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float64 -4,212
100B
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stringlengths 6
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stringlengths 7
6.48k
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stringlengths 8
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math_qa__E5Ndomc92rNqSsyn | The length of a rectangle is halved, while its breadth is tripled. What is the % change in area? Choose the most appropriate option:
A) 30 %
B) 40 %
C) 50 percent
D) 60 %
E) 70 % | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">3 * (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) - 1</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) / 1</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>C</result> | C | 50 | The length of a rectangle is halved, while its breadth is tripled. What is the % change in area? | {
"A": "30 %",
"B": "40 %",
"C": "50 percent",
"D": "60 %",
"E": "70 %"
} | multiply(divide(subtract(multiply(const_3, divide(const_1, const_2)), const_1), const_1), const_100) | divide(const_1,const_2)|multiply(#0,const_3)|subtract(#1,const_1)|divide(#2,const_1)|multiply(#3,const_100)| | "let original length = x and original breadth new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c" | geometry |
math_qa__LsxqZsmUfxcq2Xxy | John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $15, what was the price before the first discount? Choose the correct choice from the following options.
A) $ 45.10
B) $ 34.31
C) $ 28.44
D) $ 26.66
E) $ 65.23 | <gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 * 15</gadget>
<output>150_000</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 * 100</gadget>
<output>7_500</output>
<gadget id="calculator">75 * 25</gadget>
<output>1_875</output>
<gadget id="calculator">7_500 - 1_875</gadget>
<output>5_625</output>
<gadget id="calculator">150_000 / 5_625</gadget>
<output>80/3 = around 26.666667</output>
<result>D</result> | D | 26.66 | John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $15, what was the price before the first discount? | {
"A": "$ 45.10",
"B": "$ 34.31",
"C": "$ 28.44",
"D": "$ 26.66",
"E": "$ 65.23"
} | divide(multiply(multiply(const_100, const_100), 15), subtract(multiply(subtract(const_100, 25), const_100), multiply(subtract(const_100, 25), 25))) | multiply(const_100,const_100)|subtract(const_100,n0)|multiply(n2,#0)|multiply(#1,const_100)|multiply(n0,#1)|subtract(#3,#4)|divide(#2,#5)| | "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 15 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 15 solve for x x = $ 26.66 correct answer d" | gain |
math_qa__KG3sL0cn479oqvUv | The length of the bridge, which a train 155 metres long and travelling at 45 km/hr can cross in 30 seconds, is: Select.
A) 220 m
B) 225 m
C) 245 m
D) 250 m
E) 270 m | <gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 155</gadget>
<output>220</output>
<result>A</result> | A | 220 | The length of the bridge, which a train 155 metres long and travelling at 45 km/hr can cross in 30 seconds, is: | {
"A": "220 m",
"B": "225 m",
"C": "245 m",
"D": "250 m",
"E": "270 m"
} | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 155) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | "let the length of the bridge : l the equation now is l + 155 / 12.5 m / s ( 45 km / hr or 12.5 m / s ) = 30 solving , l = 220 m answer : a" | physics |
math_qa__K7YoCJ83TrqbZyTX | For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 20 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated? Choose the correct choice from the following:
A) 12 % B) 26 % C) 29 % D) 30 % E) 60 % | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 300</gadget>
<output>60</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 200</gadget>
<output>70</output>
<gadget id="calculator">60 + 70</gadget>
<output>130</output>
<gadget id="calculator">300 + 200</gadget>
<output>500</output>
<gadget id="calculator">130 / 500</gadget>
<output>13/50 = around 0.26</output>
<gadget id="calculator">(13/50) * 100</gadget>
<output>26</output>
<result>B</result> | B | 26 | For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 20 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated? | {
"A": "12 %",
"B": "26 %",
"C": "29 %",
"D": "30 %",
"E": "60 %"
} | multiply(divide(add(multiply(divide(20, const_100), 300), multiply(divide(35, const_100), 200)), add(300, 200)), const_100) | add(n0,n1)|divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(n1,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)| | "in the first plot 20 % of 300 seeds germinated , so 0.20 x 300 = 60 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 60 + 70 = 130 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 130 / 500 ) x 100 % , or 26 % . answer : b ." | general |
math_qa__XRnQkPIxG3HBDQBM | There are 20 poles with a constant distance between each pole. A car takes 22 second to reach the 12th pole. How much will it take to reach the last pole.
Choose the correct choice from the following options:
A) 38 B) 41 C) 28 D) 88 E) 22 | <gadget id="calculator">22 / 12</gadget>
<output>11/6 = around 1.833333</output>
<gadget id="calculator">(11/6) * 20</gadget>
<output>110/3 = around 36.666667</output>
<result>A</result> | A | 38 | There are 20 poles with a constant distance between each pole. A car takes 22 second to reach the 12th pole. How much will it take to reach the last pole. | {
"A": "38",
"B": "41",
"C": "28",
"D": "88",
"E": "22"
} | multiply(divide(22, 12), 20) | divide(n1,n2)|multiply(n0,#0)| | "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 22 seconds 1 pole ( 22 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 22 / 11 ) seconds = 38 seconds answer : a" | physics |
math_qa__TgpelvN8BkN88s6v | Solution A is 20% salt and Solution B is 70% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution? Pick one: A) 6 : 4 B) 6 : 14 C) 2 : 3 D) 4 : 6 E) 3 : 7 | <gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">50 * (7/10)</gadget>
<output>35</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">50 * (1/2)</gadget>
<output>25</output>
<gadget id="calculator">35 - 25</gadget>
<output>10</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(7/10) - (1/5)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">10 / (1/2)</gadget>
<output>20</output>
<gadget id="calculator">50 - 20</gadget>
<output>30</output>
<gadget id="calculator">20 / 30</gadget>
<output>2/3 = around 0.666667</output>
<result>C</result> | C | 0.666667 | Solution A is 20% salt and Solution B is 70% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution? | {
"A": "6 : 4",
"B": "6 : 14",
"C": "2 : 3",
"D": "4 : 6",
"E": "3 : 7"
} | divide(divide(subtract(multiply(50, divide(70, const_100)), multiply(50, divide(50, const_100))), subtract(divide(70, const_100), divide(20, const_100))), subtract(50, divide(subtract(multiply(50, divide(70, const_100)), multiply(50, divide(50, const_100))), subtract(divide(70, const_100), divide(20, const_100))))) | divide(n1,const_100)|divide(n4,const_100)|divide(n0,const_100)|multiply(n4,#0)|multiply(n4,#1)|subtract(#0,#2)|subtract(#3,#4)|divide(#6,#5)|subtract(n4,#7)|divide(#7,#8)| | "forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 70 - 50 ) / ( 50 - 20 ) = 2 / 3 so the volume of the two solutions will be equal . answer has to be 2 : 3 c" | other |
math_qa__kYYFIbpxvClKI7hI | In a 100 m race,A covers the distance in 36 seconds and B in 45 second.In this race A beats B by : Answers
A) 20 m B) 25 m C) 22.5 m D) 9 m E) none of these | <gadget id="calculator">100 / 45</gadget>
<output>20/9 = around 2.222222</output>
<gadget id="calculator">45 - 36</gadget>
<output>9</output>
<gadget id="calculator">(20/9) * 9</gadget>
<output>20</output>
<result>A</result> | A | 20 | In a 100 m race,A covers the distance in 36 seconds and B in 45 second.In this race A beats B by : | {
"A": "20 m",
"B": "25 m",
"C": "22.5 m",
"D": "9 m",
"E": "none of these"
} | multiply(divide(100, 45), subtract(45, 36)) | divide(n0,n2)|subtract(n2,n1)|multiply(#0,#1)| | "solution distance covered by b in 9 sec . = ( 100 / 45 x 9 ) m = 20 m . ∴ a beats b by 20 metres . answer a" | physics |
math_qa__VV6mZfCasAAPlO0m | A owner of a mart earns an income of Re 1 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 10th day of business, he earns an income of: Choose the most appropriate option:
A) 18 B) 21 C) 22 D) 20 E) 30 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">10 + 8</gadget>
<output>18</output>
<result>A</result> | A | 18 | A owner of a mart earns an income of Re 1 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 10th day of business, he earns an income of: | {
"A": "18",
"B": "21",
"C": "22",
"D": "20",
"E": "30"
} | add(10, multiply(const_4, const_2)) | multiply(const_2,const_4)|add(n1,#0) | 2 nd day he earns = 2 ( 2 – 1 ) 3 rd day he earns = 2 ( 3 – 1 ) on 10 th day he earns 2 ( 10 - 1 ) = 18 rupees answer : a | physics |
math_qa__jnHpqjQZVJTPaLda | If p=125×243×16/405, how many digits are in p? Choose the correct choice from the following options
A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">405 / 5</gadget>
<output>81</output>
<gadget id="calculator">243 / 81</gadget>
<output>3</output>
<gadget id="calculator">3 * 16</gadget>
<output>48</output>
<gadget id="calculator">125 / 5</gadget>
<output>25</output>
<gadget id="calculator">48 * 25</gadget>
<output>1_200</output>
<gadget id="calculator">100 * 3</gadget>
<output>300</output>
<gadget id="calculator">1_200 / 300</gadget>
<output>4</output>
<result>D</result> | D | 4 | If p=125×243×16/405, how many digits are in p? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | divide(multiply(multiply(divide(243, divide(405, add(const_4, const_1))), 16), divide(125, add(const_4, const_1))), multiply(const_100, const_3)) | add(const_1,const_4)|multiply(const_100,const_3)|divide(n0,#0)|divide(n3,#0)|divide(n1,#3)|multiply(n2,#4)|multiply(#2,#5)|divide(#6,#1) | p = 125 * 243 * 16 / 405 p = 5 ^ 3 * 3 * 9 ^ 2 * 4 ^ 2 / ( 5 * 9 ^ 2 ) p = 5 ^ 2 * 3 * 4 ^ 2 p = 20 ^ 2 * 3 = 1200 answer d | general |
math_qa__UD15L9xfbNWhHBXF | Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 34 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat? Choose the correct choice from the following options.
A) 20
B) 21
C) 22
D) 23
E) 25 | <gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">34 - 18</gadget>
<output>16</output>
<gadget id="calculator">9 + 16</gadget>
<output>25</output>
<result>E</result> | E | 25 | Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 34 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat? | {
"A": "20",
"B": "21",
"C": "22",
"D": "23",
"E": "25"
} | add(divide(18, const_2), subtract(34, 18)) | divide(n0,const_2)|subtract(n1,n0)|add(#0,#1)| | "check two extreme cases : jane = 18 , child = 9 , years ago = 34 - 18 = 16 - - > child ' s age now = 9 + 16 = 25 ; jane = 24 , child = 12 , years ago = 34 - 24 = 10 - - > child ' s age now = 12 + 10 = 22 . answer : e ." | general |
math_qa__NQnG9HMJFqwbkMn2 | From the sale of sleeping bags, a retailer made a gross profit of 17% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag? Pick one:
A) 3.0
B) 3.36
C) 23.93
D) 25.0
E) 31.36 | <gadget id="calculator">28 * 100</gadget>
<output>2_800</output>
<gadget id="calculator">100 + 17</gadget>
<output>117</output>
<gadget id="calculator">2_800 / 117</gadget>
<output>2_800/117 = around 23.931624</output>
<result>C</result> | C | 23.93 | From the sale of sleeping bags, a retailer made a gross profit of 17% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag? | {
"A": "3.0",
"B": "3.36",
"C": "23.93",
"D": "25.0",
"E": "31.36"
} | divide(multiply(28, const_100), add(const_100, 17)) | add(n0,const_100)|multiply(n1,const_100)|divide(#1,#0)| | "cost price * 1.17 = selling price - - > cost price * 1.17 = $ 28 - - > cost price = $ 23.93 . answer : c ." | gain |
math_qa__WQ4aK6UTuJUHkmZ8 | mixture contains alcohol and water in the ratio 4 : 3. If 6.5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture. Choose the correct choice from the following options.
A) 10 B) 99 C) 27 D) 22 E) 5.6 | <gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">6.5 * 4</gadget>
<output>26</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">26 - 12</gadget>
<output>14</output>
<gadget id="calculator">20 / 14</gadget>
<output>10/7 = around 1.428571</output>
<gadget id="calculator">(10/7) * 4</gadget>
<output>40/7 = around 5.714286</output>
<result>E</result> | E | 5.6 | mixture contains alcohol and water in the ratio 4 : 3. If 6.5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture. | {
"A": "10",
"B": "99",
"C": "27",
"D": "22",
"E": "5.6"
} | multiply(divide(multiply(4, 5), subtract(multiply(6.5, 4), multiply(3, 4))), 4) | multiply(n0,n4)|multiply(n0,n2)|multiply(n0,n1)|subtract(#1,#2)|divide(#0,#3)|multiply(n0,#4) | let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 26 x = 4 ( 3 x + 5 ) 14 x = 20 x = 1.4 quantity of alcohol = ( 4 x 1.4 ) litres = 5.6 litres . answer : e | general |
math_qa__pGq4GmJfgb9GZ6mo | The cost of carpeting a room 18 m long with a carpet 75 cm wide at 4.50 per metre is 810. The breadth of the room is:
Select the correct option: A) 7 m B) 7.5 m C) 8 m D) 8.5 m E) none of these | <gadget id="calculator">810 / 4.5</gadget>
<output>180</output>
<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">180 * (3/4)</gadget>
<output>135</output>
<gadget id="calculator">135 / 18</gadget>
<output>15/2 = around 7.5</output>
<result>B</result> | B | 7.5 | The cost of carpeting a room 18 m long with a carpet 75 cm wide at 4.50 per metre is 810. The breadth of the room is: | {
"A": "7 m",
"B": "7.5 m",
"C": "8 m",
"D": "8.5 m",
"E": "none of these"
} | divide(multiply(divide(810, 4.5), divide(75, const_100)), 18) | divide(n3,n2)|divide(n1,const_100)|multiply(#0,#1)|divide(#2,n0) | length of the carpet = totalcost / rate / m = ( 8100 ⁄ 45 ) m = 180 m . area of the room = area of the carpet = ( 180 × 75 ⁄ 100 ) m 2 = 135 m 2 ∴ breadth of the room = arealength = 135 / 18 m = 7.5 m answer b | physics |
math_qa__C5hVydnykNEzMCbF | a farmer with 1350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ? Choose the correct choice from the following options.
