id stringlengths 25 25 | question stringlengths 45 1.01k | chain stringlengths 75 4.11k | result stringclasses 5 values | result_float float64 -4,212 100B | question_without_options stringlengths 6 962 | options dict | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | rationale stringlengths 1 2.74k | category stringclasses 6 values |
|---|---|---|---|---|---|---|---|---|---|---|
math_qa__WzKRagTVF6qNBeu9 | What is the compound interest paid on a sum of Rs.3500 for the period of 2 years at 10% per annum. Answers:
A) 630 B) 735 C) 825 D) 600 E) none of these | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">3_500 * (121/100)</gadget>
<output>4_235</output>
<gadget id="calculator">4_235 - 3_500</gadget>
<output>735</output>
<result>B</result> | B | 735 | What is the compound interest paid on a sum of Rs.3500 for the period of 2 years at 10% per annum. | {
"A": "630",
"B": "735",
"C": "825",
"D": "600",
"E": "none of these"
} | subtract(multiply(3500, power(add(const_1, divide(10, const_100)), 2)), 3500) | divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|subtract(#3,n0)| | "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 3500 = 3500 * ( 21 / 100 ) = 735 answer b" | gain |
math_qa__ejo54StpS4HR1Nc9 | A grand father has 3 grand children. Age difference of two children among them is 3. Eldest child age is 3 times the youngest child’s age and the eldest child age is two year more than the sum of age of other two children. What is the age of the eldest child?
Choose the correct choice:
A) 22 B) 15 C) 28 D) 26 E) 9 | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 + 3</gadget>
<output>12</output>
<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<result>B</result> | B | 15 | A grand father has 3 grand children. Age difference of two children among them is 3. Eldest child age is 3 times the youngest child’s age and the eldest child age is two year more than the sum of age of other two children. What is the age of the eldest child? | {
"A": "22",
"B": "15",
"C": "28",
"D": "26",
"E": "9"
} | add(add(multiply(3, 3), 3), const_3) | multiply(n0,n0)|add(n0,#0)|add(#1,const_3) | as the eldest son ' s age is 3 times that of the youngest , eldest son ' s age should be a multiple of 3 . from the given options take 15 as the eldest son ' s age . then youngest son ' s age becomes 5 . but eldest sons age is 2 more than the sum of the remaining two sons . so sum of the remaining two sons is 13 . so the age of the middle son is 13 - 5 = 8 . which satisfies another condition in the question that the difference between the two sons age is 3 . so answer is 15 . answer : b | general |
math_qa__k6fUeKGcuTfTKHH8 | Of the people who responded to a market survey, 60 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 3 to 1, how many people responded to the survey? Options:
A) 80
B) 150
C) 240
D) 360
E) 480 | <gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">20 + 60</gadget>
<output>80</output>
<result>A</result> | A | 80 | Of the people who responded to a market survey, 60 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 3 to 1, how many people responded to the survey? | {
"A": "80",
"B": "150",
"C": "240",
"D": "360",
"E": "480"
} | add(divide(60, 3), 60) | divide(n0,n1)|add(n0,#0)| | "ratio = 3 : 1 = > 3 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 60 = > 3 x = 60 = > x = 20 hence total no . of respondents = 60 + 20 = 80 hence a is the answer ." | other |
math_qa__xvLCHQ3h4qk54GGZ | The average of 50 numbers id 38. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :
Choose the correct option: A) 22.3 B) 33.2 C) 22.2 D) 11.3 E) 37.5 | <gadget id="calculator">50 * 38</gadget>
<output>1_900</output>
<gadget id="calculator">45 + 55</gadget>
<output>100</output>
<gadget id="calculator">1_900 - 100</gadget>
<output>1_800</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">1_800 / 48</gadget>
<output>75/2 = around 37.5</output>
<result>E</result> | E | 37.5 | The average of 50 numbers id 38. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is : | {
"A": "22.3",
"B": "33.2",
"C": "22.2",
"D": "11.3",
"E": "37.5"
} | divide(subtract(multiply(50, 38), add(45, 55)), subtract(50, const_2)) | add(n2,n3)|multiply(n0,n1)|subtract(n0,const_2)|subtract(#1,#0)|divide(#3,#2)| | "explanation : total of 50 numbers = ( 50 × 38 ) = 1900 ( 50 × 38 ) = 1900 total of 48 numbers = ( 1900 - ( 45 + 55 ) ] = 1800 required average = 180048 = 2256 = 37.5 answer : e" | general |
math_qa__N6fSKU4ZtkcmI1cz | when fair coin is tossed 9 times find the probability of getting head at least once. Select the correct option:
A) 1 / 512 B) 511 / 512 C) 9 / 512 D) 503 / 51 E) 503 / 510 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 9</gadget>
<output>1/512 = around 0.001953</output>
<gadget id="calculator">1 - (1/512)</gadget>
<output>511/512 = around 0.998047</output>
<result>B</result> | B | 0.998047 | when fair coin is tossed 9 times find the probability of getting head at least once. | {
"A": "1 / 512",
"B": "511 / 512",
"C": "9 / 512",
"D": "503 / 51",
"E": "503 / 510"
} | subtract(const_1, power(divide(const_1, const_2), 9)) | divide(const_1,const_2)|power(#0,n0)|subtract(const_1,#1) | 1 - 1 / 2 ^ 9 = 1 - 1 / 512 = 511 / 512 answer : b | probability |
math_qa__LRbcVjr2LpS3Cvkb | An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets water in at the rate of 16 litres/min then outlet pipe would take 8 hours longer. Find the capacity of the tank. Pick one.
A) 8600 litres
B) 200 litres
C) 21600 litres
D) 11200 litres
E) 13200 litres | <gadget id="calculator">16 * 60</gadget>
<output>960</output>
<gadget id="calculator">10 + 8</gadget>
<output>18</output>
<gadget id="calculator">960 * 18</gadget>
<output>17_280</output>
<gadget id="calculator">17_280 / 8</gadget>
<output>2_160</output>
<gadget id="calculator">2_160 * 10</gadget>
<output>21_600</output>
<result>C</result> | C | 21,600 | An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets water in at the rate of 16 litres/min then outlet pipe would take 8 hours longer. Find the capacity of the tank. | {
"A": "8600 litres",
"B": "200 litres",
"C": "21600 litres",
"D": "11200 litres",
"E": "13200 litres"
} | multiply(divide(multiply(multiply(16, const_60), add(10, 8)), 8), 10) | add(n0,n2)|multiply(n1,const_60)|multiply(#0,#1)|divide(#2,n2)|multiply(n0,#3)| | "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 16 litres / min , or 16 * 60 = 960 liters / hour ; net outflow rate when both pipes operate would be x - 960 liters / hour . capacity of the tank = x * 10 hours = ( x - 960 ) * ( 10 + 8 ) hours 10 x = ( x - 960 ) * 18 - - > x = 2160 - - > capacity = 10 x = 21600 liters . answer : c ." | physics |
math_qa__iQ1k83xVo6lIDwqx | In a certain company, a third of the workers do not have a retirement plan. 50% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
Choose the correct choice from the following answers: A) 80 B) 95 C) 105 D) 156 E) 210 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/3) * (1/2)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/3) - (1/6)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/3) * (2/5)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">(1/6) + (4/15)</gadget>
<output>13/30 = around 0.433333</output>
<gadget id="calculator">120 / (13/30)</gadget>
<output>3_600/13 = around 276.923077</output>
<gadget id="calculator">(2/3) - (4/15)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(1/6) + (2/5)</gadget>
<output>17/30 = around 0.566667</output>
<gadget id="calculator">(3_600/13) * (17/30)</gadget>
<output>2_040/13 = around 156.923077</output>
<result>D</result> | D | 156 | In a certain company, a third of the workers do not have a retirement plan. 50% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women? | {
"A": "80",
"B": "95",
"C": "105",
"D": "156",
"E": "210"
} | multiply(divide(120, add(subtract(divide(const_1, const_3), multiply(divide(const_1, const_3), divide(50, const_100))), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))), add(multiply(divide(const_1, const_3), divide(50, const_100)), subtract(subtract(const_1, divide(const_1, const_3)), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100))))) | divide(const_1,const_3)|divide(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)|subtract(const_1,#0)|multiply(#2,#4)|subtract(#0,#3)|add(#5,#6)|subtract(#4,#5)|add(#3,#8)|divide(n2,#7)|multiply(#9,#10)| | "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,5 * 1 / 3 * x 120 = 13 / 30 x x = 276 276 - 120 = 156 answer d" | gain |
math_qa__8AmfRWgb4zyHj7Gv | Which number need to add to 1782452 to get a number exactly divisible by 92? Choose the correct choice from the following options: A) 44 B) 43 C) 42 D) 41 E) 48 | <gadget id="calculator">1_782_452 / 92</gadget>
<output>445_613/23 = around 19_374.478261</output>
<gadget id="calculator">floor(445_613/23)</gadget>
<output>19_374</output>
<gadget id="calculator">19_374 + 1</gadget>
<output>19_375</output>
<gadget id="calculator">19_375 - (445_613/23)</gadget>
<output>12/23 = around 0.521739</output>
<gadget id="calculator">92 * (12/23)</gadget>
<output>48</output>
<result>E</result> | E | 48 | Which number need to add to 1782452 to get a number exactly divisible by 92? | {
"A": "44",
"B": "43",
"C": "42",
"D": "41",
"E": "48"
} | multiply(92, subtract(add(floor(divide(1782452, 92)), const_1), divide(1782452, 92))) | divide(n0,n1)|floor(#0)|add(#1,const_1)|subtract(#2,#0)|multiply(n1,#3)| | "1782452 / 92 = 19374 and reminder = 44 . 92 - 44 = 48 so , the next number divisible by 92 is 48 places in front of 1782452 which means 48 + 1782452 = 1782500 48 should be added to 1782452 e" | general |
math_qa__BzDm2M09G2i8E4xA | A boat takes 19 hours for travelling downstream fro poin A to point B and coming back to a 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 answers
A) 180 km B) 190 km C) 220 km D) 230 km E) none | <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">4 + 14</gadget>
<output>18</output>
<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/20) + (1/18)</gadget>
<output>19/180 = around 0.105556</output>
<gadget id="calculator">19 / (19/180)</gadget>
<output>180</output>
<result>A</result> | A | 180 | A boat takes 19 hours for travelling downstream fro poin A to point B and coming back to a 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": "180 km",
"B": "190 km",
"C": "220 km",
"D": "230 km",
"E": "none"
} | divide(19, add(inverse(multiply(subtract(14, 4), const_2)), inverse(add(4, 14)))) | add(n1,n2)|subtract(n2,n1)|inverse(#0)|multiply(#1,const_2)|inverse(#3)|add(#4,#2)|divide(n0,#5) | sol . speed downstream = ( 14 + 4 ) km / hr = 18 km / hr ; speed upstream = ( 14 - 4 ) km / hr = 10 km / hr . let the distance between a and b be x km . then , x / 18 + ( x / 2 ) / 10 = 19 ⇔ x / 18 + x / 20 = 19 ⇒ x = 180 km . answer a | physics |
math_qa__ZxYhTsaUM6zlYYra | City X has a population 7 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z? Choose the correct choice from the following choices
A) 1 : 8 B) 1 : 4 C) 2 : 1 D) 14 : 1 E) 18 : 1 | <gadget id="calculator">7 * 2</gadget>
<output>14</output>
<result>D</result> | D | 14 | City X has a population 7 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z? | {
"A": "1 : 8",
"B": "1 : 4",
"C": "2 : 1",
"D": "14 : 1",
"E": "18 : 1"
} | multiply(7, const_2) | multiply(n0,const_2) | x = 7 y , y = 2 * z x : y , y : z 7 : 1 , 2 : 1 14 : 2 , 2 : 1 so , x : z = 14 : 1 ( d ) | general |
math_qa__HmxH8CJcbvzk9biB | In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 20 feet between each tree. How many trees can be planted if the road is 148 feet long?
Choices.
A) 8 B) 9 C) 10 D) 11 E) 16 | <gadget id="calculator">148 - 1</gadget>
<output>147</output>
<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">147 / 21</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<result>A</result> | A | 8 | In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 20 feet between each tree. How many trees can be planted if the road is 148 feet long? | {
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "16"
} | add(divide(subtract(148, const_1), add(20, const_1)), const_1) | add(n0,const_1)|subtract(n1,const_1)|divide(#1,#0)|add(#2,const_1) | let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 20 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 20 feet spaces will be t - 1 . then , the length of sidewalk required for 20 feet spaces will be 20 * ( t - 1 ) it is given that total length of sidewalk is 148 feet . or 20 ( t - 1 ) + t = 148 or 20 t - 20 + t = 148 or 21 t = 168 or t = 8 answer : - a | geometry |
math_qa__C3N914pWwUNrDy5x | How long does a train 120 m long travelling at 60 kmph takes to cross a bridge of 170 m in length?
Pick one
A) 15.8 sec B) 14.9 sec C) 12.4 sec D) 16.8 sec E) 17.4 sec | <gadget id="calculator">120 + 170</gadget>
<output>290</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">290 / (50/3)</gadget>
<output>87/5 = around 17.4</output>
<result>E</result> | E | 17.4 | How long does a train 120 m long travelling at 60 kmph takes to cross a bridge of 170 m in length? | {
"A": "15.8 sec",
"B": "14.9 sec",
"C": "12.4 sec",
"D": "16.8 sec",
"E": "17.4 sec"
} | divide(add(120, 170), multiply(60, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | "e 17.4 sec d = 120 + 170 = 290 m s = 60 * 5 / 18 = 50 / 3 t = 290 * 3 / 50 = 17.4 sec answer is e" | physics |
math_qa__tjrZfmMazKmilm0Q | The probability that a number selected at random from first 50 natural numbers is a composite number is Answers
A) 21 / 25 B) 17 / 25 C) 4 / 25 D) 8 / 25 E) 10 / 25 | <gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 - 1</gadget>
<output>17</output>
<gadget id="calculator">17 * 2</gadget>
<output>34</output>
<gadget id="calculator">34 / 50</gadget>
<output>17/25 = around 0.68</output>
<result>B</result> | B | 0.68 | The probability that a number selected at random from first 50 natural numbers is a composite number is | {
"A": "21 / 25",
"B": "17 / 25",
"C": "4 / 25",
"D": "8 / 25",
"E": "10 / 25"
} | divide(multiply(subtract(multiply(const_6, const_3), const_1), const_2), 50) | multiply(const_3,const_6)|subtract(#0,const_1)|multiply(#1,const_2)|divide(#2,n0)| | "the number of exhaustive events = 50 c 1 = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . therefore , required probability = 34 / 50 = 17 / 25 . answer : b" | probability |
math_qa__38vqemzv9tTZ1R2V | The speed of a train is 90 kmph. What is the distance covered by it in 15 minutes?
