id
stringlengths 25
25
| question
stringlengths 45
1.01k
| chain
stringlengths 75
4.11k
| result
stringclasses 5
values | result_float
float64 -4,212
100B
| question_without_options
stringlengths 6
962
| options
dict | annotated_formula
stringlengths 7
6.48k
| linear_formula
stringlengths 8
925
| rationale
stringlengths 1
2.74k
| category
stringclasses 6
values |
|---|---|---|---|---|---|---|---|---|---|---|
math_qa__ANFh2hBWg6cZG4wS | The edges of a cuboid are 2 cm, 5 cm and 3 cm. Find the volume of the cuboid? Choose the correct choice from the following answers.
A) 20 B) 60 C) 80 D) 30 E) 45 | <gadget id="calculator">2 * 5 * 3</gadget>
<output>30</output>
<result>D</result> | D | 30 | The edges of a cuboid are 2 cm, 5 cm and 3 cm. Find the volume of the cuboid? | {
"A": "20",
"B": "60",
"C": "80",
"D": "30",
"E": "45"
} | volume_rectangular_prism(2, 5, 3) | volume_rectangular_prism(n0,n1,n2) | 2 * 5 * 3 = 30 answer : d | physics |
math_qa__tUNFNHwIE1pv1GtK | A computer manufacturer produces a certain electronic component at a cost of $60 per component. Shipping costs for delivering the components are $2 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues? Pick: A) $ 28 B) $ 82 C) $ 172 D) $ 138 E) $ 192 | <gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 * 1_000</gadget>
<output>16_000</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">16_000 + 200</gadget>
<output>16_200</output>
<gadget id="calculator">60 + 2</gadget>
<output>62</output>
<gadget id="calculator">62 * 150</gadget>
<output>9_300</output>
<gadget id="calculator">16_200 + 9_300</gadget>
<output>25_500</output>
<gadget id="calculator">25_500 / 150</gadget>
<output>170</output>
<result>C</result> | C | 172 | A computer manufacturer produces a certain electronic component at a cost of $60 per component. Shipping costs for delivering the components are $2 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues? | {
"A": "$ 28",
"B": "$ 82",
"C": "$ 172",
"D": "$ 138",
"E": "$ 192"
} | divide(add(add(multiply(multiply(const_4, const_4), const_1000), multiply(2, const_100)), multiply(add(60, 2), 150)), 150) | add(n0,n1)|multiply(const_4,const_4)|multiply(n1,const_100)|multiply(#1,const_1000)|multiply(n3,#0)|add(#3,#2)|add(#5,#4)|divide(#6,n3)| | "this question can be solved easily using a equation model . 150 * p = 16500 ( fixed cost ) + 150 * 60 + 150 * 2 . = 16500 + 9000 + 300 = p = $ 172 . c" | general |
math_qa__ySJqcJHEBkA1bH7v | A beaker contains 180 liters of alcohol. On 1st day, 60 l of alcohol is taken out and replaced by water. 2nd day, 60 l of mixture iss taken out and replaced by water and the process continues day after day. What will be the quantity of alcohol in beaker after 3 days Choose the correct choice from the following answers: A) 53.3 B) 53.8 C) 53.7 D) 53.5 E) 353.3 | <gadget id="calculator">60 / 180</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) ** 3</gadget>
<output>8/27 = around 0.296296</output>
<gadget id="calculator">180 * (8/27)</gadget>
<output>160/3 = around 53.333333</output>
<result>A</result> | A | 53.3 | A beaker contains 180 liters of alcohol. On 1st day, 60 l of alcohol is taken out and replaced by water. 2nd day, 60 l of mixture iss taken out and replaced by water and the process continues day after day. What will be the quantity of alcohol in beaker after 3 days | {
"A": "53.3",
"B": "53.8",
"C": "53.7",
"D": "53.5",
"E": "353.3"
} | multiply(180, power(subtract(1, divide(60, 180)), 3)) | divide(n2,n0)|subtract(n1,#0)|power(#1,n5)|multiply(n0,#2) | use the formula , final alcohol = initial alcohol × ( 1 − replacementquantityfinalvolume ) n × ( 1 − replacementquantityfinalvolume ) n final alcohol = 180 ( 1 − 60180 ) 3180 ( 1 − 60180 ) 3 = 180 × ( 23 ) 3 = 53.3 ans : a | physics |
math_qa__Sppm2WBcyXfd7VSf | A car travels uphill at 30 km/hr and downhill at 70 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car? Select
A) 32 kmph B) 33 kmph C) 34 kmph D) 35 kmph E) 37 kmph | <gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">100 / 30</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">50 / 70</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">(10/3) + (5/7)</gadget>
<output>85/21 = around 4.047619</output>
<gadget id="calculator">150 / (85/21)</gadget>
<output>630/17 = around 37.058824</output>
<result>E</result> | E | 37 | A car travels uphill at 30 km/hr and downhill at 70 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car? | {
"A": "32 kmph",
"B": "33 kmph",
"C": "34 kmph",
"D": "35 kmph",
"E": "37 kmph"
} | divide(add(100, 50), add(divide(100, 30), divide(50, 70))) | add(n2,n3)|divide(n2,n0)|divide(n3,n1)|add(#1,#2)|divide(#0,#3) | avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 7 ; avg speed = 150 / ( 10 / 3 + 5 / 7 ) = 37 kmph answer : e | general |
math_qa__SKzZ486xxzVIysIQ | In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 77 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp? Options:
A) 550 B) 245 C) 150 D) 35 E) 350 | <gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(7/10) * (1/5)</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">77 / (7/50)</gadget>
<output>550</output>
<result>A</result> | A | 550 | In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 77 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp? | {
"A": "550",
"B": "245",
"C": "150",
"D": "35",
"E": "350"
} | divide(77, multiply(divide(subtract(const_100, 30), const_100), divide(20, const_100))) | divide(n0,const_100)|subtract(const_100,n1)|divide(#1,const_100)|multiply(#2,#0)|divide(n2,#3)| | "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 77 , so 0.14 * { total } = 77 - - > { total } = 550 . answer : a ." | gain |
math_qa__2mEm7NxUAY5wZj7h | vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ?
Choose the correct choice from the following options: A) 54 B) 72 C) 96 D) 144 E) 432 | <gadget id="calculator">factorial(9)</gadget>
<output>362_880</output>
<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">362_880 / 40_320</gadget>
<output>9</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">24 / 4</gadget>
<output>6</output>
<gadget id="calculator">9 * 6</gadget>
<output>54</output>
<result>A</result> | A | 54 | vlaudia can choose any two of 4 different candles and any 8 of 9 different flowers for a centerpiece arrangement . given these choices , how many candle + flower groupings can she select ? | {
"A": "54",
"B": "72",
"C": "96",
"D": "144",
"E": "432"
} | multiply(divide(factorial(9), factorial(8)), divide(factorial(4), multiply(const_2, const_2))) | factorial(n2)|factorial(n1)|factorial(n0)|multiply(const_2,const_2)|divide(#0,#1)|divide(#2,#3)|multiply(#4,#5) | vlaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement . 2 candles from 4 candles : 4 c 2 : 6 8 flowers from 9 flowers : 9 c 8 : 9 so total grouping 9 * 6 = 54 . answer is a . | general |
math_qa__zjSYnuCMH96QlUzU | How many odd integers from 1 to 100 (both inclusive) have odd number of factors? Choose the correct option.
A) 13 B) 14 C) 5 D) 6 E) 7 | <gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">50 / 2</gadget>
<output>25</output>
<gadget id="calculator">25 - 10</gadget>
<output>15</output>
<gadget id="calculator">15 - 10</gadget>
<output>5</output>
<result>C</result> | C | 5 | How many odd integers from 1 to 100 (both inclusive) have odd number of factors? | {
"A": "13",
"B": "14",
"C": "5",
"D": "6",
"E": "7"
} | subtract(subtract(divide(divide(100, const_2), const_2), const_10), const_10) | divide(n1,const_2)|divide(#0,const_2)|subtract(#1,const_10)|subtract(#2,const_10) | integers having odd number of factors will be perfect squares . odd numbers will have odd perfect squares . thus , the possible values for the perfect squares are : 1 , 9,25 , 49,81 and the corresponding integers are 1 , 3,5 , 7,9 ( more than 4 ) . thus c is the correct answer . | other |
math_qa__xL6W3oCY02bVmmla | How many litres of pure acid are there in 10 litres of a 25% solution
Choose the correct choice from the following:
A) 1.5 B) 1.6 C) 2.5 D) 1.8 E) 1.9 | <gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 10</gadget>
<output>5/2 = around 2.5</output>
<result>C</result> | C | 2.5 | How many litres of pure acid are there in 10 litres of a 25% solution | {
"A": "1.5",
"B": "1.6",
"C": "2.5",
"D": "1.8",
"E": "1.9"
} | multiply(divide(25, const_100), 10) | divide(n1,const_100)|multiply(n0,#0) | explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 10 * 25 / 100 = 2.5 answer : option c | gain |
math_qa__jqVXsIRxFTcdAICf | There are 15 teams in a soccer league and each team plays each of the other teams once. How many games will be played in total?
Options: A) 105 B) 110 C) 115 D) 120 E) 125 | <gadget id="calculator">factorial(15)</gadget>
<output>1_307_674_368_000</output>
<gadget id="calculator">15 - 2</gadget>
<output>13</output>
<gadget id="calculator">factorial(13)</gadget>
<output>6_227_020_800</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">6_227_020_800 * 2</gadget>
<output>12_454_041_600</output>
<gadget id="calculator">1_307_674_368_000 / 12_454_041_600</gadget>
<output>105</output>
<result>A</result> | A | 105 | There are 15 teams in a soccer league and each team plays each of the other teams once. How many games will be played in total? | {
"A": "105",
"B": "110",
"C": "115",
"D": "120",
"E": "125"
} | divide(factorial(15), multiply(factorial(subtract(15, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)| | "15 c 2 = 105 the answer is a ." | general |
math_qa__EG437IS9iM5FjO8x | Rahim bought 65 books for Rs.6500 from one shop and 35 books for Rs.2000 from another. What is the average price he paid per book ? Pick one.
A) 80 B) 138 C) 100 D) 129 E) 85 | <gadget id="calculator">6_500 + 2_000</gadget>
<output>8_500</output>
<gadget id="calculator">65 + 35</gadget>
<output>100</output>
<gadget id="calculator">8_500 / 100</gadget>
<output>85</output>
<result>E</result> | E | 85 | Rahim bought 65 books for Rs.6500 from one shop and 35 books for Rs.2000 from another. What is the average price he paid per book ? | {
"A": "80",
"B": "138",
"C": "100",
"D": "129",
"E": "85"
} | divide(add(6500, 2000), add(65, 35)) | add(n1,n3)|add(n0,n2)|divide(#0,#1)| | "average price per book = ( 6500 + 2000 ) / ( 65 + 35 ) = 8500 / 100 = rs . 85 answer : e" | general |
math_qa__uHJjjnc2utfEOazd | A man engaged a servant on the condition that he would pay him Rs.800 and a uniform after one year service. He served only for 9 months and received uniform and Rs.400, find the price of the uniform? Pick one:
A) s . 800 B) s . 85 C) s . 90 D) s . 100 E) s . 120 | <gadget id="calculator">9 * 800</gadget>
<output>7_200</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 * 400</gadget>
<output>4_800</output>
<gadget id="calculator">7_200 - 4_800</gadget>
<output>2_400</output>
<gadget id="calculator">12 * 1</gadget>
<output>12</output>
<gadget id="calculator">2_400 / 12</gadget>
<output>200</output>
<gadget id="calculator">200 * 4</gadget>
<output>800</output>
<result>A</result> | A | 800 | A man engaged a servant on the condition that he would pay him Rs.800 and a uniform after one year service. He served only for 9 months and received uniform and Rs.400, find the price of the uniform? | {
"A": "s . 800",
"B": "s . 85",
"C": "s . 90",
"D": "s . 100",
"E": "s . 120"
} | multiply(divide(subtract(multiply(9, 800), multiply(multiply(const_3, const_4), 400)), multiply(multiply(const_3, const_4), const_1)), const_4) | multiply(n0,n1)|multiply(const_3,const_4)|multiply(n2,#1)|multiply(#1,const_1)|subtract(#0,#2)|divide(#4,#3)|multiply(#5,const_4)| | "9 / 12 = 3 / 4 * 800 = 600 400 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : a" | general |
math_qa__o1a5q1HBUqNVW7sM | A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $7 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues? Choose the correct choice
A) $ 28
B) $ 82
C) $ 110
D) $ 138
E) $ 197 | <gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 * 1_000</gadget>
<output>16_000</output>
<gadget id="calculator">7 * 100</gadget>
<output>700</output>
<gadget id="calculator">16_000 + 700</gadget>
<output>16_700</output>
<gadget id="calculator">80 + 7</gadget>
<output>87</output>
<gadget id="calculator">87 * 150</gadget>
<output>13_050</output>
<gadget id="calculator">16_700 + 13_050</gadget>
<output>29_750</output>
<gadget id="calculator">29_750 / 150</gadget>
<output>595/3 = around 198.333333</output>
<result>E</result> | E | 197 | A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $7 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues? | {
"A": "$ 28",
"B": "$ 82",
"C": "$ 110",
"D": "$ 138",
"E": "$ 197"
} | divide(add(add(multiply(multiply(const_4, const_4), const_1000), multiply(7, const_100)), multiply(add(80, 7), 150)), 150) | add(n0,n1)|multiply(const_4,const_4)|multiply(n1,const_100)|multiply(#1,const_1000)|multiply(n3,#0)|add(#3,#2)|add(#5,#4)|divide(#6,n3)| | "by the question , the equation would be 150 p - 87 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 197 . answer e for me ." | general |
math_qa__SHQ7ZlmEIMK7QDLx | A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours? Choose the correct option:
A) 125 miles B) 225 miles C) 325 miles D) 425 miles E) 525 miles | <gadget id="calculator">65 * 5</gadget>
<output>325</output>
<result>C</result> | C | 325 | A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours? | {
"A": "125 miles",
"B": "225 miles",
"C": "325 miles",
"D": "425 miles",
"E": "525 miles"
} | multiply(65, 5) | multiply(n0,n1)| | "during each hour , the car travels 65 miles . for 5 hours it will travel 65 + 65 + 65 + 65 + 65 = 5 × 65 = 325 miles correct answer is c ) 325 miles" | physics |
math_qa__9yt7Mb5qqXWTMxDX | In a race where 12 cars are running, the chance that car X will win is 1/6, that Y will win is 1/10 and that Z will win is 1/8. Assuming that a dead heat is impossible, find the chance that one of them will win. Options.