A) 90 B) 150 C) 270 D) 300 E) 450 | <gadget id="calculator">1_350 * 3</gadget>
<output>4_050</output>
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">4_050 / 9</gadget>
<output>450</output>
<result>E</result> | E | 450 | a farmer with 1350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ? | {
"A": "90",
"B": "150",
"C": "270",
"D": "300",
"E": "450"
} | divide(multiply(1350, const_3), add(add(5, 2), 2)) | add(n1,n2)|multiply(n0,const_3)|add(n2,#0)|divide(#1,#2) | originally ( 2 / 9 ) * 1350 = 300 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 300 = 450 more acres were planted with tobacco . the answer is e . | other |
math_qa__ZXwCbktgCTen07gQ | A metallic sheet is of rectangular shape with dimensions 50 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
Choose the correct choice from the following answers: A) 5440 B) 5120 C) 6420 D) 7500 E) 8960 | <gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">50 - 16</gadget>
<output>34</output>
<gadget id="calculator">36 - 16</gadget>
<output>20</output>
<gadget id="calculator">34 * 20 * 8</gadget>
<output>5_440</output>
<result>A</result> | A | 5,440 | A metallic sheet is of rectangular shape with dimensions 50 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is: | {
"A": "5440",
"B": "5120",
"C": "6420",
"D": "7500",
"E": "8960"
} | volume_rectangular_prism(subtract(50, multiply(8, const_2)), subtract(36, multiply(8, const_2)), 8) | multiply(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|volume_rectangular_prism(n2,#1,#2)| | "l = ( 50 - 16 ) m = 34 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 34 x 20 x 8 ) m 3 = 5440 m 3 . answer : option a" | geometry |
math_qa__tSeK2MRVtimNWLJA | The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.3.00 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? Choices:
A) s . 1014
B) s . 1140
C) s . 1998
D) s . 1085
E) s . 1020 | <gadget id="calculator">3_136 ** (1/2)</gadget>
<output>56</output>
<gadget id="calculator">56 * 4</gadget>
<output>224</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">224 - 2</gadget>
<output>222</output>
<gadget id="calculator">222 * 3</gadget>
<output>666</output>
<gadget id="calculator">666 * 3</gadget>
<output>1_998</output>
<result>C</result> | C | 1,998 | The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.3.00 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? | {
"A": "s . 1014",
"B": "s . 1140",
"C": "s . 1998",
"D": "s . 1085",
"E": "s . 1020"
} | multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, 1)), 3.00), 3) | multiply(n3,const_2)|sqrt(n0)|multiply(#1,const_4)|subtract(#2,#0)|multiply(n2,#3)|multiply(#4,n1)| | "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 3.0 = 1998 answer : c" | physics |
math_qa__l3yICw007kYEJRJY | The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 5:4:2. Someone removes 9 pounds of clothing from the suitcase, thereby doubling the ratio of books to clothes. How many pounds do the electronics in the suitcase weigh?
Choose the correct choice from the following:
A) 7
B) 8
C) 9
D) 10
E) 11 | <gadget id="calculator">5 + 4</gadget>
<output>9</output>
<gadget id="calculator">9 + 2</gadget>
<output>11</output>
<gadget id="calculator">11 * 9</gadget>
<output>99</output>
<gadget id="calculator">-99</gadget>
<output>-99</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">11 * 4</gadget>
<output>44</output>
<gadget id="calculator">22 - 44</gadget>
<output>-22</output>
<gadget id="calculator">(-99) / (-22)</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">2 * (9/2)</gadget>
<output>9</output>
<result>C</result> | C | 9 | The ratio by weight, measured in pounds, of books to clothes to electronics in a suitcase initially stands at 5:4:2. Someone removes 9 pounds of clothing from the suitcase, thereby doubling the ratio of books to clothes. How many pounds do the electronics in the suitcase weigh? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10",
"E": "11"
} | multiply(2, divide(negate(multiply(add(add(5, 4), 2), 9)), subtract(multiply(add(add(5, 4), 2), const_2), multiply(add(add(5, 4), 2), 4)))) | add(n0,n1)|add(n2,#0)|multiply(n3,#1)|multiply(#1,const_2)|multiply(n1,#1)|negate(#2)|subtract(#3,#4)|divide(#5,#6)|multiply(n2,#7)| | "the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 9 pounds of clothes doubles the ratio of books to clothes , then 9 pounds represents half the weight of the clothes . 2 k = 9 pounds and then k = 4.5 pounds . the electronics weigh 2 ( 4.5 ) = 9 pounds . the answer is c ." | other |
math_qa__sq0MBv72CRQqLkcX | In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? Choices.
A) 20 %
B) 40 %
C) 50 %
D) 60 %
E) 70 % | <gadget id="calculator">70 + 55</gadget>
<output>125</output>
<gadget id="calculator">100 - 35</gadget>
<output>65</output>
<gadget id="calculator">125 - 65</gadget>
<output>60</output>
<result>D</result> | D | 60 | In a particular state, 70% of the counties received some rain on Monday, and 55% of the counties received some rain on Tuesday. No rain fell either day in 35% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday? | {
"A": "20 %",
"B": "40 %",
"C": "50 %",
"D": "60 %",
"E": "70 %"
} | subtract(add(70, 55), subtract(const_100, 35)) | add(n0,n1)|subtract(const_100,n2)|subtract(#0,#1) | 70 + 55 + 35 = 160 % the number is 60 % above 100 % because 60 % of the counties were counted twice . the answer is d . | gain |
math_qa__zDAXPhR4zAZx0kGZ | The present worth of a certain bill due sometime hence is Rs. 400 and the true discount is Rs. 20. What is the banker's discount? Choose one.
A) rs . 19 B) rs . 22 C) rs . 20 D) rs . 21 E) none of these | <gadget id="calculator">20 ** 2</gadget>
<output>400</output>
<gadget id="calculator">400 / 400</gadget>
<output>1</output>
<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<result>D</result> | D | 21 | The present worth of a certain bill due sometime hence is Rs. 400 and the true discount is Rs. 20. What is the banker's discount? | {
"A": "rs . 19",
"B": "rs . 22",
"C": "rs . 20",
"D": "rs . 21",
"E": "none of these"
} | add(20, divide(power(20, const_2), 400)) | power(n1,const_2)|divide(#0,n0)|add(n1,#1)| | "explanation : bg = ( td ) 2 / pw = 202 / 400 = rs . 1 bg = bd – td = > 1 = bd - 20 = > bd = 1 + 20 = rs . 21 answer : option d" | gain |
math_qa__KsdOI4rTQEyhLQeR | The true discount on a bill of Rs. 2660 is Rs. 360. What is the banker's discount? Choose the most appropriate option:
A) rs . 432
B) rs . 422
C) rs . 416
D) rs . 442
E) none of these | <gadget id="calculator">2_660 - 360</gadget>
<output>2_300</output>
<gadget id="calculator">360 / 2_300</gadget>
<output>18/115 = around 0.156522</output>
<gadget id="calculator">(18/115) * 2_660</gadget>
<output>9_576/23 = around 416.347826</output>
<result>C</result> | C | 416 | The true discount on a bill of Rs. 2660 is Rs. 360. What is the banker's discount? | {
"A": "rs . 432",
"B": "rs . 422",
"C": "rs . 416",
"D": "rs . 442",
"E": "none of these"
} | multiply(divide(360, subtract(2660, 360)), 2660) | subtract(n0,n1)|divide(n1,#0)|multiply(n0,#1)| | "explanation : f = rs . 2660 td = rs . 360 pw = f - td = 2660 - 360 = rs . 2300 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2300 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2160 for unexpired time = 360 / 2300 × 2660 = 0.16 × 2660 = rs . 416 answer : option c" | gain |
math_qa__kLU3jkq44kuKtPMR | A train covered half of the distance between stations A and B at the speed of 48 km/hr, but then it had to stop for 15 min. To make up for the delay, it increased its speed by 53 m/sec and it arrived to station B on time. Find the distance between the two stations and the speed of the train after the stop.
Choose the correct answer
A) 206
B) 216
C) 226
D) 256
E) 246 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">48 + 6</gadget>
<output>54</output>
<gadget id="calculator">15 / 60</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">54 * (1/4)</gadget>
<output>27/2 = around 13.5</output>
<gadget id="calculator">(27/2) / 6</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">(9/4) * 48</gadget>
<output>108</output>
<gadget id="calculator">108 * 2</gadget>
<output>216</output>
<result>B</result> | B | 216 | A train covered half of the distance between stations A and B at the speed of 48 km/hr, but then it had to stop for 15 min. To make up for the delay, it increased its speed by 53 m/sec and it arrived to station B on time. Find the distance between the two stations and the speed of the train after the stop. | {
"A": "206",
"B": "216",
"C": "226",
"D": "256",
"E": "246"
} | multiply(multiply(divide(multiply(add(48, multiply(const_3, const_2)), divide(15, const_60)), multiply(const_3, const_2)), 48), const_2) | divide(n1,const_60)|multiply(const_2,const_3)|add(n0,#1)|multiply(#2,#0)|divide(#3,#1)|multiply(n0,#4)|multiply(#5,const_2) | first let us determine the speed of the train after the stop . the speed was increased by 53 m / sec = 5 ⋅ 60 ⋅ 6031000 km / hr = 6 km / hr . therefore , the new speed is 48 + 6 = 54 km / hr . if it took x hours to cover the first half of the distance , then it took x − 1560 = x − 0.25 hr to cover the second part . so the equation is : 48 ⋅ x = 54 ⋅ ( x − 0.25 ) 48 ⋅ x = 54 ⋅ x − 54 ⋅ 0.25 48 ⋅ x − 54 ⋅ x = − 13.5 − 6 x = − 13.5 x = 2.25 h . the whole distance is 2 × 48 × 2.25 = 216 km . answer is b . | physics |
math_qa__hGstTS7aTEMvonCF | In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 8.0, 9.0, 6.0, and 8.8, what was the point value of the dive?
Answers:
A) 68.8 B) 73.6 C) 75.2 D) 76.8 E) 77.76 | <gadget id="calculator">7.5 + 8</gadget>
<output>15.5</output>
<gadget id="calculator">15.5 + 8.8</gadget>
<output>24.3</output>
<gadget id="calculator">24.3 * 3.2</gadget>
<output>77.76</output>
<result>E</result> | E | 77.76 | In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 8.0, 9.0, 6.0, and 8.8, what was the point value of the dive? | {
"A": "68.8",
"B": "73.6",
"C": "75.2",
"D": "76.8",
"E": "77.76"
} | multiply(add(add(7.5, 8.0), 8.8), 3.2) | add(n4,n5)|add(n8,#0)|multiply(n3,#1)| | "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.8 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8 + 8.8 ) = 24.3 point of value of the dive = 24 * 3.2 = 77.76 answer e" | general |
math_qa__u6fYouMDi53Bop35 | A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 800 grams. Find the profit percent.
Choose the correct choice from the following answers.
A) 20 B) 15 C) 25 D) 18 E) 19 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 800</gadget>
<output>200</output>
<gadget id="calculator">200 / 800</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>C</result> | C | 25 | A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 800 grams. Find the profit percent. | {
"A": "20",
"B": "15",
"C": "25",
"D": "18",
"E": "19"
} | multiply(divide(subtract(multiply(add(add(const_4, const_1), add(const_4, const_1)), const_100), 800), 800), const_100) | add(const_1,const_4)|add(#0,#0)|multiply(#1,const_100)|subtract(#2,n0)|divide(#3,n0)|multiply(#4,const_100)| | "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 800 100 + g / 100 + 0 = 1000 / 800 100 + g = 5 / 4 * 100 g = 25 answer : c" | gain |
math_qa__G7wMpRf0HvsJJX5R | What percent is 120 of 80? Options.