Choose the most appropriate option
A) 15 B) 66 C) 22.5 D) 52 E) 42 | <gadget id="calculator">15 / 60</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 90</gadget>
<output>45/2 = around 22.5</output>
<result>C</result> | C | 22.5 | The speed of a train is 90 kmph. What is the distance covered by it in 15 minutes? | {
"A": "15",
"B": "66",
"C": "22.5",
"D": "52",
"E": "42"
} | multiply(divide(15, const_60), 90) | divide(n1,const_60)|multiply(n0,#0)| | "90 * 15 / 60 = 22.5 kmph answer : c" | physics |
math_qa__MeQq2kIEisr7KkUB | 225, or 15^2, is the first perfect square that begins with two 2s. What is the sum of the digits of the next perfect square to begin with two 2s? Answers: A) 9 B) 12 C) 13 D) 14 E) 17 | <gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">48 - 1</gadget>
<output>47</output>
<gadget id="calculator">47 ** 2</gadget>
<output>2_209</output>
<gadget id="calculator">12 - 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 10</gadget>
<output>100</output>
<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">2 * 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">2_000 + 200</gadget>
<output>2_200</output>
<gadget id="calculator">2_209 - 2_200</gadget>
<output>9</output>
<gadget id="calculator">4 + 9</gadget>
<output>13</output>
<result>C</result> | C | 13 | 225, or 15^2, is the first perfect square that begins with two 2s. What is the sum of the digits of the next perfect square to begin with two 2s? | {
"A": "9",
"B": "12",
"C": "13",
"D": "14",
"E": "17"
} | add(add(2, 2), subtract(power(subtract(multiply(const_12, const_4), const_1), 2), add(multiply(const_2, multiply(subtract(const_12, const_2), multiply(subtract(const_12, const_2), subtract(const_12, const_2)))), multiply(const_2, multiply(subtract(const_12, const_2), subtract(const_12, const_2)))))) | add(n2,n2)|multiply(const_12,const_4)|subtract(const_12,const_2)|multiply(#2,#2)|subtract(#1,const_1)|multiply(#3,#2)|multiply(#3,const_2)|power(#4,n2)|multiply(#5,const_2)|add(#8,#6)|subtract(#7,#9)|add(#0,#10) | because 16 ^ 2 = 256 , y the next perfect square to begin with two 2 s can not be 3 - digit . let ' s try 4 - digit . 40 ^ 2 = 1600 and 50 ^ 2 = 2500 . so , if there is a 4 - digit perfect square to begin with two 2 s it must be between 41 ^ 2 and 49 ^ 2 . test the middle number 45 ^ 2 = 2025 . test larger number : 46 ^ 2 = 2116 . test next number : 47 ^ 2 = 2209 . bingo ! the sum of the digits = 2 + 2 + 0 + 9 = 13 . answer : c . | general |
math_qa__ZYOQk8BccwBCW3QY | Two trains are moving at 80 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Select the correct option:
A) 6 sec B) 7 sec C) 7 2 / 2 sec D) 8 sec E) 9 sec | <gadget id="calculator">150 + 100</gadget>
<output>250</output>
<gadget id="calculator">80 + 70</gadget>
<output>150</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">150 * (5/18)</gadget>
<output>125/3 = around 41.666667</output>
<gadget id="calculator">250 / (125/3)</gadget>
<output>6</output>
<result>A</result> | A | 6 | Two trains are moving at 80 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is? | {
"A": "6 sec",
"B": "7 sec",
"C": "7 2 / 2 sec",
"D": "8 sec",
"E": "9 sec"
} | divide(add(150, 100), multiply(add(80, 70), const_0_2778)) | add(n2,n3)|add(n0,n1)|multiply(#1,const_0_2778)|divide(#0,#2) | 70 + 80 = 150 * 5 / 18 = 125 / 3 mps d = 150 + 100 = 250 m t = 250 * 3 / 125 = 6 sec answer : a | physics |
math_qa__etjHp115J7a8pZ4u | If x > 0, x/50 + x/25 is what percent of x?
Pick one:
A) 6 % B) 25 % C) 37 1 / 2 % D) 60 % E) 75 % | <gadget id="calculator">1 / 50</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">1 / 25</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/50) + (1/25)</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(3/50) * 100</gadget>
<output>6</output>
<result>A</result> | A | 6 | If x > 0, x/50 + x/25 is what percent of x? | {
"A": "6 %",
"B": "25 %",
"C": "37 1 / 2 %",
"D": "60 %",
"E": "75 %"
} | multiply(add(divide(const_1, 50), divide(const_1, 25)), const_100) | divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|multiply(#2,const_100) | just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 50 + 100 / 25 = 2 + 4 = 6 6 is 6 % of 100 . answer : a | general |
math_qa__tGRoR69QPCdfE8bt | The price of commodity P increases by 40 paise every year, while the price of commodity Q increases by 15 paise every year. If in 2001, the price of commodity P was Rs. 4.20 and that of Q was Rs. 6.30, in which year commodity P will cost 40 paise more than the commodity Q ? Choose the correct choice: A) 2008 B) 2009 C) 2010 D) 2011 E) 2012 | <gadget id="calculator">2_001 + 10</gadget>
<output>2_011</output>
<result>D</result> | D | 2,011 | The price of commodity P increases by 40 paise every year, while the price of commodity Q increases by 15 paise every year. If in 2001, the price of commodity P was Rs. 4.20 and that of Q was Rs. 6.30, in which year commodity P will cost 40 paise more than the commodity Q ? | {
"A": "2008",
"B": "2009",
"C": "2010",
"D": "2011",
"E": "2012"
} | add(2001, const_10) | add(n2,const_10) | let the commodity p costs 40 paise more than the commodity q after n years . price of the commodity p in 2001 = rs . 4.20 since the price of the commodity p increases by rs 0.40 every year , price of the commodity p after n years from 2001 = rs . 4.20 + ( n × . 40 ) price of the commodity q in 2001 = rs . 6.30 since the price of the commodity q increases by rs 0.15 every year , price of the commodity q after n years from 2001 = rs . 6.30 + ( n × . 15 ) since the commodity p costs rs . 0.40 more that the commodity q after n years from 2001 , 4.20 + ( n × . 40 ) = 6.30 + ( n × . 15 ) + 0.40 = > ( 40 n - . 15 n ) = 6.30 - 4.20 + 0.40 = 2.5 = > . 25 n = 2.5 = > n = 2.5 / . 25 = 10 = > commodity p costs rs . 0.40 more that the commodity q after 10 years from 2001 . i . e . , in 2011 answer : d | general |
math_qa__QU8CWDoQEVFWIhGl | A train 110 m long running at 52 kmph crosses a platform in 30 sec. What is the length of the platform? Choose the correct choice from the following choices:
A) 287 B) 398 C) 323 D) 245 E) 267 | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">52 * (5/18)</gadget>
<output>130/9 = around 14.444444</output>
<gadget id="calculator">30 * (130/9)</gadget>
<output>1_300/3 = around 433.333333</output>
<gadget id="calculator">(1_300/3) - 110</gadget>
<output>970/3 = around 323.333333</output>
<result>C</result> | C | 323 | A train 110 m long running at 52 kmph crosses a platform in 30 sec. What is the length of the platform? | {
"A": "287",
"B": "398",
"C": "323",
"D": "245",
"E": "267"
} | subtract(multiply(30, multiply(52, const_0_2778)), 110) | multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)| | "d = 52 * 5 / 18 = 30 = 433 â € “ 110 = 323 answer : c" | physics |
math_qa__CAaLj2A0zvDhmKjs | When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 1 centimeter. The actual diameter of the tissue, in centimeters, is
Choose the correct choice from the following answers:
A) 0.005 B) 0.002 C) 0.001 D) 0.0005 E) 0.0002 | <gadget id="calculator">1 / 1_000</gadget>
<output>1/1_000 = around 0.001</output>
<result>C</result> | C | 0.001 | When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 1 centimeter. The actual diameter of the tissue, in centimeters, is | {
"A": "0.005",
"B": "0.002",
"C": "0.001",
"D": "0.0005",
"E": "0.0002"
} | divide(1, 1,000) | divide(n1,n0)| | "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 1 then x = 1 / 1000 = 0.001 . the answer is c" | geometry |
math_qa__l9Xskk0WBoU9W75Q | The distance from City A to City B is 120 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
Pick one:
A) 42
B) 44
C) 46
D) 48
E) 50 | <gadget id="calculator">120 / 30</gadget>
<output>4</output>
<gadget id="calculator">90 / 60</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">4 - (3/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">120 / (5/2)</gadget>
<output>48</output>
<result>D</result> | D | 48 | The distance from City A to City B is 120 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? | {
"A": "42",
"B": "44",
"C": "46",
"D": "48",
"E": "50"
} | divide(120, subtract(divide(120, 30), divide(90, const_60))) | divide(n0,n1)|divide(n2,const_60)|subtract(#0,#1)|divide(n0,#2)| | "the time it takes cara to drive to city b is 120 / 30 = 4 hours . dan needs to take less than 2.5 hours for the trip . dan needs to exceed a constant speed of 120 / 2.5 = 48 miles per hour . the answer is d ." | physics |
math_qa__ewPCipSuXO23jDtE | A and B began business with Rs.2000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A. Choose the correct choice from the following answers
A) 175 B) 288 C) 277 D) 877 E) 361 | <gadget id="calculator">2_000 * 8</gadget>
<output>16_000</output>
<gadget id="calculator">2_000 - 1_000</gadget>
<output>1_000</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">1_000 * 4</gadget>
<output>4_000</output>
<gadget id="calculator">16_000 + 4_000</gadget>
<output>20_000</output>
<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 + 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>
<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>
<gadget id="calculator">20_000 + 52_000</gadget>
<output>72_000</output>
<gadget id="calculator">630 / 72_000</gadget>
<output>7/800 = around 0.00875</output>
<gadget id="calculator">(7/800) * 20_000</gadget>
<output>175</output>
<result>A</result> | A | 175 | A and B began business with Rs.2000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A. | {
"A": "175",
"B": "288",
"C": "277",
"D": "877",
"E": "361"
} | multiply(divide(630, add(add(multiply(2000, 8), multiply(subtract(2000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(2000, 8), multiply(subtract(2000, 1000), subtract(const_12, 8)))) | add(n1,n3)|multiply(n0,n2)|multiply(n1,n2)|subtract(n0,n3)|subtract(const_12,n2)|multiply(#3,#4)|multiply(#0,#4)|add(#1,#5)|add(#2,#6)|add(#7,#8)|divide(n5,#9)|multiply(#7,#10)| | "( 2 * 8 + 1 * 4 ) : ( 4 * 8 + 5 * 4 ) 5 : 13 5 / 18 * 630 = 175 answer : a" | gain |
math_qa__zzAGgVu8usfJmbjV | A fair coin is tossed 9 times. What is the probability of getting more heads than tails in 9 tosses? Options.
