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__jly6NGZyDoorlQGM | The average of 6 observations is 12. A new seventh observation is included and the new average is decreased by 1. The seventh observation is : Options
A) 1 B) 3 C) 5 D) 6 E) 8 | <gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">11 * 7</gadget>
<output>77</output>
<gadget id="calculator">12 * 6</gadget>
<output>72</output>
<gadget id="calculator">77 - 72</gadget>
<output>5</output>
<result>C</result> | C | 5 | The average of 6 observations is 12. A new seventh observation is included and the new average is decreased by 1. The seventh observation is : | {
"A": "1",
"B": "3",
"C": "5",
"D": "6",
"E": "8"
} | subtract(multiply(subtract(12, 1), add(6, 1)), multiply(12, 6)) | add(n0,n2)|multiply(n0,n1)|subtract(n1,n2)|multiply(#0,#2)|subtract(#3,#1)| | "explanation : seventh observation = ( 7 × × 11 - 6 × × 12 ) = 5 correct option : c" | general |
math_qa__tzC7azOTBLw0t1xO | For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $5. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? Choose the correct answer:
A) $ 24960
B) $ 25920
C) $ 28080
D) $ 28350
E) $ 29160 | <gadget id="calculator">12 + 5</gadget>
<output>17</output>
<gadget id="calculator">17 - 9</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 12</gadget>
<output>108</output>
<gadget id="calculator">108 * 30</gadget>
<output>3_240</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">3_240 / 4</gadget>
<output>810</output>
<gadget id="calculator">810 * 3</gadget>
<output>2_430</output>
<gadget id="calculator">2_430 * 10</gadget>
<output>24_300</output>
<gadget id="calculator">810 * 5</gadget>
<output>4_050</output>
<gadget id="calculator">24_300 + 4_050</gadget>
<output>28_350</output>
<result>D</result> | D | 28,350 | For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in the morning to 5:55 in the afternoon, inclusive. The price of a regular admission ticket was $10 and the price of a student ticket was $5. If on one day 3 times as many regular admission tickets were sold as student tickets, what was the total revenue from ticket sales that day? | {
"A": "$ 24960",
"B": "$ 25920",
"C": "$ 28080",
"D": "$ 28350",
"E": "$ 29160"
} | add(multiply(multiply(divide(multiply(multiply(add(subtract(add(const_12, 5), 9), const_1), const_12), 30), add(3, const_1)), 3), 10), multiply(divide(multiply(multiply(add(subtract(add(const_12, 5), 9), const_1), const_12), 30), add(3, const_1)), 5)) | add(const_12,n4)|add(n8,const_1)|subtract(#0,n2)|add(#2,const_1)|multiply(#3,const_12)|multiply(n0,#4)|divide(#5,#1)|multiply(n8,#6)|multiply(n7,#6)|multiply(n6,#7)|add(#9,#8)| | "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 30 - - > x = 27 * 30 and 3 x = 3 * ( 27 * 30 ) = 27 * 90 . therefore , the total revenue from ticket sales that day was 27 * 30 * 5 + 27 * 90 * 10 = $ 28,350 . answer : d ." | general |
math_qa__mWdGocmOYVPMV206 | How many factors of 880 are odd numbers greater than 1? Options
A) 3
B) 4
C) 5
D) 6
E) 7 | <gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">60 / 20</gadget>
<output>3</output>
<result>A</result> | A | 3 | How many factors of 880 are odd numbers greater than 1? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | divide(const_60.0, multiply(const_10, const_2)) | multiply(const_10,const_2)|divide(const_60.0,#0)| | when factorized , 880 has 6 prime factors . of these prime factors 2 are odd and 4 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 4 . the total number of odd factors greater than 1 are 3 . ( option a ) | other |
math_qa__goR5HRP2XbSz8OvS | If it takes 30 construction workers 70 days to build a skyscraper, how long would it take 50 workers? Choose the correct option:
A) 52 days B) 47 days C) 42 days D) 37 days E) 32 days | <gadget id="calculator">70 * 30</gadget>
<output>2_100</output>
<gadget id="calculator">2_100 / 50</gadget>
<output>42</output>
<result>C</result> | C | 42 | If it takes 30 construction workers 70 days to build a skyscraper, how long would it take 50 workers? | {
"A": "52 days",
"B": "47 days",
"C": "42 days",
"D": "37 days",
"E": "32 days"
} | divide(multiply(70, 30), 50) | multiply(n0,n1)|divide(#0,n2) | 30 * 70 = 50 * x x = 42 answer : c | physics |
math_qa__PIFLTFQcLJulAn1P | there are thirty - 4 lines that are tangent to a circle , and these lines create regions in the plane . can you tell how many of these regions are not enclosed ? Choose the correct answer.
A) 50 B) 74 C) 37 D) 77 E) 68 | <gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">40 + 20</gadget>
<output>60</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">60 + 8</gadget>
<output>68</output>
<result>E</result> | E | 68 | there are thirty - 4 lines that are tangent to a circle , and these lines create regions in the plane . can you tell how many of these regions are not enclosed ? | {
"A": "50",
"B": "74",
"C": "37",
"D": "77",
"E": "68"
} | add(add(multiply(4, const_10), multiply(const_2, const_10)), multiply(4, const_2)) | multiply(n0,const_10)|multiply(const_10,const_2)|multiply(n0,const_2)|add(#0,#1)|add(#3,#2) | e 68 68 regions . each new tangent increases the non - enclosed areas by two | geometry |
math_qa__xr8EgA0vuegFPnx2 | 2 cow’s and 8 goats are brought for Rs.1400. If the average price of a goat be Rs.60. What is the average price of a cow. Select the correct option.
A) rs . 480 B) rs . 960 C) rs . 960 D) rs . 460 E) rs . 560 | <gadget id="calculator">8 * 60</gadget>
<output>480</output>
<gadget id="calculator">1_400 - 480</gadget>
<output>920</output>
<gadget id="calculator">920 / 2</gadget>
<output>460</output>
<result>D</result> | D | 460 | 2 cow’s and 8 goats are brought for Rs.1400. If the average price of a goat be Rs.60. What is the average price of a cow. | {
"A": "rs . 480",
"B": "rs . 960",
"C": "rs . 960",
"D": "rs . 460",
"E": "rs . 560"
} | divide(subtract(1400, multiply(8, 60)), 2) | multiply(n1,n3)|subtract(n2,#0)|divide(#1,n0) | explanation : average price of a goat = rs . 60 total price of 8 goats = 8 * 60 = rs . 480 but total price of 2 cows and 8 goats = rs . 1400 total price of 2 cows is = 1400 - 480 = 980 average price of a cow = 980 / 2 = rs . 460 answer : option d | general |
math_qa__gmnt7of0ZFnK1LPY | 1=6,2=36,3=363,4=364,5=365, then 36=? Select the correct option:
A) 1 B) 2 C) 345 D) 445 E) 235 | <gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">36 * 10</gadget>
<output>360</output>
<gadget id="calculator">365 - 360</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<result>B</result> | B | 2 | 1=6,2=36,3=363,4=364,5=365, then 36=? | {
"A": "1",
"B": "2",
"C": "345",
"D": "445",
"E": "235"
} | divide(subtract(subtract(365, multiply(multiply(add(const_4, const_2), add(const_4, const_2)), const_10)), 1), const_2) | add(const_2,const_4)|multiply(#0,#0)|multiply(#1,const_10)|subtract(n5,#2)|subtract(#3,n0)|divide(#4,const_2) | 1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ? 36 = 2 check the second eqn . answer : b | general |
math_qa__m9ZCHV8nrKMwQopC | what is the smallest integer that is multiple of 87 and 20
Choose the most appropriate option:
A) 141
B) 180
C) 130
D) 122
E) 280 | <gadget id="calculator">lcm(87, 20)</gadget>
<output>1_740</output>
<gadget id="calculator">1_740 / 12</gadget>
<output>145</output>
<gadget id="calculator">145 * 2</gadget>
<output>290</output>
<result>E</result> | E | 280 | what is the smallest integer that is multiple of 87 and 20 | {
"A": "141",
"B": "180",
"C": "130",
"D": "122",
"E": "280"
} | multiply(divide(lcm(87, 20), const_12), const_2) | lcm(n0,n1)|divide(#0,const_12)|multiply(#1,const_2) | correct answer : e it is the lcm of 8,7 and 20 which is 280 | general |
math_qa__XUeOdYdNzK0G3UDE | Two employees X and Y are paid a total of Rs. 600 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Choices:
A) s . 200.72 B) s . 250.72 C) s . 272.72 D) s . 300.72 E) s . 310.72 | <gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">600 * 10</gadget>
<output>6_000</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">6_000 / 22</gadget>
<output>3_000/11 = around 272.727273</output>
<result>C</result> | C | 272.72 | Two employees X and Y are paid a total of Rs. 600 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? | {
"A": "s . 200.72",
"B": "s . 250.72",
"C": "s . 272.72",
"D": "s . 300.72",
"E": "s . 310.72"
} | divide(multiply(600, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2)) | add(const_1,const_4)|multiply(#0,const_2)|add(#1,const_1)|multiply(n0,#1)|multiply(#2,const_2)|divide(#3,#4)| | "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 600 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 600 ⇒ y [ 12 / 10 + 1 ] = 600 ⇒ 22 y / 10 = 600 ⇒ 22 y = 6000 ⇒ y = 6000 / 22 = rs . 272.72 c" | general |
math_qa__KEGIaEUaeSkmoaY6 | A reduction of 20% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? Choose the correct choice from the following choices.
A) s . 42 B) s . 46 C) s . 40 D) s . 41 E) s . 32 | <gadget id="calculator">800 * 20</gadget>
<output>16_000</output>
<gadget id="calculator">16_000 / 100</gadget>
<output>160</output>
<gadget id="calculator">160 / 5</gadget>
<output>32</output>
<result>E</result> | E | 32 | A reduction of 20% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? | {
"A": "s . 42",
"B": "s . 46",
"C": "s . 40",
"D": "s . 41",
"E": "s . 32"
} | divide(divide(multiply(800, 20), const_100), 5) | multiply(n0,n2)|divide(#0,const_100)|divide(#1,n1)| | "800 * ( 20 / 100 ) = 160 - - - - 5 ? - - - - 1 = > rs . 32 answer : e" | gain |
math_qa__H1UvKbLX1sUkNprT | Mary's income is 40 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?
Choose the correct choice from the following answers:
A) 124 % B) 120 % C) 96 % D) 80 % E) 84 % | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(3/5) * (7/5)</gadget>
<output>21/25 = around 0.84</output>
<gadget id="calculator">(21/25) * 100</gadget>
<output>84</output>
<result>E</result> | E | 84 | Mary's income is 40 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income? | {
"A": "124 %",
"B": "120 %",
"C": "96 %",
"D": "80 %",
"E": "84 %"
} | multiply(multiply(subtract(const_1, divide(40, const_100)), add(const_1, divide(40, const_100))), const_100) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)| | "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 84 ( 40 percent more than tim ' s income ) . thus , mary ' s income ( 84 ) is 84 % of juan ' s income ( 100 ) . answer : e ." | general |
math_qa__vwQ7gri5567RVCli | Kim has 40 percent more money than Sal and Sal has 20 percent less money than Phil. If Sal and Phil have a combined total of $1.80, how much money does Kim have? Choices.