A) 1 / 140 B) 1 / 180 C) 27 / 410 D) 47 / 120 E) 57 / 120 | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/6) + (1/10)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(4/15) + (1/8)</gadget>
<output>47/120 = around 0.391667</output>
<result>D</result> | D | 0.391667 | In a race where 12 cars are running, the chance that car X will win is 1/6, that Y will win is 1/10 and that Z will win is 1/8. Assuming that a dead heat is impossible, find the chance that one of them will win. | {
"A": "1 / 140",
"B": "1 / 180",
"C": "27 / 410",
"D": "47 / 120",
"E": "57 / 120"
} | add(add(divide(1, 6), divide(1, 10)), divide(1, 8)) | divide(n1,n2)|divide(n1,n4)|divide(n1,n6)|add(#0,#1)|add(#3,#2)| | "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 6 + 1 / 10 + 1 / 8 = 47 / 120 answer : d" | general |
math_qa__YNtRr80lvst3Q4tg | The timing of a college is from 12 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. Choose the correct choice from the following options
A) 52 minutes
B) 45 minutes
C) 30 minutes
D) 48 minutes
E) 44 minutes | <gadget id="calculator">4.2 * 60</gadget>
<output>252</output>
<gadget id="calculator">252 / 5</gadget>
<output>252/5 = around 50.4</output>
<result>D</result> | D | 48 | The timing of a college is from 12 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. | {
"A": "52 minutes",
"B": "45 minutes",
"C": "30 minutes",
"D": "48 minutes",
"E": "44 minutes"
} | divide(multiply(4.2, const_60), 5) | multiply(n1,const_60)|divide(#0,n2) | explanation : total time a student spends in college = 4 hours 20 minutes = 260 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 260 – 20 ) / 5 = 48 minutes answer d | physics |
math_qa__b1P3vnMuQy4jpmk0 | After decreasing 50% in the price of an article costs Rs.1200. Find the actual cost of an article? Choose the correct option
A) 1200 B) 50 C) 2400 D) 100 E) 600 | <gadget id="calculator">50 / 100</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">1_200 / (1/2)</gadget>
<output>2_400</output>
<result>C</result> | C | 2,400 | After decreasing 50% in the price of an article costs Rs.1200. Find the actual cost of an article? | {
"A": "1200",
"B": "50",
"C": "2400",
"D": "100",
"E": "600"
} | divide(1200, subtract(const_1, divide(50, const_100))) | divide(n0,const_100)|subtract(const_1,#0)|divide(n1,#1)| | "cp * ( 50 / 100 ) = 1200 cp = 24 * 100 = > cp = 2400 answer : c" | gain |
math_qa__Xm2Rfs96HN0RiMen | Mary's income is 60% more Than Tim's income and Tim's income is 30% less than Juan's income.What % of Juan's income is Mary's income. Choose the correct option
A) 112 %
B) b . 100 %
C) 96 %
D) 80 %
E) 64 % | <gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">70 * (3/5)</gadget>
<output>42</output>
<gadget id="calculator">70 + 42</gadget>
<output>112</output>
<result>A</result> | A | 112 | Mary's income is 60% more Than Tim's income and Tim's income is 30% less than Juan's income.What % of Juan's income is Mary's income. | {
"A": "112 %",
"B": "b . 100 %",
"C": "96 %",
"D": "80 %",
"E": "64 %"
} | add(subtract(const_100, 30), multiply(subtract(const_100, 30), divide(60, const_100))) | divide(n0,const_100)|subtract(const_100,n1)|multiply(#0,#1)|add(#2,#1)| | "even i got 96 % j = 100 t = 100 * 0.7 = 70 m = 70 * 1.6 = 112 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 112 * 100 / 100 = 112 ans : a" | general |
math_qa__jH4sCvkh8TGMDUw3 | A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created? Choose one: A) 20 B) 22 C) 24 D) 26 E) 30 | <gadget id="calculator">3 ** 3</gadget>
<output>27</output>
<gadget id="calculator">27 - 1</gadget>
<output>26</output>
<result>D</result> | D | 26 | A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created? | {
"A": "20",
"B": "22",
"C": "24",
"D": "26",
"E": "30"
} | subtract(power(3, const_3), const_1) | power(n0,const_3)|subtract(#0,const_1) | we have 3 places ( - - - ) to fill & we can use only digits 2 , 4 , 5 first place can be filled in 3 ways 2 nd place can be filled in 3 ways because we can repeat the digits 3 rd place can be filled in 3 ways because we can repeat the digits total no of codes = 3 x 3 x 3 = 27 but one combination ( 555 ) will not be even so total no of even codes = 27 - 1 = 26 answer d | general |
math_qa__V3f5gEwvd2WV9BS2 | which no. need to add to 859622 to get a number exactly divisible by 456? Choose the correct choice.
A) 345652
B) 547678
C) 356789
D) 778990
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 number exactly divisible by 456? | {
"A": "345652",
"B": "547678",
"C": "356789",
"D": "778990",
"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__Bvqc1o4z0rnnlRKP | In what time will a train 120 m long cross an electric pole, it its speed be 185 km/hr? Choose the correct answer.
A) 2.3 sec B) 2.9 sec C) 2.7 sec D) 8.7 sec E) 8.5 sec | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">185 * (5/18)</gadget>
<output>925/18 = around 51.388889</output>
<gadget id="calculator">120 / (925/18)</gadget>
<output>432/185 = around 2.335135</output>
<result>A</result> | A | 2.3 | In what time will a train 120 m long cross an electric pole, it its speed be 185 km/hr? | {
"A": "2.3 sec",
"B": "2.9 sec",
"C": "2.7 sec",
"D": "8.7 sec",
"E": "8.5 sec"
} | divide(120, multiply(185, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | "speed = 185 * 5 / 18 = 51 m / sec time taken = 120 / 51 = 2.3 sec . answer : a" | physics |
math_qa__eBlf4Cxs3Tnc7goW | A dishonest dealer professes to sell goods at the cost price but uses a weight of 750 grams per kg, what is his percent?
Answers:
A) 25 % B) 33 % C) 29 % D) 55 % E) 45 % | <gadget id="calculator">100 / 750</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">(2/15) * 1_000</gadget>
<output>400/3 = around 133.333333</output>
<gadget id="calculator">(400/3) - 100</gadget>
<output>100/3 = around 33.333333</output>
<result>B</result> | B | 33 | A dishonest dealer professes to sell goods at the cost price but uses a weight of 750 grams per kg, what is his percent? | {
"A": "25 %",
"B": "33 %",
"C": "29 %",
"D": "55 %",
"E": "45 %"
} | subtract(multiply(divide(const_100, 750), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100) | add(const_2,const_3)|divide(const_100,n0)|multiply(#0,const_2)|multiply(#2,const_100)|multiply(#1,#3)|subtract(#4,const_100)| | "750 - - - 250 100 - - - ? = > 33.33 % answer : b" | gain |
math_qa__HTCojfKF7rXvpp8l | What ratio must a shopkeeper mix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.21? Choose the correct choice from the following answers.
A) 10 : 7 B) 9 : 8 C) 4 : 5 D) 13 : 11 E) 14 : 8 | <gadget id="calculator">25 - 21</gadget>
<output>4</output>
<gadget id="calculator">21 - 16</gadget>
<output>5</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<result>C</result> | C | 0.8 | What ratio must a shopkeeper mix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.21? | {
"A": "10 : 7",
"B": "9 : 8",
"C": "4 : 5",
"D": "13 : 11",
"E": "14 : 8"
} | divide(subtract(25, 21), subtract(21, 16)) | subtract(n1,n2)|subtract(n2,n0)|divide(#0,#1)| | "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 4 : 5" | general |
math_qa__sp8zh3cubONX69Rc | A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent E should the number of hours worked be increased? Choose the most appropriate option: A) 12.5 % B) 20 % C) 25 % D) 50 % E) 100 % | <gadget id="calculator">10 * 4</gadget>
<output>40</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">(4/5) * 10</gadget>
<output>8</output>
<gadget id="calculator">40 / 8</gadget>
<output>5</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>C</result> | C | 25 | A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent E should the number of hours worked be increased? | {
"A": "12.5 %",
"B": "20 %",
"C": "25 %",
"D": "50 %",
"E": "100 %"
} | multiply(divide(subtract(divide(multiply(const_10, const_4), multiply(divide(subtract(const_100, 20), const_100), const_10)), const_4), const_4), const_100) | multiply(const_10,const_4)|subtract(const_100,n0)|divide(#1,const_100)|multiply(#2,const_10)|divide(#0,#3)|subtract(#4,const_4)|divide(#5,const_4)|multiply(#6,const_100)| | "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked e will be 25 % greater than the original number . the answer is c ." | general |
math_qa__b4QNQ7UfkcXlBkHd | A rectangle has 20 meter length and 15 meter breadth. Find ratio between area of rectangle and square whose side is same with rectangle's length. Choose the correct choice from the following answers.
