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math_qa__ZTH3PwF7nJWLrJlh | Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 1, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
Choose the correct choice from the following answers: A) 1 : 1 B) 2 : 3 C) 5 : 2 D) 4 : 3 E) 7 : 9 | <gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">20 + 12</gadget>
<output>32</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">12 + 12</gadget>
<output>24</output>
<gadget id="calculator">32 / 24</gadget>
<output>4/3 = around 1.333333</output>
<result>D</result> | D | 1.333333 | Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 1, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ? | {
"A": "1 : 1",
"B": "2 : 3",
"C": "5 : 2",
"D": "4 : 3",
"E": "7 : 9"
} | divide(add(multiply(4, 5), multiply(3, divide(add(5, 3), const_2))), add(multiply(4, 3), multiply(3, divide(add(5, 3), const_2)))) | add(n0,n1)|multiply(n0,n4)|multiply(n1,n4)|divide(#0,const_2)|multiply(n1,#3)|add(#1,#4)|add(#2,#4)|divide(#5,#6) | mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 3 and 3 parts , respectively . this will give us in the final mixture ( 5 + 3 ) : ( 3 + 3 ) , which means 4 : 3 answer d . | other |
math_qa__6ro7V4HCRpGfSlar | If x is 11 percent greater than 70, then x = Choose the correct choice from the following answers
A) 77.7 B) 91.0 C) 88.0 D) 70.9 E) 71.2 | <gadget id="calculator">11 / 100</gadget>
<output>11/100 = around 0.11</output>
<gadget id="calculator">(11/100) * 70</gadget>
<output>77/10 = around 7.7</output>
<gadget id="calculator">70 + (77/10)</gadget>
<output>777/10 = around 77.7</output>
<result>A</result> | A | 77.7 | If x is 11 percent greater than 70, then x = | {
"A": "77.7",
"B": "91.0",
"C": "88.0",
"D": "70.9",
"E": "71.2"
} | add(70, multiply(divide(11, const_100), 70)) | divide(n0,const_100)|multiply(n1,#0)|add(n1,#1)| | "11 % of 70 = ( 70 * 0.11 ) = 7.7 11 % greater than 70 = 70 + 7.7 = 77.7 answer is clearly a ." | general |
math_qa__H6wSPYLiVFCcf6IM | If an examination 63% of the candidates in English,65% passed in Mathematics, and 27% failed in both subjects.What is the pass percentage? Choose the correct choice:
A) 55 % B) 60 % C) 65 % D) 75 % E) none . | <gadget id="calculator">100 - 63</gadget>
<output>37</output>
<gadget id="calculator">100 - 65</gadget>
<output>35</output>
<gadget id="calculator">37 + 35</gadget>
<output>72</output>
<gadget id="calculator">72 - 27</gadget>
<output>45</output>
<gadget id="calculator">100 - 45</gadget>
<output>55</output>
<result>A</result> | A | 55 | If an examination 63% of the candidates in English,65% passed in Mathematics, and 27% failed in both subjects.What is the pass percentage? | {
"A": "55 %",
"B": "60 %",
"C": "65 %",
"D": "75 %",
"E": "none ."
} | subtract(const_100, subtract(add(subtract(const_100, 63), subtract(const_100, 65)), 27)) | subtract(const_100,n0)|subtract(const_100,n1)|add(#0,#1)|subtract(#2,n2)|subtract(const_100,#3) | fail in english = 100 - 63 = 37 % fail in maths = 100 - 65 = 35 % so pass % = 100 - ( 37 + 35 - 27 ) = 55 % answer : a | gain |
math_qa__x0B9StUdpO1JOyIM | A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train? Options:
A) 250 meter B) 876 meter C) 167 meter D) 719 meter E) 169 meter | <gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 15</gadget>
<output>250</output>
<result>A</result> | A | 250 | A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train? | {
"A": "250 meter",
"B": "876 meter",
"C": "167 meter",
"D": "719 meter",
"E": "169 meter"
} | multiply(divide(multiply(60, const_1000), const_3600), 15) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 250 meter answer : a" | physics |
math_qa__PFzBqTIMKf30TI2i | Fred and Sam are standing 40 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 4 miles per hour and Sam walks at a constant speed of 4 miles per hour, how many miles has Sam walked when they meet? Choose one:
A) 5 B) 9 C) 20 D) 30 E) 45 | <gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">40 / 8</gadget>
<output>5</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<result>C</result> | C | 20 | Fred and Sam are standing 40 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 4 miles per hour and Sam walks at a constant speed of 4 miles per hour, how many miles has Sam walked when they meet? | {
"A": "5",
"B": "9",
"C": "20",
"D": "30",
"E": "45"
} | multiply(4, divide(40, add(4, 4))) | add(n1,n2)|divide(n0,#0)|multiply(n2,#1)| | "relative distance = 40 miles relative speed = 4 + 4 = 8 miles per hour time taken = 40 / 8 = 5 hours distance travelled by sam = 4 * 5 = 20 miles = c" | physics |
math_qa__EewdqFuNDa9FREWj | A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400? Pick one: A) 2998 B) 1900 C) 2788 D) 2662 E) 1122 | <gadget id="calculator">5 * 7_400</gadget>
<output>37_000</output>
<gadget id="calculator">37_000 / 100</gadget>
<output>370</output>
<gadget id="calculator">7_400 - 370</gadget>
<output>7_030</output>
<gadget id="calculator">10_000 * 3</gadget>
<output>30_000</output>
<gadget id="calculator">7_030 * 30_000</gadget>
<output>210_900_000</output>
<gadget id="calculator">6_500 * 6</gadget>
<output>39_000</output>
<gadget id="calculator">8_400 * 5</gadget>
<output>42_000</output>
<gadget id="calculator">39_000 + 42_000</gadget>
<output>81_000</output>
<gadget id="calculator">81_000 + 30_000</gadget>
<output>111_000</output>
<gadget id="calculator">210_900_000 / 111_000</gadget>
<output>1_900</output>
<result>B</result> | B | 1,900 | A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400? | {
"A": "2998",
"B": "1900",
"C": "2788",
"D": "2662",
"E": "1122"
} | divide(multiply(subtract(7400, divide(multiply(5, 7400), const_100)), multiply(10000, 3)), add(add(multiply(6500, 6), multiply(8400, 5)), multiply(10000, 3))) | multiply(n4,n5)|multiply(n3,n7)|multiply(n0,n1)|multiply(n2,n3)|add(#2,#3)|divide(#1,const_100)|add(#4,#0)|subtract(n7,#5)|multiply(#0,#7)|divide(#8,#6) | 65 * 6 : 84 * 5 : 100 * 3 26 : 28 : 20 c share = 74000 * 95 / 100 = 7030 * 20 / 74 = > 1900 answer : b | gain |
math_qa__NUyPS2vvoZHdk564 | If 25 men do a work in 96 days, in how many days will 40 men do it? Choose the most appropriate option:
A) 66
B) 53
C) 55
D) 60
E) 61 | <gadget id="calculator">25 * 96</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 / 40</gadget>
<output>60</output>
<result>D</result> | D | 60 | If 25 men do a work in 96 days, in how many days will 40 men do it? | {
"A": "66",
"B": "53",
"C": "55",
"D": "60",
"E": "61"
} | divide(multiply(25, 96), 40) | multiply(n0,n1)|divide(#0,n2)| | "25 * 96 = 40 * x x = 60 days answer : d" | physics |
math_qa__QY3yuSuXXlBp6p1g | There are 8 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.
Choose the correct choice from the following choices:
A) 53 B) 54 C) 55 D) 56 E) 57 | <gadget id="calculator">binomial(8, 2)</gadget>
<output>28</output>
<gadget id="calculator">28 + 28</gadget>
<output>56</output>
<result>D</result> | D | 56 | There are 8 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed. | {
"A": "53",
"B": "54",
"C": "55",
"D": "56",
"E": "57"
} | add(choose(8, 2), choose(8, 2)) | choose(n0,n1)|add(#0,#0)| | "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 8 and for second = 7 so total methods = 8 * 7 = 56 answer : d" | probability |
math_qa__n5ng45rzuo1NghDQ | The expression (12.86 × 12.86 + 12.86 × p + 0.14 × 0.14) will be a perfect square for p equal to Choose the correct choice from the following answers.
A) 0.28 B) 0.26 C) 1 D) 0 E) 2 | <gadget id="calculator">0.14 * 2</gadget>
<output>0.28</output>
<result>A</result> | A | 0.28 | The expression (12.86 × 12.86 + 12.86 × p + 0.14 × 0.14) will be a perfect square for p equal to | {
"A": "0.28",
"B": "0.26",
"C": "1",
"D": "0",
"E": "2"
} | multiply(0.14, const_2) | multiply(n3,const_2) | explanation : 12.86 × 12.86 + 12.86 × p + 0.14 × 0.14 = ( 12.86 ) 2 + 12.86 × p + ( 0.14 ) 2 this can be written as ( 12.86 + 0.14 ) 2 = 132 , if 12.86 × p = 2 × 12.86 × 0.14 i . e . , if p = 2 × 0.14 = 0.28 hence , p = 0.28 . answer : option a | general |
math_qa__0jgJcNMdmAmBZvqX | If the sample interest on a sum of money 20% per annum for 2 years is $400, find the compound interest on the same sum for the same period at the same rate? Choose the correct choice from the following options
A) $ 460
B) $ 510
C) $ 440
D) $ 500
E) $ 550 | <gadget id="calculator">400 * 100</gadget>
<output>40_000</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">40_000 / 40</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 * 20</gadget>
<output>20_000</output>
<gadget id="calculator">20_000 / 100</gadget>
<output>200</output>
<gadget id="calculator">1_000 + 200</gadget>
<output>1_200</output>
<gadget id="calculator">1_200 * 20</gadget>
<output>24_000</output>
<gadget id="calculator">24_000 / 100</gadget>
<output>240</output>
<gadget id="calculator">240 + 1_200</gadget>
<output>1_440</output>
<gadget id="calculator">1_440 - 1_000</gadget>
<output>440</output>
<result>C</result> | C | 440 | If the sample interest on a sum of money 20% per annum for 2 years is $400, find the compound interest on the same sum for the same period at the same rate? | {
"A": "$ 460",
"B": "$ 510",
"C": "$ 440",
"D": "$ 500",
"E": "$ 550"
} | subtract(add(divide(multiply(add(divide(multiply(400, const_100), multiply(20, 2)), divide(multiply(divide(multiply(400, const_100), multiply(20, 2)), 20), const_100)), 20), const_100), add(divide(multiply(400, const_100), multiply(20, 2)), divide(multiply(divide(multiply(400, const_100), multiply(20, 2)), 20), const_100))), divide(multiply(400, const_100), multiply(20, 2))) | multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)|multiply(n0,#2)|divide(#3,const_100)|add(#2,#4)|multiply(n0,#5)|divide(#6,const_100)|add(#5,#7)|subtract(#8,#2)| | "rate = 20 % time = 2 years s . i . = $ 400 principal = 100 * 400 / 20 * 2 = $ 1000 amount = 1000 ( 1 + 20 / 100 ) ^ 2 = $ 1440 c . i . = 1440 - 1000 = $ 440 answer is c" | gain |
math_qa__LLclUvof4kfdQYiH | A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is Choose the correct answer:
A) 36 B) 40 C) 99 D) 13 E) 12 | <gadget id="calculator">83 - 63</gadget>
<output>20</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<result>B</result> | B | 40 | A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is | {
"A": "36",
"B": "40",
"C": "99",
"D": "13",
"E": "12"
} | multiply(subtract(83, 63), const_2) | subtract(n0,n1)|multiply(#0,const_2)| | "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 . answer : b" | general |
math_qa__0vZHixWuiA8Av26g | A man travelled a distance of 80 km in 7 hours partly on foot at the rate of 8 km per hour and partly on bicycle at 16 km per hour. Find the distance travelled on foot.
Choose the correct choice:
A) 26 km B) 32 km C) 30 km D) 28 km E) none | <gadget id="calculator">16 * 7</gadget>
<output>112</output>
<gadget id="calculator">112 - 80</gadget>
<output>32</output>
<result>B</result> | B | 32 | A man travelled a distance of 80 km in 7 hours partly on foot at the rate of 8 km per hour and partly on bicycle at 16 km per hour. Find the distance travelled on foot. | {
"A": "26 km",
"B": "32 km",
"C": "30 km",
"D": "28 km",
"E": "none"
} | subtract(multiply(16, 7), 80) | multiply(n1,n3)|subtract(#0,n0) | total time = 7 hrs let the distance travelled by foot @ 8 kmph be x kms ? distance travlled by bicycle @ 16 kmph be ( 80 - x ) kms atq . 7 hr = x / 8 + ( 80 - x ) / 16 ? 7 = ( 2 x + 80 - x ) / 16 ? x = 32 kms answer : b . | physics |
math_qa__fhiecosd4cAPbK85 | After decreasing 24% in the price of an article costs Rs.820. Find the actual cost of an article?