A) 1 / 2 B) 63 / 128 C) 4 / 7 D) 61 / 256 E) 63 / 64 | <gadget id="calculator">binomial(9, 2)</gadget>
<output>36</output>
<gadget id="calculator">binomial(9, 3)</gadget>
<output>84</output>
<gadget id="calculator">36 + 84</gadget>
<output>120</output>
<gadget id="calculator">binomial(9, 4)</gadget>
<output>126</output>
<gadget id="calculator">120 + 126</gadget>
<output>246</output>
<gadget id="calculator">binomial(9, 9)</gadget>
<output>1</output>
<gadget id="calculator">246 + 1</gadget>
<output>247</output>
<gadget id="calculator">2 ** 9</gadget>
<output>512</output>
<gadget id="calculator">247 / 512</gadget>
<output>247/512 = around 0.482422</output>
<result>A</result> | A | 0.5 | A fair coin is tossed 9 times. What is the probability of getting more heads than tails in 9 tosses? | {
"A": "1 / 2",
"B": "63 / 128",
"C": "4 / 7",
"D": "61 / 256",
"E": "63 / 64"
} | divide(add(add(add(choose(9, const_2), choose(9, const_3)), choose(9, const_4)), choose(9, 9)), power(const_2, 9)) | choose(n0,const_2)|choose(n0,const_3)|choose(n0,const_4)|choose(n0,n0)|power(const_2,n0)|add(#0,#1)|add(#5,#2)|add(#6,#3)|divide(#7,#4)| | "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ." | probability |
math_qa__DWtxLg5xIThUAnrk | If 18 bindres bind 900 books in 10 days , How many binders will be required to bind 660 books in 12 days? Options:
A) 71
B) 12
C) 18
D) 11
E) 29 | <gadget id="calculator">660 * 10</gadget>
<output>6_600</output>
<gadget id="calculator">6_600 * 18</gadget>
<output>118_800</output>
<gadget id="calculator">900 * 12</gadget>
<output>10_800</output>
<gadget id="calculator">118_800 / 10_800</gadget>
<output>11</output>
<result>D</result> | D | 11 | If 18 bindres bind 900 books in 10 days , How many binders will be required to bind 660 books in 12 days? | {
"A": "71",
"B": "12",
"C": "18",
"D": "11",
"E": "29"
} | divide(multiply(multiply(660, 10), 18), multiply(900, 12)) | multiply(n2,n3)|multiply(n1,n4)|multiply(n0,#0)|divide(#2,#1) | explanation : let the required no of binders be x . less books , less binders ( direct proportion ) more days , less binders ( indirect proportion ) \ inline \ fn _ jvn \ left . \ begin { matrix } books \ : 900 : 600 \ \ days \ : \ : 12 : 10 \ end { matrix } \ right \ } : : 18 : x \ inline \ fn _ jvn \ therefore \ inline \ fn _ jvn ( 900 \ times 12 \ times x ) = ( 600 \ times 10 \ times 18 ) \ inline \ fn _ jvn \ leftrightarrow x = \ inline \ fn _ jvn \ frac { 600 \ times 10 \ times 18 } { 900 \ times 12 } = 11 answer : d | physics |
math_qa__2PW7Sqx6loY7VOVp | If a × b = 2a - 3b + ab, then 1 × 2 + 2 × 1 is equal to : Select the correct option:
A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">2 - 6</gadget>
<output>-4</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">(-4) + 2</gadget>
<output>-2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">3 * 1</gadget>
<output>3</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">(-2) + 3</gadget>
<output>1</output>
<result>A</result> | A | 1 | If a × b = 2a - 3b + ab, then 1 × 2 + 2 × 1 is equal to : | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | add(add(subtract(multiply(2, 1), multiply(3, 2)), multiply(1, 2)), add(subtract(multiply(2, 2), multiply(3, 1)), multiply(2, 1))) | multiply(n0,n2)|multiply(n0,n1)|multiply(n0,n0)|multiply(n1,n2)|subtract(#0,#1)|subtract(#2,#3)|add(#0,#4)|add(#0,#5)|add(#6,#7) | explanation : 1 ã — 2 + 2 ã — 1 = ( 2 ã — 1 - 3 ã — 2 + 1 ã — 2 ) + ( 2 ã — 2 - 3 ã — 1 + 2 ã — 1 ) = ( 2 - 6 + 2 + 4 - 3 + 2 ) = 1 . answer : a | general |
math_qa__EGS9ibn52Zr4QyZr | A train running at the speed of 60 km/hr crosses a pole in 4 seconds. Find the length of the train. Choose the correct choice from the following answers
A) 66.67 B) 882 C) 772 D) 252 E) 121 | <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) * 4</gadget>
<output>200/3 = around 66.666667</output>
<result>A</result> | A | 66.67 | A train running at the speed of 60 km/hr crosses a pole in 4 seconds. Find the length of the train. | {
"A": "66.67",
"B": "882",
"C": "772",
"D": "252",
"E": "121"
} | multiply(divide(multiply(60, const_1000), const_3600), 4) | 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 ) * 4 = 66.67 meter . answer : a" | physics |
math_qa__AraNDvR6XKd5E6mS | The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
Select the correct option:
A) 82.5 B) 52.9 C) 52.2 D) 52.5 E) 52.7 | <gadget id="calculator">30 * 40</gadget>
<output>1_200</output>
<gadget id="calculator">50 * 60</gadget>
<output>3_000</output>
<gadget id="calculator">1_200 + 3_000</gadget>
<output>4_200</output>
<gadget id="calculator">30 + 50</gadget>
<output>80</output>
<gadget id="calculator">4_200 / 80</gadget>
<output>105/2 = around 52.5</output>
<result>D</result> | D | 52.5 | The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? | {
"A": "82.5",
"B": "52.9",
"C": "52.2",
"D": "52.5",
"E": "52.7"
} | divide(add(multiply(30, 40), multiply(50, 60)), add(30, 50)) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)| | "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 1200 + 3000 = 4200 average marks of all the students = 4200 / 80 = 52.5 answer : d" | general |
math_qa__pGISUxkyCPAwIhe4 | 75 men working 8 hours per day dig 50 m deep. How many extra men should be put to dig to a depth of 70 m working 6 hours per day? Choose the correct choice from the following choices
A) 75 B) 45 C) 55 D) 65 E) 35 | <gadget id="calculator">75 * 8</gadget>
<output>600</output>
<gadget id="calculator">600 / 50</gadget>
<output>12</output>
<gadget id="calculator">12 * 70</gadget>
<output>840</output>
<gadget id="calculator">840 / 6</gadget>
<output>140</output>
<gadget id="calculator">140 - 75</gadget>
<output>65</output>
<result>D</result> | D | 65 | 75 men working 8 hours per day dig 50 m deep. How many extra men should be put to dig to a depth of 70 m working 6 hours per day? | {
"A": "75",
"B": "45",
"C": "55",
"D": "65",
"E": "35"
} | subtract(divide(multiply(divide(multiply(75, 8), 50), 70), 6), 75) | multiply(n0,n1)|divide(#0,n2)|multiply(n3,#1)|divide(#2,n4)|subtract(#3,n0) | ( 75 * 8 ) / 50 = ( x * 6 ) / 70 = > x = 140 140 â € “ 65 = 65 answer : d | physics |
math_qa__mrbuuIRKoe19cHOs | On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $20,000, in how many years, the total value of the investment plus interest will increase to $30,000? Choices:
A) 15
B) 16
C) 18
D) 20
E) 24 | <gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">30 / 5</gadget>
<output>6</output>
<gadget id="calculator">log(6)</gadget>
<output>log(6) = around 1.791759</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">4 ** (1/12)</gadget>
<output>2**(1/6) = around 1.122462</output>
<gadget id="calculator">log(2**(1/6))</gadget>
<output>log(2**(1/6)) = around 0.115525</output>
<gadget id="calculator">log(6) / log(2**(1/6))</gadget>
<output>log(6)/log(2**(1/6)) = around 15.509775</output>
<result>A</result> | A | 15 | On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $20,000, in how many years, the total value of the investment plus interest will increase to $30,000? | {
"A": "15",
"B": "16",
"C": "18",
"D": "20",
"E": "24"
} | divide(log(divide(multiply(const_3, const_10), add(const_4, const_1))), log(power(divide(multiply(const_2, const_10), add(const_4, const_1)), divide(const_1, 12)))) | add(const_1,const_4)|divide(const_1,n1)|multiply(const_10,const_3)|multiply(const_10,const_2)|divide(#2,#0)|divide(#3,#0)|log(#4)|power(#5,#1)|log(#7)|divide(#6,#8) | if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 5,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 5 , 000.00 took to double 10 , 000.00 . again , 10 , 000.00 took to double 20 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 20 , 000.00 takes the same ( 72 / x ) no of years to double 30 , 000.00 . 72 / x = 6 years . so altogather : 5,000 - 10,000 = 6 years 10,000 - 20,000 = 6 years 20,000 - 30,000 = 3 years answer a 15 years . | general |
math_qa__q32DQwYdsaTibs0s | A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 50 percent of what the collector had paid. The shop then sold the clock again at a profit of 80 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $100, for how much did the shop sell the clock the second time? Choose the correct choice.
A) $ 270
B) $ 250
C) $ 240
D) $ 220
E) $ 200 | <gadget id="calculator">100 + 80</gadget>
<output>180</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">180 * 60</gadget>
<output>10_800</output>
<gadget id="calculator">10_800 / 100</gadget>
<output>108</output>
<gadget id="calculator">100 * 108</gadget>
<output>10_800</output>
<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<gadget id="calculator">10_800 / 40</gadget>
<output>270</output>
<result>A</result> | A | 270 | A clock store sold a certain clock to a collector for 20 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 50 percent of what the collector had paid. The shop then sold the clock again at a profit of 80 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $100, for how much did the shop sell the clock the second time? | {
"A": "$ 270",
"B": "$ 250",
"C": "$ 240",
"D": "$ 220",
"E": "$ 200"
} | divide(multiply(100, divide(multiply(add(100, 80), divide(add(100, 20), const_2)), 100)), subtract(divide(add(100, 20), const_2), 20)) | add(n2,n3)|add(n0,n3)|divide(#1,const_2)|multiply(#0,#2)|subtract(#2,n0)|divide(#3,n3)|multiply(n3,#5)|divide(#6,#4) | original price = x sold to collector at 1.2 x re - buy price = 1.2 x * 0.5 = 0.6 x therefore , x - 0.6 x = 100 ; x = 250 second selling price = 1.8 * 0.6 * 250 = 270 answer : a | general |
math_qa__pp8oGBw3zCrC6orT | NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day. If in 25 days they completed 1/3 part of work .than how many more employees should NHAI hire to finish it in time working 10 hours a day? Choose the correct choice from the following
A) 22 B) 60 C) 28 D) 11 E) 218 | <gadget id="calculator">100 * 25</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 * 8</gadget>
<output>20_000</output>
<gadget id="calculator">2 * 20_000</gadget>
<output>40_000</output>
<gadget id="calculator">25 * 10</gadget>
<output>250</output>
<gadget id="calculator">40_000 / 250</gadget>
<output>160</output>
<gadget id="calculator">160 - 100</gadget>
<output>60</output>
<result>B</result> | B | 60 | NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day. If in 25 days they completed 1/3 part of work .than how many more employees should NHAI hire to finish it in time working 10 hours a day? | {
"A": "22",
"B": "60",
"C": "28",
"D": "11",
"E": "218"
} | subtract(divide(multiply(2, multiply(multiply(100, 25), 8)), multiply(25, 10)), 100) | multiply(n0,n4)|multiply(n4,n7)|multiply(n3,#0)|multiply(n1,#2)|divide(#3,#1)|subtract(#4,n0)| | "here 2 km is immaterial . the given problem can be written in a tabular form like below . we can apply chain rule now . total men required to complete the remaining work = 100 × 2525 × 810 × 2313100 × 2525 × 810 × 2313 = 160 so additional men required = 160 - 100 = 60 answer : b" | physics |
math_qa__Caytmt4xp007xzqK | Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680? Choose the correct choice from the following answers.
A) 1500 B) 2777 C) 2889 D) 27670 E) 2771 | <gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">12 / 5</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">(12/5) * 5</gadget>
<output>12</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) + 1</gadget>
<output>28/25 = around 1.12</output>
<gadget id="calculator">1_680 / (28/25)</gadget>
<output>1_500</output>
<result>A</result> | A | 1,500 | Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1680? | {
"A": "1500",
"B": "2777",
"C": "2889",
"D": "27670",
"E": "2771"
} | divide(1680, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 5), const_100), const_1)) | multiply(n1,n3)|add(n1,#0)|divide(#1,n3)|multiply(n0,#2)|divide(#3,const_100)|add(#4,const_1)|divide(n4,#5)| | "1680 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1500 . answer : a" | general |
math_qa__ZRj8UmaonbZqgLlH | What number has a 5:1 ratio to the number 13? Pick: A) 22 B) 50 C) 88 D) 65 E) 12 | <gadget id="calculator">13 * 5</gadget>
<output>65</output>
<result>D</result> | D | 65 | What number has a 5:1 ratio to the number 13? | {
"A": "22",
"B": "50",
"C": "88",
"D": "65",
"E": "12"
} | multiply(13, 5) | multiply(n0,n2)| | "5 : 1 = x : 13 x = 65 answer : d" | other |
math_qa__9b2Agd4F0U8dUyJB | Three cubes of metal whose edges are 5, 10 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube? Choose the correct choice from the following answers: A) 28 B) 77 C) 66 D) 16.5 E) 99 | <gadget id="calculator">5 ** 3</gadget>
<output>125</output>
<gadget id="calculator">10 ** 3</gadget>
<output>1_000</output>
<gadget id="calculator">125 + 1_000</gadget>
<output>1_125</output>
<gadget id="calculator">15 ** 3</gadget>
<output>3_375</output>
<gadget id="calculator">1_125 + 3_375</gadget>
<output>4_500</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">4_500 ** (1/3)</gadget>
<output>5*6**(2/3) = around 16.509636</output>
<result>D</result> | D | 16.5 | Three cubes of metal whose edges are 5, 10 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube? | {
"A": "28",
"B": "77",
"C": "66",
"D": "16.5",
"E": "99"
} | power(add(add(volume_cube(5), volume_cube(10)), volume_cube(15)), const_0_33) | volume_cube(n0)|volume_cube(n1)|volume_cube(n2)|add(#0,#1)|add(#3,#2)|power(#4,const_0_33)| | "53 + 103 + 153 = a 3 = > a = 16.5 answer : d" | physics |
math_qa__m0uSlDlsssp8L1lX | A train 490 m long, running with a speed of 63 km/hr will pass a tree in? Options
A) 15 sec B) 16 sec C) 28 sec D) 20 sec E) 25 sec | <gadget id="calculator">63 * 1_000</gadget>
<output>63_000</output>
<gadget id="calculator">490 / 63_000</gadget>
<output>7/900 = around 0.007778</output>
<gadget id="calculator">(7/900) * 3_600</gadget>
<output>28</output>
<result>C</result> | C | 28 | A train 490 m long, running with a speed of 63 km/hr will pass a tree in? | {
"A": "15 sec",
"B": "16 sec",
"C": "28 sec",
"D": "20 sec",
"E": "25 sec"
} | multiply(divide(490, multiply(63, const_1000)), const_3600) | multiply(n1,const_1000)|divide(n0,#0)|multiply(#1,const_3600)| | "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 490 * 2 / 35 = 28 sec answer : c" | physics |
math_qa__lTlEX1ufjEnSzMVb | George does 3/5th of a piece of work in 9 days. He then calls in Paul , and they finish the work in 4 days. How long would Paul take to do the work by himself?