A) 3 : 2
B) 3 : 4
C) 4 : 5
D) 2 : 3
E) 2 : 5 | <gadget id="calculator">15 * 20</gadget>
<output>300</output>
<gadget id="calculator">20 ** 2</gadget>
<output>400</output>
<gadget id="calculator">300 / 400</gadget>
<output>3/4 = around 0.75</output>
<result>B</result> | B | 0.75 | A rectangle has 20 meter length and 15 meter breadth. Find ratio between area of rectangle and square whose side is same with rectangle's length. | {
"A": "3 : 2",
"B": "3 : 4",
"C": "4 : 5",
"D": "2 : 3",
"E": "2 : 5"
} | divide(rectangle_area(15, 20), square_area(20)) | rectangle_area(n0,n1)|square_area(n0)|divide(#0,#1) | area of rectangle = 20 * 15 = 300 area of square = 20 ^ 2 = 400 ratio of rectangle ' area and square ' s area = 300 : 400 = 3 : 4 answer : b | geometry |
math_qa__7oxuCyaL6jqFlN1z | A number when divided by 221 gives a remainder 43, what remainder will be obtained by dividing the same number 17? Select the correct option:
A) 9
B) 11
C) 15
D) 5
E) 20 | <gadget id="calculator">17 * 2</gadget>
<output>34</output>
<gadget id="calculator">43 - 34</gadget>
<output>9</output>
<result>A</result> | A | 9 | A number when divided by 221 gives a remainder 43, what remainder will be obtained by dividing the same number 17? | {
"A": "9",
"B": "11",
"C": "15",
"D": "5",
"E": "20"
} | subtract(43, multiply(17, const_2)) | multiply(n2,const_2)|subtract(n1,#0) | 221 + 43 = 264 / 17 = 9 answer a | general |
math_qa__ZsAD56F2mfXVzOig | A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? Pick:
A) 20 B) 30 C) 35 D) 40 E) 55 | <gadget id="calculator">75 - 66</gadget>
<output>9</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">9 / (3/10)</gadget>
<output>30</output>
<result>B</result> | B | 30 | A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time, how many books of the special collection were loaned out during that month? | {
"A": "20",
"B": "30",
"C": "35",
"D": "40",
"E": "55"
} | divide(subtract(75, 66), subtract(const_1, divide(70, const_100))) | divide(n1,const_100)|subtract(n0,n2)|subtract(const_1,#0)|divide(#1,#2) | total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 66 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 30 . answer : b . | gain |
math_qa__aIUzYXyKj1FOEigp | If a tire rotates at 400 revolutions per minute when the car is traveling 168km/h, what is the circumference of the tire? Options:
A) 7 meters
B) 9 meters
C) 8 meters
D) 5 meters
E) 3 meters | <gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">60 * 400</gadget>
<output>24_000</output>
<gadget id="calculator">168 / 24_000</gadget>
<output>7/1_000 = around 0.007</output>
<gadget id="calculator">(7/1_000) * 1_000</gadget>
<output>7</output>
<result>A</result> | A | 7 | If a tire rotates at 400 revolutions per minute when the car is traveling 168km/h, what is the circumference of the tire? | {
"A": "7 meters",
"B": "9 meters",
"C": "8 meters",
"D": "5 meters",
"E": "3 meters"
} | multiply(divide(168, multiply(multiply(multiply(const_2, const_3), const_10), 400)), const_1000) | multiply(const_2,const_3)|multiply(#0,const_10)|multiply(n0,#1)|divide(n1,#2)|multiply(#3,const_1000)| | "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 168,000 m : c is the circumference c = 3 meters correct answer a" | physics |
math_qa__ObNLp0Kjb2MOdH3m | in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 7 people all together .how many people can sit in a bus? Pick one: A) 52 B) 49 C) 95 D) 88 E) 66 | <gadget id="calculator">15 - 3</gadget>
<output>12</output>
<gadget id="calculator">15 + 12</gadget>
<output>27</output>
<gadget id="calculator">27 * 3</gadget>
<output>81</output>
<gadget id="calculator">81 + 7</gadget>
<output>88</output>
<result>D</result> | D | 88 | in a bus left side are 15 seats available,3 few seats in right side because in rear exit door .Each seat hold 3 people.In addition ,there is a seat back can sit 7 people all together .how many people can sit in a bus? | {
"A": "52",
"B": "49",
"C": "95",
"D": "88",
"E": "66"
} | add(multiply(add(15, subtract(15, 3)), 3), 7) | subtract(n0,n1)|add(n0,#0)|multiply(n1,#1)|add(n3,#2)| | "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 7 total people can seat = 81 + 7 = 88 answer : d" | general |
math_qa__IMOtdlPmBz95ivPv | 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 2 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? Choose the correct choice from the following options
A) 1 / 7
B) 1 / 6
C) 1 / 5
D) 1 / 4
E) 1 / 3 | <gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<result>A</result> | A | 0.142857 | 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 2 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": "1 / 7",
"B": "1 / 6",
"C": "1 / 5",
"D": "1 / 4",
"E": "1 / 3"
} | inverse(add(divide(const_12, 2), 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 = 2 ( 1 - x ) p 12 xp = 2 p - 2 xp 14 xp = 2 p x = 1 / 7 the answer is a ." | general |
math_qa__l7v9FlUA9ZlObwjV | If a certain number of labours can dig earth 100m deep, 25m long, and 30m broad in 12 days, then find the number of days the same number of labours will require to dig earth 75m deep, 20m long and 50m broad. Answers:
A) 12
B) 18
C) 6
D) 1
E) 2 | <gadget id="calculator">75 * 20</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 * 50</gadget>
<output>75_000</output>
<gadget id="calculator">100 * 25</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 * 30</gadget>
<output>75_000</output>
<gadget id="calculator">75_000 / 75_000</gadget>
<output>1</output>
<gadget id="calculator">1 * 12</gadget>
<output>12</output>
<result>A</result> | A | 12 | If a certain number of labours can dig earth 100m deep, 25m long, and 30m broad in 12 days, then find the number of days the same number of labours will require to dig earth 75m deep, 20m long and 50m broad. | {
"A": "12",
"B": "18",
"C": "6",
"D": "1",
"E": "2"
} | multiply(divide(multiply(multiply(75, 20), 50), multiply(multiply(100, 25), 30)), 12) | multiply(n4,n5)|multiply(n0,n1)|multiply(n6,#0)|multiply(n2,#1)|divide(#2,#3)|multiply(n3,#4) | explanation : more number of days means more length , more depth and more width . hence , its a direct proportion . ( 100 * 25 * 30 ) : ( 75 * 20 * 50 ) : : 12 : x 75000 : 75000 : : 12 : x x = 12 answer : a | physics |
math_qa__I12Q9wMzdgjHUC6N | A shopkeeper sold an article offering a discount of 5% and earned a profit of 27.3%. What would have been the percentage of profit earned if no discount had been offered?
Choose the correct choice from the following choices
A) 28.5
B) 27.675
C) 30
D) 34 %
E) none of these | <gadget id="calculator">100 + 27.3</gadget>
<output>127.3</output>
<gadget id="calculator">127.3 * 100</gadget>
<output>12_730</output>
<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">12_730 / 95</gadget>
<output>134</output>
<gadget id="calculator">134 - 100</gadget>
<output>34</output>
<result>D</result> | D | 34 | A shopkeeper sold an article offering a discount of 5% and earned a profit of 27.3%. What would have been the percentage of profit earned if no discount had been offered? | {
"A": "28.5",
"B": "27.675",
"C": "30",
"D": "34 %",
"E": "none of these"
} | subtract(divide(multiply(add(const_100, 27.3), const_100), subtract(const_100, 5)), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,const_100)|divide(#2,#1)|subtract(#3,const_100)| | "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 27.3 ) / ( 100 â ˆ ’ 5 ) = 100 ã — 127.3 / 95 = 134 hence , required % profit = 134 â € “ 100 = 34 % answer d" | gain |
math_qa__VO5GRop2TykBRDN0 | 135 kg of an alloy A is mixed with 145 kg of alloy B. If alloy A has lead and tin in the ratio 3:5 and alloy B has tin and copper in the ratio 2:3, then the amount of tin in the new alloy is? Choose the correct option
A) 100.6 kg B) 142 kg C) 135 kg D) 110.8 kg E) 114 kg | <gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">135 / 8</gadget>
<output>135/8 = around 16.875</output>
<gadget id="calculator">(135/8) * 5</gadget>
<output>675/8 = around 84.375</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">145 / 5</gadget>
<output>29</output>
<gadget id="calculator">29 * 2</gadget>
<output>58</output>
<gadget id="calculator">(675/8) + 58</gadget>
<output>1_139/8 = around 142.375</output>
<result>B</result> | B | 142 | 135 kg of an alloy A is mixed with 145 kg of alloy B. If alloy A has lead and tin in the ratio 3:5 and alloy B has tin and copper in the ratio 2:3, then the amount of tin in the new alloy is? | {
"A": "100.6 kg",
"B": "142 kg",
"C": "135 kg",
"D": "110.8 kg",
"E": "114 kg"
} | add(multiply(divide(135, add(3, 5)), 5), multiply(divide(145, add(2, 3)), 2)) | add(n2,n3)|add(n4,n5)|divide(n0,#0)|divide(n1,#1)|multiply(n3,#2)|multiply(n4,#3)|add(#4,#5)| | "quantity of tin in 135 kg of a = 135 * 5 / 8 = 84 kg quantity of tin in 145 kg of b = 145 * 2 / 5 = 58 kg quantity of tin in the new alloy = 84 + 58 = 142 kg answer is b" | other |
math_qa__RBcs1HCqqDGBy1ps | A sum of money lent out at S.I. amounts to a total of $520 after 2 years and to $820 after a further period of 5 years. What was the initial sum of money that was invested?
Choose the correct option:
A) $ 340
B) $ 360
C) $ 380
D) $ 400
E) $ 420 | <gadget id="calculator">820 - 520</gadget>
<output>300</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">300 * (2/5)</gadget>
<output>120</output>
<gadget id="calculator">520 - 120</gadget>
<output>400</output>
<result>D</result> | D | 400 | A sum of money lent out at S.I. amounts to a total of $520 after 2 years and to $820 after a further period of 5 years. What was the initial sum of money that was invested? | {
"A": "$ 340",
"B": "$ 360",
"C": "$ 380",
"D": "$ 400",
"E": "$ 420"
} | subtract(520, multiply(subtract(820, 520), divide(2, 5))) | divide(n1,n3)|subtract(n2,n0)|multiply(#0,#1)|subtract(n0,#2)| | "s . i for 5 years = $ 820 - $ 520 = $ 300 the s . i . is $ 60 / year s . i . for 2 years = $ 120 principal = $ 520 - $ 120 = $ 400 the answer is d ." | general |
math_qa__6EDvQz2JcmEeVPcD | A small water pump would take 4 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
Answers:
A) 1 / 6 B) 4 / 9 C) 1 / 4 D) 5 / 9 E) 1 / 3 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 2</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">1 / (9/4)</gadget>
<output>4/9 = around 0.444444</output>
<result>B</result> | B | 0.444444 | A small water pump would take 4 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time? | {
"A": "1 / 6",
"B": "4 / 9",
"C": "1 / 4",
"D": "5 / 9",
"E": "1 / 3"
} | inverse(add(inverse(4), 2)) | inverse(n0)|add(n2,#0)|inverse(#1)| | "rate of the small pump is 1 / 4 tank / hour rate of the larger pump is 1 / ( 1 / 2 ) or 2 tank / hour ; combined rate of the two pumps is 1 / 4 + 2 = 9 / 4 tank / hour , together they will fill the empty tank in 1 / ( 9 / 4 ) ) = 4 / 9 hours ( time = job / rate ) . answer : b" | physics |
math_qa__3kwJlCSY353u2MS9 | A man cycling along the road noticed that every 3 minutes a bus overtakes him and every 9 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses? Choose the correct option
A) 5 minutes B) 6 minutes C) 8 minutes D) 9 / 2 minutes E) 10 minutes | <gadget id="calculator">9 + 3</gadget>
<output>12</output>
<gadget id="calculator">3 - 9</gadget>
<output>-6</output>
<gadget id="calculator">12 / (-6)</gadget>
<output>-2</output>
<gadget id="calculator">3 / (-2)</gadget>
<output>-3/2 = around -1.5</output>
<gadget id="calculator">3 - (-3/2)</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">(9/2) / 1</gadget>
<output>9/2 = around 4.5</output>
<result>D</result> | D | 4.5 | A man cycling along the road noticed that every 3 minutes a bus overtakes him and every 9 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses? | {
"A": "5 minutes",
"B": "6 minutes",
"C": "8 minutes",
"D": "9 / 2 minutes",
"E": "10 minutes"
} | divide(subtract(3, divide(3, divide(add(9, 3), subtract(3, 9)))), const_1) | add(n0,n1)|subtract(n0,n1)|divide(#0,#1)|divide(n0,#2)|subtract(n0,#3)|divide(#4,const_1)| | "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 9 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 9 , d = 9 b - 9 c ; every 3 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 3 , d = 3 b + 3 c ; d = 9 b - 9 c = 3 b + 3 c , - - > b = 2 c , - - > d = 9 b - 9 b / 2 = 9 b / 2 . interval = \ frac { d } { b } = \ frac { 9 / 2 b } { b } = 9 / 2 answer : d ( 9 / 2 minutes ) ." | physics |
math_qa__Gp916tB7HMvTokoe | A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
Answers:
A) 230 m B) 240 m C) 260 m D) 270 m E) none of the above | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 72</gadget>
<output>20</output>
<gadget id="calculator">250 / 20</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">26 - (25/2)</gadget>
<output>27/2 = around 13.5</output>
<gadget id="calculator">(27/2) * 20</gadget>
<output>270</output>
<result>D</result> | D | 270 | A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train? | {
"A": "230 m",
"B": "240 m",
"C": "260 m",
"D": "270 m",
"E": "none of the above"
} | multiply(subtract(26, divide(250, multiply(const_0_2778, 72))), multiply(const_0_2778, 72)) | multiply(n0,const_0_2778)|divide(n1,#0)|subtract(n2,#1)|multiply(#0,#2)| | "speed = ( 72 x ( 5 / 18 ) ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , ( ( x + 250 ) / 26 ) = 20 x + 250 = 520 x = 270 . d" | physics |
math_qa__1uZSmTPYHcCasHfV | What is the average of first 21 multiples of 5 ? Choose the correct option:
A) 70 B) 77 C) 55 D) 81 E) 82 | <gadget id="calculator">21 + 1</gadget>
<output>22</output>
<gadget id="calculator">21 * 22</gadget>
<output>462</output>
<gadget id="calculator">462 / 2</gadget>
<output>231</output>
<gadget id="calculator">231 / 21</gadget>
