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stringlengths 6
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stringlengths 7
6.48k
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stringlengths 8
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math_qa__9SEZHh028R5lWlgG | The Tens digit of a two digit number is 4 times of its unit digit and the sum of the digits be 10. Then the first number is Choose the correct answer: A) 67 B) 73 C) 53 D) 82 E) 89 | <gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">10 / 5</gadget>
<output>2</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<result>D</result> | D | 82 | The Tens digit of a two digit number is 4 times of its unit digit and the sum of the digits be 10. Then the first number is | {
"A": "67",
"B": "73",
"C": "53",
"D": "82",
"E": "89"
} | multiply(multiply(4, divide(10, add(const_1, 4))), const_10) | add(n0,const_1)|divide(n1,#0)|multiply(n0,#1)|multiply(#2,const_10) | let the number be 10 x + y according to the question x = 4 y x + y = 10 4 y + y = 10 or y = 2 and x = 8 so required number is = 10 * 8 + 2 = 82 answer : d | general |
math_qa__At3H5h5BwzCUsGw3 | A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ? Pick one
A) 100 m B) 120 m C) 130 m D) 150 m E) none of these | <gadget id="calculator">3 / 60</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 1_000</gadget>
<output>50</output>
<gadget id="calculator">180 - 50</gadget>
<output>130</output>
<result>C</result> | C | 130 | A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 9 km per hour respectively. What is the distance between them after 3 minutes ? | {
"A": "100 m",
"B": "120 m",
"C": "130 m",
"D": "150 m",
"E": "none of these"
} | subtract(180, multiply(divide(3, const_60), const_1000)) | divide(n3,const_60)|multiply(#0,const_1000)|subtract(n0,#1) | explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 180 - 50 ) m = 130 m . answer : c | physics |
math_qa__kNH1bPyGPz8BKac4 | In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is Choose the correct answer:
A) 50 liters B) 55 liters C) 60 liters D) 70 liters E) 75 liters | <gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">80 - 20</gadget>
<output>60</output>
<result>C</result> | C | 60 | In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is | {
"A": "50 liters",
"B": "55 liters",
"C": "60 liters",
"D": "70 liters",
"E": "75 liters"
} | subtract(multiply(subtract(60, divide(60, add(2, 1))), 2), divide(60, add(2, 1))) | add(n1,n2)|divide(n0,#0)|subtract(n0,#1)|multiply(n1,#2)|subtract(#3,#1)| | "quantity of milk = 60 x 2 litres = 40 litres . 3 quantity of water in it = ( 60 - 40 ) litres = 20 litres . new ratio = 1 : 2 let quantity of water to be added further be x litres . then , milk : water = 40 . 20 + x now , 40 = 1 20 + x 2 20 + x = 80 x = 60 . quantity of water to be added = 60 liters . c" | general |
math_qa__pFca85j9SSkqNDVp | A 280 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.
Choose the most appropriate option.
A) 210 m B) 220 m C) 230 m D) 240 m E) 250 m | <gadget id="calculator">120 + 80</gadget>
<output>200</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">200 * (5/18)</gadget>
<output>500/9 = around 55.555556</output>
<gadget id="calculator">9 * (500/9)</gadget>
<output>500</output>
<gadget id="calculator">500 - 280</gadget>
<output>220</output>
<result>B</result> | B | 220 | A 280 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train. | {
"A": "210 m",
"B": "220 m",
"C": "230 m",
"D": "240 m",
"E": "250 m"
} | subtract(multiply(9, multiply(add(120, 80), const_0_2778)), 280) | add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)| | "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 280 / 9 = 500 / 9 x = 220 ans is 220 m answer : b" | physics |
math_qa__L0J0I7Ns3pqxDD6M | Find the average of all the numbers between 11 and 34 which are divisible by 5? Choose the correct choice
A) 10
B) 20
C) 22
D) 30
E) 15 | <gadget id="calculator">11 + 4</gadget>
<output>15</output>
<gadget id="calculator">34 - 4</gadget>
<output>30</output>
<gadget id="calculator">15 + 30</gadget>
<output>45</output>
<gadget id="calculator">45 / 2</gadget>
<output>45/2 = around 22.5</output>
<result>C</result> | C | 22 | Find the average of all the numbers between 11 and 34 which are divisible by 5? | {
"A": "10",
"B": "20",
"C": "22",
"D": "30",
"E": "15"
} | divide(add(add(11, const_4), subtract(34, const_4)), const_2) | add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)| | "average = ( 15 + 20 + 25 + 30 ) 4 = 90 / 4 = 22 answer is c" | general |
math_qa__NEqV7VxseYJl4yaf | X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of work. How long did the work last?
Choose the correct choice from the following options: A) 8 days B) 10 days C) 12 days D) 13 days E) 14 days | <gadget id="calculator">4 / 20</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">20 * (4/5)</gadget>
<output>16</output>
<gadget id="calculator">12 * 16</gadget>
<output>192</output>
<gadget id="calculator">20 + 12</gadget>
<output>32</output>
<gadget id="calculator">192 / 32</gadget>
<output>6</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<result>B</result> | B | 10 | X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of work. How long did the work last? | {
"A": "8 days",
"B": "10 days",
"C": "12 days",
"D": "13 days",
"E": "14 days"
} | add(4, divide(multiply(12, multiply(20, subtract(const_1, divide(4, 20)))), add(20, 12))) | add(n0,n1)|divide(n2,n0)|subtract(const_1,#1)|multiply(n0,#2)|multiply(n1,#3)|divide(#4,#0)|add(n2,#5)| | "let the total units of work to be completed be 60 . units of work completed by x in a single day = 60 / 20 = 3 units . units of work completed by y in a single day = 60 / 12 = 5 units . thus , 8 units of work can be done by them in a single day working together . x works for 4 days alone = 12 units of work . remaining work = ( 60 - 12 ) = 48 units . now , x and y works together to complete the remaining work = 48 / 8 = 6 days hence , total days taken to complete the work = ( 6 + 4 ) = 10 days . answer : b" | physics |
math_qa__WKRlyAK82ZqB7g0M | If an integer n is to be selected at random from 1 to 100, inclusive, what is probability n(n+1) will be divisible by 8? Pick one:
A) 1 / 4
B) 1 / 3
C) 1 / 2
D) 2 / 3
E) 3 / 4 | <gadget id="calculator">2 / 8</gadget>
<output>1/4 = around 0.25</output>
<result>A</result> | A | 0.25 | If an integer n is to be selected at random from 1 to 100, inclusive, what is probability n(n+1) will be divisible by 8? | {
"A": "1 / 4",
"B": "1 / 3",
"C": "1 / 2",
"D": "2 / 3",
"E": "3 / 4"
} | divide(const_2, 8) | divide(const_2,n3)| | "because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 1 * 1 / 4 = 1 / 4 answer : a" | general |
math_qa__axB1xCl40dG26lIN | Find the curved surface area, if the radius of a cone is 7 m and slant height is 14 m? Pick.
A) 308 B) 369 C) 434 D) 476 E) 513 | <gadget id="calculator">7 * 14</gadget>
<output>98</output>
<gadget id="calculator">pi * 98</gadget>
<output>98*pi = around 307.87608</output>
<result>A</result> | A | 308 | Find the curved surface area, if the radius of a cone is 7 m and slant height is 14 m? | {
"A": "308",
"B": "369",
"C": "434",
"D": "476",
"E": "513"
} | multiply(const_pi, multiply(7, 14)) | multiply(n0,n1)|multiply(#0,const_pi)| | "cone curved surface area = ï € rl 22 / 7 ã — 7 ã — 14 = 22 ã — 14 = 308 m ( power 2 ) answer is a ." | geometry |
math_qa__Jp1tMLufdMEmn4Be | If |x| = 9x-16, then x = ? Choose the correct choice from the following answers:
A) 1
B) 1 / 2
C) 2
D) 4
E) - 1 / 2 | <gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">16 / 8</gadget>
<output>2</output>
<result>C</result> | C | 2 | If |x| = 9x-16, then x = ? | {
"A": "1",
"B": "1 / 2",
"C": "2",
"D": "4",
"E": "- 1 / 2"
} | divide(16, subtract(9, const_1)) | subtract(n0,const_1)|divide(n1,#0) | substituted option c i . e x = 2 . inequality satisfied . this eliminates all options except answer is c | general |
math_qa__jPVGqwDPecLbadEI | Sonika deposited Rs.8000 which amounted to Rs.10200 after 3 years at simple interest. Had the interest been 2% more. She would get how much? Choose the most appropriate option
A) 9680 B) 10680 C) 2999 D) 2774 E) 1212 | <gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">10_200 - 8_000</gadget>
<output>2_200</output>
<gadget id="calculator">2_200 / 3</gadget>
<output>2_200/3 = around 733.333333</output>
<gadget id="calculator">(2_200/3) / 8_000</gadget>
<output>11/120 = around 0.091667</output>
<gadget id="calculator">(1/50) + (11/120)</gadget>
<output>67/600 = around 0.111667</output>
<gadget id="calculator">(67/600) * 8_000</gadget>
<output>2_680/3 = around 893.333333</output>
<gadget id="calculator">(2_680/3) * 3</gadget>
<output>2_680</output>
<gadget id="calculator">2_680 + 8_000</gadget>
<output>10_680</output>
<result>B</result> | B | 10,680 | Sonika deposited Rs.8000 which amounted to Rs.10200 after 3 years at simple interest. Had the interest been 2% more. She would get how much? | {
"A": "9680",
"B": "10680",
"C": "2999",
"D": "2774",
"E": "1212"
} | add(multiply(multiply(add(divide(2, const_100), divide(divide(subtract(10200, 8000), 3), 8000)), 8000), 3), 8000) | divide(n3,const_100)|subtract(n1,n0)|divide(#1,n2)|divide(#2,n0)|add(#0,#3)|multiply(n0,#4)|multiply(n2,#5)|add(n0,#6)| | "( 8000 * 3 * 2 ) / 100 = 480 10200 - - - - - - - - 10680 answer : b" | gain |
math_qa__tVbFXoqlBXxRCwn5 | The average monthly salary of 24 employees in an organisation is Rs. 2400. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary? Choose the correct answer
A) rs . 3601 B) rs . 3618 C) rs . 4900 D) rs . 3619 E) rs . 3610 | <gadget id="calculator">2_400 + 100</gadget>
<output>2_500</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">2_500 * 25</gadget>
<output>62_500</output>
<gadget id="calculator">2_400 * 24</gadget>
<output>57_600</output>
<gadget id="calculator">62_500 - 57_600</gadget>
<output>4_900</output>
<result>C</result> | C | 4,900 | The average monthly salary of 24 employees in an organisation is Rs. 2400. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary? | {
"A": "rs . 3601",
"B": "rs . 3618",
"C": "rs . 4900",
"D": "rs . 3619",
"E": "rs . 3610"
} | subtract(multiply(add(2400, 100), add(24, const_1)), multiply(2400, 24)) | add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | "manager ' s monthly salary = rs . ( 2500 * 25 - 2400 * 24 ) = rs . 4900 answer : c" | general |
math_qa__7l46vRryNjaKwzlb | The S.I. on a certain sum of money for 6 years at 16% per annum is half the C.I. on Rs. 8000 for 2 years at 20% per annum. The sum placed on S.I. is?
Choose the correct choice from the following choices.