A) 150 % B) 134 1 / 3 % C) 135 1 / 3 % D) 140 1 / 3 % E) 143 1 / 3 % | <gadget id="calculator">120 / 80</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 100</gadget>
<output>150</output>
<result>A</result> | A | 150 | What percent is 120 of 80? | {
"A": "150 %",
"B": "134 1 / 3 %",
"C": "135 1 / 3 %",
"D": "140 1 / 3 %",
"E": "143 1 / 3 %"
} | multiply(divide(120, 80), const_100) | divide(n0,n1)|multiply(#0,const_100)| | "120 / 80 = 3 / 2 3 / 2 × 100 = 300 / 2 = 150 % a" | gain |
math_qa__F80IP6pPk3yLxyyH | The cost of 2 chairs and 3 tables is Rs.1600. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by? Select
A) 228 B) 287 C) 277 D) 188 E) 400 | <gadget id="calculator">3 * 1_600</gadget>
<output>4_800</output>
<gadget id="calculator">2 * 1_200</gadget>
<output>2_400</output>
<gadget id="calculator">4_800 - 2_400</gadget>
<output>2_400</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">9 - 4</gadget>
<output>5</output>
<gadget id="calculator">2_400 / 5</gadget>
<output>480</output>
<gadget id="calculator">2 * 480</gadget>
<output>960</output>
<gadget id="calculator">1_200 - 960</gadget>
<output>240</output>
<gadget id="calculator">240 / 3</gadget>
<output>80</output>
<gadget id="calculator">480 - 80</gadget>
<output>400</output>
<result>E</result> | E | 400 | The cost of 2 chairs and 3 tables is Rs.1600. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by? | {
"A": "228",
"B": "287",
"C": "277",
"D": "188",
"E": "400"
} | subtract(divide(subtract(multiply(const_3, 1600), multiply(const_2, 1200)), subtract(multiply(const_3, 3), multiply(const_2, 2))), divide(subtract(1200, multiply(2, divide(subtract(multiply(const_3, 1600), multiply(const_2, 1200)), subtract(multiply(const_3, 3), multiply(const_2, 2))))), 3)) | multiply(n2,const_3)|multiply(n3,const_2)|multiply(n1,const_3)|multiply(n0,const_2)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)|multiply(n0,#6)|subtract(n3,#7)|divide(#8,n1)|subtract(#6,#9)| | explanation : 2 c + 3 t = 1600 - - - ( 1 ) 3 c + 3 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 400 = > t - c = 400 answer : e | general |
math_qa__dSWA3d9OIEDOauei | 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 20% of the total school population of x students, what is x? Choose one.
A) 125 B) 150 C) 212 D) 250 E) 500 | <gadget id="calculator">90 * 100</gadget>
<output>9_000</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">9_000 / (1/5)</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 ** (1/2)</gadget>
<output>150*sqrt(2) = around 212.132034</output>
<result>C</result> | C | 212 | 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 20% of the total school population of x students, what is x? | {
"A": "125",
"B": "150",
"C": "212",
"D": "250",
"E": "500"
} | sqrt(divide(multiply(90, const_100), divide(20, const_100))) | divide(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)|sqrt(#2) | 90 = x / 100 * 20 / 100 * x = > x ^ 2 = 9 * 10000 / 2 = > x = 212 c | gain |
math_qa__FVv4cVtTd8uYybl9 | A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A.
Pick one
A) 237
B) 126
C) 971
D) 611
E) 150 | <gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">225 / (5/4)</gadget>
<output>180</output>
<gadget id="calculator">20 + 100</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">180 / (6/5)</gadget>
<output>150</output>
<result>E</result> | E | 150 | A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A. | {
"A": "237",
"B": "126",
"C": "971",
"D": "611",
"E": "150"
} | divide(divide(225, divide(add(const_100, 25), const_100)), divide(add(20, const_100), const_100)) | add(n1,const_100)|add(n0,const_100)|divide(#0,const_100)|divide(#1,const_100)|divide(n2,#2)|divide(#4,#3)| | "explanation : answer : e" | gain |
math_qa__SNVUTyrvtW7Enr0r | 16 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? Choose the correct choice from the following.
A) 32 B) 87 C) 30 D) 99 E) 77 | <gadget id="calculator">21 * 8</gadget>
<output>168</output>
<gadget id="calculator">16 * 3</gadget>
<output>48</output>
<gadget id="calculator">168 * 48</gadget>
<output>8_064</output>
<gadget id="calculator">21 * 2</gadget>
<output>42</output>
<gadget id="calculator">42 * 6</gadget>
<output>252</output>
<gadget id="calculator">8_064 / 252</gadget>
<output>32</output>
<gadget id="calculator">floor(32)</gadget>
<output>32</output>
<gadget id="calculator">32 + 1</gadget>
<output>33</output>
<result>A</result> | A | 32 | 16 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? | {
"A": "32",
"B": "87",
"C": "30",
"D": "99",
"E": "77"
} | add(floor(divide(multiply(multiply(21, 8), multiply(16, 3)), multiply(multiply(21, 2), 6))), const_1) | multiply(n1,n2)|multiply(n0,n5)|multiply(n4,n6)|multiply(#0,#1)|multiply(n3,#2)|divide(#3,#4)|floor(#5)|add(#6,const_1)| | "3 w = 2 m 16 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 16 * 21 * 8 = 14 * x * 6 x = 32 answer : a" | physics |
math_qa__KeAOYJjXvwlYB2xi | A and B complete a work in 4 days. A alone can do it in 6 days. If both together can do the work in how many days?
Choose the correct choice from the following answers: A) 3.75 days B) 3.7 days C) 3.6 days D) 2.4 days E) 5.75 days | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/4) + (1/6)</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">1 / (5/12)</gadget>
<output>12/5 = around 2.4</output>
<result>D</result> | D | 2.4 | A and B complete a work in 4 days. A alone can do it in 6 days. If both together can do the work in how many days? | {
"A": "3.75 days",
"B": "3.7 days",
"C": "3.6 days",
"D": "2.4 days",
"E": "5.75 days"
} | inverse(add(inverse(4), inverse(6))) | inverse(n0)|inverse(n1)|add(#0,#1)|inverse(#2)| | "1 / 4 + 1 / 6 = 5 / 12 12 / 5 = 2.4 days answer : d" | physics |
math_qa__FqW4GdbG4Vm0sENg | a 5 digit number divisible by 3 is to be formed using the digits 0 , 1 , 2 , 3 , 4 and 5 without repetitions . that total no of ways it can be done is ? Options.
A) 122
B) 210
C) 216
D) 217
E) 220 | <gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">24 * 4</gadget>
<output>96</output>
<gadget id="calculator">120 + 96</gadget>
<output>216</output>
<result>C</result> | C | 216 | a 5 digit number divisible by 3 is to be formed using the digits 0 , 1 , 2 , 3 , 4 and 5 without repetitions . that total no of ways it can be done is ? | {
"A": "122",
"B": "210",
"C": "216",
"D": "217",
"E": "220"
} | add(factorial(5), multiply(factorial(subtract(5, const_1)), subtract(5, const_1))) | factorial(n0)|subtract(n0,const_1)|factorial(#1)|multiply(#2,#1)|add(#0,#3) | first step : we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0,1 , 2,3 , 4,5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = ( 1 , 2,3 , 4,5 ) and 15 - 3 = ( 0 , 1,2 , 4,5 ) . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2,3 , 4,5 and 0 , 1,2 , 4,5 . how many 5 digit numbers can be formed using this two sets : 1 , 2,3 , 4,5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1,2 , 4,5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 96 120 + 96 = 216 answer : c . | general |
math_qa__JSoPQuGVFcfixJEN | Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X? Choose the correct choice.
A) 30 %
B) 33 1 / 3 %
C) 37 1 / 2 %
D) 40 %
E) 50 % | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">8 * (3/10)</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">2 * (3/10)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(12/5) + (3/5)</gadget>
<output>3</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">8 * (7/10)</gadget>
<output>28/5 = around 5.6</output>
<gadget id="calculator">(28/5) - 2</gadget>
<output>18/5 = around 3.6</output>
<gadget id="calculator">2 * (7/10)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(18/5) + (7/5)</gadget>
<output>5</output>
<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">3 / 8</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">100 * (3/8)</gadget>
<output>75/2 = around 37.5</output>
<result>C</result> | C | 37 | Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X? | {
"A": "30 %",
"B": "33 1 / 3 %",
"C": "37 1 / 2 %",
"D": "40 %",
"E": "50 %"
} | multiply(const_100, divide(add(multiply(8, divide(30, const_100)), multiply(2, divide(30, const_100))), add(add(multiply(8, divide(30, const_100)), multiply(2, divide(30, const_100))), add(subtract(multiply(8, divide(70, const_100)), 2), multiply(2, divide(70, const_100)))))) | divide(n0,const_100)|divide(n1,const_100)|multiply(n3,#0)|multiply(n2,#0)|multiply(n2,#1)|multiply(n3,#1)|add(#2,#3)|subtract(#5,n2)|add(#4,#7)|add(#6,#8)|divide(#6,#9)|multiply(#10,const_100)| | "at the beginning , you have 8 kg of solution y , i . e . 70 % * 8 kg = 5,6 kg of water 30 % * 8 kg = 2,4 kg of x 2 kg of water evaporate : 5,6 kg - 2 kg = 3,6 kg of water 2,4 kg of x 2 kg of liquid are added : 3,6 kg + 2 * 0,70 = 5 kg of water 2,4 kg + 2 * 0,30 = 3 kg of x so you have 3 kg of x in 8 kg ( 3 + 5 ) solution . therefore x concentration is 3 / 8 = 37,5 % answer : c" | gain |
math_qa__DRbXsFfF1pFkaMks | Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 15%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now? Answers
A) $ 146.6
B) $ 120
C) $ 180
D) $ 220
E) $ 260 | <gadget id="calculator">22 * 100</gadget>
<output>2_200</output>
<gadget id="calculator">12 + 1</gadget>
<output>13</output>
<gadget id="calculator">13 * 10</gadget>
<output>130</output>
<gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">130 - 115</gadget>
<output>15</output>
<gadget id="calculator">2_200 / 15</gadget>
<output>440/3 = around 146.666667</output>
<result>A</result> | A | 146.6 | Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/12 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 15%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now? | {
"A": "$ 146.6",
"B": "$ 120",
"C": "$ 180",
"D": "$ 220",
"E": "$ 260"
} | divide(multiply(22, const_100), subtract(multiply(add(12, 1), const_10), add(const_100, 15))) | add(n0,n1)|add(n3,const_100)|multiply(n4,const_100)|multiply(#0,const_10)|subtract(#3,#1)|divide(#2,#4) | lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 12 * ( a + e ) = = > 11 a = 13 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 22 + 1.15 e = = > 11 a = 220 + 11.5 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 13 e = 220 + 11.5 e = = > 1.5 e = 220 or e = 440 / 3 = 146.6 a | general |
math_qa__hteuw0GoHBEdcJXv | The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 17-inch screen?
Choices
A) 2 B) 4 C) 16 D) 38 E) 76 | <gadget id="calculator">21 ** 2</gadget>
<output>441</output>
<gadget id="calculator">17 ** 2</gadget>
<output>289</output>
<gadget id="calculator">441 - 289</gadget>
<output>152</output>
<gadget id="calculator">152 / 2</gadget>
<output>76</output>
<result>E</result> | E | 76 | The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 21-inch screen would be how many square inches greater than the area of a square 17-inch screen? | {
"A": "2",
"B": "4",
"C": "16",
"D": "38",
"E": "76"
} | divide(subtract(power(21, const_2), power(17, const_2)), const_2) | power(n0,const_2)|power(n1,const_2)|subtract(#0,#1)|divide(#2,const_2)| | "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 21 ^ 2 / 2 - 17 ^ 2 / 2 = 152 / 2 = 76 ans e ." | geometry |
math_qa__9QwR04c5QibSTNOu | In a urban village of india named "owlna" , 80% people have refrigerator , 82% people have television , 70% people got computers and 75% got Air-conditionor. how many people(minimum) got all these luxury. Options
A) 3 % B) 8 % C) 7 % D) 10 % E) 15 % | <gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">100 - 82</gadget>
<output>18</output>
<gadget id="calculator">20 + 18</gadget>
<output>38</output>
<gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">38 + 30</gadget>
<output>68</output>
<gadget id="calculator">100 - 75</gadget>
<output>25</output>
<gadget id="calculator">68 + 25</gadget>
<output>93</output>
<gadget id="calculator">100 - 93</gadget>
<output>7</output>
<result>C</result> | C | 7 | In a urban village of india named "owlna" , 80% people have refrigerator , 82% people have television , 70% people got computers and 75% got Air-conditionor. how many people(minimum) got all these luxury. | {
"A": "3 %",
"B": "8 %",
"C": "7 %",
"D": "10 %",
"E": "15 %"
} | subtract(const_100, add(add(add(subtract(const_100, 80), subtract(const_100, 82)), subtract(const_100, 70)), subtract(const_100, 75))) | subtract(const_100,n0)|subtract(const_100,n1)|subtract(const_100,n2)|subtract(const_100,n3)|add(#0,#1)|add(#4,#2)|add(#5,#3)|subtract(const_100,#6)| | "c 7 % 100 - [ ( 100 - 80 ) + ( 100 - 82 ) + ( 100 - 70 ) + ( 100 - 75 ) ] = 100 - ( 20 + 18 + 30 + 25 ) = 100 - 93" | general |
math_qa__xaBhKCmFrUTjkqk6 | In a certain alphabet, 8 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line? Choose the most appropriate option: A) 4 B) 8 C) 14 D) 20 E) 28 | <gadget id="calculator">8 + 24</gadget>
<output>32</output>
<gadget id="calculator">40 - 32</gadget>
<output>8</output>
<result>B</result> | B | 8 | In a certain alphabet, 8 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line? | {
"A": "4",
"B": "8",
"C": "14",
"D": "20",
"E": "28"
} | subtract(40, add(8, 24)) | add(n0,n1)|subtract(n2,#0)| | "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 8 + 24 = 32 ; next , we find the total # of letters without line : 40 - 32 = 8 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 8 - 0 = 8 . b" | other |
math_qa__6lfiGXCnvZzuD6PG | If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number W of integers that can be negative? Select: A) 2 B) 3 C) 4 D) 5 E) 6 | <gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 + 0</gadget>
<output>5</output>
<result>D</result> | D | 5 | If a, b, c, d, e and f are integers and (ab + cdef) < 0, then what is the maximum number W of integers that can be negative? | {
"A": "2",
"B": "3",
"C": "4",
"D": "5",
"E": "6"
} | add(divide(const_10, const_2), 0) | divide(const_10,const_2)|add(n0,#0)| | "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see w = 5 or 1 will give you same equation . . ans d" | general |
math_qa__f6gKEG9Mt4diyPxh | rajan is sixth from the left end and vinay is tenth from the right end in a row of boys . if there are 8 boys between rajan and vinay , how many boys are there in the row ?