Choose the correct choice from the following choices:
A) 30 B) 40 C) 50 D) 60 E) 70 | <gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">4 * (1/15)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">(2/5) - (4/15)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(2/15) / 4</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>A</result> | A | 30 | George does 3/5th of a piece of work in 9 days. He then calls in Paul , and they finish the work in 4 days. How long would Paul take to do the work by himself? | {
"A": "30",
"B": "40",
"C": "50",
"D": "60",
"E": "70"
} | inverse(divide(subtract(subtract(const_1, divide(3, 5)), multiply(4, divide(const_1, multiply(5, const_3)))), const_4)) | divide(n0,n1)|multiply(n1,const_3)|divide(const_1,#1)|subtract(const_1,#0)|multiply(n3,#2)|subtract(#3,#4)|divide(#5,const_4)|inverse(#6) | 100 % work will be done by george in 15 days ( 1 / 15 ) 9 + ( 1 / 15 + 1 / x ) 4 = 1 solving this eqn . we get x = 30 hence paul take to do the work in 30 days answer : a | physics |
math_qa__7WXy1f3d0kSdyLGo | A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water: Choose the correct option.
A) 2 B) 3 C) 4 D) 5 E) 6 | <gadget id="calculator">15 / 5</gadget>
<output>3</output>
<result>B</result> | B | 3 | A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water: | {
"A": "2",
"B": "3",
"C": "4",
"D": "5",
"E": "6"
} | divide(15, 5) | divide(n0,n1)| | "explanation : upstream speed = b - s downstream speed = b + s b - s = 15 / 5 = 3 km / h again b = 4 s therefore b - s = 3 = 3 s = > s = 1 and b = 4 km / h therefore b + s = 5 km / h therefore , time during downstream = 15 / 5 = 3 h answer : b ) 3 h" | physics |
math_qa__a85AbVhRbRlixUCA | If 15% of A is the same as 20% of B, then A : B is : Pick: A) 3 : 4 B) 4 : 3 C) 17 : 16 D) 16 : 17 E) none of these | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(1/5) / (3/20)</gadget>
<output>4/3 = around 1.333333</output>
<result>B</result> | B | 1.333333 | If 15% of A is the same as 20% of B, then A : B is : | {
"A": "3 : 4",
"B": "4 : 3",
"C": "17 : 16",
"D": "16 : 17",
"E": "none of these"
} | divide(divide(20, const_100), divide(15, const_100)) | divide(n1,const_100)|divide(n0,const_100)|divide(#0,#1)| | "expl : 15 % of a i = 20 % of b = 15 a / 100 = 20 b / 100 = 4 / 3 = 4 : 3 answer : b" | gain |
math_qa__ofOViwJr764xmU6P | Along a yard 255 metres long, 18 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees Options:
A) 18
B) 15
C) 10
D) 11
E) 12 | <gadget id="calculator">18 - 1</gadget>
<output>17</output>
<gadget id="calculator">255 / 17</gadget>
<output>15</output>
<result>B</result> | B | 15 | Along a yard 255 metres long, 18 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees | {
"A": "18",
"B": "15",
"C": "10",
"D": "11",
"E": "12"
} | divide(255, subtract(18, const_1)) | subtract(n1,const_1)|divide(n0,#0)| | "explanation : 18 trees have 17 gaps between them , required distance ( 281 / 17 ) = 15 option b" | physics |
math_qa__z8fum3VwqQZPTqGb | If the cost price is 92% of the selling price, then what is the profit percent? Options: A) 9 % B) 11 % C) 13 % D) 21 % E) 19 % | <gadget id="calculator">100 - 92</gadget>
<output>8</output>
<gadget id="calculator">8 / 92</gadget>
<output>2/23 = around 0.086957</output>
<gadget id="calculator">(2/23) * 100</gadget>
<output>200/23 = around 8.695652</output>
<result>A</result> | A | 9 | If the cost price is 92% of the selling price, then what is the profit percent? | {
"A": "9 %",
"B": "11 %",
"C": "13 %",
"D": "21 %",
"E": "19 %"
} | multiply(divide(subtract(const_100, 92), 92), const_100) | subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)| | "let s . p . = $ 100 c . p . = $ 92 profit = $ 8 profit % = 8 / 92 * 100 = 25 / 6 = 9 % approximately answer is a" | gain |
math_qa__ZOLXuYbsRImobaCG | How much time will a train of length 280 m moving at a speed of 72 kmph take to cross another train of length 360 m, moving at 36 kmph in the same direction? Choose the correct option:
A) 50
B) 99
C) 64
D) 76
E) 12 | <gadget id="calculator">280 + 360</gadget>
<output>640</output>
<gadget id="calculator">72 - 36</gadget>
<output>36</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">640 / 10</gadget>
<output>64</output>
<result>C</result> | C | 64 | How much time will a train of length 280 m moving at a speed of 72 kmph take to cross another train of length 360 m, moving at 36 kmph in the same direction? | {
"A": "50",
"B": "99",
"C": "64",
"D": "76",
"E": "12"
} | divide(add(280, 360), multiply(subtract(72, 36), const_0_2778)) | add(n0,n2)|subtract(n1,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | "the distance to be covered = sum of their lengths = 280 + 360 = 640 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 640 / 10 = 64 sec . answer : c" | physics |
math_qa__lM5JijvvNtATCqBR | Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 81 hours respectively. The ratio of their speeds is? Choose the correct choice from the following: A) 4 : 9 B) 9 : 4 C) 4 : 5 D) 4 : 1 E) 4 : 2 | <gadget id="calculator">81 ** (1/2)</gadget>
<output>9</output>
<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<gadget id="calculator">9 / 4</gadget>
<output>9/4 = around 2.25</output>
<result>B</result> | B | 2.25 | Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 81 hours respectively. The ratio of their speeds is? | {
"A": "4 : 9",
"B": "9 : 4",
"C": "4 : 5",
"D": "4 : 1",
"E": "4 : 2"
} | divide(sqrt(81), sqrt(16)) | sqrt(n1)|sqrt(n0)|divide(#0,#1)| | "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 81 : √ 16 = 9 : 4 answer : b" | physics |
math_qa__PzrvIA1gxXpepQ6k | On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2.2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? Choose the most appropriate option:
A) 2.04 % B) 6.12 % C) 8 % D) 8.25 % E) 9 % | <gadget id="calculator">2.2 * 4</gadget>
<output>8.8</output>
<result>E</result> | E | 9 | On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2.2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? | {
"A": "2.04 %",
"B": "6.12 %",
"C": "8 %",
"D": "8.25 %",
"E": "9 %"
} | multiply(2.2, const_4) | multiply(n0,const_4)| | "if the interest were compounded annually instead of quarterly then in one year the interest would be 2.2 * 4 = 8.8 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 8.8 % answer : e ." | gain |
math_qa__ikEjKx7CXaBkmUMv | A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 9:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
Choices.
A) 36 B) 35 C) 34 D) 38 E) 40 | <gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">8 + 9</gadget>
<output>17</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">5 + 6</gadget>
<output>11</output>
<gadget id="calculator">22 / 11</gadget>
<output>2</output>
<gadget id="calculator">17 * 2</gadget>
<output>34</output>
<result>C</result> | C | 34 | A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 9:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke? | {
"A": "36",
"B": "35",
"C": "34",
"D": "38",
"E": "40"
} | multiply(add(subtract(9, const_1), 9), divide(22, add(subtract(6, const_1), 6))) | subtract(n3,const_1)|subtract(n0,const_1)|add(n3,#0)|add(n0,#1)|divide(n2,#3)|multiply(#2,#4) | at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 9 strikes , there would be 8 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 12 ' o clock , the 9 strikes and 8 intervals will take 2 * ( 9 + 8 ) = 34 secs c | general |
math_qa__8UVilpPEUajH0ygc | Find the compound interest on $50000 in 2years at 4% per annum, the interest being compounded half-yearly? Choose the correct option.
A) $ 645.56
B) $ 4121.60
C) $ 954.26
D) $ 745.69
E) $ 1020.45 | <gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/25) / 2</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/50) + 1</gadget>
<output>51/50 = around 1.02</output>
<gadget id="calculator">(51/50) ** 4</gadget>
<output>6_765_201/6_250_000 = around 1.082432</output>
<gadget id="calculator">(6_765_201/6_250_000) * 50_000</gadget>
<output>6_765_201/125 = around 54_121.608</output>
<gadget id="calculator">(6_765_201/125) - 50_000</gadget>
<output>515_201/125 = around 4_121.608</output>
<result>B</result> | B | 4,121.6 | Find the compound interest on $50000 in 2years at 4% per annum, the interest being compounded half-yearly? | {
"A": "$ 645.56",
"B": "$ 4121.60",
"C": "$ 954.26",
"D": "$ 745.69",
"E": "$ 1020.45"
} | subtract(multiply(power(add(divide(divide(4, const_100), 2), const_1), 4), 50000), 50000) | divide(n2,const_100)|divide(#0,n1)|add(#1,const_1)|power(#2,n2)|multiply(n0,#3)|subtract(#4,n0) | principle = $ 50000 rate = 2 % half yearly = 4 half years amount = 50000 * ( 1 + 2 / 100 ) ^ 4 = 50000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 54121.60 c . i . = 54121.60 - 50000 = $ 4121.60 answer is b | gain |
math_qa__5IYPxvsHZCnSeZ9s | I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last? Choices:
A) 4 hours
B) 2 hours
C) 3 hours
D) 2 hours 24 minutes
E) none | <gadget id="calculator">60 * 5</gadget>
<output>300</output>
<gadget id="calculator">300 - 240</gadget>
<output>60</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">60 / 20</gadget>
<output>3</output>
<result>C</result> | C | 3 | I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last? | {
"A": "4 hours",
"B": "2 hours",
"C": "3 hours",
"D": "2 hours 24 minutes",
"E": "none"
} | divide(subtract(multiply(60, 5), 240), subtract(60, 40)) | multiply(n1,n3)|subtract(n1,n0)|subtract(#0,n2)|divide(#2,#1)| | "explanatory answer the total time of journey = 5 hours . let ' x ' hours be the time that i traveled at 40 kmph therefore , 5 - x hours would be time that i traveled at 60 kmph . hence , i would have covered x * 40 + ( 5 - x ) 60 kms in the 5 hours = 240 kms . solving , for x in the equation 40 x + ( 5 - x ) * 60 = 240 , we get 40 x + 300 - 60 x = 240 = > 20 x = 60 or x = 3 hours . answer c" | physics |
math_qa__6kUbckI64XmD6BgQ | the set s has 36 different subsets each of which contains exactly two elements . how many subsets of s could contain exactly 7 elements each ? Choices
A) 81 B) 63 C) 54 D) 36 E) 90 | <gadget id="calculator">36 * 2</gadget>
<output>72</output>
<gadget id="calculator">4 * 72</gadget>
<output>288</output>
<gadget id="calculator">288 + 1</gadget>
<output>289</output>
<gadget id="calculator">289 ** (1/2)</gadget>
<output>17</output>
<gadget id="calculator">17 + 1</gadget>
<output>18</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">factorial(9)</gadget>
<output>362_880</output>
<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">362_880 / 5_040</gadget>
<output>72</output>
<gadget id="calculator">72 / 2</gadget>
<output>36</output>
<result>D</result> | D | 36 | the set s has 36 different subsets each of which contains exactly two elements . how many subsets of s could contain exactly 7 elements each ? | {
"A": "81",
"B": "63",
"C": "54",
"D": "36",
"E": "90"
} | divide(divide(factorial(divide(add(sqrt(add(multiply(const_4, multiply(36, const_2)), const_1)), const_1), const_2)), factorial(7)), const_2) | factorial(n1)|multiply(n0,const_2)|multiply(#1,const_4)|add(#2,const_1)|sqrt(#3)|add(#4,const_1)|divide(#5,const_2)|factorial(#6)|divide(#7,#0)|divide(#8,const_2) | nc 2 = 36 = > n * ( n - 1 ) / 2 = 36 by middle term factor and n can not be negative = > n = 9 nc 7 = 9 c 7 = 9 ! / 7 ! * ( 9 - 7 ) ! = 9 * 8 * 7 ! / 7 ! * 2 = 36 so , answer is d . | general |
math_qa__5xHjLyvXJ43bk2jT | A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x? Choose the correct choice: A) 17.5 litres B) 16.67 litres C) 17.67 litres D) 16.5 litres E) 16 litres | <gadget id="calculator">25 / 36</gadget>
<output>25/36 = around 0.694444</output>
<gadget id="calculator">(25/36) ** (1/2)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">1 - (5/6)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">100 * (1/6)</gadget>
<output>50/3 = around 16.666667</output>
<result>B</result> | B | 16.67 | A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 25%. What is the value of x? | {
"A": "17.5 litres",
"B": "16.67 litres",
"C": "17.67 litres",
"D": "16.5 litres",
"E": "16 litres"
} | multiply(100, subtract(const_1, sqrt(divide(25, 36)))) | divide(n2,n1)|sqrt(#0)|subtract(const_1,#1)|multiply(n0,#2)| | "in 100 l mixture we have 36 l milk and 64 l water . hence m and w are in the ratio of 9 : 16 . x l of solution has been removed . hence we have 36 - 9 / 25 x of milk and 64 - 16 / 25 x of water . for calculation simplicity multiply and divide 9 / 25 x by 4 we get 36 / 100 x since this procedure is repeated 2 times . this was my equation 25 = 36 * ( 36 - 36 / 100 x ) ^ 2 ) / ( 36 ) ^ 2 by solving it . we get x = 100 / 6 or 50 / 3 or 16.67 answer : b" | general |
math_qa__6dI46P2U9fKKlQNe | x+(1/x) = 4 find x^2 + (1/x^2)
Select: A) 2.25 B) 3.25 C) 4.25 D) 14 E) 6.25 | <gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 - 2</gadget>
<output>14</output>
<result>D</result> | D | 14 | x+(1/x) = 4 find x^2 + (1/x^2) | {
"A": "2.25",
"B": "3.25",
"C": "4.25",
"D": "14",
"E": "6.25"
} | subtract(power(4, 2), 2) | power(n1,n2)|subtract(#0,n2)| | "squaring on both sides ( x + 1 / x ) ^ 2 = 4 ^ 2 x ^ 2 + 1 / x ^ 2 = 16 - 2 x ^ 2 + 1 / x ^ 2 = 14 answer : d" | general |
math_qa__8wNDnNPlGY37yiTp | A present value of a machine is $1200. Its value depletion rate is 10% per annum then find the machine value after 2 years? Choose one:
A) $ 972 B) $ 810 C) $ 915 D) $ 715 E) $ 795 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) ** 2</gadget>
<output>81/100 = around 0.81</output>
<gadget id="calculator">1_200 * (81/100)</gadget>
<output>972</output>
<result>A</result> | A | 972 | A present value of a machine is $1200. Its value depletion rate is 10% per annum then find the machine value after 2 years? | {
"A": "$ 972",
"B": "$ 810",
"C": "$ 915",
"D": "$ 715",
"E": "$ 795"
} | multiply(1200, power(subtract(const_1, divide(10, const_100)), 2)) | divide(n1,const_100)|subtract(const_1,#0)|power(#1,n2)|multiply(n0,#2)| | "p = $ 1200 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 1200 * 9 / 10 * 9 / 10 = $ 972 answer is a" | gain |
math_qa__xJzUFxFhJ7NFPxoQ | The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 16 cm each. The radius of the sphere is
Choose the correct choice.
