id stringlengths 25 25 | question stringlengths 45 1.01k | chain stringlengths 75 4.11k | result stringclasses 5 values | result_float float64 -4,212 100B | question_without_options stringlengths 6 962 | options dict | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | rationale stringlengths 1 2.74k | category stringclasses 6 values |
|---|---|---|---|---|---|---|---|---|---|---|
math_qa__wudDYGarAS26Ul8H | The edge of a cube is 2a cm. Find its surface? Select the correct option
A) 23 a 2 cm 2 B) 84 a 2 cm 2 C) 64 a 2 cm 2 D) 24 a 2 cm 2 E) 14 a 2 cm 2 | <gadget id="calculator">6 * (2 ** 2)</gadget>
<output>24</output>
<result>D</result> | D | 24 | The edge of a cube is 2a cm. Find its surface? | {
"A": "23 a 2 cm 2",
"B": "84 a 2 cm 2",
"C": "64 a 2 cm 2",
"D": "24 a 2 cm 2",
"E": "14 a 2 cm 2"
} | surface_cube(2) | surface_cube(n0)| | "6 a 2 = 6 * 2 a * 2 a = 24 a 2 answer : d" | geometry |
math_qa__RqrMeN8Q3kJ4x4XU | Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 2 km apart, if they walk in the same direction? Answers:
A) 5 hours
B) 6 hours
C) 1 hours
D) 10 hours
E) 12 hours | <gadget id="calculator">12 - 10</gadget>
<output>2</output>
<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<result>C</result> | C | 1 | Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 2 km apart, if they walk in the same direction? | {
"A": "5 hours",
"B": "6 hours",
"C": "1 hours",
"D": "10 hours",
"E": "12 hours"
} | divide(subtract(12, 10), 2) | subtract(n1,n0)|divide(#0,n2) | to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 2 = 1 hours answer is c | gain |
math_qa__jxmR6qHlnFcUAjwm | Of 30 applicants for a job, 10 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree? Choices
A) 14 B) 13 C) 9 D) 7 E) 5 | <gadget id="calculator">10 + 18</gadget>
<output>28</output>
<gadget id="calculator">30 - 3</gadget>
<output>27</output>
<gadget id="calculator">28 - 27</gadget>
<output>1</output>
<gadget id="calculator">18 - 10</gadget>
<output>8</output>
<gadget id="calculator">1 + 8</gadget>
<output>9</output>
<result>C</result> | C | 9 | Of 30 applicants for a job, 10 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree? | {
"A": "14",
"B": "13",
"C": "9",
"D": "7",
"E": "5"
} | add(subtract(add(10, 18), subtract(30, 3)), subtract(18, 10)) | add(n1,n3)|subtract(n0,n4)|subtract(n3,n1)|subtract(#0,#1)|add(#3,#2) | c . 9 30 - 3 = 27 27 - 10 - 18 = - 9 then 9 are in the intersection between 4 years experience and degree . answer c | general |
math_qa__6tWBz4fLLCDlY1sw | A paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper? Pick one.
A) 8.76 B) 8.79 C) 8.75 D) 8.74 E) 8.72 | <gadget id="calculator">20 ** 2</gadget>
<output>400</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">pi * (10 ** 2)</gadget>
<output>100*pi = around 314.159265</output>
<gadget id="calculator">400 - (100*pi)</gadget>
<output>400 - 100*pi = around 85.840735</output>
<gadget id="calculator">(400 - 100*pi) / 10</gadget>
<output>40 - 10*pi = around 8.584073</output>
<result>C</result> | C | 8.75 | A paper is in a square form whose one side is 20 cm. Two semi circles are drawn on its opposites as diameters. If these semi circles are cut down what is the area of the remaining paper? | {
"A": "8.76",
"B": "8.79",
"C": "8.75",
"D": "8.74",
"E": "8.72"
} | divide(subtract(square_area(20), circle_area(divide(20, const_2))), const_10) | divide(n0,const_2)|square_area(n0)|circle_area(#0)|subtract(#1,#2)|divide(#3,const_10) | ( 5 * 3.5 ) / 2 = 8.75 answer : c | geometry |
math_qa__DwiOTPLldOpfKa6X | Of 70 players on a football team, 34 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? Options
A) 54 B) 58 C) 63 D) 71 E) 92 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">70 - 34</gadget>
<output>36</output>
<gadget id="calculator">(2/3) * 36</gadget>
<output>24</output>
<gadget id="calculator">24 + 34</gadget>
<output>58</output>
<result>B</result> | B | 58 | Of 70 players on a football team, 34 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? | {
"A": "54",
"B": "58",
"C": "63",
"D": "71",
"E": "92"
} | add(multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 34)), 34) | divide(const_1,const_3)|subtract(n0,n1)|subtract(const_1,#0)|multiply(#2,#1)|add(n1,#3)| | "total = 70 thrower = 34 rest = 70 - 34 = 36 left handed = 36 / 3 = 12 right handed = 24 if all thrower are right handed then total right handed is 34 + 24 = 58 so b . 58 is the right answer" | general |
math_qa__s18y6BwNFstQgOwz | If the digits 31 in the decimal 0.00031 repeat indefinitely, what is the value of (10^5-10^3)(0.00031)? Select
A) 31 B) 0.31 C) 0.0031 D) 0.00031 E) 3.1 e - 05 | <gadget id="calculator">10 * 10</gadget>
<output>100</output>
<gadget id="calculator">100 - 1</gadget>
<output>99</output>
<gadget id="calculator">100 * 99</gadget>
<output>9_900</output>
<gadget id="calculator">31 / 99</gadget>
<output>31/99 = around 0.313131</output>
<gadget id="calculator">9_900 * (31/99)</gadget>
<output>3_100</output>
<gadget id="calculator">3_100 / 1_000</gadget>
<output>31/10 = around 3.1</output>
<gadget id="calculator">(31/10) * 10</gadget>
<output>31</output>
<result>A</result> | A | 31 | If the digits 31 in the decimal 0.00031 repeat indefinitely, what is the value of (10^5-10^3)(0.00031)? | {
"A": "31",
"B": "0.31",
"C": "0.0031",
"D": "0.00031",
"E": "3.1 e - 05"
} | multiply(divide(multiply(multiply(multiply(10, 10), subtract(multiply(10, 10), const_1)), divide(31, subtract(multiply(10, 10), const_1))), const_1000), 10) | multiply(n2,n2)|subtract(#0,const_1)|divide(n0,#1)|multiply(#0,#1)|multiply(#2,#3)|divide(#4,const_1000)|multiply(n2,#5)| | "99 * 0.31 = 30.69 approx . 31 answer : a" | general |
math_qa__jsXNyTvI7fEA2rop | The perimeter of a triangle is 48 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle? Choose one:
A) 87 cm 2 B) 28 cm 2 C) 98 cm 2 D) 26 cm 2 E) 60 cm 2 | <gadget id="calculator">(2.5 * 48) / 2</gadget>
<output>60</output>
<result>E</result> | E | 60 | The perimeter of a triangle is 48 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle? | {
"A": "87 cm 2",
"B": "28 cm 2",
"C": "98 cm 2",
"D": "26 cm 2",
"E": "60 cm 2"
} | triangle_area(2.5, 48) | triangle_area(n0,n1)| | "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 * 48 / 2 = 60 cm 2 answer : e" | geometry |
math_qa__zqUDa53RTS2usFHz | A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 24%. What quantity of whisky is replaced ? Answers
A) 1 / 3 B) 2 / 3 C) 2 / 5 D) 3 / 5 E) 16 / 21 | <gadget id="calculator">40 - 24</gadget>
<output>16</output>
<gadget id="calculator">40 - 19</gadget>
<output>21</output>
<gadget id="calculator">16 / 21</gadget>
<output>16/21 = around 0.761905</output>
<result>E</result> | E | 0.761905 | A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 24%. What quantity of whisky is replaced ? | {
"A": "1 / 3",
"B": "2 / 3",
"C": "2 / 5",
"D": "3 / 5",
"E": "16 / 21"
} | divide(subtract(40, 24), subtract(40, 19)) | subtract(n0,n2)|subtract(n0,n1)|divide(#0,#1)| | "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.24 - - - > x = 160 / 21 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 160 / 21 ) / 10 = 16 / 21 . hence , e is the correct answer ." | gain |
math_qa__cSpE6KxOFT6VBsnO | If the sum of two numbers is 30 and the sum of their squares is 840, then the product of the numbers is
Answers.
A) 40
B) 44
C) 80
D) 88
E) 30 | <gadget id="calculator">30 ** 2</gadget>
<output>900</output>
<gadget id="calculator">900 - 840</gadget>
<output>60</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<result>E</result> | E | 30 | If the sum of two numbers is 30 and the sum of their squares is 840, then the product of the numbers is | {
"A": "40",
"B": "44",
"C": "80",
"D": "88",
"E": "30"
} | divide(subtract(power(30, const_2), 840), const_2) | power(n0,const_2)|subtract(#0,n1)|divide(#1,const_2) | sol . let the numbers be x and y . then , ( x + y ) = 30 and x 2 + y 2 = 840 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 30 ) 2 - 840 = 900 - 840 = 60 xy = 30 . answer e | general |
math_qa__xnGSbMmcQBcxk56s | Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. Choose the correct choice from the following:
A) 298 km
B) 278 km
C) 278 km
D) 300 km
E) 267 km | <gadget id="calculator">2 * 30</gadget>
<output>60</output>
<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<gadget id="calculator">1 / 50</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/60) + (1/50)</gadget>
<output>11/300 = around 0.036667</output>
<gadget id="calculator">1 / (11/300)</gadget>
<output>300/11 = around 27.272727</output>
<gadget id="calculator">(300/11) * 11</gadget>
<output>300</output>
<result>D</result> | D | 300 | Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. | {
"A": "298 km",
"B": "278 km",
"C": "278 km",
"D": "300 km",
"E": "267 km"
} | multiply(inverse(add(inverse(multiply(const_2, 30)), inverse(multiply(25, const_2)))), 11) | multiply(n1,const_2)|multiply(n2,const_2)|inverse(#0)|inverse(#1)|add(#2,#3)|inverse(#4)|multiply(n0,#5)| | "let the distance travelled be x km . total time = ( x / 2 ) / 30 + ( x / 2 ) / 25 = 11 = > x / 60 + x / 50 = 11 = > ( 5 x + 6 x ) / 300 = 11 = > x = 300 km answer : d" | physics |
math_qa__xlgfXeCz3GnhHD58 | If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d| Choose the correct choice from the following options: A) 10 B) 12 C) 15 D) 18 E) 20 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">5 + 7</gadget>
<output>12</output>
<result>B</result> | B | 12 | If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d| | {
"A": "10",
"B": "12",
"C": "15",
"D": "18",
"E": "20"
} | add(add(2, const_3), add(const_3, const_4)) | add(n1,const_3)|add(const_3,const_4)|add(#0,#1) | this is the hard one , definitely a 700 + level question . we need numbers a , b , c , and d such that 6 x ^ 2 + x - 12 = ( ax + b ) ( cx + d ) this means that ac = 6 , bd = – 12 , and ad + bc = 1 . the a & c pair could be ( 1 , 6 ) or ( 2 , 3 ) , in some order . the absolute values of the b & d pair could be ( 1 , 12 ) or ( 2 , 6 ) or ( 3 , 4 ) , and of course , in each case , one of the two would have to be negative . after some trial and error , we find : 6 x ^ 2 + x - 12 = ( 2 x + 3 ) ( 3 x - 4 ) thus , we see : | a | + | b | + | c | + | d | = 2 + 3 + 3 + 4 = 12 answer = b | general |
math_qa__r50RFz7hxTz91BN8 | The speed of a boat in still water in 20 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is: Choose the correct choice from the following:
A) 9.2
B) 10.2
C) 9.8
D) 9.6
E) 10.0 | <gadget id="calculator">20 + 4</gadget>
<output>24</output>
<gadget id="calculator">24 / 60</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">24 * (2/5)</gadget>
<output>48/5 = around 9.6</output>
<result>D</result> | D | 9.6 | The speed of a boat in still water in 20 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is: | {
"A": "9.2",
"B": "10.2",
"C": "9.8",
"D": "9.6",
"E": "10.0"
} | multiply(add(20, 4), divide(24, const_60)) | add(n0,n1)|divide(n2,const_60)|multiply(#0,#1)| | "speed downstream = ( 20 + 4 ) = 24 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 24 = 9.6 km answer is d ." | physics |
math_qa__mQXWFTBxcYRd4YXz | Two cars are driving toward each other. The first car is traveling at a speed of 100 km/h, which is 25% faster than the second car's speed. If the distance between the cars is 720 km, how many hours will it take until the two cars meet? Select the correct option
A) 3 B) 3.5 C) 4 D) 4.5 E) 5 | <gadget id="calculator">100 * 4</gadget>
<output>400</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">400 / 5</gadget>
<output>80</output>
<gadget id="calculator">80 * 4</gadget>
<output>320</output>
<gadget id="calculator">400 + 320</gadget>
<output>720</output>
<gadget id="calculator">100 + 80</gadget>
<output>180</output>
<gadget id="calculator">720 / 180</gadget>
<output>4</output>
<result>C</result> | C | 4 | Two cars are driving toward each other. The first car is traveling at a speed of 100 km/h, which is 25% faster than the second car's speed. If the distance between the cars is 720 km, how many hours will it take until the two cars meet? | {
"A": "3",
"B": "3.5",
"C": "4",
"D": "4.5",
"E": "5"
} | divide(add(multiply(100, const_4), multiply(divide(multiply(const_4, 100), add(const_1, const_4)), const_4)), add(100, divide(multiply(const_4, 100), add(const_1, const_4)))) | add(const_1,const_4)|multiply(n0,const_4)|divide(#1,#0)|add(n0,#2)|multiply(#2,const_4)|add(#1,#4)|divide(#5,#3) | the speed of the first car is 100 km / h . the speed of the second car is 100 / 1.25 = 80 km / h . the two cars complete a total of 180 km each hour . the time it takes the cars to meet is 720 / 180 = 4 hours . the answer is c . | physics |
math_qa__0vRPfujuv7rN53yG | A tiger is chasing its prey at a constant speed. It entire body passes a blade of grass in 1 second. It then runs above a fallen tree trunk that is 20 meters long in 5 seconds. What is the length of the tiger? Options:
A) 6 m B) 5 m C) 4 m D) 3 m E) none of the above | <gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<result>B</result> | B | 5 | A tiger is chasing its prey at a constant speed. It entire body passes a blade of grass in 1 second. It then runs above a fallen tree trunk that is 20 meters long in 5 seconds. What is the length of the tiger? | {
"A": "6 m",
"B": "5 m",
"C": "4 m",
"D": "3 m",
"E": "none of the above"
} | divide(20, subtract(5, 1)) | subtract(n2,n0)|divide(n1,#0) | sol . let the length of the tiger be x metres and its speed be y m / sec . then , x / y = 1 ⇒ y = x ∴ ( x + 20 ) / 5 = x ⇔ x = 5 m . answer b | physics |