Select the correct option:
A) 24
B) 66
C) 88
D) 27
E) 91 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 8</gadget>
<output>14</output>
<gadget id="calculator">14 + 10</gadget>
<output>24</output>
<result>A</result> | A | 24 | rajan is sixth from the left end and vinay is tenth from the right end in a row of boys . if there are 8 boys between rajan and vinay , how many boys are there in the row ? | {
"A": "24",
"B": "66",
"C": "88",
"D": "27",
"E": "91"
} | add(add(multiply(const_3, const_2), 8), const_10) | multiply(const_2,const_3)|add(n0,#0)|add(#1,const_10) | explanation : number of boys in the row = ( 6 + 10 + 8 ) = 24 answer : a ) 24 | general |
math_qa__A7DmG9eui9ZCHhYD | Find k if 64 / k = 8. Pick:
A) 6 B) 7 C) 8 D) 4 E) 3 | <gadget id="calculator">64 / 8</gadget>
<output>8</output>
<result>C</result> | C | 8 | Find k if 64 / k = 8. | {
"A": "6",
"B": "7",
"C": "8",
"D": "4",
"E": "3"
} | divide(64, 8) | divide(n0,n1)| | "since 64 / k = 8 and 64 / 8 = 8 , then k = 8 correct answer c" | general |
math_qa__5ezPHkjDUoNThjYN | The difference of two numbers is 1097. On dividing the larger number by the smaller, we get 10 as quotient and the 17 as remainder. What is the smaller number ? Options.
A) 230
B) 120
C) 95
D) 310
E) 320 | <gadget id="calculator">1_097 + 17</gadget>
<output>1_114</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">1_114 / 9</gadget>
<output>1_114/9 = around 123.777778</output>
<result>B</result> | B | 120 | The difference of two numbers is 1097. On dividing the larger number by the smaller, we get 10 as quotient and the 17 as remainder. What is the smaller number ? | {
"A": "230",
"B": "120",
"C": "95",
"D": "310",
"E": "320"
} | divide(add(1097, 17), subtract(10, const_1)) | add(n0,n2)|subtract(n1,const_1)|divide(#0,#1)| | "solution : let the smaller number be x . then larger number = ( x + 1097 ) x + 1097 = 10 x + 17 9 x = 1080 x = 120 answer b" | general |
math_qa__8n0ZGyDfuPVLEmLg | A boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream,it takes 5 hours.What is the speed of the boat in still water ? Choose the correct choice from the following options:
A) 6 B) 7 C) 8 D) 9 E) 1 | <gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">10 + 4</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>B</result> | B | 7 | A boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream,it takes 5 hours.What is the speed of the boat in still water ? | {
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "1"
} | divide(add(divide(20, 2), divide(20, 5)), const_2) | divide(n0,n1)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2) | explanation : rate downstream = ( 20 / 2 ) kmph = 10 kmph ; rate upstream = ( 20 / 5 ) kmph = 4 kmph speed in still water = 1 / 2 ( 10 + 4 ) kmph = 7 kmph answer : b | physics |
math_qa__ufNuZZmxfkQFK9Vf | A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 4 rows or 5 rows or 6 rows, then no tree will be left. Find the least number of trees required. Choose the correct choice from the following choices
A) 30
B) 60
C) 120
D) 240
E) 480 | <gadget id="calculator">6 * 5</gadget>
<output>30</output>
<gadget id="calculator">30 * 4</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<result>B</result> | B | 60 | A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 4 rows or 5 rows or 6 rows, then no tree will be left. Find the least number of trees required. | {
"A": "30",
"B": "60",
"C": "120",
"D": "240",
"E": "480"
} | divide(multiply(multiply(6, 5), 4), const_2) | multiply(n1,n2)|multiply(n0,#0)|divide(#1,const_2)| | "the least number of trees that are required = lcm ( 4 , 5 , 6 ) = 60 . answer : b" | general |
math_qa__cq0m8WFWmXVijwRR | A and B can together finish a work in 40days. They worked together for 10days and then B left. After another 6 days, A finished the remaining work. In how many days A alone can finish the job? Choose the correct choice from the following choices: A) 10 B) 25 C) 60 D) 8 E) 20 | <gadget id="calculator">6 * 40</gadget>
<output>240</output>
<gadget id="calculator">40 - 10</gadget>
<output>30</output>
<gadget id="calculator">240 / 30</gadget>
<output>8</output>
<result>D</result> | D | 8 | A and B can together finish a work in 40days. They worked together for 10days and then B left. After another 6 days, A finished the remaining work. In how many days A alone can finish the job? | {
"A": "10",
"B": "25",
"C": "60",
"D": "8",
"E": "20"
} | divide(multiply(6, 40), subtract(40, 10)) | multiply(n0,n2)|subtract(n0,n1)|divide(#0,#1)| | "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 6 days whole work will be done by a in 6 * 4 / 3 = 8 days answer is d" | physics |
math_qa__eeenrzf1yYCjRYNT | What distance will be covered by a bus moving at 72 kmph in 30 seconds? Choose the most appropriate option
A) 877 m
B) 600 m
C) 167 m
D) 176 m
E) 546 m | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">20 * 30</gadget>
<output>600</output>
<result>B</result> | B | 600 | What distance will be covered by a bus moving at 72 kmph in 30 seconds? | {
"A": "877 m",
"B": "600 m",
"C": "167 m",
"D": "176 m",
"E": "546 m"
} | multiply(multiply(72, const_0_2778), 30) | multiply(n0,const_0_2778)|multiply(n1,#0)| | "explanation : 72 kmph = 72 * 5 / 18 = 20 mps d = speed * time = 20 * 30 = 600 m . answer : b" | physics |
math_qa__2Vxgk3nDrX3hyzVn | A rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered.If the area of the field is 600 sq.ft, how many feet of fencing will be required ? Options:
A) 130 feet
B) 22 feet
C) 20 feet
D) 15 feet
E) 10 feet | <gadget id="calculator">600 / 10</gadget>
<output>60</output>
<gadget id="calculator">60 * 2</gadget>
<output>120</output>
<gadget id="calculator">120 + 10</gadget>
<output>130</output>
<result>A</result> | A | 130 | A rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered.If the area of the field is 600 sq.ft, how many feet of fencing will be required ? | {
"A": "130 feet",
"B": "22 feet",
"C": "20 feet",
"D": "15 feet",
"E": "10 feet"
} | add(multiply(divide(600, 10), const_2), 10) | divide(n1,n0)|multiply(#0,const_2)|add(n0,#1)| | "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 10 * breadth = 600 = > breadth = 60 feet area to be fenced = 2 b + l = 2 * 60 + 10 = 130 feet answer : option a" | geometry |
math_qa__cAaCnF4qZ33XeXiO | Find the greatest number which leaves the same remainder when it divides 20, 40 and 90. Choose one: A) 18 B) 8 C) 12 D) 10 E) none of these | <gadget id="calculator">40 - 20</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>D</result> | D | 10 | Find the greatest number which leaves the same remainder when it divides 20, 40 and 90. | {
"A": "18",
"B": "8",
"C": "12",
"D": "10",
"E": "none of these"
} | divide(subtract(40, 20), const_2) | subtract(n1,n0)|divide(#0,const_2)| | "90 - 40 = 50 40 - 20 = 20 90 - 20 = 70 the h . c . f of 20 , 50 and 70 is 10 . answer : d" | general |
math_qa__4xsK3FownfR8LxcU | A bag contains 2 white marbles and 2 black marbles. If each of 2 girls and 2 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble? Choose one: A) 1 / 35 B) 1 / 10 C) 1 / 3 D) 1 / 4 E) 1 / 5 | <gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">binomial(4, 2)</gadget>
<output>6</output>
<gadget id="calculator">2 / 6</gadget>
<output>1/3 = around 0.333333</output>
<result>C</result> | C | 0.333333 | A bag contains 2 white marbles and 2 black marbles. If each of 2 girls and 2 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble? | {
"A": "1 / 35",
"B": "1 / 10",
"C": "1 / 3",
"D": "1 / 4",
"E": "1 / 5"
} | divide(const_2, choose(add(2, 2), 2)) | add(n0,n0)|choose(#0,n0)|divide(const_2,#1)| | "first , total ways to select for all boys and girls , i . e 4 ! / ( 2 ! * 2 ! ) = 4 * 3 * 2 * 1 / 2 * 1 * 2 * 1 = 6 then there are one two way girls can have all same colors , either white or black . the number of ways in which 2 girls can select 2 white balls = 2 c 2 = 1 the number of ways in which 2 girls can select 2 black balls = 2 c 2 = 1 therefore , total favorable outcomes / total outcomes = 2 / 6 = 1 / 3 c" | probability |
math_qa__NrHC1jo2GKF1CDAa | Matt and Peter can do together a piece of work in 20 days. After they have worked together for 10 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately.
Choose the correct answer.
A) 21 B) 20 C) 22 D) 23 E) 24 | <gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">10 * (1/20)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">10 / (1/2)</gadget>
<output>20</output>
<result>B</result> | B | 20 | Matt and Peter can do together a piece of work in 20 days. After they have worked together for 10 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately. | {
"A": "21",
"B": "20",
"C": "22",
"D": "23",
"E": "24"
} | divide(10, subtract(const_1, multiply(10, divide(const_1, 20)))) | divide(const_1,n0)|multiply(n1,#0)|subtract(const_1,#1)|divide(n2,#2)| | "together they complete the job in 20 days means they complete 10 / 20 of the job after 10 days . peter completes the remaining ( 10 / 20 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 10 < = > x = 10 / ( 10 / 20 ) = 20 b" | physics |
math_qa__yjLMjo2sc8AYZoed | A grocer has a sale of Rs. 7435, Rs. 7927, Rs. 7855, Rs. 8230 and Rs. 7562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7500? Options
A) rs . 1991 B) rs . 2991 C) rs . 3991 D) rs . 4991 E) rs . 5991 | <gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 7_500</gadget>
<output>45_000</output>
<gadget id="calculator">7_435 + 7_927</gadget>
<output>15_362</output>
<gadget id="calculator">15_362 + 7_855</gadget>
<output>23_217</output>
<gadget id="calculator">23_217 + 8_230</gadget>
<output>31_447</output>
<gadget id="calculator">31_447 + 7_562</gadget>
<output>39_009</output>
<gadget id="calculator">45_000 - 39_009</gadget>
<output>5_991</output>
<result>E</result> | E | 5,991 | A grocer has a sale of Rs. 7435, Rs. 7927, Rs. 7855, Rs. 8230 and Rs. 7562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7500? | {
"A": "rs . 1991",
"B": "rs . 2991",
"C": "rs . 3991",
"D": "rs . 4991",
"E": "rs . 5991"
} | subtract(multiply(add(5, const_1), 7500), add(add(add(add(7435, 7927), 7855), 8230), 7562)) | add(n5,const_1)|add(n0,n1)|add(n2,#1)|multiply(n6,#0)|add(n3,#2)|add(n4,#4)|subtract(#3,#5)| | "explanation : total sale for 5 months = rs . ( 7435 + 7927 + 7855 + 8230 + 7562 ) = rs . 39009 . required sale = rs . [ ( 7500 x 6 ) â € “ 39009 ] = rs . ( 45000 â € “ 39009 ) = rs . 5991 . answer e" | general |
math_qa__7t10ozZfhsJ8XDIK | An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 2 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?
Choose the correct answer: A) 7 : 5 B) 12 : 11 C) 17 : 15 D) 22 : 17 E) 27 : 25 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">2 * (3 + 2)</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">5 / 3</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(5/3) * 2</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">(5/3) * (10/3)</gadget>
<output>50/9 = around 5.555556</output>
<gadget id="calculator">6 / (50/9)</gadget>
<output>27/25 = around 1.08</output>
<result>E</result> | E | 1.08 | An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 2 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets? | {
"A": "7 : 5",
"B": "12 : 11",
"C": "17 : 15",
"D": "22 : 17",
"E": "27 : 25"
} | divide(rectangle_area(3, 2), rectangle_area(divide(divide(rectangle_perimeter(3, 2), 2), add(2, 1)), multiply(divide(divide(rectangle_perimeter(3, 2), 2), add(2, 1)), 2))) | add(n2,n3)|rectangle_area(n0,n1)|rectangle_perimeter(n0,n1)|divide(#2,n1)|divide(#3,#0)|multiply(n2,#4)|rectangle_area(#4,#5)|divide(#1,#6)| | "let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 2 y and y . 2 ( 3 x + 2 x ) = 2 ( 2 y + y ) 5 x = 3 y ( 5 / 3 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 2 y * y = 6 x ^ 2 : 2 y ^ 2 = 6 x ^ 2 : 2 * ( 25 / 9 ) * x ^ 2 = 54 : 50 = 27 : 25 the answer is e ." | geometry |
math_qa__FUHYKW0E6EbDd75g | mixture contains alcohol and water in the ratio 4 : 3. If 6 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture. Choose the correct choice from the following answers:
A) 10 B) 6.8 C) 27 D) 22 E) 29 | <gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">24 - 12</gadget>
<output>12</output>
<gadget id="calculator">20 / 12</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(5/3) * 4</gadget>
<output>20/3 = around 6.666667</output>
<result>B</result> | B | 6.8 | mixture contains alcohol and water in the ratio 4 : 3. If 6 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture. | {
"A": "10",
"B": "6.8",
"C": "27",
"D": "22",
"E": "29"
} | multiply(divide(multiply(4, 5), subtract(multiply(6, 4), multiply(3, 4))), 4) | multiply(n0,n4)|multiply(n0,n2)|multiply(n0,n1)|subtract(#1,#2)|divide(#0,#3)|multiply(n0,#4)| | "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 24 x = 4 ( 3 x + 5 ) 12 x = 20 x = 1.7 quantity of alcohol = ( 4 x 1.7 ) litres = 6.8 litres . answer : b" | general |
math_qa__gw09NvVVQLDyf8V7 | A cistern is filled by pipe A in 8 hours and the full cistern can be leaked out by an exhaust pipe B in 12 hours. If both the pipes are opened, in what time the cistern is full? Choose the correct answer.
