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__HNVlyd1iboWUJupQ | n and m are each 3 - digit integers . each of the numbers 2 , 34 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ? Choices:
A) 39 B) 49 C) 58 D) 113 E) 131 | <gadget id="calculator">2 - 8</gadget>
<output>-6</output>
<gadget id="calculator">(-6) * 10</gadget>
<output>-60</output>
<gadget id="calculator">100 + (-60)</gadget>
<output>40</output>
<gadget id="calculator">40 - 1</gadget>
<output>39</output>
<result>A</result> | A | 39 | n and m are each 3 - digit integers . each of the numbers 2 , 34 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ? | {
"A": "39",
"B": "49",
"C": "58",
"D": "113",
"E": "131"
} | subtract(add(const_100, multiply(subtract(2, 8), const_10)), const_1) | subtract(n1,n5)|multiply(#0,const_10)|add(#1,const_100)|subtract(#2,const_1) | you have 6 digits : 2 , 3 , 4 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 387 and 426 ( difference is 39 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 684 and 723 ( difference is 39 ) a | general |
math_qa__Tt2xNv37FLzBqVL9 | Worker A takes 5 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? Choose the correct choice from the following
A) 20 / 9 B) 40 / 9 C) 50 / 9 D) 60 / 9 E) 10 / 3 | <gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/5) + (1/10)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 / (3/10)</gadget>
<output>10/3 = around 3.333333</output>
<result>E</result> | E | 3.333333 | Worker A takes 5 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? | {
"A": "20 / 9",
"B": "40 / 9",
"C": "50 / 9",
"D": "60 / 9",
"E": "10 / 3"
} | divide(const_1, add(divide(const_1, 5), divide(const_1, 10))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)| | "one day work of a = 1 / 5 one day work of b = 1 / 10 so one day work of a and b together = 1 / 5 + 1 / 10 = 3 / 10 so total days required = 10 / 3 answer : e" | physics |
math_qa__dQ2P4VZx1lQMh9tl | Every day, the value of a stock rises by exactly two dollars in the morning, and
then falls by exactly one dollar in the afternoon. If the stock's value at the start of the first
day is $100, on what day will the stock's value first reach $200?
Choose the correct option:
A) 50 B) 99 C) 100 D) 101 E) 200 | <gadget id="calculator">200 - 100</gadget>
<output>100</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">100 / 1</gadget>
<output>100</output>
<result>B</result> | B | 99 | Every day, the value of a stock rises by exactly two dollars in the morning, and
then falls by exactly one dollar in the afternoon. If the stock's value at the start of the first
day is $100, on what day will the stock's value first reach $200? | {
"A": "50",
"B": "99",
"C": "100",
"D": "101",
"E": "200"
} | divide(subtract(200, 100), subtract(const_2, const_1)) | subtract(n1,n0)|subtract(const_2,const_1)|divide(#0,#1) | note that each day the stock is worth $ 1 more than on the previous day , and that on the first day it rises to $ 102 and then falls to $ 101 . therefore , on the nth day , the stock ' s value rises to n + 101 dollars in the morning and falls to n + 100 dollars in the afternoon . the solution is therefore the smallest n for which n + 101 = 200 , or n = 99 . in particular , the stock will be $ 200 in the middle of day 99 , although not at the end of this day . correct answer b | physics |
math_qa__6FLYvd8Q133TGaaI | Bruce purchased 8 kg of grapes at the rate of 70 per kg and 10 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Options.
A) 1040 B) 1050 C) 1055 D) 1110 E) 1075 | <gadget id="calculator">8 * 70</gadget>
<output>560</output>
<gadget id="calculator">10 * 55</gadget>
<output>550</output>
<gadget id="calculator">560 + 550</gadget>
<output>1_110</output>
<result>D</result> | D | 1,110 | Bruce purchased 8 kg of grapes at the rate of 70 per kg and 10 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? | {
"A": "1040",
"B": "1050",
"C": "1055",
"D": "1110",
"E": "1075"
} | add(multiply(8, 70), multiply(10, 55)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | "cost of 8 kg grapes = 70 × 8 = 560 . cost of 10 kg of mangoes = 55 × 10 = 550 . total cost he has to pay = 560 + 550 = 1110 d" | gain |
math_qa__RaWmodpgckWofwiA | Rebecca's annual income is $20,and Jimmy's annual income is $10,. By how much must Rebecca's annual income increase so that it constitutes 55% of Rebecca and Jimmy's combined income?
