<output>-6</output>
<gadget id="calculator">(-6) / 4</gadget>
<output>-3/2 = around -1.5</output>
<gadget id="calculator">4 - (-3/2)</gadget>
<output>11/2 = around 5.5</output>
<result>E</result> | E | 5.5 | By how much does the larger root of the equation 2q^2+5q = 12 exceed the smaller root? | {
"A": "5 / 2",
"B": "10 / 3",
"C": "7 / 2",
"D": "14 / 3",
"E": "11 / 2"
} | subtract(divide(add(5, sqrt(add(power(5, 2), multiply(multiply(2, 12), const_4)))), multiply(2, 2)), divide(subtract(5, sqrt(add(power(5, 2), multiply(multiply(2, 12), const_4)))), multiply(2, 2))) | multiply(n0,n3)|multiply(n0,n0)|power(n2,n0)|multiply(#0,const_4)|add(#3,#2)|sqrt(#4)|add(n2,#5)|subtract(n2,#5)|divide(#6,#1)|divide(#7,#1)|subtract(#8,#9)| | "for 2 q ^ 2 + 5 q = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ." | general |
math_qa__jkmom56QpQLbOOxt | For the positive integers x, x + 2, x + 4, x + 7, and x + 27, the mean is how much greater than the median? Answers
A) 0
B) 1
C) 2
D) 4
E) 7 | <gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">6 + 7</gadget>
<output>13</output>
<gadget id="calculator">13 + 27</gadget>
<output>40</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<gadget id="calculator">8 - 4</gadget>
<output>4</output>
<result>D</result> | D | 4 | For the positive integers x, x + 2, x + 4, x + 7, and x + 27, the mean is how much greater than the median? | {
"A": "0",
"B": "1",
"C": "2",
"D": "4",
"E": "7"
} | subtract(divide(add(add(add(2, 4), 7), 27), add(4, const_1)), 4) | add(n0,n1)|add(const_1,n1)|add(n2,#0)|add(n3,#2)|divide(#3,#1)|subtract(#4,n1)| | "mean = ( x + x + 2 + x + 4 + x + 7 + x + 27 ) / 5 = ( 5 x + 40 ) / 5 = x + 8 median = x + 4 thus mean - median = x + 8 - ( x + 4 ) = 4 answer = d" | general |
math_qa__q6Eg9VxZMkSRwYwS | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation g of the mean, what percent of the distribution is less than m+g?
Choose the correct choice from the following options.
A) 16 % B) 32 % C) 48 % D) 84 % E) 92 % | <gadget id="calculator">100 - 68</gadget>
<output>32</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<gadget id="calculator">100 - 16</gadget>
<output>84</output>
<result>D</result> | D | 84 | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation g of the mean, what percent of the distribution is less than m+g? | {
"A": "16 %",
"B": "32 %",
"C": "48 %",
"D": "84 %",
"E": "92 %"
} | subtract(const_100, divide(subtract(const_100, 68), const_2)) | subtract(const_100,n0)|divide(#0,const_2)|subtract(const_100,#1)| | "16 % ________________________________________________ m + g 34 % ________________________________________________ m 34 % ________________________________________________ m - g 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - g and 16 % lie above m + g now below m + g = 16 + 34 + 34 = 84 % hence d" | general |
math_qa__VLYWZmPLZAep0VHX | Pradeep has to obtain 35% of the total marks to pass. He got 185 marks and failed by 25 marks. The maximum marks are
Choose the correct option: A) 300 B) 600 C) 800 D) 1000 E) 900 | <gadget id="calculator">185 + 25</gadget>
<output>210</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">210 / (7/20)</gadget>
<output>600</output>
<result>B</result> | B | 600 | Pradeep has to obtain 35% of the total marks to pass. He got 185 marks and failed by 25 marks. The maximum marks are | {
"A": "300",
"B": "600",
"C": "800",
"D": "1000",
"E": "900"
} | divide(add(185, 25), divide(35, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1) | explanation : let their maximum marks be x . then , 35 % of x = 185 + 25 = > 35 / 100 x = 210 x = ( 210100 / 35 ) x = 600 . answer : b | general |
math_qa__HWsOKi7yy10cDHdK | In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 22 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students? Choose the correct choice from the following answers:
A) 42
B) 48
C) 64
D) 76
E) 88 | <gadget id="calculator">160 / 800</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 - 22</gadget>
<output>58</output>
<gadget id="calculator">100 - 75</gadget>
<output>25</output>
<gadget id="calculator">58 - 25</gadget>
<output>33</output>
<gadget id="calculator">33 * 800</gadget>
<output>26_400</output>
<gadget id="calculator">26_400 / 100</gadget>
<output>264</output>
<gadget id="calculator">25 * 800</gadget>
<output>20_000</output>
<gadget id="calculator">20_000 / 100</gadget>
<output>200</output>
<gadget id="calculator">264 - 200</gadget>
<output>64</output>
<result>C</result> | C | 64 | In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 22 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students? | {
"A": "42",
"B": "48",
"C": "64",
"D": "76",
"E": "88"
} | subtract(divide(multiply(subtract(subtract(subtract(const_100, multiply(divide(160, 800), const_100)), 22), subtract(const_100, 75)), 800), const_100), divide(multiply(subtract(const_100, 75), 800), const_100)) | divide(n3,n0)|subtract(const_100,n2)|multiply(#0,const_100)|multiply(n0,#1)|divide(#3,const_100)|subtract(const_100,#2)|subtract(#5,n1)|subtract(#6,#1)|multiply(n0,#7)|divide(#8,const_100)|subtract(#9,#4)| | "200 are sophomores . the number of freshmen is 600 - 160 - 0.22 ( 800 ) = 264 the answer is c ." | gain |
math_qa__ERdiTKiM1YaSTcNE | A tailor trims 6 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth? Options
A) 20 B) 22 C) 24 D) 26 E) 28 | <gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">12 + 10</gadget>
<output>22</output>
<gadget id="calculator">10 * 12</gadget>
<output>120</output>
<gadget id="calculator">120 - 120</gadget>
<output>0</output>
<gadget id="calculator">6 * 0</gadget>
<output>0</output>
<gadget id="calculator">22 ** 2</gadget>
<output>484</output>
<gadget id="calculator">0 + 484</gadget>
<output>484</output>
<gadget id="calculator">484 ** (1/2)</gadget>
<output>22</output>
<gadget id="calculator">22 + 22</gadget>
<output>44</output>
<gadget id="calculator">44 / 2</gadget>
<output>22</output>
<result>B</result> | B | 22 | A tailor trims 6 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth? | {
"A": "20",
"B": "22",
"C": "24",
"D": "26",
"E": "28"
} | divide(add(add(multiply(const_2, 6), multiply(const_2, 5)), sqrt(add(multiply(6, subtract(120, multiply(multiply(const_2, 5), multiply(const_2, 6)))), power(add(multiply(const_2, 6), multiply(const_2, 5)), const_2)))), const_2) | multiply(n0,const_2)|multiply(n1,const_2)|add(#0,#1)|multiply(#1,#0)|power(#2,const_2)|subtract(n2,#3)|multiply(#5,n0)|add(#6,#4)|sqrt(#7)|add(#2,#8)|divide(#9,const_2)| | "let the original side of the square be x . ( x - 12 ) * ( x - 10 ) = 120 = 10 * 12 x = 22 the answer is b ." | geometry |
math_qa__PS9lKHeIFkUAh08y | Find the area of a parallelogram with base 14 cm and height 24 cm.
Choose the most appropriate option.
A) 336 B) 384 C) 345 D) 244 E) 242 | <gadget id="calculator">14 * 24</gadget>
<output>336</output>
<result>A</result> | A | 336 | Find the area of a parallelogram with base 14 cm and height 24 cm. | {
"A": "336",
"B": "384",
"C": "345",
"D": "244",
"E": "242"
} | multiply(14, 24) | multiply(n0,n1)| | "area of a parallelogram = base * height = 14 * 24 = 336 cm 2 answer : option a" | geometry |
math_qa__JUd70bDXTzV6fsL5 | A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 35% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save? Answers:
A) 25 %
B) 28 %
C) 30 %
D) 32.5 %
E) 35 % | <gadget id="calculator">100 + 35</gadget>
<output>135</output>
<gadget id="calculator">135 + 100</gadget>
<output>235</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">235 - 200</gadget>
<output>35</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 100</gadget>
<output>35</output>
<result>E</result> | E | 35 | A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 35% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save? | {
"A": "25 %",
"B": "28 %",
"C": "30 %",
"D": "32.5 %",
"E": "35 %"
} | multiply(divide(subtract(add(add(100, 35), 100), multiply(2, 100)), 100), 100) | add(n0,n1)|multiply(n1,n2)|add(n1,#0)|subtract(#2,#1)|divide(#3,n1)|multiply(#4,n1)| | "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.35 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 35 % income the savings increased by 100 % . or s = . 35 i or s = 35 % of income e is the answer" | general |
math_qa__qX5WhlDff90tQsK5 | How is 5% expressed as a decimal fraction? Choose the correct choice:
A) 0.5
B) 0.05
C) 0.005
D) 0.0005
E) 5 | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<result>B</result> | B | 0.05 | How is 5% expressed as a decimal fraction? | {
"A": "0.5",
"B": "0.05",
"C": "0.005",
"D": "0.0005",
"E": "5"
} | divide(5, const_100) | divide(n0,const_100)| | "5 / 100 = 0.05 answer : b" | gain |
math_qa__oyZ6Z9Wjh4dld2lX | 34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder?
Choose the correct answer:
A) 7 B) 10 C) 8 D) 12 E) 15 | <gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">100 - 36</gadget>
<output>64</output>
<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>
<result>C</result> | C | 8 | 34. The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder? | {
"A": "7",
"B": "10",
"C": "8",
"D": "12",
"E": "15"
} | sqrt(subtract(power(10, const_2), power(6, const_2))) | power(n2,const_2)|power(n1,const_2)|subtract(#0,#1)|sqrt(#2)| | think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 8 . correct answer c . | geometry |
math_qa__2bUiBXX4ZTQzLD1L | A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds. What is the length of the train in meters?
Select.
A) 400 meters
B) 1111 meters
C) 160 meters
D) 850 meters
E) none of these | <gadget id="calculator">100 - 64</gadget>
<output>36</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">10 * 85</gadget>
<output>850</output>
<result>D</result> | D | 850 | A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds. What is the length of the train in meters? | {
"A": "400 meters",
"B": "1111 meters",
"C": "160 meters",
"D": "850 meters",
"E": "none of these"
} | multiply(multiply(subtract(100, 64), const_0_2778), 85) | subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(n2,#1) | train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 85 seconds distance = speed * time 36000 * 85 / 3600 = 850 meters . d is the answer . | physics |
math_qa__J1BZaiCyQUR5WDwo | P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 378 is divided among them . What is Q's share? Choose one
A) 114 B) 120 C) 134 D) 144 E) none of these | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">378 * 8</gadget>
<output>3_024</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">3_024 / 21</gadget>
<output>144</output>
<result>D</result> | D | 144 | P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 378 is divided among them . What is Q's share? | {
"A": "114",
"B": "120",
"C": "134",
"D": "144",
"E": "none of these"
} | divide(multiply(378, multiply(4, 2)), add(multiply(10, 2), 1)) | multiply(n1,n5)|multiply(n1,n6)|add(n0,#1)|multiply(n7,#0)|divide(#3,#2) | explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 b ' s share = 378 * ( 8 / 21 ) = 18 * 8 = 144 . answer : option d | general |
math_qa__zXXLTImOtspw69eb | A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 2013, What is the value of n?