Choose the correct choice from the following options:
A) 1400 B) 1079 C) 1200 D) 1023 E) 1523 | <gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>
<gadget id="calculator">820 / (19/25)</gadget>
<output>20_500/19 = around 1_078.947368</output>
<result>B</result> | B | 1,079 | After decreasing 24% in the price of an article costs Rs.820. Find the actual cost of an article? | {
"A": "1400",
"B": "1079",
"C": "1200",
"D": "1023",
"E": "1523"
} | divide(820, subtract(const_1, divide(24, const_100))) | divide(n0,const_100)|subtract(const_1,#0)|divide(n1,#1)| | "cp * ( 76 / 100 ) = 820 cp = 10.78 * 100 = > cp = 1079 answer : b" | gain |
math_qa__cYBnokKlvTAOk9zx | A volunteer organization is recruiting new members. In the fall they manage to increase their number by 8%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? Choose one:
A) 16.16 % B) 15.15 % C) 14.14 % D) 13.33 % E) 12.52 % | <gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">1 + (2/25)</gadget>
<output>27/25 = around 1.08</output>
<gadget id="calculator">19 / 100</gadget>
<output>19/100 = around 0.19</output>
<gadget id="calculator">1 - (19/100)</gadget>
<output>81/100 = around 0.81</output>
<gadget id="calculator">(27/25) * (81/100)</gadget>
<output>2_187/2_500 = around 0.8748</output>
<gadget id="calculator">(2_187/2_500) * 100</gadget>
<output>2_187/25 = around 87.48</output>
<gadget id="calculator">100 - (2_187/25)</gadget>
<output>313/25 = around 12.52</output>
<result>E</result> | E | 12.52 | A volunteer organization is recruiting new members. In the fall they manage to increase their number by 8%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring? | {
"A": "16.16 %",
"B": "15.15 %",
"C": "14.14 %",
"D": "13.33 %",
"E": "12.52 %"
} | subtract(const_100, multiply(multiply(add(const_1, divide(8, const_100)), subtract(const_1, divide(19, const_100))), const_100)) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5) | ( 100 % + 8 % ) * ( 100 % - 19 % ) = 1.08 * . 81 = 0.8748 1 - 0.8748 = 12.52 % lost = - 12.52 % the answer is e the organization has lost 12.52 % of its total volunteers from fall to spring . | general |
math_qa__n86CVcrQZyl2MQ3K | The side of a cube is 12 m, find the lateral surface area? Select the correct option:
A) 816 B) 516 C) 716 D) 216 E) 916 | <gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">40 + 3</gadget>
<output>43</output>
<gadget id="calculator">43 * 12</gadget>
<output>516</output>
<result>B</result> | B | 516 | The side of a cube is 12 m, find the lateral surface area? | {
"A": "816",
"B": "516",
"C": "716",
"D": "216",
"E": "916"
} | rectangle_area(add(multiply(const_4, const_10), const_3), 12) | multiply(const_10,const_4)|add(#0,const_3)|rectangle_area(n0,#1) | lateral surface = 4 a ( power ) 2 4 × 12 ( power ) 2 = 4 × 144 = > 516 m ( power ) 2 answer is b . | geometry |
math_qa__1Jpzs6t2eCHxaQJ0 | A train passes a platform in 25 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is Choose the correct choice from the following choices.
A) 75 B) 25 C) 26 D) 23 E) 22 | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 54</gadget>
<output>15</output>
<gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">15 * 5</gadget>
<output>75</output>
<result>A</result> | A | 75 | A train passes a platform in 25 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is | {
"A": "75",
"B": "25",
"C": "26",
"D": "23",
"E": "22"
} | multiply(multiply(const_0_2778, 54), subtract(25, 20)) | multiply(n2,const_0_2778)|subtract(n0,n1)|multiply(#0,#1) | speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 20 = > 300 + l = 15 × 25 = 375 = > l = 375 - 300 = 75 meter answer is a . | physics |
math_qa__mLJsJUg7OMaFtlnu | A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 250. Find the total worth of the stock? Choose the correct choice from the following options
A) 12500 B) 20000 C) 20289 D) 20027 E) 20026 | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</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">(1/20) * (4/5)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/10) * (1/5)</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/25) - (1/50)</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">250 / (1/50)</gadget>
<output>12_500</output>
<result>A</result> | A | 12,500 | A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 250. Find the total worth of the stock? | {
"A": "12500",
"B": "20000",
"C": "20289",
"D": "20027",
"E": "20026"
} | divide(250, subtract(multiply(divide(5, const_100), divide(subtract(const_100, 20), const_100)), multiply(divide(10, const_100), divide(20, const_100)))) | divide(n2,const_100)|divide(n1,const_100)|divide(n0,const_100)|subtract(const_100,n0)|divide(#3,const_100)|multiply(#1,#2)|multiply(#0,#4)|subtract(#6,#5)|divide(n3,#7)| | "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 250 = > x = 12500 answer : a" | gain |
math_qa__pP3n2i1iSY63zKH6 | A couple spent $158.40 in total while dining out and paid this amount using a credit card. The $158.40 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food. What was the actual price of the food before tax and tip?
Choose the most appropriate option
A) $ 115
B) $ 120
C) $ 125
D) $ 130
E) $ 135 | <gadget id="calculator">158.4 * 100</gadget>
<output>15_840</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">15_840 / 120</gadget>
<output>132</output>
<gadget id="calculator">132 * 100</gadget>
<output>13_200</output>
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">13_200 / 110</gadget>
<output>120</output>
<result>B</result> | B | 120 | A couple spent $158.40 in total while dining out and paid this amount using a credit card. The $158.40 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food. What was the actual price of the food before tax and tip? | {
"A": "$ 115",
"B": "$ 120",
"C": "$ 125",
"D": "$ 130",
"E": "$ 135"
} | divide(multiply(divide(multiply(158.40, const_100), add(const_100, 20)), const_100), add(const_100, 10)) | add(n2,const_100)|add(n3,const_100)|multiply(n0,const_100)|divide(#2,#0)|multiply(#3,const_100)|divide(#4,#1)| | "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 158.40 x = 120 the correct answer is b ." | general |
math_qa__Qqlp61MYRp317zNQ | We have a rectangular metallic piece of paper that covers exactly the area of a cube. The length of the piece of paper is 120 inches and the width is 108 inches. What is the volume of the cube in cubic feet is 1 feet is 12 inches? Choose the correct answer:
A) a 125
B) b 120
C) c 70
D) d 40
E) e 10 | <gadget id="calculator">120 ** (1/3)</gadget>
<output>2*15**(1/3) = around 4.932424</output>
<gadget id="calculator">(2*15**(1/3)) + 120</gadget>
<output>2*15**(1/3) + 120 = around 124.932424</output>
<result>A</result> | A | 125 | We have a rectangular metallic piece of paper that covers exactly the area of a cube. The length of the piece of paper is 120 inches and the width is 108 inches. What is the volume of the cube in cubic feet is 1 feet is 12 inches? | {
"A": "a 125",
"B": "b 120",
"C": "c 70",
"D": "d 40",
"E": "e 10"
} | add(cube_edge_by_volume(120), 120) | cube_edge_by_volume(n0)|add(n0,#0) | l = 120 / 12 = 10 ft w = 108 / 12 = 9 ft area of paper = 90 area of cube = 10 * side ^ 2 side of cube = 5 v of cube = 125 | geometry |
math_qa__Ai8g5089CwOxvpUr | In the xy-coordinate system, if (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 3, then k = Pick one: A) 1 / 2 B) 1 C) 2 D) 5 / 2 E) 4 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<result>B</result> | B | 1 | In the xy-coordinate system, if (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 3, then k = | {
"A": "1 / 2",
"B": "1",
"C": "2",
"D": "5 / 2",
"E": "4"
} | divide(subtract(add(3, 2), 3), 2) | add(n0,n2)|subtract(#0,n2)|divide(#1,n1)| | "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 3 and m + 2 = 2 * ( n + k ) + 3 . by 1 st equation we have m - 2 n = 3 and by 2 nd equation m - 2 n = 2 k + 1 - - - > 3 = 2 k + 1 - - - > k = 1 . the answer is , therefore , ( b ) ." | general |
math_qa__MahzeULDFqoMU5qD | When positive integer x is divided by positive integer y, the remainder is 5. If x/y = 96.2, what is the value of y? Select:
A) 96 B) 75 C) 48 D) 25 E) 12 | <gadget id="calculator">floor(96.2)</gadget>
<output>96</output>
<gadget id="calculator">96.2 - 96</gadget>
<output>0.2</output>
<gadget id="calculator">5 / 0.2</gadget>
<output>25</output>
<result>D</result> | D | 25 | When positive integer x is divided by positive integer y, the remainder is 5. If x/y = 96.2, what is the value of y? | {
"A": "96",
"B": "75",
"C": "48",
"D": "25",
"E": "12"
} | divide(5, subtract(96.2, floor(96.2))) | floor(n1)|subtract(n1,#0)|divide(n0,#1)| | "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.2 and remainder is 5 so . 2 x y = 5 hence y = 25 ans d" | general |
math_qa__IjeCd74YD4JXvka0 | A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 3.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? Choose one.
A) 5729 B) 5040 C) 2889 D) 2870 E) 2799 | <gadget id="calculator">8 * 60</gadget>
<output>480</output>
<gadget id="calculator">3.5 * 480</gadget>
<output>1_680</output>
<gadget id="calculator">6 * 60</gadget>
<output>360</output>
<gadget id="calculator">480 / 360</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) - 1</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1_680 / (1/3)</gadget>
<output>5_040</output>
<result>B</result> | B | 5,040 | A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 3.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? | {
"A": "5729",
"B": "5040",
"C": "2889",
"D": "2870",
"E": "2799"
} | divide(multiply(3.5, multiply(8, const_60)), subtract(divide(multiply(8, const_60), multiply(6, const_60)), const_1)) | multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4)| | "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 3.5 = 5040 . answer : b" | physics |
math_qa__1n83fpaAYAGRqbVB | What is the greater of the two numbers whose product is 2048, given that the sum of the two numbers exceeds their difference by 64? Choose the correct choice from the following answers
A) 90 B) 32 C) 64 D) 70 E) of these | <gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">16 * 2</gadget>
<output>32</output>
<gadget id="calculator">2_048 / 32</gadget>
<output>64</output>
<result>C</result> | C | 64 | What is the greater of the two numbers whose product is 2048, given that the sum of the two numbers exceeds their difference by 64? | {
"A": "90",
"B": "32",
"C": "64",
"D": "70",
"E": "of these"
} | divide(2048, multiply(power(const_2, const_4), const_2)) | power(const_2,const_4)|multiply(#0,const_2)|divide(n0,#1)| | "let the greater and the smaller number be g and s respectively . gs = 2048 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2048 / s = 64 . answer : c" | general |
math_qa__0ec8cB6cQUGMeG8S | A can finish a work in 6 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day?
Select the correct option:
A) 1 / 2 B) 1 / 6 C) 1 / 7 D) 1 / 8 E) none of these | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 2</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/6) + (1/3)</gadget>
<output>1/2 = around 0.5</output>
<result>A</result> | A | 0.5 | A can finish a work in 6 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day? | {
"A": "1 / 2",
"B": "1 / 6",
"C": "1 / 7",
"D": "1 / 8",
"E": "none of these"
} | add(divide(const_1, 6), multiply(divide(const_1, 6), const_2)) | divide(const_1,n0)|multiply(#0,const_2)|add(#0,#1)| | "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 6 b ' s 1 day work = 1 / 3 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 6 + 1 / 3 ) = 1 / 2 so in one day 1 / 2 work will be done answer : a" | physics |
math_qa__jBaCrAh5s3dpRYTP | A car averages 35 miles per hour for the first 4 hours of a trip and averages 53 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 50 miles per hour, how many hours long is the trip? Choose the correct choice from the following: A) 16 B) 18 C) 20 D) 22 E) 24 | <gadget id="calculator">50 * 4</gadget>
<output>200</output>
<gadget id="calculator">35 * 4</gadget>
<output>140</output>
<gadget id="calculator">200 - 140</gadget>
<output>60</output>
<gadget id="calculator">53 - 50</gadget>
<output>3</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">20 + 4</gadget>
<output>24</output>
<result>E</result> | E | 24 | A car averages 35 miles per hour for the first 4 hours of a trip and averages 53 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 50 miles per hour, how many hours long is the trip? | {
"A": "16",
"B": "18",
"C": "20",
"D": "22",
"E": "24"
} | add(divide(subtract(multiply(50, 4), multiply(35, 4)), subtract(53, 50)), 4) | multiply(n1,n3)|multiply(n0,n1)|subtract(n2,n3)|subtract(#0,#1)|divide(#3,#2)|add(n1,#4)| | "let t be the total time of the trip . 35 * 4 + 53 ( t - 4 ) = 50 t 3 t = 212 - 140 t = 24 the answer is e ." | physics |
math_qa__yAjyGHJTbZgfp5pO | 8 men, working 9 hours a day can complete a work in 24 days. How many hours a day must 12 men work to complete the same work in 16 days?