math_qa__XbpRnnBQMZ5W5Hfu | A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 25%. Their gross income from sales for one month increases by what percent? Choose the correct choice from the following: A) 5 % B) 7.5 % C) 10 % D) 12.5 % E) 15 % | <gadget id="calculator">25 - 10</gadget>
<output>15</output>
<gadget id="calculator">25 / 10</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">15 - (5/2)</gadget>
<output>25/2 = around 12.5</output>
<result>D</result> | D | 12.5 | A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 25%. Their gross income from sales for one month increases by what percent? | {
"A": "5 %",
"B": "7.5 %",
"C": "10 %",
"D": "12.5 %",
"E": "15 %"
} | subtract(subtract(25, 10), divide(25, 10)) | divide(n1,n0)|subtract(n1,n0)|subtract(#1,#0)| | "let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.25 x = 1.125 * ( p * x ) , an increase of 12.5 % . the answer is d ." | gain |
math_qa__PlZLQXvA5x8ylyBo | 5/8th of a job is completed in 10 days. If a person works at the same pace, how many days will he take to complete the job? Choose the correct choice from the following choices: A) 8 B) 9 C) 6 D) 2 E) 1 | <gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/8) * 10</gadget>
<output>15/4 = around 3.75</output>
<gadget id="calculator">8 / 5</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(15/4) * (8/5)</gadget>
<output>6</output>
<result>C</result> | C | 6 | 5/8th of a job is completed in 10 days. If a person works at the same pace, how many days will he take to complete the job? | {
"A": "8",
"B": "9",
"C": "6",
"D": "2",
"E": "1"
} | multiply(multiply(subtract(const_1, divide(5, 8)), 10), divide(8, 5)) | divide(n1,n0)|divide(n0,n1)|subtract(const_1,#1)|multiply(n2,#2)|multiply(#0,#3) | explanation : solution : it is given that 5 / 8 th of the work is completed in 10 days . = > remaining work = 3 / 8 th of total applying unitary method : total work will be completed in 10 * 8 / 5 days = > it takes 16 days to complete total work = > hence , remaining work days = 16 - 10 = 6 days answer : c | physics |
math_qa__I0h1Dtrha6OPxLXY | The sum of two numbers is 30 and their difference is 10. Find their product. Choose the correct choice from the following choices.
A) 104 B) 114 C) 315 D) 200 E) 335 | <gadget id="calculator">30 + 10</gadget>
<output>40</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<result>D</result> | D | 200 | The sum of two numbers is 30 and their difference is 10. Find their product. | {
"A": "104",
"B": "114",
"C": "315",
"D": "200",
"E": "335"
} | multiply(divide(add(30, 10), add(const_1, const_1)), subtract(divide(add(30, 10), add(const_1, const_1)), 10)) | add(n0,n1)|add(const_1,const_1)|divide(#0,#1)|subtract(#2,n1)|multiply(#2,#3) | let the numbers be x and y . then x + y = 30 and x - y = 10 x = 20 ; y = 10 xy = 20 * 10 = 200 answer : d | general |
math_qa__0LRAHUoaEVZ4UzKl | Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number, find the number ? Answers.
A) 2490 and 4150 B) 249 and 415 C) 2400 and 4100 D) 2290 and 4350 E) 229 and 435 | <gadget id="calculator">7.5 / 12.5</gadget>
<output>0.6</output>
<gadget id="calculator">1 - 0.6</gadget>
<output>0.4</output>
<gadget id="calculator">1_660 / 0.4</gadget>
<output>4_150</output>
<gadget id="calculator">0.6 * 4_150</gadget>
<output>2_490</output>
<result>A</result> | A | 2,490 | Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number, find the number ? | {
"A": "2490 and 4150",
"B": "249 and 415",
"C": "2400 and 4100",
"D": "2290 and 4350",
"E": "229 and 435"
} | multiply(divide(7.5, 12.5), divide(1660, subtract(const_1, divide(7.5, 12.5)))) | divide(n1,n2)|subtract(const_1,#0)|divide(n0,#1)|multiply(#0,#2) | let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1660 5 * y / 3 – y = 1660 2 * y / 3 = 1660 y = [ ( 1660 * 3 ) / 2 ] = 2490 . one number = 2490 , second number = 5 * y / 3 = 4150 answer is a . | gain |
math_qa__LOxHFAFrr9wdrZkP | Jack and Christina are standing 360 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 5 feet per second and Christina walks in a straight line toward Jack at a constant speed of 7 feet per second. Lindy runs at a constant speed of 12 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place? Options.
A) 270
B) 300
C) 330
D) 360
E) 390 | <gadget id="calculator">5 + 7</gadget>
<output>12</output>
<gadget id="calculator">360 / 12</gadget>
<output>30</output>
<gadget id="calculator">30 * 12</gadget>
<output>360</output>
<result>D</result> | D | 360 | Jack and Christina are standing 360 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 5 feet per second and Christina walks in a straight line toward Jack at a constant speed of 7 feet per second. Lindy runs at a constant speed of 12 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place? | {
"A": "270",
"B": "300",
"C": "330",
"D": "360",
"E": "390"
} | multiply(divide(360, add(5, 7)), 12) | add(n1,n2)|divide(n0,#0)|multiply(n3,#1)| | "the relative speed of jack and christina is 5 + 7 = 12 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 360 / 12 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 12 * 30 = 360 feet . answer : d ." | physics |
math_qa__2LuuVE1SAFg2fVjg | A train running at the speed of 54 km/hr crosses a pole in 9 seconds. Find the length of the train? Choose one: A) 150 meter B) 299 meter C) 135 meter D) 155 meter E) 144 meter | <gadget id="calculator">54 * 1_000</gadget>
<output>54_000</output>
<gadget id="calculator">54_000 / 3_600</gadget>
<output>15</output>
<gadget id="calculator">15 * 9</gadget>
<output>135</output>
<result>C</result> | C | 135 | A train running at the speed of 54 km/hr crosses a pole in 9 seconds. Find the length of the train? | {
"A": "150 meter",
"B": "299 meter",
"C": "135 meter",
"D": "155 meter",
"E": "144 meter"
} | multiply(divide(multiply(54, const_1000), const_3600), 9) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = 54 * ( 5 / 18 ) m / sec = 15 m / sec length of train ( distance ) = speed * time ( 15 ) * 9 = 135 meter answer : c" | physics |
math_qa__UiZrGN0DaK6O5GbO | Simplify 3/4 of 6 0 – 8/5 of 60 + ? = 12 Choose the correct choice from the following: A) 48 B) 24 C) 56 D) 63 E) 14 | <gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 60</gadget>
<output>45</output>
<gadget id="calculator">8 / 5</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) * 60</gadget>
<output>96</output>
<gadget id="calculator">45 - 96</gadget>
<output>-51</output>
<gadget id="calculator">-(-51)</gadget>
<output>51</output>
<gadget id="calculator">51 + 12</gadget>
<output>63</output>
<result>D</result> | D | 63 | Simplify 3/4 of 6 0 – 8/5 of 60 + ? = 12 | {
"A": "48",
"B": "24",
"C": "56",
"D": "63",
"E": "14"
} | add(negate(subtract(multiply(divide(3, 4), 60), multiply(divide(8, 5), 60))), 12) | divide(n0,n1)|divide(n4,n5)|multiply(n6,#0)|multiply(n6,#1)|subtract(#2,#3)|negate(#4)|add(n7,#5) | 60 × 3 / 4 = 45 , 60 × 8 / 5 = 96 45 – 96 + ? = 12 = > 96 + 12 = 108 – 45 = 63 [ 63 + 45 = 108 – 96 = 12 ] option d | general |
math_qa__P764RVuMjKMt0O5m | what is the average ( arithmetic mean ) of all the multiples of 10 from 10 to 160 inclusive ? Pick.
A) 90
B) 95
C) 70
D) 105
E) 110 | <gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">160 - 20</gadget>
<output>140</output>
<gadget id="calculator">140 / 2</gadget>
<output>70</output>
<result>C</result> | C | 70 | what is the average ( arithmetic mean ) of all the multiples of 10 from 10 to 160 inclusive ? | {
"A": "90",
"B": "95",
"C": "70",
"D": "105",
"E": "110"
} | divide(subtract(160, multiply(10, const_2)), const_2) | multiply(n0,const_2)|subtract(n2,#0)|divide(#1,const_2) | 10 and 190 inclusive would mean there are 15 terms . no need to add up all the terms and further divide by 15 since the terms are evenly spaced in ascending order from 10 , 20 , 30 . . . . . . . . 160 the middle term is the average which is the tenth term = 70 c is the answer . | general |
math_qa__j7GTyhYS41jNskoO | Michael earns $7.00 per hour for the first 40 hours he works per week, and twice this rate for overtime. If Michael earned $320 last week, how many hours did he work?
Choose the correct answer
A) 43
B) 44
C) 45
D) 46
E) 47 | <gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">40 / 14</gadget>
<output>20/7 = around 2.857143</output>
<gadget id="calculator">(20/7) + 40</gadget>
<output>300/7 = around 42.857143</output>
<result>A</result> | A | 43 | Michael earns $7.00 per hour for the first 40 hours he works per week, and twice this rate for overtime. If Michael earned $320 last week, how many hours did he work? | {
"A": "43",
"B": "44",
"C": "45",
"D": "46",
"E": "47"
} | add(divide(40, multiply(7, const_2)), 40) | multiply(n0,const_2)|divide(n1,#0)|add(n1,#1) | $ 7 * 40 + $ 12 * x = $ 320 - - > x = 3 hours . total working hours = 40 + 3 = 43 . answer : a . | physics |
math_qa__r97E90cofrkdn4kY | If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Choose one: A) rs . 8082 B) rs . 7800 C) rs . 8100 D) rs . 8112 E) rs . 9000 | <gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">104 / 100</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">(26/25) * (26/25)</gadget>
<output>676/625 = around 1.0816</output>
<gadget id="calculator">7_500 * (676/625)</gadget>
<output>8_112</output>
<result>D</result> | D | 8,112 | If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is? | {
"A": "rs . 8082",
"B": "rs . 7800",
"C": "rs . 8100",
"D": "rs . 8112",
"E": "rs . 9000"
} | multiply(7500, multiply(divide(add(const_100, 4), const_100), divide(add(const_100, 4), const_100))) | add(n1,const_100)|divide(#0,const_100)|multiply(#1,#1)|multiply(n0,#2)| | "explanation : a = 7500 ( 26 / 25 ) 2 = 8112 answer is d" | gain |
math_qa__JKLqWIg6fJ3my4ng | Pat, Kate, and Mark charged a total of 153 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
Choose the correct choice from the following choices
A) 85 B) 36 C) 72 D) 90 E) 108 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 + (1/3)</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(4/3) + (1/6)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">153 / (3/2)</gadget>
<output>102</output>
<gadget id="calculator">102 / 6</gadget>
<output>17</output>
<gadget id="calculator">102 - 17</gadget>
<output>85</output>
<result>A</result> | A | 85 | Pat, Kate, and Mark charged a total of 153 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate? | {
"A": "85",
"B": "36",
"C": "72",
"D": "90",
"E": "108"
} | subtract(divide(153, add(add(1, divide(1, 3)), divide(1, multiply(3, const_2)))), divide(divide(153, add(add(1, divide(1, 3)), divide(1, multiply(3, const_2)))), multiply(3, const_2))) | divide(n1,n2)|multiply(n2,const_2)|add(n1,#0)|divide(n1,#1)|add(#2,#3)|divide(n0,#4)|divide(#5,#1)|subtract(#5,#6)| | "85 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 153 = > x = 17 34 : 17 : 102 102 - 17 = 85 answer a" | general |
math_qa__8Z51vl0taofQhpBX | The arithmetic mean of 5 negative integers is -100. If the average of 3 of these integers is -90, what is the least possible value that one of the other 2 integers can have? Choose the correct choice
A) 229 B) - 1 C) - 229 D) 90 E) - 90 | <gadget id="calculator">5 * 90</gadget>
<output>450</output>
<gadget id="calculator">450 - 100</gadget>
<output>350</output>
<gadget id="calculator">90 - 350</gadget>
<output>-260</output>
<gadget id="calculator">90 / 3</gadget>
<output>30</output>
<gadget id="calculator">(-260) + 30</gadget>
<output>-230</output>
<gadget id="calculator">(-230) + 1</gadget>
<output>-229</output>
<result>C</result> | C | -229 | The arithmetic mean of 5 negative integers is -100. If the average of 3 of these integers is -90, what is the least possible value that one of the other 2 integers can have? | {
"A": "229",
"B": "- 1",
"C": "- 229",
"D": "90",
"E": "- 90"
} | add(add(subtract(90, subtract(multiply(5, 90), 100)), divide(90, 3)), const_1) | divide(n3,n2)|multiply(n0,n3)|subtract(#1,n1)|subtract(n3,#2)|add(#0,#3)|add(#4,const_1) | the arithmetic mean of 5 negative integers is ( a + b + c + d + e ) / 5 = - 100 so , the sum of 5 negative integers would be a + b + c + d + e = - 100 * 5 = - 500 similarly , the sum of 3 negative integers would be a + b + c = - 90 * 3 = - 270 thus , the sum of the other 2 integers is - 500 + 270 = - 230 . since we know that the integers are negative then the least one from these two can be - 229 , the other one being - 1 . hence , the correct ans is c | general |
math_qa__r6dBbouvg0CjXAa9 | Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 94 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad? Choose one: A) 3 B) 4 C) 5 D) 6 E) 10 | <gadget id="calculator">94 + 6</gadget>
<output>100</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<result>E</result> | E | 10 | Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 94 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "10"
} | divide(add(94, 6), add(4, 6)) | add(n0,n2)|add(n1,n2)|divide(#0,#1)| | "total distance = 94 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 90 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 90 / 10 = 9 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 9 = 36 + 4 = 40 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 40 / 4 = 10 hrs . . . answer e" | physics |
math_qa__3sLYCdaQBOGDnOH6 | Excluding stoppages, the speed of a train is 48 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour? Answers.