A) 24 hrs B) 60 hrs C) 70 hrs D) 80 hrs E) 90 hrs | <gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/8) - (1/12)</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">1 / (1/24)</gadget>
<output>24</output>
<result>A</result> | A | 24 | A cistern is filled by pipe A in 8 hours and the full cistern can be leaked out by an exhaust pipe B in 12 hours. If both the pipes are opened, in what time the cistern is full? | {
"A": "24 hrs",
"B": "60 hrs",
"C": "70 hrs",
"D": "80 hrs",
"E": "90 hrs"
} | divide(const_1, subtract(divide(const_1, 8), divide(const_1, 12))) | divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2) | time taken to full the cistern = ( 1 / 8 - 1 / 12 ) hrs = 1 / 24 = 24 hrs answer : a | physics |
math_qa__QrpbCh4Vp7DmcZNs | When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 86.12, what is the value of y? Pick one.
A) 96 B) 87 C) 75 D) 25 E) 12 | <gadget id="calculator">floor(86.12)</gadget>
<output>86</output>
<gadget id="calculator">86.12 - 86</gadget>
<output>0.12</output>
<gadget id="calculator">9 / 0.12</gadget>
<output>75</output>
<result>C</result> | C | 75 | When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 86.12, what is the value of y? | {
"A": "96",
"B": "87",
"C": "75",
"D": "25",
"E": "12"
} | divide(9, subtract(86.12, floor(86.12))) | floor(n1)|subtract(n1,#0)|divide(n0,#1)| | "by the definition of a remainder , the remainder here is equal to 9 / y . the remainder in decimal form is given as . 12 therefore , 9 / y = . 12 solve for y and get 75 . c" | general |
math_qa__rvThZu69sdwZ68ey | A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 57.76, the number of the member is the group is: Choices
A) 57
B) 76
C) 77
D) 87
E) 97 | <gadget id="calculator">57.76 * 100</gadget>
<output>5_776</output>
<gadget id="calculator">5_776 ** (1/2)</gadget>
<output>76</output>
<result>B</result> | B | 76 | A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 57.76, the number of the member is the group is: | {
"A": "57",
"B": "76",
"C": "77",
"D": "87",
"E": "97"
} | sqrt(multiply(57.76, const_100)) | multiply(n0,const_100)|sqrt(#0)| | "money collected = ( 57.76 x 100 ) paise = 5776 paise numbers of members = 5776 squareroot = 76 answer b" | general |
math_qa__ThozQ8KpEcbOGBcW | How many cubes of edge 2 dm can be cut out of a meter cube? Choose one.
A) 296 B) 289 C) 270 D) 125 E) 278 | <gadget id="calculator">10 ** 3</gadget>
<output>1_000</output>
<gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">1_000 / 8</gadget>
<output>125</output>
<result>D</result> | D | 125 | How many cubes of edge 2 dm can be cut out of a meter cube? | {
"A": "296",
"B": "289",
"C": "270",
"D": "125",
"E": "278"
} | divide(volume_cube(const_10), volume_cube(2)) | volume_cube(const_10)|volume_cube(n0)|divide(#0,#1) | 1 * 1 * 1 = 2 / 10 * 2 / 10 * 2 / 10 * x x = 125 answer : d | geometry |
math_qa__xnzbTdzUMdr1iIhy | Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Choices
A) 59 m B) 60 m C) 80 m D) 82 m E) 84 m | <gadget id="calculator">5_300 / 26.5</gadget>
<output>200</output>
<gadget id="calculator">2 * 20</gadget>
<output>40</output>
<gadget id="calculator">200 + 40</gadget>
<output>240</output>
<gadget id="calculator">240 / 4</gadget>
<output>60</output>
<result>A</result> | A | 59 | Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr? | {
"A": "59 m",
"B": "60 m",
"C": "80 m",
"D": "82 m",
"E": "84 m"
} | divide(add(divide(5300, 26.50), multiply(const_2, 20)), const_4) | divide(n2,n1)|multiply(n0,const_2)|add(#0,#1)|divide(#2,const_4)| | "let breadth = x metres . then , length = ( x + 18 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 18 ) + x ] = 200 2 x + 18 = 100 2 x = 82 x = 41 . hence , length = x + 18 = 59 m a" | physics |
math_qa__LPqh1KGyDLP3HCy0 | A cistern is filled by pipe A in 16 hours and the full cistern can be leaked out by an exhaust pipe B in 20 hours. If both the pipes are opened, in what time the cistern is full? Pick one.
A) 50 hrs
B) 60 hrs
C) 70 hrs
D) 80 hrs
E) 90 hrs | <gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/16) - (1/20)</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">1 / (1/80)</gadget>
<output>80</output>
<result>D</result> | D | 80 | A cistern is filled by pipe A in 16 hours and the full cistern can be leaked out by an exhaust pipe B in 20 hours. If both the pipes are opened, in what time the cistern is full? | {
"A": "50 hrs",
"B": "60 hrs",
"C": "70 hrs",
"D": "80 hrs",
"E": "90 hrs"
} | divide(const_1, subtract(divide(const_1, 16), divide(const_1, 20))) | divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)| | "time taken to full the cistern = ( 1 / 16 - 1 / 20 ) hrs = 1 / 80 = 80 hrs answer : d" | physics |
math_qa__np95AuLXQmnwMy89 | Village X has a population of 76000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal? Choose the correct choice from the following.
A) 15 B) 17 C) 11 D) 18 E) 13 | <gadget id="calculator">76_000 - 42_000</gadget>
<output>34_000</output>
<gadget id="calculator">800 + 1_200</gadget>
<output>2_000</output>
<gadget id="calculator">34_000 / 2_000</gadget>
<output>17</output>
<result>B</result> | B | 17 | Village X has a population of 76000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal? | {
"A": "15",
"B": "17",
"C": "11",
"D": "18",
"E": "13"
} | divide(subtract(76000, 42000), add(800, 1200)) | add(n1,n3)|subtract(n0,n2)|divide(#1,#0)| | "let the population of two villages be equal after p years then , 76000 - 1200 p = 42000 + 800 p 2000 p = 34000 p = 17 answer is b ." | general |
math_qa__vbZn5zrIY411E5D8 | Average of 10 matches is 34, How many runs one should should score to increase his average by 5 runs. Answers
A) 70 B) 76 C) 78 D) 89 E) 88 | <gadget id="calculator">34 + 5</gadget>
<output>39</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">39 * 11</gadget>
<output>429</output>
<gadget id="calculator">10 * 34</gadget>
<output>340</output>
<gadget id="calculator">429 - 340</gadget>
<output>89</output>
<result>D</result> | D | 89 | Average of 10 matches is 34, How many runs one should should score to increase his average by 5 runs. | {
"A": "70",
"B": "76",
"C": "78",
"D": "89",
"E": "88"
} | subtract(multiply(add(34, 5), add(10, const_1)), multiply(10, 34)) | add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | "explanation : average after 11 innings should be 39 so , required score = ( 11 * 39 ) - ( 10 * 34 ) = 429 - 340 = 89 answer : option d" | general |
math_qa__1DQk9FeEE3GxSvNM | Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it ? Choose the correct choice from the following answers.
A) 110 hours
B) 112 hours
C) 115 hours
D) 100 hours
E) none of these | <gadget id="calculator">14 * 16</gadget>
<output>224</output>
<gadget id="calculator">224 / 2</gadget>
<output>112</output>
<gadget id="calculator">14 + 16</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">15 * 8</gadget>
<output>120</output>
<gadget id="calculator">120 - 112</gadget>
<output>8</output>
<gadget id="calculator">112 * 8</gadget>
<output>896</output>
<gadget id="calculator">896 / 8</gadget>
<output>112</output>
<result>B</result> | B | 112 | Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it ? | {
"A": "110 hours",
"B": "112 hours",
"C": "115 hours",
"D": "100 hours",
"E": "none of these"
} | divide(multiply(divide(multiply(14, 16), const_2), subtract(multiply(divide(add(14, 16), const_2), divide(16, const_2)), divide(multiply(14, 16), const_2))), subtract(multiply(divide(add(14, 16), const_2), divide(16, const_2)), divide(multiply(14, 16), const_2))) | add(n0,n1)|divide(n1,const_2)|multiply(n0,n1)|divide(#2,const_2)|divide(#0,const_2)|multiply(#4,#1)|subtract(#5,#3)|multiply(#3,#6)|divide(#7,#6) | cistern filled by both pipes in one hour = 1 ⁄ 14 + 1 ⁄ 16 = 15 ⁄ 112 th ∴ both pipes filled the cistern in 112 ⁄ 15 hrs . now , due to leakage both pipes filled the cistern in 112 ⁄ 15 + 32 ⁄ 60 = 8 hrs . ∴ due to leakage , filled part in one hour 1 ⁄ 8 ∴ part of cistern emptied , due to leakage in one hour = 15 ⁄ 112 - 1 ⁄ 8 = 1 ⁄ 112 th ∴ in 112 hr , the leakage would empty the cistern . answer b | physics |
math_qa__Ft5bq9r46an6GcVP | The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %? Options:
A) 18 B) 16 C) 26 D) 17 E) 11 | <gadget id="calculator">1_500 - 1_110</gadget>
<output>390</output>
<gadget id="calculator">390 / 1_500</gadget>
<output>13/50 = around 0.26</output>
<gadget id="calculator">(13/50) * 100</gadget>
<output>26</output>
<result>C</result> | C | 26 | The cost price of a radio is Rs.1500 and it was sold for Rs.1110, find the loss %? | {
"A": "18",
"B": "16",
"C": "26",
"D": "17",
"E": "11"
} | multiply(divide(subtract(1500, 1110), 1500), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100) | explanation : 1500 - - - - 390 100 - - - - ? = > 26 % answer : c | gain |
math_qa__a62RWZwFQWrwbjau | A restaurant spends one quarter of its monthly budget for rent and quarter of the rest for food and beverages. What percentage of the budget does the restaurant spend for food and beverages? Pick one.
A) 23.5 % B) 32.5 % C) 35 % D) 18.75 % E) 20 % | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * (1/4)</gadget>
<output>3/16 = around 0.1875</output>
<gadget id="calculator">(3/16) * 100</gadget>
<output>75/4 = around 18.75</output>
<result>D</result> | D | 18.75 | A restaurant spends one quarter of its monthly budget for rent and quarter of the rest for food and beverages. What percentage of the budget does the restaurant spend for food and beverages? | {
"A": "23.5 %",
"B": "32.5 %",
"C": "35 %",
"D": "18.75 %",
"E": "20 %"
} | multiply(multiply(subtract(const_1, divide(const_1, const_4)), divide(const_1, const_4)), const_100) | divide(const_1,const_4)|subtract(const_1,#0)|multiply(#0,#1)|multiply(#2,const_100) | spend on rent = 1 / 4 spend on food and beverage = 1 / 4 of remaining = 1 / 4 * 3 / 4 = 3 / 16 so 3 / 16 = 18.75 % d is the answer | gain |
math_qa__Mntw6JN0UrBOcOKb | A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase? Pick:
A) 10 %
B) 12 %
C) 14 %
D) 16 %
E) 18 % | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(11/10) * (4/5)</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">1 - (22/25)</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) * 100</gadget>
<output>12</output>
<result>B</result> | B | 12 | A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 10% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase? | {
"A": "10 %",
"B": "12 %",
"C": "14 %",
"D": "16 %",
"E": "18 %"
} | multiply(subtract(const_1, multiply(add(divide(10, const_100), const_1), divide(80, const_100))), const_100) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|multiply(#2,#1)|subtract(const_1,#3)|multiply(#4,const_100)| | "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.8 ( 1.1 x ) = 0.88 x . the difference is 12 % . the answer is b ." | general |
math_qa__gt1elDZfpYfOKKIe | of 3 numbers , the third is twice the second and the second is 4 times the first . if their average is 78 , the smallest of the 3 numbers is : Choose the correct choice from the following options
A) 18 B) 19 C) 20 D) 21 E) 22 | <gadget id="calculator">78 * 3</gadget>
<output>234</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 1</gadget>
<output>13</output>
<gadget id="calculator">234 / 13</gadget>
<output>18</output>
<result>A</result> | A | 18 | of 3 numbers , the third is twice the second and the second is 4 times the first . if their average is 78 , the smallest of the 3 numbers is : | {
"A": "18",
"B": "19",
"C": "20",
"D": "21",
"E": "22"
} | divide(multiply(78, 3), add(add(multiply(4, const_2), 4), const_1)) | multiply(n0,n2)|multiply(n1,const_2)|add(n1,#1)|add(#2,const_1)|divide(#0,#3) | explanation : let first number be x . so , 2 nd no . = 4 x & 3 rd no . = 8 x . so , x + 4 x + 8 x = 78 × 3 = 234 . 13 x = 234 x = 234 / 13 hence , smallest number x = 18 . answer : a | general |
math_qa__QetxxmdTZQr8dmfc | In what time will a train 55 m long cross an electric pole, it its speed be 36 km/hr? Answers.