Select the correct option:
A) 22 B) 38 C) 62 D) 122 E) 672 | <gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">2_013 / 11</gadget>
<output>183</output>
<gadget id="calculator">183 / 3</gadget>
<output>61</output>
<gadget id="calculator">2 * 61</gadget>
<output>122</output>
<result>D</result> | D | 122 | A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 2013, What is the value of n? | {
"A": "22",
"B": "38",
"C": "62",
"D": "122",
"E": "672"
} | multiply(2, divide(divide(2013, add(const_10, const_1)), const_3)) | add(const_1,const_10)|divide(n4,#0)|divide(#1,const_3)|multiply(n0,#2)| | "same logic but with application of factorials . 2 * 4 * 6 * 8 * . . . * n = 2 ( 1 * 2 * 3 * 4 * . . . n / 2 ) = 2 * ( n / 2 ) ! now we have : 2 * ( n / 2 ) ! / 2013 = 2 * ( n / 2 ) ! / ( 3 × 11 × 61 ) for the expression 2 * ( n / 2 ) ! to be divisible by 2013 min value of n / 2 should be 61 . so n / 2 = 61 = > n = 122 answer d ." | general |
math_qa__Zn3H2ojKuvwPMCU2 | billy worked for 3 straight hours on his homework questions . if he solved 132 questions in the third hour , which was twice as many as he solved in the second hour , and 3 times as many questions as he solved in the first hour , how many questions did he solve total ? Pick one: A) 242 B) 312 C) 424 D) 525 E) 622 | <gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 2</gadget>
<output>22</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">132 * (1/3)</gadget>
<output>44</output>
<gadget id="calculator">44 * 2</gadget>
<output>88</output>
<gadget id="calculator">88 + 132</gadget>
<output>220</output>
<gadget id="calculator">22 + 220</gadget>
<output>242</output>
<result>A</result> | A | 242 | billy worked for 3 straight hours on his homework questions . if he solved 132 questions in the third hour , which was twice as many as he solved in the second hour , and 3 times as many questions as he solved in the first hour , how many questions did he solve total ? | {
"A": "242",
"B": "312",
"C": "424",
"D": "525",
"E": "622"
} | add(add(add(const_10, const_10), const_2), add(multiply(multiply(132, divide(const_1, 3)), const_2), 132)) | add(const_10,const_10)|divide(const_1,n0)|add(#0,const_2)|multiply(n1,#1)|multiply(#3,const_2)|add(n1,#4)|add(#2,#5) | total questions solved = questions solved in 3 rd hr + in 2 nd hr + in 1 st hr 132 + 132 / 2 + 132 / 3 = 242 a is the answer | physics |
math_qa__pVg28k4v7UpshR1m | A man buys an item at Rs. 750 and sells it at the loss of 10 percent. Then what is the selling price of that item Pick:
A) rs . 660 B) rs . 675 C) rs . 860 D) rs . 960 E) none of these | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">750 * (9/10)</gadget>
<output>675</output>
<result>B</result> | B | 675 | A man buys an item at Rs. 750 and sells it at the loss of 10 percent. Then what is the selling price of that item | {
"A": "rs . 660",
"B": "rs . 675",
"C": "rs . 860",
"D": "rs . 960",
"E": "none of these"
} | multiply(750, subtract(const_1, divide(10, const_100))) | divide(n1,const_100)|subtract(const_1,#0)|multiply(n0,#1)| | "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 90 % of 750 = 90 / 100 * 750 = 675 option b" | gain |
math_qa__G99yeD4MBR1yQtLb | For what value of “k†will the equation (2kx2 + 3kx +2)=0 have equal roots? Pick one.
A) 2 / 7 B) 9 / 4 C) 16 / 25 D) 7 / 1 E) 16 / 9 | <gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">16 / 9</gadget>
<output>16/9 = around 1.777778</output>
<result>E</result> | E | 1.777778 | For what value of “k†will the equation (2kx2 + 3kx +2)=0 have equal roots? | {
"A": "2 / 7",
"B": "9 / 4",
"C": "16 / 25",
"D": "7 / 1",
"E": "16 / 9"
} | divide(power(2, add(2, 2)), power(3, 2)) | add(n0,n0)|power(n2,n0)|power(n0,#0)|divide(#2,#1) | for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 3 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 9 answer : e | general |
math_qa__r7M0ojOHwp3KuY7q | If 9 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed? Pick one
A) 80 B) 63 C) 120 D) 1008 E) 1260 | <gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">9 * 8</gadget>
<output>72</output>
<gadget id="calculator">72 / 2</gadget>
<output>36</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">8 * 7</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<gadget id="calculator">36 * 28</gadget>
<output>1_008</output>
<result>D</result> | D | 1,008 | If 9 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed? | {
"A": "80",
"B": "63",
"C": "120",
"D": "1008",
"E": "1260"
} | multiply(divide(multiply(9, subtract(9, const_1)), const_2), divide(multiply(8, subtract(8, const_1)), const_2)) | subtract(n0,const_1)|subtract(n1,const_1)|multiply(n0,#0)|multiply(n1,#1)|divide(#2,const_2)|divide(#3,const_2)|multiply(#4,#5)| | "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 9 c 2 for vertical 8 c 2 total parallelogram is 9 c 2 * 8 c 2 = 36 * 28 = 1008 answer : d" | physics |
math_qa__5Yf2ieke1im7mekI | Entry fee in an examination was Re. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is Pick
A) 60 B) 50 C) 66 D) 54 E) none | <gadget id="calculator">20 * 100</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">20 + 100</gadget>
<output>120</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">120 / (3/4)</gadget>
<output>160</output>
<gadget id="calculator">160 - 100</gadget>
<output>60</output>
<result>A</result> | A | 60 | Entry fee in an examination was Re. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is | {
"A": "60",
"B": "50",
"C": "66",
"D": "54",
"E": "none"
} | subtract(divide(add(divide(multiply(20, const_100), const_100), const_100), subtract(const_1, divide(25, const_100))), const_100) | divide(n1,const_100)|multiply(n2,const_100)|divide(#1,const_100)|subtract(const_1,#0)|add(#2,const_100)|divide(#4,#3)|subtract(#5,const_100) | sol . let the total original sale be rs . 100 . then , original number of visitors = 100 . new number of visitors = 120 / 0.75 = 160 . ∴ increase % = 60 % . answer a | general |
math_qa__ja8Lx9YZp2CNHjTm | A retailer bought a machine at a wholesale price of $126 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine? Choose the correct choice from the following choices.
A) 81 B) 100 C) 120 D) 135 E) 168 | <gadget id="calculator">126 * 20</gadget>
<output>2_520</output>
<gadget id="calculator">2_520 / 100</gadget>
<output>126/5 = around 25.2</output>
<gadget id="calculator">126 + (126/5)</gadget>
<output>756/5 = around 151.2</output>
<gadget id="calculator">(756/5) * 100</gadget>
<output>15_120</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">15_120 / 90</gadget>
<output>168</output>
<result>E</result> | E | 168 | A retailer bought a machine at a wholesale price of $126 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine? | {
"A": "81",
"B": "100",
"C": "120",
"D": "135",
"E": "168"
} | divide(multiply(add(126, divide(multiply(126, 20), const_100)), const_100), multiply(multiply(const_3, const_3), 10)) | multiply(n0,n2)|multiply(const_3,const_3)|divide(#0,const_100)|multiply(n1,#1)|add(n0,#2)|multiply(#4,const_100)|divide(#5,#3) | my solution : wholesale price = 126 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 126 + 1 / 5 ( 126 ) x = 168 ; answer : e | gain |
math_qa__1Wd5mnIUwMUuPG5g | If Rs.10 be allowed as true discount on a bill of Rs.110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is Choose the correct choice: A) 18.20 B) 18.33 C) 18 D) 18.3 E) none of these | <gadget id="calculator">10 + 110</gadget>
<output>120</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<gadget id="calculator">20 / 120</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">110 * (1/6)</gadget>
<output>55/3 = around 18.333333</output>
<result>B</result> | B | 18.33 | If Rs.10 be allowed as true discount on a bill of Rs.110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is | {
"A": "18.20",
"B": "18.33",
"C": "18",
"D": "18.3",
"E": "none of these"
} | multiply(110, divide(subtract(add(10, 110), const_100), add(10, 110))) | add(n0,n1)|subtract(#0,const_100)|divide(#1,#0)|multiply(n1,#2)| | "explanation : present worth = amount - truediscount = 110 - 10 = rs . 100 si on rs . 100 for a certain time = rs . 10 si on rs . 100 for doube the time = rs . 20 truediscount on rs . 120 = 120 - 100 = rs . 20 truediscount on rs . 110 = ( 110 x 20 / 120 ) = rs . 18.33 answer : b" | general |
math_qa__sKZXr7OmbiaGfEpR | The grade point average of the entire class is 85. If the average of one third of the class is 97, what is the average of the rest of the class? Pick one.
A) 76 B) 77 C) 78 D) 79 E) 80 | <gadget id="calculator">85 * 4</gadget>
<output>340</output>
<gadget id="calculator">340 - 97</gadget>
<output>243</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">243 / 3</gadget>
<output>81</output>
<result>D</result> | D | 79 | The grade point average of the entire class is 85. If the average of one third of the class is 97, what is the average of the rest of the class? | {
"A": "76",
"B": "77",
"C": "78",
"D": "79",
"E": "80"
} | divide(subtract(multiply(85, const_4), 97), subtract(const_4, const_1)) | multiply(n0,const_4)|subtract(const_4,const_1)|subtract(#0,n1)|divide(#2,#1)| | "let x be the number of students in the class . let p be the average of the rest of the class . 85 x = ( 1 / 3 ) 97 x + ( 2 / 3 ) ( p ) x 255 = 97 + 2 p 2 p = 158 p = 79 . the answer is d ." | general |
math_qa__O5S3UnELKyHjPU9H | The diameter of a wheel is 0.7 m. How far will it travel in 200 revolutions Pick
A) 4.4 m B) 220 m C) 440 m D) 560 E) 650 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1_000 + 60</gadget>
<output>1_060</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 4</gadget>
<output>24</output>
<gadget id="calculator">1_060 + 24</gadget>
<output>1_084</output>
<gadget id="calculator">1_000 * 10</gadget>
<output>10_000</output>
<gadget id="calculator">1_084 / 10_000</gadget>
<output>271/2_500 = around 0.1084</output>
<gadget id="calculator">(1/4) - (271/2_500)</gadget>
<output>177/1_250 = around 0.1416</output>
<gadget id="calculator">3 + (177/1_250)</gadget>
<output>3_927/1_250 = around 3.1416</output>
<gadget id="calculator">(3_927/1_250) * 0.7</gadget>
<output>2.19912</output>
<gadget id="calculator">2.19912 * 200</gadget>
<output>439.824</output>
<result>C</result> | C | 440 | The diameter of a wheel is 0.7 m. How far will it travel in 200 revolutions | {
"A": "4.4 m",
"B": "220 m",
"C": "440 m",
"D": "560",
"E": "650"
} | multiply(multiply(add(const_3, subtract(const_0_25, divide(add(add(const_1000, const_60), add(multiply(const_2, const_10), const_4)), multiply(const_1000, const_10)))), 0.7), 200) | add(const_1000,const_60)|multiply(const_10,const_2)|multiply(const_10,const_1000)|add(#1,const_4)|add(#0,#3)|divide(#4,#2)|subtract(const_0_25,#5)|add(#6,const_3)|multiply(n0,#7)|multiply(n1,#8) | diameter ( d ) = 0.7 m circumference of the wheel , = 2 * pi * r = d * pi = 0.7 * 3.14 = 2.198 m . in one revolution , wheel will covered = 2.198 m , so , in 200 revolution , it will cover = 200 * 2.198 = 4.396 m = 440 m ( approx ) . answer : option c | physics |
math_qa__yaltiOvkBLrQmYRD | Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 35% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased? Answers.