A) 16 B) 17 C) 15 D) 10 E) 12 | <gadget id="calculator">40 / 48</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">60 * (5/6)</gadget>
<output>50</output>
<gadget id="calculator">60 - 50</gadget>
<output>10</output>
<result>D</result> | D | 10 | Excluding stoppages, the speed of a train is 48 kmph and including stoppages it is 40 kmph. Of how many minutes does the train stop per hour? | {
"A": "16",
"B": "17",
"C": "15",
"D": "10",
"E": "12"
} | subtract(const_60, multiply(const_60, divide(40, 48))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | "t = 8 / 48 * 60 = 10 answer : d" | physics |
math_qa__mFR22Tpxd0zNw1AE | If a child walks at the rate of 5m/min from his home, he is 6 minutes late for school, if he walks at the rate of 7m/min he reaches half an hour earlier. How far is his school from his home ? Answers:
A) 450 min
B) 540 min
C) 630 min
D) 360 min
E) none of these | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">60 * (1/2)</gadget>
<output>30</output>
<gadget id="calculator">30 + 6</gadget>
<output>36</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/5) - (1/7)</gadget>
<output>2/35 = around 0.057143</output>
<gadget id="calculator">36 / (2/35)</gadget>
<output>630</output>
<result>C</result> | C | 630 | If a child walks at the rate of 5m/min from his home, he is 6 minutes late for school, if he walks at the rate of 7m/min he reaches half an hour earlier. How far is his school from his home ? | {
"A": "450 min",
"B": "540 min",
"C": "630 min",
"D": "360 min",
"E": "none of these"
} | divide(add(multiply(const_60, divide(const_1, const_2)), 6), subtract(divide(const_1, 5), divide(const_1, 7))) | divide(const_1,const_2)|divide(const_1,n0)|divide(const_1,n2)|multiply(#0,const_60)|subtract(#1,#2)|add(n1,#3)|divide(#5,#4) | let the distance between home and school is x . let actual time to reach be t . thus , x / 5 = t + 6 - - - - ( 1 ) and x / 7 = t - 30 - - - - - ( 2 ) solving equation 1 and 2 x = 630 min answer : c | physics |
math_qa__bDHa1muGtROs9ujT | Evaluate: |9 - 8(3 - 12)| - |5 - 11| = ?
Choose the correct choice from the following:
A) 75 B) 50 C) 60 D) 70 E) 80 | <gadget id="calculator">3 - 12</gadget>
<output>-9</output>
<gadget id="calculator">8 * (-9)</gadget>
<output>-72</output>
<gadget id="calculator">9 - (-72)</gadget>
<output>81</output>
<gadget id="calculator">5 - 11</gadget>
<output>-6</output>
<gadget id="calculator">-(-6)</gadget>
<output>6</output>
<gadget id="calculator">81 - 6</gadget>
<output>75</output>
<result>A</result> | A | 75 | Evaluate: |9 - 8(3 - 12)| - |5 - 11| = ? | {
"A": "75",
"B": "50",
"C": "60",
"D": "70",
"E": "80"
} | subtract(subtract(9, multiply(8, subtract(3, 12))), negate(subtract(5, 11))) | subtract(n2,n3)|subtract(n4,n5)|multiply(n1,#0)|negate(#1)|subtract(n0,#2)|subtract(#4,#3) | according to order of operations , inner brackets first . hence | 9 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 9 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 9 + 72 | - | 5 - 11 | = | 81 | - | - 6 | = 81 - 6 = 75 correct answer a ) 75 | general |
math_qa__yTLm2UjUo3PC33KU | In Town X, 64 percent of the population are employed, and 50 percent of the population are employed males. What percent of the employed people in Town X are females? Options:
A) 16 % B) 22 % C) 32 % D) 40 % E) 52 % | <gadget id="calculator">64 - 50</gadget>
<output>14</output>
<gadget id="calculator">14 / 64</gadget>
<output>7/32 = around 0.21875</output>
<gadget id="calculator">(7/32) * 100</gadget>
<output>175/8 = around 21.875</output>
<result>B</result> | B | 22 | In Town X, 64 percent of the population are employed, and 50 percent of the population are employed males. What percent of the employed people in Town X are females? | {
"A": "16 %",
"B": "22 %",
"C": "32 %",
"D": "40 %",
"E": "52 %"
} | multiply(divide(subtract(64, 50), 64), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 50 are employed males , hence 14 % are employed females . ( employed females ) / ( total employed people ) = 14 / 64 = 22 % answer : b ." | gain |
math_qa__EkkqmqquFgV4dIOG | The cash difference between the selling prices of an book at a profit of 5% and 10% is $3. The ratio of the two selling prices is:
Answers: A) 21 : 22 B) 52 : 33 C) 52 : 53 D) 45 : 53 E) 51 : 34 | <gadget id="calculator">100 + 5</gadget>
<output>105</output>
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">105 / 110</gadget>
<output>21/22 = around 0.954545</output>
<result>A</result> | A | 0.954545 | The cash difference between the selling prices of an book at a profit of 5% and 10% is $3. The ratio of the two selling prices is: | {
"A": "21 : 22",
"B": "52 : 33",
"C": "52 : 53",
"D": "45 : 53",
"E": "51 : 34"
} | divide(add(const_100, 5), add(const_100, 10)) | add(n0,const_100)|add(n1,const_100)|divide(#0,#1)| | "let c . p . of the book be $ x . then , required ratio = 105 % of x / 110 % of x = 105 / 110 = 21 / 22 = 21 : 22 a" | gain |
math_qa__fnbBrLk9iWeN60ZE | A person buys an article at Rs.800. At what price should he sell the article so as to make a profit of 35%? Select the correct option:
A) 600 B) 277 C) 269 D) 261 E) 1080 | <gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">800 * (7/20)</gadget>
<output>280</output>
<gadget id="calculator">800 + 280</gadget>
<output>1_080</output>
<result>E</result> | E | 1,080 | A person buys an article at Rs.800. At what price should he sell the article so as to make a profit of 35%? | {
"A": "600",
"B": "277",
"C": "269",
"D": "261",
"E": "1080"
} | add(800, multiply(800, divide(35, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | "cost price = rs . 800 profit = 35 % of 800 = rs . 280 selling price = cost price + profit = 800 + 280 = 1080 answer : e" | gain |
math_qa__HjdrGwiNy00g3nG9 | Dacid obtained 96, 95, 82, 97 and 95 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? Options: A) 79 B) 93 C) 88 D) 88 E) 75 | <gadget id="calculator">96 + 95</gadget>
<output>191</output>
<gadget id="calculator">191 + 82</gadget>
<output>273</output>
<gadget id="calculator">273 + 97</gadget>
<output>370</output>
<gadget id="calculator">370 + 95</gadget>
<output>465</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">465 / 5</gadget>
<output>93</output>
<result>B</result> | B | 93 | Dacid obtained 96, 95, 82, 97 and 95 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? | {
"A": "79",
"B": "93",
"C": "88",
"D": "88",
"E": "75"
} | divide(add(add(add(add(96, 95), 82), 97), 95), divide(const_10, const_2)) | add(n0,n1)|divide(const_10,const_2)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | "average = ( 96 + 95 + 82 + 97 + 95 ) / 5 = 465 / 5 = 93 . answer : b" | general |
math_qa__AOUZnFepsCFyZldt | The number 0.5 is how much greater than 1/6 ?
Choose the correct choice from the following choices: A) 1 / 3 B) 2 / 10 C) 1 / 50 D) 1 / 500 E) 2 / 500 | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">0.5 - (1/6)</gadget>
<output>0.333333</output>
<result>A</result> | A | 0.333333 | The number 0.5 is how much greater than 1/6 ? | {
"A": "1 / 3",
"B": "2 / 10",
"C": "1 / 50",
"D": "1 / 500",
"E": "2 / 500"
} | subtract(0.5, divide(1, 6)) | divide(n1,n2)|subtract(n0,#0)| | "let x be the difference then . 5 - 1 / 3 = x 5 / 10 - 1 / 3 = x x = 1 / 3 ans a" | general |
math_qa__EXgolSoA3lUDDGGv | A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Choose the correct option.
A) 12 B) 20 C) 88 D) 77 E) 14 | <gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) + 1</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">70 / (7/5)</gadget>
<output>50</output>
<gadget id="calculator">70 - 50</gadget>
<output>20</output>
<result>B</result> | B | 20 | A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? | {
"A": "12",
"B": "20",
"C": "88",
"D": "77",
"E": "14"
} | subtract(70, divide(70, add(divide(2, 5), const_1))) | divide(n1,n2)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)| | "1 : 2 / 5 = 5 : 2 2 / 7 * 70 = 20 answer : b" | physics |
math_qa__MGjHoBcOXs0MpnpH | The slant height of a cone is 20 cm and radius of the base is 10 cm, find the curved surface of the cone. Choices
A) 330 B) 159 C) 150 D) 200 E) 628 | <gadget id="calculator">pi * 10</gadget>
<output>10*pi = around 31.415927</output>
<gadget id="calculator">(10*pi) * 20</gadget>
<output>200*pi = around 628.318531</output>
<result>E</result> | E | 628 | The slant height of a cone is 20 cm and radius of the base is 10 cm, find the curved surface of the cone. | {
"A": "330",
"B": "159",
"C": "150",
"D": "200",
"E": "628"
} | multiply(multiply(const_pi, 10), 20) | multiply(n1,const_pi)|multiply(n0,#0)| | "π * 10 * 20 = 628 answer : e" | geometry |
math_qa__IlY9u9WryElvBwE4 | The least number which when divided by 3, 4, 5 and 6 leaves a remainder 6, but when divided by 9 leaves no remainder, is Choose one:
A) 117 B) 126 C) 252 D) 336 E) none of these | <gadget id="calculator">lcm(3, 4)</gadget>
<output>12</output>
<gadget id="calculator">lcm(12, 5)</gadget>
<output>60</output>
<gadget id="calculator">lcm(60, 6)</gadget>
<output>60</output>
<gadget id="calculator">60 * 2</gadget>
<output>120</output>
<result>B</result> | B | 126 | The least number which when divided by 3, 4, 5 and 6 leaves a remainder 6, but when divided by 9 leaves no remainder, is | {
"A": "117",
"B": "126",
"C": "252",
"D": "336",
"E": "none of these"
} | multiply(lcm(lcm(lcm(3, 4), 5), 6), const_2) | lcm(n0,n1)|lcm(n2,#0)|lcm(n3,#1)|multiply(#2,const_2)| | "explanation : l . c . m of 3 , 4 , 5 , 6 = 60 therefore required number is of the form 60 k + 6 . least value of k for which ( 60 k + 6 ) is divisible by 9 is k = 2 therefore required number = ( 60 x 2 + 6 ) = 126 . answer : b" | general |
math_qa__q32A0nY3SvzvETKW | The ratio 10:20 expressed as percent equals to Choices.