A) 5.5 B) 4.5 C) 3.5 D) 2.5 E) 1.5 | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">55 / 10</gadget>
<output>11/2 = around 5.5</output>
<result>A</result> | A | 5.5 | In what time will a train 55 m long cross an electric pole, it its speed be 36 km/hr? | {
"A": "5.5",
"B": "4.5",
"C": "3.5",
"D": "2.5",
"E": "1.5"
} | divide(55, multiply(36, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | "speed = 36 * 5 / 18 = 10 m / sec time taken = 55 / 10 = 5.5 sec . answer : a" | physics |
math_qa__g3Td7b1Nsw0CqO11 | A leak in the bottom of a tank can empty the tank in 6 hrs. An pipe fills water at the rate of 4 ltrs/ minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hrs. The capacity of the tank is?
Select the correct option
A) 2345
B) 2350
C) 2457
D) 4657
E) 5760 | <gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">24 * 60</gadget>
<output>1_440</output>
<gadget id="calculator">1_440 * 4</gadget>
<output>5_760</output>
<result>E</result> | E | 5,760 | A leak in the bottom of a tank can empty the tank in 6 hrs. An pipe fills water at the rate of 4 ltrs/ minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hrs. The capacity of the tank is? | {
"A": "2345",
"B": "2350",
"C": "2457",
"D": "4657",
"E": "5760"
} | multiply(multiply(multiply(6, 4), const_60), 4) | multiply(n0,n1)|multiply(#0,const_60)|multiply(n1,#1)| | "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 4 = 5760 e" | physics |
math_qa__Lynb9XtsuL9WtTpk | A train is moving at 6/7 of its usual speed. The train is 10 minutes too late. What is the usual time (in hours) for the train to complete the journey? Choose the correct option: A) 0.5 B) 1 C) 1.5 D) 2 E) 2.5 | <gadget id="calculator">6 / 7</gadget>
<output>6/7 = around 0.857143</output>
<gadget id="calculator">10 * (6/7)</gadget>
<output>60/7 = around 8.571429</output>
<gadget id="calculator">1 - (6/7)</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">1 / (1/7)</gadget>
<output>7</output>
<gadget id="calculator">(60/7) * 7</gadget>
<output>60</output>
<gadget id="calculator">60 / 60</gadget>
<output>1</output>
<result>B</result> | B | 1 | A train is moving at 6/7 of its usual speed. The train is 10 minutes too late. What is the usual time (in hours) for the train to complete the journey? | {
"A": "0.5",
"B": "1",
"C": "1.5",
"D": "2",
"E": "2.5"
} | divide(multiply(multiply(10, divide(6, 7)), inverse(subtract(const_1, divide(6, 7)))), const_60) | divide(n0,n1)|multiply(n2,#0)|subtract(const_1,#0)|inverse(#2)|multiply(#3,#1)|divide(#4,const_60)| | "new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 10 minutes represents 1 / 6 of the usual time . the usual time is 1 hour . the answer is b ." | physics |
math_qa__c2GbWHRFxL61xvBv | A bag contains 6 green balls and 8 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour?
Choose the correct option:
A) 5 / 14
B) 8 / 21
C) 12 / 21
D) 43 / 91
E) 47 / 91 | <gadget id="calculator">6 + 8</gadget>
<output>14</output>
<gadget id="calculator">8 / 14</gadget>
<output>4/7 = around 0.571429</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">14 - 1</gadget>
<output>13</output>
<gadget id="calculator">7 / 13</gadget>
<output>7/13 = around 0.538462</output>
<gadget id="calculator">(4/7) * (7/13)</gadget>
<output>4/13 = around 0.307692</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">5 / 13</gadget>
<output>5/13 = around 0.384615</output>
<gadget id="calculator">6 / 14</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(5/13) * (3/7)</gadget>
<output>15/91 = around 0.164835</output>
<gadget id="calculator">(4/13) + (15/91)</gadget>
<output>43/91 = around 0.472527</output>
<result>D</result> | D | 0.472527 | A bag contains 6 green balls and 8 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour? | {
"A": "5 / 14",
"B": "8 / 21",
"C": "12 / 21",
"D": "43 / 91",
"E": "47 / 91"
} | add(multiply(divide(8, add(6, 8)), divide(subtract(8, const_1), subtract(add(6, 8), const_1))), multiply(divide(subtract(6, const_1), subtract(add(6, 8), const_1)), divide(6, add(6, 8)))) | add(n0,n1)|subtract(n1,const_1)|subtract(n0,const_1)|divide(n1,#0)|divide(n0,#0)|subtract(#0,const_1)|divide(#1,#5)|divide(#2,#5)|multiply(#3,#6)|multiply(#7,#4)|add(#8,#9) | the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 6 c 2 = 15 the number of ways to draw two white balls is 8 c 2 = 28 p ( two balls of the same colour ) = 43 / 91 the answer is d . | other |
math_qa__7zSQAcY9WUEARGdq | A snooker tournament charges $40.00 for VIP seats and $10.00 for general admission (“regular” seats). On a certain night, a total of 320 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats? Options.
A) 190 B) 180 C) 170 D) 160 E) 148 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 1_000</gadget>
<output>7_000</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">7_000 + 500</gadget>
<output>7_500</output>
<gadget id="calculator">320 * 10</gadget>
<output>3_200</output>
<gadget id="calculator">7_500 - 3_200</gadget>
<output>4_300</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">4_300 / 25</gadget>
<output>172</output>
<gadget id="calculator">320 - 172</gadget>
<output>148</output>
<result>E</result> | E | 148 | A snooker tournament charges $40.00 for VIP seats and $10.00 for general admission (“regular” seats). On a certain night, a total of 320 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats? | {
"A": "190",
"B": "180",
"C": "170",
"D": "160",
"E": "148"
} | subtract(320, divide(subtract(add(multiply(add(const_3, const_4), const_1000), multiply(add(const_2, const_3), const_100)), multiply(320, 10.00)), multiply(add(const_2, const_3), add(const_2, const_3)))) | add(const_3,const_4)|add(const_2,const_3)|multiply(n1,n2)|multiply(#0,const_1000)|multiply(#1,const_100)|multiply(#1,#1)|add(#3,#4)|subtract(#6,#2)|divide(#7,#5)|subtract(n2,#8) | let no of sits in vip enclosure is x then x * 40 + 10 ( 320 - x ) = 7500 or 25 x = 7500 - 3200 , x = 4300 / 25 = 172 vip = 172 general = 320 - 172 = 148 e | geometry |
math_qa__B8vfe1b5p4pUFVa0 | Naomi drives to the beauty parlor in 60 minutes. On the way back, her average speed is half the average speed as it was to the way to the parlor. How much time will it take Naomi to travel two round trips to the beauty parlor? Choose the correct choice from the following choices
A) 3 hours .
B) 4 hours .
C) 4 hours and 20 minutes .
D) 5 hours and 50 minutes
E) 6 hours . | <gadget id="calculator">60 / 10</gadget>
<output>6</output>
<result>E</result> | E | 6 | Naomi drives to the beauty parlor in 60 minutes. On the way back, her average speed is half the average speed as it was to the way to the parlor. How much time will it take Naomi to travel two round trips to the beauty parlor? | {
"A": "3 hours .",
"B": "4 hours .",
"C": "4 hours and 20 minutes .",
"D": "5 hours and 50 minutes",
"E": "6 hours ."
} | divide(60, const_10) | divide(n0,const_10) | s 1 = 2 s 2 since , speed is inversely proportional to time we have , s 1 / s 2 = 2 / 1 = t 2 / t 1 therefore , the time taken for one trip = 60 + 120 = 180 minutes total = 180 * 2 = 360 minutes = 6 hours answer : e | general |
math_qa__xZnCLyOENeOVTuc8 | The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is? Pick: A) 40 m 2 B) 45 m 2 C) 49 m 2 D) 51 m 2 E) 55 m 2 | <gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 2</gadget>
<output>22</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">144 * (22/7)</gadget>
<output>3_168/7 = around 452.571429</output>
<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">39 / 360</gadget>
<output>13/120 = around 0.108333</output>
<gadget id="calculator">(3_168/7) * (13/120)</gadget>
<output>1_716/35 = around 49.028571</output>
<result>C</result> | C | 49 | The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is? | {
"A": "40 m 2",
"B": "45 m 2",
"C": "49 m 2",
"D": "51 m 2",
"E": "55 m 2"
} | multiply(multiply(power(12, const_2), divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), divide(39, divide(const_3600, const_10))) | add(const_3,const_4)|divide(const_3600,const_10)|multiply(const_10,const_2)|power(n0,const_2)|add(#2,const_2)|divide(n1,#1)|divide(#4,#0)|multiply(#6,#3)|multiply(#5,#7)| | "39 / 360 * 22 / 7 * 12 * 12 = 49 m 2 answer : c" | geometry |
math_qa__6UkrNavW5jSj59ZI | The radius of the wheel of a bus is 175 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is Choose the correct answer
A) 100 B) 250 C) 300 D) 330 E) none of these | <gadget id="calculator">1_000 * 66</gadget>
<output>66_000</output>
<gadget id="calculator">100 * 66_000</gadget>
<output>6_600_000</output>
<gadget id="calculator">60 * 1</gadget>
<output>60</output>
<gadget id="calculator">6_600_000 / 60</gadget>
<output>110_000</output>
<gadget id="calculator">2 * 175</gadget>
<output>350</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">2 + 12</gadget>
<output>14</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">2 + 8</gadget>
<output>10</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">3 + (7/50)</gadget>
<output>157/50 = around 3.14</output>
<gadget id="calculator">350 * (157/50)</gadget>
<output>1_099</output>
<gadget id="calculator">110_000 / 1_099</gadget>
<output>110_000/1_099 = around 100.090992</output>
<result>A</result> | A | 100 | The radius of the wheel of a bus is 175 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is | {
"A": "100",
"B": "250",
"C": "300",
"D": "330",
"E": "none of these"
} | divide(divide(multiply(const_100, multiply(const_1000, 66)), multiply(const_60, const_1)), multiply(multiply(const_2, 175), add(const_3, divide(add(const_2, multiply(const_3, const_4)), power(add(const_2, multiply(const_4, const_2)), const_2))))) | multiply(n1,const_1000)|multiply(const_1,const_60)|multiply(const_3,const_4)|multiply(const_2,const_4)|multiply(n0,const_2)|add(#2,const_2)|add(#3,const_2)|multiply(#0,const_100)|divide(#7,#1)|power(#6,const_2)|divide(#5,#9)|add(#10,const_3)|multiply(#11,#4)|divide(#8,#12)| | "radius of the wheel of bus = 175 cm . then , circumference of wheel = 2 ï € r = 350 ï € = 1100 cm distance covered by bus in 1 minute = 66 â „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 1100 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 1100 = 100 answer a" | physics |
math_qa__wL5qKGeSKhVhtO8p | How many seconds does Sandy take to cover a distance of 500 meters, if Sandy runs at a speed of 15 km/hr?
Choose the correct answer:
A) 100 B) 120 C) 140 D) 160 E) 180 | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">15 * (5/18)</gadget>
<output>25/6 = around 4.166667</output>
<gadget id="calculator">500 / (25/6)</gadget>
<output>120</output>
<result>B</result> | B | 120 | How many seconds does Sandy take to cover a distance of 500 meters, if Sandy runs at a speed of 15 km/hr? | {
"A": "100",
"B": "120",
"C": "140",
"D": "160",
"E": "180"
} | divide(500, multiply(15, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | "15 km / hr = 15000 m / 3600 s = ( 150 / 36 ) m / s = ( 25 / 6 ) m / s time = 500 / ( 25 / 6 ) = 120 seconds the answer is b ." | physics |
math_qa__NRXWkOqqkliFmmIy | The compound ratio of 5:7, 3:2 and 4:5? Choose the correct answer.