Choose the most appropriate option:
A) 6 B) 7 C) 8 D) 9 E) 10 | <gadget id="calculator">8 * 9</gadget>
<output>72</output>
<gadget id="calculator">72 * 24</gadget>
<output>1_728</output>
<gadget id="calculator">12 * 16</gadget>
<output>192</output>
<gadget id="calculator">1_728 / 192</gadget>
<output>9</output>
<result>D</result> | D | 9 | 8 men, working 9 hours a day can complete a work in 24 days. How many hours a day must 12 men work to complete the same work in 16 days? | {
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "10"
} | divide(multiply(multiply(8, 9), 24), multiply(12, 16)) | multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|divide(#2,#1)| | "the number of hours required to complete the work is 8 * 9 * 24 = 1728 12 × 16 × ( x ) = 1728 x = 9 the answer is d ." | physics |
math_qa__3of6R5ZfwxSxEq4P | The volume of a cube is 1000 cc. Find its surface. Choose the correct option:
A) 864
B) 556
C) 255
D) 600
E) 267 | <gadget id="calculator">1_000 ** (1/3)</gadget>
<output>10</output>
<gadget id="calculator">6 * (10 ** 2)</gadget>
<output>600</output>
<result>D</result> | D | 600 | The volume of a cube is 1000 cc. Find its surface. | {
"A": "864",
"B": "556",
"C": "255",
"D": "600",
"E": "267"
} | surface_cube(cube_edge_by_volume(1000)) | cube_edge_by_volume(n0)|surface_cube(#0)| | "a 3 = 1000 = > a = 10 6 a 2 = 6 * 10 * 10 = 600 answer : d" | geometry |
math_qa__GnJXiCse4mxwb2qa | The speed of a boat in still water is 24 kmph. What is the speed of the stream if the boat can cover 64 km downstream or 32 km upstream in the same time? Choose the correct choice: A) 8 kmph B) 6 kmph C) 7 kmph D) 5 kmph E) 4 kmph | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<result>A</result> | A | 8 | The speed of a boat in still water is 24 kmph. What is the speed of the stream if the boat can cover 64 km downstream or 32 km upstream in the same time? | {
"A": "8 kmph",
"B": "6 kmph",
"C": "7 kmph",
"D": "5 kmph",
"E": "4 kmph"
} | divide(24, add(const_1, const_2)) | add(const_1,const_2)|divide(n0,#0)| | "x = the speed of the stream ( 24 + x ) / ( 24 - x ) = 2 / 1 24 + x = 48 - 2 x 3 x = 24 x = 8 km / hour if the speed of the stream is 8 km / hour , then the ' downstream ' speed of the boat is 24 + 8 = 32 km / hour and the ' upstream ' speed of the boat is 24 - 8 = 16 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 32 = 64 km downstream and 2 x 16 = 32 km / hour upstream . answer : a" | physics |
math_qa__f3ulPWrtN85S5LXY | A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number M is Choose the correct choice from the following answers
A) 74
B) m = 75
C) m = 175
D) m = 680
E) 690 | <gadget id="calculator">34 * 2</gadget>
<output>68</output>
<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<gadget id="calculator">68 - 40</gadget>
<output>28</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">28 / 4</gadget>
<output>7</output>
<gadget id="calculator">68 + 7</gadget>
<output>75</output>
<result>B</result> | B | 75 | A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number M is | {
"A": "74",
"B": "m = 75",
"C": "m = 175",
"D": "m = 680",
"E": "690"
} | add(multiply(34, const_2), divide(subtract(multiply(34, const_2), multiply(8, 5)), subtract(5, const_1))) | multiply(n2,const_2)|multiply(n0,n1)|subtract(n0,const_1)|subtract(#0,#1)|divide(#3,#2)|add(#4,#0)| | "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb" | general |
math_qa__tpzu1jFH5ztKAgIX | A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 15% food additives; 19% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research? Choose the correct choice from the following.
A) 8 ° B) 10 ° C) 18 ° D) 36 ° E) 72 ° | <gadget id="calculator">14 + 24</gadget>
<output>38</output>
<gadget id="calculator">38 + 15</gadget>
<output>53</output>
<gadget id="calculator">53 + 19</gadget>
<output>72</output>
<gadget id="calculator">72 + 8</gadget>
<output>80</output>
<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">20 * 360</gadget>
<output>7_200</output>
<gadget id="calculator">7_200 / 100</gadget>
<output>72</output>
<result>E</result> | E | 72 | A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 15% food additives; 19% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research? | {
"A": "8 °",
"B": "10 °",
"C": "18 °",
"D": "36 °",
"E": "72 °"
} | divide(multiply(subtract(const_100, add(add(add(add(14, 24), 15), 19), 8)), divide(const_3600, const_10)), const_100) | add(n0,n1)|divide(const_3600,const_10)|add(n2,#0)|add(n3,#2)|add(n4,#3)|subtract(const_100,#4)|multiply(#1,#5)|divide(#6,const_100)| | "14 % microphotonics ; 24 % home electronics ; 15 % food additives ; 19 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 15 + 19 + 8 ) = 20 % basic astrophysics . 10 % of 360 ° is 72 ° . answer : e ." | gain |
math_qa__3fUFFhSpuyLHiS72 | When asked what the time is,a person answered that the amount of time left is 1/2 of the time already completed.what is the time. Choices
A) 2 pm
B) 9 pm
C) 3 pm
D) 4 pm
E) 6 pm | <gadget id="calculator">1 * 12</gadget>
<output>12</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) + 1</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">12 / (3/2)</gadget>
<output>8</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<result>D</result> | D | 4 | When asked what the time is,a person answered that the amount of time left is 1/2 of the time already completed.what is the time. | {
"A": "2 pm",
"B": "9 pm",
"C": "3 pm",
"D": "4 pm",
"E": "6 pm"
} | subtract(multiply(1, const_12), divide(multiply(1, const_12), add(divide(1, 2), const_1))) | divide(n0,n1)|multiply(const_12,n0)|add(#0,const_1)|divide(#1,#2)|subtract(#1,#3)| | "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 1 / 2 x ⇒ x = 16 time is 4 pm answer : d" | general |
math_qa__GOZZdKioEhOhgMeK | Ajay can ride 50km in 1 hour. In how many hours he can ride 500km?
Choose the correct choice from the following
A) 10 hrs B) 15 hrs C) 20 hrs D) 25 hrs E) 18 hrs | <gadget id="calculator">500 / 50</gadget>
<output>10</output>
<result>A</result> | A | 10 | Ajay can ride 50km in 1 hour. In how many hours he can ride 500km? | {
"A": "10 hrs",
"B": "15 hrs",
"C": "20 hrs",
"D": "25 hrs",
"E": "18 hrs"
} | divide(500, 50) | divide(n2,n0)| | "1 hour he ride 50 km he ride 500 km in = 500 / 50 * 1 = 10 hours answer is a" | physics |
math_qa__BW92APPzVt8jdWxi | In a renowned city, the average birth rate is 10 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day. Pick one:
A) 32,300 B) 172,800 C) 345,600 D) 338,200 E) 259,200 | <gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 3_600</gadget>
<output>28_800</output>
<gadget id="calculator">28_800 * 12</gadget>
<output>345_600</output>
<result>C</result> | C | 345,600 | In a renowned city, the average birth rate is 10 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day. | {
"A": "32,300",
"B": "172,800",
"C": "345,600",
"D": "338,200",
"E": "259,200"
} | multiply(multiply(subtract(10, 2), const_3600), const_12) | subtract(n0,n1)|multiply(#0,const_3600)|multiply(#1,const_12)| | "every 2 seconds , 8 persons are added ( 10 - 2 ) . every second 4 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 4 = 345600 option c" | general |
math_qa__kz67WpYuVGESWNWi | Two employees M and N are paid a total of $616 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week? Choose one.
A) $ 270
B) $ 280
C) $ 290
D) $ 300
E) $ 310 | <gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) + 1</gadget>
<output>11/5 = around 2.2</output>
<gadget id="calculator">616 / (11/5)</gadget>
<output>280</output>
<result>B</result> | B | 280 | Two employees M and N are paid a total of $616 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week? | {
"A": "$ 270",
"B": "$ 280",
"C": "$ 290",
"D": "$ 300",
"E": "$ 310"
} | divide(616, add(divide(120, const_100), const_1)) | divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)| | "1.2 n + n = 616 2.2 n = 616 n = 280 the answer is b ." | general |
math_qa__mKbQ30iJKfcTCuIK | In Town X, 64 percent of the population are employed, and 38 percent of the population are employed males. What percent of the employed people in Town X are females? Choose one
A) 16 % B) 25 % C) 32 % D) 40 % E) 52 % | <gadget id="calculator">64 - 38</gadget>
<output>26</output>
<gadget id="calculator">26 / 64</gadget>
<output>13/32 = around 0.40625</output>
<gadget id="calculator">(13/32) * 100</gadget>
<output>325/8 = around 40.625</output>
<result>D</result> | D | 40 | In Town X, 64 percent of the population are employed, and 38 percent of the population are employed males. What percent of the employed people in Town X are females? | {
"A": "16 %",
"B": "25 %",
"C": "32 %",
"D": "40 %",
"E": "52 %"
} | multiply(divide(subtract(64, 38), 64), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 38 are employed males , hence 26 % are employed females . ( employed females ) / ( total employed people ) = 26 / 64 = 40 % answer : d ." | gain |
math_qa__vCnYt5vONr4putHB | There were two candidates in an election. Winner candidate received 55% of votes and won the election by 100 votes. Find the number of votes casted to the winning candidate? Pick one.
A) 550 B) 744 C) 255 D) 199 E) 231 | <gadget id="calculator">100 - 55</gadget>
<output>45</output>
<gadget id="calculator">55 - 45</gadget>
<output>10</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">100 / (1/10)</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 * 55</gadget>
<output>55_000</output>
<gadget id="calculator">55_000 / 100</gadget>
<output>550</output>
<result>A</result> | A | 550 | There were two candidates in an election. Winner candidate received 55% of votes and won the election by 100 votes. Find the number of votes casted to the winning candidate? | {
"A": "550",
"B": "744",
"C": "255",
"D": "199",
"E": "231"
} | divide(multiply(divide(100, divide(subtract(55, subtract(const_100, 55)), const_100)), 55), const_100) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)| | "w = 55 % l = 45 % 55 % - 45 % = 10 % 10 % - - - - - - - - 100 55 % - - - - - - - - ? = > 550 answer : a" | gain |
math_qa__DhufqnU6EVSquOMn | 5 friends adi , brian , close , derek and eli appeared in two aptitude tests . in the first aptitude test , derek score 50 % less than the average score of the 5 people . in the second aptitude test , derek score 50 % more than what he scored on the first aptitude test . if the score of his friend in the second aptitude test were same as their score in the first test , by approximately what percentage was derek ' s score less than the average score of the 5 people in the second aptitude ? Choose the correct option:
A) 25 %
B) 28 %
C) 33 %
D) 40 %
E) 50 % | <gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">50 * 25</gadget>
<output>1_250</output>
<gadget id="calculator">1_250 / 50</gadget>
<output>25</output>
<result>A</result> | A | 25 | 5 friends adi , brian , close , derek and eli appeared in two aptitude tests . in the first aptitude test , derek score 50 % less than the average score of the 5 people . in the second aptitude test , derek score 50 % more than what he scored on the first aptitude test . if the score of his friend in the second aptitude test were same as their score in the first test , by approximately what percentage was derek ' s score less than the average score of the 5 people in the second aptitude ? | {
"A": "25 %",
"B": "28 %",
"C": "33 %",
"D": "40 %",
"E": "50 %"
} | divide(multiply(50, multiply(5, 5)), 50) | multiply(n0,n0)|multiply(n1,#0)|divide(#1,n1) | average score in first test be x so derby score = 0.5 x ( first test ) derby score = 1.5 ( 0.5 x ) ( second test ) = . 75 x so less than x by . 25 answer a 25 % | general |
math_qa__z8FDAha3H48dqxFX | An escalator moves towards the top level at the rate of 12 ft.sec and its length is 160 feet. If a person walks on the moving escalator at the rate of 8 feet per second towards the top level, how much time does he take to cover the entire length. Choose the correct choice from the following.
A) 10 sec B) 8 sec C) 9 sec D) 7 sec E) 12 sec | <gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">160 / 20</gadget>
<output>8</output>
<result>B</result> | B | 8 | An escalator moves towards the top level at the rate of 12 ft.sec and its length is 160 feet. If a person walks on the moving escalator at the rate of 8 feet per second towards the top level, how much time does he take to cover the entire length. | {
"A": "10 sec",
"B": "8 sec",
"C": "9 sec",
"D": "7 sec",
"E": "12 sec"
} | divide(160, add(12, 8)) | add(n0,n2)|divide(n1,#0)| | "explanation : time taken to cover the entire length = tot . dist / resultant speed = 160 / ( 12 + 8 ) = 8 sec answer : b" | gain |
math_qa__ogo7QGYZQqv39dOu | If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.41 then sum is Choices:
A) s . 5000
B) s . 5100
C) s . 5800
D) s . 6000
E) s . 4100 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * (1/10)</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">41 / (1/100)</gadget>
<output>4_100</output>
<result>E</result> | E | 4,100 | If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.41 then sum is | {
"A": "s . 5000",
"B": "s . 5100",
"C": "s . 5800",
"D": "s . 6000",
"E": "s . 4100"
} | divide(41, multiply(divide(10, const_100), divide(10, const_100))) | divide(n0,const_100)|multiply(#0,#0)|divide(n2,#1)| | "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 41 4100 answer : e" | gain |
math_qa__hRAaSzAEUFv33rS3 | A leak in the bottom of a tank can empty the full tank in 4 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold?
Select
A) 7580 B) 7960 C) 8290 D) 2160 E) none | <gadget id="calculator">12 * 60</gadget>
<output>720</output>
<gadget id="calculator">6 * 720</gadget>
<output>4_320</output>
<gadget id="calculator">4 * 60</gadget>
<output>240</output>
<gadget id="calculator">720 / 240</gadget>
<output>3</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">4_320 / 2</gadget>
<output>2_160</output>
<result>D</result> | D | 2,160 | A leak in the bottom of a tank can empty the full tank in 4 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold? | {
"A": "7580",
"B": "7960",
"C": "8290",
"D": "2160",
"E": "none"
} | divide(multiply(6, multiply(12, const_60)), subtract(divide(multiply(12, const_60), multiply(4, const_60)), const_1)) | multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4) | solution work done by the inlet in 1 hour = ( 1 / 4 - 1 / 12 ) = 1 / 6 . work done by the inlet in 1 min . = ( 1 / 6 × 1 / 60 ) = 0.002778 volume of 0.002778 part = 6 litres . therefore , volume of whole = ( . 002778 × 6 ) ‹ = › 2160 litres . answer d | physics |
math_qa__k0ZxfK9rm3Maln38 | A can run 224 metre in 28 seconds and B in 32 seconds. By what distance A beat B?