A) $ 1.00 B) $ 1.12 C) $ 1.20 D) $ 1.32 E) $ 1.40 | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 + 80</gadget>
<output>180</output>
<gadget id="calculator">1.8 / 180</gadget>
<output>0.01</output>
<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">80 * 140</gadget>
<output>11_200</output>
<gadget id="calculator">11_200 / 100</gadget>
<output>112</output>
<gadget id="calculator">0.01 * 112</gadget>
<output>1.12</output>
<result>B</result> | B | 1.12 | Kim has 40 percent more money than Sal and Sal has 20 percent less money than Phil. If Sal and Phil have a combined total of $1.80, how much money does Kim have? | {
"A": "$ 1.00",
"B": "$ 1.12",
"C": "$ 1.20",
"D": "$ 1.32",
"E": "$ 1.40"
} | multiply(divide(1.8, add(const_100, subtract(const_100, 20))), divide(multiply(subtract(const_100, 20), add(const_100, 40)), const_100)) | add(n0,const_100)|subtract(const_100,n1)|add(#1,const_100)|multiply(#0,#1)|divide(n2,#2)|divide(#3,const_100)|multiply(#4,#5) | phil = x sal = 0.8 x kim = ( 1.4 ) * 0.8 x = 1.12 x x + 0.8 x = 1.8 - - > x = 1 kim = 1.12 answer : b | general |
math_qa__lgAEsBzkTHwVqacE | The sides of a rectangle are in the ratio 4:3 and its area is 972sq.m find the perimeter of rectangle Choose the correct answer
A) 120 m B) 122 m C) 124 m D) 126 m E) 128 m | <gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">972 / 12</gadget>
<output>81</output>
<gadget id="calculator">81 ** (1/2)</gadget>
<output>9</output>
<gadget id="calculator">4 * 9</gadget>
<output>36</output>
<gadget id="calculator">3 * 9</gadget>
<output>27</output>
<gadget id="calculator">2 * (36 + 27)</gadget>
<output>126</output>
<result>D</result> | D | 126 | The sides of a rectangle are in the ratio 4:3 and its area is 972sq.m find the perimeter of rectangle | {
"A": "120 m",
"B": "122 m",
"C": "124 m",
"D": "126 m",
"E": "128 m"
} | rectangle_perimeter(multiply(4, sqrt(divide(972, multiply(4, 3)))), multiply(3, sqrt(divide(972, multiply(4, 3))))) | multiply(n0,n1)|divide(n2,#0)|sqrt(#1)|multiply(n0,#2)|multiply(n1,#2)|rectangle_perimeter(#3,#4) | explanation : let 4 x and 3 x be sides of the rectangle we know that area of rectangle = l × b 4 x × 3 x = 972 12 x 2 = 972 x 2 = 81 x = 9 therefore length = 4 x = 4 × 9 = 36 m breadth = 3 x = 3 × 9 = 27 m therefore perimeter = 2 ( l + b ) = 2 ( 36 + 27 ) = 126 m answer : option d | geometry |
math_qa__tTd0Ne5s9a3EA6tg | A gambler bought $3,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 14 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back? Choices
A) $ 2,240
B) $ 2,120
C) $ 1,960
D) $ 1,920
E) $ 1,400 | <gadget id="calculator">3 * 1_000</gadget>
<output>3_000</output>
<gadget id="calculator">14 + 2</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 20</gadget>
<output>160</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">160 + 600</gadget>
<output>760</output>
<gadget id="calculator">3_000 - 760</gadget>
<output>2_240</output>
<result>A</result> | A | 2,240 | A gambler bought $3,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 14 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back? | {
"A": "$ 2,240",
"B": "$ 2,120",
"C": "$ 1,960",
"D": "$ 1,920",
"E": "$ 1,400"
} | subtract(multiply(const_3, const_1000), add(multiply(divide(add(14, 2), 2), 20), multiply(subtract(divide(add(14, 2), 2), 2), 100))) | add(n3,n5)|multiply(const_1000,const_3)|divide(#0,n5)|multiply(n1,#2)|subtract(#2,n5)|multiply(n2,#4)|add(#3,#5)|subtract(#1,#6)| | "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 14 : x + x - 2 = 14 - - > x = 8 : 8 $ 20 chips were lost and 8 - 2 = 6 $ 100 chips were lost . total worth of chips lost is 8 * 20 + 6 * 100 = $ 760 , so the gambler kept $ 3,000 - $ 760 = $ 2,240 . answer : a ." | general |
math_qa__T52XBM9ELqb22Ex6 | A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 35%. Staff are allowed a further 30% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
Choose the correct choice from the following:
A) 0.555 d B) 0.765 d C) 0.455 d D) 0.785 d E) 0.805 d | <gadget id="calculator">100 - 35</gadget>
<output>65</output>
<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(13/20) * (3/10)</gadget>
<output>39/200 = around 0.195</output>
<gadget id="calculator">(13/20) - (39/200)</gadget>
<output>91/200 = around 0.455</output>
<result>C</result> | C | 0.455 | A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 35%. Staff are allowed a further 30% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ? | {
"A": "0.555 d",
"B": "0.765 d",
"C": "0.455 d",
"D": "0.785 d",
"E": "0.805 d"
} | subtract(divide(subtract(const_100, 35), const_100), multiply(divide(subtract(const_100, 35), const_100), divide(30, const_100))) | divide(n1,const_100)|subtract(const_100,n0)|divide(#1,const_100)|multiply(#2,#0)|subtract(#2,#3)| | "effective discount = a + b + ab / 100 = - 35 - 30 + ( - 35 ) ( - 30 ) / 100 = - 54.5 sale price = d * ( 1 - 54.5 / 100 ) sale price = . 455 * d answer ( c )" | gain |
math_qa__1AYOfOZdvPQIYhEA | If k^3 is divisible by 336, what is the least possible value of integer k? Select the correct option
A) 56 B) 70 C) 84 D) 96 E) 120 | <gadget id="calculator">336 / 2</gadget>
<output>168</output>
<gadget id="calculator">168 / 2</gadget>
<output>84</output>
<result>C</result> | C | 84 | If k^3 is divisible by 336, what is the least possible value of integer k? | {
"A": "56",
"B": "70",
"C": "84",
"D": "96",
"E": "120"
} | divide(divide(336, const_2), const_2) | divide(n1,const_2)|divide(#0,const_2)| | "k ^ 3 = 336 * x = 2 ^ 4 * 3 * 7 * x the factors of k must at minimum include 2 ^ 2 * 3 * 7 = 84 . the answer is c ." | general |
math_qa__7HawYK61FHBBq1UQ | There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is Choose the correct choice from the following choices
A) 5 B) 21 C) 33 D) 60 E) 40 | <gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">6 + 5</gadget>
<output>11</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">11 + 4</gadget>
<output>15</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">15 + 3</gadget>
<output>18</output>
<gadget id="calculator">18 + 2</gadget>
<output>20</output>
<result>B</result> | B | 21 | There are 6 boxes numbered 1, 2,...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is | {
"A": "5",
"B": "21",
"C": "33",
"D": "60",
"E": "40"
} | add(add(add(add(6, subtract(6, 1)), subtract(subtract(6, 1), 1)), subtract(subtract(subtract(6, 1), 1), 1)), 2) | subtract(n0,n1)|add(n0,#0)|subtract(#0,n1)|add(#1,#2)|subtract(#2,n1)|add(#3,#4)|add(n2,#5) | given the constraints of this question , we have to consider 6 possible outcomes . . . 1 green ball : 6 options grrrrr rgrrrr rrgrrr rrrgrr rrrrgr rrrrrg 2 green balls : 5 options ggrrrr rggrrr rrggrr rrrggr rrrrgg 3 green balls : 4 options gggrrr rgggrr rrgggr rrrggg 4 green balls : 3 options ggggrr rggggr rrgggg 5 green balls : 2 options gggggr rggggg 6 green balls : 1 option gggggg 6 + 5 + 4 + 3 + 2 + 1 = 21 options . b | general |
math_qa__yQtKxtogud5NV6T5 | A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? Choose the correct choice from the following answers:
A) 20 %
B) 30 %
C) 40 %
D) 50 %
E) 55 % | <gadget id="calculator">1 ** 2</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>
<gadget id="calculator">2 - (sqrt(2))</gadget>
<output>2 - sqrt(2) = around 0.585786</output>
<gadget id="calculator">(2 - sqrt(2)) * 100</gadget>
<output>200 - 100*sqrt(2) = around 58.578644</output>
<gadget id="calculator">(200 - 100*sqrt(2)) / 2</gadget>
<output>100 - 50*sqrt(2) = around 29.289322</output>
<result>B</result> | B | 30 | A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges? | {
"A": "20 %",
"B": "30 %",
"C": "40 %",
"D": "50 %",
"E": "55 %"
} | divide(multiply(subtract(add(power(const_1, const_2), power(const_1, const_2)), sqrt(add(power(const_1, const_2), power(const_1, const_2)))), const_100), add(power(const_1, const_2), power(const_1, const_2))) | power(const_1,const_2)|add(#0,#0)|sqrt(#1)|subtract(#1,#2)|multiply(#3,const_100)|divide(#4,#1) | let the side of the square ( abcd ) be x metres . then , ab + bc = 2 x metres . ac = 2 x = ( 1.41 x ) m . saving on 2 x metres = ( 0.59 x ) m . saving % = ( 0.59 x ) / 2 x x 100 % = 30 % ( approx . ) b ) | geometry |
math_qa__p48d8Kte66uukhaM | Rs.500 amounts to Rs.670 in 5 years at simple interest. If the interest is increased by 2%, it would amount to how much? Choose the correct choice from the following options:
A) 150 B) 550 C) 760 D) 450 E) 260 | <gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">1 + (1/50)</gadget>
<output>51/50 = around 1.02</output>
<gadget id="calculator">(51/50) ** 5</gadget>
<output>345_025_251/312_500_000 = around 1.104081</output>
<gadget id="calculator">(345_025_251/312_500_000) * 500</gadget>
<output>345_025_251/625_000 = around 552.040402</output>
<result>B</result> | B | 550 | Rs.500 amounts to Rs.670 in 5 years at simple interest. If the interest is increased by 2%, it would amount to how much? | {
"A": "150",
"B": "550",
"C": "760",
"D": "450",
"E": "260"
} | multiply(power(add(const_1, divide(2, const_100)), 5), 500) | divide(n3,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2) | ( 500 * 5 * 2 ) / 100 = 50 500 + 50 = 550 answer : b | gain |
math_qa__F3Cea0dRVZOhk42u | A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 10 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled? Select the correct option: A) 4.3 hrs B) 8.9 hrs C) 2.9 hrs D) 7.2 hrs E) 8.6 hrs | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/3) - (1/10)</gadget>
<output>7/30 = around 0.233333</output>
<gadget id="calculator">1 / (7/30)</gadget>
<output>30/7 = around 4.285714</output>
<result>A</result> | A | 4.3 | A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 10 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled? | {
"A": "4.3 hrs",
"B": "8.9 hrs",
"C": "2.9 hrs",
"D": "7.2 hrs",
"E": "8.6 hrs"
} | divide(const_1, subtract(divide(const_1, 3), divide(const_1, 10))) | divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)| | "net part filled in 1 hour = ( 1 / 3 - 1 / 10 ) = 7 / 30 the cistern will be filled in 30 / 7 hrs i . e . , 4.3 hrs . answer : a" | physics |
math_qa__u1tgxMvpvWitkOk2 | A software engineer starts from home at 3pm for every walk on a route which has level road for some distance and a then a hillock.he walks speed of 4kmph on level ground and then at a speed of 3kmph on the uphill and then down the hill at a speed of6kmph to the level ground and then at a speed of 4kmph to the home if he reaches home at 9pm.what is the distance one way of his route? Choose the correct answer
A) 12 km B) 15 km C) 18 km D) 24 km E) data inadequate | <gadget id="calculator">9 - 3</gadget>
<output>6</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">10 + 7</gadget>
<output>17</output>
<gadget id="calculator">17 / 4</gadget>
<output>17/4 = around 4.25</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(17/4) - (1/4)</gadget>
<output>4</output>
<gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<result>A</result> | A | 12 | A software engineer starts from home at 3pm for every walk on a route which has level road for some distance and a then a hillock.he walks speed of 4kmph on level ground and then at a speed of 3kmph on the uphill and then down the hill at a speed of6kmph to the level ground and then at a speed of 4kmph to the home if he reaches home at 9pm.what is the distance one way of his route? | {
"A": "12 km",
"B": "15 km",
"C": "18 km",
"D": "24 km",
"E": "data inadequate"
} | divide(multiply(subtract(9, 3), subtract(divide(add(add(6, 4), add(4, 3)), const_4), const_0_25)), const_2) | add(n1,n3)|add(n0,n1)|subtract(n5,n0)|add(#0,#1)|divide(#3,const_4)|subtract(#4,const_0_25)|multiply(#2,#5)|divide(#6,const_2) | time = distance / speed so , let the distance to the level road from home be x km and the distance to the hillock from the level road be y km so , ( x / 4 + y / 3 ) + ( y / 6 + x / 4 ) = 6 x + y = 12 km . answer : a | physics |
math_qa__chE6YcDZsp6IohsM | A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 60% have red flags, what percentage of children have flags of both the colors? Choose the correct choice:
A) 5 % B) 10 % C) 15 % D) 20 % E) it can not be determined | <gadget id="calculator">60 + 60</gadget>
<output>120</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<result>D</result> | D | 20 | A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 60% have red flags, what percentage of children have flags of both the colors? | {
"A": "5 %",
"B": "10 %",
"C": "15 %",
"D": "20 %",
"E": "it can not be determined"
} | subtract(add(60, 60), const_100) | add(n0,n1)|subtract(#0,const_100)| | "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 55 % = 55 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 60 - c = 100 c = 20 option d ." | general |
math_qa__WtOm5aYvfhlRiJVa | The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 3000 resolutions? Choose the correct answer:
A) 2187 m B) 3704 m C) 4179 m D) 4224 m E) 4297 m | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 + 1</gadget>
<output>22</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">(22/7) * 22.4</gadget>
<output>70.4</output>
<gadget id="calculator">70.4 * 2</gadget>
<output>140.8</output>
<gadget id="calculator">140.8 * 3_000</gadget>
<output>422_400</output>
<gadget id="calculator">422_400 / 100</gadget>
<output>4_224</output>
<result>D</result> | D | 4,224 | The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 3000 resolutions? | {
"A": "2187 m",
"B": "3704 m",
"C": "4179 m",
"D": "4224 m",
"E": "4297 m"
} | divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 3000), const_100) | add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)| | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 3000 resolutions . = 3000 * 2 * 22 / 7 * 22.4 = 422400 cm = 4224 m answer : d" | physics |
math_qa__V2cJRrmwfTKw0DtG | Half a number plus 6 is 11.What is the number? Options.
A) 8
B) 9
C) 10
D) 11
E) 12 | <gadget id="calculator">11 - 6</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<result>C</result> | C | 10 | Half a number plus 6 is 11.What is the number? | {
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "12"
} | multiply(subtract(11, 6), const_2) | subtract(n1,n0)|multiply(#0,const_2) | let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 6 = 11 ( 1 / 2 ) x = 11 - 6 ( 1 / 2 ) x = 5 x = 10 correct answer is c | general |
math_qa__Y4E9qyWJniWdngA7 | n^(n/2)=6 is true when n=6 in the same way what is the value of n if n^(n/2) =10?