Choose the correct choice:
A) 8 B) 9 C) 7.77 D) 10 E) 11 | <gadget id="calculator">20 + 10</gadget>
<output>30</output>
<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">30 * (11/20)</gadget>
<output>33/2 = around 16.5</output>
<gadget id="calculator">(33/2) - 20</gadget>
<output>-7/2 = around -3.5</output>
<gadget id="calculator">1 - (11/20)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(-7/2) / (9/20)</gadget>
<output>-70/9 = around -7.777778</output>
<gadget id="calculator">-(-70/9)</gadget>
<output>70/9 = around 7.777778</output>
<result>C</result> | C | 7.77 | Rebecca's annual income is $20,and Jimmy's annual income is $10,. By how much must Rebecca's annual income increase so that it constitutes 55% of Rebecca and Jimmy's combined income? | {
"A": "8",
"B": "9",
"C": "7.77",
"D": "10",
"E": "11"
} | negate(divide(subtract(multiply(add(20, 10), divide(55, const_100)), 20), subtract(const_1, divide(55, const_100)))) | add(n0,n1)|divide(n2,const_100)|multiply(#0,#1)|subtract(const_1,#1)|subtract(#2,n0)|divide(#4,#3)|negate(#5) | total rebecca = x + 20 ; total = x + 20 + 10 x + 20 / x + 30 = 55 / 100 therefore x = 7.77 c | general |
math_qa__ge4hnlTDwvKFNWf5 | 162 students represent x percent of the boys at a school. If the boys at the school make up 50% of the total school population of x students, what is x? Options: A) 120 B) 150 C) 180 D) 250 E) 440 | <gadget id="calculator">162 * 100</gadget>
<output>16_200</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">16_200 / (1/2)</gadget>
<output>32_400</output>
<gadget id="calculator">32_400 ** (1/2)</gadget>
<output>180</output>
<result>C</result> | C | 180 | 162 students represent x percent of the boys at a school. If the boys at the school make up 50% of the total school population of x students, what is x? | {
"A": "120",
"B": "150",
"C": "180",
"D": "250",
"E": "440"
} | sqrt(divide(multiply(162, const_100), divide(50, const_100))) | divide(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)|sqrt(#2)| | "let b be the number of boys in the school . 162 = xb / 100 b = 0.5 x 16200 = 0.5 x ^ 2 x ^ 2 = 32400 x = 180 the answer is c ." | gain |
math_qa__e6oKBeYq1b78sY6O | If x, y, and z are positive integers, and 4x = 5y = 6z, then the least possible value of x + y + z is Choose the correct choice from the following answers
A) 15 B) 28 C) 37 D) 42 E) 60 | <gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 6</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<gadget id="calculator">60 / 5</gadget>
<output>12</output>
<gadget id="calculator">15 + 12</gadget>
<output>27</output>
<gadget id="calculator">60 / 6</gadget>
<output>10</output>
<gadget id="calculator">27 + 10</gadget>
<output>37</output>
<result>C</result> | C | 37 | If x, y, and z are positive integers, and 4x = 5y = 6z, then the least possible value of x + y + z is | {
"A": "15",
"B": "28",
"C": "37",
"D": "42",
"E": "60"
} | add(add(divide(divide(multiply(multiply(4, 5), 6), const_2), 4), divide(divide(multiply(multiply(4, 5), 6), const_2), 5)), divide(divide(multiply(multiply(4, 5), 6), const_2), 6)) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,const_2)|divide(#2,n0)|divide(#2,n1)|divide(#2,n2)|add(#3,#4)|add(#6,#5) | take lcm of 4,5 and 6 = 60 now 4 x = 60 = > x = 15 5 y = 60 = > y = 12 6 z = 60 = > z = 10 115 + 12 + 10 = 37 . option c . | general |
math_qa__kluMY8xll5IWRypV | A tank is filled by 3 pipes with uniform flow. The first two pipes operating simultaneously fill the tan in the same time during which the tank is filled by the third pipe alone. The 2nd pipe fills the tank 5 hours faster than first pipe and 4 hours slower than third pipe. The time required by first pipe is Choose the correct answer
A) 13 hours B) 45 hours C) 15 hours D) 12 hours E) 11 hours | <gadget id="calculator">5 + 4</gadget>
<output>9</output>
<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<gadget id="calculator">18 ** 2</gadget>
<output>324</output>
<gadget id="calculator">5 * 9</gadget>
<output>45</output>
<gadget id="calculator">4 * 45</gadget>
<output>180</output>
<gadget id="calculator">324 - 180</gadget>
<output>144</output>
<gadget id="calculator">144 ** (1/2)</gadget>
<output>12</output>
<gadget id="calculator">18 + 12</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<result>C</result> | C | 15 | A tank is filled by 3 pipes with uniform flow. The first two pipes operating simultaneously fill the tan in the same time during which the tank is filled by the third pipe alone. The 2nd pipe fills the tank 5 hours faster than first pipe and 4 hours slower than third pipe. The time required by first pipe is | {
"A": "13 hours",
"B": "45 hours",
"C": "15 hours",
"D": "12 hours",
"E": "11 hours"
} | divide(add(multiply(add(5, 4), 2), sqrt(subtract(power(multiply(add(5, 4), 2), const_2), multiply(const_4, multiply(5, add(5, 4)))))), const_2) | add(n2,n3)|multiply(n1,#0)|multiply(n2,#0)|multiply(#2,const_4)|power(#1,const_2)|subtract(#4,#3)|sqrt(#5)|add(#1,#6)|divide(#7,const_2) | if first pipe fills tank in x hrs , then second pipe fills tank in x - 5 hrs and 3 rd pipe fills tank in x - 9 hrs , then as per given condition 1 / x + 1 / ( x - 5 ) = 1 / ( x - 9 ) solving it , we get x = 15 hrs answer : c | physics |
math_qa__kb7SD8pPLTRVCs6a | A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 75 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 Choose the correct choice from the following answers:
A) 2500
B) 2100
C) 2200
D) 2300
E) 2400 | <gadget id="calculator">75 / 3</gadget>
<output>25</output>
<gadget id="calculator">25 * 100</gadget>
<output>2_500</output>
<result>A</result> | A | 2,500 | A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 75 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 | {
"A": "2500",
"B": "2100",
"C": "2200",
"D": "2300",
"E": "2400"
} | multiply(divide(75, 3), const_100) | divide(n2,n0)|multiply(#0,const_100)| | "1 percent for 3 years = 75 1 percent for 1 year = 25 = > 100 percent = 2500 answer : a" | gain |
math_qa__lD0JL4MhEPT00QvW | During the first two weeks of January, the total rainfall in Springdale was 40 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January? Choose the correct choice from the following answers.