A) 45 % B) 65 % C) 85 % D) 115 % E) 125 % | <gadget id="calculator">35 * 100</gadget>
<output>3_500</output>
<gadget id="calculator">20 * 100</gadget>
<output>2_000</output>
<gadget id="calculator">3_500 - 2_000</gadget>
<output>1_500</output>
<gadget id="calculator">100 - 35</gadget>
<output>65</output>
<gadget id="calculator">1_500 / 65</gadget>
<output>300/13 = around 23.076923</output>
<gadget id="calculator">(300/13) / 20</gadget>
<output>15/13 = around 1.153846</output>
<gadget id="calculator">(15/13) * 100</gadget>
<output>1_500/13 = around 115.384615</output>
<result>D</result> | D | 115 | Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 35% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased? | {
"A": "45 %",
"B": "65 %",
"C": "85 %",
"D": "115 %",
"E": "125 %"
} | multiply(divide(divide(subtract(multiply(35, const_100), multiply(20, const_100)), subtract(const_100, 35)), 20), const_100) | multiply(n0,const_100)|multiply(n1,const_100)|subtract(const_100,n0)|subtract(#0,#1)|divide(#3,#2)|divide(#4,n1)|multiply(#5,const_100)| | "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.35 ( 5 b + x ) = b + x 0.75 b = 0.65 x x = 1.15 b the answer is d ." | general |
math_qa__nOT1afNDrH2qJm9v | What is the area of square field whose side of length 16 m? Pick
A) 225 B) 777 C) 256 D) 288 E) 261 | <gadget id="calculator">16 ** 2</gadget>
<output>256</output>
<result>C</result> | C | 256 | What is the area of square field whose side of length 16 m? | {
"A": "225",
"B": "777",
"C": "256",
"D": "288",
"E": "261"
} | square_area(16) | square_area(n0)| | "16 * 16 = 256 sq m answer : c" | geometry |
math_qa__1tV4lTsME2tP8IU3 | if the average marks of 3 batches of 40 , 50 and 60 students respectively is 45 , 55 , 65 , what is the average marks of all the students ? Select: A) 56.33 B) 34.89 C) 23.67 D) 54.65 E) 43.98 | <gadget id="calculator">40 * 45</gadget>
<output>1_800</output>
<gadget id="calculator">50 * 55</gadget>
<output>2_750</output>
<gadget id="calculator">1_800 + 2_750</gadget>
<output>4_550</output>
<gadget id="calculator">60 * 65</gadget>
<output>3_900</output>
<gadget id="calculator">4_550 + 3_900</gadget>
<output>8_450</output>
<gadget id="calculator">40 + 50</gadget>
<output>90</output>
<gadget id="calculator">90 + 60</gadget>
<output>150</output>
<gadget id="calculator">8_450 / 150</gadget>
<output>169/3 = around 56.333333</output>
<result>A</result> | A | 56.33 | if the average marks of 3 batches of 40 , 50 and 60 students respectively is 45 , 55 , 65 , what is the average marks of all the students ? | {
"A": "56.33",
"B": "34.89",
"C": "23.67",
"D": "54.65",
"E": "43.98"
} | divide(add(add(multiply(40, 45), multiply(50, 55)), multiply(60, 65)), add(add(40, 50), 60)) | add(n1,n2)|multiply(n1,n4)|multiply(n2,n5)|multiply(n3,n6)|add(#1,#2)|add(n3,#0)|add(#4,#3)|divide(#6,#5) | average marks of batch 1 = 45 students in batch 1 = 40 total marks of batch 1 = 40 * 45 average marks of batch 2 = 55 students in batch 2 = 50 total marks of batch 2 = 50 × 55 average marks of batch 3 = 65 students in batch 3 = 60 total marks of batch 3 = 65 × 60 total students = 40 + 60 + 50 = 150 average marks of all the students = ( ( 40 * 45 ) + ( 50 × 55 ) + ( 65 × 60 ) ) / 150 = 169 / 3 = 56.333 answer is a . | general |
math_qa__9v2I79YhjnioShCC | In what ratio must rice of Rs.16 per kg be mixed with rice of Rs.10 per kg so that cost of mixture is Rs.12 per kg? Choose the correct choice from the following choices.
A) 2 : 3
B) 5 : 8
C) 5 : 6
D) 3 : 4
E) 1 : 2 | <gadget id="calculator">12 - 10</gadget>
<output>2</output>
<gadget id="calculator">16 - 10</gadget>
<output>6</output>
<gadget id="calculator">2 / 6</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/3) / (2/3)</gadget>
<output>1/2 = around 0.5</output>
<result>E</result> | E | 0.5 | In what ratio must rice of Rs.16 per kg be mixed with rice of Rs.10 per kg so that cost of mixture is Rs.12 per kg? | {
"A": "2 : 3",
"B": "5 : 8",
"C": "5 : 6",
"D": "3 : 4",
"E": "1 : 2"
} | divide(divide(subtract(12, 10), subtract(16, 10)), subtract(const_1, divide(subtract(12, 10), subtract(16, 10)))) | subtract(n2,n1)|subtract(n0,n1)|divide(#0,#1)|subtract(const_1,#2)|divide(#2,#3)| | "( 12 - 10 ) / ( 16 - 12 ) = 2 / 4 = 1 : 2 answer : e" | other |
math_qa__GjDAot86YeeFFRFi | in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 10 people all together .how many people can sit in a bus? Answers:
A) 52 B) 49 C) 91 D) 88 E) 66 | <gadget id="calculator">15 - 3</gadget>
<output>12</output>
<gadget id="calculator">15 + 12</gadget>
<output>27</output>
<gadget id="calculator">27 * 3</gadget>
<output>81</output>
<gadget id="calculator">81 + 10</gadget>
<output>91</output>
<result>C</result> | C | 91 | in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 10 people all together .how many people can sit in a bus? | {
"A": "52",
"B": "49",
"C": "91",
"D": "88",
"E": "66"
} | add(multiply(add(15, subtract(15, 3)), 3), 10) | subtract(n0,n1)|add(n0,#0)|multiply(n1,#1)|add(n3,#2) | right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 10 total people can seat = 81 + 10 = 91 answer : c | general |
math_qa__Ussj1sdGOlztCHA9 | If 4<x<8<y<12, then what is the greatest possible positive integer difference of x and y? Select:
A) 3 B) 4 C) 5 D) 6 E) 7 | <gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<result>E</result> | E | 7 | If 4<x<8<y<12, then what is the greatest possible positive integer difference of x and y? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | subtract(subtract(12, 4), const_1) | subtract(n2,n0)|subtract(#0,const_1)| | "let x = 4.1 and y = 11.1 greatest possible difference = 11.1 - 4.1 = 7 answer e" | general |
math_qa__GBqrueQD3Fq5bUua | The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 70 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam. Choose the correct choice
A) 22 B) 10 C) 25 D) 99 E) 21 | <gadget id="calculator">90 * 5</gadget>
<output>450</output>
<gadget id="calculator">5 * 70</gadget>
<output>350</output>
<gadget id="calculator">450 - 350</gadget>
<output>100</output>
<gadget id="calculator">90 - 80</gadget>
<output>10</output>
<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<result>B</result> | B | 10 | The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 70 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam. | {
"A": "22",
"B": "10",
"C": "25",
"D": "99",
"E": "21"
} | divide(subtract(multiply(90, 5), multiply(5, 70)), subtract(90, 80)) | multiply(n1,n3)|multiply(n1,n2)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2)| | "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 70 ) = 90 ( x - 5 ) 100 = 10 x = > x = 10 . answer : b" | general |
math_qa__va80yQ0j1AcPjs51 | At a special sale, 8 tickets can be purchased for the price of 6 tickets. If 8 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 8 tickets? Choose the correct choice from the following choices
A) 25 % B) 33.3 % C) 40 % D) 60 % E) 66.6 % | <gadget id="calculator">8 * 8</gadget>
<output>64</output>
<gadget id="calculator">6 * 8</gadget>
<output>48</output>
<gadget id="calculator">64 - 48</gadget>
<output>16</output>
<gadget id="calculator">16 * 100</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 / 64</gadget>
<output>25</output>
<result>A</result> | A | 25 | At a special sale, 8 tickets can be purchased for the price of 6 tickets. If 8 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 8 tickets? | {
"A": "25 %",
"B": "33.3 %",
"C": "40 %",
"D": "60 %",
"E": "66.6 %"
} | divide(multiply(subtract(multiply(8, 8), multiply(6, 8)), const_100), multiply(8, 8)) | multiply(n0,n0)|multiply(n0,n1)|subtract(#0,#1)|multiply(#2,const_100)|divide(#3,#0)| | "let the price of a ticket be rs . 100 , so 6 tickets cost 600 & 8 tickets cost 800 8 tickets purchased at price of 6 tickets ie . , for 600 , so amount saved s rs . 200 , % of 6 tickets = ( 200 / 800 ) * 100 = 25 % answer : a" | gain |
math_qa__1bBOTEyUFHkGkRhQ | When y is divided by 276, the remainder is 44. What is the remainder when the same y is divided by 23? Choose the correct choice from the following answers:
A) 19
B) 20
C) 21
D) 22
E) 23 | <gadget id="calculator">44 % 23</gadget>
<output>21</output>
<result>C</result> | C | 21 | When y is divided by 276, the remainder is 44. What is the remainder when the same y is divided by 23? | {
"A": "19",
"B": "20",
"C": "21",
"D": "22",
"E": "23"
} | reminder(44, 23) | reminder(n1,n2)| | "y = 276 * a + 44 = ( 23 * 12 ) * a + 23 + 21 the answer is c ." | general |
math_qa__ihmuxqrQg7proEOf | The cricket team of 11members is 29yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ? Choose the correct option:
A) 21
B) 22
C) 23
D) 26
E) 28 | <gadget id="calculator">29 + 3</gadget>
<output>32</output>
<gadget id="calculator">32 + 29</gadget>
<output>61</output>
<gadget id="calculator">11 - 2</gadget>
<output>9</output>
<gadget id="calculator">61 - 9</gadget>
<output>52</output>
<gadget id="calculator">11 - 9</gadget>
<output>2</output>
<gadget id="calculator">52 / 2</gadget>
<output>26</output>
<result>D</result> | D | 26 | The cricket team of 11members is 29yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ? | {
"A": "21",
"B": "22",
"C": "23",
"D": "26",
"E": "28"
} | divide(subtract(add(add(29, 3), 29), subtract(11, 2)), subtract(11, subtract(11, 2))) | add(n1,n2)|subtract(n0,n3)|add(n1,#0)|subtract(n0,#1)|subtract(#2,#1)|divide(#4,#3)| | "let the average age of the whole team be x years . 11 x - ( 29 + 32 ) = 9 ( x - 1 ) = > 11 x - 9 x = 52 = > 2 x = 52 = > x = 26 . so , average age of the team is 26 years . d" | general |
math_qa__oaMxnb0lN2aXO2tt | A cistern which could be filled in 5 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it? Select:
A) 76 hrs B) 99 hrs C) 55 hrs D) 90 hrs E) 10 hrs | <gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/5) - (1/10)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / (1/10)</gadget>
<output>10</output>
<result>E</result> | E | 10 | A cistern which could be filled in 5 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it? | {
"A": "76 hrs",
"B": "99 hrs",
"C": "55 hrs",
"D": "90 hrs",
"E": "10 hrs"
} | inverse(subtract(divide(const_1, 5), divide(const_1, const_10))) | divide(const_1,n0)|divide(const_1,const_10)|subtract(#0,#1)|inverse(#2)| | "1 / 5 - 1 / x = 1 / 10 = > 10 hrs answer : e" | physics |
math_qa__duMgNvc9REdAgONW | Excluding stoppages, the speed of a train is 60 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Choose the most appropriate option.
A) 12 B) 18 C) 24 D) 30 E) 36 | <gadget id="calculator">36 / 60</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">60 * (3/5)</gadget>
<output>36</output>
<gadget id="calculator">60 - 36</gadget>
<output>24</output>
<result>C</result> | C | 24 | Excluding stoppages, the speed of a train is 60 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour? | {
"A": "12",
"B": "18",
"C": "24",
"D": "30",
"E": "36"
} | subtract(const_60, multiply(const_60, divide(36, 60))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | "explanation : t = 24 / 60 * 60 = 24 answer : option c" | physics |
math_qa__Ybh6szSfRjqx0zTW | find value for x from below equation? x + 1 = 3 Choose the correct choice from the following answers: A) - 5 B) - 4 C) 4 D) 3 E) 2 | <gadget id="calculator">3 - 1</gadget>
<output>2</output>
<result>E</result> | E | 2 | find value for x from below equation? x + 1 = 3 | {
"A": "- 5",
"B": "- 4",
"C": "4",
"D": "3",
"E": "2"
} | subtract(3, 1) | subtract(n1,n0)| | "1 . subtract 1 from both sides : x + 1 - 1 = 3 - 1 2 . simplify both sides : x = 2 e" | general |
math_qa__hIdriu2fHyIewPn6 | Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 12 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?