<output>11</output>
<gadget id="calculator">11 * 5</gadget>
<output>55</output>
<result>C</result> | C | 55 | What is the average of first 21 multiples of 5 ? | {
"A": "70",
"B": "77",
"C": "55",
"D": "81",
"E": "82"
} | multiply(divide(divide(multiply(21, add(21, const_1)), const_2), 21), 5) | add(n0,const_1)|multiply(n0,#0)|divide(#1,const_2)|divide(#2,n0)|multiply(n1,#3) | required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 5 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 55 c | general |
math_qa__jMZhy8lhFpjduO7M | The sale price sarees listed for Rs.560 after successive discount is 20% and 30% is? Choose the most appropriate option: A) 321 B) 314 C) 316 D) 265 E) 162 | <gadget id="calculator">560 * 20</gadget>
<output>11_200</output>
<gadget id="calculator">11_200 / 100</gadget>
<output>112</output>
<gadget id="calculator">560 - 112</gadget>
<output>448</output>
<gadget id="calculator">448 * 30</gadget>
<output>13_440</output>
<gadget id="calculator">13_440 / 100</gadget>
<output>672/5 = around 134.4</output>
<gadget id="calculator">448 - (672/5)</gadget>
<output>1_568/5 = around 313.6</output>
<result>B</result> | B | 314 | The sale price sarees listed for Rs.560 after successive discount is 20% and 30% is? | {
"A": "321",
"B": "314",
"C": "316",
"D": "265",
"E": "162"
} | subtract(subtract(560, divide(multiply(560, 20), const_100)), divide(multiply(subtract(560, divide(multiply(560, 20), const_100)), 30), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | "explanation : 560 * ( 80 / 100 ) * ( 70 / 100 ) = 314 answer : b" | gain |
math_qa__CIx9ENVtpFiq9Iob | Given that E and F are events such that P(E) = 25, P(F) = 75 and P(E n F) = 75,
find P (E|F) and P(F|E) Answers:
A) 5 B) 46 C) 52 D) 12 E) 3 | <gadget id="calculator">75 / 25</gadget>
<output>3</output>
<result>E</result> | E | 3 | Given that E and F are events such that P(E) = 25, P(F) = 75 and P(E n F) = 75,
find P (E|F) and P(F|E) | {
"A": "5",
"B": "46",
"C": "52",
"D": "12",
"E": "3"
} | divide(75, 25) | divide(n1,n0) | here , e and f are events p ( e | f ) = p ( enf ) / p ( f ) = 75 / 25 = 3 p ( f | e ) = p ( enf ) / p ( e ) = 75 / 75 = 1 . e ) | general |
math_qa__LMl3QnMCwrJaeap4 | A train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train? Select the correct option:
A) 90
B) 60
C) 120
D) 180
E) 360 | <gadget id="calculator">2_500 / 1_000</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">100 / 3_600</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">(5/2) / (1/36)</gadget>
<output>90</output>
<result>A</result> | A | 90 | A train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train? | {
"A": "90",
"B": "60",
"C": "120",
"D": "180",
"E": "360"
} | divide(divide(2500, const_1000), divide(100, const_3600)) | divide(n0,const_1000)|divide(n1,const_3600)|divide(#0,#1)| | "length = speed * time speed = l / t s = 2500 / 100 s = 25 m / sec speed = 25 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 90 kmph answer : a" | physics |
math_qa__ZVIAs9ZeBiwzuSSG | if 360 is divided into 4 parts proportional to 5 , 7 , 4 , 8 then the smallest part is : Pick one: A) 50 B) 60 C) 40 D) 18 E) 22 | <gadget id="calculator">5 + 7</gadget>
<output>12</output>
<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">16 + 8</gadget>
<output>24</output>
<gadget id="calculator">4 / 24</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 360</gadget>
<output>60</output>
<result>B</result> | B | 60 | if 360 is divided into 4 parts proportional to 5 , 7 , 4 , 8 then the smallest part is : | {
"A": "50",
"B": "60",
"C": "40",
"D": "18",
"E": "22"
} | multiply(divide(4, add(add(add(5, 7), 4), 8)), 360) | add(n2,n3)|add(n1,#0)|add(n5,#1)|divide(n1,#2)|multiply(n0,#3) | given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24 : . the smallest part = ( 360 * 4 / 24 ) = 60 answer : b | general |
math_qa__JiYuV7hcQELdK9j0 | A scale 10 ft. 5 inches long is divided into 5 equal parts. Find the length of each part. Options: A) 25 inches B) 77 inches C) 66 inches D) 97 inches E) 66 inches | <gadget id="calculator">10 * 12</gadget>
<output>120</output>
<gadget id="calculator">120 + 5</gadget>
<output>125</output>
<gadget id="calculator">125 / 5</gadget>
<output>25</output>
<result>A</result> | A | 25 | A scale 10 ft. 5 inches long is divided into 5 equal parts. Find the length of each part. | {
"A": "25 inches",
"B": "77 inches",
"C": "66 inches",
"D": "97 inches",
"E": "66 inches"
} | divide(add(multiply(10, const_12), 5), 5) | multiply(n0,const_12)|add(n1,#0)|divide(#1,n2)| | "explanation : total length of scale in inches = ( 10 * 12 ) + 5 = 125 inches length of each of the 5 parts = 125 / 5 = 25 inches answer : a" | general |
math_qa__sXQqOINBr3auIr2o | A train 150 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is Select
A) 54 kmph B) 60 kmph C) 66 kmph D) 72 kmph E) 84 kmph | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">6 * (5/18)</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(5/3) * 6</gadget>
<output>10</output>
<gadget id="calculator">150 - 10</gadget>
<output>140</output>
<gadget id="calculator">140 / 6</gadget>
<output>70/3 = around 23.333333</output>
<gadget id="calculator">(70/3) / (5/18)</gadget>
<output>84</output>
<result>E</result> | E | 84 | A train 150 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is | {
"A": "54 kmph",
"B": "60 kmph",
"C": "66 kmph",
"D": "72 kmph",
"E": "84 kmph"
} | divide(divide(subtract(150, multiply(multiply(6, const_0_2778), 6)), 6), const_0_2778) | multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778)| | "speed of train relative to man : 150 / 6 * 18 / 5 km / hr = 90 km / hr let speed of train = x therefore x + 6 = 90 x = 90 - 6 x = 84 km / hr answer : e" | physics |
math_qa__Aq1OzBSfeJIPoyRC | A thief runs away from A with a speed of 20 km/hr. A police from a station 60 km away started chasing him after 1 hr. with a speed of 40 km/hr. Time taken by the police to catch the thief is :
Choose the correct choice from the following answers:
A) 4 hrs
B) 4.5 hrs
C) 5.4 hrs
D) 6 hrs .
E) none of these | <gadget id="calculator">20 * 1</gadget>
<output>20</output>
<gadget id="calculator">60 + 20</gadget>
<output>80</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">80 / 20</gadget>
<output>4</output>
<result>A</result> | A | 4 | A thief runs away from A with a speed of 20 km/hr. A police from a station 60 km away started chasing him after 1 hr. with a speed of 40 km/hr. Time taken by the police to catch the thief is : | {
"A": "4 hrs",
"B": "4.5 hrs",
"C": "5.4 hrs",
"D": "6 hrs .",
"E": "none of these"
} | divide(add(60, multiply(20, 1)), subtract(60, 40)) | multiply(n0,n2)|subtract(n1,n3)|add(n1,#0)|divide(#2,#1) | explanation : solution : distance traveled by the thief in 1 hr . = 20 km . total distance of them after 1 hr = ( 60 + 20 ) km = 80 km . their relative speed = ( 40 - 20 ) = 20 km / hr . time taken to catch the thief = 80 / 20 = 4 hrs . answer : a | physics |
math_qa__CAi0VksAUDv4b8Lw | What is the square root of 16, divided by 2?
Pick
A) 9
B) 2
C) 122
D) 6
E) 1 | <gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<result>B</result> | B | 2 | What is the square root of 16, divided by 2? | {
"A": "9",
"B": "2",
"C": "122",
"D": "6",
"E": "1"
} | divide(sqrt(16), 2) | sqrt(n0)|divide(#0,n1)| | "square root is a number times itself square root of 16 = 4 , 4 / 2 = 2 ( b ) 2" | other |
math_qa__LitYOPnmGTbFFvI9 | The value of (4.7 × 13.26 + 4.7 × 9.43 + 4.7 × 77.31) is : Choose the correct answer: A) 0.47 B) 47 C) 470 D) 4700 E) none of these | <gadget id="calculator">13.26 + 9.43</gadget>
<output>22.69</output>
<gadget id="calculator">22.69 + 77.31</gadget>
<output>100</output>
<gadget id="calculator">4.7 * 100</gadget>
<output>470</output>
<result>C</result> | C | 470 | The value of (4.7 × 13.26 + 4.7 × 9.43 + 4.7 × 77.31) is : | {
"A": "0.47",
"B": "47",
"C": "470",
"D": "4700",
"E": "none of these"
} | multiply(4.7, add(add(13.26, 9.43), 77.31)) | add(n1,n3)|add(n5,#0)|multiply(n0,#1) | solution given expression = 4.7 × ( 13.26 + 9.43 + 77.31 ) = 4.7 × 100 = 470 . answer c | general |
math_qa__3Ifnieq0evlk8hKm | An ant walks an average of 500 meters in 60 minutes. A beetle walks 15% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h? Choices.
A) 1.0 B) 0.5 C) 0.75 D) 0.425 E) 0.3 | <gadget id="calculator">500 / 1_000</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">60 / 60</gadget>
<output>1</output>
<gadget id="calculator">(1/2) / 1</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">(1/2) * (17/20)</gadget>
<output>17/40 = around 0.425</output>
<result>D</result> | D | 0.425 | An ant walks an average of 500 meters in 60 minutes. A beetle walks 15% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h? | {
"A": "1.0",
"B": "0.5",
"C": "0.75",
"D": "0.425",
"E": "0.3"
} | multiply(divide(divide(500, const_1000), divide(60, const_60)), subtract(const_1, divide(15, const_100))) | divide(n0,const_1000)|divide(n1,const_60)|divide(n2,const_100)|divide(#0,#1)|subtract(const_1,#2)|multiply(#3,#4)| | "the ant walks an average of 500 meters in 60 minutes 500 meters in 1 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 60 minutes 0.425 km in 1 hours speed = 0.425 * 1 = 0.425 km / h i guess option d should be 0.425" | general |
math_qa__S2rbCE3bv3jkJznx | A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 10 Gallons of water and 20 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?
Choose the correct option
A) 37.5
B) 75
C) 100
D) 150
E) 175 | <gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">40 - 10</gadget>
<output>30</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(4/5) * (1/4)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(4/5) - (1/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">2 * (1/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(3/5) - (2/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">30 / (1/5)</gadget>
<output>150</output>
<result>D</result> | D | 150 | A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 10 Gallons of water and 20 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x? | {
"A": "37.5",
"B": "75",
"C": "100",
"D": "150",
"E": "175"
} | divide(subtract(multiply(20, const_2), 10), subtract(subtract(subtract(1, divide(20, const_100)), multiply(subtract(1, divide(20, const_100)), divide(1, const_4))), multiply(const_2, divide(20, const_100)))) | divide(n0,const_100)|divide(n4,const_4)|multiply(n2,const_2)|multiply(#0,const_2)|subtract(#2,n1)|subtract(n4,#0)|multiply(#1,#5)|subtract(#5,#6)|subtract(#7,#3)|divide(#4,#8)| | "original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 20 gallons salt is added and 10 gallons of water is added . so salt now becomes - > ( 0.2 x + 20 ) and water - - > ( 0.6 x + 10 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 20 ) = ( 0.6 x + 10 ) / 2 , solving , x = 150 . answer : d" | general |
math_qa__Sg2f84YDG4v03Avv | Roses can be purchased individually for $2.30, one dozen for $36, or two dozen for $50. What is the greatest number of roses that can be purchased for $680? Choose the correct choice from the following: A) 156 B) 162 C) 325 D) 324 E) 326 | <gadget id="calculator">680 / 50</gadget>
<output>68/5 = around 13.6</output>
<gadget id="calculator">floor(68/5)</gadget>
<output>13</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">13 * 24</gadget>
<output>312</output>
<gadget id="calculator">13 * 50</gadget>
<output>650</output>
<gadget id="calculator">680 - 650</gadget>
<output>30</output>
<gadget id="calculator">30 / 2.3</gadget>
<output>13.043478</output>
<gadget id="calculator">floor(13.043478)</gadget>
<output>13</output>
<gadget id="calculator">312 + 13</gadget>
<output>325</output>
<result>C</result> | C | 325 | Roses can be purchased individually for $2.30, one dozen for $36, or two dozen for $50. What is the greatest number of roses that can be purchased for $680? | {
"A": "156",
"B": "162",
"C": "325",
"D": "324",
"E": "326"
} | add(multiply(floor(divide(680, 50)), multiply(const_12, const_2)), floor(divide(subtract(680, multiply(floor(divide(680, 50)), 50)), 2.30))) | divide(n3,n2)|multiply(const_12,const_2)|floor(#0)|multiply(n2,#2)|multiply(#2,#1)|subtract(n3,#3)|divide(#5,n0)|floor(#6)|add(#7,#4)| | "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 2.3 = ~ 13 roses for that amount . total = 312 + 13 = 325 . answer : c ." | general |
math_qa__0gCRpT4WEhbNoQeo | In the Land of Oz only one or two-letter words are used. The local language has 65 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition? Choices:
A) 65
B) 66
C) 67
D) 131
E) 130 | <gadget id="calculator">1 + 65</gadget>
<output>66</output>
<gadget id="calculator">66 + 65</gadget>
<output>131</output>
<result>E</result> | E | 130 | In the Land of Oz only one or two-letter words are used. The local language has 65 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition? | {
"A": "65",
"B": "66",
"C": "67",
"D": "131",
"E": "130"
} | add(add(const_1, 65), 65) | add(n0,const_1)|add(n0,#0) | the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 65 letters is 65 ; the number of 2 letter words ( xx ) that can be made from 65 letters is 65 * 65 , since each x can take 65 values . total : 65 + 65 * 65 . similarly : the number of 1 letter words ( x ) that can be made from 64 letters is 64 ; the number of 2 letter words ( xx ) that can be made from 64 letters is 64 * 64 , since each x can take 64 values . total : 64 + 64 * 64 . the difference is ( 65 + 65 * 65 ) - ( 64 + 64 * 64 ) = 130 . answer : e . | general |
math_qa__8GhROhiPZXUnOR2C | Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton? Pick one.