A) 1 : 7 B) 6 : 5 C) 6 : 7 D) 4 : 7 E) 6 : 9 | <gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">15 / 14</gadget>
<output>15/14 = around 1.071429</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(15/14) / (6/5)</gadget>
<output>25/28 = around 0.892857</output>
<result>C</result> | C | 0.857143 | The compound ratio of 5:7, 3:2 and 4:5? | {
"A": "1 : 7",
"B": "6 : 5",
"C": "6 : 7",
"D": "4 : 7",
"E": "6 : 9"
} | divide(divide(multiply(5, 3), multiply(7, 2)), divide(multiply(3, 4), multiply(2, 5))) | multiply(n0,n2)|multiply(n1,n3)|multiply(n2,n4)|multiply(n3,n5)|divide(#0,#1)|divide(#2,#3)|divide(#4,#5)| | "5 / 7 * 3 / 2 * 4 / 5 = 6 / 7 6 : 7 answer : c" | other |
math_qa__x6Zu5onqUFm00Xow | In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars? Choices: A) 320 $ B) 380 $ C) 420 $ D) 450 $ E) 480 $ | <gadget id="calculator">0.65 * 55</gadget>
<output>35.75</output>
<gadget id="calculator">35.75 * 12</gadget>
<output>429</output>
<result>D</result> | D | 450 | In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars? | {
"A": "320 $",
"B": "380 $",
"C": "420 $",
"D": "450 $",
"E": "480 $"
} | multiply(multiply(0.65, 55), 12) | multiply(n1,n3)|multiply(n2,#0)| | "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 55 ) = 21 + 429 = > 450 hence answer will be ( d ) 450" | general |
math_qa__ewxS8NRAObt6kIpl | The ratio of the incomes of Rajan and Balan is 7:6 and the ratio of their expenditure is 6:5. If at the end of the year, each saves $1000 then the income of Rajan is? Answers
A) $ 7600 B) $ 7000 C) $ 8000 D) $ 9000 E) $ 5000 | <gadget id="calculator">7 / 6</gadget>
<output>7/6 = around 1.166667</output>
<gadget id="calculator">(7/6) * 1_000</gadget>
<output>3_500/3 = around 1_166.666667</output>
<gadget id="calculator">1_000 - (3_500/3)</gadget>
<output>-500/3 = around -166.666667</output>
<gadget id="calculator">6 / 5</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(7/6) - (6/5)</gadget>
<output>-1/30 = around -0.033333</output>
<gadget id="calculator">(-500/3) / (-1/30)</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 + 1_000</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 * 7</gadget>
<output>42_000</output>
<gadget id="calculator">42_000 / 6</gadget>
<output>7_000</output>
<result>B</result> | B | 7,000 | The ratio of the incomes of Rajan and Balan is 7:6 and the ratio of their expenditure is 6:5. If at the end of the year, each saves $1000 then the income of Rajan is? | {
"A": "$ 7600",
"B": "$ 7000",
"C": "$ 8000",
"D": "$ 9000",
"E": "$ 5000"
} | divide(multiply(add(divide(subtract(1000, multiply(divide(7, 6), 1000)), subtract(divide(7, 6), divide(6, 5))), 1000), 7), 6) | divide(n0,n1)|divide(n1,n3)|multiply(n4,#0)|subtract(#0,#1)|subtract(n4,#2)|divide(#4,#3)|add(n4,#5)|multiply(n0,#6)|divide(#7,n1) | let the income of rajan and balan be $ 7 x and $ 6 x let their expenditures be $ 6 y and $ 5 y 7 x - 6 y = 1000 - - - - - - - 1 ) 6 x - 5 y = 1000 - - - - - - - 2 ) from 1 ) and 2 ) x = 1000 rajan ' s income = 7 x = 7 * 1000 = $ 7000 answer is b | other |
math_qa__OfmcFsqoWfOHfiMR | Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 12 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel? Answers:
A) 54 B) 66 C) 80 D) 36 E) 96 | <gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">18 / 6</gadget>
<output>3</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<result>D</result> | D | 36 | Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 12 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel? | {
"A": "54",
"B": "66",
"C": "80",
"D": "36",
"E": "96"
} | multiply(12, divide(divide(36, const_2), 6)) | divide(n1,const_2)|divide(#0,n0)|multiply(n2,#1) | d 36 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 12 mph = 36 miles | physics |
math_qa__JJmZ9hynIwg6rwyv | A 300 meter long train crosses a platform in 51 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? Pick: A) 550 B) 289 C) 350 D) 882 E) 281 | <gadget id="calculator">300 / 18</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 51</gadget>
<output>850</output>
<gadget id="calculator">850 - 300</gadget>
<output>550</output>
<result>A</result> | A | 550 | A 300 meter long train crosses a platform in 51 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? | {
"A": "550",
"B": "289",
"C": "350",
"D": "882",
"E": "281"
} | subtract(multiply(divide(300, 18), 51), 300) | divide(n0,n2)|multiply(n1,#0)|subtract(#1,n0)| | "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 51 = 50 / 3 3 ( x + 300 ) = 2550 è x = 550 m . answer : a" | physics |
math_qa__HAoBniL5VDEuLYOS | A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be: Choose the correct choice.
A) 43
B) 26
C) 33
D) 21
E) 28 | <gadget id="calculator">48 * 4</gadget>
<output>192</output>
<gadget id="calculator">192 - 140</gadget>
<output>52</output>
<gadget id="calculator">52 / 2</gadget>
<output>26</output>
<result>B</result> | B | 26 | A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be: | {
"A": "43",
"B": "26",
"C": "33",
"D": "21",
"E": "28"
} | divide(subtract(multiply(48, const_4), 140), const_2) | multiply(n0,const_4)|subtract(#0,n1)|divide(#1,const_2)| | "b 26 let the number of hens be x and the number of cows be y . then , x + y = 48 . . . . ( i ) and 2 x + 4 y = 140 x + 2 y = 70 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 26 , y = 22 . the required answer = 26 ." | general |
math_qa__2dnkDkCvVraElsHK | Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quarterly Options:
A) 2875
B) 2654
C) 2645
D) 2456
E) 2522 | <gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 3</gadget>
<output>9_261/8_000 = around 1.157625</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 * 100</gadget>
<output>1_600</output>
<gadget id="calculator">100 ** (1/2)</gadget>
<output>10</output>
<gadget id="calculator">1_600 * 10</gadget>
<output>16_000</output>
<gadget id="calculator">(9_261/8_000) * 16_000</gadget>
<output>18_522</output>
<gadget id="calculator">18_522 - 16_000</gadget>
<output>2_522</output>
<result>E</result> | E | 2,522 | Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quarterly | {
"A": "2875",
"B": "2654",
"C": "2645",
"D": "2456",
"E": "2522"
} | subtract(multiply(power(add(const_1, divide(divide(20, const_4), const_100)), const_3), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100))), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100))) | divide(n1,const_4)|multiply(const_4,const_4)|sqrt(const_100)|divide(#0,const_100)|multiply(#1,const_100)|add(#3,const_1)|multiply(#4,#2)|power(#5,const_3)|multiply(#6,#7)|subtract(#8,#6) | principal = rs . 16000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = rs . [ 16000 x ( 1 + ( 5 / 100 ) ) 3 ] = rs . 18522 . ci . = rs . ( 18522 - 16000 ) = rs . 2522 answer : e | gain |
math_qa__tepoiUnHmYyWLjQY | A number is doubled and 9 is added. If the resultant is trebled, it becomes 51. What is that number? Choose the correct choice from the following answers:
A) 3.5 B) 6 C) 8 D) 7 E) 4 | <gadget id="calculator">3 * 9</gadget>
<output>27</output>
<gadget id="calculator">51 - 27</gadget>
<output>24</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">24 / 6</gadget>
<output>4</output>
<result>E</result> | E | 4 | A number is doubled and 9 is added. If the resultant is trebled, it becomes 51. What is that number? | {
"A": "3.5",
"B": "6",
"C": "8",
"D": "7",
"E": "4"
} | divide(subtract(51, multiply(const_3, 9)), multiply(const_3, const_2)) | multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)| | "let the number be x . then , 3 ( 2 x + 9 ) = 51 2 x = 8 = > x = 4 answer : e" | general |
math_qa__0PBzFYXIPFP0Qw1o | A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced? Options:
A) 1 / 4
B) 1 / 3
C) 1 / 2
D) 2 / 3
E) 3 / 4 | <gadget id="calculator">35 - 25</gadget>
<output>10</output>
<gadget id="calculator">40 - 35</gadget>
<output>5</output>
<gadget id="calculator">10 / 5</gadget>
<output>2</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<result>B</result> | B | 0.333333 | A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced? | {
"A": "1 / 4",
"B": "1 / 3",
"C": "1 / 2",
"D": "2 / 3",
"E": "3 / 4"
} | inverse(add(divide(subtract(35, 25), subtract(40, 35)), const_1)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)|add(#2,const_1)|inverse(#3)| | "original quantity = a substituted quantity = b then : ( a * 0.4 + 0.25 * b т а у 0.4 * b ) / a = 0.35 0.4 + ( b / a ) * ( - 0.15 ) = 0.35 b / a = - 0.05 / - 0.15 = 1 / 3 answer : b" | other |
math_qa__8whVqlI8JTFfvCHq | On the first day of her vacation, Louisa traveled 250 miles. On the second day, traveling at the same average speed, she traveled 350 miles. If the 250-mile trip took 3 hours less than the 350-mile trip, what was the average speed, in miles per hour? Select:
A) 31 B) 33.33 C) 35 D) 37 E) 39.33 | <gadget id="calculator">350 - 250</gadget>
<output>100</output>
<gadget id="calculator">100 / 3</gadget>
<output>100/3 = around 33.333333</output>
<result>B</result> | B | 33.33 | On the first day of her vacation, Louisa traveled 250 miles. On the second day, traveling at the same average speed, she traveled 350 miles. If the 250-mile trip took 3 hours less than the 350-mile trip, what was the average speed, in miles per hour? | {
"A": "31",
"B": "33.33",
"C": "35",
"D": "37",
"E": "39.33"
} | divide(subtract(350, 250), 3) | subtract(n1,n0)|divide(#0,n3)| | "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 250 / t = 350 / ( t + 3 ) - - > 5 / t = 7 / ( t + 3 ) - - > 5 t + 15 = 7 t - - - - > 2 t = 15 . t = 7.5 - - - - > ( rate ) = 250 / 7.5 = 33.33 answer : b" | physics |
math_qa__GSEu0uBvCkJw8gne | 30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq.m. Find the length of each stone slab? Choose the correct answer: A) 150 cm B) 767 cm C) 88 cm D) 666 cm E) 776 cm | <gadget id="calculator">67.5 / 30</gadget>
<output>2.25</output>
<gadget id="calculator">2.25 ** (1/2)</gadget>
<output>1.5</output>
<gadget id="calculator">1.5 * 100</gadget>
<output>150</output>
<result>A</result> | A | 150 | 30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq.m. Find the length of each stone slab? | {
"A": "150 cm",
"B": "767 cm",
"C": "88 cm",
"D": "666 cm",
"E": "776 cm"
} | multiply(sqrt(divide(67.5, 30)), const_100) | divide(n1,n0)|sqrt(#0)|multiply(#1,const_100)| | "area of each slab = 67.5 / 30 m 2 = 2.25 m 2 length of each slab √ 2.25 = 1.5 m = 150 cm" | geometry |
math_qa__VWdSZrq5ApLQiZ21 | Machine R takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine R to make 40 widgets? Options:
A) 5 B) 6 C) 8 D) 10 E) 12 | <gadget id="calculator">40 - 25</gadget>
<output>15</output>
<gadget id="calculator">15 - 3</gadget>
<output>12</output>
<result>E</result> | E | 12 | Machine R takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine R to make 40 widgets? | {
"A": "5",
"B": "6",
"C": "8",
"D": "10",
"E": "12"
} | subtract(subtract(40, 25), const_3) | subtract(n4,n2)|subtract(#0,const_3) | i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of r is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and r reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of r . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer | physics |
math_qa__ooGzHvdJ7UhoIkCx | I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss? Options
A) rs . 28 B) rs . 280 C) rs . 140 D) rs . 70 E) rs . 80 | <gadget id="calculator">100 + 19</gadget>
<output>119</output>
<gadget id="calculator">480 * 119</gadget>
<output>57_120</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 + 119</gadget>
<output>204</output>
<gadget id="calculator">57_120 / 204</gadget>
<output>280</output>
<result>B</result> | B | 280 | I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss? | {
"A": "rs . 28",
"B": "rs . 280",
"C": "rs . 140",
"D": "rs . 70",
"E": "rs . 80"
} | divide(multiply(480, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19))) | add(n2,const_100)|subtract(const_100,n1)|add(#0,#1)|multiply(n0,#0)|divide(#3,#2) | x * ( 85 / 100 ) = ( 480 - x ) 119 / 100 x = 280 answer : b | gain |
math_qa__l3EgvwsZxUb7ERhN | A gardener changed the size of his rectangle shaped garden by increasing it's length by 40% & decreasing is's width by 20%.Find area of new garden. Choose the correct answer:
A) 1.04 B) 1.12 C) 1.24 D) 1.4 E) 1.5 | <gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">140 / 100</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(7/5) * (4/5)</gadget>
<output>28/25 = around 1.12</output>
<result>B</result> | B | 1.12 | A gardener changed the size of his rectangle shaped garden by increasing it's length by 40% & decreasing is's width by 20%.Find area of new garden. | {
"A": "1.04",
"B": "1.12",
"C": "1.24",
"D": "1.4",
"E": "1.5"
} | multiply(divide(add(const_100, 40), const_100), divide(subtract(const_100, 20), const_100)) | add(n0,const_100)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3) | a 1 = l * b a 2 = ( l * 140 / 100 ) * ( b * 80 / 100 ) = 1.12 * lb so , area of garden is by 1.12 times of old area . answer : b | geometry |
math_qa__mXNs2EGI9z0lQVUJ | The cost of one photocopy is $0.02. However, a 25% discount is offered on orders of more than 100 photocopies. If Steve and Dennison have to make 80 copies each, how much will each of them save if they submit a single order of 160 copies?