A) 3000.33
B) 2802.33
C) 1833.33
D) 2990.33
E) 2982.33 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) ** 2</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">8_000 * (36/25)</gadget>
<output>11_520</output>
<gadget id="calculator">11_520 - 8_000</gadget>
<output>3_520</output>
<gadget id="calculator">3_520 / 2</gadget>
<output>1_760</output>
<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">6 * (4/25)</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">1_760 / (24/25)</gadget>
<output>5_500/3 = around 1_833.333333</output>
<result>C</result> | C | 1,833.33 | The S.I. on a certain sum of money for 6 years at 16% per annum is half the C.I. on Rs. 8000 for 2 years at 20% per annum. The sum placed on S.I. is? | {
"A": "3000.33",
"B": "2802.33",
"C": "1833.33",
"D": "2990.33",
"E": "2982.33"
} | divide(divide(subtract(multiply(8000, power(add(const_1, divide(20, const_100)), 2)), 8000), 2), multiply(6, divide(16, const_100))) | divide(n4,const_100)|divide(n1,const_100)|add(#0,const_1)|multiply(n0,#1)|power(#2,n3)|multiply(n2,#4)|subtract(#5,n2)|divide(#6,n3)|divide(#7,#3)| | c . i . = [ 8000 * ( 1 + 20 / 100 ) 2 - 8000 ] = ( 8000 * 6 / 5 * 6 / 5 - 8000 ) = rs . 3520 . sum = ( 3520 * 100 ) / ( 6 * 16 ) = rs . 1833.33 answer : c | gain |
math_qa__aZKYhf2umnrPZJhH | a techno company has 14 machines of equal efficiency in its factory . the annual manufacturing costs are rs 42000 and establishment charges are rs 12000 . the annual output of the company is rs 70000 . the annual output and manufacturing costs are directly proportional to the number of machines . the shareholders get 12.5 profit , which is directly proportional to the annual output of the company . if 7.14 machines remain closed throughout the year , then the percentage decrease in the amount of profit of the shareholders would be :
Choose the correct choice: A) 12 % B) 12.5 % C) 13.5 % D) 13 % E) 14 % | <gadget id="calculator">12.5 / 100</gadget>
<output>0.125</output>
<gadget id="calculator">70_000 - 42_000</gadget>
<output>28_000</output>
<gadget id="calculator">28_000 - 12_000</gadget>
<output>16_000</output>
<gadget id="calculator">0.125 * 16_000</gadget>
<output>2_000</output>
<gadget id="calculator">14 - 1</gadget>
<output>13</output>
<gadget id="calculator">13 / 14</gadget>
<output>13/14 = around 0.928571</output>
<gadget id="calculator">(13/14) * 28_000</gadget>
<output>26_000</output>
<gadget id="calculator">26_000 - 12_000</gadget>
<output>14_000</output>
<gadget id="calculator">14_000 * 0.125</gadget>
<output>1_750</output>
<gadget id="calculator">2_000 - 1_750</gadget>
<output>250</output>
<gadget id="calculator">250 / 2_000</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<result>B</result> | B | 12.5 | a techno company has 14 machines of equal efficiency in its factory . the annual manufacturing costs are rs 42000 and establishment charges are rs 12000 . the annual output of the company is rs 70000 . the annual output and manufacturing costs are directly proportional to the number of machines . the shareholders get 12.5 profit , which is directly proportional to the annual output of the company . if 7.14 machines remain closed throughout the year , then the percentage decrease in the amount of profit of the shareholders would be : | {
"A": "12 %",
"B": "12.5 %",
"C": "13.5 %",
"D": "13 %",
"E": "14 %"
} | multiply(divide(subtract(multiply(divide(12.5, const_100), subtract(subtract(70000, 42000), 12000)), multiply(subtract(multiply(divide(subtract(14, const_1), 14), subtract(70000, 42000)), 12000), divide(12.5, const_100))), multiply(divide(12.5, const_100), subtract(subtract(70000, 42000), 12000))), const_100) | divide(n4,const_100)|subtract(n3,n1)|subtract(n0,const_1)|divide(#2,n0)|subtract(#1,n2)|multiply(#0,#4)|multiply(#3,#1)|subtract(#6,n2)|multiply(#0,#7)|subtract(#5,#8)|divide(#9,#5)|multiply(#10,const_100) | explanation : the original profit is : - = > 70000 − 42000 − 12000 = 16000 . if 7.14 % of 14 i . e . one of the machines closed throughout the year , then the change in profit will be : - = > ( 13 / 14 ) × [ 70000 − 42000 ] . = > 14000 . thus , decrease in the profit % is : - = > ( 2000 / 16000 ) × 100 . = > 12.5 % . answer : b | general |
math_qa__JugNK2F6wM0lumVA | P and Q can complete a work in 80 days and 48 days respectively. P alone started the work and Q joined him after 8 days till the completion of the work. How long did the work last? Pick.
A) 35 days B) 10 days C) 14 days D) 22 days E) 26 days | <gadget id="calculator">8 / 80</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">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">1 / 48</gadget>
<output>1/48 = around 0.020833</output>
<gadget id="calculator">(1/80) + (1/48)</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(9/10) / (1/30)</gadget>
<output>27</output>
<gadget id="calculator">8 + 27</gadget>
<output>35</output>
<result>A</result> | A | 35 | P and Q can complete a work in 80 days and 48 days respectively. P alone started the work and Q joined him after 8 days till the completion of the work. How long did the work last? | {
"A": "35 days",
"B": "10 days",
"C": "14 days",
"D": "22 days",
"E": "26 days"
} | add(8, divide(subtract(const_1, divide(8, 80)), add(inverse(80), inverse(48)))) | divide(n2,n0)|inverse(n0)|inverse(n1)|add(#1,#2)|subtract(const_1,#0)|divide(#4,#3)|add(n2,#5)| | "explanation : work done by p in 1 day = 1 / 80 work done by q in 1 day = 1 / 48 work done by p in 8 days = 8 ã — ( 1 / 80 ) = 1 / 10 remaining work = 1 â € “ 1 / 10 = 9 / 10 work done by p and q in 1 day = 1 / 80 + 1 / 48 = 1 / 30 number of days p and q take to complete the remaining work = ( 9 / 10 ) / ( 1 / 30 ) = 27 total days = 8 + 27 = 35 answer : option a" | physics |
math_qa__e5mJrGpn3U80ZFax | A and B together can complete work in 6 days. A alone starts working and leaves it after working for 3 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?
Choose the correct answer.
A) 3 B) 8 C) 5 D) 6 E) 7 | <gadget id="calculator">3 / 6</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">6 * (1/2)</gadget>
<output>3</output>
<result>A</result> | A | 3 | A and B together can complete work in 6 days. A alone starts working and leaves it after working for 3 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B? | {
"A": "3",
"B": "8",
"C": "5",
"D": "6",
"E": "7"
} | multiply(6, divide(3, 6)) | divide(n1,n0)|multiply(n0,#0) | explanation : ( a + b ) one day work = 1 / 6 now a does half of the work in 3 days so a can complete the whole work in 6 days a ’ s one day work = 1 / 6 b ’ s one day work = 1 / 6 - 1 / 6 = 1 / 6 b alone can complete the work in 6 days so half of the work in 3 days answer : option a | physics |
math_qa__Gcd4JbwCpQyR8N00 | Two mixtures of A and B have A and B in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of A to B is 5:4? Pick one.
A) 6 : 1
B) 5 : 4
C) 20 : 7
D) 10 : 9
E) 14 : 11 | <gadget id="calculator">5 + 4</gadget>
<output>9</output>
<gadget id="calculator">5 / 9</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(5/9) - (3/7)</gadget>
<output>8/63 = around 0.126984</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) - (5/9)</gadget>
<output>2/45 = around 0.044444</output>
<gadget id="calculator">(8/63) / (2/45)</gadget>
<output>20/7 = around 2.857143</output>
<result>C</result> | C | 2.857143 | Two mixtures of A and B have A and B in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of A to B is 5:4? | {
"A": "6 : 1",
"B": "5 : 4",
"C": "20 : 7",
"D": "10 : 9",
"E": "14 : 11"
} | divide(subtract(divide(5, add(5, 4)), divide(const_3, add(3, 4))), subtract(divide(3, 5), divide(5, add(5, 4)))) | add(n3,n4)|add(n0,n3)|divide(n0,n4)|divide(n4,#0)|divide(const_3,#1)|subtract(#3,#4)|subtract(#2,#3)|divide(#5,#6) | i got c but with a different , yet slightly longer approach , which i constantly use for proportion problems such as this one . usually , this approach is very efficient when used with slightly difficult questions , but this problem is quite hard so i had to slightly tweak it . i will show you how i usually use the approach and later show you how to use it with this specific problem . example . 1 liter of solution a contains 45 % alcohol , while 1 liter of solution b contains 20 % alcohol . in what ratio must the two solutions be used to get a solution with 30 % alcohol solution : 1 . 45 / 100 * [ a / ( a + b ) ] + 20 / 100 * [ b / ( a + b ) ] = 30 / 100 2 . multiply 100 to both sides to arrive at 45 a / ( a + b ) + 20 b / ( a + b ) = 30 3 . multiply ( a + b ) to both sides to arrive at 45 a + 20 b = 30 a + 30 b 4 . distribute to arrive at 15 a = 10 b 5 . thus the ratio is a / b = 10 / 15 = 2 / 3 now using this same approach , we tackle gopu 106 ’ s question . it is important to first think of x in the mixture as the alcohol in the problem above ; hence , a mixture of x and y in the ratio of 3 : 2 translates to x is 3 / 5 of the solution . applying this concept to all three equations , we write : 1 . 3 / 5 * [ a / ( a + b ) ] + 3 / 7 * [ b / ( a + b ) ] = 5 / 9 2 . now here is the tweak that must be made to continue with this approach . you must find the common denominator for all three numbers and organize the fractions accordingly . by finding the common denominator of 5 , 79 ( or 315 ) we re - write the equations as follows 3 . 189 / 315 * [ a / ( a + b ) ] + 135 / 315 * [ b / ( a + b ) ] = 175 / 315 4 . multiply 315 to both sides to arrive at 189 a / ( a + b ) + 135 b / ( a + b ) = 175 5 . multiply ( a + b ) to both sides to arrive at 189 a + 135 b = 175 a + 175 b 6 . distribute to arrive at 14 a = 40 b 7 . thus the ratio is a / b = 40 / 14 = 20 / 7 or answer c | other |
math_qa__WqClB0ScS7UmRpXx | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 60 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ? Choices
A) 80 % B) 32 % C) 48 % D) 84 % E) 92 % | <gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<result>A</result> | A | 80 | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 60 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ? | {
"A": "80 %",
"B": "32 %",
"C": "48 %",
"D": "84 %",
"E": "92 %"
} | subtract(const_100, divide(subtract(const_100, 60), const_2)) | subtract(const_100,n0)|divide(#0,const_2)|subtract(const_100,#1)| | "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 60 % is one st . dev , then on either side of m we have 60 / 2 = 30 % . so , 30 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 30 = 80 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 80 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it a" | general |
math_qa__yq7dPGO297CUMstX | 8 kilograms of rice costing rs . 16 per kg is mixed with 4 kilograms of rice costing rs . 22 per kg . what is the average price of the mixture ? Choose the correct choice from the following answers.
A) 20
B) 18
C) 16
D) 19
E) 17 | <gadget id="calculator">22 * 4</gadget>
<output>88</output>
<gadget id="calculator">8 * 16</gadget>
<output>128</output>
<gadget id="calculator">88 + 128</gadget>
<output>216</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">216 / 12</gadget>
<output>18</output>
<result>B</result> | B | 18 | 8 kilograms of rice costing rs . 16 per kg is mixed with 4 kilograms of rice costing rs . 22 per kg . what is the average price of the mixture ? | {
"A": "20",
"B": "18",
"C": "16",
"D": "19",
"E": "17"
} | divide(add(multiply(22, 4), multiply(8, 16)), add(8, 4)) | add(n0,n2)|multiply(n2,n3)|multiply(n0,n1)|add(#1,#2)|divide(#3,#0) | p 1 = rs . 16 per kg , p 2 = rs . 22 per kg , q 1 = 8 kg , q 2 = 4 kg now , p = ( p 1 q 1 + p 2 q 2 ) / ( q 1 + q 2 ) average price of the mixture = 8 * 16 + 4 * 22 / 12 = 128 + 88 / 12 = 216 / 12 = 18 answer : b | general |
math_qa__nPDUMQVksdvUiRRP | The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 70 metres? Options:
A) 22 seconds
B) 65 seconds
C) 78 seconds
D) 12 seconds
E) 14 seconds | <gadget id="calculator">15 + 3</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">70 / 5</gadget>
<output>14</output>
<result>E</result> | E | 14 | The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 70 metres? | {
"A": "22 seconds",
"B": "65 seconds",
"C": "78 seconds",
"D": "12 seconds",
"E": "14 seconds"
} | divide(70, multiply(add(15, 3), const_0_2778)) | add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1)| | "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 70 / 5 = 14 seconds . answer : e" | physics |
math_qa__fGYyTXoq6CZFXwE2 | If the numbers 1 to 99 are written on 99 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite? Answers
A) 1 / 50 B) 1 / 25 C) 1 / 99 D) 1 E) 2 | <gadget id="calculator">1 / 99</gadget>
<output>1/99 = around 0.010101</output>
<result>C</result> | C | 0.010101 | If the numbers 1 to 99 are written on 99 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite? | {
"A": "1 / 50",
"B": "1 / 25",
"C": "1 / 99",
"D": "1",
"E": "2"
} | divide(1, 99) | divide(n0,n1)| | "there are 25 primes , 73 composite numbers from 1 to 100 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 99 . answer : c" | other |
math_qa__wQ63TzRiZ17kNwWb | A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%? Choose the correct choice from the following
A) 21000 B) 21009 C) 21029 D) 21298 E) 21098 | <gadget id="calculator">100 + 32</gadget>
<output>132</output>
<gadget id="calculator">132 / 100</gadget>
<output>33/25 = around 1.32</output>
<gadget id="calculator">(33/25) * 35_000</gadget>
<output>46_200</output>
<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(13/10) * 35_000</gadget>
<output>45_500</output>
<gadget id="calculator">46_200 - 45_500</gadget>
<output>700</output>