Choose the correct choice from the following choices: A) 38 metre B) 28 metre C) 23 metre D) 15 metre E) 28 metre | <gadget id="calculator">224 / 32</gadget>
<output>7</output>
<gadget id="calculator">7 * 28</gadget>
<output>196</output>
<gadget id="calculator">224 - 196</gadget>
<output>28</output>
<result>B</result> | B | 28 | A can run 224 metre in 28 seconds and B in 32 seconds. By what distance A beat B? | {
"A": "38 metre",
"B": "28 metre",
"C": "23 metre",
"D": "15 metre",
"E": "28 metre"
} | subtract(224, multiply(divide(224, 32), 28)) | divide(n0,n2)|multiply(n1,#0)|subtract(n0,#1)| | "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 224 / 32 = 28 / 4 = 7 m / sdistance covered by b in 4 seconds = speed × time = 7 × 4 = 28 metre i . e . , a beat b by 28 metre answer is b" | physics |
math_qa__KkD63yauwgmmOHXl | In the manufacture of a certain product, 8 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale? Choose the correct choice from the following answers:
A) 0.125 % B) 0.32 % C) 0.8 % D) 1.25 % E) 2.0 % | <gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">8 * (1/25)</gadget>
<output>8/25 = around 0.32</output>
<result>B</result> | B | 0.32 | In the manufacture of a certain product, 8 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale? | {
"A": "0.125 %",
"B": "0.32 %",
"C": "0.8 %",
"D": "1.25 %",
"E": "2.0 %"
} | multiply(8, divide(4, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | "percent of defective produced = 8 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 8 / 100 ) * 100 % = ( 32 / 10000 ) * 100 % = ( 32 / 100 ) % = . 32 % answer b" | gain |
math_qa__pnFSPPzWm6b1kAJL | $700 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is Choose the correct choice from the following answers.
A) $ 100 B) $ 150 C) $ 125 D) $ 280 E) $ 250 | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">700 / (5/3)</gadget>
<output>420</output>
<gadget id="calculator">420 * (2/3)</gadget>
<output>280</output>
<result>D</result> | D | 280 | $700 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is | {
"A": "$ 100",
"B": "$ 150",
"C": "$ 125",
"D": "$ 280",
"E": "$ 250"
} | multiply(divide(700, add(divide(const_2, const_3), const_1)), divide(const_2, const_3)) | divide(const_2,const_3)|add(#0,const_1)|divide(n0,#1)|multiply(#2,#0) | a : ( b + c ) = 2 : 3 a ' s share = 700 * 2 / 5 = $ 280 answer is d | general |
math_qa__iLNbyEJU2pOEob4f | The salary of a worker is first increased by 20% and afterwards reduced by 20%. What is the net change in the worker's salary? Pick one:
A) 4 % decrease B) 8 % decrease C) 4 % increase D) 8 % increase E) no change | <gadget id="calculator">20 + 100</gadget>
<output>120</output>
<gadget id="calculator">120 * 20</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 / 100</gadget>
<output>24</output>
<gadget id="calculator">120 - 24</gadget>
<output>96</output>
<gadget id="calculator">100 - 96</gadget>
<output>4</output>
<result>A</result> | A | 4 | The salary of a worker is first increased by 20% and afterwards reduced by 20%. What is the net change in the worker's salary? | {
"A": "4 % decrease",
"B": "8 % decrease",
"C": "4 % increase",
"D": "8 % increase",
"E": "no change"
} | subtract(const_100, subtract(add(20, const_100), divide(multiply(add(20, const_100), 20), const_100))) | add(n0,const_100)|multiply(n0,#0)|divide(#1,const_100)|subtract(#0,#2)|subtract(const_100,#3)| | "let x be the original salary . the final salary is 0.8 ( 1.2 x ) = 0.96 x the answer is a ." | gain |
math_qa__rWCkTtK7NhHXKp8K | The average age of applicants for a new job is 31, with a standard deviation of 5. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
Select.
A) 11 B) 14 C) 15 D) 18 E) 30 | <gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<result>A</result> | A | 11 | The average age of applicants for a new job is 31, with a standard deviation of 5. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants? | {
"A": "11",
"B": "14",
"C": "15",
"D": "18",
"E": "30"
} | add(multiply(5, const_2), const_1) | multiply(n1,const_2)|add(#0,const_1) | within one standard deviation of the average age means 31 + / - 7 26 - - 31 - - 36 number of dif . ages - 26 27 28 29 30 31 32 33 34 35 36 total = 11 a | general |
math_qa__mLqcxwfLJTVhL5L9 | A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 78 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 Choose one: A) 2000 B) 2600 C) 2200 D) 2300 E) 2400 | <gadget id="calculator">78 / 3</gadget>
<output>26</output>
<gadget id="calculator">26 * 100</gadget>
<output>2_600</output>
<result>B</result> | B | 2,600 | A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 78 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 | {
"A": "2000",
"B": "2600",
"C": "2200",
"D": "2300",
"E": "2400"
} | multiply(divide(78, 3), const_100) | divide(n2,n0)|multiply(#0,const_100)| | "1 percent for 3 years = 78 1 percent for 1 year = 26 = > 100 percent = 2600 answer : b" | gain |
math_qa__z1IPkvLznMQsRuEQ | A can do a work in 15 days and B in 20 days. If they work on it together for 8 days, then the fraction of the work that is left is Choose the correct choice from the following.
A) 8 / 17 B) 7 / 15 C) 3 / 15 D) 8 / 15 E) 1 / 15 | <gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">(7/60) * 8</gadget>
<output>14/15 = around 0.933333</output>
<gadget id="calculator">1 - (14/15)</gadget>
<output>1/15 = around 0.066667</output>
<result>E</result> | E | 0.066667 | A can do a work in 15 days and B in 20 days. If they work on it together for 8 days, then the fraction of the work that is left is | {
"A": "8 / 17",
"B": "7 / 15",
"C": "3 / 15",
"D": "8 / 15",
"E": "1 / 15"
} | subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 8)) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)|subtract(const_1,#3)| | "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 8 = 280 remaining work is 300 - 280 = 20 remaining fraction of work is = 20 / 300 = 1 / 15 answer e" | physics |
math_qa__eHRGZVOdnKCRgLPH | In a college the ratio of the numbers of boys to the girls is 5:7. If there are 140 girls, the total number of students in the college is? Choose the correct choice from the following.
A) 200 B) 240 C) 160 D) 250 E) 310 | <gadget id="calculator">5 / 7</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">(5/7) * 140</gadget>
<output>100</output>
<gadget id="calculator">100 + 140</gadget>
<output>240</output>
<result>B</result> | B | 240 | In a college the ratio of the numbers of boys to the girls is 5:7. If there are 140 girls, the total number of students in the college is? | {
"A": "200",
"B": "240",
"C": "160",
"D": "250",
"E": "310"
} | add(multiply(divide(5, 7), 140), 140) | divide(n0,n1)|multiply(n2,#0)|add(n2,#1)| | "let the number of boys and girls be 5 x and 7 x then , 7 x = 140 x = 20 total number of students = 12 x = 12 * 20 = 240 answer is b" | other |
math_qa__dgVU4k6GGPT4PhA1 | A boat takes 38 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?
Choose the correct choice from the following options: A) 240 km B) 120 km C) 360 km D) 180 km E) none of these | <gadget id="calculator">14 + 4</gadget>
<output>18</output>
<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">14 - 4</gadget>
<output>10</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/18) + (1/20)</gadget>
<output>19/180 = around 0.105556</output>
<gadget id="calculator">38 / (19/180)</gadget>
<output>360</output>
<result>C</result> | C | 360 | A boat takes 38 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B? | {
"A": "240 km",
"B": "120 km",
"C": "360 km",
"D": "180 km",
"E": "none of these"
} | divide(38, add(divide(const_1, add(14, 4)), divide(const_1, multiply(subtract(14, 4), const_2)))) | add(n1,n2)|subtract(n2,n1)|divide(const_1,#0)|multiply(#1,const_2)|divide(const_1,#3)|add(#2,#4)|divide(n0,#5)| | "explanation : velocity of the stream = 4 kmph speed of the boat in still water is 14 kmph speed downstream = ( 14 + 4 ) = 18 kmph speed upstream = ( 14 - 4 ) = 10 kmph let the distance between a and b be x km time taken to travel downstream from a to b + time taken to travel upstream from b to c ( mid of a and b ) = 38 hours ⇒ x / 18 + ( x / 2 ) 10 = 38 ⇒ x / 18 + x / 20 = 38 ⇒ 19 x / 180 = 38 ⇒ x / 180 = 2 ⇒ x = 360 i . e . , the distance between a and b = 360 km . answer : option c" | physics |
math_qa__6Ni55sTIuxyk8DPZ | 30 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres? Choose the correct choice.
A) 30 B) 32 C) 45 D) data inadequate E) none of these | <gadget id="calculator">13.5 * 30</gadget>
<output>405</output>
<gadget id="calculator">405 / 9</gadget>
<output>45</output>
<result>C</result> | C | 45 | 30 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres? | {
"A": "30",
"B": "32",
"C": "45",
"D": "data inadequate",
"E": "none of these"
} | divide(multiply(13.5, 30), 9) | multiply(n0,n1)|divide(#0,n2)| | "capacity of the tank = 30 ã — 13.5 = 405 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 405 â „ 9 = 45 answer c" | physics |
math_qa__nmZUZMFNQ7lknUMb | A man two flats for $675958 each. On one he gains 14% while on the other he loses 14%. How much does he gain or lose in the whole transaction? Choose the correct option: A) 1.96 % B) 2.56 % C) 3.12 % D) 4.65 % E) 5.12 % | <gadget id="calculator">100 + 14</gadget>
<output>114</output>
<gadget id="calculator">100 / 114</gadget>
<output>50/57 = around 0.877193</output>
<gadget id="calculator">(50/57) * 675_958</gadget>
<output>33_797_900/57 = around 592_945.614035</output>
<gadget id="calculator">100 - 14</gadget>
<output>86</output>
<gadget id="calculator">100 / 86</gadget>
<output>50/43 = around 1.162791</output>
<gadget id="calculator">(50/43) * 675_958</gadget>
<output>33_797_900/43 = around 785_997.674419</output>
<gadget id="calculator">(33_797_900/57) + (33_797_900/43)</gadget>
<output>3_379_790_000/2_451 = around 1_378_943.288454</output>
<gadget id="calculator">675_958 + 675_958</gadget>
<output>1_351_916</output>
<gadget id="calculator">(3_379_790_000/2_451) - 1_351_916</gadget>
<output>66_243_884/2_451 = around 27_027.288454</output>
<gadget id="calculator">(66_243_884/2_451) / (3_379_790_000/2_451)</gadget>
<output>49/2_500 = around 0.0196</output>
<gadget id="calculator">(49/2_500) * 100</gadget>
<output>49/25 = around 1.96</output>
<result>A</result> | A | 1.96 | A man two flats for $675958 each. On one he gains 14% while on the other he loses 14%. How much does he gain or lose in the whole transaction? | {
"A": "1.96 %",
"B": "2.56 %",
"C": "3.12 %",
"D": "4.65 %",
"E": "5.12 %"
} | multiply(divide(subtract(add(multiply(divide(const_100, add(const_100, 14)), 675958), multiply(divide(const_100, subtract(const_100, 14)), 675958)), add(675958, 675958)), add(multiply(divide(const_100, add(const_100, 14)), 675958), multiply(divide(const_100, subtract(const_100, 14)), 675958))), const_100) | add(n1,const_100)|add(n0,n0)|subtract(const_100,n1)|divide(const_100,#0)|divide(const_100,#2)|multiply(n0,#3)|multiply(n0,#4)|add(#5,#6)|subtract(#7,#1)|divide(#8,#7)|multiply(#9,const_100)| | "in such a case there is always a loss loss % = ( 14 / 10 ) ^ 2 = 49 / 25 = 1.96 % answer is a" | gain |
math_qa__6LMdWAewYNlHcHSd | How many pairs (r, r+1) have one or more prime factors common, where r is an integer and 2 ≤ r ≤9 ? Options: A) 0 B) 1 C) 2 D) 3 E) 4 | <gadget id="calculator">1 - 1</gadget>
<output>0</output>
<result>A</result> | A | 0 | How many pairs (r, r+1) have one or more prime factors common, where r is an integer and 2 ≤ r ≤9 ? | {
"A": "0",
"B": "1",
"C": "2",
"D": "3",
"E": "4"
} | subtract(const_1, const_1) | subtract(const_1,const_1) | r and r + 1 are consecutive integers . two consecutive integers are co - prime , which means that they do n ' t share any common factor but 1 . for example 20 and 21 are consecutive integers , thus only common factor they share is 1 . answer : a . | general |
math_qa__ttS61lykoYCr0GQ9 | Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 7 weeks have been $406, $413, $420, $436, $395, $410, $360. What must his average (arithmetic mean) income over the next two weeks be to decrease his average weekly income to $400 over the 9-week period? Options
A) $ 360 B) $ 380 C) $ 430 D) $ 290 E) $ 520 | <gadget id="calculator">400 * 9</gadget>
<output>3_600</output>
<gadget id="calculator">406 + 413</gadget>
<output>819</output>
<gadget id="calculator">819 + 420</gadget>
<output>1_239</output>
<gadget id="calculator">1_239 + 436</gadget>
<output>1_675</output>
<gadget id="calculator">1_675 + 395</gadget>
<output>2_070</output>
<gadget id="calculator">2_070 + 410</gadget>
<output>2_480</output>
<gadget id="calculator">2_480 + 360</gadget>
<output>2_840</output>
<gadget id="calculator">3_600 - 2_840</gadget>
<output>760</output>
<gadget id="calculator">760 / 2</gadget>
<output>380</output>
<result>B</result> | B | 380 | Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 7 weeks have been $406, $413, $420, $436, $395, $410, $360. What must his average (arithmetic mean) income over the next two weeks be to decrease his average weekly income to $400 over the 9-week period? | {
"A": "$ 360",
"B": "$ 380",
"C": "$ 430",
"D": "$ 290",
"E": "$ 520"
} | divide(subtract(multiply(400, 9), add(add(add(add(add(add(406, 413), 420), 436), 395), 410), 360)), const_2) | add(n1,n2)|multiply(n8,n9)|add(n3,#0)|add(n4,#2)|add(n5,#3)|add(n6,#4)|add(n7,#5)|subtract(#1,#6)|divide(#7,const_2) | official solution : ( b ) first , we need to add up the wages over the past 7 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 + $ 410 + $ 360 = $ 2840 . to average $ 400 over 9 weeks , the salesman would need to earn : $ 400 × 9 = $ 3600 . subtract $ 2840 from $ 3600 to determine how much he would need to earn , in total , over the next 2 weeks to average $ 400 for the 9 weeks : $ 3600 – $ 2840 = $ 760 . dividing $ 760 by 2 will give us the amount he needs to earn on average over the next 2 weeks : $ 760 / 2 = $ 380 . the correct answer is choice ( b ) . | general |
math_qa__SF1mqTR669PbhZiX | A furniture manufacturer has two machines, but only one can be used at a time. Machine Q is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine Q can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule? Answers.