A) 50 % B) 80 % C) 40 % D) 90 % E) 100 % | <gadget id="calculator">10 / 20</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>A</result> | A | 50 | The ratio 10:20 expressed as percent equals to | {
"A": "50 %",
"B": "80 %",
"C": "40 %",
"D": "90 %",
"E": "100 %"
} | multiply(divide(10, 20), const_100) | divide(n0,n1)|multiply(#0,const_100)| | "explanation : actually it means 10 is what percent of 20 , which can be calculated as , ( 10 / 20 ) * 100 = 10 * 5 = 50 answer : option a" | general |
math_qa__yEwkIvsys9zSO6Z0 | The speed of a train is 120 kmph. What is the distance covered by it in 40 minutes? Choose the correct choice.
A) 50 kmph B) 60 kmph C) 70 kmph D) 80 kmph E) 85 kmph | <gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 120</gadget>
<output>80</output>
<result>D</result> | D | 80 | The speed of a train is 120 kmph. What is the distance covered by it in 40 minutes? | {
"A": "50 kmph",
"B": "60 kmph",
"C": "70 kmph",
"D": "80 kmph",
"E": "85 kmph"
} | multiply(divide(40, const_60), 120) | divide(n1,const_60)|multiply(n0,#0)| | "120 * 40 / 60 = 80 kmph answer : d" | physics |
math_qa__HCQTIjhOm6nURGEt | A right triangle AEC has to be constructed in the xy-plane so that the right angle is at A and AE is parallel to x axis. The coordinates of A, E and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? Pick one:
A) 63 B) 336 C) 567 D) 3024 E) 5040 | <gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">24 * 6</gadget>
<output>144</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">144 * 14</gadget>
<output>2_016</output>
<gadget id="calculator">5_040 - 2_016</gadget>
<output>3_024</output>
<result>D</result> | D | 3,024 | A right triangle AEC has to be constructed in the xy-plane so that the right angle is at A and AE is parallel to x axis. The coordinates of A, E and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties? | {
"A": "63",
"B": "336",
"C": "567",
"D": "3024",
"E": "5040"
} | subtract(factorial(7), multiply(multiply(multiply(subtract(7, 1), const_4), subtract(7, 1)), multiply(7, const_2))) | factorial(n1)|multiply(n1,const_2)|subtract(n1,n0)|multiply(#2,const_4)|multiply(#3,#2)|multiply(#4,#1)|subtract(#0,#5) | all the cordinates are integer hence , possible ae values are { - 10 } , { - 11 } . . . . { - 17 } : 8 ways . . . . { 7 , - 1 } , { 70 } . . . . . . { 76 } : 8 ways 9 * 8 ways = 72 for ac values can be { 12 } , { 13 } . . . . { 17 } : 6 ways . . . . . . { 71 } , { 72 } . . . . . { 76 } : 6 ways 7 * 6 = 42 total = 72 * 42 = 3024 hence d | geometry |
math_qa__cgHjXmiKDnFySn73 | If 25 typists can type 60 letters in 20 minutes, then how many letters will 75 typists working at the same rate complete in 1 hour? Select the correct option
A) 270 B) 540 C) 610 D) 510 E) 500 | <gadget id="calculator">60 * 3</gadget>
<output>180</output>
<gadget id="calculator">180 / 25</gadget>
<output>36/5 = around 7.2</output>
<gadget id="calculator">(36/5) * 75</gadget>
<output>540</output>
<result>B</result> | B | 540 | If 25 typists can type 60 letters in 20 minutes, then how many letters will 75 typists working at the same rate complete in 1 hour? | {
"A": "270",
"B": "540",
"C": "610",
"D": "510",
"E": "500"
} | multiply(divide(multiply(60, const_3), 25), 75) | multiply(n1,const_3)|divide(#0,n0)|multiply(n3,#1) | no . of letters typing by 25 typists in 20 minutes = 60 no . of letters typing by 25 typists in 60 minutes = 60 * 3 = 180 no . of letters typing by 75 typists in 60 minutes = 180 / 25 * 75 = 540 answer : b | physics |
math_qa__RDI8E4Vm8ykAqPev | In the junior basketball league there are 18 teams, 2/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad
Pick.
A) 4 . B) 6 . C) 7 . D) 10 . E) 8 . | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">18 * (1/2)</gadget>
<output>9</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<result>D</result> | D | 10 | In the junior basketball league there are 18 teams, 2/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad | {
"A": "4 .",
"B": "6 .",
"C": "7 .",
"D": "10 .",
"E": "8 ."
} | add(multiply(18, divide(const_1, 2)), const_1) | divide(const_1,n1)|multiply(n0,#0)|add(#1,const_1)| | "total teams = 18 bad teams = ( 2 / 3 ) * 18 = 12 rich teams = 9 so maximum value that the both rich and bad can take will be 9 . so e = 10 can not be that value . ans d ." | general |
math_qa__awuLcsrY0JvH9z5W | The sum of the present age of Henry and Jill is 43. What is their present ages if 5 years ago Henry was twice the age of Jill? Choose the correct choice from the following answers: A) and 27 B) and 24 C) and 22 D) and 29 E) of these | <gadget id="calculator">43 + 5</gadget>
<output>48</output>
<gadget id="calculator">48 / 3</gadget>
<output>16</output>
<gadget id="calculator">43 - 16</gadget>
<output>27</output>
<result>A</result> | A | 27 | The sum of the present age of Henry and Jill is 43. What is their present ages if 5 years ago Henry was twice the age of Jill? | {
"A": "and 27",
"B": "and 24",
"C": "and 22",
"D": "and 29",
"E": "of these"
} | subtract(43, divide(add(43, 5), const_3)) | add(n0,n1)|divide(#0,const_3)|subtract(n0,#1)| | "let the age of jill 5 years ago be x , age of henry be 2 x x + 5 + 2 x + 5 = 43 x = 11 present ages will be 16 and 27 answer : a" | general |
math_qa__cIuwbFDla74Tkrdm | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 84 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ? Choose the correct answer
A) 16 % B) 32 % C) 48 % D) 84 % E) 92 % | <gadget id="calculator">100 - 84</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">100 - 8</gadget>
<output>92</output>
<result>E</result> | E | 92 | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 84 percent of the distribution lies within one standard deviation d of the mean, what percent 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, 84), 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 84 % is one st . dev , then on either side of m we have 84 / 2 = 42 % . so , 84 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 42 = 92 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 92 % 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 e" | general |
math_qa__OS2LSRhcQ1qBV05F | The compound ratio of 5:8, 3:2 and 4:5? Choose the correct choice from the following answers
A) 1 : 1 B) 1 : 87 C) 3 : 4 D) 1 : 9 E) 1 : 2 | <gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">15 / 16</gadget>
<output>15/16 = around 0.9375</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">(15/16) / (6/5)</gadget>
<output>25/32 = around 0.78125</output>
<result>C</result> | C | 0.75 | The compound ratio of 5:8, 3:2 and 4:5? | {
"A": "1 : 1",
"B": "1 : 87",
"C": "3 : 4",
"D": "1 : 9",
"E": "1 : 2"
} | divide(divide(multiply(5, 3), multiply(8, 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)| | "5 / 8 * 3 / 2 * 4 / 5 = 3 / 4 1 : 1 answer : c" | other |
math_qa__ehXgYuqSbf453OP0 | I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last Choose the correct option.
A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">60 * 5</gadget>
<output>300</output>
<gadget id="calculator">300 - 240</gadget>
<output>60</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">60 / 20</gadget>
<output>3</output>
<result>C</result> | C | 3 | I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | divide(subtract(multiply(60, 5), 240), subtract(60, 40)) | multiply(n1,n3)|subtract(n1,n0)|subtract(#0,n2)|divide(#2,#1) | the total time of journey = 5 hours . let ' x ' hours be the time that i travelled at 40 kmph therefore , 5 – x hours would be time that i travelled at 60 kmph . hence , i would have covered x × 40 + ( 5 − x ) 60 kms in the 5 hours = 240 kms . solving , for x in the equation 40 x + ( 5 – x ) × 60 = 240 , we get 40 x + 300 – 60 x = 240 ⇒ 20 x = 60 or x = 3 hours answer : c | physics |
math_qa__FT4CcrQnDGq2KWNa | If 4 cats can kill 4 rats in 4 minutes, how long will it take 100 cats to kill 100 rats? Choose the correct choice from the following choices.
A) 1 minutes B) 2 minutes C) 3 minutes D) 4 minutes E) 5 minutes | <gadget id="calculator">4 * 1</gadget>
<output>4</output>
<result>D</result> | D | 4 | If 4 cats can kill 4 rats in 4 minutes, how long will it take 100 cats to kill 100 rats? | {
"A": "1 minutes",
"B": "2 minutes",
"C": "3 minutes",
"D": "4 minutes",
"E": "5 minutes"
} | multiply(4, const_1) | multiply(n0,const_1)| | "it will take 4 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 4 minutes , so 100 cats can kill 100 rats in 4 minutes answer d" | physics |
math_qa__686ZPwjoXcjQN4xH | How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr? Choose the correct choice from the following choices: A) 25 B) 30 C) 99 D) 88 E) 61 | <gadget id="calculator">75 - 3</gadget>
<output>72</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">500 / 20</gadget>
<output>25</output>
<result>A</result> | A | 25 | How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 75 km/hr? | {
"A": "25",
"B": "30",
"C": "99",
"D": "88",
"E": "61"
} | divide(500, multiply(subtract(75, 3), const_0_2778)) | subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)| | "speed of train relative to man = 75 - 3 = 72 km / hr . = 72 * 5 / 18 = 20 m / sec . time taken to pass the man = 500 * 1 / 20 = 25 sec . answer : a" | physics |
math_qa__vyTdjnlyzhlJj93I | If the volume of the cube is 729, then the surface area of the cube will be Choose the correct choice:
A) 486 B) 255 C) 2866 D) 265 E) 872 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">729 ** (1/3)</gadget>
<output>9</output>
<gadget id="calculator">9 ** 2</gadget>
<output>81</output>
<gadget id="calculator">6 * 81</gadget>
<output>486</output>
<result>A</result> | A | 486 | If the volume of the cube is 729, then the surface area of the cube will be | {
"A": "486",
"B": "255",
"C": "2866",
"D": "265",
"E": "872"
} | multiply(multiply(const_3, const_2), power(cube_edge_by_volume(729), const_2)) | cube_edge_by_volume(n0)|multiply(const_2,const_3)|power(#0,const_2)|multiply(#1,#2) | explanation : \ inline \ fn _ jvn a ^ 3 = 729 ; a = 9 surface area = ( 6 x 9 x 9 ) = 486 \ inline \ fn _ jvn cm ^ 2 answer : a ) 486 sq . cm | geometry |
math_qa__VUVSzdUfycRVwXxZ | When the circumference and area of a circle are numerically equal, then the diameter is numerically equal to
Options
A) area B) circumference C) 4 D) 2 π E) none of these | <gadget id="calculator">2 * pi</gadget>
<output>2*pi = around 6.283185</output>
<gadget id="calculator">(2*pi) / pi</gadget>
<output>2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<result>C</result> | C | 4 | When the circumference and area of a circle are numerically equal, then the diameter is numerically equal to | {
"A": "area",
"B": "circumference",
"C": "4",
"D": "2 π",
"E": "none of these"
} | multiply(divide(multiply(const_2, const_pi), const_pi), const_2) | multiply(const_2,const_pi)|divide(#0,const_pi)|multiply(#1,const_2) | according to question , circumference of circle = area of circle or π d = π ( d ⁄ 2 ) 2 [ where d = diameter ] ∴ d = 4 answer c | geometry |
math_qa__SpYOkupw3UvzEnJ3 | In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was Choose the correct choice from the following choices
A) 2500 B) 2700 C) 3000 D) 3100 E) nobe | <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">55 / 100</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">1 - (11/20)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(4/5) * (9/20)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) * 7_500</gadget>
<output>2_700</output>
<result>B</result> | B | 2,700 | In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was | {
"A": "2500",
"B": "2700",
"C": "3000",
"D": "3100",
"E": "nobe"
} | multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 7500) | divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|multiply(#2,#3)|multiply(n2,#4) | solution number of valid votes = 80 % of 7500 = 6000 . valid votes polled by other candidates = 45 % of 6000 ( 45 / 100 × 6000 ) = 2700 . answer b | gain |
math_qa__Qra05NRexV2VgAqc | Find the circumference and area of radius 6 cm. Choose the correct choice
A) 113 cm ² B) 144 cm ² C) 154 cm ² D) 184 cm ² E) 194 cm ² | <gadget id="calculator">pi * (6 ** 2)</gadget>
<output>36*pi = around 113.097336</output>
<result>A</result> | A | 113 | Find the circumference and area of radius 6 cm. | {
"A": "113 cm ²",
"B": "144 cm ²",
"C": "154 cm ²",
"D": "184 cm ²",
"E": "194 cm ²"
} | circle_area(6) | circle_area(n0) | area of circle = π r ² = 22 / 7 × 6 × 6 cm ² = 113 cm ² answer : a | geometry |
math_qa__L259BPmTAYmMigKa | Cost is expressed by the formula tb^4. If b is doubled, the new cost R is what percent of the original cost? Choose the correct answer:
A) r = 200 B) r = 600 C) r = 800 D) r = 1600 E) r = 50 | <gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">16 * 100</gadget>
<output>1_600</output>
<result>D</result> | D | 1,600 | Cost is expressed by the formula tb^4. If b is doubled, the new cost R is what percent of the original cost? | {
"A": "r = 200",
"B": "r = 600",
"C": "r = 800",
"D": "r = 1600",
"E": "r = 50"
} | multiply(power(const_2, 4), const_100) | power(const_2,n0)|multiply(#0,const_100) | original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600 | general |
math_qa__DIwKmYPDFxfrCfxA | There are two concentric circles with radii 5 and 4. If the radius of the outer circle is increased by 20% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase?