<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">140 / 100</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(7/5) - (13/10)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">700 / (1/10)</gadget>
<output>7_000</output>
<gadget id="calculator">35_000 - 7_000</gadget>
<output>28_000</output>
<gadget id="calculator">28_000 - 7_000</gadget>
<output>21_000</output>
<result>A</result> | A | 21,000 | A trader purchased two colour televisions for a total of Rs. 35000. He sold one colour television at 30% profit and the other 40% profit. Find the difference in the cost prices of the two televisions if he made an overall profit of 32%? | {
"A": "21000",
"B": "21009",
"C": "21029",
"D": "21298",
"E": "21098"
} | subtract(subtract(35000, divide(subtract(multiply(divide(add(const_100, 32), const_100), 35000), multiply(divide(add(const_100, 30), const_100), 35000)), subtract(divide(add(const_100, 40), const_100), divide(add(const_100, 30), const_100)))), divide(subtract(multiply(divide(add(const_100, 32), const_100), 35000), multiply(divide(add(const_100, 30), const_100), 35000)), subtract(divide(add(const_100, 40), const_100), divide(add(const_100, 30), const_100)))) | add(n3,const_100)|add(n1,const_100)|add(n2,const_100)|divide(#0,const_100)|divide(#1,const_100)|divide(#2,const_100)|multiply(n0,#3)|multiply(n0,#4)|subtract(#5,#4)|subtract(#6,#7)|divide(#9,#8)|subtract(n0,#10)|subtract(#11,#10) | let the cost prices of the colour television sold at 30 % profit and 40 % profit be rs . x and rs . ( 35000 - x ) respectively . total selling price of televisions = x + 30 / 100 x + ( 35000 - x ) + 40 / 100 ( 35000 - x ) = > 130 / 100 x + 140 / 100 ( 35000 - x ) = 35000 + 32 / 100 ( 35000 ) x = 28000 35000 - x = 7000 difference in the cost prices of televisions = rs . 21000 answer : a | gain |
math_qa__IF0oWOAX8LL8sUvC | 9!/(9-3)!=? Choices:
A) 336 B) 346 C) 356 D) 366 E) 504 | <gadget id="calculator">factorial(9)</gadget>
<output>362_880</output>
<gadget id="calculator">9 - 3</gadget>
<output>6</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">362_880 / 720</gadget>
<output>504</output>
<result>E</result> | E | 504 | 9!/(9-3)!=? | {
"A": "336",
"B": "346",
"C": "356",
"D": "366",
"E": "504"
} | divide(factorial(9), factorial(subtract(9, 3))) | factorial(n0)|subtract(n0,n2)|factorial(#1)|divide(#0,#2) | 9 ! / ( 9 - 3 ) ! = 9 ! / 6 ! = 9 * 8 * 7 = 504 . hence , the correct answer is e . | general |
math_qa__JCfLv9tfjrK89Vz2 | If 213 × 16 = 3408, then 1.6 × 21.3 is equal to : Choose the correct choice from the following:
A) 0.3408
B) 3.408
C) 34.08
D) 340.8
E) none of these | <gadget id="calculator">1.6 * 21.3</gadget>
<output>34.08</output>
<result>C</result> | C | 34.08 | If 213 × 16 = 3408, then 1.6 × 21.3 is equal to : | {
"A": "0.3408",
"B": "3.408",
"C": "34.08",
"D": "340.8",
"E": "none of these"
} | multiply(1.6, 21.3) | multiply(n4,n3)| | "solution 1.6 × 21.3 = ( 16 / 10 x 213 / 10 ) = ( 16 x 213 / 100 ) = 3408 / 100 = 34.08 . answer c" | general |
math_qa__Dw0OJ7SRJ0bm3z6W | The true discount on a bill due 9 months hence at 16% per annum is Rs. 150. The amount of the bill is Choices: A) 1200 B) 1764 C) 1400 D) 1354 E) none of these | <gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 16</gadget>
<output>12</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">150 / (3/25)</gadget>
<output>1_250</output>
<gadget id="calculator">1_250 + 150</gadget>
<output>1_400</output>
<result>C</result> | C | 1,400 | The true discount on a bill due 9 months hence at 16% per annum is Rs. 150. The amount of the bill is | {
"A": "1200",
"B": "1764",
"C": "1400",
"D": "1354",
"E": "none of these"
} | add(divide(150, divide(multiply(divide(9, multiply(const_4, const_3)), 16), const_100)), 150) | multiply(const_3,const_4)|divide(n0,#0)|multiply(n1,#1)|divide(#2,const_100)|divide(n2,#3)|add(n2,#4) | explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 150 . x ã — 16 ã — ( 9 / 12 ) ã — ( 1 / 100 ) = 150 or x = 1250 . p . w . = rs . 1250 sum due = p . w . + t . d . = rs . ( 1250 150 ) = rs . 1400 answer : c | gain |
math_qa__OkFeDfmvRnvTSamn | Andrew travelling to 7 cities. Gasoline prices varied from city to city. $1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.81. What is the median gasoline price? Choose the correct option
A) $ 1 B) $ 1.81 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 + 1.81</gadget>
<output>13.12</output>
<gadget id="calculator">13.12 / 7</gadget>
<output>1.874286</output>
<gadget id="calculator">min(1.874286, 1.81)</gadget>
<output>1.81</output>
<result>B</result> | B | 1.81 | Andrew travelling to 7 cities. Gasoline prices varied from city to city. $1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.81. What is the median gasoline price? | {
"A": "$ 1",
"B": "$ 1.81",
"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), 1.81), 7), 1.81) | 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 , $ 1.81 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.81 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b" | general |
math_qa__v3Uby4ZTP88QDZMK | a freight elevator can carry a maximum load of 1100 pounds . sean , who weighs 200 pounds , is in the elevator with two packages weighing 150 pounds and 280 pounds . if he needs to fit 3 more packages in the elevator that weigh as much as possible without exceeding the elevator limit , what is the difference between their average and the average of the two packages already in the elevator ? Pick one:
A) 59
B) 85
C) 190
D) 215
E) 210 | <gadget id="calculator">150 + 280</gadget>
<output>430</output>
<gadget id="calculator">430 / 2</gadget>
<output>215</output>
<gadget id="calculator">1_100 - 200</gadget>
<output>900</output>
<gadget id="calculator">900 - 430</gadget>
<output>470</output>
<gadget id="calculator">470 / 3</gadget>
<output>470/3 = around 156.666667</output>
<gadget id="calculator">215 - (470/3)</gadget>
<output>175/3 = around 58.333333</output>
<result>A</result> | A | 59 | a freight elevator can carry a maximum load of 1100 pounds . sean , who weighs 200 pounds , is in the elevator with two packages weighing 150 pounds and 280 pounds . if he needs to fit 3 more packages in the elevator that weigh as much as possible without exceeding the elevator limit , what is the difference between their average and the average of the two packages already in the elevator ? | {
"A": "59",
"B": "85",
"C": "190",
"D": "215",
"E": "210"
} | subtract(divide(add(150, 280), const_2), divide(subtract(subtract(1100, 200), add(150, 280)), 3)) | add(n2,n3)|subtract(n0,n1)|divide(#0,const_2)|subtract(#1,#0)|divide(#3,n4)|subtract(#2,#4) | the average of existing 2 package is 150 + 280 / 2 = 430 / 2 = 215 remaining allowed weight = 1100 - 200 - 430 = 470 . allowed per package = 470 / 3 = 156 so difference in average of existing and allowable = 215 - 156 = 59 hence a | general |
math_qa__U1OGhAs9Gn9FiKwe | power windows : 60 % anti - lock brakes : 25 % cd player : 75 % the table above shows the number of vehicles at bill ' s car dealership that have certain features . no vehicle has all 3 features , but 10 % have power windows and anti - lock brakes , 15 % have anti - lock brakes and a cd player , and 22 % have power windows and a cd player . what percent of the vehicles at bill ' s car dealership have a cd player but no power windows or anti - lock brakes ? Answers
A) 25 B) 18 C) 11 D) 38 E) 0 | <gadget id="calculator">75 - 15</gadget>
<output>60</output>
<gadget id="calculator">60 - 22</gadget>
<output>38</output>
<result>D</result> | D | 38 | power windows : 60 % anti - lock brakes : 25 % cd player : 75 % the table above shows the number of vehicles at bill ' s car dealership that have certain features . no vehicle has all 3 features , but 10 % have power windows and anti - lock brakes , 15 % have anti - lock brakes and a cd player , and 22 % have power windows and a cd player . what percent of the vehicles at bill ' s car dealership have a cd player but no power windows or anti - lock brakes ? | {
"A": "25",
"B": "18",
"C": "11",
"D": "38",
"E": "0"
} | subtract(subtract(75, 15), 22) | subtract(n2,n5)|subtract(#0,n6) | answer : d were looking for the number of cars with a cd player but no other features . we know that 40 % of the cars have a cd player , 15 % have a cd player and anti - lock brakes , while 22 % have a cd player and power windows . since no car has all three features , those account for all of the possibilities except for what were looking for . if a car has a cd player , it must either have anti - lock brakes , power windows , or no other features . since the total of cars with a cd player is 75 % , we can set up the following equation : 75 = 15 + 22 + x x = 38 , choiced . | gain |
math_qa__IWeOzyHHgoz3z8Pz | The value of (log9 27 + log8 32) is: Choose the correct choice from the following choices
A) 7 / 2
B) 19 / 6
C) 5 / 3
D) 7
E) 8 | <gadget id="calculator">log(32)</gadget>
<output>log(32) = around 3.465736</output>
<gadget id="calculator">log(8)</gadget>
<output>log(8) = around 2.079442</output>
<gadget id="calculator">log(32) / log(8)</gadget>
<output>log(32)/log(8) = around 1.666667</output>
<result>C</result> | C | 1.666667 | The value of (log9 27 + log8 32) is: | {
"A": "7 / 2",
"B": "19 / 6",
"C": "5 / 3",
"D": "7",
"E": "8"
} | divide(log(32), log(8)) | log(n3)|log(n2)|divide(#0,#1) | let log 9 27 = x . then , 9 x = 27 = > ( 32 ) x = 33 = > 2 x = 3 = > x = 3 / 2 let log 8 32 = y . then 8 y = 32 = > ( 23 ) y = 25 = > 3 y = 5 = > y = 5 / 3 answer : c | other |
math_qa__nZ6nQ8AJlBhA9jBU | Walking with 4/5 of my usual speed, I miss the bus by 4 minutes. What is my usual time? Choose the correct option: A) 16 min B) 26 min C) 34 min D) 20 min E) 12 min | <gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">4 / (5/4)</gadget>
<output>16/5 = around 3.2</output>
<gadget id="calculator">(16/5) * 5</gadget>
<output>16</output>
<result>A</result> | A | 16 | Walking with 4/5 of my usual speed, I miss the bus by 4 minutes. What is my usual time? | {
"A": "16 min",
"B": "26 min",
"C": "34 min",
"D": "20 min",
"E": "12 min"
} | multiply(divide(4, divide(5, 4)), 5) | divide(n1,n0)|divide(n2,#0)|multiply(n1,#1)| | "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 5 1 - - - - - - - - 4 4 - - - - - - - - - ? è 16 answer : a" | physics |
math_qa__PZHksXK9N0Ye0KUo | Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 22 in two years, at the same percent rate per annum?
Select:
A) s . 520 B) s . 480 C) s . 420 D) s . 100 E) s . 200 | <gadget id="calculator">22 - 20</gadget>
<output>2</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<result>D</result> | D | 100 | Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 22 in two years, at the same percent rate per annum? | {
"A": "s . 520",
"B": "s . 480",
"C": "s . 420",
"D": "s . 100",
"E": "s . 200"
} | divide(multiply(subtract(22, 20), const_100), const_2) | subtract(n1,n0)|multiply(#0,const_100)|divide(#1,const_2) | explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 22 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 22 – 20 ) / 20 ] * 100 = 10 % p . a . let the principal be rs . x time = t = 2 years % rate = 10 % p . a . si = ( prt / 100 ) 20 = ( x * 10 * 2 ) / 100 x = rs . 100 answer : d | gain |
math_qa__qLiaQKjqmmhpElWd | If x/(11p) is an odd prime number, where x is a positive integer and p is a prime number, what is the least value of x? Choose the correct choice.
A) 22 B) 33 C) 44 D) 66 E) 99 | <gadget id="calculator">3 * 11</gadget>
<output>33</output>
<gadget id="calculator">33 * 2</gadget>
<output>66</output>
<result>D</result> | D | 66 | If x/(11p) is an odd prime number, where x is a positive integer and p is a prime number, what is the least value of x? | {
"A": "22",
"B": "33",
"C": "44",
"D": "66",
"E": "99"
} | multiply(multiply(const_3, 11), const_2) | multiply(n0,const_3)|multiply(#0,const_2) | x / ( 11 p ) = odd prime number x = odd prime number * 11 p least value of x = lowest odd prime number * 11 * lowest value of p = 3 * 11 * 2 = 66 answer d | general |
math_qa__axtts4Lqpo8EjPNu | 9 persons went to a hotel for taking their meals . 8 of them spent rs . 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them . Options: A) rs . 115 B) rs . 116 C) rs . 117 D) rs . 118 E) none | <gadget id="calculator">12 + 9</gadget>
<output>21</output>
<gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">21 + 96</gadget>
<output>117</output>
<result>C</result> | C | 117 | 9 persons went to a hotel for taking their meals . 8 of them spent rs . 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them . | {
"A": "rs . 115",
"B": "rs . 116",
"C": "rs . 117",
"D": "rs . 118",
"E": "none"
} | add(add(12, 9), multiply(8, 12)) | add(n0,n2)|multiply(n1,n2)|add(#0,#1) | solution : let the average expenditure of all the nine be x . then , 12 × 8 + ( x + 8 ) = 9 x . therefore , x = 13 . total money spent , = 9 x = rs . ( 9 × 13 ) = rs . 117 answer : option c | general |
math_qa__rLTXO76xB8cXWEym | The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number? Choose the correct choice from the following:
A) 4
B) 5
C) 6
D) 8
E) 9 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">36 / 9</gadget>
<output>4</output>
<result>A</result> | A | 4 | The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number? | {
"A": "4",
"B": "5",
"C": "6",
"D": "8",
"E": "9"
} | divide(36, subtract(const_10, const_1)) | subtract(const_10,const_1)|divide(n0,#0)| | "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 36 ⇔ 9 ( x - y ) = 36 ⇔ x - y = 4 answer a" | general |
math_qa__fpDYZdzTt1vw5OUA | A snail, climbing a 66 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?