A) 14 B) 13 C) 11 D) 9 E) 7 | <gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/24) + (1/30)</gadget>
<output>3/40 = around 0.075</output>
<gadget id="calculator">(1/24) / 2</gadget>
<output>1/48 = around 0.020833</output>
<gadget id="calculator">(1/30) / 2</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">(1/48) + (1/60)</gadget>
<output>3/80 = around 0.0375</output>
<gadget id="calculator">(3/40) + (3/80)</gadget>
<output>9/80 = around 0.1125</output>
<gadget id="calculator">1 / (9/80)</gadget>
<output>80/9 = around 8.888889</output>
<result>D</result> | D | 9 | A furniture manufacturer has two machines, but only one can be used at a time. Machine Q is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine Q can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule? | {
"A": "14",
"B": "13",
"C": "11",
"D": "9",
"E": "7"
} | divide(const_1, add(add(divide(const_1, multiply(12, const_2)), divide(const_1, multiply(15, const_2))), add(divide(divide(const_1, multiply(12, const_2)), const_2), divide(divide(const_1, multiply(15, const_2)), const_2)))) | multiply(n0,const_2)|multiply(n1,const_2)|divide(const_1,#0)|divide(const_1,#1)|add(#2,#3)|divide(#2,const_2)|divide(#3,const_2)|add(#5,#6)|add(#4,#7)|divide(const_1,#8) | machine q finish the job in 2 * 12 shifts = 24 shifts machine b finish the job in 2 * 15 shifts = 30 shifts lets assume total work require 120 shifts therefore , rate of q = 5 shifts / day rate of b = 4 shifts / day rate of ( q + b ) = 9 shifts / day according to current schedule work complete in a day = 5 + 4 + ( 9 / 2 ) = 13.5 shifts / day therefore , time required to finish 120 shifts = ( 120 / 13.5 ) = 8.88 . . days ~ 9 days = d | physics |
math_qa__enVA0Wwpjjz8kGZF | A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 4 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used? Choose the correct choice from the following options: A) 3 B) 4 C) 9 / 5 D) 9 / 8 E) 12 | <gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/36) + (1/4)</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">2 * (5/18)</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">1 / (5/9)</gadget>
<output>9/5 = around 1.8</output>
<result>C</result> | C | 1.8 | A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 4 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used? | {
"A": "3",
"B": "4",
"C": "9 / 5",
"D": "9 / 8",
"E": "12"
} | divide(const_1, multiply(const_2.0, add(divide(const_1, 36), divide(const_1, 4)))) | divide(const_1,n0)|divide(const_1,const_2.0)|add(#0,#1)|multiply(n1,#2)|divide(const_1,#3)| | "yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 4 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 4 lets say x machines are used to attain the desired rate , thus x / 36 + x / 4 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + 9 x ) / 36 = 1 / 2 10 x / 36 = 1 / 2 x = 9 / 5 . qa = 9 / 5 ( answer c )" | gain |
math_qa__IPCArk4wZtQez91Y | A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 79, how many questions did Student A answer correctly? Choose the correct choice from the following answers:
A) 55
B) 60
C) 93
D) 82
E) 91 | <gadget id="calculator">100 - 79</gadget>
<output>21</output>
<gadget id="calculator">21 / 3</gadget>
<output>7</output>
<gadget id="calculator">100 - 7</gadget>
<output>93</output>
<result>C</result> | C | 93 | A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 79, how many questions did Student A answer correctly? | {
"A": "55",
"B": "60",
"C": "93",
"D": "82",
"E": "91"
} | subtract(100, divide(subtract(100, 79), const_3)) | subtract(n0,n1)|divide(#0,const_3)|subtract(n0,#1)| | "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 79 ( subtracting twice of incorrect from correct ) 3 x = 279 x = 93 answer : c" | general |
math_qa__ufG9MaK8gAiPxZZu | The edges of three metal cubes are 2 cm, 3 cm, and 4 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)?
Choose the correct choice from the following choices: A) 4.0 B) 4.2 C) 4.4 D) 4.6 E) 4.8 | <gadget id="calculator">4 ** 3</gadget>
<output>64</output>
<gadget id="calculator">3 ** 3</gadget>
<output>27</output>
<gadget id="calculator">2 + 27</gadget>
<output>29</output>
<gadget id="calculator">64 + 29</gadget>
<output>93</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">93 ** (1/3)</gadget>
<output>93**(1/3) = around 4.530655</output>
<result>D</result> | D | 4.6 | The edges of three metal cubes are 2 cm, 3 cm, and 4 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)? | {
"A": "4.0",
"B": "4.2",
"C": "4.4",
"D": "4.6",
"E": "4.8"
} | power(add(power(4, 3), add(2, power(3, 3))), const_0_33) | power(n1,n1)|power(n2,n1)|add(n0,#0)|add(#2,#1)|power(#3,const_0_33)| | "the total volume is 2 ^ 3 + 3 ^ 3 + 4 ^ 3 = 99 the edge of the new cube is the cube root of 99 which is about 4.6 cm . the answer is d ." | physics |
math_qa__H2kO2o9gpxV7zFaS | Rahim bought 50 books for Rs.1000 from one shop and 40 books for Rs.800 from another. What is the average price he paid per book ?
Choose the correct choice from the following answers
A) 28 B) 20 C) 27 D) 29 E) 21 | <gadget id="calculator">1_000 + 800</gadget>
<output>1_800</output>
<gadget id="calculator">50 + 40</gadget>
<output>90</output>
<gadget id="calculator">1_800 / 90</gadget>
<output>20</output>
<result>B</result> | B | 20 | Rahim bought 50 books for Rs.1000 from one shop and 40 books for Rs.800 from another. What is the average price he paid per book ? | {
"A": "28",
"B": "20",
"C": "27",
"D": "29",
"E": "21"
} | divide(add(1000, 800), add(50, 40)) | add(n1,n3)|add(n0,n2)|divide(#0,#1)| | "average price per book = ( 1000 + 800 ) / ( 50 + 40 ) = 1800 / 90 = rs . 20 answer : b" | general |
math_qa__MiuS4koo9YIkjgWJ | A store’s selling price of $2500 for a certain computer would yield a profit of 40 percent of the store’s cost for the computer. What selling price would yield a profit of 50 percent of the computer’s cost? Select:
A) $ 2678 B) $ 2464 C) $ 2650 D) $ 2732 E) $ 2800 | <gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">150 / 140</gadget>
<output>15/14 = around 1.071429</output>
<gadget id="calculator">2_500 * (15/14)</gadget>
<output>18_750/7 = around 2_678.571429</output>
<result>A</result> | A | 2,678 | A store’s selling price of $2500 for a certain computer would yield a profit of 40 percent of the store’s cost for the computer. What selling price would yield a profit of 50 percent of the computer’s cost? | {
"A": "$ 2678",
"B": "$ 2464",
"C": "$ 2650",
"D": "$ 2732",
"E": "$ 2800"
} | multiply(2500, divide(add(const_100, 50), add(const_100, 40))) | add(n2,const_100)|add(n1,const_100)|divide(#0,#1)|multiply(n0,#2) | 1.4 x = 2500 x = 2500 / 1.4 so , 1.5 x = 2500 * 1.5 / 1.4 = 2478 answer : - a | gain |
math_qa__RAl2f7i0nKTIBzBc | What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 10 nor by 35?
Choose the correct choice from the following answers:
A) 884
B) 890
C) 892
D) 910
E) 945 | <gadget id="calculator">1_000 / 10</gadget>
<output>100</output>
<gadget id="calculator">1_000 / 35</gadget>
<output>200/7 = around 28.571429</output>
<gadget id="calculator">100 + (200/7)</gadget>
<output>900/7 = around 128.571429</output>
<gadget id="calculator">10 * 35</gadget>
<output>350</output>
<gadget id="calculator">1_000 / 350</gadget>
<output>20/7 = around 2.857143</output>
<gadget id="calculator">(900/7) - (20/7)</gadget>
<output>880/7 = around 125.714286</output>
<gadget id="calculator">1_000 - (880/7)</gadget>
<output>6_120/7 = around 874.285714</output>
<result>D</result> | D | 910 | What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 10 nor by 35? | {
"A": "884",
"B": "890",
"C": "892",
"D": "910",
"E": "945"
} | subtract(1000, subtract(add(divide(1000, 10), divide(1000, 35)), divide(1000, multiply(10, 35)))) | divide(n1,n2)|divide(n1,n3)|multiply(n2,n3)|add(#0,#1)|divide(n1,#2)|subtract(#3,#4)|subtract(n1,#5)| | "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 910 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? d" | other |
math_qa__AMzuZ4AUgt8Uvtjq | The average age of applicants for a new job is 31, with a standard deviation of 9. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
Choose the correct choice from the following
A) 8 B) 14 C) 15 D) 18 E) 19 | <gadget id="calculator">9 * 2</gadget>
<output>18</output>
<gadget id="calculator">18 + 1</gadget>
<output>19</output>
<result>E</result> | E | 19 | The average age of applicants for a new job is 31, with a standard deviation of 9. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants? | {
"A": "8",
"B": "14",
"C": "15",
"D": "18",
"E": "19"
} | add(multiply(9, const_2), const_1) | multiply(n1,const_2)|add(#0,const_1)| | "within one standard deviation of the average age means 31 + / - 7 24 - - 31 - - 38 number of dif . ages - 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 total = 19 e" | general |
math_qa__TS0GFosBLhf0sw4t | A man walks at a rate of 10 mph. After every ten miles, he rests for 8 minutes. How much time does he take to walk 50 miles? Choose the correct choice from the following options
A) 300
B) 318
C) 322
D) 324
E) 332 | <gadget id="calculator">8 * 4</gadget>
<output>32</output>
<gadget id="calculator">50 / 10</gadget>
<output>5</output>
<gadget id="calculator">5 * 60</gadget>
<output>300</output>
<gadget id="calculator">32 + 300</gadget>
<output>332</output>
<result>E</result> | E | 332 | A man walks at a rate of 10 mph. After every ten miles, he rests for 8 minutes. How much time does he take to walk 50 miles? | {
"A": "300",
"B": "318",
"C": "322",
"D": "324",
"E": "332"
} | add(multiply(8, const_4), multiply(divide(50, 10), const_60)) | divide(n2,n0)|multiply(n1,const_4)|multiply(#0,const_60)|add(#1,#2)| | "to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 8 = 32 minutes . total time = 300 + 32 = 332 minutes . answer : e ." | physics |
math_qa__6HHRHquNxX8q65Pa | Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 6 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them? Choose the most appropriate option: A) 22 km B) 20 km C) 65 km D) 18 km E) 36 km | <gadget id="calculator">6 + 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 4</gadget>
<output>36</output>
<result>E</result> | E | 36 | Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 6 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them? | {
"A": "22 km",
"B": "20 km",
"C": "65 km",
"D": "18 km",
"E": "36 km"
} | multiply(add(6, 3), 4) | add(n0,n1)|multiply(n2,#0) | distance = relative speed * time = ( 6 + 3 ) * 4 = 36 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : e | physics |
math_qa__pmOXmfXY3Docof17 | The price of a book is increased from $300 to $360. What is the % of increase in its price?