A) 5 inches B) 6 inches C) 9 inches D) 10 inches E) 24 inches | <gadget id="calculator">1 + 1.5</gadget>
<output>2.5</output>
<gadget id="calculator">1.5 / 2.5</gadget>
<output>0.6</output>
<gadget id="calculator">40 * 0.6</gadget>
<output>24</output>
<result>E</result> | E | 24 | During the first two weeks of January, the total rainfall in Springdale was 40 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January? | {
"A": "5 inches",
"B": "6 inches",
"C": "9 inches",
"D": "10 inches",
"E": "24 inches"
} | multiply(40, divide(1.5, add(const_1, 1.5))) | add(n1,const_1)|divide(n1,#0)|multiply(n0,#1)| | "total rainfall in 2 weeks = 40 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 40 inches x = 16 and 1.5 x = 24 rainfall during second week = 24 inches option e" | general |
math_qa__2O8ix1cg3P6COL6z | A van takes 5 hours to cover a distance of 450 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time? Pick one.
A) 56 B) 60 C) 64 D) 68 E) 72 | <gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 5</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">450 / (15/2)</gadget>
<output>60</output>
<result>B</result> | B | 60 | A van takes 5 hours to cover a distance of 450 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time? | {
"A": "56",
"B": "60",
"C": "64",
"D": "68",
"E": "72"
} | divide(450, multiply(divide(3, 2), 5)) | divide(n2,n3)|multiply(n0,#0)|divide(n1,#1)| | "( 3 / 2 ) * 5 = 7.5 hours 450 / 7.5 = 60 kph the answer is b ." | physics |
math_qa__INJSWBkLulTJb0dd | What is the compound interest paid on a sum of Rs.4500 for the period of 2 years at 10% per annum.
Choose the correct choice.
A) 945 B) 620 C) 610 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">4_500 * (121/100)</gadget>
<output>5_445</output>
<gadget id="calculator">5_445 - 4_500</gadget>
<output>945</output>
<result>A</result> | A | 945 | What is the compound interest paid on a sum of Rs.4500 for the period of 2 years at 10% per annum. | {
"A": "945",
"B": "620",
"C": "610",
"D": "600",
"E": "none of these"
} | subtract(multiply(4500, power(add(const_1, divide(10, const_100)), 2)), 4500) | 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 % 4500 = 4500 * ( 21 / 100 ) = 945 answer a" | gain |
math_qa__xZV5Eyvs2qQQVDxI | If 10 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
Choose the correct choice from the following options
A) 80 B) 63 C) 120 D) 160 E) 1260 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">10 * 9</gadget>
<output>90</output>
<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">8 * 7</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<gadget id="calculator">45 * 28</gadget>
<output>1_260</output>
<result>E</result> | E | 1,260 | If 10 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed? | {
"A": "80",
"B": "63",
"C": "120",
"D": "160",
"E": "1260"
} | multiply(divide(multiply(10, subtract(10, const_1)), const_2), divide(multiply(8, subtract(8, const_1)), const_2)) | subtract(n0,const_1)|subtract(n1,const_1)|multiply(n0,#0)|multiply(n1,#1)|divide(#2,const_2)|divide(#3,const_2)|multiply(#4,#5)| | "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 10 c 2 for vertical 8 c 2 total parallelogram is 10 c 2 * 8 c 2 = 45 * 28 = 1260 answer : e" | physics |
math_qa__8ERglw0vZycWxozh | On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 5 cups of tea. Last week Mo drank a total of 22 cups of tea and hot chocolate together. If during that week Mo drank 8 more tea cups than hot chocolate cups, then how many rainy days were there last week? Select the correct option.
A) 2
B) 4
C) 3
D) 5
E) 6 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">22 + 8</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">15 / 5</gadget>
<output>3</output>
<gadget id="calculator">7 - 3</gadget>
<output>4</output>
<result>B</result> | B | 4 | On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 5 cups of tea. Last week Mo drank a total of 22 cups of tea and hot chocolate together. If during that week Mo drank 8 more tea cups than hot chocolate cups, then how many rainy days were there last week? | {
"A": "2",
"B": "4",
"C": "3",
"D": "5",
"E": "6"
} | subtract(add(const_4, const_3), divide(divide(add(22, 8), const_2), 5)) | add(const_3,const_4)|add(n1,n2)|divide(#1,const_2)|divide(#2,n0)|subtract(#0,#3)| | "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 22 t - c = 8 - > t = 15 . c = 7 . mo drinks 5 cups of tea a day then number of days that are not rainy = 15 / 5 = 3 so number of rainy days = 7 - 3 = 4 b is the answer ." | general |
math_qa__xoDcQv42ihoOKjBf | Two spherical balls lie on the ground touching. If one of the balls has a radius of 4 cm, and the point of contact is 6 cm above the ground, what is the radius of the other ball?