Choose the correct choice from the following answers:
A) 20 B) 21 C) 22 D) 23 E) 24 | <gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">32 - 18</gadget>
<output>14</output>
<gadget id="calculator">9 + 14</gadget>
<output>23</output>
<result>D</result> | D | 23 | Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 12 years ago. What is the current age of the oldest person for whom Jane could have baby-sat? | {
"A": "20",
"B": "21",
"C": "22",
"D": "23",
"E": "24"
} | add(divide(18, const_2), subtract(32, 18)) | divide(n0,const_2)|subtract(n1,n0)|add(#0,#1)| | "check two extreme cases : jane = 18 , child = 9 , years ago = 32 - 18 = 14 - - > child ' s age now = 9 + 14 = 23 ; jane = 20 , child = 10 , years ago = 32 - 20 = 12 - - > child ' s age now = 10 + 12 = 22 . answer : d ." | general |
math_qa__LmtjesWO7s5d5DEA | What is the remainder of R=3^19 when divided by 10?
Select the correct option.
A) 0 B) 1 C) 5 D) 7 E) 9 | <gadget id="calculator">19 % 4</gadget>
<output>3</output>
<gadget id="calculator">3 ** 3</gadget>
<output>27</output>
<gadget id="calculator">27 % 10</gadget>
<output>7</output>
<result>D</result> | D | 7 | What is the remainder of R=3^19 when divided by 10? | {
"A": "0",
"B": "1",
"C": "5",
"D": "7",
"E": "9"
} | reminder(power(3, reminder(19, const_4)), 10) | reminder(n1,const_4)|power(n0,#0)|reminder(#1,n2)| | "i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , r = when divided by 10 , the remainder must be 7 . d" | general |
math_qa__IpXMmbZRgQMARvO0 | John makes $30 a week from his job. He earns a raise andnow makes $40 a week. What is the % increase? Choose the correct option
A) 16 % B) 33.33 % C) 33.69 % D) 33.98 % E) 37 % | <gadget id="calculator">40 - 30</gadget>
<output>10</output>
<gadget id="calculator">10 / 30</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>B</result> | B | 33.33 | John makes $30 a week from his job. He earns a raise andnow makes $40 a week. What is the % increase? | {
"A": "16 %",
"B": "33.33 %",
"C": "33.69 %",
"D": "33.98 %",
"E": "37 %"
} | multiply(divide(subtract(40, 30), 30), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | "increase = ( 10 / 30 ) * 100 = ( 1 / 3 ) * 100 = 33.33 % . b" | gain |
math_qa__VPqlFbxcb0LmM5vs | Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 8) and (6, -4). What is the slope of line m? Choose the correct choice from the following.
A) - 3
B) - 1
C) - 1 / 3
D) 0
E) 1 | <gadget id="calculator">8 - 4</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">2 + 6</gadget>
<output>8</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">4 / 4</gadget>
<output>1</output>
<result>E</result> | E | 1 | Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 8) and (6, -4). What is the slope of line m? | {
"A": "- 3",
"B": "- 1",
"C": "- 1 / 3",
"D": "0",
"E": "1"
} | divide(add(divide(subtract(8, 4), 2), 2), divide(add(2, 6), 2)) | add(n1,n3)|subtract(n2,n4)|divide(#1,n1)|divide(#0,n1)|add(#2,n0)|divide(#4,#3)| | "the midpoint of ( 2,8 ) and ( 6 , - 4 ) is ( 4,2 ) . the slope of a line through ( 0 , - 2 ) and ( 4,2 ) is ( 2 - ( - 2 ) ) / ( 4 - 0 ) = 4 / 4 = 1 the answer is e ." | general |
math_qa__ZAFkIvSQIrTBuOAq | The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years B in which the population would be doubled assuming there is no emigration or immigration is
Choose the correct choice from the following
A) 20 B) 25 C) b = 30 D) b = 35 E) b = 40 | <gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">39.4 - 19.4</gadget>
<output>20</output>
<gadget id="calculator">20 / 1_000</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/50) * 100</gadget>
<output>2</output>
<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<result>D</result> | D | 35 | The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years B in which the population would be doubled assuming there is no emigration or immigration is | {
"A": "20",
"B": "25",
"C": "b = 30",
"D": "b = 35",
"E": "b = 40"
} | divide(subtract(const_100, multiply(const_10, const_3)), multiply(divide(subtract(39.4, 19.4), 1000), const_100)) | multiply(const_10,const_3)|subtract(n1,n2)|divide(#1,n0)|subtract(const_100,#0)|multiply(#2,const_100)|divide(#3,#4)| | "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ." | general |
math_qa__6vp7Gusji92AYflm | If 36 men can do a piece of work in 5 hours, in how many hours will15 men do it? Choose the correct choice from the following choices:
A) 12 B) 38 C) 60 D) 88 E) 72 | <gadget id="calculator">36 * 5</gadget>
<output>180</output>
<gadget id="calculator">180 / 15</gadget>
<output>12</output>
<result>A</result> | A | 12 | If 36 men can do a piece of work in 5 hours, in how many hours will15 men do it? | {
"A": "12",
"B": "38",
"C": "60",
"D": "88",
"E": "72"
} | divide(multiply(36, 5), 15) | multiply(n0,n1)|divide(#0,n2)| | "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 5 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 5 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 5 } { 15 } = 12 hence , 15 men can do it in 12 hours . answer : a ) 12" | physics |
math_qa__UFM59aYnS30FulOC | The letters O,L and T are rearranged to form the word 'Lot'. Find its probability.
Answers:
A) 1 / 18
B) 1 / 12
C) 1 / 4
D) 1 / 8
E) 1 / 6 | <gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<result>E</result> | E | 0.166667 | The letters O,L and T are rearranged to form the word 'Lot'. Find its probability. | {
"A": "1 / 18",
"B": "1 / 12",
"C": "1 / 4",
"D": "1 / 8",
"E": "1 / 6"
} | divide(const_1, factorial(const_3)) | factorial(const_3)|divide(const_1,#0) | explanation : there are total 3 letters . the probability that o gets the first position is 1 / 3 . likewise , probability for l and t are 1 / 2 and 1 / 1 . hence , the required probability is : - = > ( 1 / 3 ) x ( 1 / 2 ) x 1 . = > 1 / 6 . answer : e | probability |
math_qa__zFQhiNgle1WpaxBT | A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 64, how many questions did Student A answer correctly?
Choose the most appropriate option: A) 55 B) 60 C) 73 D) 82 E) 88 | <gadget id="calculator">100 - 64</gadget>
<output>36</output>
<gadget id="calculator">36 / 3</gadget>
<output>12</output>
<gadget id="calculator">100 - 12</gadget>
<output>88</output>
<result>E</result> | E | 88 | A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 64, how many questions did Student A answer correctly? | {
"A": "55",
"B": "60",
"C": "73",
"D": "82",
"E": "88"
} | subtract(100, divide(subtract(100, 64), const_3)) | subtract(n0,n1)|divide(#0,const_3)|subtract(n0,#1)| | "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 64 ( subtracting twice of incorrect from correct ) 3 x = 264 x = 88 answer : e" | general |
math_qa__O0WFdZHvgB0d5D9I | a wildlife preserve is being planned for 8000 rhinoceroses . the preserve is to contain a total of 10000 acres of watering area , plus 100 acres of grazing area for each rhinoceros . if the number of rhinoceroses is expected to increase by 10 percent , how many 1000 acres should the preserve have in order to provide for the increased population ? Choose the correct choice from the following answers: A) 340 B) 330 C) 320 D) 310 E) 890 | <gadget id="calculator">100 * 8_000</gadget>
<output>800_000</output>
<gadget id="calculator">800_000 / 10</gadget>
<output>80_000</output>
<gadget id="calculator">800_000 + 80_000</gadget>
<output>880_000</output>
<gadget id="calculator">880_000 + 10_000</gadget>
<output>890_000</output>
<gadget id="calculator">890_000 / 1_000</gadget>
<output>890</output>
<result>E</result> | E | 890 | a wildlife preserve is being planned for 8000 rhinoceroses . the preserve is to contain a total of 10000 acres of watering area , plus 100 acres of grazing area for each rhinoceros . if the number of rhinoceroses is expected to increase by 10 percent , how many 1000 acres should the preserve have in order to provide for the increased population ? | {
"A": "340",
"B": "330",
"C": "320",
"D": "310",
"E": "890"
} | divide(add(add(multiply(100, 8000), divide(multiply(100, 8000), 10)), 10000), 1000) | multiply(n0,n2)|divide(#0,n3)|add(#1,#0)|add(n1,#2)|divide(#3,n4) | number of rhinos = 8000 watering area = 10,000 acres number of rhino to increase by 10 percent , then number of rhino = 8800 grazing area for a rhino = 100 total grazing area for 8800 rhinos = 8800 * 100 = 8 , 80,000 total area required for the wildlife preserve = 8 , 80,000 + 10,000 = 8 , 90,000 = 890 * 1000 answer e | general |
math_qa__HFsaGXxAVfpxl95r | At a certain organisation, the number of male members went up by 14% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000? Pick:
A) 1 : 2
B) 1 : 3
C) 2 : 3
D) 3 : 2
E) 4 : 7 | <gadget id="calculator">1.2 / 100</gadget>
<output>0.012</output>
<gadget id="calculator">1 + 0.012</gadget>
<output>1.012</output>
<gadget id="calculator">1.012 * 1_000</gadget>
<output>1_012</output>
<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">1 - (3/50)</gadget>
<output>47/50 = around 0.94</output>
<gadget id="calculator">(47/50) * 1_000</gadget>
<output>940</output>
<gadget id="calculator">1_012 - 940</gadget>
<output>72</output>
<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">1 + (7/50)</gadget>
<output>57/50 = around 1.14</output>
<gadget id="calculator">(57/50) * 1_000</gadget>
<output>1_140</output>
<gadget id="calculator">1_140 - 1_012</gadget>
<output>128</output>
<gadget id="calculator">72 / 128</gadget>
<output>9/16 = around 0.5625</output>
<result>E</result> | E | 0.571429 | At a certain organisation, the number of male members went up by 14% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000? | {
"A": "1 : 2",
"B": "1 : 3",
"C": "2 : 3",
"D": "3 : 2",
"E": "4 : 7"
} | divide(subtract(multiply(add(const_1, divide(1.2, const_100)), const_1000), multiply(subtract(const_1, divide(6, const_100)), const_1000)), subtract(multiply(add(const_1, divide(14, const_100)), const_1000), multiply(add(const_1, divide(1.2, const_100)), const_1000))) | divide(n4,const_100)|divide(n3,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#2,const_1)|subtract(const_1,#1)|multiply(#3,const_1000)|multiply(#5,const_1000)|multiply(#4,const_1000)|subtract(#6,#7)|subtract(#8,#6)|divide(#9,#10)| | "men increase by 14 % = = > 1.14 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.14 m + 0.94 f = 1.012 * ( m + f ) 1.14 m + 0.94 f = 1.012 m + 1.012 f 1.14 m - 1.012 m = 1.012 f - 0.94 f 0.128 m = 0.072 f m / f = ( 0.072 ) / ( 0.128 ) = 72 / 128 = 4 / 7 answer = ( e )" | other |
math_qa__VXlYPYZfA2wcM3IZ | Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 50 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the distance traveled by Maxwell when they meet in the middle? Choose the correct choice from the following answers.
A) 16 B) 18 C) 20 D) 24 E) 30 | <gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">50 / 10</gadget>
<output>5</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<result>C</result> | C | 20 | Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 50 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the distance traveled by Maxwell when they meet in the middle? | {
"A": "16",
"B": "18",
"C": "20",
"D": "24",
"E": "30"
} | multiply(4, divide(50, add(4, 6))) | add(n1,n2)|divide(n0,#0)|multiply(n1,#1)| | "distance between maxwell ' s and brad ' s home = 50 km maxwell ' s speed = 4 km / h brad ' s speed = 6 km / h relative speed of approach = 10 km / h time = 50 / 10 = 5 hours distance traveled by maxwell when they meet in the middle = 4 * 5 = 20 km answer c" | physics |
math_qa__eMF2ohAKI2YpnwQx | A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 10 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720?