A) 330 B) 300 C) 252 D) 225 E) 210 | <gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 7</gadget>
<output>42</output>
<gadget id="calculator">42 * 5</gadget>
<output>210</output>
<result>E</result> | E | 210 | Baker Ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton? | {
"A": "330",
"B": "300",
"C": "252",
"D": "225",
"E": "210"
} | multiply(multiply(add(const_4, const_2), 7), 5) | add(const_2,const_4)|multiply(n4,#0)|multiply(n5,#1) | baker ram is storing cake boxes in cartons the dimensions of the carton are 25 x 42 x 60 and those of each cake box are 8 x 7 x 5 . to maximize number of boxes try and fit maximum into the base of the box . if you take the base as 25 x 42 and fit 5 x 6 boxes of 5 x 7 , then the total number of boxes is 5 x 6 x integer ( 60 / 8 ) = 5 x 6 x 7 = 210 . alternatively you could try taking the base as 60 x 42 and fit 12 x 6 boxes of 5 x 7 , then the total number of boxes is 12 x 6 x integer ( 25 / 8 ) = 12 x 6 x 3 = 216 . but since that is not an answer option , i go with ( e ) 210 . | general |
math_qa__gPkucy6AYefSUlqh | A 40-liter solution of alcohol and water is 5 percent alcohol. If 4.5 liters of alcohol and 5.5 liters of water are added to this solution, what percent of the solution produced is alcohol?
Choose the correct choice from the following answers
A) 7 %
B) 10 %
C) 13 %
D) 16 %
E) 19 % | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">40 * (1/20)</gadget>
<output>2</output>
<gadget id="calculator">2 + 4.5</gadget>
<output>6.5</output>
<gadget id="calculator">4.5 + 5.5</gadget>
<output>10</output>
<gadget id="calculator">40 + 10</gadget>
<output>50</output>
<gadget id="calculator">6.5 / 50</gadget>
<output>0.13</output>
<gadget id="calculator">0.13 * 100</gadget>
<output>13</output>
<result>C</result> | C | 13 | A 40-liter solution of alcohol and water is 5 percent alcohol. If 4.5 liters of alcohol and 5.5 liters of water are added to this solution, what percent of the solution produced is alcohol? | {
"A": "7 %",
"B": "10 %",
"C": "13 %",
"D": "16 %",
"E": "19 %"
} | multiply(divide(add(multiply(40, divide(5, const_100)), 4.5), add(40, add(4.5, 5.5))), const_100) | add(n2,n3)|divide(n1,const_100)|add(n0,#0)|multiply(n0,#1)|add(n2,#3)|divide(#4,#2)|multiply(#5,const_100) | the percent of alcohol in the solution is ( 0.05 ( 40 ) + 4.5 ) / 50 = 6.5 / 50 = 13 % the answer is c . | general |
math_qa__KMD4QQYuHBQEHePf | If n is the smallest integer such that 432 times n is the square of an integer, what is the value of n? Choose the correct choice from the following choices:
A) 2
B) 3
C) 6
D) 12
E) 24 | <gadget id="calculator">432 / 2</gadget>
<output>216</output>
<gadget id="calculator">216 / 2</gadget>
<output>108</output>
<gadget id="calculator">108 / 2</gadget>
<output>54</output>
<gadget id="calculator">54 / 2</gadget>
<output>27</output>
<gadget id="calculator">27 / 3</gadget>
<output>9</output>
<gadget id="calculator">9 / 3</gadget>
<output>3</output>
<result>B</result> | B | 3 | If n is the smallest integer such that 432 times n is the square of an integer, what is the value of n? | {
"A": "2",
"B": "3",
"C": "6",
"D": "12",
"E": "24"
} | divide(divide(divide(divide(divide(divide(432, const_2), const_2), const_2), const_2), const_3), const_3) | divide(n0,const_2)|divide(#0,const_2)|divide(#1,const_2)|divide(#2,const_2)|divide(#3,const_3)|divide(#4,const_3) | the prime factorization of a square has to have even powers of all its prime factors . if the original number has a factor , say of 7 , then when it ’ s squared , the square will have a factor of 7 ^ 2 . another way to say that is : any positive integer all of whose prime factors have even powers must be a perfect square of some other integer . look at the prime factorization of 432 432 = ( 2 ^ 4 ) * ( 3 ^ 3 ) the factor of 2 already has an even power — - that ’ s all set . the factor of 3 currently has an odd power . if n = 3 , then 432 * n would have an even power of 2 and an even power of 3 ; therefore , it would be a perfect square . thus , n = 3 is a choice that makes 432 * n a perfect square . answer : b . | geometry |
math_qa__EJAVm1ltG5eFuHyA | The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average? Choose the correct answer.
A) 72 B) 23 C) 29 D) 26 E) 13 | <gadget id="calculator">36 * 2</gadget>
<output>72</output>
<result>A</result> | A | 72 | The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average? | {
"A": "72",
"B": "23",
"C": "29",
"D": "26",
"E": "13"
} | multiply(36, const_2) | multiply(n1,const_2)| | "sum of the marks for the 12 students = 12 * 36 = 432 . the marks of each student are doubled , the sum also will be doubled . the new sum = 432 * 2 = 864 . so , the new average = 864 / 12 = 72 . answer : a" | general |
math_qa__I9lloeyXHYWKISIp | A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 20 per metre of cloth. What is the cost price of one metre of cloth? Choose one.
A) 21
B) 28
C) 90
D) 85
E) 11 | <gadget id="calculator">8_925 / 85</gadget>
<output>105</output>
<gadget id="calculator">105 - 20</gadget>
<output>85</output>
<result>D</result> | D | 85 | A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 20 per metre of cloth. What is the cost price of one metre of cloth? | {
"A": "21",
"B": "28",
"C": "90",
"D": "85",
"E": "11"
} | subtract(divide(8925, 85), 20) | divide(n1,n0)|subtract(#0,n2)| | "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 20 = rs . 85 . answer : d" | physics |
math_qa__MSRbRKHC5CK8UdwV | If the simple interest on $1500 increase by $20,when the time increase by 2 years. Find the rate percent per annum.
Choose the correct choice:
A) 0.6 %
B) 0.5 %
C) 0.1 %
D) 0.2 %
E) 0.7 % | <gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 / 1_500</gadget>
<output>1/150 = around 0.006667</output>
<gadget id="calculator">(1/150) * 100</gadget>
<output>2/3 = around 0.666667</output>
<result>E</result> | E | 0.7 | If the simple interest on $1500 increase by $20,when the time increase by 2 years. Find the rate percent per annum. | {
"A": "0.6 %",
"B": "0.5 %",
"C": "0.1 %",
"D": "0.2 %",
"E": "0.7 %"
} | multiply(divide(divide(20, 2), 1500), const_100) | divide(n1,n2)|divide(#0,n0)|multiply(#1,const_100) | applying the above formula , we have 20 = 1500 * r * 2 / 100 r = 20 * 100 / 1500 * 2 = 0.7 % . answer is e | gain |
math_qa__ujsQV5BvXeNxqOGT | A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.8.40 less, he would have gained 30%. Find the cost of the article. Choose the correct answer
A) 30 B) 40 C) 50 D) 60 E) 70 | <gadget id="calculator">8.4 * 100</gadget>
<output>840</output>
<gadget id="calculator">25 + 100</gadget>
<output>125</output>
<gadget id="calculator">30 + 100</gadget>
<output>130</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">130 * 80</gadget>
<output>10_400</output>
<gadget id="calculator">10_400 / 100</gadget>
<output>104</output>
<gadget id="calculator">125 - 104</gadget>
<output>21</output>
<gadget id="calculator">840 / 21</gadget>
<output>40</output>
<result>B</result> | B | 40 | A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.8.40 less, he would have gained 30%. Find the cost of the article. | {
"A": "30",
"B": "40",
"C": "50",
"D": "60",
"E": "70"
} | divide(multiply(8.40, const_100), subtract(add(25, const_100), divide(multiply(add(30, const_100), subtract(const_100, 20)), const_100))) | add(n0,const_100)|add(n3,const_100)|multiply(n2,const_100)|subtract(const_100,n1)|multiply(#1,#3)|divide(#4,const_100)|subtract(#0,#5)|divide(#2,#6)| | "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 8.40 when c . p = ( 100 * 8.40 ) / 21 = 40 answer : b" | gain |
math_qa__rkTlMVq9TPbBWi3V | The cube root of what integer power of 2 is closest to 50? Choose one:
A) 16
B) 17
C) 18
D) 19
E) 20 | <gadget id="calculator">50 / 2</gadget>
<output>25</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">25 - 8</gadget>
<output>17</output>
<result>B</result> | B | 17 | The cube root of what integer power of 2 is closest to 50? | {
"A": "16",
"B": "17",
"C": "18",
"D": "19",
"E": "20"
} | subtract(divide(50, 2), add(const_4, const_4)) | add(const_4,const_4)|divide(n1,n0)|subtract(#1,#0) | integer powers of 2 = 2 , 2 ^ 2 , 2 ^ 3 , 2 ^ 4 , 2 ^ 5 , 2 ^ 6 , 2 ^ 7 etc . let , cube root of x is closest to 50 i . e . x is closest to cube of 50 = 50 * 50 * 50 = 125000 but x must be equivalent to an integer power of 2 2 ^ 10 = 1024 2 ^ 7 = 128 i . e . 2 ^ 17 = 128 * 1024 = 128000 ( approx . ) i . e . 2 ^ 18 = 256 * 1024 = 256000 ( approx . ) i . e . 2 ^ 16 = 64 * 1024 = 64000 ( approx . ) i . e . 2 ^ 17 which is closest to 125000 i . e . integer power of 2 must be 7 answer : option b | geometry |
math_qa__3bQLQHaeb6nFanB9 | A watch was sold at a loss of 10%. If it was sold for Rs.190 more, there would have been a gain of 4%. What is the cost price? Choices:
A) s . 1000 B) s . 1009 C) s . 1007 D) s . 1357.1 E) s . 1002 | <gadget id="calculator">190 * 100</gadget>
<output>19_000</output>
<gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">104 - 90</gadget>
<output>14</output>
<gadget id="calculator">19_000 / 14</gadget>
<output>9_500/7 = around 1_357.142857</output>
<result>D</result> | D | 1,357.1 | A watch was sold at a loss of 10%. If it was sold for Rs.190 more, there would have been a gain of 4%. What is the cost price? | {
"A": "s . 1000",
"B": "s . 1009",
"C": "s . 1007",
"D": "s . 1357.1",
"E": "s . 1002"
} | divide(multiply(190, const_100), subtract(add(const_100, 4), subtract(const_100, 10))) | add(const_100,n2)|multiply(n1,const_100)|subtract(const_100,n0)|subtract(#0,#2)|divide(#1,#3)| | "explanation : 90 % 104 % - - - - - - - - 14 % - - - - 190 100 % - - - - ? = > rs . 1357.1 answer : d" | gain |
math_qa__xDRASzcnr69GsicP | if 3 ^ x * 4 ^ y = 19683 and x – y = 9 , then x = ? Pick: A) 8 B) 9 C) 10 D) 11 E) 12 | <gadget id="calculator">3 ** 9</gadget>
<output>19_683</output>
<gadget id="calculator">19_683 / 19_683</gadget>
<output>1</output>
<gadget id="calculator">log(1)</gadget>
<output>0</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">log(12)</gadget>
<output>log(12) = around 2.484907</output>
<gadget id="calculator">0 / log(12)</gadget>
<output>0</output>
<gadget id="calculator">9 - 0</gadget>
<output>9</output>
<result>B</result> | B | 9 | if 3 ^ x * 4 ^ y = 19683 and x – y = 9 , then x = ? | {
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "12"
} | subtract(9, divide(log(divide(power(3, 9), 19683)), log(multiply(3, 4)))) | multiply(n0,n1)|power(n0,n3)|divide(#1,n2)|log(#0)|log(#2)|divide(#4,#3)|subtract(n3,#5) | since 19,683 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 9 and y = 0 , then x = 9 . the answer is b . | general |
math_qa__RlXqYS4nVtDLvCrp | In triangle PQR, the angle Q = 90 degree, PQ = 2 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ Choices:
A) 1.6 cm
B) 2.4 cm
C) 4.8 cm
D) 2.16 cm
E) 3.2 cm | <gadget id="calculator">2 * 8</gadget>
<output>16</output>
<gadget id="calculator">16 / 10</gadget>
<output>8/5 = around 1.6</output>
<result>A</result> | A | 1.6 | In triangle PQR, the angle Q = 90 degree, PQ = 2 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ | {
"A": "1.6 cm",
"B": "2.4 cm",
"C": "4.8 cm",
"D": "2.16 cm",
"E": "3.2 cm"
} | divide(multiply(2, 8), const_10) | multiply(n1,n2)|divide(#0,const_10)| | "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 2 = 8 : 10 - - > qy = 1.6 . answer : a ." | geometry |
math_qa__183H0lteoIjq3xxN | 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.210 only. Men’s wages are?