Pick one.
A) 42 B) 63 C) 77 D) 80 E) 91 | <gadget id="calculator">66 - 4</gadget>
<output>62</output>
<result>B</result> | B | 63 | A snail, climbing a 66 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall? | {
"A": "42",
"B": "63",
"C": "77",
"D": "80",
"E": "91"
} | subtract(66, 4) | subtract(n0,n1)| | "total transaction in two days = 4 - 2 = 2 feet in 62 days it will climb 62 feet on the 63 rd day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 63 b" | physics |
math_qa__34I2qvllcQKXSWai | If 6Pr = 360 and If 6Cr = 15, find r ? Choices:
A) 5 B) 6 C) 4 D) 3 E) 2 | <gadget id="calculator">360 / 15</gadget>
<output>24</output>
<gadget id="calculator">24 / 6</gadget>
<output>4</output>
<result>C</result> | C | 4 | If 6Pr = 360 and If 6Cr = 15, find r ? | {
"A": "5",
"B": "6",
"C": "4",
"D": "3",
"E": "2"
} | divide(divide(360, 15), 6) | divide(n1,n3)|divide(#0,n0) | solution : npr = ncr � r ! 6 pr = 15 * r ! 360 = 15 * r ! r ! = 360 / 15 = 24 r ! = 4 * 3 * 2 * 1 = > r ! = 4 ! therefore , r = 4 . answer : option c | general |
math_qa__DGg7k1unUdbYKRUc | By selling 90 pens, a trader gains the cost of 15 pens. Find his gain percentage?
Choose the correct choice from the following answers: A) 16.66 % B) 17.66 % C) 18.66 % D) 19.66 % E) 20.66 % | <gadget id="calculator">15 / 90</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 100</gadget>
<output>50/3 = around 16.666667</output>
<result>A</result> | A | 16.66 | By selling 90 pens, a trader gains the cost of 15 pens. Find his gain percentage? | {
"A": "16.66 %",
"B": "17.66 %",
"C": "18.66 %",
"D": "19.66 %",
"E": "20.66 %"
} | multiply(divide(15, 90), const_100) | divide(n1,n0)|multiply(#0,const_100)| | "let the cp of each pen be rs . 1 . cp of 90 pens = rs . 90 profit = cost of 15 pens = rs . 15 profit % = 15 / 90 * 100 = 16.66 % answer : a" | gain |
math_qa__I3afB7gnico5XrnR | How many paying stones, each measuring 2 m * 2 m are required to pave a rectangular court yard 30 m long and 18 m board? Pick:
A) 99 B) 18 C) 135 D) 17 E) 12 | <gadget id="calculator">30 * 18</gadget>
<output>540</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">540 / 4</gadget>
<output>135</output>
<result>C</result> | C | 135 | How many paying stones, each measuring 2 m * 2 m are required to pave a rectangular court yard 30 m long and 18 m board? | {
"A": "99",
"B": "18",
"C": "135",
"D": "17",
"E": "12"
} | divide(rectangle_area(30, 18), rectangle_area(2, 2)) | rectangle_area(n2,n3)|rectangle_area(n0,n1)|divide(#0,#1)| | "30 * 18 = 2 * 2 * x = > x = 135 answer : c" | physics |
math_qa__PvErqC3wZWHjvrA3 | A pupil's marks were wrongly entered as 73 instead of 65. Due to the average marks for the class got increased by half. The number of pupils in the class is? Select
A) 18 B) 82 C) 16 D) 27 E) 29 | <gadget id="calculator">73 - 65</gadget>
<output>8</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<result>C</result> | C | 16 | A pupil's marks were wrongly entered as 73 instead of 65. Due to the average marks for the class got increased by half. The number of pupils in the class is? | {
"A": "18",
"B": "82",
"C": "16",
"D": "27",
"E": "29"
} | multiply(subtract(73, 65), const_2) | subtract(n0,n1)|multiply(#0,const_2)| | "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 65 ) = > x / 2 = 8 = > x = 16 . answer : c" | general |
math_qa__BzQw7GTTGzrcj7gA | A shopkeeper sold an article at $100 with 30% profit. Then find its cost price? Select the correct option: A) $ 120 B) $ 100 C) $ 91 D) $ 77 E) $ 69 | <gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">100 / 130</gadget>
<output>10/13 = around 0.769231</output>
<gadget id="calculator">100 * (10/13)</gadget>
<output>1_000/13 = around 76.923077</output>
<result>D</result> | D | 77 | A shopkeeper sold an article at $100 with 30% profit. Then find its cost price? | {
"A": "$ 120",
"B": "$ 100",
"C": "$ 91",
"D": "$ 77",
"E": "$ 69"
} | multiply(100, divide(100, add(100, 30))) | add(n1,n0)|divide(n0,#0)|multiply(n0,#1)| | "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 130 = $ 77 ( approximately ) answer is d" | gain |
math_qa__n2dcyHHRbj88FGLk | In an election between two candidates, the first candidate got 80% of the votes and the second candidate got 480 votes. What was the total number of votes? Choose the correct choice from the following choices:
A) 1600 B) 1800 C) 2000 D) 2200 E) 2400 | <gadget id="calculator">480 * 100</gadget>
<output>48_000</output>
<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">48_000 / 20</gadget>
<output>2_400</output>
<result>E</result> | E | 2,400 | In an election between two candidates, the first candidate got 80% of the votes and the second candidate got 480 votes. What was the total number of votes? | {
"A": "1600",
"B": "1800",
"C": "2000",
"D": "2200",
"E": "2400"
} | divide(multiply(480, const_100), subtract(const_100, 80)) | multiply(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)| | "let v be the total number of votes . 0.2 v = 480 v = 2400 the answer is e ." | gain |
math_qa__gi0PeoGDTIU7gUYo | Peter invested a certain sum of money in a simple interest bond whose value grew to $400 at the end of 4 years and to $ 500 at the end of another 2 years. What was the rate of interest in which he invested his sum? Choose the correct choice from the following
A) 12 % B) 12.5 % C) 67 % D) 25 % E) 33 % | <gadget id="calculator">500 - 400</gadget>
<output>100</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">50 * 4</gadget>
<output>200</output>
<gadget id="calculator">400 - 200</gadget>
<output>200</output>
<gadget id="calculator">50 / 200</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>D</result> | D | 25 | Peter invested a certain sum of money in a simple interest bond whose value grew to $400 at the end of 4 years and to $ 500 at the end of another 2 years. What was the rate of interest in which he invested his sum? | {
"A": "12 %",
"B": "12.5 %",
"C": "67 %",
"D": "25 %",
"E": "33 %"
} | multiply(divide(divide(subtract(500, 400), 2), subtract(400, multiply(divide(subtract(500, 400), 2), 4))), const_100) | subtract(n2,n0)|divide(#0,n3)|multiply(n1,#1)|subtract(n0,#2)|divide(#1,#3)|multiply(#4,const_100)| | "lets assume the principal amount ( initial amount invested ) to be p rate of interest to berand time as t . we need to find r now after a time of 4 years the principal p amounts to $ 400 and after a time of 6 years ( question says after another 6 years so 4 + 2 ) p becomes $ 500 . formulating the above data amount ( a 1 ) at end of 4 years a 1 = p ( 1 + 4 r / 100 ) = 400 amount ( a 2 ) at end of 6 years a 2 = p ( 1 + 2 r / 100 ) = 500 dividing a 2 by a 1 we get ( 1 + 4 r / 100 ) / ( 1 + 2 r / 100 ) = 5 / 4 after cross multiplication we are left with 4 r = 100 which gives r = 25 % option : d" | gain |
math_qa__RlNEk9xNGGfElGgb | Twenty-one dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle?
Choose one: A) 1299 B) 1305 C) 1311 D) 1317 E) 1323 | <gadget id="calculator">21 - 1</gadget>
<output>20</output>
<gadget id="calculator">21 * 20</gadget>
<output>420</output>
<gadget id="calculator">20 - 1</gadget>
<output>19</output>
<gadget id="calculator">420 * 19</gadget>
<output>7_980</output>
<gadget id="calculator">7_980 / 3</gadget>
<output>2_660</output>
<gadget id="calculator">2_660 / 2</gadget>
<output>1_330</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">1_330 - 7</gadget>
<output>1_323</output>
<result>E</result> | E | 1,323 | Twenty-one dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle? | {
"A": "1299",
"B": "1305",
"C": "1311",
"D": "1317",
"E": "1323"
} | subtract(divide(divide(multiply(multiply(21, subtract(21, const_1)), subtract(subtract(21, const_1), const_1)), const_3), const_2), add(const_3, const_4)) | add(const_3,const_4)|subtract(n0,const_1)|multiply(n0,#1)|subtract(#1,const_1)|multiply(#2,#3)|divide(#4,const_3)|divide(#5,const_2)|subtract(#6,#0) | the total number of ways we can choose three dots is 21 c 3 = 1330 . we can form seven equilateral triangles from these twenty - one dots . there are 1330 - 7 = 1323 combinations which do not form an equilateral triangle . the answer is e . | geometry |
math_qa__S2KXZSymHbkmMhMV | If the area of circle is 616 sq cm then its circumference? Choose the correct option
A) 76 B) 55 C) 88 D) 21 E) 11 | <gadget id="calculator">616 / pi</gadget>
<output>616/pi = around 196.07889</output>
<gadget id="calculator">(616/pi) ** (1/2)</gadget>
<output>2*sqrt(154)/sqrt(pi) = around 14.002817</output>
<gadget id="calculator">2 * pi * (2*sqrt(154)/sqrt(pi))</gadget>
<output>4*sqrt(154)*sqrt(pi) = around 87.982295</output>
<result>C</result> | C | 88 | If the area of circle is 616 sq cm then its circumference? | {
"A": "76",
"B": "55",
"C": "88",
"D": "21",
"E": "11"
} | circumface(sqrt(divide(616, const_pi))) | divide(n0,const_pi)|sqrt(#0)|circumface(#1) | the area of circle = pie * r ^ 2 = 616 = > r = 14 2 * 22 / 7 * 14 = 88 answer : c | geometry |
math_qa__H4bnWa0zmfmLTdjz | The ratio of boarders to day scholars at a school is 7 to 16. However, after a few new students join the initial 560 boarders, the ratio changed to 1 to 2, respectively. If no boarders became day scholars and vice versa, and no students left the school, how many boarders joined the school? Choose the correct choice from the following choices:
A) 48
B) 64
C) 70
D) 80
E) 84 | <gadget id="calculator">560 / 7</gadget>
<output>80</output>
<gadget id="calculator">80 * 16</gadget>
<output>1_280</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1_280 / (2/3)</gadget>
<output>1_920</output>
<gadget id="calculator">560 + 1_280</gadget>
<output>1_840</output>
<gadget id="calculator">1_920 - 1_840</gadget>
<output>80</output>
<result>D</result> | D | 80 | The ratio of boarders to day scholars at a school is 7 to 16. However, after a few new students join the initial 560 boarders, the ratio changed to 1 to 2, respectively. If no boarders became day scholars and vice versa, and no students left the school, how many boarders joined the school? | {
"A": "48",
"B": "64",
"C": "70",
"D": "80",
"E": "84"
} | subtract(divide(multiply(divide(560, 7), 16), divide(2, add(1, 2))), add(560, multiply(divide(560, 7), 16))) | add(n3,n4)|divide(n2,n0)|divide(n4,#0)|multiply(n1,#1)|add(n2,#3)|divide(#3,#2)|subtract(#5,#4) | let day scholars be ds and boarders be b given b / ds = 7 / 16 - - - > eq 1 initially b = 560 and x be new boarders joined then from eq 1 , we get ds = 16 / 7 * 560 = 1280 now , new ration is 560 + x / ds = 1 / 2 560 + x / 1280 = 1 / 2 = > 1120 + 2 x = 1280 = > 2 x = 160 = > x = 80 ans option d | other |
math_qa__JDGE8qO11cx1Hi1r | When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 6. When N is divided by (P + 2), the quotient is 15 and the remainder is 3. What is the value of N?