Choose the correct choice from the following answers
A) $ 112.00 B) $ 64.80 C) $ 90.00 D) $ 100.80 E) $ 154.80 | <gadget id="calculator">1_720 - 600</gadget>
<output>1_120</output>
<gadget id="calculator">1_120 * 10</gadget>
<output>11_200</output>
<gadget id="calculator">11_200 / 100</gadget>
<output>112</output>
<result>A</result> | A | 112 | A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 10 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720? | {
"A": "$ 112.00",
"B": "$ 64.80",
"C": "$ 90.00",
"D": "$ 100.80",
"E": "$ 154.80"
} | divide(multiply(subtract(1720, 600), 10), const_100) | subtract(n3,n0)|multiply(n1,#0)|divide(#1,const_100)| | "correct answer : a the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.1 ( $ 1120 ) = $ 112 . the correct answer is a ." | general |
math_qa__r9CsnaclNkKS9MVY | A man is 37 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
Choose one:
A) 78 years B) 22 years C) 88 years D) 35 years E) 65 years | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">37 - 2</gadget>
<output>35</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">35 / 1</gadget>
<output>35</output>
<result>D</result> | D | 35 | A man is 37 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is | {
"A": "78 years",
"B": "22 years",
"C": "88 years",
"D": "35 years",
"E": "65 years"
} | divide(subtract(37, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | "let ' s son age is x , then father age is x + 37 . = > 2 ( x + 2 ) = ( x + 37 + 2 ) = > 2 x + 4 = x + 39 = > x = 35 years answer : d" | general |
math_qa__iOeQccE7YdiLQqMc | What is the sum of the digits of integer k, if k = (10^40- 79)
Choose the correct choice from the following:
A) 345 B) 340 C) 343 D) 349 E) 338 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">40 - 2</gadget>
<output>38</output>
<gadget id="calculator">9 * 38</gadget>
<output>342</output>
<gadget id="calculator">342 + 10</gadget>
<output>352</output>
<result>A</result> | A | 345 | What is the sum of the digits of integer k, if k = (10^40- 79) | {
"A": "345",
"B": "340",
"C": "343",
"D": "349",
"E": "338"
} | add(multiply(subtract(10, const_1), subtract(40, const_2)), 10) | subtract(n0,const_1)|subtract(n1,const_2)|multiply(#0,#1)|add(#2,n0)| | "there are 41 digits in 10 ^ 40 when we subtract 79 from it , there will be 40 digits left . 10 ^ 40 can be written as 9999999 . . . . ( 40 times ) + 1 so , 10 ^ 40 - 79 = 9999999 . . . . ( 40 times ) + 1 - 79 = 9999999 . . . . ( 40 times ) - 78 consider the last 2 digits , 99 - 78 = 21 the last 2 digits will be 21 . and our number would be 99999 . . . . . . 99921 with 2 less 9 s after subtraction . number of 9 s left are 38 and the last two digits are 21 the sum of the digits will be ( 38 * 9 ) + 2 + 1 = 345 answer : - a" | general |
math_qa__bpHVCNzfdoakblhm | By investing in 16 % stock at 64, one earns Rs. 1500. The investment made is:
Choose the correct choice from the following choices
A) 5760 B) 7667 C) 4445 D) 4566 E) 3344 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 8</gadget>
<output>64</output>
<gadget id="calculator">64 * 3</gadget>
<output>192</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">192 / 50</gadget>
<output>96/25 = around 3.84</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">1_500 - 400</gadget>
<output>1_100</output>
<gadget id="calculator">(96/25) * 1_100</gadget>
<output>4_224</output>
<result>C</result> | C | 4,445 | By investing in 16 % stock at 64, one earns Rs. 1500. The investment made is: | {
"A": "5760",
"B": "7667",
"C": "4445",
"D": "4566",
"E": "3344"
} | multiply(divide(multiply(multiply(multiply(const_4, const_2), multiply(const_4, const_2)), const_3), divide(const_100, const_2)), subtract(1500, multiply(const_4, const_100))) | divide(const_100,const_2)|multiply(const_2,const_4)|multiply(const_100,const_4)|multiply(#1,#1)|subtract(n2,#2)|multiply(#3,const_3)|divide(#5,#0)|multiply(#6,#4)| | "explanation : to earn rs . , investment = rs . 64 . to earn rs . 1500 , investment = = rs . 5760 . answer : c ) 5760" | gain |
math_qa__DWvzjFfkZCA5OVOB | If 80 percent of 600 is 50 percent of x, then x=? Choices.
A) 960 B) 1000 C) 1020 D) 1080 E) 1075 | <gadget id="calculator">80 * 600</gadget>
<output>48_000</output>
<gadget id="calculator">48_000 / 50</gadget>
<output>960</output>
<result>A</result> | A | 960 | If 80 percent of 600 is 50 percent of x, then x=? | {
"A": "960",
"B": "1000",
"C": "1020",
"D": "1080",
"E": "1075"
} | divide(multiply(80, 600), 50) | multiply(n0,n1)|divide(#0,n2) | 0.8 * 600 = 0.5 * x x = 8 / 5 * 600 = 960 | general |
math_qa__8wUO8ygolw97iK16 | If a2 + b2 + c2 = 560 and ab + bc + ca =8, then a + b + c is Pick one:
A) 4 B) 52 C) 16 D) 24 E) 64 | <gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">560 + 16</gadget>
<output>576</output>
<gadget id="calculator">576 ** (1/2)</gadget>
<output>24</output>
<result>D</result> | D | 24 | If a2 + b2 + c2 = 560 and ab + bc + ca =8, then a + b + c is | {
"A": "4",
"B": "52",
"C": "16",
"D": "24",
"E": "64"
} | sqrt(add(560, multiply(8, 2))) | multiply(n4,n0)|add(n3,#0)|sqrt(#1)| | "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 560 and ab + bc + ca = 8 , ( a + b + c ) ^ 2 = 560 + 2 ( 8 ) = 576 = 24 ^ 2 therefore : a + b + c = 24 answer : d" | general |
math_qa__woJm8jcMtv63cgEG | A man whose speed is 6.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey ? Select:
A) 1 kmph
B) 5 kmph
C) 5.5 kmph
D) 4 kmph
E) 7 kmph | <gadget id="calculator">6.5 - 2.5</gadget>
<output>4</output>
<gadget id="calculator">6.5 + 4</gadget>
<output>10.5</output>
<gadget id="calculator">10.5 / 2</gadget>
<output>5.25</output>
<result>C</result> | C | 5.5 | A man whose speed is 6.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey ? | {
"A": "1 kmph",
"B": "5 kmph",
"C": "5.5 kmph",
"D": "4 kmph",
"E": "7 kmph"
} | divide(add(6.5, subtract(6.5, 2.5)), const_2) | subtract(n0,n1)|add(n0,#0)|divide(#1,const_2)| | "explanation : speed of man = 6.5 kmph speed of stream = 2.5 kmph speed in downstream = 9 kmph speed in upstream = 4 kmph average speed = ( 2 x 9 x 4 ) / 13 = 5.5 kmph . answer : c" | general |
math_qa__DQnoSW0DCjFHYUtK | A and B can do a work in 8 days, B and C can do the same work in 12 days. A,B and C together can finish it in 6 days. A and C together will do it in how many days? Choose the correct choice from the following options
A) 7
B) 6
C) 5
D) 8
E) 9 | <gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">8 * 6</gadget>
<output>48</output>
<gadget id="calculator">48 / 6</gadget>
<output>8</output>
<result>D</result> | D | 8 | A and B can do a work in 8 days, B and C can do the same work in 12 days. A,B and C together can finish it in 6 days. A and C together will do it in how many days? | {
"A": "7",
"B": "6",
"C": "5",
"D": "8",
"E": "9"
} | divide(multiply(8, add(divide(8, const_2), const_2)), 6) | divide(n0,const_2)|add(#0,const_2)|multiply(n0,#1)|divide(#2,n2)| | "let the total units of work be 48 . units of work completed by a and b in one day = 6 . units of work completed by b and c in one day = 4 units of work completed by a , b , and c in one day = 8 . from the above information we get the work completed by a and c in one day is 6 units . therefore , the number of days taken by a and c to complete the whole work = 48 / 6 = 8 days . answer : d" | physics |
math_qa__dIzyO4EbrBHWA4Mn | The percentage increase in the area of rectangle , if each of its side is increased by 10% is?
Choose the correct choice from the following choices:
A) 21 % B) 30 % C) 25 % D) 40 % E) 50 % | <gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) * (11/10)</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">(121/100) - 1</gadget>
<output>21/100 = around 0.21</output>
<gadget id="calculator">(21/100) * 100</gadget>
<output>21</output>
<result>A</result> | A | 21 | The percentage increase in the area of rectangle , if each of its side is increased by 10% is? | {
"A": "21 %",
"B": "30 %",
"C": "25 %",
"D": "40 %",
"E": "50 %"
} | multiply(subtract(multiply(divide(add(const_100, 10), const_100), divide(add(const_100, 10), const_100)), const_1), const_100) | add(n0,const_100)|divide(#0,const_100)|multiply(#1,#1)|subtract(#2,const_1)|multiply(#3,const_100)| | "let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 110 x / 100 new breadth = 110 y / 100 = 11 y / 10 new area = 11 x / 10 * 11 y / 10 = 121 xy / 100 m ^ 2 increase percent = 21 xy / 100 * 1 / xy * 100 = 21 % answer is a" | geometry |
math_qa__OIG0PW5TnkgQbfRO | A fill pipe can fill 1/2 of cistern in 35 minutes. In how many minutes, it can fill 1/2 of the cistern?
Select.
A) 20 min
B) 25 min
C) 30 min
D) 35 min
E) 40 min | <gadget id="calculator">35 / 1</gadget>
<output>35</output>
<result>D</result> | D | 35 | A fill pipe can fill 1/2 of cistern in 35 minutes. In how many minutes, it can fill 1/2 of the cistern? | {
"A": "20 min",
"B": "25 min",
"C": "30 min",
"D": "35 min",
"E": "40 min"
} | divide(35, 1) | divide(n2,n0)| | "required time = 35 * 2 * 1 / 2 = 20 minutes answer is d" | physics |
math_qa__nqwkctE12NTTvc4z | The diameter of a cylindrical tin is 6cm and height is 5 cm. Find the volume of the cylinder? Choose the correct option
A) 33 B) 45 C) 66 D) 77 E) 21 | <gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">pi * (3 ** 2) * 5</gadget>
<output>45*pi = around 141.371669</output>
<gadget id="calculator">(45*pi) / pi</gadget>
<output>45</output>
<result>B</result> | B | 45 | The diameter of a cylindrical tin is 6cm and height is 5 cm. Find the volume of the cylinder? | {
"A": "33",
"B": "45",
"C": "66",
"D": "77",
"E": "21"
} | divide(volume_cylinder(divide(6, const_2), 5), const_pi) | divide(n0,const_2)|volume_cylinder(#0,n1)|divide(#1,const_pi) | r = 3 h = 5 π * 3 * 3 * 5 = 45 π cc answer : b | geometry |
math_qa__cW1jlHsdAnofNmx9 | B completes a work in 9 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days?
Choose the most appropriate option
A) 3.75 days B) 4.73 days C) 5.75 days D) 6.75 days E) 7.73 days | <gadget id="calculator">10 * 9</gadget>
<output>90</output>
<gadget id="calculator">9 + 10</gadget>
<output>19</output>
<gadget id="calculator">90 / 19</gadget>
<output>90/19 = around 4.736842</output>
<result>B</result> | B | 4.73 | B completes a work in 9 days. A alone can do it in 10 days. If both work together, the work can be completed in how many days? | {
"A": "3.75 days",
"B": "4.73 days",
"C": "5.75 days",
"D": "6.75 days",
"E": "7.73 days"
} | divide(multiply(10, 9), add(9, 10)) | add(n0,n1)|multiply(n0,n1)|divide(#1,#0)| | "1 / 9 + 1 / 10 = 19 / 90 90 / 19 = 4.73 days answer : b" | physics |
math_qa__oQv6o8n8FGD15kh0 | The number of sailors on a ship is 80% more than the number of officers. The ratio of sailors to officers would be Pick one:
A) 33 : 25
B) 9 : 5
C) 47 : 25
D) 22 : 25
E) 97 : 50 | <gadget id="calculator">80 + 100</gadget>
<output>180</output>
<gadget id="calculator">180 / 100</gadget>
<output>9/5 = around 1.8</output>
<result>B</result> | B | 1.8 | The number of sailors on a ship is 80% more than the number of officers. The ratio of sailors to officers would be | {
"A": "33 : 25",
"B": "9 : 5",
"C": "47 : 25",
"D": "22 : 25",
"E": "97 : 50"
} | divide(add(80, const_100), const_100) | add(n0,const_100)|divide(#0,const_100)| | "sailor = 1.80 * officer sailor / officer = 1.80 / 1 = 180 / 100 = 9 / 5 answer will be b" | other |
math_qa__eYZwyX9aYVQiPKRd | A small college reduced its faculty by approximately 20 percent to 195 professors. What was the original number of faculty members?