Choose the correct option
A) 8
B) 12
C) 10
D) 16
E) 18 | <gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<result>C</result> | C | 10 | n^(n/2)=6 is true when n=6 in the same way what is the value of n if n^(n/2) =10? | {
"A": "8",
"B": "12",
"C": "10",
"D": "16",
"E": "18"
} | divide(power(10, 2), 10) | power(n4,n0)|divide(#0,n4)| | n ^ ( n / 2 ) = 10 apply log n / 2 logn = log 10 nlogn = 2 log 10 = log 10 ^ 2 = log 100 logn = log 100 now apply antilog n = 100 / n now n = 10 . answer : c | general |
math_qa__LJKgxHRyHsbZBfym | the average age of 11 boys is 50 , if the average age of first 6 boys is 49 and that of the last 6 is 52 . find the boy age ? Choose one:
A) 48
B) 50
C) 56
D) 62
E) 64 | <gadget id="calculator">6 * 52</gadget>
<output>312</output>
<gadget id="calculator">11 * 50</gadget>
<output>550</output>
<gadget id="calculator">6 * 49</gadget>
<output>294</output>
<gadget id="calculator">550 - 294</gadget>
<output>256</output>
<gadget id="calculator">312 - 256</gadget>
<output>56</output>
<result>C</result> | C | 56 | the average age of 11 boys is 50 , if the average age of first 6 boys is 49 and that of the last 6 is 52 . find the boy age ? | {
"A": "48",
"B": "50",
"C": "56",
"D": "62",
"E": "64"
} | subtract(multiply(6, 52), subtract(multiply(11, 50), multiply(6, 49))) | multiply(n2,n5)|multiply(n0,n1)|multiply(n2,n3)|subtract(#1,#2)|subtract(#0,#3) | 1 to 11 = 11 * 50 = 550 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6 th = 294 + 312 – 550 = 56 c | general |
math_qa__8gNBdzngniynlhQs | After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6840. Find the actual price of the good. Choose the correct choice from the following answers
A) rs . 6000
B) rs . 9000
C) rs . 10800
D) rs . 10000
E) rs . 9980 | <gadget id="calculator">6_840 * 100</gadget>
<output>684_000</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 * 10</gadget>
<output>800</output>
<gadget id="calculator">800 / 100</gadget>
<output>8</output>
<gadget id="calculator">80 - 8</gadget>
<output>72</output>
<gadget id="calculator">72 * 5</gadget>
<output>360</output>
<gadget id="calculator">360 / 100</gadget>
<output>18/5 = around 3.6</output>
<gadget id="calculator">72 - (18/5)</gadget>
<output>342/5 = around 68.4</output>
<gadget id="calculator">684_000 / (342/5)</gadget>
<output>10_000</output>
<result>D</result> | D | 10,000 | After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6840. Find the actual price of the good. | {
"A": "rs . 6000",
"B": "rs . 9000",
"C": "rs . 10800",
"D": "rs . 10000",
"E": "rs . 9980"
} | divide(multiply(6840, const_100), subtract(subtract(subtract(const_100, 20), divide(multiply(subtract(const_100, 20), 10), const_100)), divide(multiply(subtract(subtract(const_100, 20), divide(multiply(subtract(const_100, 20), 10), const_100)), 5), const_100))) | multiply(n3,const_100)|subtract(const_100,n0)|multiply(n1,#1)|divide(#2,const_100)|subtract(#1,#3)|multiply(n2,#4)|divide(#5,const_100)|subtract(#4,#6)|divide(#0,#7)| | "let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6840 1 = 6840 / 68.4 100 = ( 6840 * 100 ) / 68.4 = rs . 10,000 . answer : option d" | gain |
math_qa__MlxZrRGfCSIIXcME | In a school of 900 students, 44% wear blue shirts, 28% wear red shirts, 10% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? Choose the correct choice from the following choices.
A) 144 B) 153 C) 162 D) 171 E) 180 | <gadget id="calculator">44 / 100</gadget>
<output>11/25 = around 0.44</output>
<gadget id="calculator">(11/25) * 900</gadget>
<output>396</output>
<gadget id="calculator">28 / 100</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">(7/25) * 900</gadget>
<output>252</output>
<gadget id="calculator">396 + 252</gadget>
<output>648</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 900</gadget>
<output>90</output>
<gadget id="calculator">648 + 90</gadget>
<output>738</output>
<gadget id="calculator">900 - 738</gadget>
<output>162</output>
<result>C</result> | C | 162 | In a school of 900 students, 44% wear blue shirts, 28% wear red shirts, 10% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)? | {
"A": "144",
"B": "153",
"C": "162",
"D": "171",
"E": "180"
} | subtract(900, add(add(multiply(divide(44, const_100), 900), multiply(divide(28, const_100), 900)), multiply(divide(10, const_100), 900))) | 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)| | "44 + 28 + 10 = 82 % 100 – 82 = 18 % 900 * 18 / 100 = 162 the answer is c ." | gain |
math_qa__TLF61s2INadzlb1T | If c is 14% of a and 40% of b, what percent of a is b? Options: A) 2.5 % B) 15 % C) 25 % D) 35 % E) 250 % | <gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(7/50) / (2/5)</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 100</gadget>
<output>35</output>
<result>D</result> | D | 35 | If c is 14% of a and 40% of b, what percent of a is b? | {
"A": "2.5 %",
"B": "15 %",
"C": "25 %",
"D": "35 %",
"E": "250 %"
} | multiply(divide(divide(14, const_100), divide(40, const_100)), const_100) | divide(n0,const_100)|divide(n1,const_100)|divide(#0,#1)|multiply(#2,const_100)| | "answer = d 14 a / 100 = 40 b / 100 b = 14 a / 40 = 35 a / 100 = 35 %" | gain |
math_qa__7ZRdF4TqefS0BRQh | A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 2 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete? Choices
A) 11 / 30 B) 29 / 60 C) 17 / 30 D) 19 / 30 E) 7 / 15 | <gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/3) * (1/5)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">7 * (1/15)</gadget>
<output>7/15 = around 0.466667</output>
<result>E</result> | E | 0.466667 | A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 2 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete? | {
"A": "11 / 30",
"B": "29 / 60",
"C": "17 / 30",
"D": "19 / 30",
"E": "7 / 15"
} | multiply(add(multiply(2, 3), 1), multiply(divide(1, 3), divide(1, 5))) | divide(n1,n2)|divide(n1,n4)|multiply(n0,n2)|add(n1,#2)|multiply(#0,#1)|multiply(#3,#4) | i think e - 7 / 15 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 2 x so old = x , new = x now 1 / 3 of x are occupied and 1 / 5 of x are occupied which simplifies to ( 1 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 1 / 5 of x occupied in the new ward . add them up to get 8 / 15 of x there are x beds in new tower so ratio is : ( 8 / 15 ) x / x = 8 / 15 of x subtract that from 15 / 15 of x and you get the number of un - occupied beds to total capacity of new towerb = 7 / 15 . e | general |
math_qa__mbB9DRCZFc916y8o | Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 222 runs? Choose the correct choice from the following answers: A) 6 B) 6.25 C) 7.25 D) 7.5 E) 4.75 | <gadget id="calculator">3.2 * 10</gadget>
<output>32</output>
<gadget id="calculator">222 - 32</gadget>
<output>190</output>
<gadget id="calculator">190 / 40</gadget>
<output>19/4 = around 4.75</output>
<result>E</result> | E | 4.75 | Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 222 runs? | {
"A": "6",
"B": "6.25",
"C": "7.25",
"D": "7.5",
"E": "4.75"
} | divide(subtract(222, multiply(3.2, 10)), 40) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | "required run rate = 222 - ( 3.2 x 10 ) = 190 = 4.75 40 40 e" | gain |
math_qa__oYVt4Jtdq9jqu8g7 | If the sum of a number and its square is 342, What is the number? Choose the correct choice.
A) 16
B) 77
C) 25
D) 87
E) 18 | <gadget id="calculator">342 ** (1/2)</gadget>
<output>3*sqrt(38) = around 18.493242</output>
<gadget id="calculator">floor(3*sqrt(38))</gadget>
<output>18</output>
<result>E</result> | E | 18 | If the sum of a number and its square is 342, What is the number? | {
"A": "16",
"B": "77",
"C": "25",
"D": "87",
"E": "18"
} | floor(sqrt(342)) | sqrt(n0)|floor(#0)| | "explanation : let the integer be x . then , x + x 2 = 342 x 2 + x - 342 = 0 ( x + 19 ) ( x – 18 ) = 0 x = 18 answer : e" | geometry |
math_qa__r2ty6u5di2esSwdR | The arithmetic mean and standard deviation of a certain normal distribution are 16.2 and 2.3, respectively. What value is exactly 2 standard deviations less than the mean? Choose the correct choice: A) 10.5 B) 11 C) 11.6 D) 12 E) 12.5 | <gadget id="calculator">2 * 2.3</gadget>
<output>4.6</output>
<gadget id="calculator">16.2 - 4.6</gadget>
<output>11.6</output>
<result>C</result> | C | 11.6 | The arithmetic mean and standard deviation of a certain normal distribution are 16.2 and 2.3, respectively. What value is exactly 2 standard deviations less than the mean? | {
"A": "10.5",
"B": "11",
"C": "11.6",
"D": "12",
"E": "12.5"
} | subtract(16.2, multiply(2, 2.3)) | multiply(n1,n2)|subtract(n0,#0)| | "mean = 16.2 two standard deviations is 2.3 + 2.3 = 4.6 there could be two calues for this . mean + two standard deviations = 20.8 mean - two standard deviations = 11.6 answer choice has 11.6 and so c is the answer ." | general |
math_qa__MGD5Ajse3mgPcfUk | A shopkeeper has 280 kg of apples. He sells 40% of these at 10% profit and remaining 60% at 30% profit. Find his % profit on total. Select: A) 22 % B) 25 % C) 26 % D) 28 % E) 35 % | <gadget id="calculator">280 * 40</gadget>
<output>11_200</output>
<gadget id="calculator">11_200 / 100</gadget>
<output>112</output>
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">112 * (11/10)</gadget>
<output>616/5 = around 123.2</output>
<gadget id="calculator">280 * 60</gadget>
<output>16_800</output>
<gadget id="calculator">16_800 / 100</gadget>
<output>168</output>
<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">168 * (13/10)</gadget>
<output>1_092/5 = around 218.4</output>
<gadget id="calculator">(616/5) + (1_092/5)</gadget>
<output>1_708/5 = around 341.6</output>
<gadget id="calculator">(1_708/5) - 280</gadget>
<output>308/5 = around 61.6</output>
<gadget id="calculator">(308/5) * 100</gadget>
<output>6_160</output>
<gadget id="calculator">6_160 / 280</gadget>
<output>22</output>
<result>A</result> | A | 22 | A shopkeeper has 280 kg of apples. He sells 40% of these at 10% profit and remaining 60% at 30% profit. Find his % profit on total. | {
"A": "22 %",
"B": "25 %",
"C": "26 %",
"D": "28 %",
"E": "35 %"
} | divide(multiply(subtract(add(multiply(divide(multiply(280, 40), const_100), divide(add(const_100, 10), const_100)), multiply(divide(multiply(280, 60), const_100), divide(add(const_100, 30), const_100))), 280), const_100), 280) | add(n2,const_100)|add(n4,const_100)|multiply(n0,n1)|multiply(n0,n3)|divide(#2,const_100)|divide(#0,const_100)|divide(#3,const_100)|divide(#1,const_100)|multiply(#4,#5)|multiply(#6,#7)|add(#8,#9)|subtract(#10,n0)|multiply(#11,const_100)|divide(#12,n0) | if the total quantity was 100 then 40 x 10 % + 60 x 30 % = 22 this profit will remain same for any total quantity unless the % of products remains the same . hence ' a ' is the answer | gain |
math_qa__sneskgj45GzdYDnb | The simple interest on a sum of money will be Rs. 600 after 10 years.If the principal is trebled after 5 years,what will be the total interest at the end of the tenth year ? Select the correct option.
A) rs . 600 B) rs . 900 C) 1200 rupees D) rs . 1500 E) none | <gadget id="calculator">600 / 10</gadget>
<output>60</output>
<gadget id="calculator">60 * 5</gadget>
<output>300</output>
<gadget id="calculator">300 * 3</gadget>
<output>900</output>
<gadget id="calculator">900 + 300</gadget>
<output>1_200</output>
<result>C</result> | C | 1,200 | The simple interest on a sum of money will be Rs. 600 after 10 years.If the principal is trebled after 5 years,what will be the total interest at the end of the tenth year ? | {
"A": "rs . 600",
"B": "rs . 900",
"C": "1200 rupees",
"D": "rs . 1500",
"E": "none"
} | add(multiply(multiply(divide(600, 10), 5), const_3), multiply(divide(600, 10), 5)) | divide(n0,n1)|multiply(n2,#0)|multiply(#1,const_3)|add(#2,#1) | solution 22.22 let the sum be rs . x . now , s . i . = rs . 600 , t = 10 years . rate = % = ( 100 x 600 / x x 10 ) % = ( 6000 / x ) % s . i . for first 5 years = rs . ( x x 5 x 6000 / x x 100 ) = rs . 300 . s . i . for first 5 years = rs . ( 3 x x 5 x 6000 / x x 100 ) = rs . 900 . ∴ total interest = rs . 1200 . answer c | general |
math_qa__kOZC4gmlqxjYJ3ic | We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value W of the ratio A/B?