Choose the correct choice from the following answers
A) 10 % B) 20 % C) 35 % D) 40 % E) 50 % | <gadget id="calculator">360 - 300</gadget>
<output>60</output>
<gadget id="calculator">60 / 300</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>B</result> | B | 20 | The price of a book is increased from $300 to $360. What is the % of increase in its price? | {
"A": "10 %",
"B": "20 %",
"C": "35 %",
"D": "40 %",
"E": "50 %"
} | multiply(divide(subtract(360, 300), 300), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | "explanation : change in the price = rs 360 – rs 300 = rs 60 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 60 300 ) * 100 = 20 % b" | gain |
math_qa__oSr9rX1TFiLOko0W | The simple interest on Rs. 26 for 6 months at the rate of 7 paise per rupeeper month is Choose the correct choice.
A) 1.2 B) 10.92 C) 12.98 D) 12.38 E) none | <gadget id="calculator">26 * 6</gadget>
<output>156</output>
<gadget id="calculator">156 * 7</gadget>
<output>1_092</output>
<gadget id="calculator">1_092 / 100</gadget>
<output>273/25 = around 10.92</output>
<result>B</result> | B | 10.92 | The simple interest on Rs. 26 for 6 months at the rate of 7 paise per rupeeper month is | {
"A": "1.2",
"B": "10.92",
"C": "12.98",
"D": "12.38",
"E": "none"
} | divide(multiply(multiply(26, 6), 7), const_100) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,const_100)| | "sol . s . i . = rs . [ 26 * 7 / 100 * 6 ] = rs . 10.92 answer b" | gain |
math_qa__ImiCzdm5XB7JMFuy | ms . mary sold two properties , x and y , for $ 25000 each . she sold property x for 20 % more than she paid for it and sold property y for 20 % less than she paid for it . if expenses are disregarded , what was her total net gain or loss , if any , on the two properties ?
Choose the correct option: A) $ 2100 B) $ 2222 C) $ 2320 D) $ 2083.33 E) $ 2183.33 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 25_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 - 1_000</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 / 2</gadget>
<output>2_000</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 + 3</gadget>
<output>83</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">83 + (1/3)</gadget>
<output>250/3 = around 83.333333</output>
<gadget id="calculator">2_000 + (250/3)</gadget>
<output>6_250/3 = around 2_083.333333</output>
<result>D</result> | D | 2,083.33 | ms . mary sold two properties , x and y , for $ 25000 each . she sold property x for 20 % more than she paid for it and sold property y for 20 % less than she paid for it . if expenses are disregarded , what was her total net gain or loss , if any , on the two properties ? | {
"A": "$ 2100",
"B": "$ 2222",
"C": "$ 2320",
"D": "$ 2083.33",
"E": "$ 2183.33"
} | add(divide(subtract(multiply(divide(20, const_100), 25000), const_1000), const_2), add(add(subtract(const_100, 20), const_3), const_0_33)) | divide(n1,const_100)|subtract(const_100,n1)|add(#1,const_3)|multiply(n0,#0)|add(#2,const_0_33)|subtract(#3,const_1000)|divide(#5,const_2)|add(#4,#6) | there is a property to solve such questions withcommon selling priceandcommon % gain and loss . such cases always result in a loss and . . . total % loss = ( common gain % or loss % / 10 ) ^ 2 hence here loss % = ( 20 / 10 ) ^ 2 = 4 % which means he recovered only 96 % of his investment which amount to a total revenue = 25000 + 25000 = 50000 i . e . 96 % of cost = 40000 therefore , 4 % of cost ( loss ) = $ 2083.33 answer : d | general |
math_qa__PpqGOnIIscn2Z00u | An engineer undertakes a project to build a road 10 km long in 150 days and employs 30 men for the purpose. After 50 days, he finds only 2 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time. Choices
A) 22 B) 30 C) 15 D) 18 E) 20 | <gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">30 * 8</gadget>
<output>240</output>
<gadget id="calculator">240 * 50</gadget>
<output>12_000</output>
<gadget id="calculator">150 - 50</gadget>
<output>100</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">12_000 / 200</gadget>
<output>60</output>
<gadget id="calculator">60 - 30</gadget>
<output>30</output>
<result>B</result> | B | 30 | An engineer undertakes a project to build a road 10 km long in 150 days and employs 30 men for the purpose. After 50 days, he finds only 2 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time. | {
"A": "22",
"B": "30",
"C": "15",
"D": "18",
"E": "20"
} | subtract(divide(multiply(multiply(30, subtract(10, 2)), 50), multiply(2, subtract(150, 50))), 30) | subtract(n0,n4)|subtract(n1,n3)|multiply(n2,#0)|multiply(n4,#1)|multiply(n3,#2)|divide(#4,#3)|subtract(#5,n2)| | "30 workers working already let x be the total men required to finish the task in next 100 days 2 km done hence remaining is 8 km also , work has to be completed in next 100 days ( 150 - 50 = 100 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 50 ) / ( 2 * 100 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : b" | physics |
math_qa__wcp3hcoO1xxsKUb2 | The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 8 years will be Choose the correct choice from the following.
A) 4 : 3 B) 12 : 11 C) 7 : 4 D) 6 : 5 E) 6 : 11 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">28 / 7</gadget>
<output>4</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 + 8</gadget>
<output>24</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">24 / 20</gadget>
<output>6/5 = around 1.2</output>
<result>D</result> | D | 1.2 | The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 8 years will be | {
"A": "4 : 3",
"B": "12 : 11",
"C": "7 : 4",
"D": "6 : 5",
"E": "6 : 11"
} | divide(add(multiply(4, divide(28, add(4, 3))), 8), add(multiply(3, divide(28, add(4, 3))), 8)) | add(n0,n1)|divide(n2,#0)|multiply(n0,#1)|multiply(n1,#1)|add(n3,#2)|add(n3,#3)|divide(#4,#5)| | "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 28 x = 4 mini ’ s age = 16 years and minakshi ’ s age = 12 years ratio of their ages after 8 years = ( 16 + 8 ) : ( 12 + 8 ) = 24 : 20 = 6 : 5 answer : d" | general |
math_qa__PaHDshNFddOk5n80 | What is the difference between the place values of two 1's in the numeral 135.21 Select the correct option:
A) 99.999
B) 100.2
C) 134
D) 99.99
E) 99.9 | <gadget id="calculator">1 * 100</gadget>
<output>100</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">100 - (1/100)</gadget>
<output>9_999/100 = around 99.99</output>
<result>D</result> | D | 99.99 | What is the difference between the place values of two 1's in the numeral 135.21 | {
"A": "99.999",
"B": "100.2",
"C": "134",
"D": "99.99",
"E": "99.9"
} | subtract(multiply(1, const_100), divide(1, const_100)) | divide(n0,const_100)|multiply(n0,const_100)|subtract(#1,#0) | required difference = 100 - 0.01 = 99.99 answer is d | general |
math_qa__g3TKLfvl1DtzcGe6 | If x + (1/x) = 5, what is the value of E=x^2 + (1/x)^2?
Select
A) e = 21 B) e = 22 C) e = 23 D) 24 E) 27 | <gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">25 - 2</gadget>
<output>23</output>
<result>C</result> | C | 23 | If x + (1/x) = 5, what is the value of E=x^2 + (1/x)^2? | {
"A": "e = 21",
"B": "e = 22",
"C": "e = 23",
"D": "24",
"E": "27"
} | subtract(power(5, 2), 2) | power(n1,n2)|subtract(#0,n2)| | "squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c" | general |
math_qa__1hDsZHZ6qUufgwd5 | 8 is 4% of a, and 4 is 8% of b. c equals b/a. What is the value of c? Answers.
A) 1 / 32 B) 1 / 4 C) 1 D) 4 E) 5 | <gadget id="calculator">4 / 8</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<gadget id="calculator">8 / 4</gadget>
<output>2</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">50 / 200</gadget>
<output>1/4 = around 0.25</output>
<result>B</result> | B | 0.25 | 8 is 4% of a, and 4 is 8% of b. c equals b/a. What is the value of c? | {
"A": "1 / 32",
"B": "1 / 4",
"C": "1",
"D": "4",
"E": "5"
} | divide(multiply(divide(4, 8), const_100), multiply(divide(8, 4), const_100)) | divide(n1,n0)|divide(n0,n1)|multiply(#0,const_100)|multiply(#1,const_100)|divide(#2,#3)| | "explanation : given , = > 4 a / 100 = 8 . = > a = 8 × ( 100 / 4 ) = 200 . - - - - - - - - - ( i ) and , = > ( 8 / 100 ) × b = 4 . = > b = 50 . - - - - - - - - - ( ii ) now , c = b / a ( from ( i ) and ( ii ) ) = > 50 / 200 . = > 1 / 4 . answer : b" | general |
math_qa__Wan56LcfWdwgDJWk | The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire? Choose the most appropriate option
A) 2 : 5 B) 2 : 9 C) 2 : 2 D) 2 : 9 E) 2 : 1 | <gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 2</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/10) / (1/4)</gadget>
<output>2/5 = around 0.4</output>
<result>A</result> | A | 0.4 | The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire? | {
"A": "2 : 5",
"B": "2 : 9",
"C": "2 : 2",
"D": "2 : 9",
"E": "2 : 1"
} | divide(divide(1, 10), power(divide(1, 2), const_2)) | divide(n0,n1)|divide(n0,n3)|power(#1,const_2)|divide(#0,#2) | the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 10 = ( 1 ) 2 h 1 / ( 2 ) 2 h 2 = > h 1 / h 2 = 2 / 5 i . e . h 1 : h 2 = 2 : 5 answer : a | geometry |
math_qa__1cczuMbcdJcTkNon | The average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added. If average weight of the whole group after including the additional 30 members is 40 kg, what is the average weight of the additional friends? Choose the correct answer
A) 50 kg
B) 60 kg
C) 61 kg
D) 62 kg
E) 91 kg | <gadget id="calculator">30 + 30</gadget>
<output>60</output>
<gadget id="calculator">60 * 40</gadget>
<output>2_400</output>
<gadget id="calculator">40 - 10</gadget>
<output>30</output>
<gadget id="calculator">30 * 30</gadget>
<output>900</output>
<gadget id="calculator">2_400 - 900</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 / 30</gadget>
<output>50</output>
<result>A</result> | A | 50 | The average weight of a group of 30 friends increases by 10 kg when the weight of additional 30 friends was added. If average weight of the whole group after including the additional 30 members is 40 kg, what is the average weight of the additional friends? | {
"A": "50 kg",
"B": "60 kg",
"C": "61 kg",
"D": "62 kg",
"E": "91 kg"
} | divide(subtract(multiply(add(30, 30), 40), multiply(30, subtract(40, 10))), 30) | add(n0,n0)|subtract(n4,n1)|multiply(n4,#0)|multiply(n0,#1)|subtract(#2,#3)|divide(#4,n0) | let a = avg . wt . of additional 30 friends original total weight = ( 30 friends ) ( 30 kg avge ) = 900 kg ( 900 + 30 a ) / ( 30 + 30 ) = 40 kg avge a = 50 kg answer - a | general |
math_qa__r0S7k99S0fPaIgsv | Sum of two numbers is 50. Two times of the difference of first and seceond is 20. Then the numbers will be? Select the correct option:
A) 10 , 40 B) 20 , 30 C) 35 , 15 D) 30 , 20 E) 15 , 35 | <gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">50 - 10</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">50 - 20</gadget>
<output>30</output>
<result>D</result> | D | 30 | Sum of two numbers is 50. Two times of the difference of first and seceond is 20. Then the numbers will be? | {
"A": "10 , 40",
"B": "20 , 30",
"C": "35 , 15",
"D": "30 , 20",
"E": "15 , 35"
} | subtract(50, divide(subtract(50, divide(20, const_2)), const_2)) | divide(n1,const_2)|subtract(n0,#0)|divide(#1,const_2)|subtract(n0,#2) | explanation : x + y = 50 2 x ã ¢ â ‚ ¬ â € œ 2 y = 20 x = 30 y = 20 answer : d | general |
math_qa__WsenZDGC4MRADTSR | If the average (arithmetic mean) of a and b is 110, and the average of b and c is 160, what is the value of a − c? Choose the correct choice from the following:
A) − 220 B) − 100 C) 100 D) 135 E) it can not be determined from the information given | <gadget id="calculator">60 * 2</gadget>
<output>120</output>
<gadget id="calculator">110 * 2</gadget>
<output>220</output>
<gadget id="calculator">120 - 220</gadget>
<output>-100</output>
<result>B</result> | B | -100 | If the average (arithmetic mean) of a and b is 110, and the average of b and c is 160, what is the value of a − c? | {
"A": "− 220",
"B": "− 100",
"C": "100",
"D": "135",
"E": "it can not be determined from the information given"
} | subtract(multiply(const_60.0, const_2), multiply(110, const_2)) | multiply(const_60.0,const_2)|multiply(n0,const_2)|subtract(#0,#1)| | "( a + b ) / 2 = 110 = = = > a + b = 220 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 220 - 320 = = = > a + b - b - c = - 100 = = = > a - c = - 100 answer : b" | general |
math_qa__WWtzRklG5pxXqFIs | If a and b are the roots of the equation x2 - 7x + 7 = 0, then the value of a2 + b2 is:
Select the correct option: A) 35 B) 24 C) 17 D) 6 E) 5 | <gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">4 * 7</gadget>
<output>28</output>
<gadget id="calculator">49 - 28</gadget>
<output>21</output>
<gadget id="calculator">21 ** (1/2)</gadget>
<output>sqrt(21) = around 4.582576</output>
<gadget id="calculator">7 - (sqrt(21))</gadget>
<output>7 - sqrt(21) = around 2.417424</output>
<gadget id="calculator">(7 - sqrt(21)) / 2</gadget>
<output>7/2 - sqrt(21)/2 = around 1.208712</output>
<gadget id="calculator">(7/2 - sqrt(21)/2) ** 2</gadget>
<output>(7/2 - sqrt(21)/2)**2 = around 1.460985</output>
<gadget id="calculator">7 + (sqrt(21))</gadget>
<output>sqrt(21) + 7 = around 11.582576</output>
<gadget id="calculator">(sqrt(21) + 7) / 2</gadget>
<output>sqrt(21)/2 + 7/2 = around 5.791288</output>
<gadget id="calculator">(sqrt(21)/2 + 7/2) ** 2</gadget>
<output>(sqrt(21)/2 + 7/2)**2 = around 33.539015</output>
<gadget id="calculator">((7/2 - sqrt(21)/2)**2) + ((sqrt(21)/2 + 7/2)**2)</gadget>
<output>(7/2 - sqrt(21)/2)**2 + (sqrt(21)/2 + 7/2)**2 = around 35</output>
<result>A</result> | A | 35 | If a and b are the roots of the equation x2 - 7x + 7 = 0, then the value of a2 + b2 is: | {
"A": "35",
"B": "24",
"C": "17",
"D": "6",
"E": "5"
} | add(power(divide(subtract(7, sqrt(subtract(power(7, const_2), multiply(const_4, 7)))), const_2), 2), power(divide(add(7, sqrt(subtract(power(7, const_2), multiply(const_4, 7)))), const_2), 2)) | multiply(n1,const_4)|power(n1,const_2)|subtract(#1,#0)|sqrt(#2)|add(n1,#3)|subtract(n1,#3)|divide(#5,const_2)|divide(#4,const_2)|power(#6,n0)|power(#7,n0)|add(#8,#9) | sol . ( b ) the sum of roots = a + b = 7 product of roots = ab = 8 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 49 - 14 = 35 answer a | general |
math_qa__zEKvvadcyB3FZdAa | Each Machine of type A has 4 steel parts and 2 chrome parts. Each machine of type B has 2 steel parts and 1 chrome parts. If a certain group of type A and type B machines has a total of 30 steel parts and 33 chrome parts, how many machines are in the group Options:
A) 12 B) 13 C) 14 D) 16 E) 19 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">33 / 3</gadget>
<output>11</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">30 / 6</gadget>
<output>5</output>
<gadget id="calculator">11 + 5</gadget>
<output>16</output>
<result>D</result> | D | 16 | Each Machine of type A has 4 steel parts and 2 chrome parts. Each machine of type B has 2 steel parts and 1 chrome parts. If a certain group of type A and type B machines has a total of 30 steel parts and 33 chrome parts, how many machines are in the group | {
"A": "12",
"B": "13",
"C": "14",
"D": "16",
"E": "19"
} | add(divide(33, add(1, 2)), divide(30, add(4, 2))) | add(n1,n3)|add(n0,n1)|divide(n5,#0)|divide(n4,#1)|add(#2,#3)| | "look at the below representation of the problem : steel chrome total a 4 2 30 > > no . of type a machines = 30 / 6 = 5 b 2 1 33 > > no . of type b machines = 33 / 3 = 11 so the answer is 16 i . e d . hope its clear ." | general |
math_qa__DDYDz9pONwphUQnf | A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug out. Choose the correct choice from the following: A) 40 m 3 B) 42 m 3 C) 44 m 3 D) 46 m 3 E) none of these | <gadget id="calculator">2 / 2</gadget>
<output>1</output>
<gadget id="calculator">pi * (1 ** 2) * 14</gadget>
<output>14*pi = around 43.982297</output>
<result>C</result> | C | 44 | A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug out. | {
"A": "40 m 3",
"B": "42 m 3",
"C": "44 m 3",
"D": "46 m 3",
"E": "none of these"
} | volume_cylinder(divide(2, const_2), 14) | divide(n0,const_2)|volume_cylinder(#0,n1) | explanation : volume = π r 2 hvolume = ( 22 / 7 ∗ 1 ∗ 1 ∗ 14 ) m 3 = 44 m 3 option c | geometry |
math_qa__lp2Z0ndQuYv8eG8Y | There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female? Select the correct option
A) 75 B) 100 C) 125 D) 175 E) 225 | <gadget id="calculator">750 / 3</gadget>
<output>250</output>
<gadget id="calculator">250 * 4</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 750</gadget>
<output>250</output>
<gadget id="calculator">250 / 2</gadget>
<output>125</output>
<result>C</result> | C | 125 | There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female? | {
"A": "75",
"B": "100",
"C": "125",
"D": "175",
"E": "225"
} | divide(subtract(multiply(divide(750, const_3), const_4), 750), const_2) | divide(n0,const_3)|multiply(#0,const_4)|subtract(#1,n0)|divide(#2,const_2)| | "female = x male = 750 - x x / 2 + 750 - x / 4 = 1 / 3 * ( 750 ) = 250 x = 250 x / 2 = 125 is supposed to be the answer answer : c" | general |
math_qa__fooy4oQp8ukV3ySG | If m = 3^n, what is the greatest value of n for which m is a factor of 16!
Pick: A) 8 B) 10 C) 6 D) 14 E) 16 | <gadget id="calculator">16 / 3</gadget>
<output>16/3 = around 5.333333</output>
<gadget id="calculator">floor(16/3)</gadget>
<output>5</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">16 / 9</gadget>
<output>16/9 = around 1.777778</output>
<gadget id="calculator">floor(16/9)</gadget>
<output>1</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<result>C</result> | C | 6 | If m = 3^n, what is the greatest value of n for which m is a factor of 16! | {
"A": "8",
"B": "10",
"C": "6",
"D": "14",
"E": "16"
} | add(floor(divide(16, 3)), floor(divide(16, power(3, const_2)))) | divide(n1,n0)|power(n0,const_2)|divide(n1,#1)|floor(#0)|floor(#2)|add(#3,#4)| | "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 - - - - count 3 ' s = 6 so answer is 6" | other |
math_qa__x44DCkP23HmXdnkn | If 25% of x is 5 less than 10% of 500, then x is? Choose the correct choice: A) 188 B) 180 C) 156 D) 840 E) 121 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">500 * (1/10)</gadget>
<output>50</output>
<gadget id="calculator">50 - 5</gadget>
<output>45</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">45 / (1/4)</gadget>
<output>180</output>
<result>B</result> | B | 180 | If 25% of x is 5 less than 10% of 500, then x is? | {
"A": "188",
"B": "180",
"C": "156",
"D": "840",
"E": "121"
} | divide(subtract(multiply(500, divide(10, const_100)), 5), divide(25, const_100)) | divide(n2,const_100)|divide(n0,const_100)|multiply(n3,#0)|subtract(#2,n1)|divide(#3,#1)| | "25 % of x = x / 4 ; 10 % of 500 = 10 / 100 * 500 = 50 given that , x / 4 = 50 - 5 = > x / 4 = 45 = > x = 180 . answer : b" | general |
math_qa__XDyP0ndOfMm6rqNt | Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 675meters, after what time will they meet at the starting point? Choose the correct choice from the following answers: A) 20 sec B) 15 sec C) 45 sec D) 50 sec E) 1 min | <gadget id="calculator">8 + 7</gadget>
<output>15</output>
<gadget id="calculator">675 / 15</gadget>
<output>45</output>
<result>C</result> | C | 45 | Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 675meters, after what time will they meet at the starting point? | {
"A": "20 sec",
"B": "15 sec",
"C": "45 sec",
"D": "50 sec",
"E": "1 min"
} | divide(675, add(8, 7)) | add(n0,n1)|divide(n2,#0)| | "they meet every 675 / 7 + 8 = 45 sec answer is c" | physics |
math_qa__di6vAx6ct9SHSeBE | What is the least possible value of expression E = (x-1)(x-3)(x-4)(x-6)+10 for real values of x? Select:
A) 1 B) 10 C) 9 D) 0 E) 8 | <gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">11 - 10</gadget>
<output>1</output>
<result>A</result> | A | 1 | What is the least possible value of expression E = (x-1)(x-3)(x-4)(x-6)+10 for real values of x? | {
"A": "1",
"B": "10",
"C": "9",
"D": "0",
"E": "8"
} | subtract(add(10, 1), add(6, 4)) | add(n0,n4)|add(n2,n3)|subtract(#0,#1) | explanation : e = ( x - 1 ) ( x - 6 ) ( x - 3 ) ( x - 4 ) + 10 e = ( x 2 - 7 x + 6 ) ( x 2 - 7 x + 12 ) + 10 let x 2 - 7 x + 6 = y e = y 2 + 6 y + 10 e = ( y + 3 ) 2 + 1 minimum value = 1 , when y = - 3 answer : a | general |
math_qa__TCrjCXmTJdP8o2cp | A and B can finish a work in 12 days while A alone can do the same work in 20 days. In how many days B alone will complete the work? Pick one: A) 76 days B) 30 days C) 98 days D) 31 days E) 22 days | <gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/12) - (1/20)</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>B</result> | B | 30 | A and B can finish a work in 12 days while A alone can do the same work in 20 days. In how many days B alone will complete the work? | {
"A": "76 days",
"B": "30 days",
"C": "98 days",
"D": "31 days",
"E": "22 days"
} | inverse(subtract(inverse(12), inverse(20))) | inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2)| | "b = 1 / 12 – 1 / 20 = 2 / 60 = 1 / 30 = > 30 days answer : b" | physics |
math_qa__uaCJFRfaqO9sx9dm | A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? Choose the correct choice from the following answers.
A) 76 sec
B) 67 sec
C) 98 sec
D) 36 sec
E) 32 sec | <gadget id="calculator">200 + 120</gadget>
<output>320</output>
<gadget id="calculator">45 - 9</gadget>
<output>36</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">5 / 18</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">320 / 10</gadget>
<output>32</output>
<result>E</result> | E | 32 | A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? | {
"A": "76 sec",
"B": "67 sec",
"C": "98 sec",
"D": "36 sec",
"E": "32 sec"
} | divide(add(200, 120), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2)))) | add(n1,n2)|divide(const_10,const_2)|subtract(n3,n0)|divide(#2,const_2)|divide(#1,#3)|multiply(#4,#2)|divide(#0,#5) | speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 120 = 320 m . time taken = 320 / 10 = 32 sec . answer : e | general |
math_qa__n52liGyAd6ajIPJE | A certain tax rate is $82 per $100.00. What is the rate, expressed as a percent? Select the correct option:
A) 82 % B) 8.2 % C) 0.82 % D) 0.082 % E) 0.0082 % | <gadget id="calculator">82 / 100</gadget>
<output>41/50 = around 0.82</output>
<gadget id="calculator">(41/50) * 100</gadget>
<output>82</output>
<result>A</result> | A | 82 | A certain tax rate is $82 per $100.00. What is the rate, expressed as a percent? | {
"A": "82 %",
"B": "8.2 %",
"C": "0.82 %",
"D": "0.082 %",
"E": "0.0082 %"
} | multiply(divide(82, 100.00), 100.00) | divide(n0,n1)|multiply(#0,n1)| | "here in question it is asking $ . 82 is what percent of $ 100 . suppose $ . 82 is x % of 100 means 100 * ( x / 100 ) = 82 hence x = 82 % so answer is a" | gain |
math_qa__mdHhgv5EIUdZqPqV | x, a, z, and b are single digit positive integers. x = 1/6 a. z = 1/6 b. (10a + b) – (10x + z) could NOT equal Pick.