A) 3 cm B) 4 cm C) 6 cm D) 8 cm E) none | <gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">16 * 8</gadget>
<output>128</output>
<gadget id="calculator">pi * 128</gadget>
<output>128*pi = around 402.12386</output>
<gadget id="calculator">(128*pi) * 2</gadget>
<output>256*pi = around 804.247719</output>
<gadget id="calculator">pi * 4</gadget>
<output>4*pi = around 12.566371</output>
<gadget id="calculator">(256*pi) / (4*pi)</gadget>
<output>64</output>
<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>
<result>D</result> | D | 8 | The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 16 cm each. The radius of the sphere is | {
"A": "3 cm",
"B": "4 cm",
"C": "6 cm",
"D": "8 cm",
"E": "none"
} | sqrt(divide(multiply(multiply(const_pi, multiply(16, divide(16, const_2))), const_2), multiply(const_pi, const_4))) | divide(n0,const_2)|multiply(const_4,const_pi)|multiply(n0,#0)|multiply(#2,const_pi)|multiply(#3,const_2)|divide(#4,#1)|sqrt(#5)| | "solution 4 î r 2 = 2 î 8 x 16 â ‡ ’ r 2 = ( 8 x 16 / 2 ) â ‡ ’ 64 â ‡ ’ r = 8 cm . answer d" | geometry |
math_qa__aVhalCx8eaPPVMK4 | For what value of k will the two equations 2x + 4 = 4(x - 2) and -x + k = 2x - 1 have the same solution? Select.
A) 15 B) 16 C) 18 D) 19 E) 17 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">10 + 7</gadget>
<output>17</output>
<result>E</result> | E | 17 | For what value of k will the two equations 2x + 4 = 4(x - 2) and -x + k = 2x - 1 have the same solution? | {
"A": "15",
"B": "16",
"C": "18",
"D": "19",
"E": "17"
} | add(const_10, add(4, const_3)) | add(n1,const_3)|add(#0,const_10) | solve the first equation 2 x + 4 = 4 ( x - 2 ) to obtain . x = 6 substitute x by 6 ( same solution ) in the second equation and solve for k . - 6 + k = 2 ( 6 ) - 1 solve for k . k = 17 correct answer e | general |
math_qa__Pbk0MzK3yBzQWijL | The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 7967 for a computer table, then what was the cost price of the computer table? Select the correct option: A) 7297 B) 6425 C) 2871 D) 6725 E) 2981 | <gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 + (6/25)</gadget>
<output>31/25 = around 1.24</output>
<gadget id="calculator">7_967 / (31/25)</gadget>
<output>6_425</output>
<result>B</result> | B | 6,425 | The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 7967 for a computer table, then what was the cost price of the computer table? | {
"A": "7297",
"B": "6425",
"C": "2871",
"D": "6725",
"E": "2981"
} | divide(7967, add(const_1, divide(24, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | "explanation : cp = sp * ( 100 / ( 100 + profit % ) ) = 7967 ( 100 / 124 ) = rs . 6425 . answer : b" | gain |
math_qa__pvj3LXhPMqYhBpK8 | A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is? Choose one: A) 16 B) 18 C) 17 D) 12 E) 12 | <gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 * 20</gadget>
<output>2_200</output>
<gadget id="calculator">2_200 / 100</gadget>
<output>22</output>
<gadget id="calculator">110 - 22</gadget>
<output>88</output>
<gadget id="calculator">100 - 88</gadget>
<output>12</output>
<result>D</result> | D | 12 | A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is? | {
"A": "16",
"B": "18",
"C": "17",
"D": "12",
"E": "12"
} | subtract(const_100, subtract(add(const_100, 10), divide(multiply(add(const_100, 10), 20), const_100))) | add(n0,const_100)|multiply(n1,#0)|divide(#1,const_100)|subtract(#0,#2)|subtract(const_100,#3)| | "suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 80 . s . p . of each item = rs . 1.10 total sale = 1.10 * 80 = rs . 88 hence , loss % = 12 / 100 * 100 = 12 % answer : d" | gain |
math_qa__vWhUzm73iJtQgMUC | A boat having a length 4 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is: Select the correct option
A) 12 kg
B) 60 kg
C) 72 kg
D) 80 kg
E) none of these | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">8 * (1/100)</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) * 1_000</gadget>
<output>80</output>
<result>D</result> | D | 80 | A boat having a length 4 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is: | {
"A": "12 kg",
"B": "60 kg",
"C": "72 kg",
"D": "80 kg",
"E": "none of these"
} | multiply(multiply(multiply(4, 2), divide(1, const_100)), const_1000) | divide(n2,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(#2,const_1000)| | "explanation : volume of water displaced = ( 4 x 2 x 0.01 ) m 3 = 0.08 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.08 x 1000 ) kg = 80 kg . answer : d" | physics |
math_qa__GsNVR25aANNiLstN | for an international mathematics olympiad , country d will send 6 delegates in total — two will be supervisors and 4 will be contestants . there are 210 ways in which the 6 delegates can be chosen and there are 7 candidates competing for the 4 contestants ’ places available . how many candidates are competing for the two supervisors ’ slots available ?
Choose the correct option.
A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">210 / 6</gadget>
<output>35</output>
<gadget id="calculator">7 / 4</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">35 + (7/4)</gadget>
<output>147/4 = around 36.75</output>
<gadget id="calculator">(147/4) / 6</gadget>
<output>49/8 = around 6.125</output>
<gadget id="calculator">(49/8) - 2</gadget>
<output>33/8 = around 4.125</output>
<result>D</result> | D | 4 | for an international mathematics olympiad , country d will send 6 delegates in total — two will be supervisors and 4 will be contestants . there are 210 ways in which the 6 delegates can be chosen and there are 7 candidates competing for the 4 contestants ’ places available . how many candidates are competing for the two supervisors ’ slots available ? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | subtract(divide(add(divide(210, 6), divide(7, 4)), 6), const_2) | divide(n2,n0)|divide(n4,n1)|add(#0,#1)|divide(#2,n0)|subtract(#3,const_2) | option a wrong as 2 supervisor need to be selected . going by statement : 4 contestant chosen from 7 - - 7 c 4 = = 35 and total ways = 210 consider 2 supervisor will be chosen from : x people . so as per question : 35 * x = 210 x = 6 so by using options , option a already decided wrong . option b 2 c 2 will be 1 not 6 . option c 3 c 2 will be 3 not 6 option d 4 c 2 will be 6 correct answer option e 5 c 2 will be 10 not 6 . ans : d | general |
math_qa__UR3ugaAXOcdEUBAT | The cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 700 square meters, what is the depth of the channel (in meters)? Select the correct option
A) 50 B) 60 C) 70 D) 80 E) 90 | <gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">700 / 10</gadget>
<output>70</output>
<result>C</result> | C | 70 | The cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 700 square meters, what is the depth of the channel (in meters)? | {
"A": "50",
"B": "60",
"C": "70",
"D": "80",
"E": "90"
} | divide(700, divide(add(12, 8), const_2)) | add(n0,n1)|divide(#0,const_2)|divide(n2,#1) | 1 / 2 * d * ( 12 + 8 ) = 700 d = 70 the answer is c . | physics |
math_qa__3vA59hxGnOaU40uS | Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 292 runs? Choose the correct choice from the following answers
A) 6 B) 6.5 C) 7.25 D) 7.5 E) 8 | <gadget id="calculator">3.2 * 10</gadget>
<output>32</output>
<gadget id="calculator">292 - 32</gadget>
<output>260</output>
<gadget id="calculator">260 / 40</gadget>
<output>13/2 = around 6.5</output>
<result>B</result> | B | 6.5 | Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 292 runs? | {
"A": "6",
"B": "6.5",
"C": "7.25",
"D": "7.5",
"E": "8"
} | divide(subtract(292, multiply(3.2, 10)), 40) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | "required run rate = 262 - ( 3.2 x 10 ) = 250 = 6.5 40 40 b" | gain |
math_qa__rUR2FDiGUcw4JSsE | Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is: Choose the correct choice from the following answers:
A) 17523
B) 2788
C) 1750
D) 2787
E) 29899 | <gadget id="calculator">4_000 * 10</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 / 100</gadget>
<output>400</output>
<gadget id="calculator">4_000 + 400</gadget>
<output>4_400</output>
<gadget id="calculator">4_400 * 10</gadget>
<output>44_000</output>
<gadget id="calculator">44_000 / 100</gadget>
<output>440</output>
<gadget id="calculator">400 + 440</gadget>
<output>840</output>
<gadget id="calculator">840 / 2</gadget>
<output>420</output>
<gadget id="calculator">420 / 3</gadget>
<output>140</output>
<gadget id="calculator">140 * 100</gadget>
<output>14_000</output>
<gadget id="calculator">14_000 / 8</gadget>
<output>1_750</output>
<result>C</result> | C | 1,750 | Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is: | {
"A": "17523",
"B": "2788",
"C": "1750",
"D": "2787",
"E": "29899"
} | divide(multiply(divide(divide(add(divide(multiply(4000, 10), const_100), divide(multiply(add(4000, divide(multiply(4000, 10), const_100)), 10), const_100)), 2), 3), const_100), 8) | multiply(n2,n4)|divide(#0,const_100)|add(n2,#1)|multiply(n4,#2)|divide(#3,const_100)|add(#1,#4)|divide(#5,n3)|divide(#6,n0)|multiply(#7,const_100)|divide(#8,n1)| | "explanation : c . i . = rs . [ 4000 * ( 1 + 10 / 100 ) ^ 2 - 4000 ] = rs . 840 sum = rs . ( 420 * 100 ) / 3 * 8 = rs . 1750 \ answer : c ) rs , 1750" | gain |
math_qa__xs4rGUrqnnHrmH51 | 3 numbers are such that the second is as much lesser than thr third as the first is lesser than the second . if the product of the two smaller numbers is 85 and product of two larger number is 115 then find the middle number Select the correct option
A) 8 B) 9 C) 10 D) 12 E) 15 | <gadget id="calculator">115 + 85</gadget>
<output>200</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">200 / 20</gadget>
<output>10</output>
<result>C</result> | C | 10 | 3 numbers are such that the second is as much lesser than thr third as the first is lesser than the second . if the product of the two smaller numbers is 85 and product of two larger number is 115 then find the middle number | {
"A": "8",
"B": "9",
"C": "10",
"D": "12",
"E": "15"
} | divide(add(115, 85), multiply(const_2, const_10)) | add(n1,n2)|multiply(const_10,const_2)|divide(#0,#1) | explanation : its a bit funny sum . if you see the first sentence actually it saying that the numbers are in a . p . now as the first two numbers product is 85 so if you take factor 85 you get 5 and 17 . . now as per option 17 can not be the middle number so from intuition and seeing the option only 10 could be the middle number where 8.5 is the first number and 11.5 is the last answer : c | general |
math_qa__7YeFfiwMaoJxdMm1 | After decreasing 20% in the price of an article costs Rs.200. Find the actual cost of an article? Choose the correct choice from the following answers.
A) 280 B) 250 C) 260 D) 270 E) 300 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">200 / (4/5)</gadget>
<output>250</output>
<result>B</result> | B | 250 | After decreasing 20% in the price of an article costs Rs.200. Find the actual cost of an article? | {
"A": "280",
"B": "250",
"C": "260",
"D": "270",
"E": "300"
} | divide(200, subtract(const_1, divide(20, const_100))) | divide(n0,const_100)|subtract(const_1,#0)|divide(n1,#1)| | "cp * ( 80 / 100 ) = 200 cp = 2.5 * 100 = > cp = 250 answer : b" | gain |
math_qa__G0d71UeUGj8RkJEg | The sale price sarees listed for Rs.480 after successive discount is 15% and 25% is? Choose the correct choice: A) 298 B) 237 C) 306 D) 876 E) 291 | <gadget id="calculator">480 * 15</gadget>
<output>7_200</output>
<gadget id="calculator">7_200 / 100</gadget>
<output>72</output>
<gadget id="calculator">480 - 72</gadget>
<output>408</output>
<gadget id="calculator">408 * 25</gadget>
<output>10_200</output>
<gadget id="calculator">10_200 / 100</gadget>
<output>102</output>
<gadget id="calculator">408 - 102</gadget>
<output>306</output>
<result>C</result> | C | 306 | The sale price sarees listed for Rs.480 after successive discount is 15% and 25% is? | {
"A": "298",
"B": "237",
"C": "306",
"D": "876",
"E": "291"
} | subtract(subtract(480, divide(multiply(480, 15), const_100)), divide(multiply(subtract(480, divide(multiply(480, 15), const_100)), 25), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | "480 * ( 85 / 100 ) * ( 75 / 100 ) = 306 answer : c" | gain |
math_qa__yLuVHTCyoxXd36BG | P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day? Choose one:
A) rs . 40 B) rs . 70 C) rs . 90 D) rs . 100 E) rs . 120 | <gadget id="calculator">600 / 5</gadget>
<output>120</output>
<gadget id="calculator">910 / 7</gadget>
<output>130</output>
<gadget id="calculator">120 + 130</gadget>
<output>250</output>
<gadget id="calculator">1_620 / 9</gadget>
<output>180</output>
<gadget id="calculator">250 - 180</gadget>
<output>70</output>
<result>B</result> | B | 70 | P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day? | {
"A": "rs . 40",
"B": "rs . 70",
"C": "rs . 90",
"D": "rs . 100",
"E": "rs . 120"
} | subtract(add(divide(600, 5), divide(910, 7)), divide(1620, 9)) | divide(n2,n3)|divide(n5,n4)|divide(n0,n1)|add(#0,#1)|subtract(#3,#2)| | "explanation : amount earned by p , q and r in 1 day = 1620 / 9 = 180 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 180 = 70 = > amount earned by r in 1 day = 70 answer : option b" | physics |
math_qa__om07RgTap5iLXzP3 | Two motor cycles A & B are started from one point at 4 Kmph & 6 Kmph; After 45 min B starts returning, at what time they will meet ? Choose one.