Choose the correct choice from the following answers:
A) 1 / 2 B) 1 / 3 C) 2 / 3 D) 1 / 4 E) 1 / 5 | <gadget id="calculator">2_020 / 2_020</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<result>A</result> | A | 0.5 | We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value W of the ratio A/B? | {
"A": "1 / 2",
"B": "1 / 3",
"C": "2 / 3",
"D": "1 / 4",
"E": "1 / 5"
} | divide(divide(2020, 2020), add(divide(2020, 2020), divide(2020, 2020))) | divide(n6,n6)|add(#0,#0)|divide(#0,#1)| | "w - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ." | general |
math_qa__MklD7HgymYHpUocr | out of 3 consecutive odd numbers 8 times the first number is equal to addition of thrice the third number and adding 5 to twice the second . what is the first number ? Choose the correct choice from the following: A) 5 B) 6 C) 7 D) 8 E) 9 | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">4 + 12</gadget>
<output>16</output>
<gadget id="calculator">16 + 5</gadget>
<output>21</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">8 - 5</gadget>
<output>3</output>
<gadget id="calculator">21 / 3</gadget>
<output>7</output>
<result>C</result> | C | 7 | out of 3 consecutive odd numbers 8 times the first number is equal to addition of thrice the third number and adding 5 to twice the second . what is the first number ? | {
"A": "5",
"B": "6",
"C": "7",
"D": "8",
"E": "9"
} | divide(add(add(multiply(const_2, const_2), multiply(3, const_4)), 5), subtract(8, add(3, const_2))) | add(n0,const_2)|multiply(const_2,const_2)|multiply(n0,const_4)|add(#1,#2)|subtract(n1,#0)|add(n2,#3)|divide(#5,#4) | description : = > 8 x = 2 ( x + 2 ) + 5 + 3 ( x + 4 ) = > 3 x = 21 , x = 7 = > x + 4 = 11 x = 11 - 4 = 7 answer c | general |
math_qa__Yk25MrWZSpfPTNjy | A train running at the speed of 60 km/hr crosses a pole in 30 sec. What is the length of the train? Choose one:
A) 535 m B) 178 m C) 186 m D) 168 m E) 500 m | <gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 30</gadget>
<output>500</output>
<result>E</result> | E | 500 | A train running at the speed of 60 km/hr crosses a pole in 30 sec. What is the length of the train? | {
"A": "535 m",
"B": "178 m",
"C": "186 m",
"D": "168 m",
"E": "500 m"
} | multiply(divide(multiply(60, const_1000), const_3600), 30) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 30 = 500 m answer : e" | physics |
math_qa__d8uWZthbTO0rkbys | A, B, C, D and E are 5 consecutive points on a straight line. If BC = 3CD, DE = 8, AB = 5 and AC = 11, what is the length of AE?
Pick: A) 15 B) 17 C) 19 D) 21 E) 23 | <gadget id="calculator">11 - 5</gadget>
<output>6</output>
<gadget id="calculator">6 / 3</gadget>
<output>2</output>
<gadget id="calculator">11 + 2</gadget>
<output>13</output>
<gadget id="calculator">13 + 8</gadget>
<output>21</output>
<result>D</result> | D | 21 | A, B, C, D and E are 5 consecutive points on a straight line. If BC = 3CD, DE = 8, AB = 5 and AC = 11, what is the length of AE? | {
"A": "15",
"B": "17",
"C": "19",
"D": "21",
"E": "23"
} | add(add(11, divide(subtract(11, 5), 3)), 8) | subtract(n4,n0)|divide(#0,n1)|add(n4,#1)|add(n2,#2)| | "ac = 11 and ab = 5 , so bc = 6 . bc = 3 cd so cd = 2 . the length of ae is ab + bc + cd + de = 5 + 6 + 2 + 8 = 21 the answer is d ." | physics |
math_qa__qh5KL1xy2SzA24jf | What is the smallest number which when increased by 3 is divisible by 9, 35, 25 and 21? Choose the correct choice from the following options:
A) 1572
B) 1782
C) 1992
D) 2122
E) 2342 | <gadget id="calculator">lcm(9, 35)</gadget>
<output>315</output>
<gadget id="calculator">lcm(25, 21)</gadget>
<output>525</output>
<gadget id="calculator">lcm(315, 525)</gadget>
<output>1_575</output>
<gadget id="calculator">1_575 + 3</gadget>
<output>1_578</output>
<result>A</result> | A | 1,572 | What is the smallest number which when increased by 3 is divisible by 9, 35, 25 and 21? | {
"A": "1572",
"B": "1782",
"C": "1992",
"D": "2122",
"E": "2342"
} | add(lcm(lcm(9, 35), lcm(25, 21)), 3) | lcm(n1,n2)|lcm(n3,n4)|lcm(#0,#1)|add(n0,#2)| | "when increased by 3 , the number must include at least 3 ^ 2 * 5 ^ 2 * 7 = 1575 the answer is a ." | general |
math_qa__YnOj2D5ncdZmNXSB | If |r+s|=|r-s|, then r*s must be equal to: Choose the correct choice from the following: A) - 2 B) 2 C) 0 D) - 3 E) 3 | <gadget id="calculator">10 - 10</gadget>
<output>0</output>
<result>C</result> | C | 0 | If |r+s|=|r-s|, then r*s must be equal to: | {
"A": "- 2",
"B": "2",
"C": "0",
"D": "- 3",
"E": "3"
} | subtract(const_10, const_10) | subtract(const_10,const_10) | solution 1 : distance perspective | r - s | = | r + s | = = > the distance of r and s is equal to the distance of r and - s . < = = = = = = = ( - s ) = = = = = = = 0 = = = = = = = ( s ) = = = = = = > only 0 is the value that has a distance equal to s and - s . solution 2 : | r - s | = | r + s | ( square both ) r ^ 2 - 2 rs + s ^ 2 = r ^ 2 + 2 rs + s ^ 2 4 rs = 0 rs = 0 answer : c | general |
math_qa__cujR5eXMnRAS7m5v | 8 cups of milk are to be poured into a 4-cup bottle and a 8-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 8-cup bottle?
Choose the correct choice from the following choices
A) 16 / 3 B) 7 / 3 C) 5 / 2 D) 4 / 3 E) 3 | <gadget id="calculator">4 + 8</gadget>
<output>12</output>
<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 8</gadget>
<output>16/3 = around 5.333333</output>
<result>A</result> | A | 5.333333 | 8 cups of milk are to be poured into a 4-cup bottle and a 8-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 8-cup bottle? | {
"A": "16 / 3",
"B": "7 / 3",
"C": "5 / 2",
"D": "4 / 3",
"E": "3"
} | multiply(divide(8, add(4, 8)), 8) | add(n0,n1)|divide(n0,#0)|multiply(n0,#1) | let x be the # of cups going into the 8 cup bottle . so . . . . x / 8 = ( ( 8 - x ) / 4 ) 64 - 8 x = 4 x 64 = 12 x x = 16 / 3 . answer : a | general |
math_qa__M6bZiRkSEPOdUwfW | There are some people in party, 1/3rd left the party . Then 2/5th of the remaining left the party , then 2/3rd of the remaining left the party . At last 6 were remaining . How many people were in total ? Options:
A) 45
B) 27
C) 28
D) 26
E) 91 | <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">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(2/3) * (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(2/5) * (1/3)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">6 / (2/15)</gadget>
<output>45</output>
<result>A</result> | A | 45 | There are some people in party, 1/3rd left the party . Then 2/5th of the remaining left the party , then 2/3rd of the remaining left the party . At last 6 were remaining . How many people were in total ? | {
"A": "45",
"B": "27",
"C": "28",
"D": "26",
"E": "91"
} | divide(6, multiply(multiply(subtract(const_1, divide(1, 3)), subtract(const_1, divide(2, 5))), subtract(const_1, divide(2, 3)))) | divide(n0,n1)|divide(n2,n3)|divide(n2,n1)|subtract(const_1,#0)|subtract(const_1,#1)|subtract(const_1,#2)|multiply(#3,#4)|multiply(#6,#5)|divide(n6,#7) | sol : 45 if x persons were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 6 x × 2 / 3 × 3 / 5 × 1 / 3 = 6 x = 6 × 5 × 3 / 2 = 45 answer : a | general |
math_qa__XssZocKh6BsY2Cgm | In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.67 per Kg? Choose the correct option
A) 3 : 1 B) 3 : 2 C) 4 : 3 D) 5 : 3 E) 1 : 1 | <gadget id="calculator">72 - 67</gadget>
<output>5</output>
<gadget id="calculator">67 - 62</gadget>
<output>5</output>
<gadget id="calculator">5 / 5</gadget>
<output>1</output>
<result>E</result> | E | 1 | In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.67 per Kg? | {
"A": "3 : 1",
"B": "3 : 2",
"C": "4 : 3",
"D": "5 : 3",
"E": "1 : 1"
} | divide(subtract(72, 67), subtract(67, 62)) | subtract(n1,n2)|subtract(n2,n0)|divide(#0,#1)| | "required ratio = 500 : 500 = 3 : 1 answer e" | other |
math_qa__fCDRuJCHICIFCSTZ | A 8% stock yielding 10% is quoted at : Choose the most appropriate option
A) 80 B) 110 C) 112 D) 120 E) 160 | <gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">10 * 8</gadget>
<output>80</output>
<result>A</result> | A | 80 | A 8% stock yielding 10% is quoted at : | {
"A": "80",
"B": "110",
"C": "112",
"D": "120",
"E": "160"
} | multiply(divide(const_100, 10), 8) | divide(const_100,n1)|multiply(n0,#0)| | "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 8 , money invested = rs . ( 100 / 10 x 8 ) = rs . 80 . â ˆ ´ market value of rs . 100 stock = rs . 80 answer a" | gain |
math_qa__oB1a2TcacAGt1J4d | If it is assumed that 50 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed? Pick: A) 400 B) 420 C) 480 D) 500 E) 600 | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">300 / (1/2)</gadget>
<output>600</output>
<result>E</result> | E | 600 | If it is assumed that 50 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed? | {
"A": "400",
"B": "420",
"C": "480",
"D": "500",
"E": "600"
} | divide(300, divide(50, const_100)) | divide(n0,const_100)|divide(n1,#0)| | "minimum no of mail to be sent for getting 300 responses at 50 % = 300 / 0.5 = 600 option e" | gain |
math_qa__WtosxhmBUYhYHu1b | An error 8% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square? Answers.
A) 6.64 % B) 16.64 % C) 15.64 % D) 26.64 % E) 10.64 % | <gadget id="calculator">100 + 8</gadget>
<output>108</output>
<gadget id="calculator">108 ** 2</gadget>
<output>11_664</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">11_664 - 10_000</gadget>
<output>1_664</output>
<gadget id="calculator">1_664 * 100</gadget>
<output>166_400</output>
<gadget id="calculator">166_400 / 10_000</gadget>
<output>416/25 = around 16.64</output>
<result>B</result> | B | 16.64 | An error 8% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square? | {
"A": "6.64 %",
"B": "16.64 %",
"C": "15.64 %",
"D": "26.64 %",
"E": "10.64 %"
} | divide(multiply(subtract(square_area(add(const_100, 8)), square_area(const_100)), const_100), square_area(const_100)) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)| | "percentage error in calculated area = ( 8 + 8 + ( 8 × 8 ) / 100 ) % = 16.64 % answer : b" | gain |
math_qa__D5W7aWY7bopgLIUJ | The average age of 15 students of a class is 15 years. Out of these, the average age of 7 students is 14 years and that of the other 7 students is 16 years. The age of the 15th student is Choose the correct choice from the following choices: A) 9 years B) 11 years C) 15 years D) 21 years E) 25 years | <gadget id="calculator">15 * 15</gadget>
<output>225</output>
<gadget id="calculator">7 * 14</gadget>
<output>98</output>
<gadget id="calculator">7 * 16</gadget>
<output>112</output>
<gadget id="calculator">98 + 112</gadget>
<output>210</output>
<gadget id="calculator">225 - 210</gadget>
<output>15</output>
<result>C</result> | C | 15 | The average age of 15 students of a class is 15 years. Out of these, the average age of 7 students is 14 years and that of the other 7 students is 16 years. The age of the 15th student is | {
"A": "9 years",
"B": "11 years",
"C": "15 years",
"D": "21 years",
"E": "25 years"
} | subtract(multiply(15, 15), add(multiply(7, 14), multiply(7, 16))) | multiply(n0,n0)|multiply(n2,n3)|multiply(n4,n5)|add(#1,#2)|subtract(#0,#3)| | "solution age of the 15 th student = [ 15 x 15 - ( 14 x 7 + 16 x 7 ) ] = ( 225 - 210 ) = 15 years . answer c" | general |
math_qa__LsjvnaMUt6yR88oX | car a travels at 3 times the average speed of car b . car a started to travel at 12 : 00 o ' clock , car b started to travel at 16 : 00 o ' clock . what is the speed of car b ( in km / h ) if the total distance that both cars traveled until 18 : 00 was 1000 km ? Choose the most appropriate option: A) 10 . B) 25 . C) 30 . D) 38 E) 50 . | <gadget id="calculator">18 - 12</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 - 16</gadget>
<output>2</output>
<gadget id="calculator">18 + 2</gadget>
<output>20</output>
<gadget id="calculator">1_000 / 20</gadget>
<output>50</output>
<result>E</result> | E | 50 | car a travels at 3 times the average speed of car b . car a started to travel at 12 : 00 o ' clock , car b started to travel at 16 : 00 o ' clock . what is the speed of car b ( in km / h ) if the total distance that both cars traveled until 18 : 00 was 1000 km ? | {
"A": "10 .",
"B": "25 .",
"C": "30 .",
"D": "38",
"E": "50 ."
} | divide(1000, add(multiply(subtract(18, 12), 3), subtract(18, 16))) | subtract(n5,n1)|subtract(n5,n3)|multiply(n0,#0)|add(#2,#1)|divide(n7,#3) | total distance - 1000 km time ratio a : b - 3 : 1 speed ratio a : b - 3 : 1 so distance ( speed * time ) ratio will be - 3 * 3 : 1 * 1 - 9 : 1 so total distance traveled by b - 100 km time taken by b ( 18 : 00 - 16 : 00 = 2 ) - 2 hours speed of b - 50 kmph answer : e | general |
math_qa__MrzUUWymoJKksmvI | There are 6 books on a shelf, of which 2 are paperbacks and 4 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback?
Choose the correct choice from the following options
A) 40
B) 14
C) 50
D) 55
E) 60 | <gadget id="calculator">binomial(6, 4)</gadget>
<output>15</output>
<gadget id="calculator">binomial(4, 4)</gadget>
<output>1</output>
<gadget id="calculator">15 - 1</gadget>
<output>14</output>
<result>B</result> | B | 14 | There are 6 books on a shelf, of which 2 are paperbacks and 4 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback? | {
"A": "40",
"B": "14",
"C": "50",
"D": "55",
"E": "60"
} | subtract(choose(6, 4), choose(4, 4)) | choose(n0,n3)|choose(n2,n3)|subtract(#0,#1)| | "approach 1 at - least 1 paper back = total - no paper back 6 c 4 - 4 c 4 = 14 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 2 c 1 * 4 c 3 + 2 c 2 * 4 c 2 = 14 answer is b" | probability |
math_qa__RFseJxJd1My0LZ3T | Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.931. Find the cost of each ice-cream cup?