Options: A) 56 B) 156 C) 256 D) 356 E) 456 | <gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">5 * (6/5)</gadget>
<output>6</output>
<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">4 * (1/2)</gadget>
<output>2</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">36 - 4</gadget>
<output>32</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">25 - 16</gadget>
<output>9</output>
<gadget id="calculator">32 - 9</gadget>
<output>23</output>
<gadget id="calculator">23 / 9</gadget>
<output>23/9 = around 2.555556</output>
<gadget id="calculator">(23/9) * 100</gadget>
<output>2_300/9 = around 255.555556</output>
<result>C</result> | C | 256 | There are two concentric circles with radii 5 and 4. If the radius of the outer circle is increased by 20% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase? | {
"A": "56",
"B": "156",
"C": "256",
"D": "356",
"E": "456"
} | multiply(divide(subtract(subtract(power(multiply(5, divide(add(const_100, 20), const_100)), const_2), power(multiply(4, divide(subtract(const_100, 50), const_100)), const_2)), subtract(power(5, const_2), power(4, const_2))), subtract(power(5, const_2), power(4, const_2))), const_100) | add(n2,const_100)|power(n0,const_2)|power(n1,const_2)|subtract(const_100,n3)|divide(#0,const_100)|divide(#3,const_100)|subtract(#1,#2)|multiply(n0,#4)|multiply(n1,#5)|power(#7,const_2)|power(#8,const_2)|subtract(#9,#10)|subtract(#11,#6)|divide(#12,#6)|multiply(#13,const_100) | the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 25 pi . the area of the small circle is 16 pi . the area a 1 between the circles is 9 pi . when the big circle ' s radius increases , the new area is 36 pi . when the small circle ' s radius decreases , the new area is 4 pi . the area a 2 between the circles is 32 pi . the ratio of a 2 / a 1 is 32 / 9 = 3.56 which is an increase of 256 % . the answer is c . | gain |
math_qa__jTpG2AXMFWeMT2Et | The ratio of the area of a square to that of the square drawn on its diagonal is? Pick.
A) 2 : 5 B) 3 : 4 C) 3 : 5 D) 1 : 2 E) 2 : 3 | <gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>
<gadget id="calculator">1 / (sqrt(2))</gadget>
<output>sqrt(2)/2 = around 0.707107</output>
<gadget id="calculator">(sqrt(2)/2) ** 2</gadget>
<output>1/2 = around 0.5</output>
<result>D</result> | D | 0.5 | The ratio of the area of a square to that of the square drawn on its diagonal is? | {
"A": "2 : 5",
"B": "3 : 4",
"C": "3 : 5",
"D": "1 : 2",
"E": "2 : 3"
} | power(divide(const_1, sqrt(const_2)), const_2) | sqrt(const_2)|divide(const_1,#0)|power(#1,const_2) | explanation : a 2 : ( a â ˆ š 2 ) 2 a 2 : 2 a 2 - > 1 : 2 answer is d | geometry |
math_qa__RbU7TA30Hu1xSvlc | there are 6 positive and 8 negative numbers . 4 numbers are choosen at random and multiplied . the probability that the product is positive is :
Options
A) 500 / 1001 B) 503 / 1001 C) 303 / 1001 D) 301 / 1001 E) 505 / 1001 | <gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<gadget id="calculator">720 / 48</gadget>
<output>15</output>
<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">24 * 24</gadget>
<output>576</output>
<gadget id="calculator">40_320 / 576</gadget>
<output>70</output>
<gadget id="calculator">15 + 70</gadget>
<output>85</output>
<gadget id="calculator">720 * 2</gadget>
<output>1_440</output>
<gadget id="calculator">40_320 / 1_440</gadget>
<output>28</output>
<gadget id="calculator">15 * 28</gadget>
<output>420</output>
<gadget id="calculator">85 + 420</gadget>
<output>505</output>
<gadget id="calculator">6 + 8</gadget>
<output>14</output>
<gadget id="calculator">factorial(14)</gadget>
<output>87_178_291_200</output>
<gadget id="calculator">14 - 4</gadget>
<output>10</output>
<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>
<gadget id="calculator">3_628_800 * 24</gadget>
<output>87_091_200</output>
<gadget id="calculator">87_178_291_200 / 87_091_200</gadget>
<output>1_001</output>
<gadget id="calculator">505 / 1_001</gadget>
<output>505/1_001 = around 0.504496</output>
<result>E</result> | E | 0.504496 | there are 6 positive and 8 negative numbers . 4 numbers are choosen at random and multiplied . the probability that the product is positive is : | {
"A": "500 / 1001",
"B": "503 / 1001",
"C": "303 / 1001",
"D": "301 / 1001",
"E": "505 / 1001"
} | divide(add(add(divide(factorial(6), multiply(factorial(4), factorial(const_2))), divide(factorial(8), multiply(factorial(4), factorial(4)))), multiply(divide(factorial(6), multiply(factorial(4), factorial(const_2))), divide(factorial(8), multiply(factorial(6), factorial(const_2))))), divide(factorial(add(6, 8)), multiply(factorial(subtract(add(6, 8), 4)), factorial(4)))) | add(n0,n1)|factorial(n0)|factorial(n2)|factorial(const_2)|factorial(n1)|factorial(#0)|multiply(#2,#3)|multiply(#2,#2)|multiply(#1,#3)|subtract(#0,n2)|divide(#1,#6)|divide(#4,#7)|divide(#4,#8)|factorial(#9)|add(#10,#11)|multiply(#10,#12)|multiply(#13,#2)|add(#14,#15)|divide(#5,#16)|divide(#17,#18) | 6 c 4 / 14 c 4 + ( 6 c 2 * 8 c 2 ) / 14 c 4 + 8 c 4 / 14 c 4 = 505 / 1001 case 1 : only 4 positive no . case 2 : 2 positive and 2 negative no . case 3 : 4 negative no . answer : e | general |
math_qa__vJRJNwQ2SYiJjeDv | Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 35%, then find the population of city atthe end of the year 2007 Choose the correct answer.
A) 976374 B) 979923 C) 1009125 D) 2356677 E) 1083875 | <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_000_000 * (8_073/8_000)</gadget>
<output>1_009_125</output>
<result>C</result> | C | 1,009,125 | Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 35%, then find the population of city atthe end of the year 2007 | {
"A": "976374",
"B": "979923",
"C": "1009125",
"D": "2356677",
"E": "1083875"
} | multiply(1000000, 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 + 35 / 100 ) = 1009125 c | gain |
math_qa__vMmanY0UK22dTt5J | f(x) is a function such that f(x) + 3f(8 - x) = x for all real numbers x. Find the value of f(2).
Pick one.
A) 5 B) 4 C) 3 D) 2 E) 1 | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<gadget id="calculator">2 - 18</gadget>
<output>-16</output>
<gadget id="calculator">1 - 9</gadget>
<output>-8</output>
<gadget id="calculator">(-16) / (-8)</gadget>
<output>2</output>
<result>D</result> | D | 2 | f(x) is a function such that f(x) + 3f(8 - x) = x for all real numbers x. Find the value of f(2). | {
"A": "5",
"B": "4",
"C": "3",
"D": "2",
"E": "1"
} | divide(subtract(2, multiply(multiply(3, 3), const_2)), subtract(const_1, multiply(3, 3))) | multiply(n0,n0)|multiply(#0,const_2)|subtract(const_1,#0)|subtract(n2,#1)|divide(#3,#2) | f ( x ) + 3 f ( 8 - x ) = x : given f ( 2 ) + 3 f ( 6 ) = 2 : x = 2 above f ( 6 ) + 3 f ( 2 ) = 6 : x = 6 above f ( 6 ) = 6 - 3 f ( 2 ) : solve equation c for f ( 6 ) f ( 2 ) + 3 ( 6 - 3 f ( 2 ) ) = 2 : substitute f ( 2 ) = 2 : solve above equation . correct answer is d ) 2 | general |
math_qa__HLnEzhLXQSvNKmCc | A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there? Choose the correct choice from the following answers
A) 20 coins
B) 30 coins
C) 40 coins
D) 60 coins
E) none of these | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) + 1</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">105 / (7/4)</gadget>
<output>60</output>
<result>D</result> | D | 60 | A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there? | {
"A": "20 coins",
"B": "30 coins",
"C": "40 coins",
"D": "60 coins",
"E": "none of these"
} | divide(105, add(add(inverse(const_4), inverse(const_2)), const_1)) | inverse(const_4)|inverse(const_2)|add(#0,#1)|add(#2,const_1)|divide(n2,#3)| | "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 105 ⇒ 1.75 x = 105 ⇒ x = 60 coins answer d" | general |
math_qa__wQpuB0pFyXp2CKr6 | John can complete a given task in 20 days. Jane will take only 10 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 5 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together? Choose the correct choice from the following options
A) 8 B) 10 C) 12 D) 16 E) 20 | <gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">200 - 50</gadget>
<output>150</output>
<gadget id="calculator">10 + 20</gadget>
<output>30</output>
<gadget id="calculator">150 / 30</gadget>
<output>5</output>
<gadget id="calculator">5 + 5</gadget>
<output>10</output>
<result>B</result> | B | 10 | John can complete a given task in 20 days. Jane will take only 10 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 5 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together? | {
"A": "8",
"B": "10",
"C": "12",
"D": "16",
"E": "20"
} | add(5, divide(subtract(multiply(20, 10), multiply(10, 5)), add(10, 20))) | add(n0,n1)|multiply(n0,n1)|multiply(n1,n2)|subtract(#1,#2)|divide(#3,#0)|add(n2,#4) | in such questions , you need to start from the end . last 5 days john works alone and completes 5 * ( 1 / 20 ) = 1 / 4 of the work . so 3 / 4 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 20 + 1 / 10 = 3 / 20 time taken to complete 3 / 4 of the work = ( 3 / 4 ) / ( 3 / 20 ) = 5 days . so total number of days taken to complete the work = 5 + 5 = 10 days . b | physics |
math_qa__D0QN0xpK4b1ZOCeT | List K consists of 10 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K? Choose the correct choice from the following options:
A) 5 B) 6 C) 7 D) 11 E) 4 | <gadget id="calculator">10 - 4</gadget>
<output>6</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<result>E</result> | E | 4 | List K consists of 10 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K? | {
"A": "5",
"B": "6",
"C": "7",
"D": "11",
"E": "4"
} | subtract(subtract(subtract(10, 4), const_1), const_1) | subtract(n0,n1)|subtract(#0,const_1)|subtract(#1,const_1)| | "answer = e = 4 if least = - 4 , then largest = 5 range = 5 - 1 = 4" | general |
math_qa__FvGlhvnD0Tw1PaIs | In a school of 400 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
Options:
A) 41
B) 63
C) 72
D) 63
E) 50 | <gadget id="calculator">44 + 28</gadget>
<output>72</output>
<gadget id="calculator">72 + 10</gadget>
<output>82</output>
<gadget id="calculator">100 - 82</gadget>
<output>18</output>
<gadget id="calculator">400 * 18</gadget>
<output>7_200</output>
<gadget id="calculator">7_200 / 100</gadget>
<output>72</output>
<result>C</result> | C | 72 | In a school of 400 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? | {
"A": "41",
"B": "63",
"C": "72",
"D": "63",
"E": "50"
} | divide(multiply(400, subtract(const_100, add(add(44, 28), 10))), const_100) | add(n1,n2)|add(n3,#0)|subtract(const_100,#1)|multiply(n0,#2)|divide(#3,const_100)| | "44 + 28 + 10 = 82 % 100 – 82 = 18 % 400 * 18 / 100 = 72 answer : c" | gain |
math_qa__Ruv1foTJWCRT7WCM | Two trains of equal lengths take 12 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? Choose the most appropriate option:
A) 16 sec B) 12 sec C) 17 sec D) 15 sec E) 23 sec | <gadget id="calculator">120 * 2</gadget>
<output>240</output>
<gadget id="calculator">120 / 20</gadget>
<output>6</output>
<gadget id="calculator">120 / 12</gadget>
<output>10</output>
<gadget id="calculator">6 + 10</gadget>
<output>16</output>
<gadget id="calculator">240 / 16</gadget>
<output>15</output>
<result>D</result> | D | 15 | Two trains of equal lengths take 12 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? | {
"A": "16 sec",
"B": "12 sec",
"C": "17 sec",
"D": "15 sec",
"E": "23 sec"
} | divide(multiply(120, const_2), add(speed(120, 20), speed(120, 12))) | multiply(n2,const_2)|speed(n2,n1)|speed(n2,n0)|add(#1,#2)|divide(#0,#3)| | "speed of the first train = 120 / 12 = 10 m / sec . speed of the second train = 120 / 20 = 6 m / sec . relative speed = 10 + 6 = 16 m / sec . required time = ( 120 + 120 ) / 16 = 15 sec . answer : d" | physics |
math_qa__k6vJDQ7HCYziruLT | A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 20%. Their gross income from sales for one month increases by what percent? Select
A) 2 %
B) 4 %
C) 5 %
D) 8 %
E) 12 % | <gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">20 / 10</gadget>
<output>2</output>
<gadget id="calculator">10 - 2</gadget>
<output>8</output>
<result>D</result> | D | 8 | A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 20%. Their gross income from sales for one month increases by what percent? | {
"A": "2 %",
"B": "4 %",
"C": "5 %",
"D": "8 %",
"E": "12 %"
} | subtract(subtract(20, 10), divide(20, 10)) | divide(n1,n0)|subtract(n1,n0)|subtract(#1,#0)| | "let list price of an item = 100 discount on each item = 10 % discounted price of an item = . 9 * 100 = 90 if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 20 % originally if 10 items were sold in a month , with the new discount 12 items will be sold original revenue = no of items * price of an item = 10 * 100 = 1000 new revenue = 12 * 90 = 1080 increase in gross income = 1080 - 1000 = 80 % increase in gross revenue = 80 / 1000 * 100 % = 8 % answer d" | gain |
math_qa__Ng9fpMnS1F2SmBH2 | The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
Select
A) 3000
B) 2802
C) 1750
D) 2990
E) 2982 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">4_000 * (121/100)</gadget>
<output>4_840</output>
<gadget id="calculator">4_840 - 4_000</gadget>
<output>840</output>
<gadget id="calculator">840 / 2</gadget>
<output>420</output>
<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">3 * (2/25)</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">420 / (6/25)</gadget>
<output>1_750</output>
<result>C</result> | C | 1,750 | The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? | {
"A": "3000",
"B": "2802",
"C": "1750",
"D": "2990",
"E": "2982"
} | divide(divide(subtract(multiply(4000, power(add(const_1, divide(10, const_100)), 2)), 4000), 2), multiply(3, divide(8, 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 . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 8 ) = rs . 1750 answer : c" | gain |
math_qa__bUNeK1H9yHWY4ZJ4 | A person buys an article at Rs.460. At what price should he sell the article so as to make a profit of 18%?