A) 54 mins
B) 55 mins
C) 56 mins
D) 57 mins
E) 58 mins | <gadget id="calculator">45 / 60</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">6 * (3/4)</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">4 * (3/4)</gadget>
<output>3</output>
<gadget id="calculator">(9/2) - 3</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">(3/2) / 10</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 60</gadget>
<output>9</output>
<gadget id="calculator">45 + 9</gadget>
<output>54</output>
<result>A</result> | A | 54 | Two motor cycles A & B are started from one point at 4 Kmph & 6 Kmph; After 45 min B starts returning, at what time they will meet ? | {
"A": "54 mins",
"B": "55 mins",
"C": "56 mins",
"D": "57 mins",
"E": "58 mins"
} | add(45, multiply(divide(subtract(multiply(6, divide(45, const_60)), multiply(4, divide(45, const_60))), add(4, 6)), const_60)) | add(n0,n1)|divide(n2,const_60)|multiply(n1,#1)|multiply(n0,#1)|subtract(#2,#3)|divide(#4,#0)|multiply(#5,const_60)|add(n2,#6) | distance covered by a in 45 mins = 3 kms . distance covered by b in 45 mins = 4.5 kms . distance between and b after 45 mins = 1.5 kms . relative speed when b is returning = 4 + 6 = 10 kmph distance between a and b is covered in 1.5 / 10 = 0.15 hrs = 9 mins so they will meet again after 54 mins from starting time . answer : a | physics |
math_qa__Mib4rTx2Bw4ZXnA6 | If 20% of a number = 1000, then 120% of that number will be? Choose the most appropriate option: A) 20 B) 120 C) 360 D) 6000 E) 820 | <gadget id="calculator">120 * 1_000</gadget>
<output>120_000</output>
<gadget id="calculator">120_000 / 20</gadget>
<output>6_000</output>
<result>D</result> | D | 6,000 | If 20% of a number = 1000, then 120% of that number will be? | {
"A": "20",
"B": "120",
"C": "360",
"D": "6000",
"E": "820"
} | divide(multiply(120, 1000), 20) | multiply(n1,n2)|divide(#0,n0)| | "let the number x . then , 20 % of x = 1000 x = ( 1000 * 100 ) / 20 = 5000 120 % of x = ( 120 / 100 * 5000 ) = 6000 . answer : d" | gain |
math_qa__LMLo8PkTmQdYUK6U | The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15, the no.of candidateswho passed the examination is? Pick one
A) 80 B) 90 C) 100 D) 120 E) 140 | <gadget id="calculator">120 * 35</gadget>
<output>4_200</output>
<gadget id="calculator">120 * 15</gadget>
<output>1_800</output>
<gadget id="calculator">4_200 - 1_800</gadget>
<output>2_400</output>
<gadget id="calculator">39 - 15</gadget>
<output>24</output>
<gadget id="calculator">2_400 / 24</gadget>
<output>100</output>
<result>C</result> | C | 100 | The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15, the no.of candidateswho passed the examination is? | {
"A": "80",
"B": "90",
"C": "100",
"D": "120",
"E": "140"
} | divide(subtract(multiply(120, 35), multiply(120, 15)), subtract(39, 15)) | multiply(n0,n1)|multiply(n0,n4)|subtract(n2,n4)|subtract(#0,#1)|divide(#3,#2)| | "let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 ⇒ 24 y = 4200 - 1800 ∴ y = 2400 / 24 = 100 c" | general |
math_qa__YdLCHFC4ldlUSxfc | A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.32, find the sum of money? Choose the correct choice:
A) 288
B) 262
C) 72
D) 205
E) 164 | <gadget id="calculator">32 / 40</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">100 + 65</gadget>
<output>165</output>
<gadget id="calculator">165 + 40</gadget>
<output>205</output>
<gadget id="calculator">(4/5) * 205</gadget>
<output>164</output>
<result>E</result> | E | 164 | A certain sum of money is divided among A, B and C so that for each Rs. A has, B has 65 paisa and C 40 paisa. If C's share is Rs.32, find the sum of money? | {
"A": "288",
"B": "262",
"C": "72",
"D": "205",
"E": "164"
} | multiply(divide(32, 40), add(add(const_100, 65), 40)) | add(n0,const_100)|divide(n2,n1)|add(n1,#0)|multiply(#2,#1)| | "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 32 41 - - - - ? = > rs . 164 answer : e" | general |
math_qa__GtpUJJUXoGwkS0K4 | On the first of the year, James invested x dollars at Proudstar bank in an account that yields 1.5% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? Choose the correct choice from the following
A) 2.04 %
B) 6.12 %
C) 8 %
D) 8.25 %
E) 10 % | <gadget id="calculator">1.5 * 4</gadget>
<output>6</output>
<result>B</result> | B | 6.12 | On the first of the year, James invested x dollars at Proudstar bank in an account that yields 1.5% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year? | {
"A": "2.04 %",
"B": "6.12 %",
"C": "8 %",
"D": "8.25 %",
"E": "10 %"
} | multiply(1.5, const_4) | multiply(n0,const_4)| | "if the interest were compounded annually instead of quarterly then in one year the interest would be 1.5 * 4 = 6 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 6 % . answer : b ." | gain |
math_qa__k8mMcSeZiBFziaAw | a1, a5, a13 (terms of AP) are in GP and a6 + a15 =63. Find a23
Choose the correct choice from the following:
A) 181 / 3 B) 182 / 3 C) 183 / 3 D) 184 / 3 E) 182 / 5 | <gadget id="calculator">13 - 5</gadget>
<output>8</output>
<gadget id="calculator">2 * 8</gadget>
<output>16</output>
<gadget id="calculator">6 + 15</gadget>
<output>21</output>
<gadget id="calculator">21 - 2</gadget>
<output>19</output>
<gadget id="calculator">16 + 19</gadget>
<output>35</output>
<gadget id="calculator">63 / 35</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">(9/5) * 8</gadget>
<output>72/5 = around 14.4</output>
<gadget id="calculator">23 - 1</gadget>
<output>22</output>
<gadget id="calculator">22 * (9/5)</gadget>
<output>198/5 = around 39.6</output>
<gadget id="calculator">(72/5) + (198/5)</gadget>
<output>54</output>
<gadget id="calculator">54 + 4</gadget>
<output>58</output>
<result>B</result> | B | 60.666667 | a1, a5, a13 (terms of AP) are in GP and a6 + a15 =63. Find a23 | {
"A": "181 / 3",
"B": "182 / 3",
"C": "183 / 3",
"D": "184 / 3",
"E": "182 / 5"
} | add(add(multiply(divide(63, add(multiply(const_2, subtract(13, 5)), subtract(add(6, 15), const_2))), subtract(13, 5)), multiply(subtract(23, const_1), divide(63, add(multiply(const_2, subtract(13, 5)), subtract(add(6, 15), const_2))))), const_4) | add(n3,n4)|subtract(n2,n1)|subtract(n6,const_1)|multiply(#1,const_2)|subtract(#0,const_2)|add(#3,#4)|divide(n5,#5)|multiply(#6,#1)|multiply(#6,#2)|add(#7,#8)|add(#9,const_4) | a 1 a 5 = a 1 + 4 d a 13 = a 1 + 12 d now a 5 / a 1 = a 13 / a 5 - - - - > > a 1 = 4 d . . . . . . . . ( 1 ) given a 6 + a 15 = 63 - - - - > a 1 + 5 d + a 1 + 14 d = 63 - - - - > 2 a 1 + 19 d = 63 - - - - > 8 d + 19 d = 63 from ( 1 ) - - - - > d = 63 / 27 = 7 / 3 so a = 4 d = 4 * 7 / 3 = 28 / 3 from ( 1 ) a 23 = a 1 + 22 d = 28 / 3 + 22 * 7 / 3 = 182 / 3 answer : b | general |
math_qa__0ySiuYSJ917tq5Gh | If 3/p=4 & 3/q=18 then p-q=? Choose the correct choice:
A) 5 / 24 B) 7 / 12 C) 7 / 24 D) 8 / 24 E) 9 / 24 | <gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">3 / 18</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(3/4) - (1/6)</gadget>
<output>7/12 = around 0.583333</output>
<result>B</result> | B | 0.583333 | If 3/p=4 & 3/q=18 then p-q=? | {
"A": "5 / 24",
"B": "7 / 12",
"C": "7 / 24",
"D": "8 / 24",
"E": "9 / 24"
} | subtract(divide(3, 4), divide(3, 18)) | divide(n0,n1)|divide(n0,n3)|subtract(#0,#1)| | "p = 3 / 4 , q = 3 / 18 = > q = 1 / 6 therefore p - q = ( 3 / 4 ) - ( 1 / 6 ) = 7 / 12 answer : b" | general |
math_qa__Zt1wR8eTLz14l5rB | The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 2700 sq m, then what is the breadth of the rectangular plot? Choose the most appropriate option:
A) 11 B) 17 C) 18 D) 101 E) 30 | <gadget id="calculator">2_700 / 3</gadget>
<output>900</output>
<gadget id="calculator">900 ** (1/2)</gadget>
<output>30</output>
<result>E</result> | E | 30 | The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 2700 sq m, then what is the breadth of the rectangular plot? | {
"A": "11",
"B": "17",
"C": "18",
"D": "101",
"E": "30"
} | sqrt(divide(2700, const_3)) | divide(n0,const_3)|sqrt(#0)| | "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 2700 3 b 2 = 2700 b 2 = 900 = 30 ( b > 0 ) b = 30 m . answer : e" | geometry |
math_qa__rR7s448EP0I7kXyQ | Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h
Choose the correct answer:
A) 334
B) 160
C) 387
D) 278
E) 112 | <gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<gadget id="calculator">4 * 120</gadget>
<output>480</output>
<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>
<gadget id="calculator">480 / 3</gadget>
<output>160</output>
<result>B</result> | B | 160 | Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h | {
"A": "334",
"B": "160",
"C": "387",
"D": "278",
"E": "112"
} | divide(multiply(sqrt(16), 120), sqrt(9)) | sqrt(n0)|sqrt(n1)|multiply(n2,#0)|divide(#2,#1) | answer : b ) 160 km / h | physics |
math_qa__RoPHpeQNrRteXwQ1 | A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 12 days, how long will a woman take to complete the work?
Options.
A) 12 days B) 10 days C) 9 days D) 8 days E) 11 days | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/6) + (1/12)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/3) - (1/4)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>A</result> | A | 12 | A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 12 days, how long will a woman take to complete the work? | {
"A": "12 days",
"B": "10 days",
"C": "9 days",
"D": "8 days",
"E": "11 days"
} | inverse(subtract(inverse(3), add(inverse(6), inverse(12)))) | inverse(n0)|inverse(n1)|inverse(n2)|add(#1,#2)|subtract(#0,#3)|inverse(#4)| | "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 1 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 12 = 1 / 4 therefore , 1 woman ’ s 1 day ’ s work = 1 / 3 – 1 / 4 = 1 / 12 therefore , the woman alone can finish the work in 12 days . answer : option a" | physics |
math_qa__O4ac40qBTTyQNcS7 | The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $400 per sq. metre.