Choose the correct choice from the following
A) 151 B) 331 C) 168 D) 691 E) 871 | <gadget id="calculator">15 * 2</gadget>
<output>30</output>
<gadget id="calculator">30 + 3</gadget>
<output>33</output>
<gadget id="calculator">33 - 6</gadget>
<output>27</output>
<gadget id="calculator">18 - 15</gadget>
<output>3</output>
<gadget id="calculator">27 / 3</gadget>
<output>9</output>
<gadget id="calculator">18 * 9</gadget>
<output>162</output>
<result>C</result> | C | 168 | When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 6. When N is divided by (P + 2), the quotient is 15 and the remainder is 3. What is the value of N? | {
"A": "151",
"B": "331",
"C": "168",
"D": "691",
"E": "871"
} | multiply(18, divide(subtract(add(multiply(15, 2), 3), 6), subtract(18, 15))) | multiply(n2,n3)|subtract(n0,n3)|add(n4,#0)|subtract(#2,n1)|divide(#3,#1)|multiply(n0,#4) | n / p = 18 6 / p = 18 p + 6 n / ( p + 2 ) = 15 2 / ( p + 2 ) = 15 p + 30 + 3 solving these two equations we get p = 9 n = 168 answer is c . | general |
math_qa__FMWGoWEehHQFOpg1 | In an examination, 25% of total students failed in Hindi, 35% failed in English and 40% in both. The percentage of these who passed in both the subjects is : Choices:
A) 10 % B) 20 % C) 60 % D) 80 % E) 50 % | <gadget id="calculator">25 + 35</gadget>
<output>60</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<result>D</result> | D | 80 | In an examination, 25% of total students failed in Hindi, 35% failed in English and 40% in both. The percentage of these who passed in both the subjects is : | {
"A": "10 %",
"B": "20 %",
"C": "60 %",
"D": "80 %",
"E": "50 %"
} | subtract(const_100, subtract(add(25, 35), 40)) | add(n0,n1)|subtract(#0,n2)|subtract(const_100,#1)| | "pass percentage = 100 - ( 25 + 35 - 40 ) = 100 - 20 = 80 answer : d" | general |
math_qa__gEc8w3A0528LyJnh | Population of a city in 20004 was 1400000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
Select the correct option
A) 354354 B) 545454 C) 465785 D) 456573 E) 2818075 / 2 | <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">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">1 - (7/20)</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">(23/20) * (13/20)</gadget>
<output>299/400 = around 0.7475</output>
<gadget id="calculator">1 + (7/20)</gadget>
<output>27/20 = around 1.35</output>
<gadget id="calculator">(299/400) * (27/20)</gadget>
<output>8_073/8_000 = around 1.009125</output>
<gadget id="calculator">1_400_000 * (8_073/8_000)</gadget>
<output>1_412_775</output>
<result>E</result> | E | 1,409,037.5 | Population of a city in 20004 was 1400000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007 | {
"A": "354354",
"B": "545454",
"C": "465785",
"D": "456573",
"E": "2818075 / 2"
} | multiply(1400000, multiply(multiply(add(const_1, divide(15, const_100)), subtract(const_1, divide(35, const_100))), add(const_1, divide(35, const_100)))) | divide(n5,const_100)|divide(n3,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(const_1,#0)|multiply(#3,#4)|multiply(#2,#5)|multiply(n1,#6)| | "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 2818075 / 2 e" | gain |
math_qa__5Qk4AlnRy8rAdzqY | The slant height of a cone is 15 cm and radius of the base is 3cm, find the curved surface of the cone?
Select
A) 26 B) 134 C) 141 D) 190 E) 28 | <gadget id="calculator">pi * 3</gadget>
<output>3*pi = around 9.424778</output>
<gadget id="calculator">(3*pi) * 15</gadget>
<output>45*pi = around 141.371669</output>
<result>C</result> | C | 141 | The slant height of a cone is 15 cm and radius of the base is 3cm, find the curved surface of the cone? | {
"A": "26",
"B": "134",
"C": "141",
"D": "190",
"E": "28"
} | multiply(multiply(const_pi, 3), 15) | multiply(n1,const_pi)|multiply(n0,#0)| | "π * 15 * 3 = 141 answer : c" | geometry |
math_qa__mqNCaGCPk2ddoLBr | If (55^55+55) is divided by 56, then the remainder is:? Choose the correct choice from the following options:
A) 54 B) 55 C) 53 D) 56 E) 57 | <gadget id="calculator">55 - 56</gadget>
<output>-1</output>
<gadget id="calculator">55 + (-1)</gadget>
<output>54</output>
<result>A</result> | A | 54 | If (55^55+55) is divided by 56, then the remainder is:? | {
"A": "54",
"B": "55",
"C": "53",
"D": "56",
"E": "57"
} | add(55, subtract(55, 56)) | subtract(n0,n3)|add(n0,#0) | solution : ( x ^ n + 1 ) is divisible by ( x + 1 ) , when n is odd . . ' . ( 55 ^ 55 + 1 ) is divisible by ( 55 + 1 ) = 56 . when ( 55 ^ 55 + 1 ) + 54 is divided by 56 , the remainder is 54 . answer a | general |
math_qa__wtqjnSVM6TADLyU5 | g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(a) is divisible by 4^11, what is the smallest possible value for a? Choose one:
A) 22 B) 24 C) 28 D) 32 E) 44 | <gadget id="calculator">2 * 12</gadget>
<output>24</output>
<result>B</result> | B | 24 | g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(a) is divisible by 4^11, what is the smallest possible value for a? | {
"A": "22",
"B": "24",
"C": "28",
"D": "32",
"E": "44"
} | multiply(2, 12) | multiply(n2,n7)| | "g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b" | general |
math_qa__7csZjS7QEUI4K1uw | The least common multiple of positive integer m and 3-digit integer n is 690. If n is not divisible by 3 and m is not divisible by 2, what is the value of n? Choices: A) 115 B) 230 C) 460 D) 575 E) 690 | <gadget id="calculator">690 / 3</gadget>
<output>230</output>
<result>B</result> | B | 230 | The least common multiple of positive integer m and 3-digit integer n is 690. If n is not divisible by 3 and m is not divisible by 2, what is the value of n? | {
"A": "115",
"B": "230",
"C": "460",
"D": "575",
"E": "690"
} | divide(690, 3) | divide(n1,n0) | the lcm of n and m is 690 = 2 * 3 * 5 * 23 . m is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to m . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b . | general |
math_qa__mIzbjod44FYeP0F9 | If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is: Select: A) rs . 50 B) rs . 160 C) rs . 200 D) rs . 225 E) rs . 325 | <gadget id="calculator">350 - 340</gadget>
<output>10</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">10 / (1/20)</gadget>
<output>200</output>
<result>C</result> | C | 200 | If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is: | {
"A": "rs . 50",
"B": "rs . 160",
"C": "rs . 200",
"D": "rs . 225",
"E": "rs . 325"
} | divide(subtract(350, 340), divide(5, const_100)) | divide(n0,const_100)|subtract(n1,n2)|divide(#1,#0)| | "let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c" | gain |
math_qa__KDArTOkUR3S70Ctq | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent F of the distribution is less than m +d ? Select
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 percent of the distribution lies within one standard deviation d of the mean, what percent F of the distribution is less than m +d ? | {
"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)| | "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , f = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d" | general |
math_qa__GPRssizcwbfBNUxt | A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
Choose one
A) 220 km B) 224 km C) 230 km D) 234 km E) 255 km | <gadget id="calculator">21 * 24</gadget>
<output>504</output>
<gadget id="calculator">504 * 10</gadget>
<output>5_040</output>
<gadget id="calculator">21 + 24</gadget>
<output>45</output>
<gadget id="calculator">5_040 / 45</gadget>
<output>112</output>
<gadget id="calculator">2 * 112</gadget>
<output>224</output>
<result>B</result> | B | 224 | A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. | {
"A": "220 km",
"B": "224 km",
"C": "230 km",
"D": "234 km",
"E": "255 km"
} | multiply(const_2, divide(multiply(multiply(21, 24), 10), add(21, 24))) | add(n1,n2)|multiply(n1,n2)|multiply(n0,#1)|divide(#2,#0)|multiply(#3,const_2)| | "( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 x / 21 + x / 24 = 20 15 x = 168 x 20 x = [ 168 x 20 / 15 ] = 224 km answer is b" | physics |
math_qa__KgIGYaFWfgvbRQtr | The compound ratio of 3:4, 3:2 and 4:5? Choices.
A) 1 : 9 B) 1 : 7 C) 1 : 2 D) 9 : 10 E) 1 : 4 | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">9 / 8</gadget>
<output>9/8 = around 1.125</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(9/8) / (6/5)</gadget>
<output>15/16 = around 0.9375</output>
<result>D</result> | D | 0.9 | The compound ratio of 3:4, 3:2 and 4:5? | {
"A": "1 : 9",
"B": "1 : 7",
"C": "1 : 2",
"D": "9 : 10",
"E": "1 : 4"
} | divide(divide(multiply(3, 3), multiply(4, 2)), divide(multiply(3, 4), multiply(2, 5))) | multiply(n0,n2)|multiply(n1,n3)|multiply(n2,n4)|multiply(n3,n5)|divide(#0,#1)|divide(#2,#3)|divide(#4,#5)| | "3 / 4 * 3 / 2 * 4 / 5 = 9 / 10 = 9 : 10 answer : d" | other |
math_qa__wLhvMRoAjezEPzqB | The true discount on a bill of Rs. 2460 is Rs. 360. What is the banker's discount? Choose the correct choice from the following choices.
A) rs . 432 B) rs . 422 C) rs . 412 D) rs . 442 E) none of these | <gadget id="calculator">2_460 - 360</gadget>
<output>2_100</output>
<gadget id="calculator">360 / 2_100</gadget>
<output>6/35 = around 0.171429</output>
<gadget id="calculator">(6/35) * 2_460</gadget>
<output>2_952/7 = around 421.714286</output>
<result>B</result> | B | 422 | The true discount on a bill of Rs. 2460 is Rs. 360. What is the banker's discount? | {
"A": "rs . 432",
"B": "rs . 422",
"C": "rs . 412",
"D": "rs . 442",
"E": "none of these"
} | multiply(divide(360, subtract(2460, 360)), 2460) | subtract(n0,n1)|divide(n1,#0)|multiply(n0,#1)| | "explanation : f = rs . 2460 td = rs . 360 pw = f - td = 2460 - 360 = rs . 2100 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2100 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2460 for unexpired time = 360 / 2100 × 2460 = 0.17 × 2460 = rs . 422 answer : option b" | gain |
math_qa__HnjPWncOOIxhx54T | A number is doubled and 5 is added. If the resultant is trebled, it becomes 111. What is that number? Select the correct option:
A) 12 B) 29 C) 27 D) 16 E) 99 | <gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">111 - 15</gadget>
<output>96</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">96 / 6</gadget>
<output>16</output>
<result>D</result> | D | 16 | A number is doubled and 5 is added. If the resultant is trebled, it becomes 111. What is that number? | {
"A": "12",
"B": "29",
"C": "27",
"D": "16",
"E": "99"
} | divide(subtract(111, multiply(const_3, 5)), multiply(const_3, const_2)) | multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)| | "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 111 6 x + 15 = 111 6 x = 96 x = 16 answer : d" | general |
math_qa__a61Q1a6IUwAimR5j | Find the difference between C.I and S.I on a sum of money Rs. 2000 for 2 years. at 4% p.a Choose the correct answer:
A) rs . 2.20 B) rs . 3.20 C) rs . 4.20 D) rs . 5.20 E) rs . 3.25 | <gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">2_000 * (26/25)</gadget>
<output>2_080</output>
<gadget id="calculator">2_080 * (26/25)</gadget>
<output>10_816/5 = around 2_163.2</output>
<gadget id="calculator">(10_816/5) - 2_000</gadget>
<output>816/5 = around 163.2</output>
<gadget id="calculator">2_000 * (1/25)</gadget>
<output>80</output>
<gadget id="calculator">2 * 80</gadget>
<output>160</output>
<gadget id="calculator">(816/5) - 160</gadget>
<output>16/5 = around 3.2</output>
<result>B</result> | B | 3.2 | Find the difference between C.I and S.I on a sum of money Rs. 2000 for 2 years. at 4% p.a | {
"A": "rs . 2.20",
"B": "rs . 3.20",
"C": "rs . 4.20",
"D": "rs . 5.20",
"E": "rs . 3.25"
} | subtract(subtract(multiply(multiply(2000, add(const_1, divide(4, const_100))), add(const_1, divide(4, const_100))), 2000), multiply(2, multiply(2000, divide(4, const_100)))) | divide(n2,const_100)|add(#0,const_1)|multiply(n0,#0)|multiply(n0,#1)|multiply(n1,#2)|multiply(#1,#3)|subtract(#5,n0)|subtract(#6,#4) | p 9 r / 100 ) ^ 2 = 2000 ( 4 / 100 ) ^ 2 = rs . 3.20 answer : b | general |
math_qa__5hik9QJCjlN18ll2 | If 5 machines can produce 20 units in 10 hours, how long would it take 10 machines to produce 100 units?
Choose the correct choice from the following choices: A) 25 B) 30 C) 35 D) 24 E) 96 | <gadget id="calculator">10 / 10</gadget>
<output>1</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 20</gadget>
<output>4</output>
<gadget id="calculator">100 / 4</gadget>
<output>25</output>
<result>A</result> | A | 25 | If 5 machines can produce 20 units in 10 hours, how long would it take 10 machines to produce 100 units? | {
"A": "25",
"B": "30",
"C": "35",
"D": "24",
"E": "96"
} | divide(100, multiply(divide(divide(10, 10), 5), 20)) | divide(n3,n2)|divide(#0,n0)|multiply(n1,#1)|divide(n4,#2)| | "5 machines would produce 100 units in 50 hours . increasing the amount of machines by 2 would mean dividing 50 hours by 2 . 50 / 2 = 25 answer : a" | physics |
math_qa__jOwUp1bhVkqvHqBu | The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.00 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? Pick: A) s . 666 B) s . 1140 C) s . 999 D) s . 1085 E) s . 1020 | <gadget id="calculator">3_136 ** (1/2)</gadget>
<output>56</output>
<gadget id="calculator">56 * 4</gadget>
<output>224</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">224 - 2</gadget>
<output>222</output>
<gadget id="calculator">222 * 1</gadget>
<output>222</output>
<gadget id="calculator">222 * 3</gadget>
<output>666</output>
<result>A</result> | A | 666 | The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.00 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? | {
"A": "s . 666",
"B": "s . 1140",
"C": "s . 999",
"D": "s . 1085",
"E": "s . 1020"
} | multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, 1)), 1.00), 3) | multiply(n3,const_2)|sqrt(n0)|multiply(#1,const_4)|subtract(#2,#0)|multiply(n2,#3)|multiply(#4,n1)| | "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 1.0 = 666 answer : a" | physics |
math_qa__LH0nUcQ0wA0OcCH9 | The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 5 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house? Choose one.