Choose the correct choice from the following answers:
A) 6 rs
B) 2 rs
C) 4 rs
D) 9 rs
E) 14 rs | <gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">210 / 15</gadget>
<output>14</output>
<result>E</result> | E | 14 | 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.210 only. Men’s wages are? | {
"A": "6 rs",
"B": "2 rs",
"C": "4 rs",
"D": "9 rs",
"E": "14 rs"
} | divide(210, multiply(const_3, 5)) | multiply(n0,const_3)|divide(n2,#0)| | "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 210 rs . 5 m + 5 m + 5 m - - - - - 210 rs . 15 m - - - - - - 210 rs . = > 1 m = 14 rs . answer : e" | general |
math_qa__AruoY48kpG3GkLMd | Express a speed of 60 kmph in meters per second? Choose the correct choice from the following options.
A) 10 mps B) 16.67 mps C) 97.67 mps D) 17.67 mps E) 18 mps | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 60</gadget>
<output>50/3 = around 16.666667</output>
<result>B</result> | B | 16.67 | Express a speed of 60 kmph in meters per second? | {
"A": "10 mps",
"B": "16.67 mps",
"C": "97.67 mps",
"D": "17.67 mps",
"E": "18 mps"
} | multiply(const_0_2778, 60) | multiply(n0,const_0_2778)| | "60 * 5 / 18 = 16.67 mps answer : b" | physics |
math_qa__FXpY95MsLznQavwa | A person decided to build a house in 100days. He employed 100men in the beginning and 100 more after 50 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished? Choose the correct option
A) 40 B) 80 C) 50 D) 60 E) 50 | <gadget id="calculator">100 - 50</gadget>
<output>50</output>
<result>C</result> | C | 50 | A person decided to build a house in 100days. He employed 100men in the beginning and 100 more after 50 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished? | {
"A": "40",
"B": "80",
"C": "50",
"D": "60",
"E": "50"
} | subtract(100, 50) | subtract(n0,n3) | 200 men do the rest of the work in 100 - 50 = 50 days 100 men can do the rest of the work in 50 * 200 / 100 = 100 days required number of days = 100 - 50 = 50 days answer is c | general |
math_qa__1RTgtcPU5TmmdTLX | How many multiples of 6 are there between 30 and 140, 30 and 140 inclusive ? Choose the correct choice from the following choices.
A) 18 B) 16 C) 17 D) 19 E) 15 | <gadget id="calculator">140 - 30</gadget>
<output>110</output>
<gadget id="calculator">110 / 6</gadget>
<output>55/3 = around 18.333333</output>
<gadget id="calculator">(55/3) + 1</gadget>
<output>58/3 = around 19.333333</output>
<result>D</result> | D | 19 | How many multiples of 6 are there between 30 and 140, 30 and 140 inclusive ? | {
"A": "18",
"B": "16",
"C": "17",
"D": "19",
"E": "15"
} | add(divide(subtract(140, 30), 6), const_1) | subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)| | "6 multiples are . . . 30 , 36,42 , 48,54 , 60,66 , 72,78 , 84,90 , 96,102 , 108,114 , 120,126 , 132,138 , . . . , . . . , the answer is = 19 answer is d" | general |
math_qa__uJGF3hlfUKT6uZWx | How many seconds will a 400 metre long train take to cross a man running with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 46 km/hr? Choose the correct answer:
A) 25 B) 30 C) 40 D) 45 E) 36 | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">46 - 6</gadget>
<output>40</output>
<gadget id="calculator">(5/18) * 40</gadget>
<output>100/9 = around 11.111111</output>
<gadget id="calculator">400 / (100/9)</gadget>
<output>36</output>
<result>E</result> | E | 36 | How many seconds will a 400 metre long train take to cross a man running with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 46 km/hr? | {
"A": "25",
"B": "30",
"C": "40",
"D": "45",
"E": "36"
} | divide(400, multiply(const_0_2778, subtract(46, 6))) | subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)| | "explanation : speed of train relatively to man = ( 46 - 6 ) km / hr = 40 km / hr = ( 40 x 5 / 18 ) m / sec = 11.11 m / sec time taken to pass the man = ( 400 / 11.11 ) sec = 36 sec . answer : e" | physics |
math_qa__hb3YnbnNLUQmXzZx | If x+y=24, x-y=40, for integers of x and y, x=? Choices.
A) 20 B) 23 C) 25 D) 32 E) 42 | <gadget id="calculator">24 + 40</gadget>
<output>64</output>
<gadget id="calculator">64 / 2</gadget>
<output>32</output>
<result>D</result> | D | 32 | If x+y=24, x-y=40, for integers of x and y, x=? | {
"A": "20",
"B": "23",
"C": "25",
"D": "32",
"E": "42"
} | divide(add(24, 40), const_2) | add(n0,n1)|divide(#0,const_2)| | "x + y = 24 x - y = 40 2 x = 64 x = 32 answer is d" | general |
math_qa__ebtrE2xI8w6A7Ru3 | A car traveling at a certain constant speed takes 12 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
Choose the correct choice from the following answers.
A) 60 B) 72 C) 72.5 D) 73 E) 73.5 | <gadget id="calculator">1 / 75</gadget>
<output>1/75 = around 0.013333</output>
<gadget id="calculator">3_600 * (1/75)</gadget>
<output>48</output>
<gadget id="calculator">48 + 12</gadget>
<output>60</output>
<gadget id="calculator">60 / 3_600</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">1 / (1/60)</gadget>
<output>60</output>
<result>A</result> | A | 60 | A car traveling at a certain constant speed takes 12 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? | {
"A": "60",
"B": "72",
"C": "72.5",
"D": "73",
"E": "73.5"
} | divide(1, divide(add(multiply(const_3600, divide(1, 75)), 12), const_3600)) | divide(n1,n3)|multiply(#0,const_3600)|add(n0,#1)|divide(#2,const_3600)|divide(n1,#3)| | "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 75 kilometers per hour is 1 / 75 hours = 3,600 / 75 seconds = 48 seconds ; time to cover this distance at regular speed is 48 + 12 = 60 seconds = 60 / 3,600 hours = 1 / 60 hours ; so , we get that to cover 1 kilometer 1 / 60 hours is needed - - > regular speed 60 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : a" | physics |
math_qa__Dwrajx7Z8xXF1sT1 | If 222 = 6
333 = 12
444 = 20
Then, 555 = ?? Choose the most appropriate option.
A) 30
B) 35
C) 40
D) 45
E) 50 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 6</gadget>
<output>30</output>
<result>A</result> | A | 30 | If 222 = 6
333 = 12
444 = 20
Then, 555 = ?? | {
"A": "30",
"B": "35",
"C": "40",
"D": "45",
"E": "50"
} | multiply(add(const_2, const_3), 6) | add(const_2,const_3)|multiply(n1,#0) | 222 = 2 * 2 + 2 = 6 333 = 3 * 3 + 3 = 12 444 = 4 * 4 + 4 = 20 555 = 5 * 5 + 5 = 30 answer : a | general |
math_qa__oRVCWFKvvH7xxV1l | A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth?
Pick.
A) 205 B) 200 C) 180 D) 195 E) 175 | <gadget id="calculator">25 / 0.128</gadget>
<output>195.3125</output>
<result>D</result> | D | 195 | A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth? | {
"A": "205",
"B": "200",
"C": "180",
"D": "195",
"E": "175"
} | divide(25, 0.128) | divide(n1,n0)| | "explanation : let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.128 : 25 : : 1 : x ⇒ 0.128 x = 25 ⇒ x = 25 / 0.128 = 25000 / 128 = 3125 / 16 ≈ 195 answer : option d" | physics |
math_qa__LzYcqhcrpNidcwgM | A man goes from A to B at a speed of 14 kmph and comes back to A at a speed of 10 kmph. Find his average speed for the entire journey?
Answers.
A) 11.6 kmph B) 12.9 kmph C) 12.8 kmph D) 11.9 kmph E) 12.6 kmph | <gadget id="calculator">14 + 10</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<result>A</result> | A | 11.6 | A man goes from A to B at a speed of 14 kmph and comes back to A at a speed of 10 kmph. Find his average speed for the entire journey? | {
"A": "11.6 kmph",
"B": "12.9 kmph",
"C": "12.8 kmph",
"D": "11.9 kmph",
"E": "12.6 kmph"
} | divide(add(14, 10), const_2) | add(n0,n1)|divide(#0,const_2)| | "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 14 ) + ( d / 10 ] = ( 2 d ) / [ 12 d / 70 ) = > 11.6 kmph . answer : a" | physics |
math_qa__hcP7MAVNQolQBKVx | If f(x) = 5 - 2x, then f -1(-3) = ?
Select
A) 1 B) 8 C) 6 D) 4 E) 3 | <gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<result>E</result> | E | 3 | If f(x) = 5 - 2x, then f -1(-3) = ? | {
"A": "1",
"B": "8",
"C": "6",
"D": "4",
"E": "3"
} | subtract(5, multiply(divide(subtract(3, 1), 2), 2)) | subtract(n3,n2)|divide(#0,n1)|multiply(n1,#1)|subtract(n0,#2) | find f - 1 ( x ) and then find f - 1 ( - 3 ) y = 5 - 2 x , given x = 5 - 2 y , interchange x and y 2 y = 5 - x , y = log 2 ( 5 - x ) , solve for y f - 1 ( x ) = log 2 ( 5 - x ) , inverse function f - 1 ( - 3 ) = log 2 ( 5 + 3 ) = log 2 ( 23 ) = 3 correct answer e | general |
math_qa__Y6eXP14ctOKQmi6V | The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 2 type B widgets, and the weight of 4 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget? Choose the correct answer
A) 3 : 5
B) 5 : 7
C) 7 : 9
D) 9 : 11
E) 11 : 13 | <gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">1 + (7/2)</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">(7/2) + 2</gadget>
<output>11/2 = around 5.5</output>
<gadget id="calculator">(9/2) / (11/2)</gadget>
<output>9/11 = around 0.818182</output>
<result>D</result> | D | 0.818182 | The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 2 type B widgets, and the weight of 4 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget? | {
"A": "3 : 5",
"B": "5 : 7",
"C": "7 : 9",
"D": "9 : 11",
"E": "11 : 13"
} | divide(add(1, divide(7, 2)), add(divide(7, 2), divide(4, 2))) | divide(n0,n1)|divide(n2,n1)|add(n4,#0)|add(#0,#1)|divide(#2,#3)| | "4 b = 7 c and so b = 7 c / 4 7 a = 2 b and so a = 2 b / 7 = c / 2 a + b = c / 2 + 7 c / 4 = 9 c / 4 b + c = 7 c / 4 + c = 11 c / 4 the ratio of a + b : b + c = 9 : 11 the answer is d ." | general |
math_qa__0gaiKuZXkWeTgNTp | How many seconds will a 700 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ? Select: A) 48 B) 36 C) 42 D) 11 E) 18 | <gadget id="calculator">63 - 3</gadget>
<output>60</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">700 / (50/3)</gadget>
<output>42</output>
<result>C</result> | C | 42 | How many seconds will a 700 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ? | {
"A": "48",
"B": "36",
"C": "42",
"D": "11",
"E": "18"
} | divide(700, multiply(subtract(63, 3), const_0_2778)) | subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | "explanation : here distance d = 700 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 42 sec . answer : c" | physics |
math_qa__DnZHk3DoR7LMfnOY | Joan and Karl each bought a telescopes and the sum of their purchases was $400. If twice of what Joan paid was $74 more than what Karl paid, what did Joan pay for her telescope? Choose the correct choice from the following choices: A) $ 150 B) $ 152 C) $ 154 D) $ 156 E) $ 158 | <gadget id="calculator">400 * 2</gadget>
<output>800</output>
<gadget id="calculator">800 - 74</gadget>
<output>726</output>
<gadget id="calculator">726 / 3</gadget>
<output>242</output>
<gadget id="calculator">400 - 242</gadget>
<output>158</output>
<result>E</result> | E | 158 | Joan and Karl each bought a telescopes and the sum of their purchases was $400. If twice of what Joan paid was $74 more than what Karl paid, what did Joan pay for her telescope? | {
"A": "$ 150",
"B": "$ 152",
"C": "$ 154",
"D": "$ 156",
"E": "$ 158"
} | subtract(400, divide(subtract(multiply(400, const_2), 74), const_3)) | multiply(n0,const_2)|subtract(#0,n1)|divide(#1,const_3)|subtract(n0,#2) | j + k = 400 so k = 400 - j 2 j = k + 74 2 j = ( 400 - j ) + 74 3 j = 474 j = 158 the answer is e . | general |
math_qa__rNo9jVujIXQ26Ubl | A can do a piece of work in 8 days. He works at it for 4 days and then B finishes it in 6 days. In how many days can A and B together finish the work? Select the correct option:
A) 4.1 days
B) 4.8 days
C) 3.8 days
D) 2.8 days
E) 4.5 days | <gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/8) + (1/12)</gadget>
<output>5/24 = around 0.208333</output>
<gadget id="calculator">1 / (5/24)</gadget>
<output>24/5 = around 4.8</output>
<result>B</result> | B | 4.8 | A can do a piece of work in 8 days. He works at it for 4 days and then B finishes it in 6 days. In how many days can A and B together finish the work? | {
"A": "4.1 days",
"B": "4.8 days",
"C": "3.8 days",
"D": "2.8 days",
"E": "4.5 days"
} | inverse(add(divide(const_1, 8), divide(const_1, multiply(6, const_2)))) | divide(const_1,n0)|multiply(n2,const_2)|divide(const_1,#1)|add(#0,#2)|inverse(#3) | 4 / 8 + 6 / x = 1 = > x = 12 1 / 8 + 1 / 12 = 5 / 24 = > 4.8 days answer : b | physics |
math_qa__cSEcGuFoz4l2dutF | A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 12 minutes. Then the speed of the current is : Choose the correct choice from the following: A) 1 kmph B) 2 kmph C) 3 kmph D) 2.5 kmph E) 3.5 kmph | <gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/12) * 60</gadget>
<output>5</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 60</gadget>
<output>3</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<result>A</result> | A | 1 | A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 12 minutes. Then the speed of the current is : | {
"A": "1 kmph",
"B": "2 kmph",
"C": "3 kmph",
"D": "2.5 kmph",
"E": "3.5 kmph"
} | divide(subtract(multiply(divide(1, 12), const_60), multiply(divide(1, 20), const_60)), const_2) | divide(n0,n3)|divide(n0,n1)|multiply(#0,const_60)|multiply(#1,const_60)|subtract(#2,#3)|divide(#4,const_2) | rate upstream = ( 1 / 20 * 60 ) = 3 kmph rate dowm stream = 1 / 12 * 60 = 5 kmph rate of the current = ½ ( 5 - 3 ) = 1 kmph answer : a | physics |
math_qa__xxoAecQKRhK4CWYV | A parking garage rents parking spaces for $10 per week or $40 per month. How much does a person save in a year by renting by the month rather than by the week? Options.