Answers.
A) 25 B) 76 C) 29 D) 12 E) 20 | <gadget id="calculator">16 * 6</gadget>
<output>96</output>
<gadget id="calculator">931 - 96</gadget>
<output>835</output>
<gadget id="calculator">5 * 45</gadget>
<output>225</output>
<gadget id="calculator">835 - 225</gadget>
<output>610</output>
<gadget id="calculator">7 * 70</gadget>
<output>490</output>
<gadget id="calculator">610 - 490</gadget>
<output>120</output>
<gadget id="calculator">120 / 6</gadget>
<output>20</output>
<result>E</result> | E | 20 | Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.931. Find the cost of each ice-cream cup? | {
"A": "25",
"B": "76",
"C": "29",
"D": "12",
"E": "20"
} | divide(subtract(subtract(subtract(931, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6) | multiply(n0,n3)|multiply(n1,n5)|multiply(n2,n6)|subtract(n7,#0)|subtract(#3,#1)|subtract(#4,#2)|divide(#5,n3)| | "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 931 96 + 225 + 490 + 6 x = 931 6 x = 120 = > x = 20 . answer : e" | general |
math_qa__jFRAY3vkuWjziazu | The average weight of 10 men is increased by 2 ½ kg when one of the men who weighs 68 kg is replaced by a new man. What is the weight of the new man? Choose the correct choice
A) 80 kg
B) 93 kg
C) 70 kg
D) 75 kg
E) 85 kg | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">10 * (5/2)</gadget>
<output>25</output>
<gadget id="calculator">68 + 25</gadget>
<output>93</output>
<result>B</result> | B | 93 | The average weight of 10 men is increased by 2 ½ kg when one of the men who weighs 68 kg is replaced by a new man. What is the weight of the new man? | {
"A": "80 kg",
"B": "93 kg",
"C": "70 kg",
"D": "75 kg",
"E": "85 kg"
} | add(68, multiply(10, add(2, divide(const_1, 2)))) | divide(const_1,n1)|add(n1,#0)|multiply(n0,#1)|add(n2,#2)| | "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 68 + 10 x 2.5 68 + 25 = 93 kg ans : ' b '" | general |
math_qa__mnMRuY4GM3lgr2oJ | In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 176 of the workers of that company are men, how many of the workers are women?
Choose one.
A) 80 B) 95 C) 105 D) 120 E) 154 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/3) * (1/5)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/3) - (1/15)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/3) * (2/5)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">(4/15) + (4/15)</gadget>
<output>8/15 = around 0.533333</output>
<gadget id="calculator">176 / (8/15)</gadget>
<output>330</output>
<gadget id="calculator">(2/3) - (4/15)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(1/15) + (2/5)</gadget>
<output>7/15 = around 0.466667</output>
<gadget id="calculator">330 * (7/15)</gadget>
<output>154</output>
<result>E</result> | E | 154 | In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 176 of the workers of that company are men, how many of the workers are women? | {
"A": "80",
"B": "95",
"C": "105",
"D": "120",
"E": "154"
} | multiply(divide(176, add(subtract(divide(const_1, const_3), multiply(divide(const_1, const_3), divide(20, const_100))), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))), add(multiply(divide(const_1, const_3), divide(20, const_100)), subtract(subtract(const_1, divide(const_1, const_3)), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100))))) | divide(const_1,const_3)|divide(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)|subtract(const_1,#0)|multiply(#2,#4)|subtract(#0,#3)|add(#5,#6)|subtract(#4,#5)|add(#3,#8)|divide(n2,#7)|multiply(#9,#10)| | "set up equation : x = total number of workers 176 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 176 = 16 / 30 x x = 330 330 - 176 = 154 answer e" | gain |
math_qa__pCn1Omkvbepss3xx | Elena’s bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 6 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed? Pick one:
A) 1
B) 4
C) 9
D) 13
E) 24 | <gadget id="calculator">4 * 6</gadget>
<output>24</output>
<result>E</result> | E | 24 | Elena’s bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 6 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed? | {
"A": "1",
"B": "4",
"C": "9",
"D": "13",
"E": "24"
} | multiply(4, 6) | multiply(n1,n2)| | "solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 6 we get : 18 b + 24 f = 6 x therefore , we got 18 ounces of butter and 6 x amount of quantity when we use 24 ounces of floor . ans : e" | general |
math_qa__uYjibxV81XcsX5ZB | In how many W ways can 5 people from a group of 6 people be seated around a circular table Select the correct option:
A) 56 B) 80 C) 100 D) 120 E) 144 | <gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">720 / 5</gadget>
<output>144</output>
<result>E</result> | E | 144 | In how many W ways can 5 people from a group of 6 people be seated around a circular table | {
"A": "56",
"B": "80",
"C": "100",
"D": "120",
"E": "144"
} | divide(factorial(6), 5) | factorial(n1)|divide(#0,n0) | w = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e | geometry |
math_qa__caq6PCRoDN7zKxvU | Suganya and Suriya are partners in a business. Suganya invests Rs. 35,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.30,570. Suganya's share is Choose the correct choice
A) rs . 9471 B) rs . 12,628 C) rs . 262.8 D) rs . 241.7 E) none | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<gadget id="calculator">25 * 10</gadget>
<output>250</output>
<result>D</result> | D | 241.7 | Suganya and Suriya are partners in a business. Suganya invests Rs. 35,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.30,570. Suganya's share is | {
"A": "rs . 9471",
"B": "rs . 12,628",
"C": "rs . 262.8",
"D": "rs . 241.7",
"E": "none"
} | multiply(multiply(const_0_25, const_100), 10) | multiply(const_0_25,const_100)|multiply(n3,#0) | solution ratio of their shares = ( 35000 ã — 8 ) : ( 42000 ã — 10 ) = 128 : 125 suganya ' s share = rs . ( 30570 ã — 2 / 253 ) = rs . 241.7 . answer d | gain |
math_qa__B2KcwHAiDuihzIhi | A space shuttle orbits the earth at about 9 kilometers per second. This speed is equal to how many kilometers per hour? Answers.
A) 480 B) 2,880 C) 4,800 D) 28,800 E) 32,400 | <gadget id="calculator">9 * 3_600</gadget>
<output>32_400</output>
<result>E</result> | E | 32,400 | A space shuttle orbits the earth at about 9 kilometers per second. This speed is equal to how many kilometers per hour? | {
"A": "480",
"B": "2,880",
"C": "4,800",
"D": "28,800",
"E": "32,400"
} | multiply(9, const_3600) | multiply(n0,const_3600)| | "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 9 * 3600 = 32,400 answer : e" | physics |
math_qa__D4dkY2nl4aNu8sMx | 7 liters of a 22 percent solution of alcohol in water are mixed with 3 liters of an 11 percent alcohol in water solution. What is the percentage of alcohol in the new solution?
Choose the correct choice.
A) 17.5 % B) 17.8 % C) 18.1 % D) 18.4 % E) 18.7 % | <gadget id="calculator">22 / 100</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">7 * (11/50)</gadget>
<output>77/50 = around 1.54</output>
<gadget id="calculator">11 / 100</gadget>
<output>11/100 = around 0.11</output>
<gadget id="calculator">(11/100) * (77/50)</gadget>
<output>847/5_000 = around 0.1694</output>
<gadget id="calculator">(77/50) + (847/5_000)</gadget>
<output>8_547/5_000 = around 1.7094</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">(8_547/5_000) / 9</gadget>
<output>2_849/15_000 = around 0.189933</output>
<gadget id="calculator">(2_849/15_000) * 100</gadget>
<output>2_849/150 = around 18.993333</output>
<result>E</result> | E | 18.7 | 7 liters of a 22 percent solution of alcohol in water are mixed with 3 liters of an 11 percent alcohol in water solution. What is the percentage of alcohol in the new solution? | {
"A": "17.5 %",
"B": "17.8 %",
"C": "18.1 %",
"D": "18.4 %",
"E": "18.7 %"
} | multiply(divide(add(multiply(7, divide(22, const_100)), multiply(divide(11, const_100), multiply(7, divide(22, const_100)))), add(7, const_2.0)), const_100) | add(n0,const_2.0)|divide(n1,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(#2,#3)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)| | "the total amount of alcohol is 0.22 ( 7 ) + 0.11 ( 3 ) = 1.87 liters . the percentage is 1.87 / 10 = 18.7 / 100 which is 18.7 % the answer is e ." | general |
math_qa__nQ7udcSaK0XCogUy | A cricketer scored 136 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets. Choices:
A) 46.2 %
B) 54.54 %
C) 55.88 %
D) 70 %
E) none of these | <gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">48 + 12</gadget>
<output>60</output>
<gadget id="calculator">136 - 60</gadget>
<output>76</output>
<gadget id="calculator">76 / 136</gadget>
<output>19/34 = around 0.558824</output>
<gadget id="calculator">(19/34) * 100</gadget>
<output>950/17 = around 55.882353</output>
<result>C</result> | C | 55.88 | A cricketer scored 136 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets. | {
"A": "46.2 %",
"B": "54.54 %",
"C": "55.88 %",
"D": "70 %",
"E": "none of these"
} | multiply(divide(subtract(136, add(multiply(12, const_4), multiply(2, multiply(2, const_3)))), 136), const_100) | multiply(n1,const_4)|multiply(n2,const_3)|multiply(n2,#1)|add(#0,#2)|subtract(n0,#3)|divide(#4,n0)|multiply(#5,const_100)| | "explanation : number of runs made by running = 136 - ( 12 x 4 + 2 x 6 ) = 136 - ( 60 ) = 76 now , we need to calculate 72 is what percent of 136 . = > 76 / 136 * 100 = 55.88 % answer : c" | general |
math_qa__pi1mJC99FiHiBB8l | There are 6 people in the elevator. Their average weight is 160 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person.
Answers:
A) 97
B) 168
C) 189
D) 190
E) 200 | <gadget id="calculator">151 * 7</gadget>
<output>1_057</output>
<gadget id="calculator">6 * 160</gadget>
<output>960</output>
<gadget id="calculator">1_057 - 960</gadget>
<output>97</output>
<result>A</result> | A | 97 | There are 6 people in the elevator. Their average weight is 160 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person. | {
"A": "97",
"B": "168",
"C": "189",
"D": "190",
"E": "200"
} | subtract(multiply(151, 7), multiply(6, 160)) | multiply(n2,n3)|multiply(n0,n1)|subtract(#0,#1)| | "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 160 ) = 1057 - 960 = 97 . answer a" | general |
math_qa__OLvmWcAWui75lh4F | What least fraction should be added to
1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ....... + 1/(21 × 22)
so that the result is unity? Choose the correct choice
A) 5 / 11 B) 6 / 11 C) 4 / 11 D) 7 / 11 E) 8 / 11 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">6 + 5</gadget>
<output>11</output>
<gadget id="calculator">6 / 11</gadget>
<output>6/11 = around 0.545455</output>
<result>B</result> | B | 0.545455 | What least fraction should be added to
1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ....... + 1/(21 × 22)
so that the result is unity? | {
"A": "5 / 11",
"B": "6 / 11",
"C": "4 / 11",
"D": "7 / 11",
"E": "8 / 11"
} | divide(multiply(3, 2), add(multiply(3, 2), add(2, 3))) | add(n1,n2)|multiply(n1,n2)|add(#0,#1)|divide(#1,#2) | explanation : given expression = 1 / ( 2 × 3 ) + 1 / ( 3 × 4 ) + 1 / ( 4 × 5 ) + . . . . . . + 1 / ( 21 × 22 ) = ( 1 / 2 - 1 / 3 ) + ( 1 / 3 - 1 / 4 ) + ( 1 / 4 - 1 / 5 ) + . . . . . . . . . . = ( 1 / 21 - 1 / 22 ) = 1 / 2 - 1 / 22 = 10 / 22 = 5 / 11 thus , least fraction to be added = 1 - 5 / 11 = 6 / 11 answer : option b | general |
math_qa__ze7mffa3Ryi6ZkcY | how many 5 - digit numbers that do not contain the digits 4 or 7 are there ?