Choose the correct choice from the following options: A) 10 cm B) 12 cm C) 14 cm D) 16 cm E) 18 cm | <gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">10 + 4</gadget>
<output>14</output>
<result>C</result> | C | 14 | Two spherical balls lie on the ground touching. If one of the balls has a radius of 4 cm, and the point of contact is 6 cm above the ground, what is the radius of the other ball? | {
"A": "10 cm",
"B": "12 cm",
"C": "14 cm",
"D": "16 cm",
"E": "18 cm"
} | add(add(4, 6), const_4) | add(n0,n1)|add(#0,const_4) | similar triangle properties . . 2 / r + 4 = 4 / r - 4 giving r = 14 . answer : c | physics |
math_qa__cttxsM73GKPliB9D | Mary and Mike enter into a partnership by investing $650 and $350 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $600 more than Mike did, what was the profit made by their business in that year? Select the correct option
A) $ 3000 B) $ 3200 C) $ 3300 D) $ 3400 E) $ 4000 | <gadget id="calculator">650 / 1_000</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">350 / 1_000</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(13/20) - (7/20)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(3/10) * (2/3)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">600 / (1/5)</gadget>
<output>3_000</output>
<result>A</result> | A | 3,000 | Mary and Mike enter into a partnership by investing $650 and $350 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $600 more than Mike did, what was the profit made by their business in that year? | {
"A": "$ 3000",
"B": "$ 3200",
"C": "$ 3300",
"D": "$ 3400",
"E": "$ 4000"
} | divide(600, multiply(subtract(divide(650, const_1000), divide(350, const_1000)), subtract(const_1, divide(const_1, const_3)))) | divide(n0,const_1000)|divide(n1,const_1000)|divide(const_1,const_3)|subtract(#0,#1)|subtract(const_1,#2)|multiply(#3,#4)|divide(n2,#5)| | "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 6.5 : 3.5 i . e . , 65 % of 2 x would go to mary and 35 % of 2 x would go to mike . hence , mary would get ( 65 - 35 ) % of 2 x more than mike or 30 % of 2 x = $ 600 i . e . , ( 30 / 100 ) * 2 x = 600 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : a" | general |
math_qa__CcDt1H8I3vOdgL00 | A train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train. Choose the correct choice
A) 45 kmph B) 50 kmph C) 85 kmph D) 60 kmph E) 70 kmph | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">6 * (5/18)</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">150 / (5/3)</gadget>
<output>90</output>
<gadget id="calculator">90 - 5</gadget>
<output>85</output>
<result>C</result> | C | 85 | A train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train. | {
"A": "45 kmph",
"B": "50 kmph",
"C": "85 kmph",
"D": "60 kmph",
"E": "70 kmph"
} | subtract(divide(150, multiply(6, const_0_2778)), 5) | multiply(n1,const_0_2778)|divide(n0,#0)|subtract(#1,n2)| | "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 150 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2700 < = > x = 85 speed of the train is 85 kmph . answer : option c" | physics |
math_qa__liJiNayhKcWNjegM | In a college, the ratio of the number of boys to girls is 8 : 4. If there are 200 girls, the total number of students in the college is
Choose the correct choice from the following answers.
A) 420 B) 520 C) 600 D) 720 E) 820 | <gadget id="calculator">200 / 4</gadget>
<output>50</output>
<gadget id="calculator">50 * 8</gadget>
<output>400</output>
<gadget id="calculator">200 + 400</gadget>
<output>600</output>
<result>C</result> | C | 600 | In a college, the ratio of the number of boys to girls is 8 : 4. If there are 200 girls, the total number of students in the college is | {
"A": "420",
"B": "520",
"C": "600",
"D": "720",
"E": "820"
} | add(200, multiply(divide(200, 4), 8)) | divide(n2,n1)|multiply(n0,#0)|add(n2,#1)| | "explanation : let the boy are 8 x and girls are 4 x = > 4 x = 200 = > x = 50 total students = 8 x + 4 x = 12 x = 12 ( 50 ) = 600 option c" | other |
math_qa__aFm8WqYswHMKHmtN | A certain bag contains 60 balls — 22 white, 18 green, 5 yellow, 6 red, and 9 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple? Choose the correct option:
A) 0.09
B) 0.15
C) 0.54
D) 0.75
E) 0.91 | <gadget id="calculator">22 + 18</gadget>
<output>40</output>
<gadget id="calculator">40 + 5</gadget>
<output>45</output>
<gadget id="calculator">45 / 60</gadget>
<output>3/4 = around 0.75</output>
<result>D</result> | D | 0.75 | A certain bag contains 60 balls — 22 white, 18 green, 5 yellow, 6 red, and 9 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple? | {
"A": "0.09",
"B": "0.15",
"C": "0.54",
"D": "0.75",
"E": "0.91"
} | divide(add(add(22, 18), 5), 60) | add(n1,n2)|add(n3,#0)|divide(#1,n0) | according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 5 ) / 60 = 45 / 60 = 0.75 . answer : d . | other |
math_qa__6uFwMEuqPDcahhk8 | on a certain date , pat invested $ 6000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24000 , in how many years total will the total value of the investment plus interest increase to $ 48000 ? Choose the correct choice from the following answers
A) 15 B) 16 C) 18 D) 20 E) 24 | <gadget id="calculator">24_000 + 48_000</gadget>
<output>72_000</output>
<gadget id="calculator">72_000 / 6_000</gadget>
<output>12</output>
<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<result>A</result> | A | 15 | on a certain date , pat invested $ 6000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24000 , in how many years total will the total value of the investment plus interest increase to $ 48000 ? | {
"A": "15",
"B": "16",
"C": "18",
"D": "20",
"E": "24"
} | add(divide(add(24000, 48000), 6000), const_3) | add(n2,n3)|divide(#0,n0)|add(#1,const_3) | 24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a . | general |
math_qa__NCciFs1yjyhxDJDA | Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/6 full and other jar 1/5 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water? Answers
A) 1 / 7 B) 2 / 7 C) 1 / 3 D) 7 / 12 E) 2 / 3 | <gadget id="calculator">2 / 6</gadget>
<output>1/3 = around 0.333333</output>
<result>C</result> | C | 0.333333 | Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/6 full and other jar 1/5 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water? | {
"A": "1 / 7",
"B": "2 / 7",
"C": "1 / 3",
"D": "7 / 12",
"E": "2 / 3"