Choose the correct choice:
A) $ 8250 B) $ 8350 C) $ 8650 D) $ 8450 E) $ 8500 | <gadget id="calculator">5.5 * 3.75</gadget>
<output>20.625</output>
<gadget id="calculator">400 * 20.625</gadget>
<output>8_250</output>
<result>A</result> | A | 8,250 | The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $400 per sq. metre. | {
"A": "$ 8250",
"B": "$ 8350",
"C": "$ 8650",
"D": "$ 8450",
"E": "$ 8500"
} | multiply(400, multiply(5.5, 3.75)) | multiply(n0,n1)|multiply(n2,#0)| | "area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 400 hence , total cost = 5.5 × 3.75 × 400 = $ 8250 a" | physics |
math_qa__1oseAQGmQ4e0xSCA | The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 80 minutes after it was poured was how many degrees Fahrenheit? Choose the correct choice:
A) 45 B) 56 C) 60.4 D) 85 E) 90 | <gadget id="calculator">60 / 10</gadget>
<output>6</output>
<gadget id="calculator">1 - 2</gadget>
<output>-1</output>
<gadget id="calculator">6 * (-1)</gadget>
<output>-6</output>
<gadget id="calculator">2 ** (-6)</gadget>
<output>1/64 = around 0.015625</output>
<gadget id="calculator">(1/64) * 120</gadget>
<output>15/8 = around 1.875</output>
<gadget id="calculator">(15/8) + 60</gadget>
<output>495/8 = around 61.875</output>
<result>C</result> | C | 60.4 | The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 80 minutes after it was poured was how many degrees Fahrenheit? | {
"A": "45",
"B": "56",
"C": "60.4",
"D": "85",
"E": "90"
} | add(multiply(power(2, multiply(divide(60, 10), subtract(const_1, 2))), 120), 60) | divide(n4,n0)|subtract(const_1,n3)|multiply(#0,#1)|power(n3,#2)|multiply(n1,#3)|add(n4,#4)| | "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 80 minutes after it was poured is : f = 120 ( 2 ^ - 80 / 10 ) + 60 f = 120 * 1 / 256 + 60 f = 15 / 32 + 60 f = 1935 / 32 = 60.4 c" | general |
math_qa__PJVQ0O2qLXPkTYUM | The average of 11 results is 20. The average of first 5 of them is 15 and that of last 5 is 22 . Find the 6th result? Choose the correct choice:
A) 35 B) 50 C) 100 D) 120 E) 150 | <gadget id="calculator">11 * 20</gadget>
<output>220</output>
<gadget id="calculator">5 * 22</gadget>
<output>110</output>
<gadget id="calculator">220 - 110</gadget>
<output>110</output>
<gadget id="calculator">5 * 15</gadget>
<output>75</output>
<gadget id="calculator">110 - 75</gadget>
<output>35</output>
<result>A</result> | A | 35 | The average of 11 results is 20. The average of first 5 of them is 15 and that of last 5 is 22 . Find the 6th result? | {
"A": "35",
"B": "50",
"C": "100",
"D": "120",
"E": "150"
} | subtract(subtract(multiply(11, 20), multiply(5, 22)), multiply(5, 15)) | multiply(n0,n1)|multiply(n2,n5)|multiply(n2,n3)|subtract(#0,#1)|subtract(#3,#2)| | "6 th result = sum of 11 results - sum of 10 results = 11 * 20 - 5 * 15 - 5 * 22 = 220 - 75 - 110 = 35 answer is a" | general |
math_qa__3OgKVgL0nMdcz62n | 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 -5/6=
Choose the correct answer: A) 0 B) 2 / 15 C) 2 / 5 D) 9 / 20 E) 5 / 6 | <gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>
<result>E</result> | E | 0.833333 | 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 -5/6= | {
"A": "0",
"B": "2 / 15",
"C": "2 / 5",
"D": "9 / 20",
"E": "5 / 6"
} | divide(5, 6) | divide(n4,n5) | we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let ’ s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 – 5 / 6 = 0 looking at the 2 nd group of the fractions ( 1 / 5 , 1 / 4 , and 9 / 20 ) , notice that 1 / 5 and 1 / 4 share a common denominator of 20 with 9 / 20 . 1 / 5 + 1 / 4 = 4 / 20 + 5 / 20 = 9 / 20 thus , 9 / 20 – 9 / 20 = 0 . thus , the result of 1 / 3 + 1 / 2 – 5 / 6 + 1 / 5 + 1 / 4 – 9 / 20 is 5 / 6 . answer : e | general |
math_qa__hHJkN80DX2q97vDe | Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 240 square feet. How many feet offence does Frank use? Choose the correct choice from the following choices: A) 14 B) 52 C) 54 D) 180 E) 240 | <gadget id="calculator">240 / 40</gadget>
<output>6</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">12 + 40</gadget>
<output>52</output>
<result>B</result> | B | 52 | Frank the Fencemaker needs to fence in a rectangular yard. He fences in the entire yard, except for one full side of the yard, which equals 40 feet. The yard has an area of 240 square feet. How many feet offence does Frank use? | {
"A": "14",
"B": "52",
"C": "54",
"D": "180",
"E": "240"
} | add(add(divide(240, 40), divide(240, 40)), 40) | divide(n1,n0)|add(#0,#0)|add(n0,#1)| | "area = length x breadth 240 = 40 x breadth so , breadth = 6 units fencing required is - breadth + breadth + length 6 + 6 + 40 = > 52 feet answer must be ( b ) 52" | geometry |
math_qa__2uvfquIJaY15STeH | The total of 334 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is Choose the correct choice from the following options: A) 250 B) 277 C) 278 D) 200 E) 288 | <gadget id="calculator">334 * 25</gadget>
<output>8_350</output>
<gadget id="calculator">71 * 100</gadget>
<output>7_100</output>
<gadget id="calculator">8_350 - 7_100</gadget>
<output>1_250</output>
<gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">1_250 / 5</gadget>
<output>250</output>
<result>A</result> | A | 250 | The total of 334 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is | {
"A": "250",
"B": "277",
"C": "278",
"D": "200",
"E": "288"
} | divide(subtract(multiply(334, 25), multiply(71, const_100)), subtract(25, 20)) | multiply(n0,n2)|multiply(n3,const_100)|subtract(n2,n1)|subtract(#0,#1)|divide(#3,#2)| | "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 334 - x ) . 0.20 * ( x ) + 0.25 ( 334 - x ) = 71 = > x = 250 . . answer : a ) 250" | general |
math_qa__mG7eKGyQxRsWntvt | The Guests at a football banquet consumed a total of 337 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet? Choose the correct option:
A) 160 B) 161 C) 162 D) 163 E) 169 | <gadget id="calculator">337 / 2</gadget>
<output>337/2 = around 168.5</output>
<gadget id="calculator">floor(337/2)</gadget>
<output>168</output>
<gadget id="calculator">168 + 1</gadget>
<output>169</output>
<result>E</result> | E | 169 | The Guests at a football banquet consumed a total of 337 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet? | {
"A": "160",
"B": "161",
"C": "162",
"D": "163",
"E": "169"
} | add(floor(divide(337, 2)), const_1) | divide(n0,n1)|floor(#0)|add(#1,const_1)| | "to minimize one quantity maximize other . 168 * 2 ( max possible amount of food a guest could consume ) = 336 pounds , so there must be more than 168 guests , next integer is 169 . answer : e ." | general |
math_qa__xwjYrweZldWUKqZr | A plant manager must assign 10 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers? Choose the correct choice from the following options: A) 2430 B) 2700 C) 3300 D) 4860 E) 5400 | <gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>
<gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">40_320 * 2</gadget>
<output>80_640</output>
<gadget id="calculator">3_628_800 / 80_640</gadget>
<output>45</output>
<gadget id="calculator">60 * 45</gadget>
<output>2_700</output>
<result>B</result> | B | 2,700 | A plant manager must assign 10 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers? | {
"A": "2430",
"B": "2700",
"C": "3300",
"D": "4860",
"E": "5400"
} | multiply(divide(factorial(divide(10, 2)), const_2), divide(factorial(10), multiply(factorial(subtract(10, 2)), factorial(2)))) | divide(n0,n1)|factorial(n0)|factorial(n1)|subtract(n0,n1)|factorial(#0)|factorial(#3)|divide(#4,const_2)|multiply(#5,#2)|divide(#1,#7)|multiply(#6,#8)| | "my take selecting team of 2 out of 10 to assign to the shifts = 10 c 2 = 45 ways . now 2 out of 10 means total of 5 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 5 * 4 * 3 * 2 * 1 = 120 here alt and alt are the same : so 120 / 2 = 60 ways . total ways of selecting = ( selecting 2 out of 10 ) * arranging those teams in shifts = 45 * 60 = 2700 ans : b" | physics |
math_qa__mTWa7ETKIfdaZhcP | There are 5 red shoes & 4 green shoes . If two of red shoes are drawn what is the probability of getting red shoes Choose the correct choice.
A) 1 / 18 B) 1 / 14 C) 5 / 18 D) 1 / 15 E) 1 / 16 | <gadget id="calculator">binomial(5, 2)</gadget>
<output>10</output>
<gadget id="calculator">5 + 4</gadget>
<output>9</output>
<gadget id="calculator">binomial(9, 2)</gadget>
<output>36</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<result>C</result> | C | 0.277778 | There are 5 red shoes & 4 green shoes . If two of red shoes are drawn what is the probability of getting red shoes | {
"A": "1 / 18",
"B": "1 / 14",
"C": "5 / 18",
"D": "1 / 15",
"E": "1 / 16"
} | divide(choose(5, const_2), choose(add(5, 4), const_2)) | add(n0,n1)|choose(n0,const_2)|choose(#0,const_2)|divide(#1,#2) | taking 2 red shoe the probability is 5 c 2 from 9 shoes probability of taking 2 red shoes is 5 c 2 / 9 c 2 = 5 / 18 answer : c | probability |
math_qa__JTvsu94mRBYk5kO3 | to fill a tank , 200 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 4 - fifths of its present ? Choose the correct choice from the following choices
A) 50 B) 100 C) 150 D) 200 E) 250 | <gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">200 / (4/5)</gadget>
<output>250</output>
<result>E</result> | E | 250 | to fill a tank , 200 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 4 - fifths of its present ? | {
"A": "50",
"B": "100",
"C": "150",
"D": "200",
"E": "250"
} | divide(200, divide(4, divide(const_10, const_2))) | divide(const_10,const_2)|divide(n1,#0)|divide(n0,#1) | let the capacity of 1 bucket = x . then , the capacity of tank = 200 x . new capacity of bucket = 4 / 5 x therefore , required number of buckets = ( 200 x ) / ( 4 x / 5 ) = ( 200 x ) x 5 / 4 x = 1000 / 4 = 250 answer is e . | physics |
math_qa__DNJ9CjLdnMxiAZ0q | John was 31 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now 7/9 of John's. How old is Betty? Choose one
A) 24 B) 26 C) 28 D) 30 E) 32 | <gadget id="calculator">7 / 9</gadget>
<output>7/9 = around 0.777778</output>
<gadget id="calculator">31 + 4</gadget>
<output>35</output>
<gadget id="calculator">(7/9) * 35</gadget>
<output>245/9 = around 27.222222</output>
<result>C</result> | C | 28 | John was 31 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now 7/9 of John's. How old is Betty? | {
"A": "24",
"B": "26",
"C": "28",
"D": "30",
"E": "32"
} | multiply(divide(7, 9), add(31, const_4)) | add(n0,const_4)|divide(n1,n2)|multiply(#0,#1)| | "assume betty ' s age on marriage = x years . john ' s age on marriage = 31 john ' s age after 5 years = 36 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 9 ( 36 ) = 28 therefore betty ' s current age = 28 option c" | general |
math_qa__seWPPArPsNmPaymF | If the volume of two cubes are in the ratio 27:1, the ratio of their edges is: Pick: A) 3 : 1 B) 3 : 2 C) 3 : 5 D) 3 : 7 E) none of these | <gadget id="calculator">27 ** (1/3)</gadget>
<output>3</output>
<result>A</result> | A | 3 | If the volume of two cubes are in the ratio 27:1, the ratio of their edges is: | {
"A": "3 : 1",
"B": "3 : 2",
"C": "3 : 5",
"D": "3 : 7",
"E": "none of these"
} | cube_edge_by_volume(27) | cube_edge_by_volume(n0)| | "explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 27 / 1 = > ( a / b ) 3 = ( 3 / 1 ) 3 a / b = 3 / 1 = > a : b = 3 : 1 option a" | geometry |
math_qa__tIfRPxye7Vne2SBb | Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 65 per kg. How much amount did he pay to the shopkeeper?
Choose the correct choice from the following options:
A) 1040
B) 1145
C) 1055
D) 1060
E) 1075 | <gadget id="calculator">8 * 70</gadget>
<output>560</output>
<gadget id="calculator">9 * 65</gadget>
<output>585</output>
<gadget id="calculator">560 + 585</gadget>
<output>1_145</output>
<result>B</result> | B | 1,145 | Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 65 per kg. How much amount did he pay to the shopkeeper? | {
"A": "1040",
"B": "1145",
"C": "1055",
"D": "1060",
"E": "1075"
} | add(multiply(8, 70), multiply(9, 65)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 65 × 9 = 585 . total cost he has to pay = 560 + 585 = 1145 . b )" | gain |
math_qa__LZJGbCiGvncHAYte | A man can row 4 kmph is still water. If the river is running at 2 kmph it takes 90 min to row to a place and back. How far is the place
Choose one
A) 2 km B) 4 km C) 5 km D) 2.25 km E) none of these | <gadget id="calculator">90 / 60</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/6) + (1/2)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(3/2) / (2/3)</gadget>
<output>9/4 = around 2.25</output>
<result>D</result> | D | 2.25 | A man can row 4 kmph is still water. If the river is running at 2 kmph it takes 90 min to row to a place and back. How far is the place | {
"A": "2 km",
"B": "4 km",
"C": "5 km",
"D": "2.25 km",
"E": "none of these"
} | divide(divide(90, const_60), add(inverse(add(4, 2)), inverse(subtract(4, 2)))) | add(n0,n1)|divide(n2,const_60)|subtract(n0,n1)|inverse(#0)|inverse(#2)|add(#3,#4)|divide(#1,#5) | explanation : speed in still water = 4 kmph speed of the stream = 2 kmph speed upstream = ( 4 - 2 ) = 2 kmph speed downstream = ( 4 + 2 ) = 6 kmph total time = 90 minutes = 90 ⁄ 60 hour = 3 ⁄ 2 hour let l be the distance . then ( l / 6 ) + ( l / 2 ) = 32 = > l + 3 l = 9 = > 4 l = 9 = > l = 9 ⁄ 4 = 2.25 km . answer : option d | physics |
math_qa__CQAi0EZ3sewuo3mx | What is the least number should be added to 929, so the sum of the number is completely divisible by 30? Choose the correct choice from the following answers.