A) 25 km
B) 30 km
C) 40 km
D) 50 km
E) 60 km | <gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 / 60</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">60 * (5/12)</gadget>
<output>25</output>
<result>A</result> | A | 25 | The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 5 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house? | {
"A": "25 km",
"B": "30 km",
"C": "40 km",
"D": "50 km",
"E": "60 km"
} | multiply(60, divide(multiply(5, 5), 60)) | multiply(n1,n2)|divide(#0,n0)|multiply(n0,#1)| | "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 5 = 25 km imo , correct answer is ` ` a . ' '" | physics |
math_qa__XVAow2EfaPgtk1EZ | A positive number x is multiplied by 10, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ? Choices:
A) 9 / 4 B) 3 / 2 C) 4 / 3 D) 2 / 3 E) 10 / 3 | <gadget id="calculator">10 / 3</gadget>
<output>10/3 = around 3.333333</output>
<result>E</result> | E | 3.333333 | A positive number x is multiplied by 10, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ? | {
"A": "9 / 4",
"B": "3 / 2",
"C": "4 / 3",
"D": "2 / 3",
"E": "10 / 3"
} | divide(10, 3) | divide(n0,n1)| | "sq rt ( 10 x / 3 ) = x = > 10 x / 3 = x ^ 2 = > x = 10 / 3 ans - e" | general |
math_qa__hgr0rpuk1rUHcxlc | In a group of dogs and people, the number of legs was 28 more than twice the number of
heads. How many dogs were there? [Assume none of the people or dogs is missing a leg.]
Options
A) 4
B) 7
C) 12
D) 14
E) 28 | <gadget id="calculator">28 / 2</gadget>
<output>14</output>
<result>D</result> | D | 14 | In a group of dogs and people, the number of legs was 28 more than twice the number of
heads. How many dogs were there? [Assume none of the people or dogs is missing a leg.] | {
"A": "4",
"B": "7",
"C": "12",
"D": "14",
"E": "28"
} | divide(28, const_2) | divide(n0,const_2) | if there were only people , there would be exactly twice the number of legs as heads . each dog contributes two extra legs over and above this number . so 28 extra legs means 14 dogs . correct answer d | general |
math_qa__Z8O2wjRJpqOMWVZ0 | In a company, 50 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women? Choose one
A) 85 %
B) 80 %
C) 75 %
D) 70 %
E) 65 % | <gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">60 * (7/10)</gadget>
<output>42</output>
<gadget id="calculator">60 - 42</gadget>
<output>18</output>
<gadget id="calculator">50 - 18</gadget>
<output>32</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">32 / 40</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">100 * (4/5)</gadget>
<output>80</output>
<result>B</result> | B | 80 | In a company, 50 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women? | {
"A": "85 %",
"B": "80 %",
"C": "75 %",
"D": "70 %",
"E": "65 %"
} | multiply(const_100, divide(subtract(subtract(const_100, 50), subtract(60, multiply(60, divide(70, const_100)))), subtract(const_100, 60))) | divide(n2,const_100)|subtract(const_100,n0)|subtract(const_100,n1)|multiply(n1,#0)|subtract(n1,#3)|subtract(#1,#4)|divide(#5,#2)|multiply(#6,const_100)| | "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 50 % of all employees are women , so non - union women are 50 % - 18 % = 32 % 40 % of all employees are non - union . the percent of non - union employees who are women is 32 % / 40 % = 80 % the answer is b ." | gain |
math_qa__2OdyVLg1Paz4hrJD | The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 5 ? Select the correct option
A) 96 B) 106 C) 128 D) 137 E) 122 | <gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">5 + 32</gadget>
<output>37</output>
<gadget id="calculator">21 * 37</gadget>
<output>777</output>
<gadget id="calculator">20 * 32</gadget>
<output>640</output>
<gadget id="calculator">777 - 640</gadget>
<output>137</output>
<result>D</result> | D | 137 | The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 5 ? | {
"A": "96",
"B": "106",
"C": "128",
"D": "137",
"E": "122"
} | subtract(multiply(add(20, const_1), add(5, 32)), multiply(20, 32)) | add(n0,const_1)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 5 = 37 runs total runs = new avg x new no . of innings = 37 * 21 = 777 runs made in the 11 th inning = 777 - 640 = 137 answer : d" | general |
math_qa__Ep4kBgmpVIqWzAWS | Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent? Choose the correct choice: A) 654 B) 655 C) 656 D) 588 E) 658 | <gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">(7/10) * 840</gadget>
<output>588</output>
<result>D</result> | D | 588 | Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent? | {
"A": "654",
"B": "655",
"C": "656",
"D": "588",
"E": "658"
} | multiply(divide(subtract(const_100, 30), const_100), 840.00) | subtract(const_100,n1)|divide(#0,const_100)|multiply(n0,#1)| | "total cost 840 840 * 30 / 100 = 252 so the cut in amount is 252 the less amount to be spend is 840 - 252 = 588 answer : d" | general |
math_qa__H8KextXgXnKvLkQY | A man walking at a rate of 10km/hr crosses a bridge in 18 minutes. The length of the bridge is? Choose the correct choice from the following choices
A) 1521 B) 3000 C) 1667 D) 1254 E) 1112 | <gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 60</gadget>
<output>500/3 = around 166.666667</output>
<gadget id="calculator">(500/3) * 18</gadget>
<output>3_000</output>
<result>B</result> | B | 3,000 | A man walking at a rate of 10km/hr crosses a bridge in 18 minutes. The length of the bridge is? | {
"A": "1521",
"B": "3000",
"C": "1667",
"D": "1254",
"E": "1112"
} | multiply(divide(multiply(10, const_1000), const_60), 18) | multiply(n0,const_1000)|divide(#0,const_60)|multiply(n1,#1)| | "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 18 * 60 = 3000 m answer is b" | gain |
math_qa__LYGgx4S7A2DJT7Ij | The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle. Choices
A) 84 B) 86 C) 82 D) 80 E) none of them | <gadget id="calculator">440 / pi</gadget>
<output>440/pi = around 140.05635</output>
<gadget id="calculator">(440/pi) / 2</gadget>
<output>220/pi = around 70.028175</output>
<gadget id="calculator">14 + (220/pi)</gadget>
<output>14 + 220/pi = around 84.028175</output>
<result>A</result> | A | 84 | The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle. | {
"A": "84",
"B": "86",
"C": "82",
"D": "80",
"E": "none of them"
} | add(14, divide(divide(440, const_pi), const_2)) | divide(n1,const_pi)|divide(#0,const_2)|add(n0,#1) | let inner radius be r metres . then , 2 ( 22 / 7 ) r = 440 = r = ( 440 x ( 7 / 44 ) ) = 70 m . radius of outer circle = ( 70 + 14 ) m = 84 m . answer is a | physics |
math_qa__sfzQKPvG4wlAWFFU | Elena’s bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 7 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed? Pick one:
A) 1 B) 4 C) 9 D) 13 E) 28 | <gadget id="calculator">4 * 7</gadget>
<output>28</output>
<result>E</result> | E | 28 | Elena’s bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 7 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed? | {
"A": "1",
"B": "4",
"C": "9",
"D": "13",
"E": "28"
} | multiply(4, 7) | multiply(n1,n2)| | "solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 7 we get : 21 b + 28 f = 7 x therefore , we got 21 ounces of butter and 7 x amount of quantity when we use 28 ounces of floor . ans : e" | general |
math_qa__Uw02p3Jat5CEb0pS | Find the area, diameter = 13m. Choose the correct choice from the following: A) 132.00 square meter B) 132.04 square meter C) 132.78 square meter D) 132.24 square meter E) 113.43 square meter | <gadget id="calculator">13 / 2</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">pi * ((13/2) ** 2)</gadget>
<output>169*pi/4 = around 132.73229</output>
<result>C</result> | C | 132.78 | Find the area, diameter = 13m. | {
"A": "132.00 square meter",
"B": "132.04 square meter",
"C": "132.78 square meter",
"D": "132.24 square meter",
"E": "113.43 square meter"
} | circle_area(divide(13, const_2)) | divide(n0,const_2)|circle_area(#0)| | "diameter = 13 meter . radius = diameter / 2 . = 13 / 2 . = 6.5 meter . area of a circle = ï € r 2 . here , pi ( ï € ) = 3.14 meter , radius ( r ) = 6.5 area of a circle = 3.14 ã — 6.5 ã — 6.5 . = 3.14 ã — 42.25 . = 132.78 square meter answer : c" | physics |
math_qa__jj88gE4TVQNQ4oSq | In a can, there is a mixture of milk and water in the ratio 4:3. If the can is filled with an additional 8 liters of milk, the can would be full and the ratio of milk and water would become 2:1. Find the capacity of the can?
Choose one
A) 40 B) 36 C) 32 D) 28 E) 24 | <gadget id="calculator">1 * 8</gadget>
<output>8</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">1 * 4</gadget>
<output>4</output>
<gadget id="calculator">6 - 4</gadget>
<output>2</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 + 8</gadget>
<output>24</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">24 + 12</gadget>
<output>36</output>
<result>B</result> | B | 36 | In a can, there is a mixture of milk and water in the ratio 4:3. If the can is filled with an additional 8 liters of milk, the can would be full and the ratio of milk and water would become 2:1. Find the capacity of the can? | {
"A": "40",
"B": "36",
"C": "32",
"D": "28",
"E": "24"
} | add(add(multiply(divide(multiply(1, 8), subtract(multiply(3, 2), multiply(1, 4))), 4), 8), multiply(divide(multiply(1, 8), subtract(multiply(3, 2), multiply(1, 4))), 3)) | multiply(n2,n4)|multiply(n1,n3)|multiply(n0,n4)|subtract(#1,#2)|divide(#0,#3)|multiply(n0,#4)|multiply(n1,#4)|add(n2,#5)|add(#7,#6)| | "let c be the capacity of the can . ( 4 / 7 ) * ( c - 8 ) + 8 = ( 2 / 3 ) * c 12 c - 96 + 168 = 14 c 2 c = 72 c = 36 the answer is b ." | general |
math_qa__RRN5wKNYnnRrlmFZ | According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 272 6 ounces servings of orange juice?
Pick one: A) 25 B) 34 C) 50 D) 67 E) 100 | <gadget id="calculator">272 * 6</gadget>
<output>1_632</output>
<gadget id="calculator">1_632 / 12</gadget>
<output>136</output>
<gadget id="calculator">136 / 4</gadget>
<output>34</output>
<result>B</result> | B | 34 | According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 272 6 ounces servings of orange juice? | {
"A": "25",
"B": "34",
"C": "50",
"D": "67",
"E": "100"
} | divide(divide(multiply(272, 6), 12), const_4) | multiply(n3,n4)|divide(#0,n2)|divide(#1,const_4)| | "its b . total juice rquired = 272 * 6 = 1632 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1632 / 48 = 34 . answer b" | general |
math_qa__UTiVJhE4SklEcIrJ | What is the length of a bridge (in meters), which a train 156 meters long and travelling at 45 km/h can cross in 40 seconds?
Choose the correct choice from the following: A) 308 B) 320 C) 332 D) 344 E) 356 | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">45 * (5/18)</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 40</gadget>
<output>500</output>
<gadget id="calculator">500 - 156</gadget>
<output>344</output>
<result>D</result> | D | 344 | What is the length of a bridge (in meters), which a train 156 meters long and travelling at 45 km/h can cross in 40 seconds? | {
"A": "308",
"B": "320",
"C": "332",
"D": "344",
"E": "356"
} | subtract(multiply(multiply(45, const_0_2778), 40), 156) | multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)| | "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 40 seconds , the train can travel 25 / 2 * 40 = 500 meters 500 = length of train + length of bridge length of bridge = 500 - 156 = 344 meters the answer is d ." | physics |
math_qa__qc0tZeUL1qyq9L5k | If 10 men can reap 120 acres of land in 15 days, how many acres of land can 20 men reap in 30 days? Options
A) 120 B) 240 C) 360 D) 1200 E) 480 | <gadget id="calculator">20 / 10</gadget>
<output>2</output>
<gadget id="calculator">30 / 15</gadget>
<output>2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">120 * 4</gadget>
<output>480</output>
<result>E</result> | E | 480 | If 10 men can reap 120 acres of land in 15 days, how many acres of land can 20 men reap in 30 days? | {
"A": "120",
"B": "240",
"C": "360",
"D": "1200",
"E": "480"
} | multiply(120, multiply(divide(20, 10), divide(30, 15))) | divide(n3,n0)|divide(n4,n2)|multiply(#0,#1)|multiply(n1,#2)| | "10 men 120 acres 15 days 20 men ? 30 days 120 * 20 / 10 * 30 / 15 120 * 2 * 2 120 * 4 = 480 answer : e" | physics |
math_qa__XfHvjVjIiBCIuqc4 | The profit earned by selling an article for 852 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?