A) 35
B) 30
C) 43
D) 60
E) 65 | <gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">36 + 60</gadget>
<output>96</output>
<gadget id="calculator">60 + 6</gadget>
<output>66</output>
<gadget id="calculator">96 - 66</gadget>
<output>30</output>
<gadget id="calculator">30 + 10</gadget>
<output>40</output>
<gadget id="calculator">40 + 3</gadget>
<output>43</output>
<result>C</result> | C | 43 | x, a, z, and b are single digit positive integers. x = 1/6 a. z = 1/6 b. (10a + b) – (10x + z) could NOT equal | {
"A": "35",
"B": "30",
"C": "43",
"D": "60",
"E": "65"
} | add(add(subtract(add(multiply(6, 6), multiply(6, 10)), add(multiply(6, 10), 6)), 10), const_3) | multiply(n1,n1)|multiply(n1,n4)|add(#0,#1)|add(n1,#1)|subtract(#2,#3)|add(n4,#4)|add(#5,const_3)| | "a = 6 x , b = 6 z therefore ( 6 x . 10 + 6 z ) - ( 10 x + z ) = ( 6 - 1 ) ( 10 x + z ) = 5 . ( 10 x + z ) number should be divisible by 5 c" | general |
math_qa__EIJlgCXTSgTaZH1p | The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/18 of the area of the field. What is the length of the field? Pick: A) 23 B) 32 C) 34 D) 43 E) 48 | <gadget id="calculator">8 ** 2</gadget>
<output>64</output>
<gadget id="calculator">64 * 18</gadget>
<output>1_152</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1_152 / (1/2)</gadget>
<output>2_304</output>
<gadget id="calculator">2_304 ** (1/2)</gadget>
<output>48</output>
<result>E</result> | E | 48 | The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/18 of the area of the field. What is the length of the field? | {
"A": "23",
"B": "32",
"C": "34",
"D": "43",
"E": "48"
} | sqrt(divide(multiply(square_area(8), 18), inverse(const_2))) | inverse(const_2)|square_area(n0)|multiply(n2,#1)|divide(#2,#0)|sqrt(#3)| | "explanation : a / 18 = 8 * 8 = > a = 8 * 8 * 18 x * 2 x = 8 * 8 * 18 x = 24 = > 2 x = 48 answer : option e" | geometry |
math_qa__9ESzQAvjFkr3eyMr | If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 290 pounds. What is Jake’s present weight, in pounds? Pick one:
A) 131
B) 135
C) 169
D) 196
E) 212 | <gadget id="calculator">290 - 8</gadget>
<output>282</output>
<gadget id="calculator">282 / 3</gadget>
<output>94</output>
<gadget id="calculator">94 * 2</gadget>
<output>188</output>
<gadget id="calculator">188 + 8</gadget>
<output>196</output>
<result>D</result> | D | 196 | If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 290 pounds. What is Jake’s present weight, in pounds? | {
"A": "131",
"B": "135",
"C": "169",
"D": "196",
"E": "212"
} | add(multiply(divide(subtract(290, 8), const_3), const_2), 8) | subtract(n1,n0)|divide(#0,const_3)|multiply(#1,const_2)|add(n0,#2)| | "lets say j is the weight of jack and s is the wt of his sister . if he loses 8 pounds , he s twice as heavy as his sister . j - 8 = 2 * s also , together they weight 290 pounds j + s = 290 solvong the 2 equation , we get j = 196 pounds ! d" | general |
math_qa__9NqGtMVl9kLS5sit | On a trip covering 850 km, a bicyclist travels the first 400 km at 20 km per hour and the remainder of the distance at 15 km per hour. What is the average speed, in km per hour, for the entire trip? Choose the correct choice from the following:
A) 16.0
B) 16.5
C) 17.0
D) 17.5
E) 18.0 | <gadget id="calculator">400 / 20</gadget>
<output>20</output>
<gadget id="calculator">850 - 400</gadget>
<output>450</output>
<gadget id="calculator">450 / 15</gadget>
<output>30</output>
<gadget id="calculator">20 + 30</gadget>
<output>50</output>
<gadget id="calculator">850 / 50</gadget>
<output>17</output>
<result>C</result> | C | 17 | On a trip covering 850 km, a bicyclist travels the first 400 km at 20 km per hour and the remainder of the distance at 15 km per hour. What is the average speed, in km per hour, for the entire trip? | {
"A": "16.0",
"B": "16.5",
"C": "17.0",
"D": "17.5",
"E": "18.0"
} | speed(850, add(divide(400, 20), divide(subtract(850, 400), 15))) | divide(n1,n2)|subtract(n0,n1)|divide(#1,n3)|add(#0,#2)|speed(n0,#3)| | "time 1 = 400 / 20 = 20 hours time 2 = 450 / 15 = 30 hours total time = 50 hours average speed = 850 / 50 = 17 km / hr the answer is c ." | physics |
math_qa__18FA7Vf6GMQHSkvX | The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 15 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes. Choose the correct choice from the following answers:
A) $ 0.94 B) $ 0.96 C) $ 0.98 D) $ 1.02 E) $ 1.20 | <gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">1 + (2/25)</gadget>
<output>27/25 = around 1.08</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">0.8 / (17/20)</gadget>
<output>0.941176</output>
<gadget id="calculator">(27/25) * 0.941176</gadget>
<output>1.01647</output>
<result>D</result> | D | 1.02 | The manager of a produce market purchased a quantity of tomatoes for $0.80 per pound. Due to improper handling, 15 percent of the tomatoes, by weight, were ruined and discarded. At what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes. | {
"A": "$ 0.94",
"B": "$ 0.96",
"C": "$ 0.98",
"D": "$ 1.02",
"E": "$ 1.20"
} | multiply(add(const_1, divide(8, const_100)), divide(0.80, divide(subtract(const_100, 15), const_100))) | divide(n2,const_100)|subtract(const_100,n1)|add(#0,const_1)|divide(#1,const_100)|divide(n0,#3)|multiply(#2,#4)| | "assume the manager bought 100 tomatoes . cost price = 80 given : 15 % are damaged - - > available tomatoes to sell = 85 85 * x - 80 = 0.08 * 80 85 x - 80 = 6.4 85 x = 86.64 x = 86.64 / 85 = 87 / 85 ( approx ) = 1.023 x is slightly under 1.023 = 1.02 answer : d" | gain |
math_qa__2IFueO3QX2RDoqrS | The greatest number which on dividing 1642 and 1856 leaves remainders 6 and 4 respectively, is: Answers.
A) 123
B) 127
C) 235
D) 4
E) 505 | <gadget id="calculator">1_856 - 4</gadget>
<output>1_852</output>
<gadget id="calculator">1_642 - 6</gadget>
<output>1_636</output>
<gadget id="calculator">gcd(1_852, 1_636)</gadget>
<output>4</output>
<result>D</result> | D | 4 | The greatest number which on dividing 1642 and 1856 leaves remainders 6 and 4 respectively, is: | {
"A": "123",
"B": "127",
"C": "235",
"D": "4",
"E": "505"
} | gcd(subtract(1856, 4), subtract(1642, 6)) | subtract(n1,n3)|subtract(n0,n2)|gcd(#0,#1)| | "explanation : required number = h . c . f . of ( 1642 - 6 ) and ( 1856 - 4 ) = h . c . f . of 1636 and 1852 = 4 . answer : d" | general |
math_qa__S9H9gXvOSQtdv3nA | Marcella has 27 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left? Pick one
A) 22 B) 20 C) 19 D) 16 E) 15 | <gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">floor(9/2)</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">27 - 5</gadget>
<output>22</output>
<result>A</result> | A | 22 | Marcella has 27 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left? | {
"A": "22",
"B": "20",
"C": "19",
"D": "16",
"E": "15"
} | subtract(27, add(floor(divide(9, const_2)), const_1)) | divide(n1,const_2)|floor(#0)|add(#1,const_1)|subtract(n0,#2)| | "marcella has 27 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 27 pairs of shoes minus the 5 ' destroyed ' pairs yields 22 pairs that still fulfill the requirements . answer : a" | general |
math_qa__3JAUhNph7bX2hyCH | How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? Options:
A) 5
B) 4
C) 20
D) 25
E) 30 | <gadget id="calculator">5 * 4</gadget>
<output>20</output>
<result>C</result> | C | 20 | How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? | {
"A": "5",
"B": "4",
"C": "20",
"D": "25",
"E": "30"
} | multiply(5, const_4) | multiply(n3,const_4) | since each desired number is divisible by 5 , so we must have 5 at the unit place . so , there is 1 way of doing it . the tens place can now be filled by any of the remaining 5 digits ( 2 , 3 , 6 , 7 , 9 ) . so , there are 5 ways of filling the tens place . the hundreds place can now be filled by any of the remaining 4 digits . so , there are 4 ways of filling it . required number of numbers = ( 1 x 5 x 4 ) = 20 . answer c | general |
math_qa__b81tw8gyVwsNdw6P | A man invests some money partly in 12% stock at 105 and partly in 8% stock at 88. To obtain equal dividends from both, he must invest the money in the ratio.
Choose the correct choice:
A) 35 : 44 B) 34 : 44 C) 22 : 44 D) 20 : 40 E) 50 : 45 | <gadget id="calculator">105 * 2</gadget>
<output>210</output>
<gadget id="calculator">88 * 3</gadget>
<output>264</output>
<gadget id="calculator">210 / 264</gadget>
<output>35/44 = around 0.795455</output>
<result>A</result> | A | 0.795455 | A man invests some money partly in 12% stock at 105 and partly in 8% stock at 88. To obtain equal dividends from both, he must invest the money in the ratio. | {
"A": "35 : 44",
"B": "34 : 44",
"C": "22 : 44",
"D": "20 : 40",
"E": "50 : 45"
} | divide(multiply(105, const_2), multiply(88, const_3)) | multiply(n1,const_2)|multiply(n3,const_3)|divide(#0,#1) | in case of stock 1 , if he invest rs . 105 , he will get a dividend of rs . 12 ( assume face value = 100 ) in case of stock 2 , if he invest rs . 88 , he will get a dividend of rs . 8 ( assume face value = 100 ) ie , if he invest rs . ( 88 * 12 ) / 8 , he will get a dividend of rs . 12 required ratio = 105 : ( 88 × 12 ) / 8 = 105 : ( 11 × 12 ) = 35 : ( 11 × 4 ) = 35 : 44 answer is a . | other |
math_qa__2AI8be5ZjQehHTDt | A merchant sells an item at a 10% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?
Pick one
A) 30 % B) 40 % C) 50 % D) 60 % E) 75 % | <gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 - 20</gadget>
<output>70</output>
<gadget id="calculator">100 - 70</gadget>
<output>30</output>
<result>A</result> | A | 30 | A merchant sells an item at a 10% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount? | {
"A": "30 %",
"B": "40 %",
"C": "50 %",
"D": "60 %",
"E": "75 %"
} | subtract(const_100, subtract(subtract(const_100, 10), 20)) | subtract(const_100,n0)|subtract(#0,n1)|subtract(const_100,#1) | original sp = x cost = c current selling price = . 9 x ( 10 % discount ) . 9 x = 1.2 c ( 20 % profit ) x = 1.2 / . 9 * c x = 4 / 3 c original selling price is 1.3 c which is 30 % profit answer a | gain |
math_qa__P8JQM2AvUqrG5G6A | The average age of applicants for a new job is 20, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants? Choose the correct choice from the following answers
A) 8
B) 16
C) 17
D) 18
E) 34 | <gadget id="calculator">20 + 8</gadget>
<output>28</output>
<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<gadget id="calculator">28 - 12</gadget>
<output>16</output>
<gadget id="calculator">16 + 1</gadget>
<output>17</output>
<result>C</result> | C | 17 | The average age of applicants for a new job is 20, with a standard deviation of 8. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants? | {
"A": "8",
"B": "16",
"C": "17",
"D": "18",
"E": "34"
} | add(subtract(add(20, 8), subtract(20, 8)), const_1) | add(n0,n1)|subtract(n0,n1)|subtract(#0,#1)|add(#2,const_1)| | "minimum age = average - 1 standard deviation = 20 - 8 = 12 maximum age = average + 1 standard deviation = 20 + 8 = 28 maximum number of different ages of the applicants = 28 - 12 + 1 = 17 answer c" | general |
math_qa__P9qJAz5Ba1chvuDj | P, Q and R have $7000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
Options: A) 2800 B) 2403 C) 3998 D) 2539 E) 1930 | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">7_000 * 4</gadget>
<output>28_000</output>
<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) * 3</gadget>
<output>4</output>
<gadget id="calculator">1 * 3</gadget>
<output>3</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">7 + 3</gadget>
<output>10</output>
<gadget id="calculator">28_000 / 10</gadget>
<output>2_800</output>
<result>A</result> | A | 2,800 | P, Q and R have $7000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R? | {
"A": "2800",
"B": "2403",
"C": "3998",
"D": "2539",
"E": "1930"
} | divide(multiply(7000, multiply(const_2, const_2)), add(add(multiply(divide(multiply(const_2, const_2), const_3), const_3), multiply(const_1, const_3)), multiply(const_1, const_3))) | multiply(const_2,const_2)|multiply(const_1,const_3)|divide(#0,const_3)|multiply(n0,#0)|multiply(#2,const_3)|add(#4,#1)|add(#5,#1)|divide(#3,#6) | a 2800 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 7000 - r ) = > 3 r = 14000 - 2 r = > 5 r = 14000 = > r = 2800 . | general |
math_qa__OwcGr77AZnPLnzPa | Unit size cubes are stacked inside a big rectangular box having dimensions corresponding to three consecutive multiples of 5. Choose exact number of cubes that can completely fill the box. Choose the correct choice from the following answers
A) 750
B) 850
C) 950
D) 1050
E) none of the above | <gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">5 * 10 * 15</gadget>
<output>750</output>
<gadget id="calculator">1 ** 3</gadget>
<output>1</output>
<gadget id="calculator">750 / 1</gadget>
<output>750</output>
<result>A</result> | A | 750 | Unit size cubes are stacked inside a big rectangular box having dimensions corresponding to three consecutive multiples of 5. Choose exact number of cubes that can completely fill the box. | {
"A": "750",
"B": "850",
"C": "950",
"D": "1050",
"E": "none of the above"
} | divide(volume_rectangular_prism(5, multiply(5, const_2), multiply(5, const_3)), volume_cube(const_1)) | multiply(n0,const_2)|multiply(n0,const_3)|volume_cube(const_1)|volume_rectangular_prism(n0,#0,#1)|divide(#3,#2) | let the dimensions of the box be , length = 5 * a , breadth = 5 * ( a + 1 ) , height = 5 * ( a + 2 ) hence , volume = 5 * 5 * 5 * a * ( a + 1 ) * ( a + 2 ) among any 3 consecutive positive integers , we will either have ( a number that is divisible by both 23 ) or ( a number divisible by 2 and another number divisible by 3 ) . volume = multiple of ( 125 * 2 * 3 ) 750 = 125 * 2 * 3 answer : a | geometry |
math_qa__78bLmPu0AV87hW0T | P and Q started a business investing Rs 85000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.
Pick: A) 17 : 5 B) 17 : 3 C) 17 : 6 D) 17 : 7 E) 17 : 8 | <gadget id="calculator">85_000 / 15_000</gadget>
<output>17/3 = around 5.666667</output>
<result>B</result> | B | 5.666667 | P and Q started a business investing Rs 85000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively. | {
"A": "17 : 5",
"B": "17 : 3",
"C": "17 : 6",
"D": "17 : 7",
"E": "17 : 8"
} | divide(85000, 15000) | divide(n0,n1)| | "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 85000 : 15000 = 85 : 15 = 17 : 3 option b" | gain |
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