Answers:
A) $ 0.32 B) $ 0.40 C) $ 0.45 D) $ 0.48 E) $ 0.54 | <gadget id="calculator">80 * 0.02</gadget>
<output>1.6</output>
<gadget id="calculator">2 * 1.6</gadget>
<output>3.2</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">160 * (3/4)</gadget>
<output>120</output>
<gadget id="calculator">120 * 0.02</gadget>
<output>2.4</output>
<gadget id="calculator">3.2 - 2.4</gadget>
<output>0.8</output>
<gadget id="calculator">0.8 / 2</gadget>
<output>0.4</output>
<result>B</result> | B | 0.4 | The cost of one photocopy is $0.02. However, a 25% discount is offered on orders of more than 100 photocopies. If Steve and Dennison have to make 80 copies each, how much will each of them save if they submit a single order of 160 copies? | {
"A": "$ 0.32",
"B": "$ 0.40",
"C": "$ 0.45",
"D": "$ 0.48",
"E": "$ 0.54"
} | divide(subtract(multiply(const_2, multiply(80, 0.02)), multiply(multiply(160, divide(subtract(100, 25), 100)), 0.02)), const_2) | multiply(n0,n3)|subtract(n2,n1)|divide(#1,n2)|multiply(#0,const_2)|multiply(n4,#2)|multiply(n0,#4)|subtract(#3,#5)|divide(#6,const_2)| | "if steve and dennison submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined no discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ." | gain |
math_qa__zSl5z0sayoHiEJf6 | 9000 + 16 2/3 % of ? = 10500 Choose the correct choice from the following choices.
A) 2387 B) 2888 C) 9000 D) 2837 E) 2271 | <gadget id="calculator">16 * 2</gadget>
<output>32</output>
<gadget id="calculator">3 / 3</gadget>
<output>1</output>
<gadget id="calculator">32 / 1</gadget>
<output>32</output>
<gadget id="calculator">9_000 + 32</gadget>
<output>9_032</output>
<result>C</result> | C | 9,000 | 9000 + 16 2/3 % of ? = 10500 | {
"A": "2387",
"B": "2888",
"C": "9000",
"D": "2837",
"E": "2271"
} | add(9000, divide(multiply(16, 2), divide(3, const_3.0))) | divide(n3,const_3.0)|multiply(n1,n2)|divide(#1,#0)|add(n0,#2)| | "explanation : 9000 + 16 2 / 3 % of ? = 10500 = > 9000 + 50 / 3 % of ? = 10500 50 / ( 3 * 100 ) of ? = 1500 = > ? = 1500 * 6 ? = 9000 answer : c" | general |
math_qa__oa8cpCToiadWC80A | The ratio of the cost price and selling price is 2:3. The profit percent is? Select the correct option: A) 20 % B) 25 % C) 50 % D) 75 % E) 100 % | <gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) - 1</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>C</result> | C | 50 | The ratio of the cost price and selling price is 2:3. The profit percent is? | {
"A": "20 %",
"B": "25 %",
"C": "50 %",
"D": "75 %",
"E": "100 %"
} | multiply(subtract(divide(3, 2), const_1), const_100) | divide(n1,n0)|subtract(#0,const_1)|multiply(#1,const_100) | let the c . p . = $ 2 x then s . p . = $ 3 x then , gain = 3 x - 2 x = $ x gain % = x / 2 x * 100 = 50 % answer is c | gain |
math_qa__u5eOQELBJ6wnNG7C | 10 is 6% of a, and 6 is 10% of b. c equals b/a. What is the value of c?
Choose the correct choice from the following:
A) 3 / 10 B) 6 / 17 C) 9 / 25 D) 10 / 33 E) 12 / 35 | <gadget id="calculator">6 / 10</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<gadget id="calculator">10 / 6</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(5/3) * 100</gadget>
<output>500/3 = around 166.666667</output>
<gadget id="calculator">60 / (500/3)</gadget>
<output>9/25 = around 0.36</output>
<result>C</result> | C | 0.36 | 10 is 6% of a, and 6 is 10% of b. c equals b/a. What is the value of c? | {
"A": "3 / 10",
"B": "6 / 17",
"C": "9 / 25",
"D": "10 / 33",
"E": "12 / 35"
} | divide(multiply(divide(6, 10), const_100), multiply(divide(10, 6), const_100)) | divide(n1,n0)|divide(n0,n1)|multiply(#0,const_100)|multiply(#1,const_100)|divide(#2,#3)| | "6 a / 100 = 10 a = 500 / 3 b / 10 = 6 b = 60 c = b / a = 60 * 3 / 500 = 9 / 25 the answer is c ." | general |
math_qa__NIm8xPo6GSrW8tFJ | Points A, B, C, and D, in that order, lie on a line. If AB = 2 cm, AC = 5 cm, and BD = 6 cm, what is CD, in centimeters? Answers:
A) 1
B) 2
C) 3
D) 4
E) 5 | <gadget id="calculator">5 - 2</gadget>
<output>3</output>
<result>C</result> | C | 3 | Points A, B, C, and D, in that order, lie on a line. If AB = 2 cm, AC = 5 cm, and BD = 6 cm, what is CD, in centimeters? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | subtract(5, 2) | subtract(n1,n0) | putting a value to each point , lets use the following : a - 0 b - 2 ( ab = 2 ) c - 5 ( ac = 5 ) d - 8 ( bd = 6 ) cd is 8 - 5 = 3 . ans c | physics |
math_qa__t6cHXNcDzetPylO3 | In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (11, 0), (0, -3.5), (-11, 0)?
Select the correct option: A) 56 B) 77 C) 112 D) 116 E) 120 | <gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">3.5 * 2</gadget>
<output>7</output>
<gadget id="calculator">(22 * 7) / 2</gadget>
<output>77</output>
<result>B</result> | B | 77 | In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (11, 0), (0, -3.5), (-11, 0)? | {
"A": "56",
"B": "77",
"C": "112",
"D": "116",
"E": "120"
} | rhombus_area(multiply(11, const_2), multiply(3.5, const_2)) | multiply(n2,const_2)|multiply(n1,const_2)|rhombus_area(#0,#1)| | "area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 11 + 11 = 22 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 22 * 7 = 77 b is the answer" | geometry |
math_qa__Z9bLzo72iQgEb8hh | A 21% stock yielding 10% is quoted at : Choose the most appropriate option
A) 83.33 B) 210 C) 112 D) 120 E) 160 | <gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">10 * 21</gadget>
<output>210</output>
<result>B</result> | B | 210 | A 21% stock yielding 10% is quoted at : | {
"A": "83.33",
"B": "210",
"C": "112",
"D": "120",
"E": "160"
} | multiply(divide(const_100, 10), 21) | divide(const_100,n1)|multiply(n0,#0)| | "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 21 , money invested = rs . ( 100 / 10 x 21 ) = rs . 210 . â ˆ ´ market value of rs . 100 stock = rs . 210 answer b" | gain |
math_qa__aUoasnOOSAWLklAr | Which no. need to add to 859622 to get a no. exactly divisible by 456? Choose one.
A) 546577 B) 674645 C) 566578 D) 465766 E) 859622 | <gadget id="calculator">859_622 % 456</gadget>
<output>62</output>
<gadget id="calculator">859_622 - 62</gadget>
<output>859_560</output>
<result>E</result> | E | 859,622 | Which no. need to add to 859622 to get a no. exactly divisible by 456? | {
"A": "546577",
"B": "674645",
"C": "566578",
"D": "465766",
"E": "859622"
} | subtract(859622, reminder(859622, 456)) | reminder(n0,n1)|subtract(n0,#0) | dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e | general |
math_qa__GBMfYb3Ch0vP1x0e | A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is Choose the correct choice from the following choices:
A) 15 % B) 12 % C) 8 % D) 7 % E) 5 % | <gadget id="calculator">12_005 - 9_800</gadget>
<output>2_205</output>
<gadget id="calculator">9_800 * 8</gadget>
<output>78_400</output>
<gadget id="calculator">5 * 12_005</gadget>
<output>60_025</output>
<gadget id="calculator">78_400 - 60_025</gadget>
<output>18_375</output>
<gadget id="calculator">2_205 / 18_375</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) * 100</gadget>
<output>12</output>
<result>B</result> | B | 12 | A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is | {
"A": "15 %",
"B": "12 %",
"C": "8 %",
"D": "7 %",
"E": "5 %"
} | multiply(divide(subtract(12005, 9800), subtract(multiply(9800, 8), multiply(5, 12005))), const_100) | multiply(n0,n3)|multiply(n1,n2)|subtract(n2,n0)|subtract(#0,#1)|divide(#2,#3)|multiply(#4,const_100)| | "explanation : simple interest for 3 years = ( rs . 12005 - rs . 9800 ) = rs . 2205 simple interest for 5 years = 22053 × 5 = rs . 3675 principal ( p ) = ( rs . 9800 - rs . 3675 ) = rs . 6125 r = 100 × si / pt = 100 × 3675 / 6125 × 5 = 12 % answer : option b" | gain |
math_qa__MRxdzpJ8bhlRjUhG | A invested some money in 8% stock at 96.If B wants to invest in an equally good 10% stock ,he must purchase a stock worth of : Choose the correct choice from the following choices:
A) rs . 120
B) rs . 60
C) rs . 128
D) rs . 130
E) rs . 140 | <gadget id="calculator">96 / 8</gadget>
<output>12</output>
<gadget id="calculator">12 * 10</gadget>
<output>120</output>
<result>A</result> | A | 120 | A invested some money in 8% stock at 96.If B wants to invest in an equally good 10% stock ,he must purchase a stock worth of : | {
"A": "rs . 120",
"B": "rs . 60",
"C": "rs . 128",
"D": "rs . 130",
"E": "rs . 140"
} | multiply(divide(96, 8), 10) | divide(n1,n0)|multiply(n2,#0)| | "solution for an income of rs . 8 , investment = rs . 96 . for an income of rs . 10 , investment = rs . ( 96 / 8 x 10 ) = rs . 120 answer a" | gain |
math_qa__p4SlKlMJQKgxgXyd | How many digits 2^400 has? Choose the correct choice
A) 31 B) 35 C) 50 D) 99 E) 121 | <gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>
<gadget id="calculator">log(10)</gadget>
<output>log(10) = around 2.302585</output>
<gadget id="calculator">log(2) / log(10)</gadget>
<output>log(2)/log(10) = around 0.30103</output>
<gadget id="calculator">(log(2)/log(10)) * 400</gadget>
<output>400*log(2)/log(10) = around 120.411998</output>
<gadget id="calculator">1 + (400*log(2)/log(10))</gadget>
<output>1 + 400*log(2)/log(10) = around 121.411998</output>
<gadget id="calculator">floor(1 + 400*log(2)/log(10))</gadget>
<output>121</output>
<result>E</result> | E | 121 | How many digits 2^400 has? | {
"A": "31",
"B": "35",
"C": "50",
"D": "99",
"E": "121"
} | floor(add(const_1, multiply(divide(log(2), log(const_10)), 400))) | log(n0)|log(const_10)|divide(#0,#1)|multiply(n1,#2)|add(#3,const_1)|floor(#4)| | "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 120 therefore 121 digits would be my best guess e" | general |
math_qa__I3iSDpGaLgGnNO9X | A committee is reviewing a total of 40x black-and-white films and 4y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction of the selected films are in color? Choose the most appropriate option.
A) 20 / 11 B) 16 / 11 C) 17 / 11 D) 10 / 11 E) 19 / 11 | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) + 4</gadget>
<output>22/5 = around 4.4</output>
<gadget id="calculator">4 / (22/5)</gadget>
<output>10/11 = around 0.909091</output>
<result>D</result> | D | 0.909091 | A committee is reviewing a total of 40x black-and-white films and 4y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction of the selected films are in color? | {
"A": "20 / 11",
"B": "16 / 11",
"C": "17 / 11",
"D": "10 / 11",
"E": "19 / 11"
} | divide(4, add(divide(40, const_100), 4)) | divide(n0,const_100)|add(n1,#0)|divide(n1,#1)| | "say x = y = 10 . in this case we would have : 40 x = 200 black - and - white films ; 4 y = 40 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 40 color films , thus total of 44 films were selected . color films thus compose 40 / 44 = 10 / 11 of the selected films . answer : d" | general |
math_qa__KJFhERHp6asS635m | A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month? Answers
A) 6 / 25 B) 5 / 16 C) 4 / 9 D) 3 / 7 E) 2 / 5 | <gadget id="calculator">12 / 8</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) + 1</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">1 / (5/2)</gadget>
<output>2/5 = around 0.4</output>
<result>E</result> | E | 0.4 | A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month? | {
"A": "6 / 25",
"B": "5 / 16",
"C": "4 / 9",
"D": "3 / 7",
"E": "2 / 5"
} | inverse(add(divide(const_12, 8), const_1)) | divide(const_12,n0)|add(#0,const_1)|inverse(#1) | let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 8 ( 1 - x ) p 12 xp = 8 p - 8 xp 20 xp = 8 p x = 2 / 5 the answer is e . | general |
math_qa__E4bvsRQLkcG2B1VZ | If x is equal to the sum of the integers from 50 to 70, inclusive, and y is the number of even integers from 50 to 70, inclusive, what is the value of x + y? Choose the correct choice from the following:
A) 1211 B) 1231 C) 1251 D) 1271 E) 1291 | <gadget id="calculator">50 + 70</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">70 - 50</gadget>
<output>20</output>
<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">60 * 21</gadget>
<output>1_260</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">1_260 + 11</gadget>
<output>1_271</output>
<result>D</result> | D | 1,271 | If x is equal to the sum of the integers from 50 to 70, inclusive, and y is the number of even integers from 50 to 70, inclusive, what is the value of x + y? | {
"A": "1211",
"B": "1231",
"C": "1251",
"D": "1271",
"E": "1291"
} | add(multiply(divide(add(50, 70), const_2), add(subtract(70, 50), const_1)), add(divide(subtract(70, 50), const_2), const_1)) | add(n0,n1)|subtract(n1,n0)|add(#1,const_1)|divide(#1,const_2)|divide(#0,const_2)|add(#3,const_1)|multiply(#2,#4)|add(#5,#6)| | "x = 50 + 51 + . . . + 70 = 21 ( 60 ) = 1260 y = 11 x + y = 1271 the answer is d ." | general |
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