Select the correct option.
A) 542
B) 882
C) 772
D) 662
E) 521 | <gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">460 * (9/50)</gadget>
<output>414/5 = around 82.8</output>
<gadget id="calculator">460 + (414/5)</gadget>
<output>2_714/5 = around 542.8</output>
<result>A</result> | A | 542 | A person buys an article at Rs.460. At what price should he sell the article so as to make a profit of 18%? | {
"A": "542",
"B": "882",
"C": "772",
"D": "662",
"E": "521"
} | add(460, multiply(460, divide(18, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | "cost price = rs . 460 profit = 18 % of 460 = rs . 82 selling price = cost price + profit = 460 + 82 = 542 answer : a" | gain |
math_qa__QfyAhjxpx6pSGImR | If an integer n is to be chosen at random from the integers 1 to 86, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
Choose the correct choice from the following answers
A) 1 / 4
B) 3 / 8
C) 1 / 2
D) 55 / 86
E) 3 / 4 | <gadget id="calculator">86 / 2</gadget>
<output>43</output>
<gadget id="calculator">86 / 8</gadget>
<output>43/4 = around 10.75</output>
<gadget id="calculator">43 + (43/4)</gadget>
<output>215/4 = around 53.75</output>
<gadget id="calculator">(215/4) / 86</gadget>
<output>5/8 = around 0.625</output>
<result>D</result> | D | 0.639535 | If an integer n is to be chosen at random from the integers 1 to 86, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8? | {
"A": "1 / 4",
"B": "3 / 8",
"C": "1 / 2",
"D": "55 / 86",
"E": "3 / 4"
} | divide(add(divide(86, 2), divide(86, 8)), 86) | divide(n1,n3)|divide(n1,n4)|add(#0,#1)|divide(#2,n1)| | "n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 86 , there are 43 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 43 + 12 ) / 96 = 55 / 86 ans isd" | general |
math_qa__l2lHrKNxVm8hiQ6n | A school has received 60% of the amount it needs for a new building by receiving a donation of $600 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
Choose one
A) $ 200
B) $ 177.78
C) $ 100
D) $ 277.78
E) $ 377.78 | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 600</gadget>
<output>240</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">240 / (3/5)</gadget>
<output>400</output>
<gadget id="calculator">400 * (2/5)</gadget>
<output>160</output>
<gadget id="calculator">160 / (3/5)</gadget>
<output>800/3 = around 266.666667</output>
<result>D</result> | D | 277.78 | A school has received 60% of the amount it needs for a new building by receiving a donation of $600 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? | {
"A": "$ 200",
"B": "$ 177.78",
"C": "$ 100",
"D": "$ 277.78",
"E": "$ 377.78"
} | divide(multiply(divide(multiply(divide(40, const_100), 600), divide(60, const_100)), divide(40, const_100)), divide(60, const_100)) | divide(n2,const_100)|divide(n0,const_100)|multiply(n1,#0)|divide(#2,#1)|multiply(#3,#0)|divide(#4,#1) | let the amount school needs = x let total people school plans to solicit = t school has received 60 % of x = > ( 3 / 5 ) x people already solicited = 40 % of t = > ( 2 / 5 ) t now , as per the information given in the question : ( 3 / 5 ) x = $ 400 . ( 2 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 remaning amount is 40 % i . e ( 2 / 5 ) x - - - - - - because school has already received 60 % and the remaining people are 60 % i . e ( 3 / 5 ) . t - - - - - because 40 % of the people are already solicited so , average contribution required from the remaining targeted people is ( 2 / 5 ) x = ( amount required ) . ( 3 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 divide eqn 1 by eqn 2 amount required = $ 277.78 d | general |
math_qa__kPyvFdlCQvSBwprI | In a group of 6 boys and 4 girls are to be selected. In how many different ways can they be selected such that at least one boy should be there ? Choose the correct choice from the following.
A) 209 B) 200 C) 210 D) 225 E) 221 | <gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">24 * 720</gadget>
<output>17_280</output>
<gadget id="calculator">3_628_800 / 17_280</gadget>
<output>210</output>
<result>A</result> | A | 209 | In a group of 6 boys and 4 girls are to be selected. In how many different ways can they be selected such that at least one boy should be there ? | {
"A": "209",
"B": "200",
"C": "210",
"D": "225",
"E": "221"
} | divide(factorial(add(6, 4)), multiply(factorial(4), factorial(6))) | add(n0,n1)|factorial(n1)|factorial(n0)|factorial(#0)|multiply(#1,#2)|divide(#3,#4) | no of boys = 6 no of girls = 4 therefore , no of ways at least 1 boy can be selected = 6 c 4 * 4 c 0 + 6 c 3 * 4 c 1 + 6 c 2 * 4 c 2 + 6 c 1 * 4 c 3 = 15 + 80 + 90 + 24 = 209 ans - a | other |
math_qa__hq5akno443Drbu2Z | a,b,c weighted separately 1st like a, b, c , then a & b, then b & c ,then c & a at last a & b & c, the last weight was 167,then what will be the average weight of the 7 reading? Options:
A) 95
B) 95.42
C) 95.45
D) 94
E) 93 | <gadget id="calculator">4 * 167</gadget>
<output>668</output>
<gadget id="calculator">668 / 7</gadget>
<output>668/7 = around 95.428571</output>
<result>B</result> | B | 95.42 | a,b,c weighted separately 1st like a, b, c , then a & b, then b & c ,then c & a at last a & b & c, the last weight was 167,then what will be the average weight of the 7 reading? | {
"A": "95",
"B": "95.42",
"C": "95.45",
"D": "94",
"E": "93"
} | divide(multiply(const_4, 167), 7) | multiply(n1,const_4)|divide(#0,n2) | the sum of 7 weights = weights of [ a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] = weights of [ 4 * ( a + b + c ) = 4 * 167 = 668 therefore the average weight of 7 readings is 668 / 7 = 95.428 answer : b | general |
math_qa__DIXXOWWMFYbT6QOA | A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a plce and come back, how far is the place?
Choose the correct choice from the following answers.
A) 2 km B) 2.4 km C) 2.5 km D) 3.4 km E) none | <gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">12 / 5</gadget>
<output>12/5 = around 2.4</output>
<result>B</result> | B | 2.4 | A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a plce and come back, how far is the place? | {
"A": "2 km",
"B": "2.4 km",
"C": "2.5 km",
"D": "3.4 km",
"E": "none"
} | divide(multiply(subtract(5, 1), const_3), 5) | subtract(n0,n1)|multiply(#0,const_3)|divide(#1,n0)| | "sol . speed downstream = ( 5 + 1 ) kmph = 6 kmph ; speed upstream = ( 5 - 1 ) kmph = 4 kmph . let the required distance be x km . then , x / 6 + x / 4 = 1 ⇔ 2 x + 3 x = 12 ⇔ 5 x = 12 ⇔ x = 2.4 km . answer b" | physics |
math_qa__WhwpRGkIFGLsB3H5 | A box contains 24 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is Select the correct option:
A) 4 / 19
B) 7 / 19
C) 12 / 19
D) 24 / 77
E) none | <gadget id="calculator">24 - 4</gadget>
<output>20</output>
<gadget id="calculator">binomial(20, 2)</gadget>
<output>190</output>
<gadget id="calculator">binomial(24, 2)</gadget>
<output>276</output>
<gadget id="calculator">190 / 276</gadget>
<output>95/138 = around 0.688406</output>
<gadget id="calculator">1 - (95/138)</gadget>
<output>43/138 = around 0.311594</output>
<result>D</result> | D | 0.311688 | A box contains 24 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is | {
"A": "4 / 19",
"B": "7 / 19",
"C": "12 / 19",
"D": "24 / 77",
"E": "none"
} | subtract(const_1, divide(choose(subtract(24, 4), const_2), choose(24, const_2))) | choose(n0,const_2)|subtract(n0,n1)|choose(#1,const_2)|divide(#2,#0)|subtract(const_1,#3)| | "solution p ( none is defective ) = 20 c 2 / 24 c 2 = 53 / 77 . p ( at least one is defective ) = ( 1 - 53 / 77 ) = 24 / 77 . answer d" | probability |
math_qa__oEywMCIgGoLsmW8s | One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field in meter square Select the correct option.