Answers:
A) 960
B) 975
C) 1,200
D) 920
E) none of these | <gadget id="calculator">852 + 448</gadget>
<output>1_300</output>
<gadget id="calculator">1_300 / 2</gadget>
<output>650</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">650 * (3/2)</gadget>
<output>975</output>
<result>B</result> | B | 975 | The profit earned by selling an article for 852 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit? | {
"A": "960",
"B": "975",
"C": "1,200",
"D": "920",
"E": "none of these"
} | multiply(divide(add(852, 448), const_2), add(const_1, divide(50, const_100))) | add(n0,n1)|divide(n2,const_100)|add(#1,const_1)|divide(#0,const_2)|multiply(#2,#3)| | "let the profit or loss be x and 852 – x = 448 + x or , x = 404 ⁄ 2 = 202 \ cost price of the article = 852 – x = 448 + x = 650 \ sp of the article = 650 × 150 ⁄ 100 = 975 answer b" | gain |
math_qa__Dpx40Ujg5HabxckY | Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 6% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Choose the correct choice from the following answers:
A) 2 : 9 B) 2 : 7 C) 1 : 6 D) 1 : 1 E) 1 : 3 | <gadget id="calculator">6 - 2</gadget>
<output>4</output>
<gadget id="calculator">10 - 6</gadget>
<output>4</output>
<gadget id="calculator">4 / 4</gadget>
<output>1</output>
<result>D</result> | D | 1 | Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 6% sugar, what should be the ratio of Cereal A to Cereal B, by weight? | {
"A": "2 : 9",
"B": "2 : 7",
"C": "1 : 6",
"D": "1 : 1",
"E": "1 : 3"
} | divide(subtract(6, 2), subtract(10, 6)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)| | "( 10 / 100 ) a + ( 2 / 100 ) b = ( 6 / 100 ) ( a + b ) 4 a = 4 b = > a / b = 1 / 1 answer is d ." | general |
math_qa__Kzslpkj98YhAe4bm | Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 7 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 7 questions did Zachary answer correctly? Choose the correct choice from the following choices:
A) 6
B) 7
C) 8
D) 9
E) 10 | <gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">10 - 6</gadget>
<output>4</output>
<gadget id="calculator">4 + 31</gadget>
<output>35</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">35 / 5</gadget>
<output>7</output>
<result>B</result> | B | 7 | Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 7 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 7 questions did Zachary answer correctly? | {
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "10"
} | divide(add(subtract(multiply(2, subtract(7, 2)), multiply(3, 2)), 31), add(3, 2)) | add(n0,n2)|multiply(n0,n2)|subtract(n1,n2)|multiply(n2,#2)|subtract(#3,#1)|add(n3,#4)|divide(#5,#0)| | "i got two equations : 3 x - 2 y = 25 x + y = 7 3 x - 2 ( 7 - x ) = 25 3 x - 14 + 2 x = 25 5 x = 39 x = 7.8 or between 7 and 8 . ( ans b )" | general |
math_qa__qAsDzLp4cEsqKkZy | Find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case. Select
A) 366 B) 236 C) 367 D) 365 E) 386 | <gadget id="calculator">lcm(35, 11)</gadget>
<output>385</output>
<gadget id="calculator">1 + 385</gadget>
<output>386</output>
<result>E</result> | E | 386 | Find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case. | {
"A": "366",
"B": "236",
"C": "367",
"D": "365",
"E": "386"
} | add(1, lcm(35, 11)) | lcm(n0,n1)|add(n2,#0)| | "explanation : the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 35 , 11 ) + 1 = 386 . answer : e" | general |
math_qa__HBZheffGGvz4GpHp | The speed of a car is 90 km in the first hour and 75 km in the second hour. What is the average speed of the car?
Choose the correct answer.
A) 89 kmph B) 82.5 kmph C) 75 kmph D) 65 kmph E) 77 kmph | <gadget id="calculator">90 + 75</gadget>
<output>165</output>
<gadget id="calculator">165 / 2</gadget>
<output>165/2 = around 82.5</output>
<result>B</result> | B | 82.5 | The speed of a car is 90 km in the first hour and 75 km in the second hour. What is the average speed of the car? | {
"A": "89 kmph",
"B": "82.5 kmph",
"C": "75 kmph",
"D": "65 kmph",
"E": "77 kmph"
} | divide(add(90, 75), const_2) | add(n0,n1)|divide(#0,const_2)| | "s = ( 90 + 75 ) / 2 = 82.5 kmph b" | physics |
math_qa__RDQ6EREolWnkvc81 | A larger cube has 64 cubic inch as a volume and in the cube there are 64 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 64 smaller cubes and the surface area of the larger cube, in square inch? Choose the correct choice from the following answers.
A) 54 B) 64 C) 81 D) 288 E) 120 | <gadget id="calculator">1 ** (1/3)</gadget>
<output>1</output>
<gadget id="calculator">6 * (1 ** 2)</gadget>
<output>6</output>
<gadget id="calculator">6 * 64</gadget>
<output>384</output>
<gadget id="calculator">64 ** (1/3)</gadget>
<output>4</output>
<gadget id="calculator">6 * (4 ** 2)</gadget>
<output>96</output>
<gadget id="calculator">384 - 96</gadget>
<output>288</output>
<result>D</result> | D | 288 | A larger cube has 64 cubic inch as a volume and in the cube there are 64 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 64 smaller cubes and the surface area of the larger cube, in square inch? | {
"A": "54",
"B": "64",
"C": "81",
"D": "288",
"E": "120"
} | subtract(multiply(surface_cube(cube_edge_by_volume(1)), 64), surface_cube(cube_edge_by_volume(64))) | cube_edge_by_volume(n2)|cube_edge_by_volume(n0)|surface_cube(#0)|surface_cube(#1)|multiply(n0,#2)|subtract(#4,#3)| | "volume of larger cube = 64 = 4 ^ 3 side of larger cube = 4 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 4 ^ 2 = 96 surface area of 27 smaller cubes = 64 * 6 * 1 = 384 difference = 384 - 96 = 288 answer : d" | geometry |
math_qa__CwY2pyh6GOyjwUIo | A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/8 hours to fill the tank. The leak can drain all the water of the tank in?
Choose one:
A) 17 hr
B) 19 hr
C) 10 hr
D) 34 hr
E) 36 hr | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 * 8</gadget>
<output>16</output>
<gadget id="calculator">16 + 1</gadget>
<output>17</output>
<gadget id="calculator">17 / 8</gadget>
<output>17/8 = around 2.125</output>
<gadget id="calculator">1 / (17/8)</gadget>
<output>8/17 = around 0.470588</output>
<gadget id="calculator">(1/2) - (8/17)</gadget>
<output>1/34 = around 0.029412</output>
<gadget id="calculator">1 / (1/34)</gadget>
<output>34</output>
<result>D</result> | D | 34 | A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/8 hours to fill the tank. The leak can drain all the water of the tank in? | {
"A": "17 hr",
"B": "19 hr",
"C": "10 hr",
"D": "34 hr",
"E": "36 hr"
} | inverse(subtract(divide(1, 2), inverse(divide(add(multiply(2, 8), 1), 8)))) | divide(n2,n0)|multiply(n0,n3)|add(n2,#1)|divide(#2,n3)|inverse(#3)|subtract(#0,#4)|inverse(#5)| | "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 8 ) = 1 / 34 leak will empty the tank in 34 hrs . answer : d" | physics |
math_qa__hFakywTWMaNG7XjM | Two buses each 3125 m long are running in opposite directions on parallel roads. Their speeds are 40 km/hr and 35 km/hr respectively. Find the time taken by the slower bus to pass the driver of the faster one?
Choose the correct choice from the following options.
A) 50 sec B) 66 sec C) 48 sec D) 55 sec E) 45 sec | <gadget id="calculator">40 + 35</gadget>
<output>75</output>
<gadget id="calculator">75 * 1_000</gadget>
<output>75_000</output>
<gadget id="calculator">75_000 / 3_600</gadget>
<output>125/6 = around 20.833333</output>
<gadget id="calculator">3_125 / (125/6)</gadget>
<output>150</output>
<gadget id="calculator">150 / 3</gadget>
<output>50</output>
<result>A</result> | A | 50 | Two buses each 3125 m long are running in opposite directions on parallel roads. Their speeds are 40 km/hr and 35 km/hr respectively. Find the time taken by the slower bus to pass the driver of the faster one? | {
"A": "50 sec",
"B": "66 sec",
"C": "48 sec",
"D": "55 sec",
"E": "45 sec"
} | divide(divide(3125, divide(multiply(add(40, 35), const_1000), const_3600)), const_3) | add(n1,n2)|multiply(#0,const_1000)|divide(#1,const_3600)|divide(n0,#2)|divide(#3,const_3) | relative speed = 40 + 35 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 3125 + 3125 = 6250 m . required time = 6250 * 6 / 125 = 50 sec . answer : a | physics |
math_qa__wbMHa6oeS72sbGnX | If the perimeter of a rectangular garden is 500 m, its length when its breadth is 100 m is? Choose the correct choice
A) 299 m B) 777 m C) 200 m D) 167 m E) 150 m | <gadget id="calculator">500 / 2</gadget>
<output>250</output>
<gadget id="calculator">250 - 100</gadget>
<output>150</output>
<result>E</result> | E | 150 | If the perimeter of a rectangular garden is 500 m, its length when its breadth is 100 m is? | {
"A": "299 m",
"B": "777 m",
"C": "200 m",
"D": "167 m",
"E": "150 m"
} | subtract(divide(500, const_2), 100) | divide(n0,const_2)|subtract(#0,n1)| | "2 ( l + 100 ) = 500 = > l = 150 m answer : e" | physics |
math_qa__CWtgthW3mbA8O44x | A man goes from A to B at a speed of 15 kmph and comes back to A at a speed of 12 kmph. Find his average speed for the entire journey? Pick one:
A) 13.7 kmph B) 13.3 kmph C) 13.8 kmph D) 13.9 kmph E) 12.3 kmph | <gadget id="calculator">15 + 12</gadget>
<output>27</output>
<gadget id="calculator">27 / 2</gadget>
<output>27/2 = around 13.5</output>
<result>B</result> | B | 13.3 | A man goes from A to B at a speed of 15 kmph and comes back to A at a speed of 12 kmph. Find his average speed for the entire journey? | {
"A": "13.7 kmph",
"B": "13.3 kmph",
"C": "13.8 kmph",
"D": "13.9 kmph",
"E": "12.3 kmph"
} | divide(add(15, 12), const_2) | add(n0,n1)|divide(#0,const_2) | distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 15 ) + ( d / 12 ] = ( 2 d ) / [ 9 d / 60 ) = > 13.3 kmph . answer : b | physics |
math_qa__YrLhkDRM9TdAoVwG | The perimeter of a triangle is 60 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle Choose the correct option:
A) 72 B) 828 C) 729 D) 75 E) 35 | <gadget id="calculator">(2.5 * 60) / 2</gadget>
<output>75</output>
<result>D</result> | D | 75 | The perimeter of a triangle is 60 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle | {
"A": "72",
"B": "828",
"C": "729",
"D": "75",
"E": "35"
} | triangle_area(2.5, 60) | triangle_area(n0,n1)| | "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 60 / 2 = 35 cm 2 answer : option d" | geometry |
math_qa__sxU9nmalRB5nKdHY | he total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
Pick: A) 55 B) 65 C) 75 D) 85 E) 95 | <gadget id="calculator">150 / 2</gadget>
<output>75</output>
<result>C</result> | C | 75 | he total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics? | {
"A": "55",
"B": "65",
"C": "75",
"D": "85",
"E": "95"
} | divide(150, const_2) | divide(n0,const_2)| | "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : c" | general |
math_qa__FbcG2EG8AXgx2kJs | A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/7 hours to fill the tank. The leak can drain all the water of the tank in?
Select: A) 17 hr B) 19 hr C) 10 hr D) 24 hr E) 30 hr | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 * 7</gadget>
<output>14</output>
<gadget id="calculator">14 + 1</gadget>
<output>15</output>
<gadget id="calculator">15 / 7</gadget>
<output>15/7 = around 2.142857</output>
<gadget id="calculator">1 / (15/7)</gadget>
<output>7/15 = around 0.466667</output>
<gadget id="calculator">(1/2) - (7/15)</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>E</result> | E | 30 | A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/7 hours to fill the tank. The leak can drain all the water of the tank in? | {
"A": "17 hr",
"B": "19 hr",
"C": "10 hr",
"D": "24 hr",
"E": "30 hr"
} | inverse(subtract(divide(1, 2), inverse(divide(add(multiply(2, 7), 1), 7)))) | divide(n2,n0)|multiply(n0,n3)|add(n2,#1)|divide(#2,n3)|inverse(#3)|subtract(#0,#4)|inverse(#5)| | "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 7 ) = 1 / 30 leak will empty the tank in 30 hrs . answer : e" | physics |
math_qa__gqfPcBfyTHPRZuXg | A ranch has both horses and ponies. Exactly 5/7 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch? Pick one
A) 33 B) 37 C) 41 D) 45 E) 49 | <gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">(7/2) * 3</gadget>
<output>21/2 = around 10.5</output>
<gadget id="calculator">lcm(7, 21/2)</gadget>
<output>21</output>
<gadget id="calculator">21 + 3</gadget>
<output>24</output>
<gadget id="calculator">24 + 21</gadget>
<output>45</output>
<result>D</result> | D | 45 | A ranch has both horses and ponies. Exactly 5/7 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch? | {
"A": "33",
"B": "37",
"C": "41",
"D": "45",
"E": "49"
} | add(add(lcm(7, multiply(divide(7, 2), 3)), 3), lcm(7, multiply(divide(7, 2), 3))) | divide(n1,n2)|multiply(n3,#0)|lcm(n1,#1)|add(n4,#2)|add(#3,#2)| | "5 / 7 * p are ponies with horseshoes , so p is a multiple of 7 . 2 / 3 * 5 / 7 * p = 10 / 21 * p are icelandic ponies with horseshoes , so p is a multiple of 21 . the minimum value of p is 21 . then h = p + 3 = 24 . the minimum number of horses and ponies is 45 . the answer is d ." | general |
math_qa__uYBL2nGXRoZXde05 | A student gets 70% in one subject, 80% in the other. To get an overall of 75% how much should get in third subject.