A) 1
B) 2
C) 5
D) 6
E) 8 | <gadget id="calculator">929 / 30</gadget>
<output>929/30 = around 30.966667</output>
<gadget id="calculator">floor(929/30)</gadget>
<output>30</output>
<gadget id="calculator">30 + 1</gadget>
<output>31</output>
<gadget id="calculator">31 * 30</gadget>
<output>930</output>
<gadget id="calculator">930 - 929</gadget>
<output>1</output>
<result>A</result> | A | 1 | What is the least number should be added to 929, so the sum of the number is completely divisible by 30? | {
"A": "1",
"B": "2",
"C": "5",
"D": "6",
"E": "8"
} | subtract(multiply(add(floor(divide(929, 30)), const_1), 30), 929) | divide(n0,n1)|floor(#0)|add(#1,const_1)|multiply(n1,#2)|subtract(#3,n0)| | "( 929 / 30 ) gives remainder 29 29 + 1 = 30 , so we need to add 1 answer : a" | general |
math_qa__WemyacdB5xqSImLk | The sale price sarees listed for Rs.495 after successive discount is 15% and 10% is? Choose the correct choice from the following choices: A) 288 B) 378 C) 342 D) 662 E) 262 | <gadget id="calculator">495 * 15</gadget>
<output>7_425</output>
<gadget id="calculator">7_425 / 100</gadget>
<output>297/4 = around 74.25</output>
<gadget id="calculator">495 - (297/4)</gadget>
<output>1_683/4 = around 420.75</output>
<gadget id="calculator">(1_683/4) * 10</gadget>
<output>8_415/2 = around 4_207.5</output>
<gadget id="calculator">(8_415/2) / 100</gadget>
<output>1_683/40 = around 42.075</output>
<gadget id="calculator">(1_683/4) - (1_683/40)</gadget>
<output>15_147/40 = around 378.675</output>
<result>B</result> | B | 378 | The sale price sarees listed for Rs.495 after successive discount is 15% and 10% is? | {
"A": "288",
"B": "378",
"C": "342",
"D": "662",
"E": "262"
} | subtract(subtract(495, divide(multiply(495, 15), const_100)), divide(multiply(subtract(495, divide(multiply(495, 15), const_100)), 10), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | "495 * ( 85 / 100 ) * ( 90 / 100 ) = 378 answer : b" | gain |
math_qa__opbmWtJVBGQ8xTLU | How many numbers from 29 to 119 are exactly divisible by 11?
Choose the correct choice.
A) 5
B) 7
C) 9
D) 8
E) 12 | <gadget id="calculator">119 / 11</gadget>
<output>119/11 = around 10.818182</output>
<gadget id="calculator">floor(119/11)</gadget>
<output>10</output>
<gadget id="calculator">10 * 11</gadget>
<output>110</output>
<gadget id="calculator">29 / 11</gadget>
<output>29/11 = around 2.636364</output>
<gadget id="calculator">floor(29/11)</gadget>
<output>2</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">3 * 11</gadget>
<output>33</output>
<gadget id="calculator">110 - 33</gadget>
<output>77</output>
<gadget id="calculator">77 / 11</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<result>D</result> | D | 8 | How many numbers from 29 to 119 are exactly divisible by 11? | {
"A": "5",
"B": "7",
"C": "9",
"D": "8",
"E": "12"
} | add(divide(subtract(multiply(floor(divide(119, 11)), 11), multiply(add(floor(divide(29, 11)), const_1), 11)), 11), const_1) | divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)| | "29 / 11 = 2 and 119 / 11 = 10 = = > 10 - 2 = 8 numbers answer : d" | general |
math_qa__VsxiedVudju4lzOx | The points A(0, 0), B(0, 4a - 2) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? Pick one:
A) 58
B) 70
C) 63
D) 65
E) 72 | <gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 - 2</gadget>
<output>14</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">14 * 9</gadget>
<output>126</output>
<gadget id="calculator">126 / 2</gadget>
<output>63</output>
<result>C</result> | C | 63 | The points A(0, 0), B(0, 4a - 2) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? | {
"A": "58",
"B": "70",
"C": "63",
"D": "65",
"E": "72"
} | divide(multiply(subtract(multiply(divide(add(6, 2), 2), 4), 2), add(multiply(divide(add(6, 2), 2), subtract(4, 2)), const_1)), const_2) | add(n4,n8)|subtract(n3,n4)|divide(#0,n4)|multiply(#2,#1)|multiply(n3,#2)|add(#3,const_1)|subtract(#4,n4)|multiply(#5,#6)|divide(#7,const_2) | 1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 6 ) now 4 a - 2 = 2 a + 6 2 a = 8 . a = 4 therefore , a ( 0,0 ) ; b ( 0,14 ) ; c ( 9,14 ) 1 / 2 * 9 * 14 = 63 answer : c | geometry |
math_qa__3htYCdHQ9YTNJgXa | A fellow borrowed a certain sum of money at 8% per annum at simple interest and in 8 years the interest amounted to Rs.900 less than the sum lent. What was the sum lent? Choose the correct choice from the following
A) 1050 B) 1220 C) 2500 D) 1060 E) 1110 | <gadget id="calculator">8 * 8</gadget>
<output>64</output>
<gadget id="calculator">64 / 100</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">1 - (16/25)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">900 / (9/25)</gadget>
<output>2_500</output>
<result>C</result> | C | 2,500 | A fellow borrowed a certain sum of money at 8% per annum at simple interest and in 8 years the interest amounted to Rs.900 less than the sum lent. What was the sum lent? | {
"A": "1050",
"B": "1220",
"C": "2500",
"D": "1060",
"E": "1110"
} | divide(900, subtract(const_1, divide(multiply(8, 8), const_100))) | multiply(n0,n0)|divide(#0,const_100)|subtract(const_1,#1)|divide(n2,#2)| | "p - 900 = ( p * 8 * 8 ) / 100 p = 2500 answer : c" | gain |
math_qa__HknprZ91KeCJQYqJ | When sold at a 40% discount, a sweater nets the merchant a 30% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price? Choices:
A) 20 % B) 40 % C) 50 % D) 53.85 % E) 100 % | <gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">60 / (13/10)</gadget>
<output>600/13 = around 46.153846</output>
<gadget id="calculator">100 - (600/13)</gadget>
<output>700/13 = around 53.846154</output>
<result>D</result> | D | 53.85 | When sold at a 40% discount, a sweater nets the merchant a 30% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price? | {
"A": "20 %",
"B": "40 %",
"C": "50 %",
"D": "53.85 %",
"E": "100 %"
} | subtract(const_100, divide(subtract(const_100, 40), add(const_1, divide(30, const_100)))) | divide(n1,const_100)|subtract(const_100,n0)|add(#0,const_1)|divide(#1,#2)|subtract(const_100,#3)| | "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 40 % of 100 = 60 . . profit = 30 % . . therefore the wholesale purchase cost = x . . . . 1.3 x = 60 or x = 46.15 . . . marked price was 100 so . . . so answer is 53.85 % . . d" | gain |
math_qa__I7EGyU3rIPZt061d | The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 78 respectively. The sum is: Choose the correct choice from the following choices: A) 1360 B) 1450 C) 1600 D) 947 E) none | <gadget id="calculator">85 * 78</gadget>
<output>6_630</output>
<gadget id="calculator">85 - 78</gadget>
<output>7</output>
<gadget id="calculator">6_630 / 7</gadget>
<output>6_630/7 = around 947.142857</output>
<result>D</result> | D | 947 | The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 78 respectively. The sum is: | {
"A": "1360",
"B": "1450",
"C": "1600",
"D": "947",
"E": "none"
} | divide(multiply(85, 78), subtract(85, 78)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1) | sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 85 * 78 / ( 85 - 78 ) = rs . 947 . answer d | gain |
math_qa__oxJjtvVmw9mwXyvc | A cycle is bought for Rs.675 and sold for Rs.1080, find the gain percent? Select the correct option:
A) 22 B) 60 C) 99 D) 88 E) 11 | <gadget id="calculator">1_080 - 675</gadget>
<output>405</output>
<gadget id="calculator">405 / 675</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<result>B</result> | B | 60 | A cycle is bought for Rs.675 and sold for Rs.1080, find the gain percent? | {
"A": "22",
"B": "60",
"C": "99",
"D": "88",
"E": "11"
} | multiply(divide(subtract(1080, 675), 675), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | "675 - - - - 180 100 - - - - ? = > 60 % answer : b" | gain |
math_qa__BNBgPaKFBJwfzVFU | TWO WORKERS A AND B ARE ENGAGED TO DO A WORK. A WORKING ALONE TAKES 8 HOURS MORE TO COMPLETE THE JOB THAN IF BOTH WORKED TOGETHER. IF B WORKED ALONE, HE WOULD NEED 4 1/2 HOURS MORE TO COMPLETE THE JOB THAN THEY BOTH WORKING TOGETHER. WHAT TIME WOULD THEY TAKE TO DO THE WORK TOGETHER? Options.
A) 4 hours B) 5 hours C) 6 hours D) 7 hours E) none of these | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">4 + (1/2)</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">(9/2) * 8</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<result>C</result> | C | 6 | TWO WORKERS A AND B ARE ENGAGED TO DO A WORK. A WORKING ALONE TAKES 8 HOURS MORE TO COMPLETE THE JOB THAN IF BOTH WORKED TOGETHER. IF B WORKED ALONE, HE WOULD NEED 4 1/2 HOURS MORE TO COMPLETE THE JOB THAN THEY BOTH WORKING TOGETHER. WHAT TIME WOULD THEY TAKE TO DO THE WORK TOGETHER? | {
"A": "4 hours",
"B": "5 hours",
"C": "6 hours",
"D": "7 hours",
"E": "none of these"
} | sqrt(multiply(add(4, divide(1, 2)), 8)) | divide(n2,n3)|add(n1,#0)|multiply(n0,#1)|sqrt(#2) | let a and be together take x hours to complete the work . then , a alone takes ( x + 8 ) hrs and b alone takes ( x + 9 / 2 ) hrs to complete the work . then , 1 / ( x + 8 ) + 1 / ( x + 9 / 2 ) = 1 / x , 1 / ( x + 8 ) + 2 / ( 2 x + 9 ) = 1 / x x ( 4 x + 25 ) = ( x + 8 ) ( 2 x + 9 ) 2 x ^ 2 = 72 , x ^ 2 = 36 , x = 6 correct option : c | general |
math_qa__VjAWIOFA7gZpHbnY | A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 80 sq. feet, how many feet of fencing will be required?
Choose one
A) 28 B) 40 C) 68 D) 88 E) 78 | <gadget id="calculator">80 / 20</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 20</gadget>
<output>28</output>
<result>A</result> | A | 28 | A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 80 sq. feet, how many feet of fencing will be required? | {
"A": "28",
"B": "40",
"C": "68",
"D": "88",
"E": "78"
} | add(multiply(divide(80, 20), const_2), 20) | divide(n1,n0)|multiply(#0,const_2)|add(n0,#1)| | "we have : l = 20 ft and lb = 80 sq . ft . so , b = 4 ft . length of fencing = ( l + 2 b ) = ( 20 + 8 ) ft = 28 ft . answer : a" | geometry |
math_qa__t57MJaEJitp8ZhH1 | A can do a work in 6days. B can do in 12days. If both A&B are working together in how many days they can finish the work? Answers.
A) 4 B) 5 C) 6 D) 10 E) 15 | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/6) + (1/12)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / (1/4)</gadget>
<output>4</output>
<result>A</result> | A | 4 | A can do a work in 6days. B can do in 12days. If both A&B are working together in how many days they can finish the work? | {
"A": "4",
"B": "5",
"C": "6",
"D": "10",
"E": "15"
} | divide(const_1, add(divide(const_1, 6), divide(const_1, 12))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2) | 1 day work of a = 1 / 6 1 day work of b = 1 / 12 1 day work of a & b = 1 / 6 + 1 / 12 = 1 / 4 a & b finish the work in 4 days answer is a | physics |
math_qa__9DKB1ZMgxycD0Svy | A 240 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Choose the correct choice from the following choices:
A) 230 m
B) 240 m
C) 260 m
D) 320 m
E) 330 m | <gadget id="calculator">120 + 80</gadget>
<output>200</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">200 * (5/18)</gadget>
<output>500/9 = around 55.555556</output>
<gadget id="calculator">(500/9) * 9</gadget>
<output>500</output>
<gadget id="calculator">500 - 240</gadget>
<output>260</output>
<result>C</result> | C | 260 | A 240 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? | {
"A": "230 m",
"B": "240 m",
"C": "260 m",
"D": "320 m",
"E": "330 m"
} | subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 240) | add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)| | "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 240 ) / 9 = 500 / 9 x + 240 = 500 x = 260 . c" | physics |
math_qa__xQ4kCyUeZiCrkEzf | Kavi had a stock of 600 bags in his bookshop. He sold 25 on Monday, 70 on Tuesday, 100 on Wednesday, 110 on Thursday and 145 on Friday. What percentage of the bags were not sold? Choose the correct choice from the following answers: A) 10 % B) 25 % C) 64 % D) 42 % E) 17 % | <gadget id="calculator">25 + 70</gadget>
<output>95</output>
<gadget id="calculator">95 + 100</gadget>
<output>195</output>
<gadget id="calculator">195 + 110</gadget>
<output>305</output>
<gadget id="calculator">305 + 145</gadget>
<output>450</output>
<gadget id="calculator">600 - 450</gadget>
<output>150</output>
<gadget id="calculator">150 / 600</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>B</result> | B | 25 | Kavi had a stock of 600 bags in his bookshop. He sold 25 on Monday, 70 on Tuesday, 100 on Wednesday, 110 on Thursday and 145 on Friday. What percentage of the bags were not sold? | {
"A": "10 %",
"B": "25 %",
"C": "64 %",
"D": "42 %",
"E": "17 %"
} | multiply(divide(subtract(600, add(add(add(add(25, 70), 100), 110), 145)), 600), const_100) | add(n1,n2)|add(n3,#0)|add(n4,#1)|add(n5,#2)|subtract(n0,#3)|divide(#4,n0)|multiply(#5,const_100) | let n be the total number of bags sold . hence n = 25 + 70 + 100 + 110 + 145 = 450 let m be the bags not sold m = 600 - n = 600 - 450 = 150 percentage bags not sold / total number of bags = 150 / 600 = 0.25 = 25 % correct answer b | gain |
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