Choose the correct choice from the following answers
A) 182 B) 208 C) 224 D) 254 E) 244 | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">195 / (4/5)</gadget>
<output>975/4 = around 243.75</output>
<result>E</result> | E | 244 | A small college reduced its faculty by approximately 20 percent to 195 professors. What was the original number of faculty members? | {
"A": "182",
"B": "208",
"C": "224",
"D": "254",
"E": "244"
} | divide(195, divide(subtract(const_100, 20), const_100)) | subtract(const_100,n0)|divide(#0,const_100)|divide(n1,#1)| | "if x is the original number of faculty members , then after 20 % reduction in faculty members number is . 80 x but we are given . 80 x = 195 x = 244 so the original number of faculty members is 244 correct answer - e" | gain |
math_qa__bVR6LAKqkNxsCNxv | The arithmetic mean and standard deviation of a certain normal distribution are 15.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean? Choose the correct choice from the following choices
A) 10.5 B) 11 C) 11.5 D) 12 E) 12.5 | <gadget id="calculator">2 * 1.5</gadget>
<output>3</output>
<gadget id="calculator">15.5 - 3</gadget>
<output>12.5</output>
<result>E</result> | E | 12.5 | The arithmetic mean and standard deviation of a certain normal distribution are 15.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean? | {
"A": "10.5",
"B": "11",
"C": "11.5",
"D": "12",
"E": "12.5"
} | subtract(15.5, multiply(2, 1.5)) | multiply(n1,n2)|subtract(n0,#0)| | "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 15.5 - 2 * 1.5 = 12.5 . answer : e ." | general |
math_qa__PNfTWNcPKaR2o6dQ | A circle is inscribed in a Triangle of side 6cm. And a square is inscribed in the Circle. What is the area of square? Choose the correct choice from the following options.
A) 4 cm ^ 2 B) 6 cm ^ 2 C) 5 cm ^ 2 D) 7 cm ^ 2 E) 8 cm ^ 2 | <gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<result>B</result> | B | 6 | A circle is inscribed in a Triangle of side 6cm. And a square is inscribed in the Circle. What is the area of square? | {
"A": "4 cm ^ 2",
"B": "6 cm ^ 2",
"C": "5 cm ^ 2",
"D": "7 cm ^ 2",
"E": "8 cm ^ 2"
} | sqrt(multiply(6, 6)) | multiply(n0,n0)|sqrt(#0) | the radius of the incircle in a equilateral triangle is a / 2 ( sqrt ) 3 where a = side of triangle = 6 cm so the diameter of the circle would be the diagonal of square so diagonal = 2 * a / 2 ( sqrt ) 3 = a / ( sqrt ) 3 so area of square = 1 / 2 * ( diagonal ) ^ 2 = 6 * 6 / 2 * 3 = 6 cm ^ 2 answer : b | geometry |
math_qa__2GWU8N7Htgsp6VqR | Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 60 km and the other at the rate of 90 kmph. In what time will they be completely clear of each other from the moment they meet? Answers: A) 4.85 B) 7.85 C) 6.85 D) 5.85 E) 6.62 | <gadget id="calculator">111 + 165</gadget>
<output>276</output>
<gadget id="calculator">60 + 90</gadget>
<output>150</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">150 * (5/18)</gadget>
<output>125/3 = around 41.666667</output>
<gadget id="calculator">276 / (125/3)</gadget>
<output>828/125 = around 6.624</output>
<result>E</result> | E | 6.62 | Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 60 km and the other at the rate of 90 kmph. In what time will they be completely clear of each other from the moment they meet? | {
"A": "4.85",
"B": "7.85",
"C": "6.85",
"D": "5.85",
"E": "6.62"
} | divide(add(111, 165), multiply(add(60, 90), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | "t = ( 111 + 165 ) / ( 60 + 90 ) * 18 / 5 t = 6.62 answer : e" | physics |
math_qa__lWGpK9j2xLJOnMRk | All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? Choose the correct choice
A) 1184 B) 1723 C) 1129 D) 2613 E) 1372 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">62.5 / 100</gadget>
<output>0.625</output>
<gadget id="calculator">1 - 0.625</gadget>
<output>0.375</output>
<gadget id="calculator">(1/2) - 0.375</gadget>
<output>0.125</output>
<gadget id="calculator">148 / 0.125</gadget>
<output>1_184</output>
<result>A</result> | A | 1,184 | All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A? | {
"A": "1184",
"B": "1723",
"C": "1129",
"D": "2613",
"E": "1372"
} | divide(148, subtract(inverse(const_2), subtract(const_1, divide(62.5, const_100)))) | divide(n0,const_100)|inverse(const_2)|subtract(const_1,#0)|subtract(#1,#2)|divide(n1,#3)| | "a 1184 b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 148 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 148 = 3 k + 148 = > 2 k = 296 = > k = 148 the initial quantity of milk in a = 8 k = 8 * 148 = 1184 liters ." | general |
math_qa__VvoYWEkQFB8pUdvK | In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, the dividend is Choose the most appropriate option
A) 5336
B) 4306
C) 4236
D) 4336
E) none | <gadget id="calculator">5 * 46</gadget>
<output>230</output>
<gadget id="calculator">230 / 10</gadget>
<output>23</output>
<gadget id="calculator">230 * 23</gadget>
<output>5_290</output>
<result>A</result> | A | 5,336 | In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, the dividend is | {
"A": "5336",
"B": "4306",
"C": "4236",
"D": "4336",
"E": "none"
} | multiply(multiply(5, 46), divide(multiply(5, 46), 10)) | multiply(n1,n2)|divide(#0,n0)|multiply(#1,#0) | sol . divisor = ( 5 × 46 ) = 230 . also , 10 × q = 230 ⇒ q = 23 . and , r = 46 . dividend = ( 230 × 23 + 46 ) = 5336 . answer a | general |
math_qa__ULpwfV0og2bVzpcG | In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy. Pick:
A) 8.8 % B) 9 % C) 9.2 % D) 9.1 % E) 8.4 % | <gadget id="calculator">12 * 15</gadget>
<output>180</output>
<gadget id="calculator">180 / 100</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">8 * 40</gadget>
<output>320</output>
<gadget id="calculator">320 / 100</gadget>
<output>16/5 = around 3.2</output>
<gadget id="calculator">(9/5) + (16/5)</gadget>
<output>5</output>
<gadget id="calculator">15 + 40</gadget>
<output>55</output>
<gadget id="calculator">5 / 55</gadget>
<output>1/11 = around 0.090909</output>
<gadget id="calculator">(1/11) * 100</gadget>
<output>100/11 = around 9.090909</output>
<result>D</result> | D | 9.1 | In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy. | {
"A": "8.8 %",
"B": "9 %",
"C": "9.2 %",
"D": "9.1 %",
"E": "8.4 %"
} | multiply(divide(add(divide(multiply(12, 15), const_100), divide(multiply(8, 40), const_100)), add(15, 40)), const_100) | add(n2,n3)|multiply(n0,n2)|multiply(n1,n3)|divide(#1,const_100)|divide(#2,const_100)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)| | "the amount of chromium in the new 15 + 40 = 55 kg alloy is 0.12 * 15 + 0.08 * 40 = 5 kg , so the percentage is 5 / 55 * 100 = 9.1 % . answer : d ." | gain |
math_qa__OmZmzfxxbKqrFLmM | The owner of a furniture shop charges his customer 15% more than the cost price. If a customer paid Rs. 5750 for a computer table, then what was the cost price of the computer table? Choose the correct choice from the following answers:
A) 2299
B) 2699
C) 2670
D) 6725
E) 5000 | <gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">5_750 / (23/20)</gadget>
<output>5_000</output>
<result>E</result> | E | 5,000 | The owner of a furniture shop charges his customer 15% more than the cost price. If a customer paid Rs. 5750 for a computer table, then what was the cost price of the computer table? | {
"A": "2299",
"B": "2699",
"C": "2670",
"D": "6725",
"E": "5000"
} | divide(5750, add(const_1, divide(15, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | "cp = sp * ( 100 / ( 100 + profit % ) ) = 5750 ( 100 / 115 ) = rs . 5000 answer : e" | gain |
math_qa__rufextG67NJJiABw | On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on october 1 than were in stock on January 1? Choose the correct answer.
A) 8 B) 12 C) 20 D) 32 E) 36 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 4</gadget>
<output>36</output>
<result>E</result> | E | 36 | On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on october 1 than were in stock on January 1? | {
"A": "8",
"B": "12",
"C": "20",
"D": "32",
"E": "36"
} | multiply(subtract(const_10, const_1), 4) | subtract(const_10,const_1)|multiply(n1,#0) | jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 oct 1 = c - 36 difference between stock on october 1 than were in stock on january 1 will be - c - ( c - 36 ) = 36 hence answer will be ( e ) | gain |
math_qa__qmkpbEf63kHoroOF | The speed at which a man can row a boat in still water is 9.5 kmph. If he rows downstream, where the speed of current is 8.5 kmph, what time will he take to cover 45.5 metres? Pick:
A) 18 seconds B) 8.4 seconds C) 5 seconds D) 9.1 seconds E) 9.5 econds | <gadget id="calculator">9.5 + 8.5</gadget>
<output>18</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">18 * (5/18)</gadget>
<output>5</output>
<gadget id="calculator">45.5 / 5</gadget>
<output>9.1</output>
<result>D</result> | D | 9.1 | The speed at which a man can row a boat in still water is 9.5 kmph. If he rows downstream, where the speed of current is 8.5 kmph, what time will he take to cover 45.5 metres? | {
"A": "18 seconds",
"B": "8.4 seconds",
"C": "5 seconds",
"D": "9.1 seconds",
"E": "9.5 econds"
} | divide(45.5, multiply(add(9.5, 8.5), const_0_2778)) | add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1)| | "speed of the boat downstream = 9.5 + 8.5 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 45.5 m = 45.5 / 5 = 9.1 seconds . answer : d" | physics |
math_qa__a4wz6ktWW4ijRyEz | In what time will a railway train 65 m long moving at the rate of 36 kmph pass a telegraph post on its way? Choose one: A) 8 sec B) 7 sec C) 2 sec D) 6.5 sec E) 9 sec | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">65 / 10</gadget>
<output>13/2 = around 6.5</output>
<result>D</result> | D | 6.5 | In what time will a railway train 65 m long moving at the rate of 36 kmph pass a telegraph post on its way? | {
"A": "8 sec",
"B": "7 sec",
"C": "2 sec",
"D": "6.5 sec",
"E": "9 sec"
} | divide(65, multiply(36, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | "t = 65 / 36 * 18 / 5 = 6.5 sec answer : d" | physics |
math_qa__F4dirvc2kjlZuPCa | Of 70 players on a football team, 46 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? Choose the correct option: A) 54 B) 59 C) 63 D) 71 E) 62 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">70 - 46</gadget>
<output>24</output>
<gadget id="calculator">(2/3) * 24</gadget>
<output>16</output>
<gadget id="calculator">16 + 46</gadget>
<output>62</output>
<result>E</result> | E | 62 | Of 70 players on a football team, 46 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? | {
"A": "54",
"B": "59",
"C": "63",
"D": "71",
"E": "62"
} | add(multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 46)), 46) | divide(const_1,const_3)|subtract(n0,n1)|subtract(const_1,#0)|multiply(#2,#1)|add(n1,#3)| | "total = 70 thrower = 46 rest = 70 - 46 = 24 left handed = 24 / 3 = 8 right handed = 16 if all thrower are right handed then total right handed is 46 + 16 = 62 so e . 62 is the right answer" | general |
math_qa__zjOwLC7HiNCA4WhG | How many minutes will it take for a car that is traveling at a constant rate of 9 miles per hour to travel a distance of 106 yards? (1 mile = 1,160 yards)
Choose the correct choice from the following choices:
A) 2
B) 5
C) 4
D) 3.61
E) 4.3 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 100</gadget>
<output>700</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">700 + 60</gadget>
<output>760</output>
<gadget id="calculator">760 + 1_000</gadget>
<output>1_760</output>
<gadget id="calculator">106 / 1_760</gadget>
<output>53/880 = around 0.060227</output>
<gadget id="calculator">(53/880) * 60</gadget>
<output>159/44 = around 3.613636</output>
<result>D</result> | D | 3.61 | How many minutes will it take for a car that is traveling at a constant rate of 9 miles per hour to travel a distance of 106 yards? (1 mile = 1,160 yards) | {
"A": "2",
"B": "5",
"C": "4",
"D": "3.61",
"E": "4.3"
} | multiply(divide(106, add(add(multiply(add(const_3, const_4), const_100), multiply(multiply(const_2, const_3), const_10)), const_1000)), const_60) | add(const_3,const_4)|multiply(const_2,const_3)|multiply(#0,const_100)|multiply(#1,const_10)|add(#2,#3)|add(#4,const_1000)|divide(n1,#5)|multiply(#6,const_60) | speed = 9 miles / hr = 4.4 yard / s = 29.33 yards / min distance = 106 yards time = distance / speed = 106 / 29.33 = 3.61 minutes ans - d | physics |
math_qa__tgMRKzFDyvGbWWRF | 5^100 is divided by 18 then what is the remainder? Options
A) 10 B) 11 C) 13 D) 15 E) 16 | <gadget id="calculator">18 - 5</gadget>
<output>13</output>
<result>C</result> | C | 13 | 5^100 is divided by 18 then what is the remainder? | {
"A": "10",
"B": "11",
"C": "13",
"D": "15",
"E": "16"
} | subtract(18, 5) | subtract(n2,n0) | here n = 18 = 2 × 32 ϕ ( 18 ) = 18 ( 1 − 12 ) ( 1 − 13 ) = 6 so 56 when divided by 18 , remainder is 1 . so we can write the given expression 5100 = ( 56 ) 16 × 54 = ( 1 ) 16 × 54 = 52 × 52 = 7 × 7 = 49 now 49 when divided by 18 , remainder is 13 . c | general |
math_qa__mQsZNG7FwXrcweOH | If (A+B) = 4, (B+C) = 7 and (C+D) = 5, what is the value of (A+D)? Choices:
A) 16 .