A) 100 B) 110 C) 120 D) 130 E) 140 | <gadget id="calculator">17 ** 2</gadget>
<output>289</output>
<gadget id="calculator">15 ** 2</gadget>
<output>225</output>
<gadget id="calculator">289 - 225</gadget>
<output>64</output>
<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>
<gadget id="calculator">15 * 8</gadget>
<output>120</output>
<result>C</result> | C | 120 | One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field in meter square | {
"A": "100",
"B": "110",
"C": "120",
"D": "130",
"E": "140"
} | rectangle_area(15, sqrt(subtract(power(17, const_2), power(15, const_2)))) | power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|sqrt(#2)|rectangle_area(n0,#3)| | "other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . option c" | geometry |
math_qa__oPDWN1pZ9TECR9Rf | In a sample of Christ college students, 30 percent are third year students and 90 percent are not second-year students. What fraction of those students who are not third-year students are second-year students? Pick:
A) 3 / 4 B) 2 / 3 C) 4 / 7 D) 1 / 2 E) 1 / 7 | <gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">90 - 30</gadget>
<output>60</output>
<gadget id="calculator">70 - 60</gadget>
<output>10</output>
<gadget id="calculator">10 / 70</gadget>
<output>1/7 = around 0.142857</output>
<result>E</result> | E | 0.142857 | In a sample of Christ college students, 30 percent are third year students and 90 percent are not second-year students. What fraction of those students who are not third-year students are second-year students? | {
"A": "3 / 4",
"B": "2 / 3",
"C": "4 / 7",
"D": "1 / 2",
"E": "1 / 7"
} | divide(subtract(subtract(const_100, 30), subtract(90, 30)), subtract(const_100, 30)) | subtract(const_100,n0)|subtract(n1,n0)|subtract(#0,#1)|divide(#2,#0) | = 10 / 70 . = 1 / 7 my answer is e too | gain |
math_qa__GiJQY9CLJGEFAmmh | In a school of 800 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? Choices:
A) 120 B) 128 C) 136 D) 144 E) 152 | <gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(9/20) * 800</gadget>
<output>360</output>
<gadget id="calculator">23 / 100</gadget>
<output>23/100 = around 0.23</output>
<gadget id="calculator">(23/100) * 800</gadget>
<output>184</output>
<gadget id="calculator">360 + 184</gadget>
<output>544</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 800</gadget>
<output>120</output>
<gadget id="calculator">544 + 120</gadget>
<output>664</output>
<gadget id="calculator">800 - 664</gadget>
<output>136</output>
<result>C</result> | C | 136 | In a school of 800 students, 45% wear blue shirts, 23% wear red shirts, 15% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? | {
"A": "120",
"B": "128",
"C": "136",
"D": "144",
"E": "152"
} | subtract(800, add(add(multiply(divide(45, const_100), 800), multiply(divide(23, const_100), 800)), multiply(divide(15, const_100), 800))) | divide(n1,const_100)|divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#0)|multiply(n0,#1)|multiply(n0,#2)|add(#3,#4)|add(#6,#5)|subtract(n0,#7)| | "45 + 23 + 15 = 83 % 100 – 83 = 17 % 800 * 17 / 100 = 136 the answer is c ." | gain |
math_qa__z8ktenM6ZyFdDeav | Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 10% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit? Choices: A) 127 % B) 120 % C) 121 % D) 135 % E) 140 % | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) / 2</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">(21/20) ** 5</gadget>
<output>4_084_101/3_200_000 = around 1.276282</output>
<gadget id="calculator">(4_084_101/3_200_000) * 100</gadget>
<output>4_084_101/32_000 = around 127.628156</output>
<result>A</result> | A | 127 | Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 10% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit? | {
"A": "127 %",
"B": "120 %",
"C": "121 %",
"D": "135 %",
"E": "140 %"
} | multiply(power(add(1, divide(divide(10, const_100), const_2)), add(const_2, const_3)), const_100) | add(const_2,const_3)|divide(n2,const_100)|divide(#1,const_2)|add(#2,n0)|power(#3,#0)|multiply(#4,const_100)| | "since michelle earns 10 % interest compounded semiannually , then she earns 5 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 5 % * 5 = 25 % . but , since the interest is compounded every 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 25 % , only answer choice a fits . answer : a" | gain |
math_qa__BPzWEz8t2y3WxcJp | John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $70. What is the percent decrease? Choose the correct option
A) 20 % B) 30 % C) 40 % D) 50 % E) 60 % | <gadget id="calculator">100 - 70</gadget>
<output>30</output>
<result>B</result> | B | 30 | John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $70. What is the percent decrease? | {
"A": "20 %",
"B": "30 %",
"C": "40 %",
"D": "50 %",
"E": "60 %"
} | subtract(100, 70) | subtract(n0,n1)| | "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 70 = 30 . the â € œ original â € is our starting point ; in this case , it â € ™ s 100 . ( 30 / 100 ) * 100 = ( 0.3 ) * 100 = 30 % . b" | general |
math_qa__HbjSae0L4txxgzbj | The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 10000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is: Choose the correct choice from the following answers:
A) 23 B) 19 C) 22 D) 20 E) 14 | <gadget id="calculator">10_000 - 8_000</gadget>
<output>2_000</output>
<gadget id="calculator">7 * 2_000</gadget>
<output>14_000</output>
<gadget id="calculator">8_000 - 6_000</gadget>
<output>2_000</output>
<gadget id="calculator">14_000 / 2_000</gadget>
<output>7</output>
<gadget id="calculator">7 + 7</gadget>
<output>14</output>
<result>E</result> | E | 14 | The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 10000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is: | {
"A": "23",
"B": "19",
"C": "22",
"D": "20",
"E": "14"
} | add(7, divide(multiply(7, subtract(10000, 8000)), subtract(8000, 6000))) | subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)| | "let the total number of workers be x . then , 8000 x = ( 10000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 28000 = x = 14 . answer : e" | general |
math_qa__65lU40WtJLRCp7Ms | A picture is copied onto a sheet of paper 8.5 inches by 10 inches. A 1.5 inch margin is left all around. What area in square inches does the picture cover? Choose the most appropriate option
A) 76 B) 65 C) 59.5 D) 49 E) 38.5 | <gadget id="calculator">1.5 * 2</gadget>
<output>3</output>
<gadget id="calculator">8.5 - 3</gadget>
<output>5.5</output>
<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">5.5 * 7</gadget>
<output>38.5</output>
<result>E</result> | E | 38.5 | A picture is copied onto a sheet of paper 8.5 inches by 10 inches. A 1.5 inch margin is left all around. What area in square inches does the picture cover? | {
"A": "76",
"B": "65",
"C": "59.5",
"D": "49",
"E": "38.5"
} | multiply(subtract(8.5, multiply(1.5, const_2)), subtract(10, multiply(1.5, const_2))) | multiply(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|multiply(#1,#2) | area covered by picture = ( 8.5 - 3 ) * ( 10 - 3 ) = 5.5 * 7 = 38.5 answer e | geometry |
math_qa__ZLkthfSHxiHavoXe | A cistern 9 m long and 6 m wide contains water up to a breadth of 2 m 25 cm. Find the total area of the wet surface.
Choose the correct choice from the following answers.
A) 142 m sqaure B) 122 m sqaure C) 135 m sqaure D) 188 m sqaure E) none of these | <gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 2</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">(9/4) * 6</gadget>
<output>27/2 = around 13.5</output>
<gadget id="calculator">(9/4) * 9</gadget>
<output>81/4 = around 20.25</output>
<gadget id="calculator">(27/2) + (81/4)</gadget>
<output>135/4 = around 33.75</output>
<gadget id="calculator">2 * (135/4)</gadget>
<output>135/2 = around 67.5</output>
<gadget id="calculator">6 * 9</gadget>
<output>54</output>
<gadget id="calculator">(135/2) + 54</gadget>
<output>243/2 = around 121.5</output>
<result>B</result> | B | 122 | A cistern 9 m long and 6 m wide contains water up to a breadth of 2 m 25 cm. Find the total area of the wet surface. | {
"A": "142 m sqaure",
"B": "122 m sqaure",
"C": "135 m sqaure",
"D": "188 m sqaure",
"E": "none of these"
} | add(multiply(const_2, add(multiply(add(divide(25, const_100), 2), 6), multiply(add(divide(25, const_100), 2), 9))), multiply(6, 9)) | divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|add(#3,#4)|multiply(#5,const_2)|add(#6,#1)| | "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 6 * 2.25 + 9 * 2.25 ) ] + 9 * 6 = 122 m square option b" | physics |
math_qa__4oEUbChqRO41jP7G | A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth? Choose one.
A) 18 B) 20 C) 24 D) 26 E) 40 | <gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">8 + 6</gadget>
<output>14</output>
<gadget id="calculator">6 * 8</gadget>
<output>48</output>
<gadget id="calculator">120 - 48</gadget>
<output>72</output>
<gadget id="calculator">4 * 72</gadget>
<output>288</output>
<gadget id="calculator">14 ** 2</gadget>
<output>196</output>
<gadget id="calculator">288 + 196</gadget>
<output>484</output>
<gadget id="calculator">484 ** (1/2)</gadget>
<output>22</output>
<gadget id="calculator">14 + 22</gadget>
<output>36</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<result>A</result> | A | 18 | A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth? | {
"A": "18",
"B": "20",
"C": "24",
"D": "26",
"E": "40"
} | divide(add(add(multiply(const_2, 4), multiply(const_2, 3)), sqrt(add(multiply(const_4, subtract(120, multiply(multiply(const_2, 3), multiply(const_2, 4)))), power(add(multiply(const_2, 4), multiply(const_2, 3)), const_2)))), const_2) | multiply(n0,const_2)|multiply(n1,const_2)|add(#0,#1)|multiply(#1,#0)|power(#2,const_2)|subtract(n2,#3)|multiply(#5,const_4)|add(#6,#4)|sqrt(#7)|add(#2,#8)|divide(#9,const_2) | let the original side of the square be x . ( x - 8 ) * ( x - 6 ) = 120 = 10 * 12 x = 18 the answer is a . | geometry |
math_qa__v7XKjVn6NCX1BS33 | In a company, 54 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? Pick one.
A) 55 % B) 60 % C) 65 % D) 70 % E) 75 % | <gadget id="calculator">100 - 54</gadget>
<output>46</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">46 - 18</gadget>
<output>28</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">28 / 40</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">100 * (7/10)</gadget>
<output>70</output>
<result>D</result> | D | 70 | In a company, 54 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": "55 %",
"B": "60 %",
"C": "65 %",
"D": "70 %",
"E": "75 %"
} | multiply(const_100, divide(subtract(subtract(const_100, 54), 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 % 46 % of all employees are women , so non - union women are 46 % - 18 % = 28 % 40 % of all employees are non - union . the percent of non - union employees who are women is 28 % / 40 % = 70 % the answer is d . | gain |
math_qa__5YoE79w9kGjDvyKa | 10women can complete a work in 7days&10children take 14days to complete the work. How many days will 5women and 10children take to complete the work? Choose the correct choice from the following choices
A) 5 days B) 7 days C) 8 days D) 9 days E) 11 days | <gadget id="calculator">10 * 7</gadget>
<output>70</output>
<gadget id="calculator">1 / 70</gadget>
<output>1/70 = around 0.014286</output>
<gadget id="calculator">(1/70) * 5</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">10 * 14</gadget>
<output>140</output>
<gadget id="calculator">1 / 140</gadget>
<output>1/140 = around 0.007143</output>
<gadget id="calculator">(1/140) * 10</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">(1/14) + (1/14)</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">1 / (1/7)</gadget>
<output>7</output>
<result>B</result> | B | 7 | 10women can complete a work in 7days&10children take 14days to complete the work. How many days will 5women and 10children take to complete the work? | {
"A": "5 days",
"B": "7 days",
"C": "8 days",
"D": "9 days",
"E": "11 days"
} | inverse(add(multiply(divide(const_1, multiply(10, 7)), 5), multiply(divide(const_1, multiply(10, 14)), 10))) | multiply(n0,n1)|multiply(n0,n3)|divide(const_1,#0)|divide(const_1,#1)|multiply(n4,#2)|multiply(n0,#3)|add(#4,#5)|inverse(#6) | 1 woman ' s 1 day ' s work = 1 / 70 1 child ' s 1 day ' s work = 1 / 140 5 women and 10 children 1 day work = ( 5 / 70 + 10 / 140 ) = 1 / 7 so 5 women and 10 children will finish the work in 7 days . b ) | physics |
math_qa__IaXxqVleAamMl1de | The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $30 less. What was the total cost cost of the vacation? Choose the correct choice from the following
A) $ 200 B) $ 360 C) $ 400 D) $ 500 E) $ 600 | <gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">30 / 1</gadget>
<output>30</output>
<gadget id="calculator">12 * 30</gadget>
<output>360</output>
<result>B</result> | B | 360 | The total cost of a vacation was divided among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $30 less. What was the total cost cost of the vacation? | {
"A": "$ 200",
"B": "$ 360",
"C": "$ 400",
"D": "$ 500",
"E": "$ 600"
} | multiply(multiply(4, 3), divide(30, subtract(4, 3))) | multiply(n0,n1)|subtract(n1,n0)|divide(n2,#1)|multiply(#2,#0)| | "c for cost . p price per person . c = 3 * p c = 4 * p - 120 substituting the value of p from the first equation onto the second we get p = 120 . plugging in the value of p in the first equation , we get c = 360 . which leads us to answer choice b" | general |
math_qa__4ZqWeBAhJ3cjLFRY | Mary's income is 60% more Than Tim's income and Tim's income is 20% less than Juan's income.What % of Juan's income is Mary's income. Choose the most appropriate option: A) 128 % B) b . 120 % C) 96 % D) 80 % E) 64 % | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">80 * (3/5)</gadget>
<output>48</output>
<gadget id="calculator">80 + 48</gadget>
<output>128</output>
<result>A</result> | A | 128 | Mary's income is 60% more Than Tim's income and Tim's income is 20% less than Juan's income.What % of Juan's income is Mary's income. | {
"A": "128 %",
"B": "b . 120 %",
"C": "96 %",
"D": "80 %",
"E": "64 %"
} | add(subtract(const_100, 20), multiply(subtract(const_100, 20), divide(60, const_100))) | divide(n0,const_100)|subtract(const_100,n1)|multiply(#0,#1)|add(#2,#1) | even i got 96 % j = 100 t = 100 * 0.8 = 80 m = 80 * 1.6 = 128 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 128 * 100 / 100 = 128 ans : a | general |
math_qa__gDNKgaXB9fwSYjcU | A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m?
Answers:
A) 24000
B) 23000
C) 22000
D) 25000
E) 26000 | <gadget id="calculator">25 * 100</gadget>
<output>2_500</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">2_500 * 200</gadget>
<output>500_000</output>
<gadget id="calculator">0.75 * 100</gadget>
<output>75</output>
<gadget id="calculator">500_000 * 75</gadget>
<output>37_500_000</output>
<gadget id="calculator">37_500_000 / 20</gadget>
<output>1_875_000</output>
<gadget id="calculator">1_875_000 / 10</gadget>
<output>187_500</output>
<gadget id="calculator">187_500 / 7.5</gadget>
<output>25_000</output>
<result>D</result> | D | 25,000 | A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m? | {
"A": "24000",
"B": "23000",
"C": "22000",
"D": "25000",
"E": "26000"
} | divide(divide(divide(multiply(multiply(multiply(25, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5) | multiply(n3,const_100)|multiply(n4,const_100)|multiply(n5,const_100)|multiply(#0,#1)|multiply(#3,#2)|divide(#4,n0)|divide(#5,n1)|divide(#6,n2)| | "25 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 25 = 1 / 100 * x = > x = 25000 answer : d" | physics |
math_qa__eY5Ec9peB2CA8mzA | The ratio of the incomes of A and B is 5:4 and the ratio of their expenditure is 3:2. If at the end of the year, each saves $1600 then the income of A is? Choose the correct choice from the following.