Pick one: A) 75 % B) 25 % C) 45 % D) 55 % E) 65 % | <gadget id="calculator">75 * 3</gadget>
<output>225</output>
<gadget id="calculator">70 + 80</gadget>
<output>150</output>
<gadget id="calculator">225 - 150</gadget>
<output>75</output>
<result>A</result> | A | 75 | A student gets 70% in one subject, 80% in the other. To get an overall of 75% how much should get in third subject. | {
"A": "75 %",
"B": "25 %",
"C": "45 %",
"D": "55 %",
"E": "65 %"
} | subtract(multiply(75, const_3), add(70, 80)) | add(n0,n1)|multiply(n2,const_3)|subtract(#1,#0)| | "a student gets 70 % in one subject , 80 % in the other . average of 2 subjects is 75 % , if they have equal weightage . to get an overall of 75 % , he should get 75 % in third subject to maintain same % age . . if they have equal weightage . answer : a" | gain |
math_qa__l2GdTkjF6IqvXlu2 | Carina has 85 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have? Choices.
A) 5 B) 6 C) 7 D) 8 E) 9 | <gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">85 - 10</gadget>
<output>75</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">75 / 15</gadget>
<output>5</output>
<result>A</result> | A | 5 | Carina has 85 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have? | {
"A": "5",
"B": "6",
"C": "7",
"D": "8",
"E": "9"
} | divide(subtract(85, multiply(5, 2)), add(10, 5)) | add(n1,n2)|multiply(n1,n3)|subtract(n0,#1)|divide(#2,#0)| | "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 85 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 85 - > y = 75 / 15 . = 5 a" | general |
math_qa__FvCq6hIhWmTJRNWy | How much water must be added to 56 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? Choose the correct choice from the following choices: A) 10 litres B) 12 litres C) 14 litres D) 18 litres E) none of these | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">20 / (3/2)</gadget>
<output>40/3 = around 13.333333</output>
<result>C</result> | C | 14 | How much water must be added to 56 litres of milk at 1 1⁄2 litres for 20 so as to have a mixture worth 10 2⁄3 a litre? | {
"A": "10 litres",
"B": "12 litres",
"C": "14 litres",
"D": "18 litres",
"E": "none of these"
} | divide(20, add(1, divide(1, 2))) | divide(n1,n3)|add(n1,#0)|divide(n4,#1)| | "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 56 litres of milk = ( 1 ⁄ 4 × 56 ) litres = 14 litres . answer c" | general |
math_qa__otnrdu0nTx0PJ8EZ | If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2000 less than the principal. What was the principal? Pick one:
A) 1500 B) 2500 C) 2507 D) 3200 E) 11500 | <gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">2_000 / (4/5)</gadget>
<output>2_500</output>
<result>B</result> | B | 2,500 | If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2000 less than the principal. What was the principal? | {
"A": "1500",
"B": "2500",
"C": "2507",
"D": "3200",
"E": "11500"
} | divide(2000, subtract(const_1, divide(multiply(4, 5), const_100))) | multiply(n0,n1)|divide(#0,const_100)|subtract(const_1,#1)|divide(n2,#2)| | "p - 2000 = ( p * 5 * 4 ) / 100 p = 2500 answer : b" | gain |
math_qa__NH16fANntrLbUmN9 | The sum of the numbers is 110. If the first number be twice the second and third number be one-third of the first, then the second number is: Pick one
A) 30 B) 54 C) 72 D) 84 E) 27 | <gadget id="calculator">110 * 3</gadget>
<output>330</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">330 / 11</gadget>
<output>30</output>
<result>A</result> | A | 30 | The sum of the numbers is 110. If the first number be twice the second and third number be one-third of the first, then the second number is: | {
"A": "30",
"B": "54",
"C": "72",
"D": "84",
"E": "27"
} | divide(multiply(110, const_3), add(const_10, const_1)) | add(const_1,const_10)|multiply(n0,const_3)|divide(#1,#0)| | "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 110 11 x / 3 = 110 x = 30 answer : a" | general |
math_qa__pcFxggiivTZOWF2Q | total dinning bill of 3 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared . Choose the correct choice from the following answers:
A) 21.84 B) 50.96 C) 53.84 D) 24.84 E) 50.26 | <gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">139 * (11/10)</gadget>
<output>1_529/10 = around 152.9</output>
<gadget id="calculator">(1_529/10) / 3</gadget>
<output>1_529/30 = around 50.966667</output>
<result>B</result> | B | 50.96 | total dinning bill of 3 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared . | {
"A": "21.84",
"B": "50.96",
"C": "53.84",
"D": "24.84",
"E": "50.26"
} | divide(multiply(139.00, add(divide(const_1, 10), const_1)), 3) | divide(const_1,n2)|add(#0,const_1)|multiply(n1,#1)|divide(#2,n0)| | "dinner bill of 3 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 3 = $ 50.96 answer : b" | general |
math_qa__xvlpCRc88Q1U31oF | The ratio of the radius of two circles is 5: 3, and then the ratio of their areas is? Choices:
A) 1 : 8 B) 1 : 6 C) 25 : 9 D) 1 : 3 E) 1 : 2 | <gadget id="calculator">pi * (5 ** 2)</gadget>
<output>25*pi = around 78.539816</output>
<gadget id="calculator">pi * (3 ** 2)</gadget>
<output>9*pi = around 28.274334</output>
<gadget id="calculator">(25*pi) / (9*pi)</gadget>
<output>25/9 = around 2.777778</output>
<result>C</result> | C | 2.777778 | The ratio of the radius of two circles is 5: 3, and then the ratio of their areas is? | {
"A": "1 : 8",
"B": "1 : 6",
"C": "25 : 9",
"D": "1 : 3",
"E": "1 : 2"
} | divide(circle_area(5), circle_area(3)) | circle_area(n0)|circle_area(n1)|divide(#0,#1)| | "r 1 : r 2 = 5 : 3 π r 12 : π r 22 r 12 : r 22 = 25 : 9 answer : c" | geometry |
math_qa__e5W9nI3Ov7bm3P4l | If the price of gasoline increases by 20% and a driver intends to spend only 14% more on gasoline, by how much percent should the driver reduce the quantity of gasoline that he buys?
Select the correct option.
A) 1 %
B) 2 %
C) 4 %
D) 5 %
E) 6 % | <gadget id="calculator">20 + 100</gadget>
<output>120</output>
<gadget id="calculator">14 + 100</gadget>
<output>114</output>
<gadget id="calculator">120 - 114</gadget>
<output>6</output>
<gadget id="calculator">6 / 120</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 100</gadget>
<output>5</output>
<result>D</result> | D | 5 | If the price of gasoline increases by 20% and a driver intends to spend only 14% more on gasoline, by how much percent should the driver reduce the quantity of gasoline that he buys? | {
"A": "1 %",
"B": "2 %",
"C": "4 %",
"D": "5 %",
"E": "6 %"
} | multiply(divide(subtract(add(20, const_100), add(14, const_100)), add(20, const_100)), const_100) | add(n0,const_100)|add(n1,const_100)|subtract(#0,#1)|divide(#2,#0)|multiply(#3,const_100) | let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.2 * p ) y = 1.14 ( p * x ) y = ( 1.14 / 1.2 ) x = 0.95 x which is a reduction of 5 % . the answer is d . | general |
math_qa__csCM2zCgRAYWjBBn | The average of 7 consecutive numbers is 20. The largest of these numbers is :
Choices.
A) 21 B) 22 C) 23 D) 24 E) 25 | <gadget id="calculator">20 * 7</gadget>
<output>140</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">1 + 7</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">10 + 11</gadget>
<output>21</output>
<gadget id="calculator">140 - 21</gadget>
<output>119</output>
<gadget id="calculator">119 / 7</gadget>
<output>17</output>
<gadget id="calculator">17 + 6</gadget>
<output>23</output>
<result>C</result> | C | 23 | The average of 7 consecutive numbers is 20. The largest of these numbers is : | {
"A": "21",
"B": "22",
"C": "23",
"D": "24",
"E": "25"
} | add(divide(subtract(multiply(20, 7), add(add(add(add(const_1, add(add(add(add(add(const_1, const_2), const_1), const_1), const_1), const_1)), const_1), const_1), add(add(add(add(const_1, add(add(add(add(add(const_1, const_2), const_1), const_1), const_1), const_1)), const_1), const_1), const_1))), 7), add(add(add(add(const_1, const_2), const_1), const_1), const_1)) | add(const_1,const_2)|multiply(n0,n1)|add(#0,const_1)|add(#2,const_1)|add(#3,const_1)|add(#4,const_1)|add(#5,const_1)|add(#6,const_1)|add(#7,const_1)|add(#8,const_1)|add(#8,#9)|subtract(#1,#10)|divide(#11,n0)|add(#4,#12)| | "explanation : let the numbers be x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5 and x + 6 , then ( x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) ) / 7 = 20 . or 7 x + 21 = 140 or 7 x = 119 or x = 17 . latest number = x + 6 = 23 . answer : c" | general |
math_qa__EggZ2G64cJXSs0fo | 9 neighbors are to split the cost of topsoil . the cost of the 5 truck loads of dirt was $ 690.47 . what is the least amount of money ( in whole number of dollars ) that they must add to bill if they wants to split this money evenly among his 9 neighbors ? Answers.
A) 690.48 B) 690.49 C) 690.5 D) 690.51 E) 690.52 | <gadget id="calculator">min(690.47, 690.47)</gadget>
<output>690.47</output>
<result>A</result> | A | 690.48 | 9 neighbors are to split the cost of topsoil . the cost of the 5 truck loads of dirt was $ 690.47 . what is the least amount of money ( in whole number of dollars ) that they must add to bill if they wants to split this money evenly among his 9 neighbors ? | {
"A": "690.48",
"B": "690.49",
"C": "690.5",
"D": "690.51",
"E": "690.52"
} | min(690.47, 690.47) | min(n2,n2) | if the bill was $ 690.47 dollars , how much money should be removed with 1 cent as the smallest unit ? this is equivalent to finding the first number that is divisible by 9 that occurs after 690.47 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 6 + 9 + 0 + 4 + 7 = 26 . if you add 1 , the number is divisible by 9 ( 26 + 1 ) . 27 is divisible by 9 . hence , we need to add 1 cent from this number for it to be divisible by 9 . correct option : a | general |
math_qa__OePTQDf8ptStchYN | Evaluate: 11 + sqrt(- 4 + 6×4÷3) Answers
A) 9 B) 10 C) 11 D) 12 E) 13 | <gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<gadget id="calculator">8 - 4</gadget>
<output>4</output>
<gadget id="calculator">4 ** (1/2)</gadget>
<output>2</output>
<gadget id="calculator">11 + 2</gadget>
<output>13</output>
<result>E</result> | E | 13 | Evaluate: 11 + sqrt(- 4 + 6×4÷3) | {
"A": "9",
"B": "10",
"C": "11",
"D": "12",
"E": "13"
} | add(11, sqrt(subtract(divide(multiply(6, 4), 3), 4))) | multiply(n1,n2)|divide(#0,n4)|subtract(#1,n1)|sqrt(#2)|add(n0,#3)| | "according to order of operations , inner brackets first where 6 × 4 ÷ 3 is first calculated since it has a multiplication and a division . 6 × 4 ÷ 3 = 24 ÷ 3 = 8 hence 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer e ) 13" | general |
math_qa__WsZ6Vm6bG9jIa9bI | Total dinning bill for 7 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share Choose the most appropriate option
A) $ 30.14
B) 45.14
C) 34.66
D) 32.29
E) 33.16 | <gadget id="calculator">15 * 211</gadget>
<output>3_165</output>
<gadget id="calculator">3_165 / 100</gadget>
<output>633/20 = around 31.65</output>
<gadget id="calculator">211 + (633/20)</gadget>
<output>4_853/20 = around 242.65</output>
<gadget id="calculator">(4_853/20) / 7</gadget>
<output>4_853/140 = around 34.664286</output>
<result>C</result> | C | 34.66 | Total dinning bill for 7 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share | {
"A": "$ 30.14",
"B": "45.14",
"C": "34.66",
"D": "32.29",
"E": "33.16"
} | divide(add(211.00, divide(multiply(15, 211.00), const_100)), 7) | multiply(n1,n2)|divide(#0,const_100)|add(n1,#1)|divide(#2,n0)| | "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 7 = 34.66 answer : c" | general |
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