} | divide(const_2, 6) | divide(const_2,n1)| | "same amount of water made bigger jar 1 / 6 full , thenthe same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 6 + 1 / 6 = 2 / 6 = 1 / 3 full . answer : c ." | general |
math_qa__QaJEWqRQN9MpMxAj | The price of lunch for 14 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? Answers
A) 11.73 B) 12.85 C) 13.8 D) 14 E) 15.87 | <gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">207 * 85</gadget>
<output>17_595</output>
<gadget id="calculator">17_595 / 100</gadget>
<output>3_519/20 = around 175.95</output>
<gadget id="calculator">(3_519/20) / 14</gadget>
<output>3_519/280 = around 12.567857</output>
<result>B</result> | B | 12.85 | The price of lunch for 14 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? | {
"A": "11.73",
"B": "12.85",
"C": "13.8",
"D": "14",
"E": "15.87"
} | divide(divide(multiply(207, subtract(const_100, 15)), const_100), 14) | subtract(const_100,n2)|multiply(n1,#0)|divide(#1,const_100)|divide(#2,n0)| | "clearly b is the answer i used poe here lets consider option ( b ) 14 * 12.85 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo b" | general |
math_qa__vkXbGby0ng1xlHvt | In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ? Select:
A) 2 / 3
B) 5 / 8
C) 3 / 5
D) 3 / 8
E) 4 / 9 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(1/4) + (3/4)</gadget>
<output>1</output>
<gadget id="calculator">(1/2) + 1</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">1 + (3/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) / 4</gadget>
<output>5/8 = around 0.625</output>
<result>B</result> | B | 0.625 | In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ? | {
"A": "2 / 3",
"B": "5 / 8",
"C": "3 / 5",
"D": "3 / 8",
"E": "4 / 9"
} | divide(add(1, add(divide(const_1, const_2), add(divide(1, add(1, 3)), divide(3, add(1, 3))))), add(1, 3)) | add(n0,n1)|divide(const_1,const_2)|divide(n1,#0)|divide(n0,#0)|add(#2,#3)|add(#4,#1)|add(n1,#5)|divide(#6,#0) | since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b | probability |
math_qa__EmvCQswc5ZWGm5Vk | 1000 men have provisions for 20 days. If 200 more men join them, for how many days will the provisions last now? Choose the correct choice from the following answers
A) 12.8 B) 12.6 C) 12.5 D) 12.2 E) 16.6 | <gadget id="calculator">20 * 1_000</gadget>
<output>20_000</output>
<gadget id="calculator">1_000 + 200</gadget>
<output>1_200</output>
<gadget id="calculator">20_000 / 1_200</gadget>
<output>50/3 = around 16.666667</output>
<result>E</result> | E | 16.6 | 1000 men have provisions for 20 days. If 200 more men join them, for how many days will the provisions last now? | {
"A": "12.8",
"B": "12.6",
"C": "12.5",
"D": "12.2",
"E": "16.6"
} | divide(multiply(20, 1000), add(1000, 200)) | add(n0,n2)|multiply(n0,n1)|divide(#1,#0)| | "1000 * 20 = 1200 * x x = 16.6 . answer : e" | physics |
math_qa__N7alQi1avLQ9fVmF | If x is less than y by 20% then y exceed x by: Choose the most appropriate option:
A) 33.33 %
B) 25 %
C) 75 %
D) 66.66 %
E) none of these | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 / 80</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) - 1</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>B</result> | B | 25 | If x is less than y by 20% then y exceed x by: | {
"A": "33.33 %",
"B": "25 %",
"C": "75 %",
"D": "66.66 %",
"E": "none of these"
} | multiply(subtract(divide(const_100, subtract(const_100, 20)), const_1), const_100) | subtract(const_100,n0)|divide(const_100,#0)|subtract(#1,const_1)|multiply(#2,const_100) | using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 20 % ) = > 20 / ( 100 - 20 ) * 100 = 25 % answer : b | general |
math_qa__V7yitpxN9QNfyxcZ | A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic? Options:
A) 240
B) 65
C) 110
D) 130
E) 200 | <gadget id="calculator">200 - 20</gadget>
<output>180</output>
<gadget id="calculator">180 / 2</gadget>
<output>90</output>
<gadget id="calculator">90 + 20</gadget>
<output>110</output>
<gadget id="calculator">110 - 20</gadget>
<output>90</output>
<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<gadget id="calculator">45 + 20</gadget>
<output>65</output>
<result>B</result> | B | 65 | A picnic attracts 200 persons. There are 20 more men than women, and 20 more adults than children. How many men are at this picnic? | {
"A": "240",
"B": "65",
"C": "110",
"D": "130",
"E": "200"
} | add(divide(subtract(add(divide(subtract(200, 20), const_2), 20), 20), const_2), 20) | subtract(n0,n1)|divide(#0,const_2)|add(n1,#1)|subtract(#2,n1)|divide(#3,const_2)|add(n1,#4) | adult + children = 200 let , children = y then , adult = y + 20 i . e . y + ( y + 20 ) = 200 i . e . y = 900 i . e . adult = 90 + 20 = 110 adults include only men and women i . e . men + women = 110 let women , w = x then men , m = x + 20 i . e . x + ( x + 20 ) = 2 x + 20 = 110 i . e . x = 45 i . e . men , m = 45 + 20 = 65 answer : option b | general |
math_qa__WU8f1l3n4VZyvauC | The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is: Choose one.
A) 30 / 7
B) 30 / 98
C) 60 / 147
D) 50 / 294
E) 52 / 294 | <gadget id="calculator">6 * 5</gadget>
<output>30</output>
<gadget id="calculator">30 / 7</gadget>
<output>30/7 = around 4.285714</output>
<result>A</result> | A | 4.285714 | The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is: | {
"A": "30 / 7",
"B": "30 / 98",
"C": "60 / 147",
"D": "50 / 294",
"E": "52 / 294"
} | divide(multiply(6, 5), 7) | multiply(n0,n2)|divide(#0,n1) | required fraction = l . c . m of 6 / 7 , 5 / 14 , 10 / 21 = ( l . c . m of 6 , 5 , 10 ) / ( h . c . f of 7 , 14 , 21 ) = 30 / 7 answer : a | general |
math_qa__REQKJn8iohZUEX3r | what is rate of interest if principal.amount be 400,simple interest 180 and time 2year. Choose the correct choice:
A) 10 B) 12.5 C) 25 D) 22.5 E) 14.5 | <gadget id="calculator">400 * 2</gadget>
<output>800</output>
<gadget id="calculator">180 / 800</gadget>
<output>9/40 = around 0.225</output>
<gadget id="calculator">(9/40) * 100</gadget>
<output>45/2 = around 22.5</output>
<result>D</result> | D | 22.5 | what is rate of interest if principal.amount be 400,simple interest 180 and time 2year. | {
"A": "10",
"B": "12.5",
"C": "25",
"D": "22.5",
"E": "14.5"
} | multiply(divide(180, multiply(400, 2)), const_100) | multiply(n0,n2)|divide(n1,#0)|multiply(#1,const_100)| | "s . i = ( p * r * t ) / 100 180 = 800 r / 100 r = 180 / 8 = 22.5 % answer d" | gain |
math_qa__EnFh4TaAScu2Pcqk | David biked 16 1/3 miles in 2 hours and 20 minutes. What was his average rate of speed in miles per hour? Select the correct option.