A) $ 1500 B) $ 4000 C) $ 2000 D) $ 2500 E) $ 3200 | <gadget id="calculator">5 / 2</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) * 1_600</gadget>
<output>4_000</output>
<result>B</result> | B | 4,000 | The ratio of the incomes of A and B is 5:4 and the ratio of their expenditure is 3:2. If at the end of the year, each saves $1600 then the income of A is? | {
"A": "$ 1500",
"B": "$ 4000",
"C": "$ 2000",
"D": "$ 2500",
"E": "$ 3200"
} | multiply(divide(5, 2), 1600) | divide(n0,n3)|multiply(n4,#0) | let the income of a and b be $ 5 x and $ 4 x let their expenditures be $ 3 y and $ 2 y 5 x - 3 y = 1600 - - - - - - - 1 ) 4 x - 2 y = 1600 - - - - - - - 2 ) from 1 ) and 2 ) x = 800 a ' s income = 5 x = 5 * 800 = $ 4000 answer is b | other |
math_qa__BBfprSavFled6noA | The speed of the boat in still water in 12 kmph. It can travel downstream through 60 kms in 3 hrs. In what time would it cover the same distance upstream?
Choose the correct answer:
A) 8 hours B) 6 hours C) 4 hours D) 15 hours E) 6 hours | <gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">20 - 12</gadget>
<output>8</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<result>D</result> | D | 15 | The speed of the boat in still water in 12 kmph. It can travel downstream through 60 kms in 3 hrs. In what time would it cover the same distance upstream? | {
"A": "8 hours",
"B": "6 hours",
"C": "4 hours",
"D": "15 hours",
"E": "6 hours"
} | divide(60, subtract(12, subtract(divide(60, 3), 12))) | divide(n1,n2)|subtract(#0,n0)|subtract(n0,#1)|divide(n1,#2)| | "still water = 12 km / hr downstream = 60 / 3 = 20 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 20 / 2 = 4 km / hr so time taken in upstream = 60 / 4 = 15 hrs answer : d" | physics |
math_qa__RPucdCdJ872xtZ3x | If there are 200 questions in a 3 hr examination. Among these questions are 25 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? Choose one
A) 40 min B) 62 min C) 70 min D) 74 min E) 76 min | <gadget id="calculator">3 * 60</gadget>
<output>180</output>
<gadget id="calculator">200 - 25</gadget>
<output>175</output>
<gadget id="calculator">2 * 25</gadget>
<output>50</output>
<gadget id="calculator">175 + 50</gadget>
<output>225</output>
<gadget id="calculator">180 / 225</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">2 * (4/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) * 25</gadget>
<output>40</output>
<result>A</result> | A | 40 | If there are 200 questions in a 3 hr examination. Among these questions are 25 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? | {
"A": "40 min",
"B": "62 min",
"C": "70 min",
"D": "74 min",
"E": "76 min"
} | multiply(multiply(const_2, divide(multiply(3, const_60), add(subtract(200, 25), multiply(const_2, 25)))), 25) | multiply(n1,const_60)|multiply(n2,const_2)|subtract(n0,n2)|add(#1,#2)|divide(#0,#3)|multiply(#4,const_2)|multiply(n2,#5)| | "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 175 x + 25 * 2 x = 180 x = 180 / 225 x = 0.8 time taken for type a problem = 25 * 2 * 0.8 = 40 min answer : a" | general |
math_qa__smiRJGpdKJA8VPC1 | The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 20-inch screen would be how many square inches greater than the area of a square 18-inch screen?
Choose the correct option:
A) 2 B) 4 C) 16 D) 38 E) 40 | <gadget id="calculator">20 ** 2</gadget>
<output>400</output>
<gadget id="calculator">18 ** 2</gadget>
<output>324</output>
<gadget id="calculator">400 - 324</gadget>
<output>76</output>
<gadget id="calculator">76 / 2</gadget>
<output>38</output>
<result>D</result> | D | 38 | The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 20-inch screen would be how many square inches greater than the area of a square 18-inch screen? | {
"A": "2",
"B": "4",
"C": "16",
"D": "38",
"E": "40"
} | divide(subtract(power(20, const_2), power(18, const_2)), const_2) | power(n0,const_2)|power(n1,const_2)|subtract(#0,#1)|divide(#2,const_2)| | "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 20 ^ 2 / 2 - 18 ^ 2 / 2 = 76 / 2 = 38 ans d ." | geometry |
math_qa__2qpc59DNJ7NO5vqV | In a group of 8 engineers, 3 engineers have a PHD degree; the others have only an MS or BS degree. A team of 3 engineers is to be chosen which must have at least 1 engineer with a PHD, how many different teams can be chosen? Choose the correct choice
A) 56 B) 46 C) 64 D) 65 E) 10 | <gadget id="calculator">8 - 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">1 + 45</gadget>
<output>46</output>
<result>B</result> | B | 46 | In a group of 8 engineers, 3 engineers have a PHD degree; the others have only an MS or BS degree. A team of 3 engineers is to be chosen which must have at least 1 engineer with a PHD, how many different teams can be chosen? | {
"A": "56",
"B": "46",
"C": "64",
"D": "65",
"E": "10"
} | add(1, multiply(multiply(subtract(8, 3), 3), 3)) | subtract(n0,n1)|multiply(n1,#0)|multiply(n1,#1)|add(n3,#2) | the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 8 r = 3 so , total teams is 8 c 3 = 8 ! / ( 3 ! ( 8 - 3 ) ! ) = 56 , and n = 8 - 3 = 5 r = 3 for teams without a phd is 5 c 3 = 5 ! / ( 3 ! ( 5 - 3 ) ! ) = 10 , so , teams with at least 1 phd = 56 - 10 = 46 answer : b | other |
math_qa__eOgmtZLd6dztW7tm | In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 4 ounces of corn syrup, how many ounces of water does it contain?
Choose the most appropriate option.
A) 45 B) 50 C) 55 D) 60 E) 63 | <gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/12) * 3</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/30) / 2</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">(1/4) / (1/60)</gadget>
<output>15</output>
<gadget id="calculator">15 * 4</gadget>
<output>60</output>
<result>D</result> | D | 60 | In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 4 ounces of corn syrup, how many ounces of water does it contain? | {
"A": "45",
"B": "50",
"C": "55",
"D": "60",
"E": "63"
} | multiply(divide(multiply(divide(1, 12), const_3), divide(divide(1, 30), const_2)), 4) | divide(n0,n1)|divide(n0,n2)|divide(#1,const_2)|multiply(#0,const_3)|divide(#3,#2)|multiply(n3,#4)| | "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 4 * 180 / 12 = 60 ounces of water d" | other |
math_qa__fPXtc1vrfuuNseRV | In an election between two candidates, the winner has a margin of 20% of the votes polled. If 1000 people change their mind and vote for the loser, the loser would have won by a margin of 20% of the votes polled. Find the total number of votes polled in the election? Choose one: A) 10000 B) 5000 C) 15000 D) 20000 E) 6000 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1_000 / (1/5)</gadget>
<output>5_000</output>
<result>B</result> | B | 5,000 | In an election between two candidates, the winner has a margin of 20% of the votes polled. If 1000 people change their mind and vote for the loser, the loser would have won by a margin of 20% of the votes polled. Find the total number of votes polled in the election? | {
"A": "10000",
"B": "5000",
"C": "15000",
"D": "20000",
"E": "6000"
} | divide(1000, divide(20, const_100)) | divide(n0,const_100)|divide(n1,#0) | winner - looser 60 % - 40 % if 1000 people change their mind and vote for the loser : winner - looser 40 % - 60 % thus 1,000 people compose 20 % of all voters , which means that the total number of votes is 5,000 . answer : b | gain |
math_qa__LxLmbpJipI8HY1zi | There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? Choose the correct choice from the following choices
A) 243 B) 265 C) 375 D) 390 E) 400 | <gadget id="calculator">600 / 5</gadget>
<output>120</output>
<gadget id="calculator">120 * 3</gadget>
<output>360</output>
<result>C</result> | C | 375 | There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school? | {
"A": "243",
"B": "265",
"C": "375",
"D": "390",
"E": "400"
} | multiply(divide(600, 5), 3) | divide(n0,n2)|multiply(n1,#0) | in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 600 . hence 3 x + 5 x = 600 solve for x 8 x = 600 x = 75 number of boys 3 x = 3 × 75 = 225 number of girls 5 x = 5 × 75 = 375 c | other |
math_qa__Whem3Poqc8815BPn | 8 is 2% of a, and 2 is 8% of b. c equals b/a. What is the value of c?
Choices.
A) 1 / 16
B) 1 / 4
C) 1
D) 4
E) 8 | <gadget id="calculator">2 / 8</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">25 / 400</gadget>
<output>1/16 = around 0.0625</output>
<result>A</result> | A | 0.0625 | 8 is 2% of a, and 2 is 8% of b. c equals b/a. What is the value of c? | {
"A": "1 / 16",
"B": "1 / 4",
"C": "1",
"D": "4",
"E": "8"
} | divide(multiply(divide(2, 8), const_100), multiply(divide(8, 2), const_100)) | divide(n1,n0)|divide(n0,n1)|multiply(#0,const_100)|multiply(#1,const_100)|divide(#2,#3)| | "2 a / 100 = 8 a = 400 8 b / 100 = 2 b = 25 c = b / a = 25 / 400 = 1 / 16 the answer is a ." | general |
math_qa__Sx8cTNsJCCahI4d3 | A certain psychologist charges $30 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $400, what is the total charge to a patient who receives only 3 hours of therapy ? Choose the correct choice from the following.
A) $ 120 B) $ 135 C) $ 150 D) $ 165 E) $ 252 | <gadget id="calculator">400 - 30</gadget>
<output>370</output>
<gadget id="calculator">370 / 5</gadget>
<output>74</output>
<gadget id="calculator">74 * 3</gadget>
<output>222</output>
<gadget id="calculator">222 + 30</gadget>
<output>252</output>
<result>E</result> | E | 252 | A certain psychologist charges $30 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $400, what is the total charge to a patient who receives only 3 hours of therapy ? | {
"A": "$ 120",
"B": "$ 135",
"C": "$ 150",
"D": "$ 165",
"E": "$ 252"
} | add(multiply(divide(subtract(400, 30), 5), 3), 30) | subtract(n2,n0)|divide(#0,n1)|multiply(n3,#1)|add(n0,#2)| | "let the charge for first hour = x + 30 then charge for each additional hour = x x + 30 + 4 x = 400 = > 5 x = 370 = > x = 74 total charge for patient for 3 hours of therapy = x + 30 + 2 x = 3 x + 30 = 252 $ answer e" | general |
math_qa__csdXS6JOmQqQC1dO | In a race, the speeds of A and B are in the ratio 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is? Choose the correct choice from the following answers
A) 1 hr B) 2 hr C) 1.5 hr D) 2.5 hr E) 3 hr | <gadget id="calculator">3 * 30</gadget>
<output>90</output>
<gadget id="calculator">30 + 90</gadget>
<output>120</output>
<gadget id="calculator">120 / 60</gadget>
<output>2</output>
<result>B</result> | B | 2 | In a race, the speeds of A and B are in the ratio 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is? | {
"A": "1 hr",
"B": "2 hr",
"C": "1.5 hr",
"D": "2.5 hr",
"E": "3 hr"
} | divide(add(30, multiply(3, 30)), const_60) | multiply(n0,n2)|add(n2,#0)|divide(#1,const_60) | explanation : ratio of speeds = 3 : 4 distance remaining constant , the ratio of time taken = 4 : 3 a takes 0.5 hours more than bhence time taken by a = 4 × 0.5 = 2 hour answer : b | physics |
math_qa__yzKtxljCKgnfSGUQ | By selling an article at Rs.800, a profit of 25% is made. Find its cost price? Choose the correct choice from the following answers:
A) s . 486 B) s . 455 C) s . 640 D) s . 480 E) s . 489 | <gadget id="calculator">800 * 100</gadget>
<output>80_000</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">80_000 / 125</gadget>
<output>640</output>
<result>C</result> | C | 640 | By selling an article at Rs.800, a profit of 25% is made. Find its cost price? | {
"A": "s . 486",
"B": "s . 455",
"C": "s . 640",
"D": "s . 480",
"E": "s . 489"
} | divide(multiply(800, const_100), add(const_100, 25)) | add(n1,const_100)|multiply(n0,const_100)|divide(#1,#0) | sp = 800 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / ( 100 + 25 ) ] = 800 * [ 100 / 125 ] = rs . 640 answer : c | gain |
math_qa__Ip0N2DpygFGXD1Cq | Kanul spent $500 in buying raw materials, $400 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
Choose the correct choice from the following options.
A) $ 1010 B) $ 1025 C) $ 1125 D) $ 1100 E) $ 1000 | <gadget id="calculator">500 + 400</gadget>
<output>900</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">900 / (9/10)</gadget>
<output>1_000</output>
<result>E</result> | E | 1,000 | Kanul spent $500 in buying raw materials, $400 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount? | {
"A": "$ 1010",
"B": "$ 1025",
"C": "$ 1125",
"D": "$ 1100",
"E": "$ 1000"
} | divide(add(500, 400), subtract(const_1, divide(10, const_100))) | add(n0,n1)|divide(n2,const_100)|subtract(const_1,#1)|divide(#0,#2)| | "let the total amount be x then , ( 100 - 10 ) % of x = 500 + 400 90 % of x = 900 90 x / 100 = 9000 / 9 x = $ 1000 answer is e" | gain |
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