A) $ 40 B) $ 160 C) $ 220 D) $ 240 E) $ 260 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">50 + 2</gadget>
<output>52</output>
<gadget id="calculator">52 * 10</gadget>
<output>520</output>
<gadget id="calculator">40 * 12</gadget>
<output>480</output>
<gadget id="calculator">520 - 480</gadget>
<output>40</output>
<result>A</result> | A | 40 | A parking garage rents parking spaces for $10 per week or $40 per month. How much does a person save in a year by renting by the month rather than by the week? | {
"A": "$ 40",
"B": "$ 160",
"C": "$ 220",
"D": "$ 240",
"E": "$ 260"
} | subtract(multiply(add(multiply(10, add(const_3, const_2)), const_2), 10), multiply(40, const_12)) | add(const_2,const_3)|multiply(n1,const_12)|multiply(#0,n0)|add(#2,const_2)|multiply(n0,#3)|subtract(#4,#1)| | "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 40 = 480 $ 520 - 480 = 40 ans a" | general |
math_qa__mRmS2iNZuzP3hlYW | What sum of money will produce Rs.70 as simple interest in 4 years at 4 1/2 percent?
Pick
A) 263 B) 500 C) 388.9 D) 368 E) 339 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">4 + (1/2)</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">4 * (9/2)</gadget>
<output>18</output>
<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">70 / (9/50)</gadget>
<output>3_500/9 = around 388.888889</output>
<result>C</result> | C | 388.9 | What sum of money will produce Rs.70 as simple interest in 4 years at 4 1/2 percent? | {
"A": "263",
"B": "500",
"C": "388.9",
"D": "368",
"E": "339"
} | divide(70, divide(multiply(4, add(4, divide(1, 2))), const_100)) | divide(n3,n4)|add(n2,#0)|multiply(n1,#1)|divide(#2,const_100)|divide(n0,#3)| | "70 = ( p * 4 * 9 / 2 ) / 100 p = 388.9 answer : c" | gain |
math_qa__YsIlcXsYUNgJhabA | In a dairy farm, 34 cows eat 34 bags of husk in 34 days. In how many days one cow will eat one bag of husk ? Choose the correct choice from the following answers.
A) 34 days B) 40 days C) 46 days D) 50 days E) none of these | <gadget id="calculator">34 / 34</gadget>
<output>1</output>
<gadget id="calculator">1 * 34</gadget>
<output>34</output>
<result>A</result> | A | 34 | In a dairy farm, 34 cows eat 34 bags of husk in 34 days. In how many days one cow will eat one bag of husk ? | {
"A": "34 days",
"B": "40 days",
"C": "46 days",
"D": "50 days",
"E": "none of these"
} | multiply(divide(34, 34), 34) | divide(n0,n0)|multiply(n0,#0)| | "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 34 bags 34 1 ] : : 34 : x = > x ∗ 34 ∗ 1 = 34 ∗ 1 ∗ 34 = > x = 34 option a" | physics |
math_qa__tE0qPSVo0l3fTH8J | If the sides of a triangle are 28 cm, 24 cm and 15 cm, what is its area?
Choose the correct choice from the following answers.
A) 180 cm 2 B) 112 cm 2 C) 776 cm 2 D) 666 cm 2 E) 886 cm 2 | <gadget id="calculator">24 * 15</gadget>
<output>360</output>
<gadget id="calculator">360 / 2</gadget>
<output>180</output>
<result>A</result> | A | 180 | If the sides of a triangle are 28 cm, 24 cm and 15 cm, what is its area? | {
"A": "180 cm 2",
"B": "112 cm 2",
"C": "776 cm 2",
"D": "666 cm 2",
"E": "886 cm 2"
} | divide(multiply(24, 15), const_2) | multiply(n1,n2)|divide(#0,const_2)| | "the triangle with sides 28 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : a" | geometry |
math_qa__GoskznYouevfJnQS | 10 play kabadi, 20 play kho kho only, 5 play both gmaes. Then how many in total? Choose the correct choice from the following options
A) 30
B) 35
C) 38
D) 40
E) 45 | <gadget id="calculator">20 + 5</gadget>
<output>25</output>
<gadget id="calculator">10 + 25</gadget>
<output>35</output>
<gadget id="calculator">35 - 5</gadget>
<output>30</output>
<result>A</result> | A | 30 | 10 play kabadi, 20 play kho kho only, 5 play both gmaes. Then how many in total? | {
"A": "30",
"B": "35",
"C": "38",
"D": "40",
"E": "45"
} | subtract(add(10, add(20, 5)), 5) | add(n1,n2)|add(n0,#0)|subtract(#1,n2)| | "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 20 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 20 + 5 = 25 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 25 - 5 = 30 answer : a" | general |
math_qa__SAo4gEaq3fLwWN1D | If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 210 games will be played during the tournament. What is the number of participants? Choose the correct answer.
A) 18 B) 19 C) 20 D) 21 E) 22 | <gadget id="calculator">210 * 2</gadget>
<output>420</output>
<gadget id="calculator">420 * 4</gadget>
<output>1_680</output>
<gadget id="calculator">1_680 + 1</gadget>
<output>1_681</output>
<gadget id="calculator">1_681 ** (1/2)</gadget>
<output>41</output>
<gadget id="calculator">41 + 1</gadget>
<output>42</output>
<gadget id="calculator">42 / 2</gadget>
<output>21</output>
<result>D</result> | D | 21 | If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 210 games will be played during the tournament. What is the number of participants? | {
"A": "18",
"B": "19",
"C": "20",
"D": "21",
"E": "22"
} | divide(add(sqrt(add(multiply(multiply(210, const_2), const_4), const_1)), const_1), const_2) | multiply(n0,const_2)|multiply(#0,const_4)|add(#1,const_1)|sqrt(#2)|add(#3,const_1)|divide(#4,const_2)| | "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 210 n * ( n - 1 ) = 420 = 21 * 20 ( trial and error ) the answer is d ." | general |
math_qa__nzUjv17nV2HBN8Hw | Sandy is younger than Molly by 14 years. If the ratio of their ages is 7:9, how old is Sandy?
Choose the most appropriate option: A) 42 B) 49 C) 56 D) 63 E) 70 | <gadget id="calculator">9 - 7</gadget>
<output>2</output>
<gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">(7/2) * 14</gadget>
<output>49</output>
<result>B</result> | B | 49 | Sandy is younger than Molly by 14 years. If the ratio of their ages is 7:9, how old is Sandy? | {
"A": "42",
"B": "49",
"C": "56",
"D": "63",
"E": "70"
} | multiply(divide(7, subtract(9, 7)), 14) | subtract(n2,n1)|divide(n1,#0)|multiply(n0,#1)| | "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 14 x = 7 sandy is 49 years old . the answer is b ." | other |
math_qa__HsVKRzbOdJ4l5qNL | A train 605 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Choose one:
A) 51
B) 64
C) 11
D) 22
E) 33 | <gadget id="calculator">605 / 1_000</gadget>
<output>121/200 = around 0.605</output>
<gadget id="calculator">60 + 6</gadget>
<output>66</output>
<gadget id="calculator">(121/200) / 66</gadget>
<output>11/1_200 = around 0.009167</output>
<gadget id="calculator">3_600 * (11/1_200)</gadget>
<output>33</output>
<result>E</result> | E | 33 | A train 605 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? | {
"A": "51",
"B": "64",
"C": "11",
"D": "22",
"E": "33"
} | multiply(const_3600, divide(divide(605, const_1000), add(60, 6))) | add(n1,n2)|divide(n0,const_1000)|divide(#1,#0)|multiply(#2,const_3600)| | "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 605 * 3 / 55 ] sec = 33 sec answer : e" | physics |
math_qa__LRBbGNBrHG36ccSU | The average of 13 numbers is 60. Average of the first 6 of them is 57 and that of the last 8 is 61. Find the 8th number? Choose the correct choice from the following answers: A) 46 B) 48 C) 50 D) 52 E) 54 | <gadget id="calculator">8 * 61</gadget>
<output>488</output>
<gadget id="calculator">13 * 60</gadget>
<output>780</output>
<gadget id="calculator">57 * 6</gadget>
<output>342</output>
<gadget id="calculator">780 - 342</gadget>
<output>438</output>
<gadget id="calculator">488 - 438</gadget>
<output>50</output>
<result>C</result> | C | 50 | The average of 13 numbers is 60. Average of the first 6 of them is 57 and that of the last 8 is 61. Find the 8th number? | {
"A": "46",
"B": "48",
"C": "50",
"D": "52",
"E": "54"
} | subtract(multiply(8, 61), subtract(multiply(13, 60), multiply(57, 6))) | multiply(n5,n6)|multiply(n0,n1)|multiply(n2,n3)|subtract(#1,#2)|subtract(#0,#3)| | "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 6 of them = 6 * 57 = 342 sum of the last 8 of them = 8 * 61 = 488 so , the 8 th number = 342 + 488 - 780 = 50 . answer : c" | general |
math_qa__3q0MbOrSYX934p7q | is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, then how old is B?
Pick: A) 7 B) 8 C) 9 D) 10 E) 11 | <gadget id="calculator">22 - 2</gadget>
<output>20</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<result>B</result> | B | 8 | is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 22, then how old is B? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10",
"E": "11"
} | multiply(divide(subtract(22, const_2), add(const_3, const_2)), const_2) | add(const_2,const_3)|subtract(n0,const_2)|divide(#1,#0)|multiply(#2,const_2)| | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 5 x = 20 = > x = 4 hence , b ' s age = 2 x = 8 years . answer : b" | general |
math_qa__EQJgGzFWXsfYysl3 | In a fuel station the service costs $2.20 per vehicle and every liter of fuel costs $0.70. Assuming that you fill up 3 mini-vans and 2 trucks, what will be the total cost, if a mini-van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty?