Options
A) 44648 B) 27844 C) 28642 D) 16864 E) 32458 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">8 ** 4</gadget>
<output>4_096</output>
<gadget id="calculator">4_096 * 7</gadget>
<output>28_672</output>
<result>C</result> | C | 28,642 | how many 5 - digit numbers that do not contain the digits 4 or 7 are there ? | {
"A": "44648",
"B": "27844",
"C": "28642",
"D": "16864",
"E": "32458"
} | multiply(power(multiply(const_4, const_2), subtract(5, const_1)), 7) | multiply(const_2,const_4)|subtract(n0,const_1)|power(#0,#1)|multiply(n2,#2) | we can have 7 digits ( 1 , 2,3 , 5,6 , 8,9 ) for the first place ( ten thousand ' s place ) . and similarly 8 digits for thousand ' s , hundred ' s , tenth ' s and unit digit . ( 0,1 , 2,3 , 5,6 , 8,9 ) so in total 7 * 8 * 8 * 8 * 8 = 28672 hence c | general |
math_qa__BqKRg76RvI9KuDyM | How many positive integers I less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ? Options:
A) 19 B) 18 C) 17 D) 16 E) 15 | <gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<result>E</result> | E | 15 | How many positive integers I less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ? | {
"A": "19",
"B": "18",
"C": "17",
"D": "16",
"E": "15"
} | add(add(9, const_1), add(2, const_3)) | add(n2,const_1)|add(n1,const_3)|add(#0,#1) | we ' re asked to deal with the positive integers less than 20 . there are only 19 numbers in that group ( 1 to 19 , inclusive ) . we ' re asked to find all of the numbers that fit one ( or more ) of the given descriptions . looking at the answer choices , we have every value form 15 to 19 , inclusive , so most ( if not all ) of the numbers from 1 to 19 fit one ( or more ) of the descriptions . how long would it take you to find the ones that do n ' t fit . . . . . ? the first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 ( and sums of those multiples ) . so what odd numbers are less than 9 ? 1 , 3 , 5 , 7 none of these values fit the given descriptions . that ' s 4 out of 19 that we know for sure do not fit . 19 - 4 = 15 = e | general |
math_qa__9TUHx7GYSFJThOes | the weights of 3 bags are in the ratio 4 : 5 : 6 . if the sum of the weights of the heaviest and the lightest bag is 45 kg more than the weight of the third bag , what is the weight of the lightest bag ? Options:
A) 45 kg
B) 38 kg
C) 66 kg
D) 36 kg
E) of these | <gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">10 - 5</gadget>
<output>5</output>
<gadget id="calculator">45 / 5</gadget>
<output>9</output>
<gadget id="calculator">9 * 4</gadget>
<output>36</output>
<result>D</result> | D | 36 | the weights of 3 bags are in the ratio 4 : 5 : 6 . if the sum of the weights of the heaviest and the lightest bag is 45 kg more than the weight of the third bag , what is the weight of the lightest bag ? | {
"A": "45 kg",
"B": "38 kg",
"C": "66 kg",
"D": "36 kg",
"E": "of these"
} | multiply(divide(45, subtract(add(4, 6), 5)), 4) | add(n1,n3)|subtract(#0,n2)|divide(n4,#1)|multiply(n1,#2) | let the weights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 45 = > 5 k = 45 = > k = 9 therefore the weight of the lightest boy = 4 k = 4 ( 9 ) = 36 kg . answer : d | general |
math_qa__keW5IlC2dDy6eF8a | The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.70 per metre. Choose the correct choice from the following answers
A) 2399 B) 6204 C) 2999 D) 5808 E) 2888 | <gadget id="calculator">13.86 / pi</gadget>
<output>13.86/pi = around 4.411775</output>
<gadget id="calculator">(13.86/pi) ** (1/2)</gadget>
<output>3.72290209379726/sqrt(pi) = around 2.100423</output>
<gadget id="calculator">(3.72290209379726/sqrt(pi)) * 100</gadget>
<output>372.290209379726/sqrt(pi) = around 210.042258</output>
<gadget id="calculator">2 * pi * (372.290209379726/sqrt(pi))</gadget>
<output>744.580418759452*sqrt(pi) = around 1_319.734431</output>
<gadget id="calculator">(744.580418759452*sqrt(pi)) * 4.7</gadget>
<output>3499.52796816942*sqrt(pi) = around 6_202.751824</output>
<result>B</result> | B | 6,204 | The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.70 per metre. | {
"A": "2399",
"B": "6204",
"C": "2999",
"D": "5808",
"E": "2888"
} | multiply(circumface(multiply(sqrt(divide(13.86, const_pi)), const_100)), 4.70) | divide(n0,const_pi)|sqrt(#0)|multiply(#1,const_100)|circumface(#2)|multiply(#3,n1)| | "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.70 ) = rs . 6204 . answer : b ) 6204" | geometry |
math_qa__N8K976VxcuCat3gD | A room is 6 meters 72 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room. Choices.
A) 107 B) 126 C) 117 D) 136 E) 147 | <gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">600 + 72</gadget>
<output>672</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">400 + 32</gadget>
<output>432</output>
<gadget id="calculator">672 * 432</gadget>
<output>290_304</output>
<gadget id="calculator">gcd(672, 432)</gadget>
<output>48</output>
<gadget id="calculator">48 * 48</gadget>
<output>2_304</output>
<gadget id="calculator">290_304 / 2_304</gadget>
<output>126</output>
<result>B</result> | B | 126 | A room is 6 meters 72 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room. | {
"A": "107",
"B": "126",
"C": "117",
"D": "136",
"E": "147"
} | divide(multiply(add(multiply(6, const_100), 72), add(multiply(4, const_100), 32)), multiply(gcd(add(multiply(6, const_100), 72), add(multiply(4, const_100), 32)), gcd(add(multiply(6, const_100), 72), add(multiply(4, const_100), 32)))) | multiply(n0,const_100)|multiply(n2,const_100)|add(n1,#0)|add(n3,#1)|gcd(#2,#3)|multiply(#2,#3)|multiply(#4,#4)|divide(#5,#6) | let us calculate both the length and width of the room in centimeters . length = 6 meters and 72 centimeters = 672 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 672 and 432 = 48 thus , the number of square tiles required = ( 672 x 432 ) / ( 48 x 48 ) = 14 x 9 = 126 answer : b | general |
math_qa__BH04wZPbJ5jjriw7 | In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 12 people were made to stand in a column, how many columns could be formed? Choose the correct choice from the following.
A) 20 B) 30 C) 40 D) 50 E) 60 | <gadget id="calculator">12 / 16</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">30 / (3/4)</gadget>
<output>40</output>
<result>C</result> | C | 40 | In a group of people, if 30 people were made to stand in each column, 16 columns could be formed. If 12 people were made to stand in a column, how many columns could be formed? | {
"A": "20",
"B": "30",
"C": "40",
"D": "50",
"E": "60"
} | divide(30, divide(12, 16)) | divide(n2,n1)|divide(n0,#0)| | "16 * 30 = 12 * n n = 40 the answer is c ." | other |
math_qa__5JDRExwCWFmayiQK | If x is a positive integer with fewer than 3 digits, what is the probability Q that x*(x + 1) is a multiple of either 4 or 5? Answers: A) 4 / 99 B) 2 / 25 C) 8 / 99 D) 49 / 100 E) 86 / 99 | <gadget id="calculator">100 / 4</gadget>
<output>25</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">50 + 40</gadget>
<output>90</output>
<gadget id="calculator">90 - 4</gadget>
<output>86</output>
<gadget id="calculator">100 - 1</gadget>
<output>99</output>
<gadget id="calculator">86 / 99</gadget>
<output>86/99 = around 0.868687</output>
<result>E</result> | E | 0.868687 | If x is a positive integer with fewer than 3 digits, what is the probability Q that x*(x + 1) is a multiple of either 4 or 5? | {
"A": "4 / 99",
"B": "2 / 25",
"C": "8 / 99",
"D": "49 / 100",
"E": "86 / 99"
} | divide(subtract(add(multiply(divide(const_100, 4), const_2), multiply(divide(const_100, 5), const_2)), 4), subtract(const_100, const_1)) | divide(const_100,n2)|divide(const_100,n3)|subtract(const_100,const_1)|multiply(#0,const_2)|multiply(#1,const_2)|add(#3,#4)|subtract(#5,n2)|divide(#6,#2) | interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability q that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) . | general |
math_qa__AUSEthTcmlALsXwe | By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 200 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution? Select: A) 1.42 % B) 1.9 % C) 10 % D) 15 % E) 19 % | <gadget id="calculator">200 * 0.8</gadget>
<output>160</output>
<gadget id="calculator">700 * 1.8</gadget>
<output>1_260</output>
<gadget id="calculator">160 + 1_260</gadget>
<output>1_420</output>
<gadget id="calculator">1_420 / 1_000</gadget>
<output>71/50 = around 1.42</output>
<result>A</result> | A | 1.42 | By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 200 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution? | {
"A": "1.42 %",
"B": "1.9 %",
"C": "10 %",
"D": "15 %",
"E": "19 %"
} | divide(add(multiply(200, 0.8), multiply(700, 1.8)), const_1000) | multiply(n0,n2)|multiply(n1,n3)|add(#0,#1)|divide(#2,const_1000)| | "i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 200 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 200 ) / 100 + ( 1.8 * 700 ) / 100 = 14.2 gms % of liquid x in resultant mixture = ( 14.2 / 1000 ) * 100 = 1.42 % a" | gain |
math_qa__y6cWSIgk2XKIgmzr | The S.I. on a certain sum of money for 3 years at 5% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
Choose the correct choice: A) 2197 B) 2800 C) 1750 D) 2267 E) 1262 | <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">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">3 * (1/20)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">420 / (3/20)</gadget>
<output>2_800</output>
<result>B</result> | B | 2,800 | The S.I. on a certain sum of money for 3 years at 5% 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": "2197",
"B": "2800",
"C": "1750",
"D": "2267",
"E": "1262"
} | divide(divide(subtract(multiply(4000, power(add(const_1, divide(10, const_100)), 2)), 4000), 2), multiply(3, divide(5, 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)| | "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 5 ) = rs . 2800 answer : b" | gain |
math_qa__QBB3buoLjbw8lPH2 | Two train each 500 m long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is
Choose the correct choice from the following answers:
A) 50 sec B) 58 sec C) 24 sec D) 22 sec E) 21 sec | <gadget id="calculator">45 + 30</gadget>
<output>75</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">75 * (5/18)</gadget>
<output>125/6 = around 20.833333</output>
<gadget id="calculator">500 / (125/6)</gadget>
<output>24</output>
<result>C</result> | C | 24 | Two train each 500 m long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is | {
"A": "50 sec",
"B": "58 sec",
"C": "24 sec",
"D": "22 sec",
"E": "21 sec"
} | divide(500, multiply(add(45, 30), const_0_2778)) | add(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | "explanation : relative speed = 45 + 30 = 75 km / hr = 750 / 36 m / s = 125 / 6 m / s we are calculating the time taken by the slower train to pass the driver of the faster one . hence the distance = length of the smaller train = 500 m time = distance / speed = 500 / ( 125 / 6 ) = 24 sec answer : option c" | physics |
math_qa__T4KzgXlDXBMPkqcg | Two trains of length 100 meters and 200 meters are 630 meters apart. They are moving towards each other on parallel tracks, at speeds of 90 km/h and 72 km/h. After how many seconds will the trains meet?
Choose the correct choice from the following options
A) 12 B) 14 C) 16 D) 18 E) 20 | <gadget id="calculator">90 + 72</gadget>
<output>162</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">162 * (5/18)</gadget>
<output>45</output>
<gadget id="calculator">630 / 45</gadget>
<output>14</output>
<result>B</result> | B | 14 | Two trains of length 100 meters and 200 meters are 630 meters apart. They are moving towards each other on parallel tracks, at speeds of 90 km/h and 72 km/h. After how many seconds will the trains meet? | {
"A": "12",
"B": "14",
"C": "16",
"D": "18",
"E": "20"
} | divide(630, multiply(add(90, 72), const_0_2778)) | add(n3,n4)|multiply(#0,const_0_2778)|divide(n2,#1) | the speeds are 90000 / 3600 = 25 m / s and 72000 / 3600 = 20 m / s the relative speed is 45 m / s . time = 630 / 45 = 14 seconds the answer is b . | physics |
math_qa__CutA4ODmzvwfeiFi | Find the value of y from (12)^3 x 6^4 ÷ 432 = y? Select the correct option
A) 2450
B) 2560
C) 2650
D) 3500
E) 5184 | <gadget id="calculator">12 ** 3</gadget>
<output>1_728</output>
<gadget id="calculator">6 ** 4</gadget>
<output>1_296</output>
<gadget id="calculator">1_728 * 1_296</gadget>
<output>2_239_488</output>
<gadget id="calculator">2_239_488 / 432</gadget>
<output>5_184</output>
<result>E</result> | E | 5,184 | Find the value of y from (12)^3 x 6^4 ÷ 432 = y? | {
"A": "2450",
"B": "2560",
"C": "2650",
"D": "3500",
"E": "5184"
} | divide(multiply(power(12, 3), power(6, 4)), 432) | power(n0,n1)|power(n2,n3)|multiply(#0,#1)|divide(#2,n4)| | "given exp . = ( 12 ) 3 x 64 = ( 12 ) 3 x 64 = ( 12 ) 2 x 62 = ( 72 ) 2 = 5184 432 12 x 62 e" | general |
math_qa__QW6hfeySII0SDCjN | In a graduating class, 40 percent of the students are male. In this class, 60 percent of the male students and 40 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old? Pick one.