A) 7 B) 7 2 / 3 C) 8 1 / 3 D) 9 E) 9 1 / 3 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">16 + (1/3)</gadget>
<output>49/3 = around 16.333333</output>
<gadget id="calculator">20 / 60</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">2 + (1/3)</gadget>
<output>7/3 = around 2.333333</output>
<gadget id="calculator">(49/3) / (7/3)</gadget>
<output>7</output>
<result>A</result> | A | 7 | David biked 16 1/3 miles in 2 hours and 20 minutes. What was his average rate of speed in miles per hour? | {
"A": "7",
"B": "7 2 / 3",
"C": "8 1 / 3",
"D": "9",
"E": "9 1 / 3"
} | divide(add(16, const_0_33), add(2, divide(20, const_60))) | add(n0,const_0_33)|divide(n4,const_60)|add(n3,#1)|divide(#0,#2) | d = 16 ( 1 / 3 ) = 49 / 3 t = 2 ( 1 / 3 ) = 7 / 3 s = d / t = 7 answer = a | physics |
math_qa__1eJKu8RrxvQKuY55 | A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 50% have red flags, what percentage of children have flags of both the colors? Choose the correct choice from the following:
A) 5 % B) 10 % C) 15 % D) 20 % E) it can not be determined | <gadget id="calculator">60 + 50</gadget>
<output>110</output>
<gadget id="calculator">110 - 100</gadget>
<output>10</output>
<result>B</result> | B | 10 | A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 50% have red flags, what percentage of children have flags of both the colors? | {
"A": "5 %",
"B": "10 %",
"C": "15 %",
"D": "20 %",
"E": "it can not be determined"
} | subtract(add(60, 50), const_100) | add(n0,n1)|subtract(#0,const_100)| | "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 50 % = 50 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 50 - c = 100 c = 10 option b ." | general |
math_qa__OM7nQ1oVsc6VxvXZ | Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quartely. Choose the most appropriate option
A) rs . 2522 B) rs . 2512 C) rs . 2572 D) rs . 2592 E) none | <gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 3</gadget>
<output>9_261/8_000 = around 1.157625</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 * 100</gadget>
<output>1_600</output>
<gadget id="calculator">100 ** (1/2)</gadget>
<output>10</output>
<gadget id="calculator">1_600 * 10</gadget>
<output>16_000</output>
<gadget id="calculator">(9_261/8_000) * 16_000</gadget>
<output>18_522</output>
<gadget id="calculator">18_522 - 16_000</gadget>
<output>2_522</output>
<result>A</result> | A | 2,522 | Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quartely. | {
"A": "rs . 2522",
"B": "rs . 2512",
"C": "rs . 2572",
"D": "rs . 2592",
"E": "none"
} | subtract(multiply(power(add(const_1, divide(divide(20, const_4), const_100)), const_3), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100))), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100))) | divide(n1,const_4)|multiply(const_4,const_4)|sqrt(const_100)|divide(#0,const_100)|multiply(#1,const_100)|add(#3,const_1)|multiply(#4,#2)|power(#5,const_3)|multiply(#6,#7)|subtract(#8,#6)| | "solution principal = rs . 16,000 ; time = 9 months = 3 quarters ; amount = rs . [ 16000 x ( 1 + 5 / 100 ) ³ ] = [ 16000 x 21 / 20 x 21 / 20 x 21 / 20 ] = rs . 18522 . c . i = rs . ( 18522 - 16000 ) = rs . 2522 . answer a" | gain |
math_qa__xwQgIIobCouxJBSx | The mean of 50 observations was 36. It was found later that an observation 28 was wrongly taken as 23. The corrected new mean is : Answers:
A) 36.0
B) 36.5
C) 36.1
D) 36.2
E) 36.8 | <gadget id="calculator">36 * 50</gadget>
<output>1_800</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 - 23</gadget>
<output>25</output>
<gadget id="calculator">1_800 + 25</gadget>
<output>1_825</output>
<gadget id="calculator">1_825 / 50</gadget>
<output>73/2 = around 36.5</output>
<result>C</result> | C | 36.1 | The mean of 50 observations was 36. It was found later that an observation 28 was wrongly taken as 23. The corrected new mean is : | {
"A": "36.0",
"B": "36.5",
"C": "36.1",
"D": "36.2",
"E": "36.8"
} | divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50) | multiply(n0,n1)|subtract(n0,const_2)|subtract(#1,n3)|add(#0,#2)|divide(#3,n0)| | "explanation : correct sum = ( 36 * 50 + 28 - 23 ) = 1825 . correct mean = = 1805 / 50 = 36.1 answer : c ) 36.1" | general |
math_qa__VNBiaRi7r26JOLnN | In a games hour 4 different types of players came to the ground? cricket 22, hokey 15, football 21, softball 19. How many players are present in the ground? Choices
A) 70 B) 52 C) 62 D) 77 E) 79 | <gadget id="calculator">22 + 15</gadget>
<output>37</output>
<gadget id="calculator">21 + 19</gadget>
<output>40</output>
<gadget id="calculator">37 + 40</gadget>
<output>77</output>
<result>D</result> | D | 77 | In a games hour 4 different types of players came to the ground? cricket 22, hokey 15, football 21, softball 19. How many players are present in the ground? | {
"A": "70",
"B": "52",
"C": "62",
"D": "77",
"E": "79"
} | add(add(22, 15), add(21, 19)) | add(n1,n2)|add(n3,n4)|add(#0,#1)| | "total number of players = 22 + 15 + 21 + 19 = 77 answer is d" | physics |