Select the correct option
A) $ 341.50 B) $ 344.60 C) $ 347.70 D) $ 350.80 E) $ 353.90 | <gadget id="calculator">120 * 65</gadget>
<output>7_800</output>
<gadget id="calculator">7_800 / 100</gadget>
<output>78</output>
<gadget id="calculator">78 + 65</gadget>
<output>143</output>
<gadget id="calculator">143 * 2</gadget>
<output>286</output>
<gadget id="calculator">286 * 0.7</gadget>
<output>200.2</output>
<gadget id="calculator">3 * 65</gadget>
<output>195</output>
<gadget id="calculator">195 * 0.7</gadget>
<output>136.5</output>
<gadget id="calculator">200.2 + 136.5</gadget>
<output>336.7</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">2.2 * 5</gadget>
<output>11</output>
<gadget id="calculator">336.7 + 11</gadget>
<output>347.7</output>
<result>C</result> | C | 347.7 | In a fuel station the service costs $2.20 per vehicle and every liter of fuel costs $0.70. Assuming that you fill up 3 mini-vans and 2 trucks, what will be the total cost, if a mini-van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty? | {
"A": "$ 341.50",
"B": "$ 344.60",
"C": "$ 347.70",
"D": "$ 350.80",
"E": "$ 353.90"
} | add(add(multiply(multiply(add(divide(multiply(120, 65), const_100), 65), 2), 0.70), multiply(multiply(3, 65), 0.70)), multiply(2.20, add(3, 2))) | add(n2,n3)|multiply(n4,n5)|multiply(n2,n4)|divide(#1,const_100)|multiply(n1,#2)|multiply(n0,#0)|add(n4,#3)|multiply(n3,#6)|multiply(n1,#7)|add(#8,#4)|add(#9,#5)| | "the service cost of 3 vans and 2 trucks is 5 * 2.20 $ 11.00 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.7 = $ 336.70 the total cost is $ 336.70 + $ 11.00 = $ 347.70 the answer is c ." | general |
math_qa__o36vXCKXCbMwIt62 | An article is bought for Rs.600 and sold for Rs.550, find the loss percent? Options
A) 8.33 % B) 16 7 / 3 % C) 16 2 / 8 % D) 16 2 / 3 % E) 76 2 / 3 % | <gadget id="calculator">550 * 100</gadget>
<output>55_000</output>
<gadget id="calculator">55_000 / 600</gadget>
<output>275/3 = around 91.666667</output>
<gadget id="calculator">100 - (275/3)</gadget>
<output>25/3 = around 8.333333</output>
<result>A</result> | A | 8.33 | An article is bought for Rs.600 and sold for Rs.550, find the loss percent? | {
"A": "8.33 %",
"B": "16 7 / 3 %",
"C": "16 2 / 8 %",
"D": "16 2 / 3 %",
"E": "76 2 / 3 %"
} | subtract(const_100, divide(multiply(550, const_100), 600)) | multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)| | "600 - - - - 50 100 - - - - ? = > 8.33 % answer : a" | gain |
math_qa__g0Nd7kvHGu5TsvNK | It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 120 pages? Select:
A) 12 B) 18 C) 20 D) 24 E) 36 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">120 * 12</gadget>
<output>1_440</output>
<gadget id="calculator">1_440 / 40</gadget>
<output>36</output>
<result>E</result> | E | 36 | It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 120 pages? | {
"A": "12",
"B": "18",
"C": "20",
"D": "24",
"E": "36"
} | divide(multiply(120, add(multiply(4, const_2), 4)), 40) | multiply(n0,const_2)|add(n0,#0)|multiply(n4,#1)|divide(#2,n1)| | "if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 120 / 50 = 36 minutes to print 120 pages ( answer e )" | physics |
math_qa__LNRWSt92al3lAnjk | John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $30. What is the percent decrease? Choose the correct choice
A) 20 % B) 30 % C) 40 % D) 70 % E) 80 % | <gadget id="calculator">100 - 30</gadget>
<output>70</output>
<result>D</result> | D | 70 | John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $30. What is the percent decrease? | {
"A": "20 %",
"B": "30 %",
"C": "40 %",
"D": "70 %",
"E": "80 %"
} | subtract(100, 30) | subtract(n0,n1)| | "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 30 = 70 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 70 / 100 ) * 100 = ( 0.7 ) * 100 = 70 % . d" | general |
math_qa__g9spMkd6nu1qUIE7 | For the symbol, m”n=n^2−m for all values of m and n. What is the value of 5”3? Choose the most appropriate option.
A) 5 B) 3 C) 2 D) 4 E) 0 | <gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">9 - 5</gadget>
<output>4</output>
<result>D</result> | D | 4 | For the symbol, m”n=n^2−m for all values of m and n. What is the value of 5”3? | {
"A": "5",
"B": "3",
"C": "2",
"D": "4",
"E": "0"
} | subtract(power(3, 2), 5) | power(n2,n0)|subtract(#0,n1)| | "5 ” 3 = 9 - 5 = 4 answer : d" | general |
math_qa__jDUoVrGMxl5g4sq0 | If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 44 kmh, what was the average speed of the car for the entire trip?
Choose the correct choice from the following answers:
A) 39 kmh B) 40 kmh C) 42 kmh D) 44 kmh E) 50 kmh | <gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/80) + (1/24)</gadget>
<output>13/240 = around 0.054167</output>
<gadget id="calculator">1 / 44</gadget>
<output>1/44 = around 0.022727</output>
<gadget id="calculator">(13/240) + (1/44)</gadget>
<output>203/2_640 = around 0.076894</output>
<gadget id="calculator">3 / (203/2_640)</gadget>
<output>7_920/203 = around 39.014778</output>
<result>A</result> | A | 39 | If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 44 kmh, what was the average speed of the car for the entire trip? | {
"A": "39 kmh",
"B": "40 kmh",
"C": "42 kmh",
"D": "44 kmh",
"E": "50 kmh"
} | divide(const_3, add(add(divide(const_1, 80), divide(const_1, 24)), divide(const_1, 44))) | divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|add(#3,#2)|divide(const_3,#4)| | "assume d / 3 = 2640 ( this number is convenient because it is divisible by 80 , 24 and 44 ) so : 2640 = 80 * t 1 = 33 hrs 2640 = 24 * t 2 = 110 hrs 2640 = 44 * t 3 = 60 hrs t = t 1 + t 2 + t 3 = 203 hrs d = rt ( 2640 * 3 ) = r * 203 r = 39 answer : a" | physics |
math_qa__feekWS8yZGRkcBGT | There are 408 boys and 312 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed. Pick one:
A) 31 B) 32 C) 35 D) 30 E) 45 | <gadget id="calculator">408 + 312</gadget>
<output>720</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">720 / 24</gadget>
<output>30</output>
<result>D</result> | D | 30 | There are 408 boys and 312 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed. | {
"A": "31",
"B": "32",
"C": "35",
"D": "30",
"E": "45"
} | divide(add(408, 312), multiply(multiply(multiply(const_2, const_2), const_2), const_3)) | add(n0,n1)|multiply(const_2,const_2)|multiply(#1,const_2)|multiply(#2,const_3)|divide(#0,#3)| | "explanation : hcf ( 408 , 312 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 312 / 24 = 17 + 13 = 30 answer : d" | general |
math_qa__kQ4HrOcM7rnrfYl1 | In 20 years, A will be twice as old as B was 20 years ago. If A is now 10 years older than B, the present age of B is?
Choose the correct choice from the following: A) 35 yrs B) 40 yrs C) 50 yrs D) 60 yrs E) 70 yrs | <gadget id="calculator">2 * 20</gadget>
<output>40</output>
<gadget id="calculator">40 + 20</gadget>
<output>60</output>
<gadget id="calculator">60 + 10</gadget>
<output>70</output>
<result>E</result> | E | 70 | In 20 years, A will be twice as old as B was 20 years ago. If A is now 10 years older than B, the present age of B is? | {
"A": "35 yrs",
"B": "40 yrs",
"C": "50 yrs",
"D": "60 yrs",
"E": "70 yrs"
} | add(add(multiply(const_2, 20), 20), 10) | multiply(n0,const_2)|add(n0,#0)|add(n2,#1)| | "let b ' s present age = x years then a ' s present age = x + 10 years x + 10 + 20 = 2 ( x - 20 ) x + 30 = 2 x - 40 x = 70 years answer is e" | general |
math_qa__giMvUtLID27bc2rE | If a 10 percent deposit that has been paid toward the purchase of a certain product is $105, how much more remains to be paid? Select the correct option:
A) $ 945
B) $ 965
C) $ 1025
D) $ 1050
E) $ 1105 | <gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">105 * 10</gadget>
<output>1_050</output>
<gadget id="calculator">1_050 - 105</gadget>
<output>945</output>
<result>A</result> | A | 945 | If a 10 percent deposit that has been paid toward the purchase of a certain product is $105, how much more remains to be paid? | {
"A": "$ 945",
"B": "$ 965",
"C": "$ 1025",
"D": "$ 1050",
"E": "$ 1105"
} | subtract(multiply(105, divide(const_100, 10)), 105) | divide(const_100,n0)|multiply(n1,#0)|subtract(#1,n1)| | "90 % remains to be paid so the remaining amount is 9 * 105 = $ 945 . the answer is a ." | general |
math_qa__LHWlfdaKhGg7mpas | Calculate the dividend from Caleb's stock, if Caleb he invested Rs. 2500 at 79 to obtain an income of Rs. 200. Choose the correct choice from the following choices: A) 6.32 B) 5.32 C) 7.32 D) 2.32 E) 1.32 | <gadget id="calculator">2_500 / 79</gadget>
<output>2_500/79 = around 31.64557</output>
<gadget id="calculator">200 / (2_500/79)</gadget>
<output>158/25 = around 6.32</output>
<result>A</result> | A | 6.32 | Calculate the dividend from Caleb's stock, if Caleb he invested Rs. 2500 at 79 to obtain an income of Rs. 200. | {
"A": "6.32",
"B": "5.32",
"C": "7.32",
"D": "2.32",
"E": "1.32"
} | divide(200, divide(2500, 79)) | divide(n0,n1)|divide(n2,#0) | by investing rs . 2500 , income = rs . 200 by investing rs . 79 , income = 200 ã — 79 / 2500 = 6.32 ie , dividend = 6.32 % answer is a . | gain |
math_qa__FQHBmTdDETjjTLpj | In the biology lab of "Jefferson" High School there are 5.4*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish? Choose the correct answer:
A) 100 B) 200 C) 500 D) 1000 E) 5000 | <gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 * 100</gadget>
<output>1_000_000</output>
<gadget id="calculator">5.4 * 1_000_000</gadget>
<output>5_400_000</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 100</gadget>
<output>800</output>
<gadget id="calculator">10_000 + 800</gadget>
<output>10_800</output>
<gadget id="calculator">5_400_000 / 10_800</gadget>
<output>500</output>
<result>C</result> | C | 500 | In the biology lab of "Jefferson" High School there are 5.4*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish? | {
"A": "100",
"B": "200",
"C": "500",
"D": "1000",
"E": "5000"
} | divide(multiply(5.4, multiply(multiply(const_100, const_100), const_100)), add(multiply(const_100, const_100), multiply(multiply(const_4, const_2), const_100))) | multiply(const_100,const_100)|multiply(const_2,const_4)|multiply(#0,const_100)|multiply(#1,const_100)|add(#0,#3)|multiply(n0,#2)|divide(#5,#4) | 5.4 * 10 ^ 6 / 10800 = = > 54 * 10 ^ 3 / 108 = = > 54000 / 108 = 500 answer : c | general |
math_qa__ruplMN4bqJ422wKF | A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent R should the number of hours worked be increased?
Choose the correct choice from the following:
A) 12.5 % B) 20 % C) 25 % D) 50 % E) 100 % | <gadget id="calculator">10 * 4</gadget>
<output>40</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">(4/5) * 10</gadget>
<output>8</output>
<gadget id="calculator">40 / 8</gadget>
<output>5</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>C</result> | C | 25 | A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent R should the number of hours worked be increased? | {
"A": "12.5 %",
"B": "20 %",
"C": "25 %",
"D": "50 %",
"E": "100 %"
} | multiply(divide(subtract(divide(multiply(const_10, const_4), multiply(divide(subtract(const_100, 20), const_100), const_10)), const_4), const_4), const_100) | multiply(const_10,const_4)|subtract(const_100,n0)|divide(#1,const_100)|multiply(#2,const_10)|divide(#0,#3)|subtract(#4,const_4)|divide(#5,const_4)|multiply(#6,const_100)| | "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked r will be 25 % greater than the original number . the answer is c ." | general |
math_qa__BZYSMqYsUldZhKV1 | At what rate percent per annum will a sum of money double in 16 years. Answers: A) 2.45 % B) 5.62 % C) 5.35 % D) 6.9 % E) 6.25 % | <gadget id="calculator">100 / 16</gadget>
<output>25/4 = around 6.25</output>
<result>E</result> | E | 6.25 | At what rate percent per annum will a sum of money double in 16 years. | {
"A": "2.45 %",
"B": "5.62 %",
"C": "5.35 %",
"D": "6.9 %",
"E": "6.25 %"
} | divide(const_100, 16) | divide(const_100,n0)| | "let principal = p then s . i . = p t = 16 yrs rate = ( 100 * p ) / ( p * 16 ) = 25 / 4 = 6.25 % p . a . answer is e" | gain |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.