A) 0.4 B) 0.44 C) 0.48 D) 0.52 E) 0.56 | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(2/5) * (3/5)</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(6/25) + (6/25)</gadget>
<output>12/25 = around 0.48</output>
<gadget id="calculator">1 - (12/25)</gadget>
<output>13/25 = around 0.52</output>
<result>D</result> | D | 0.52 | In a graduating class, 40 percent of the students are male. In this class, 60 percent of the male students and 40 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old? | {
"A": "0.4",
"B": "0.44",
"C": "0.48",
"D": "0.52",
"E": "0.56"
} | subtract(const_1, add(multiply(divide(40, const_100), divide(60, const_100)), multiply(divide(40, const_100), subtract(const_1, divide(40, const_100))))) | divide(n0,const_100)|divide(n1,const_100)|divide(n2,const_100)|multiply(#0,#1)|subtract(const_1,#0)|multiply(#2,#4)|add(#3,#5)|subtract(const_1,#6)| | "let x be the total number of students . the number students who are younger than 25 is 0.4 * 0.4 x + 0.6 * 0.6 x = 0.52 x the answer is d ." | general |
math_qa__ffSM9Y5qu6W6p7Zz | At a tanning salon, customers are charged $10 for their first visit in a calendar month and $8 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon? Answers:
A) $ 1220
B) $ 1240
C) $ 1300
D) $ 1340
E) $ 1880 | <gadget id="calculator">10 + 8</gadget>
<output>18</output>
<gadget id="calculator">18 * 30</gadget>
<output>540</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 * 10</gadget>
<output>700</output>
<gadget id="calculator">540 + 700</gadget>
<output>1_240</output>
<result>B</result> | B | 1,240 | At a tanning salon, customers are charged $10 for their first visit in a calendar month and $8 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those visits were the only source of revenue for the salon, what was the revenue for the last calendar month at the salon? | {
"A": "$ 1220",
"B": "$ 1240",
"C": "$ 1300",
"D": "$ 1340",
"E": "$ 1880"
} | add(multiply(add(10, 8), 30), multiply(subtract(100, 30), 10)) | add(n0,n1)|subtract(n2,n3)|multiply(n3,#0)|multiply(n0,#1)|add(#2,#3) | i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 8 ) = $ 320 total revenue : 1000 + 320 = $ 1320 the answer is b . | physics |
math_qa__jp2svHJgCPZeVivU | If n is a positive integer, what is the remainder when (7^(4n+2))(6^n) is divided by 10? Choose the correct choice from the following: A) 1 B) 2 C) 4 D) 6 E) 8 | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 6</gadget>
<output>54</output>
<gadget id="calculator">54 % 10</gadget>
<output>4</output>
<result>C</result> | C | 4 | If n is a positive integer, what is the remainder when (7^(4n+2))(6^n) is divided by 10? | {
"A": "1",
"B": "2",
"C": "4",
"D": "6",
"E": "8"
} | reminder(multiply(multiply(const_3, const_3), 6), 10) | multiply(const_3,const_3)|multiply(n3,#0)|reminder(#1,n4) | this one took me bout 3 1 / 2 min . just testin numbers and what not . first notice that n is positive . save time by noticing thati worked out one solution where n = 0 only to find that thats not an option : p . 1 - 7 stands for ^ 1 thru 7 1 : 7 * 1 = 7 2 : 7 * 7 = 9 3 : 7 * 9 = 3 4 : 7 * 3 = 1 5 : 7 * 1 = 7 6 : 7 * 7 = 9 7 : 7 * 9 = 3 pattern repeats every @ 5 . notice every ^ 4 or multiple of 4 is always going to be 1 . this is just for future notice for similar problems . so 7 ^ 4 n + 3 - - - > if n = 1 then its ( ( 7 ^ 7 ) * 6 ) ) / 10 which can say is going to be 3 * 8 - - > 18 / 10 - - > r = 8 now from here if id double check just to make sure . 7 ^ 4 ( 2 ) + 3 * 6 ^ 2 - - - > 7 ^ 11 * 36 or we can just say again 7 ^ 11 * 6 ( b / c we are only interested in the units digit ) . since ^ 12 is going to be 1 that means ^ 11 is going to be 3 ( as taken from our pattern ) so again 3 * 6 = 18 / 10 - - - > r = 4 . c or j in this problem . | general |
math_qa__A1TEAap5ABuqdAGI | Sahil purchased a machine at Rs 11000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it. Choose the correct choice from the following answers:
A) rs . 22500
B) rs . 25500
C) rs . 26000
D) rs . 28000
E) none of these | <gadget id="calculator">11_000 + 5_000</gadget>
<output>16_000</output>
<gadget id="calculator">16_000 + 1_000</gadget>
<output>17_000</output>
<gadget id="calculator">17_000 / 100</gadget>
<output>170</output>
<gadget id="calculator">170 * 50</gadget>
<output>8_500</output>
<gadget id="calculator">17_000 + 8_500</gadget>
<output>25_500</output>
<result>B</result> | B | 25,500 | Sahil purchased a machine at Rs 11000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it. | {
"A": "rs . 22500",
"B": "rs . 25500",
"C": "rs . 26000",
"D": "rs . 28000",
"E": "none of these"
} | add(add(add(11000, 5000), 1000), multiply(divide(add(add(11000, 5000), 1000), const_100), 50)) | add(n0,n1)|add(n2,#0)|divide(#1,const_100)|multiply(n3,#2)|add(#1,#3)| | "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 11000 + 5000 + 1000 = 17000 150 % of 17000 = 150 / 100 * 17000 = 25500 option b" | gain |
math_qa__MJCaAmlYOShkDDMJ | A boat can travel with a speed of 16 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 60 km downstream. Pick.
A) 2 hours . B) 3 hours . C) 4 hours . D) 5 hours . E) 6 hours . | <gadget id="calculator">16 + 4</gadget>
<output>20</output>
<gadget id="calculator">60 / 20</gadget>
<output>3</output>
<result>B</result> | B | 3 | A boat can travel with a speed of 16 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 60 km downstream. | {
"A": "2 hours .",
"B": "3 hours .",
"C": "4 hours .",
"D": "5 hours .",
"E": "6 hours ."
} | divide(60, add(16, 4)) | add(n0,n1)|divide(n2,#0)| | "speed downstream = ( 16 + 4 ) km / hr = 20 km / hr . time taken to travel 60 km downstream = 60 / 20 = 3 hours . answer : b" | physics |
math_qa__ptGsJhZ9OvwBfmZr | Walking 5/4 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? Choices: A) 22 B) 99 C) 27 D) 28 E) 20 | <gadget id="calculator">4 * 5</gadget>
<output>20</output>
<result>E</result> | E | 20 | Walking 5/4 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? | {
"A": "22",
"B": "99",
"C": "27",
"D": "28",
"E": "20"
} | multiply(4, 5) | multiply(n0,n2)| | "speed ratio = 1 : 5 / 4 = 4 : 5 time ratio = 5 : 4 1 - - - - - - - - 5 4 - - - - - - - - - ? 20 m . answer : e" | gain |
math_qa__KvW5cg04nvVkeSXJ | Mahesh can do a piece of work in 50days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work?
Options.
A) 45
B) 25
C) 37
D) 41
E) 50 | <gadget id="calculator">1 / 50</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">20 * (1/50)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) / 30</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">1 / (1/50)</gadget>
<output>50</output>
<result>E</result> | E | 50 | Mahesh can do a piece of work in 50days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work? | {
"A": "45",
"B": "25",
"C": "37",
"D": "41",
"E": "50"
} | divide(const_1, divide(subtract(const_1, multiply(20, divide(const_1, 50))), 30)) | divide(const_1,n0)|multiply(n1,#0)|subtract(const_1,#1)|divide(#2,n2)|divide(const_1,#3)| | "work done by mahesh in 50 days = 20 * 1 / 50 = 2 / 5 remaining work = 1 - 2 / 5 = 3 / 5 3 / 5 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 5 / 3 = 50 days answer is e" | physics |
math_qa__IT3ECxkeEkJFArRX | The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square. Options.
A) 5 : 78 B) 5 : 11 C) 5 : 12 D) 5 : 19 E) 5 : 16 | <gadget id="calculator">4_096 ** (1/2)</gadget>
<output>64</output>
<gadget id="calculator">64 - 24</gadget>
<output>40</output>
<gadget id="calculator">64 * 2</gadget>
<output>128</output>
<gadget id="calculator">40 / 128</gadget>
<output>5/16 = around 0.3125</output>
<result>E</result> | E | 0.3125 | The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square. | {
"A": "5 : 78",
"B": "5 : 11",
"C": "5 : 12",
"D": "5 : 19",
"E": "5 : 16"
} | divide(subtract(sqrt(4096), 24), multiply(sqrt(4096), const_2)) | sqrt(n0)|multiply(#0,const_2)|subtract(#0,n1)|divide(#2,#1) | let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4096 = 212 a = ( 212 ) 1 / 2 = 26 = 64 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 40 : 128 = 5 : 16 answer : e | geometry |
math_qa__4NbN6bzJt4GV61Bl | A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 5 and peanut cookies in batches of 6. If he makes exactly 94 cookies, what is the minimum number of chocolate chip cookies he makes? Choose the correct choice from the following choices
A) 7
B) 14
C) 21
D) 28
E) 40 | <gadget id="calculator">5 + 6</gadget>
<output>11</output>
<gadget id="calculator">94 % 11</gadget>
<output>6</output>
<gadget id="calculator">94 - 6</gadget>
<output>88</output>
<gadget id="calculator">88 / 11</gadget>
<output>8</output>
<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<result>E</result> | E | 40 | A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 5 and peanut cookies in batches of 6. If he makes exactly 94 cookies, what is the minimum number of chocolate chip cookies he makes? | {
"A": "7",
"B": "14",
"C": "21",
"D": "28",
"E": "40"
} | multiply(divide(subtract(94, reminder(94, add(5, 6))), add(5, 6)), 5) | add(n0,n1)|reminder(n2,#0)|subtract(n2,#1)|divide(#2,#0)|multiply(n0,#3) | 5 c + 6 p = 94 we need to maximize p to minimize c so that the eq is also satisfied try substitution for cp to solve so that eqn is satisfied the least value of c for which equation gets satisfied is 5 i . e . 5 * 8 + 6 * 9 = 40 + 54 = 94 hence e is the answer | general |
math_qa__hsmG9RY7DQUcqByw | When y is divided by 264, the remainder is 42. What is the remainder when the same y is divided by 22?
Pick:
A) 12 B) 14 C) 16 D) 18 E) 20 | <gadget id="calculator">42 % 22</gadget>
<output>20</output>
<result>E</result> | E | 20 | When y is divided by 264, the remainder is 42. What is the remainder when the same y is divided by 22? | {
"A": "12",
"B": "14",
"C": "16",
"D": "18",
"E": "20"
} | reminder(42, 22) | reminder(n1,n2)| | "y = 264 * a + 42 = ( 22 * 12 ) * a + 22 + 20 the answer is e ." | general |
math_qa__FDRuQhZt7QdjdREZ | A 12% stock yielding 8% is quoted at? Choose the correct choice: A) 165 B) 170 C) 175 D) 150 E) 185 | <gadget id="calculator">100 / 8</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 12</gadget>
<output>150</output>
<result>D</result> | D | 150 | A 12% stock yielding 8% is quoted at? | {
"A": "165",
"B": "170",
"C": "175",
"D": "150",
"E": "185"
} | multiply(divide(const_100, 8), 12) | divide(const_100,n1)|multiply(n0,#0)| | "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 12 , money invested = 100 × 12 / 8 = rs . 150 ie , market value of the stock = rs . 150 answer is d ." | gain |
math_qa__eKrrm7S8wFEl5QvR | 9 people are planning to share equally the cost of a rental van . if one person withdraws from the arrangement and the others share equally the cost of the rental van , then the share of each of the remaining people will increase by . . . ? Select:
A) 1 / 9 B) 1 / 8 C) 1 / 7 D) 7 / 8 E) 8 / 7 | <gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/8) - (1/9)</gadget>
<output>1/72 = around 0.013889</output>
<gadget id="calculator">(1/72) / (1/9)</gadget>
<output>1/8 = around 0.125</output>
<result>B</result> | B | 0.125 | 9 people are planning to share equally the cost of a rental van . if one person withdraws from the arrangement and the others share equally the cost of the rental van , then the share of each of the remaining people will increase by . . . ? | {
"A": "1 / 9",
"B": "1 / 8",
"C": "1 / 7",
"D": "7 / 8",
"E": "8 / 7"
} | divide(subtract(divide(const_1, subtract(9, const_1)), divide(const_1, 9)), divide(const_1, 9)) | divide(const_1,n0)|subtract(n0,const_1)|divide(const_1,#1)|subtract(#2,#0)|divide(#3,#0) | let p = total cost of the rental van . the original share per person is p / 9 . the new share per person is p / 8 . p / 8 = p / 9 * 9 / 8 = ( 1 + 1 / 8 ) * original share the answer is b . | general |
math_qa__vgGJxWOCHa1Y3tGx | What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 50%? Choose the most appropriate option:
A) 125 %
B) 150 %
C) 100 %
D) 90 %
E) 85 % | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) ** 2</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">(9/4) - 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 100</gadget>
<output>125</output>
<result>A</result> | A | 125 | What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 50%? | {
"A": "125 %",
"B": "150 %",
"C": "100 %",
"D": "90 %",
"E": "85 %"
} | multiply(subtract(power(add(const_1, divide(50, const_100)), const_2), const_1), const_100) | divide(n0,const_100)|add(#0,const_1)|power(#1,const_2)|subtract(#2,const_1)|multiply(#3,const_100)| | "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 50 % increase a surface = 6 * ( ( 1.5 a ) ^ 2 ) = 6 * 2.25 * a ^ 2 the increase in the surface area = ( 6 * 2.25 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 2.25 - 1 ) ) / ( 6 * a ^ 2 ) = 2.25 - 1 = 1.25 = 125 % answer : a" | geometry |
math_qa__C5eV5hRv6dj50skO | In an election between two candidates, the first candidate got 60% of the votes and the second candidate got 480 votes. What was the total number of votes? Options:
A) 900 B) 1200 C) 1500 D) 1800 E) 2100 | <gadget id="calculator">480 * 100</gadget>
<output>48_000</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">48_000 / 40</gadget>
<output>1_200</output>
<result>B</result> | B | 1,200 | In an election between two candidates, the first candidate got 60% of the votes and the second candidate got 480 votes. What was the total number of votes? | {
"A": "900",
"B": "1200",
"C": "1500",
"D": "1800",
"E": "2100"
} | divide(multiply(480, const_100), subtract(const_100, 60)) | multiply(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)| | "let v be the total number of votes . 0.4 v = 480 v = 1200 the answer is b ." | gain |
math_qa__dTk5PNecy7kcxkaB | A jogger running at 9 km/hr along side a railway track is 260 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? Options
A) 67 sec
B) 89 sec
C) 38 sec
D) 87 sec
E) 45 sec | <gadget id="calculator">260 + 120</gadget>
<output>380</output>
<gadget id="calculator">45 - 9</gadget>
<output>36</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">5 / 18</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">380 / 10</gadget>
<output>38</output>
<result>C</result> | C | 38 | A jogger running at 9 km/hr along side a railway track is 260 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? | {
"A": "67 sec",
"B": "89 sec",
"C": "38 sec",
"D": "87 sec",
"E": "45 sec"
} | divide(add(260, 120), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2)))) | add(n1,n2)|divide(const_10,const_2)|subtract(n3,n0)|divide(#2,const_2)|divide(#1,#3)|multiply(#4,#2)|divide(#0,#5)| | "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 260 + 120 = 380 m . time taken = 380 / 10 = 38 sec . answer : c" | general |
math_qa__1k423nzX8d04Krcb | Pipe A that can fill a tank in an hour and pipe B that can fill the tank in 15 are opened simultaneously when the tank is empty. Pipe B is shut 15 minutes before the tank overflows. When will the tank overflow? Choose the correct choice from the following choices.