math_qa__d8c3qoKWtKKLQUgE | An alloy is to contain copper and zinc in the ratio 5:3. The zinc required to be melted with 40kg of copper is? Select: A) 15 kg B) 20 kg C) 8 kg D) 24 kg E) 32 kg | <gadget id="calculator">40 * 3</gadget>
<output>120</output>
<gadget id="calculator">120 / 5</gadget>
<output>24</output>
<result>D</result> | D | 24 | An alloy is to contain copper and zinc in the ratio 5:3. The zinc required to be melted with 40kg of copper is? | {
"A": "15 kg",
"B": "20 kg",
"C": "8 kg",
"D": "24 kg",
"E": "32 kg"
} | divide(multiply(40, 3), 5) | multiply(n1,n2)|divide(#0,n0) | let the required quantity of copper be x kg 5 : 3 : : 40 : x 5 x = 40 * 3 x = 24 kg answer is d | other |
math_qa__AOQQ8iz9RGhXd6Ls | If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 348, the cost of the article is Choose the most appropriate option:
A) 289
B) 231
C) 200
D) 40
E) 111 | <gadget id="calculator">350 - 348</gadget>
<output>2</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">2 / (1/20)</gadget>
<output>40</output>
<result>D</result> | D | 40 | If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 348, the cost of the article is | {
"A": "289",
"B": "231",
"C": "200",
"D": "40",
"E": "111"
} | divide(subtract(350, 348), divide(5, const_100)) | divide(n0,const_100)|subtract(n1,n2)|divide(#1,#0)| | "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 348 = 2 x / 20 = 2 = > x = 40 answer : d" | gain |
math_qa__9Qy2kfIi8ra96ySi | Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 20 percent alcohol by volume? Choices
A) 200
B) 300
C) 400
D) 500
E) 600 | <gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">30 - 20</gadget>
<output>10</output>
<gadget id="calculator">10 / 10</gadget>
<output>1</output>
<gadget id="calculator">1 * 200</gadget>
<output>200</output>
<result>A</result> | A | 200 | Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 20 percent alcohol by volume? | {
"A": "200",
"B": "300",
"C": "400",
"D": "500",
"E": "600"
} | multiply(divide(subtract(20, 10), subtract(30, 20)), 200) | subtract(n3,n0)|subtract(n1,n3)|divide(#0,#1)|multiply(n2,#2)| | "20 % is an equal distance between 10 % and 30 % . thus there should be equal parts of both solutions . we should add 200 ml of solution y . the answer is a ." | general |
math_qa__Rl06PoTiA244liSi | The ratio 6 : 3 expressed as a percent equals
Choose one.
A) 12.5 % B) 40 % C) 80 % D) 200 % E) none | <gadget id="calculator">6 / 3</gadget>
<output>2</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<result>D</result> | D | 200 | The ratio 6 : 3 expressed as a percent equals | {
"A": "12.5 %",
"B": "40 %",
"C": "80 %",
"D": "200 %",
"E": "none"
} | multiply(divide(6, 3), const_100) | divide(n0,n1)|multiply(#0,const_100)| | "solution 6 : 3 = 6 / 3 = ( 6 / 3 x 100 ) % . = 200 % . answer d" | general |
math_qa__e1vSz5xgnmzg8ddQ | The average weight of 8 person's increases by 6 kg when a new person comes in place of one of them weighing 40 kg. What might be the weight of the new person? Options.
A) 80 kg B) 85 kg C) 90 kg D) 88 kg E) 110 kg | <gadget id="calculator">8 * 6</gadget>
<output>48</output>
<gadget id="calculator">48 + 40</gadget>
<output>88</output>
<result>D</result> | D | 88 | The average weight of 8 person's increases by 6 kg when a new person comes in place of one of them weighing 40 kg. What might be the weight of the new person? | {
"A": "80 kg",
"B": "85 kg",
"C": "90 kg",
"D": "88 kg",
"E": "110 kg"
} | add(multiply(8, 6), 40) | multiply(n0,n1)|add(n2,#0)| | "total weight increased = ( 8 x 6 ) kg = 48 kg . weight of new person = ( 40 + 48 ) kg = 88 kg . answer : d" | general |
math_qa__MhwYBhkpdKWizhgn | 16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work? Choose the correct choice from the following
A) 23 B) 27 C) 20 D) 27 E) 11 | <gadget id="calculator">25 * 16</gadget>
<output>400</output>
<gadget id="calculator">400 / 20</gadget>
<output>20</output>
<result>C</result> | C | 20 | 16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work? | {
"A": "23",
"B": "27",
"C": "20",
"D": "27",
"E": "11"
} | divide(multiply(25, 16), 20) | multiply(n0,n1)|divide(#0,n2)| | "16 * 25 = 20 * x = > x = 20 days answer : c" | physics |
math_qa__YFtX2om5RLrDkqtY | If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 30
Choose the correct choice from the following options: A) 11 B) 13 C) 15 D) 17 E) 18 | <gadget id="calculator">432 * 44</gadget>
<output>19_008</output>
<gadget id="calculator">19_008 % 30</gadget>
<output>18</output>
<result>E</result> | E | 18 | If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 30 | {
"A": "11",
"B": "13",
"C": "15",
"D": "17",
"E": "18"
} | reminder(multiply(432, 44), 30) | multiply(n0,n1)|reminder(#0,n3)| | "p ã · 44 = 432 = > p = 432 * 44 = 19008 p / 30 = 19008 / 30 = 633 , remainder = 18 e" | general |
math_qa__aQWduXiQjSUxpgDP | In country Z, 18% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?