B) 8 .
C) 7 .
D) 2 .
E) - 2 . | <gadget id="calculator">4 + 5</gadget>
<output>9</output>
<gadget id="calculator">9 - 7</gadget>
<output>2</output>
<result>D</result> | D | 2 | If (A+B) = 4, (B+C) = 7 and (C+D) = 5, what is the value of (A+D)? | {
"A": "16 .",
"B": "8 .",
"C": "7 .",
"D": "2 .",
"E": "- 2 ."
} | subtract(add(4, 5), 7) | add(n0,n2)|subtract(#0,n1)| | "given a + b = 4 b + c = 7 c + d = 5 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 4 - 7 + 5 = 2 . option d . . ." | general |
math_qa__fWDfZrorim3AiPrJ | A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 20 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s) Select the correct option: A) 4200 B) 5400 C) 6600 D) 7800 E) 8900 | <gadget id="calculator">330 * 20</gadget>
<output>6_600</output>
<result>C</result> | C | 6,600 | A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 20 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s) | {
"A": "4200",
"B": "5400",
"C": "6600",
"D": "7800",
"E": "8900"
} | multiply(330, 20) | multiply(n1,n3)| | "the distance the sound traveled to the man is 20 * 330 = 6600 meters the answer is c ." | physics |
math_qa__MFETzmZFxJ9BwcR7 | If the area of a triangle with base 6 cm is equal to the area of a square with side 6 cm, then the altitude of the triangle is Pick.
A) 12 cm B) 10 cm C) 11 cm D) 15 cm E) 20 cm | <gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">36 * 2</gadget>
<output>72</output>
<gadget id="calculator">72 / 6</gadget>
<output>12</output>
<result>A</result> | A | 12 | If the area of a triangle with base 6 cm is equal to the area of a square with side 6 cm, then the altitude of the triangle is | {
"A": "12 cm",
"B": "10 cm",
"C": "11 cm",
"D": "15 cm",
"E": "20 cm"
} | divide(multiply(square_area(6), const_2), 6) | square_area(n0)|multiply(#0,const_2)|divide(#1,n0) | area of square = 6 ^ 2 = 36 area of triangle = 36 1 / 2 bh = 36 h = 12 cm answer a | geometry |
math_qa__GiPq5bB7dLC3euEm | Walking at 3/4 of his usual place, a man reaches his office 20 minute late. Find his usual time?
Choose the correct choice from the following choices
A) 2 hr B) 1 hr C) 3 hr D) 1.5 hr E) 2.5 hr | <gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<gadget id="calculator">15 * 4</gadget>
<output>60</output>
<gadget id="calculator">60 * 2</gadget>
<output>120</output>
<gadget id="calculator">120 / 60</gadget>
<output>2</output>
<result>A</result> | A | 2 | Walking at 3/4 of his usual place, a man reaches his office 20 minute late. Find his usual time? | {
"A": "2 hr",
"B": "1 hr",
"C": "3 hr",
"D": "1.5 hr",
"E": "2.5 hr"
} | divide(multiply(multiply(divide(multiply(20, 3), 4), 4), const_2), const_60) | multiply(n0,n2)|divide(#0,n1)|multiply(n1,#1)|multiply(#2,const_2)|divide(#3,const_60) | let the original speed be s and time be t if new speed = s ã — 3 / 4 , then new time would be t ã — 4 / 3 ( d = st = constant ) . given , 3 t / 4 â ˆ ’ t = 20 t / 3 â ‡ ’ t = 60 minutes = 1 hour answer : a | physics |
math_qa__DP74nOEVHh145RnE | Andrew travelling to 7 cities. Gasoline prices varied from city to city. $1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.86. What is the median gasoline price?
Choose the correct choice from the following choices
A) $ 1 B) $ 1.86 C) $ 1.92 D) $ 2.13 E) $ 2.15 | <gadget id="calculator">1.75 + 1.61</gadget>
<output>3.36</output>
<gadget id="calculator">3.36 + 1.79</gadget>
<output>5.15</output>
<gadget id="calculator">5.15 + 2.11</gadget>
<output>7.26</output>
<gadget id="calculator">7.26 + 1.96</gadget>
<output>9.22</output>
<gadget id="calculator">9.22 + 2.09</gadget>
<output>11.31</output>
<gadget id="calculator">11.31 + 1.86</gadget>
<output>13.17</output>
<gadget id="calculator">13.17 / 7</gadget>
<output>1.881429</output>
<gadget id="calculator">min(1.881429, 1.86)</gadget>
<output>1.86</output>
<result>B</result> | B | 1.86 | Andrew travelling to 7 cities. Gasoline prices varied from city to city. $1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.86. What is the median gasoline price? | {
"A": "$ 1",
"B": "$ 1.86",
"C": "$ 1.92",
"D": "$ 2.13",
"E": "$ 2.15"
} | min(divide(add(add(add(add(add(add(1.75, 1.61), 1.79), 2.11), 1.96), 2.09), 1.86), 7), 1.86) | add(n1,n2)|add(n3,#0)|add(n4,#1)|add(n5,#2)|add(n6,#3)|add(n7,#4)|divide(#5,n0)|min(n7,#6)| | "ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.86 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.86 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b" | general |
math_qa__Yqwbdclt0hLdJErF | A pump can fill a tank with water in 6 hours. Because of a leak, it took 12 hours to fill the tank. The leak can drain all the water in ?
Choices:
A) 12 hr B) 11 hr C) 13 hr D) 14 hr E) 16 hr | <gadget id="calculator">6 * 12</gadget>
<output>72</output>
<gadget id="calculator">12 - 6</gadget>
<output>6</output>
<gadget id="calculator">72 / 6</gadget>
<output>12</output>
<result>A</result> | A | 12 | A pump can fill a tank with water in 6 hours. Because of a leak, it took 12 hours to fill the tank. The leak can drain all the water in ? | {
"A": "12 hr",
"B": "11 hr",
"C": "13 hr",
"D": "14 hr",
"E": "16 hr"
} | divide(multiply(6, 12), subtract(12, 6)) | multiply(n0,n1)|subtract(n1,n0)|divide(#0,#1) | work done by the leak in 1 hour = 1 / 6 - 1 / 12 = 1 / 12 leak will empty the tank in 12 hours answer is a | physics |
math_qa__vV4zzT0YoaOlxtef | A container holding 15 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water. What is the ratio of alcohol to water in the resulting solution? Options.
A) 2 : 5 B) 3 : 7 C) 3 : 5 D) 4 : 7 E) 7 : 16 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">15 * (1/3)</gadget>
<output>5</output>
<gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">8 * (1/4)</gadget>
<output>2</output>
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">15 + 8</gadget>
<output>23</output>
<gadget id="calculator">23 - 7</gadget>
<output>16</output>
<gadget id="calculator">7 / 16</gadget>
<output>7/16 = around 0.4375</output>
<result>E</result> | E | 0.4375 | A container holding 15 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 8 ounces of a solution that is 1 part alcohol to 3 parts water. What is the ratio of alcohol to water in the resulting solution? | {
"A": "2 : 5",
"B": "3 : 7",
"C": "3 : 5",
"D": "4 : 7",
"E": "7 : 16"
} | divide(add(multiply(15, divide(1, add(1, 2))), multiply(8, divide(1, add(1, 3)))), subtract(add(15, 8), add(multiply(15, divide(1, add(1, 2))), multiply(8, divide(1, add(1, 3)))))) | add(n1,n2)|add(n1,n5)|add(n0,n3)|divide(n1,#0)|divide(n1,#1)|multiply(n0,#3)|multiply(n3,#4)|add(#5,#6)|subtract(#2,#7)|divide(#7,#8) | container 1 has 15 ounces in the ratio 1 : 2 or , x + 2 x = 15 gives x ( alcohol ) = 5 and remaining water = 10 container 2 has 8 ounces in the ratio 1 : 3 or , x + 3 x = 8 gives x ( alcohol ) = 2 and remaining water = 6 mixing both we have alcohol = 5 + 2 and water = 10 + 6 ratio thus alcohol / water = 7 / 16 answer e | other |
math_qa__cjKnPcPFNIc5w2ZX | How many plants will be there in a circular bed whose outer edge measure 31 cms, allowing 4 cm2 for each plant ? Choose the correct choice from the following
A) 19 B) 750 C) 24 D) 120 E) none of these | <gadget id="calculator">2 * pi</gadget>
<output>2*pi = around 6.283185</output>
<gadget id="calculator">31 / (2*pi)</gadget>
<output>31/(2*pi) = around 4.933803</output>
<gadget id="calculator">pi * ((31/(2*pi)) ** 2)</gadget>
<output>961/(4*pi) = around 76.47395</output>
<gadget id="calculator">(961/(4*pi)) / 4</gadget>
<output>961/(16*pi) = around 19.118488</output>
<result>A</result> | A | 19 | How many plants will be there in a circular bed whose outer edge measure 31 cms, allowing 4 cm2 for each plant ? | {
"A": "19",
"B": "750",
"C": "24",
"D": "120",
"E": "none of these"
} | divide(circle_area(divide(31, multiply(2, const_pi))), const_4) | multiply(n2,const_pi)|divide(n0,#0)|circle_area(#1)|divide(#2,const_4) | circumference of circular bed = 31 cm area of circular bed = ( 31 ) 2 â „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 31 ) 2 â „ 4 ï € ã · 4 = 19.11 = 19 ( approx ) answer a | physics |
math_qa__bXFVoF7hj0eWZbVu | 3 cannons are firing at a target . if their individual probabilities to hit the target are 0.5 , 0.2 , and 0.3 respectively , what is the probability that none of the cannons will hit the target after one round of fire ? prob . that all the cannons will hit the target = . 06 prob . that none of the cannons will hit = 1 - . 06 = . 94 Choose the correct choice from the following:
A) 0.06 B) 0.12 C) 0.21 D) 0.29 E) 0.28 | <gadget id="calculator">1 - 0.3</gadget>
<output>0.7</output>
<gadget id="calculator">1 - 0.2</gadget>
<output>0.8</output>
<gadget id="calculator">0.7 * 0.8</gadget>
<output>0.56</output>
<gadget id="calculator">1 - 0.5</gadget>
<output>0.5</output>
<gadget id="calculator">0.56 * 0.5</gadget>
<output>0.28</output>
<result>E</result> | E | 0.28 | 3 cannons are firing at a target . if their individual probabilities to hit the target are 0.5 , 0.2 , and 0.3 respectively , what is the probability that none of the cannons will hit the target after one round of fire ? prob . that all the cannons will hit the target = . 06 prob . that none of the cannons will hit = 1 - . 06 = . 94 | {
"A": "0.06",
"B": "0.12",
"C": "0.21",
"D": "0.29",
"E": "0.28"
} | multiply(multiply(subtract(const_1, 0.3), subtract(const_1, 0.2)), subtract(const_1, 0.5)) | subtract(const_1,n3)|subtract(const_1,n2)|subtract(const_1,n1)|multiply(#0,#1)|multiply(#3,#2) | the probability that eachdoesn ' thit is : 0.5 , 0.8 , and 0.7 . when we have multiple independent events , we multiply the probabilities : . 5 * . 8 * . 7 = 0.28 . option : e | general |
math_qa__Tzhr47Ik8nQKaSRU | If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 5000 in a long term bond that pays 4 percent interest, compounded annually, what will be the approximate total amount of investment 36 years later, when Pat is ready for college? Choose one:
A) $ 20000 B) $ 15000 C) $ 12000 D) $ 10000 E) $ 9000 | <gadget id="calculator">5_000 * 2</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 * 2</gadget>
<output>20_000</output>
<result>A</result> | A | 20,000 | If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 5000 in a long term bond that pays 4 percent interest, compounded annually, what will be the approximate total amount of investment 36 years later, when Pat is ready for college? | {
"A": "$ 20000",
"B": "$ 15000",
"C": "$ 12000",
"D": "$ 10000",
"E": "$ 9000"
} | multiply(multiply(5000, const_2), const_2) | multiply(n1,const_2)|multiply(#0,const_2)| | "since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 18 years investment will become $ 5,000 * 2 = $ 10,000 and in another 18 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a ." | general |
math_qa__ZA1Zln5mw9w7SJVG | If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability that this product will be a multiple of 45?