A) 40 mins
B) 35 mins
C) 30 mins
D) 32 mins
E) 36 mins | <gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) / 3</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 60</gadget>
<output>15</output>
<gadget id="calculator">15 + 15</gadget>
<output>30</output>
<result>C</result> | C | 30 | Pipe A that can fill a tank in an hour and pipe B that can fill the tank in 15 are opened simultaneously when the tank is empty. Pipe B is shut 15 minutes before the tank overflows. When will the tank overflow? | {
"A": "40 mins",
"B": "35 mins",
"C": "30 mins",
"D": "32 mins",
"E": "36 mins"
} | add(multiply(divide(divide(const_3, const_4), const_3), const_60), 15) | divide(const_3,const_4)|divide(#0,const_3)|multiply(#1,const_60)|add(n0,#2) | the last 15 minutes only pipe a was open . since it needs 1 hour to fill the tank , then in 15 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 4 = 5 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 5 = 3 / 20 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : c | physics |
math_qa__2LlKBTPT8UH6sYuI | John has exactly 31 pens, and each pen is either bule, black, or red. If he has 5 more black pens than red pens, and twice as many blue pens as black pens, how many blue pens does john has ? Choose the correct choice from the following answers: A) 15 B) 18 C) 20 D) 22 E) 17 | <gadget id="calculator">31 + 5</gadget>
<output>36</output>
<gadget id="calculator">36 / 4</gadget>
<output>9</output>
<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<result>B</result> | B | 18 | John has exactly 31 pens, and each pen is either bule, black, or red. If he has 5 more black pens than red pens, and twice as many blue pens as black pens, how many blue pens does john has ? | {
"A": "15",
"B": "18",
"C": "20",
"D": "22",
"E": "17"
} | multiply(divide(add(31, 5), const_4), const_2) | add(n0,n1)|divide(#0,const_4)|multiply(#1,const_2) | x = the number of blue pens y = the number of black pens z = the number of red pens from the first sentence we have equation # 1 : x + y + z = 31 . . . he has 5 more black pens than red pens . . . equation # 2 : y = 5 + z . . . twice as many blue pens as black pens . . . equation # 3 : x = 2 y solve equation # 1 for z : z = y - 5 now , we can replace both x and z with y in equation # 1 2 y + y + ( y - 5 ) = 31 4 y - 5 = 31 4 y = 36 y = 9 there are 9 black pens . this is 5 more than the number of red pens , so z = 4 . hence the answer is . x = 18 , and just for check 18 + 9 + 4 = 31 . answer = 18 , ( b ) | general |
math_qa__y4ma8ssm61ULCPom | The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 500. What is the manager's monthly salary ? Choose the most appropriate option
A) rs . 16003
B) rs . 16029
C) rs . 1288
D) rs . 16108
E) rs . 12000 | <gadget id="calculator">1_500 + 500</gadget>
<output>2_000</output>
<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">2_000 * 21</gadget>
<output>42_000</output>
<gadget id="calculator">1_500 * 20</gadget>
<output>30_000</output>
<gadget id="calculator">42_000 - 30_000</gadget>
<output>12_000</output>
<result>E</result> | E | 12,000 | The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 500. What is the manager's monthly salary ? | {
"A": "rs . 16003",
"B": "rs . 16029",
"C": "rs . 1288",
"D": "rs . 16108",
"E": "rs . 12000"
} | subtract(multiply(add(1500, 500), add(20, const_1)), multiply(1500, 20)) | add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | "explanation : manager ' s monthly salary rs . ( 2000 * 21 - 1500 * 20 ) = rs . 12000 . answer : e" | general |
math_qa__Xu36uQztBXbL2mui | A rectangular tiled patio is composed of 50 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 50 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout? Select: A) 5 B) 6 C) 10 D) 13 E) 28 | <gadget id="calculator">-4</gadget>
<output>-4</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">16 + 400</gadget>
<output>416</output>
<gadget id="calculator">416 ** (1/2)</gadget>
<output>4*sqrt(26) = around 20.396078</output>
<gadget id="calculator">(-4) + (4*sqrt(26))</gadget>
<output>-4 + 4*sqrt(26) = around 16.396078</output>
<gadget id="calculator">(-4 + 4*sqrt(26)) / 2</gadget>
<output>-2 + 2*sqrt(26) = around 8.198039</output>
<gadget id="calculator">50 / (-2 + 2*sqrt(26))</gadget>
<output>50/(-2 + 2*sqrt(26)) = around 6.09902</output>
<result>B</result> | B | 6 | A rectangular tiled patio is composed of 50 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 50 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout? | {
"A": "5",
"B": "6",
"C": "10",
"D": "13",
"E": "28"
} | divide(50, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(50, 2))))), 2)) | multiply(n0,n1)|negate(n2)|power(n2,n1)|multiply(n2,#0)|add(#3,#2)|sqrt(#4)|add(#1,#5)|divide(#6,n1)|divide(n0,#7)| | "r * c = 50 and ( 6 + 4 ) ( 7 - 2 ) = 50 - - > r = 6 and c = 7 . answer : b ." | geometry |
math_qa__szo7eH5jp8Fs2slP | The tax on a commodity is diminished by 20% but its consumption is increased by 15%. Find the decrease percent in the revenue derived from it? Choose the correct choice from the following choices.
A) 12 % B) 14 % C) 16 % D) 20 % E) 8 % | <gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">115 * 80</gadget>
<output>9_200</output>
<gadget id="calculator">9_200 / 100</gadget>
<output>92</output>
<gadget id="calculator">100 - 92</gadget>
<output>8</output>
<result>E</result> | E | 8 | The tax on a commodity is diminished by 20% but its consumption is increased by 15%. Find the decrease percent in the revenue derived from it? | {
"A": "12 %",
"B": "14 %",
"C": "16 %",
"D": "20 %",
"E": "8 %"
} | subtract(const_100, divide(multiply(add(const_100, 15), subtract(const_100, 20)), const_100)) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)| | "explanation : 100 * 100 = 10000 80 * 115 = 9200 10000 - - - - - - - 800 100 - - - - - - - ? = 8 % e )" | general |
math_qa__oxhK2k0g2frMONNY | Find the area of a parallelogram with base 24 cm and height 10 cm? Choose the correct choice from the following options: A) 240 cm 2 B) 384 cm 2 C) 279 cm 2 D) 200 cm 2 E) 297 cm 2 | <gadget id="calculator">24 * 10</gadget>
<output>240</output>
<result>A</result> | A | 240 | Find the area of a parallelogram with base 24 cm and height 10 cm? | {
"A": "240 cm 2",
"B": "384 cm 2",
"C": "279 cm 2",
"D": "200 cm 2",
"E": "297 cm 2"
} | multiply(24, 10) | multiply(n0,n1)| | "area of a parallelogram = base * height = 24 * 10 = 240 cm 2 answer : a" | geometry |
math_qa__K3Ktqc03Vf7H2HFT | Beginning in Town A, Biker Bob rides his bike 8 miles west, 5 miles north, 4 miles east, and then 15 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)
Choices:
A) 25 miles B) 20.4 miles C) 30 miles D) 32 miles E) 33 miles | <gadget id="calculator">5 + 15</gadget>
<output>20</output>
<gadget id="calculator">20 ** 2</gadget>
<output>400</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">400 + 16</gadget>
<output>416</output>
<gadget id="calculator">416 ** (1/2)</gadget>
<output>4*sqrt(26) = around 20.396078</output>
<result>B</result> | B | 20.4 | Beginning in Town A, Biker Bob rides his bike 8 miles west, 5 miles north, 4 miles east, and then 15 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.) | {
"A": "25 miles",
"B": "20.4 miles",
"C": "30 miles",
"D": "32 miles",
"E": "33 miles"
} | sqrt(add(power(add(5, 15), const_2), power(4, const_2))) | add(n1,n3)|power(n2,const_2)|power(#0,const_2)|add(#2,#1)|sqrt(#3)| | "using pythagoras we have one side i , e total distance traveled in north direction = 15 + 5 = 20 m other being the base ie distance traveled west - distance traveled eat = 8 - 4 = 4 m now this third side or the distance between town a and town b = 20 ^ 2 + 4 ^ 2 = sq root 416 = 20.4 miles answer : b" | physics |
math_qa__sA32Hi328VGIPAYh | A rectangular field is to be fenced on three sides leaving a side of 40 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
Choose the correct choice from the following:
A) 44 ft
B) 88 ft
C) 74 ft
D) 11 ft
E) 66 ft | <gadget id="calculator">680 / 40</gadget>
<output>17</output>
<gadget id="calculator">17 * 2</gadget>
<output>34</output>
<gadget id="calculator">34 + 40</gadget>
<output>74</output>
<result>C</result> | C | 74 | A rectangular field is to be fenced on three sides leaving a side of 40 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required? | {
"A": "44 ft",
"B": "88 ft",
"C": "74 ft",
"D": "11 ft",
"E": "66 ft"
} | add(multiply(divide(680, 40), const_2), 40) | divide(n1,n0)|multiply(#0,const_2)|add(n0,#1)| | "given that length and area , so we can find the breadth . length x breadth = area 40 x breadth = 680 breadth = 17 feet area to be fenced = 2 b + l = 2 ( 17 ) + 40 = 74 feet answer : c ) 74 ft" | geometry |
math_qa__XhaI9cerjkYAB6Lb | In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 140?
Choose the most appropriate option: A) 28 B) 29 C) 30 D) 31 E) 32 | <gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">140 - 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 5</gadget>
<output>24</output>
<gadget id="calculator">24 + 8</gadget>
<output>32</output>
<result>E</result> | E | 32 | In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 140? | {
"A": "28",
"B": "29",
"C": "30",
"D": "31",
"E": "32"
} | add(divide(subtract(140, add(add(add(2, add(2, 2)), add(add(2, 2), 2)), add(add(add(2, 2), 2), 2))), 5), add(add(add(2, 2), 2), 2)) | add(n1,n1)|add(n1,#0)|add(n1,#1)|add(#1,#1)|add(#3,#2)|subtract(n2,#4)|divide(#5,n0)|add(#2,#6)| | "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 140 5 x - 20 = 140 5 x = 160 x = 32 the answer is e ." | general |
math_qa__YVgPnRWcuKZYrQj9 | A chemical supply company has 60 liters of a 45% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution? Choose one:
A) 6
B) 15
C) 20
D) 24
E) 30 | <gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">60 * 45</gadget>
<output>2_700</output>
<gadget id="calculator">2_700 / 100</gadget>
<output>27</output>
<gadget id="calculator">30 - 27</gadget>
<output>3</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<result>A</result> | A | 6 | A chemical supply company has 60 liters of a 45% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution? | {
"A": "6",
"B": "15",
"C": "20",
"D": "24",
"E": "30"
} | multiply(subtract(divide(60, const_2), divide(multiply(60, 45), const_100)), const_2) | divide(n0,const_2)|multiply(n0,n1)|divide(#1,const_100)|subtract(#0,#2)|multiply(#3,const_2)| | "60 liters of a 45 % hno 3 solution means hno 3 = 27 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 27 + x = 50 % of ( 60 + x ) or x = 6 . hence , a" | gain |
math_qa__ONtdDks53sRrxXyq | Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%? Choose the correct choice: A) 30000 B) 40000 C) 50000 D) 60000 E) 70000 | <gadget id="calculator">50_000 * 20</gadget>
<output>1_000_000</output>
<gadget id="calculator">1_000_000 / 100</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 - 7_000</gadget>
<output>3_000</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">3_000 / (1/10)</gadget>
<output>30_000</output>
<result>A</result> | A | 30,000 | Rs 50000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 7000 Find money given by 10%? | {
"A": "30000",
"B": "40000",
"C": "50000",
"D": "60000",
"E": "70000"
} | divide(subtract(divide(multiply(50000, 20), const_100), 7000), divide(10, const_100)) | divide(n1,const_100)|multiply(n0,n2)|divide(#1,const_100)|subtract(#2,n3)|divide(#3,#0)| | "let first parrt is x and second part is y then x + y = 50000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 7000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 70000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 70000 = 50000 + y so y = 20000 then x = 50000 - 20000 = 30000 first part = 30000 answer : a" | gain |
math_qa__O2LivmAdbQlpRVXE | Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 20 km/hr. For how many minutes does the bus stop per hour? Choose the correct choice from the following
A) 22 B) 88 C) 77 D) 40 E) 99 | <gadget id="calculator">1 * 60</gadget>
<output>60</output>
<gadget id="calculator">20 / 60</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 60</gadget>
<output>20</output>
<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<result>D</result> | D | 40 | Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 20 km/hr. For how many minutes does the bus stop per hour? | {
"A": "22",
"B": "88",
"C": "77",
"D": "40",
"E": "99"
} | subtract(multiply(const_1, const_60), multiply(divide(20, 60), const_60)) | divide(n1,n0)|multiply(const_1,const_60)|multiply(#0,const_60)|subtract(#1,#2)| | "in 1 hr , the bus covers 60 km without stoppages and 20 km with stoppages . stoppage time = time take to travel ( 60 - 20 ) km i . e 40 km at 60 km / hr . stoppage time = 40 / 60 hrs = 40 min . answer : d" | general |
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