Choose the correct choice from the following answers.
A) 1 / 32 B) 1 / 28 C) 1 / 24 D) 1 / 16 E) 1 / 14 | <gadget id="calculator">20 + 4</gadget>
<output>24</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<result>C</result> | C | 0.041667 | If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability that this product will be a multiple of 45? | {
"A": "1 / 32",
"B": "1 / 28",
"C": "1 / 24",
"D": "1 / 16",
"E": "1 / 14"
} | divide(const_1, add(20, const_4)) | add(n1,const_4)|divide(const_1,#0) | there are 3 single digit multiple of 3 , that is , 3 , 69 . there are 8 prime nos less than 20 - 23 , 57 , 1113 , 1719 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability = 1 / 24 . answer c . | general |
math_qa__XbEw9mIBlwIh3vm2 | If p^2 – 13p + 40 = h, and p is a positive integer between 1 and 10, inclusive, what is the probability that h < 0? Choose the correct choice from the following choices
A) 1 / 10 B) 1 / 5 C) 2 / 5 D) 3 / 5 E) 3 / 10 | <gadget id="calculator">2 / 10</gadget>
<output>1/5 = around 0.2</output>
<result>B</result> | B | 0.2 | If p^2 – 13p + 40 = h, and p is a positive integer between 1 and 10, inclusive, what is the probability that h < 0? | {
"A": "1 / 10",
"B": "1 / 5",
"C": "2 / 5",
"D": "3 / 5",
"E": "3 / 10"
} | divide(const_2, 10) | divide(const_2,n4) | p 2 – 13 p + 40 = h so ( p – 8 ) ( p – 5 ) = h for q to be negative , the expressions ( p – 8 ) and ( p – 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p – 8 ) and ( p – 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer ) . that means that there are only two integer values for p , 6 and 7 , that would yield a negative q . with a total of 10 possible p values , only 2 yield a negative q , so the probability is 2 / 10 or 1 / 5 . the correct answer is b . | general |
math_qa__4oMBgesDZDdA3lXk | ABCD is a square where AB =√4004. Let X be a point on AB and Y be a point on CD such that AX = CY . Compute the area of trapezoid AXYD. Choose the correct choice: A) 3008 B) 2002 C) 1008 D) 2016 E) 3000 | <gadget id="calculator">4_004 / 2</gadget>
<output>2_002</output>
<result>B</result> | B | 2,002 | ABCD is a square where AB =√4004. Let X be a point on AB and Y be a point on CD such that AX = CY . Compute the area of trapezoid AXYD. | {
"A": "3008",
"B": "2002",
"C": "1008",
"D": "2016",
"E": "3000"
} | divide(4004, const_2) | divide(n0,const_2)| | "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4004 / 2 = 2002 . correct answer b" | geometry |
math_qa__oKLfghsOtn3pm5vt | Two-third of a positive number and 16/216 of its reciprocal are equal. The number is: Choose the most appropriate option: A) 5 / 12 B) 12 / 5 C) 1 / 3 D) 144 / 25 E) 146 / 25 | <gadget id="calculator">16 * 3</gadget>
<output>48</output>
<gadget id="calculator">216 * 2</gadget>
<output>432</output>
<gadget id="calculator">48 / 432</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/9) ** (1/2)</gadget>
<output>1/3 = around 0.333333</output>
<result>C</result> | C | 0.333333 | Two-third of a positive number and 16/216 of its reciprocal are equal. The number is: | {
"A": "5 / 12",
"B": "12 / 5",
"C": "1 / 3",
"D": "144 / 25",
"E": "146 / 25"
} | sqrt(divide(multiply(16, const_3), multiply(216, const_2))) | multiply(n0,const_3)|multiply(n1,const_2)|divide(#0,#1)|sqrt(#2) | let the number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 = 1 / 9 x = 1 / 3 answer : c | general |
math_qa__PJ4CBv8eJFxoLrOA | If x < y < z and y-x > 9, where x is an even integer and y and z are odd integers, what is the least possible value of z - x? Choose the correct choice from the following options:
A) 6 B) 7 C) 8 D) 13 E) 10 | <gadget id="calculator">9 + 2</gadget>
<output>11</output>
<gadget id="calculator">11 + 2</gadget>
<output>13</output>
<result>D</result> | D | 13 | If x < y < z and y-x > 9, where x is an even integer and y and z are odd integers, what is the least possible value of z - x? | {
"A": "6",
"B": "7",
"C": "8",
"D": "13",
"E": "10"
} | add(add(9, const_2), const_2) | add(n0,const_2)|add(#0,const_2) | we have : 1 ) x < y < z 2 ) y - x > 9 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 9 , the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 13 ( y - 2 = 11 , y = 13 ) 2 < 13 < z , since z is odd , the least possible value for z is 15 z - x = 15 - 2 = 13 answer d | general |
math_qa__Kr6iyym2J5JzPgq6 | A train running at the speed of 60 km/hr crosses a pole in 5 seconds. Find the length of the train. Choose the most appropriate option:
A) 83.33
B) 882
C) 772
D) 252
E) 121 | <gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 5</gadget>
<output>250/3 = around 83.333333</output>
<result>A</result> | A | 83.33 | A train running at the speed of 60 km/hr crosses a pole in 5 seconds. Find the length of the train. | {
"A": "83.33",
"B": "882",
"C": "772",
"D": "252",
"E": "121"
} | multiply(divide(multiply(60, const_1000), const_3600), 5) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 5 = 83.33 meter . answer : a" | physics |
math_qa__xko3GW9nuynWg9W8 | On a purchase of $118, a store offered a payment plan consisting of a $18 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan? Choose the correct choice from the following answers
A) 16.7 % B) 16.2 % C) 16.5 % D) 15.5 % E) 15.3 % | <gadget id="calculator">10 * 12</gadget>
<output>120</output>
<gadget id="calculator">120 + 18</gadget>
<output>138</output>
<gadget id="calculator">138 - 120</gadget>
<output>18</output>
<gadget id="calculator">18 / 118</gadget>
<output>9/59 = around 0.152542</output>
<gadget id="calculator">(9/59) * 100</gadget>
<output>900/59 = around 15.254237</output>
<result>E</result> | E | 15.3 | On a purchase of $118, a store offered a payment plan consisting of a $18 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan? | {
"A": "16.7 %",
"B": "16.2 %",
"C": "16.5 %",
"D": "15.5 %",
"E": "15.3 %"
} | multiply(divide(subtract(add(multiply(10, 12), 18), multiply(10, 12)), 118), const_100) | multiply(n2,n3)|add(n1,#0)|subtract(#1,#0)|divide(#2,n0)|multiply(#3,const_100)| | "12 * 10 + 18 = 138 ( 18 / 118 ) * 100 = 15.3 answer : e" | gain |
math_qa__Z9wLRkTzch2o2ETR | If 70 honey bees make 70 grams of honey in 70 days, then 1 honey bee will make 1 gram of honey in how many days?
Choose the correct answer
A) 1 B) 3.5 C) 20 D) 49 E) 70 | <gadget id="calculator">1 / 70</gadget>
<output>1/70 = around 0.014286</output>
<gadget id="calculator">1 / (1/70)</gadget>
<output>70</output>
<result>E</result> | E | 70 | If 70 honey bees make 70 grams of honey in 70 days, then 1 honey bee will make 1 gram of honey in how many days? | {
"A": "1",
"B": "3.5",
"C": "20",
"D": "49",
"E": "70"
} | divide(1, divide(1, 70)) | divide(n3,n0)|divide(n3,#0)| | "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 70 : : 70 : x honey 70 : 1 = > 1 x 70 x x = 70 x 1 x 70 = > x = 70 . answer : e" | physics |
math_qa__XDqhC8VzkuLHfC7b | 3 times the first of 3 consecutive odd integers is 3 more than twice the third . the third integer is ?
Choose the correct choice from the following answers:
A) 15 B) 17 C) 19 D) 21 E) 26 | <gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 + 3</gadget>
<output>11</output>
<gadget id="calculator">11 + 4</gadget>
<output>15</output>
<result>A</result> | A | 15 | 3 times the first of 3 consecutive odd integers is 3 more than twice the third . the third integer is ? | {
"A": "15",
"B": "17",
"C": "19",
"D": "21",
"E": "26"
} | add(add(multiply(const_2, const_4), 3), const_4) | multiply(const_2,const_4)|add(n0,#0)|add(#1,const_4) | let the three integers be x , x + 2 and x + 4 . then , 3 x = 2 ( x + 4 ) + 3 x = 11 . third integer = x + 4 = 15 . option a | general |
math_qa__xbegYLCaTImKH2kx | Two trains, each 100 m long, moving in opposite directions, cross other in 10 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Pick one
A) 76 km / hr B) 66 km / hr C) 48 km / hr D) 67 km / hr E) 22 km / hr | <gadget id="calculator">100 + 100</gadget>
<output>200</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">200 / 30</gadget>
<output>20/3 = around 6.666667</output>
<gadget id="calculator">(20/3) * 2</gadget>
<output>40/3 = around 13.333333</output>
<gadget id="calculator">(40/3) * 3_600</gadget>
<output>48_000</output>
<gadget id="calculator">48_000 / 1_000</gadget>
<output>48</output>
<result>C</result> | C | 48 | Two trains, each 100 m long, moving in opposite directions, cross other in 10 sec. If one is moving twice as fast the other, then the speed of the faster train is? | {
"A": "76 km / hr",
"B": "66 km / hr",
"C": "48 km / hr",
"D": "67 km / hr",
"E": "22 km / hr"
} | divide(multiply(multiply(divide(add(100, 100), multiply(10, add(const_1, const_2))), const_2), const_3600), const_1000) | add(n0,n0)|add(const_1,const_2)|multiply(n1,#1)|divide(#0,#2)|multiply(#3,const_2)|multiply(#4,const_3600)|divide(#5,const_1000) | let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 10 = 3 x = > x = 20 / 3 . so , speed of the faster train = 40 / 3 = 40 / 3 * 18 / 5 = 48 km / hr . answer : c | physics |
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