Choose the correct choice from the following answers
A) 37 % B) 45 % C) 55 % D) 65 % E) 75 % | <gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">25 * 60</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 / 100</gadget>
<output>15</output>
<gadget id="calculator">40 - 18</gadget>
<output>22</output>
<gadget id="calculator">15 + 22</gadget>
<output>37</output>
<result>A</result> | A | 37 | In country Z, 18% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma? | {
"A": "37 %",
"B": "45 %",
"C": "55 %",
"D": "65 %",
"E": "75 %"
} | add(divide(multiply(25, subtract(const_100, 40)), const_100), subtract(40, 18)) | subtract(const_100,n2)|subtract(n2,n0)|multiply(n1,#0)|divide(#2,const_100)|add(#3,#1)| | "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 18 % job of choice total = 40 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 25 % of 60 % = 15 % . we can also see that 30 % of the people have their job of choice and a diploma ( 40 % - 18 % = 22 % ) . 22 % + 15 % = 37 % . therefore 37 % of the people in country z have a diploma . ans a" | gain |
math_qa__7ZSgtgBab33ZZge9 | If 0.5 of a number is equal to 0.09 of another number, the ratio of the numbers i Pick one:
A) 2 : 3
B) 3 : 4
C) 3 : 20
D) 3 : 7
E) 9 : 50 | <gadget id="calculator">0.09 * 100</gadget>
<output>9</output>
<gadget id="calculator">0.5 * 100</gadget>
<output>50</output>
<gadget id="calculator">9 / 50</gadget>
<output>9/50 = around 0.18</output>
<result>E</result> | E | 0.18 | If 0.5 of a number is equal to 0.09 of another number, the ratio of the numbers i | {
"A": "2 : 3",
"B": "3 : 4",
"C": "3 : 20",
"D": "3 : 7",
"E": "9 : 50"
} | divide(multiply(0.09, const_100), multiply(0.5, const_100)) | multiply(n1,const_100)|multiply(n0,const_100)|divide(#0,#1) | sol . 0.5 a = 0.09 b â ‡ ” a / b = 0.09 / 0.50 = 9 / 50 â ˆ ´ a : b = 9 : 50 . answer e | other |
math_qa__Wc2AiLhylup9dfNT | Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 70 km apart both 3 and 6 hours after start, then find the distance between the two stations. Choose the correct option:
A) 210 km
B) 240 km
C) 220 km
D) 180 km
E) 190 km | <gadget id="calculator">70 * 2</gadget>
<output>140</output>
<gadget id="calculator">140 + 70</gadget>
<output>210</output>
<result>A</result> | A | 210 | Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 70 km apart both 3 and 6 hours after start, then find the distance between the two stations. | {
"A": "210 km",
"B": "240 km",
"C": "220 km",
"D": "180 km",
"E": "190 km"
} | add(multiply(70, 2), 70) | multiply(n1,n2)|add(n2,#0) | in first 3 hours t 1 travels r km and t 2 travels s km . after 6 hours they traveled r + s + 70 + 700 2 ( r + s ) = r + s + 140 r + s = 140 hence distance between xy is r + s + 70 = 140 + 70 = 210 answer : a | physics |
math_qa__mN3Mu7KwW4vQMcB5 | among 7 numbers the average of first 4 numbers is 13 and the average of last 4 numbers is 15 . the sum of last 3 numbers is 55 . the square of the fourth number is equal to the last number then what is the last number ? Options.
A) 60 B) 52 C) 5 D) 25 E) 125 | <gadget id="calculator">4 * 15</gadget>
<output>60</output>
<gadget id="calculator">60 - 55</gadget>
<output>5</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<result>D</result> | D | 25 | among 7 numbers the average of first 4 numbers is 13 and the average of last 4 numbers is 15 . the sum of last 3 numbers is 55 . the square of the fourth number is equal to the last number then what is the last number ? | {
"A": "60",
"B": "52",
"C": "5",
"D": "25",
"E": "125"
} | power(subtract(multiply(4, 15), 55), const_2) | multiply(n1,n4)|subtract(#0,n6)|power(#1,const_2) | let the numbers be a , b , c , d , e , f , g d + e + f + g = 15 * 4 = 60 e + f + g = 55 , 60 - 55 = 5 so the fourth number is 5 . the square is 25 . the answer is option d . | general |
math_qa__DByeWHS7QPG83FQr | A driver would have reduced the time it took to drive from home to the store by 1/3 if the average speed had been increased by 12 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store?
Choices: A) 16 B) 20 C) 24 D) 28 E) 32 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 12</gadget>
<output>8</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">8 / (1/3)</gadget>
<output>24</output>
<result>C</result> | C | 24 | A driver would have reduced the time it took to drive from home to the store by 1/3 if the average speed had been increased by 12 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store? | {
"A": "16",
"B": "20",
"C": "24",
"D": "28",
"E": "32"
} | divide(multiply(subtract(1, divide(1, 3)), 12), subtract(1, subtract(1, divide(1, 3)))) | divide(n0,n1)|subtract(n0,#0)|multiply(#1,n2)|subtract(n0,#1)|divide(#2,#3)| | "since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 12 r / 2 = 12 r = 24 the answer is c ." | general |
math_qa__qBoTlAIoAEuuz5J6 | The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum Q of all the digits of the integers from 0 to 99 inclusive?
Select.
A) 450 B) 810 C) 900 D) 1000 E) 1100 | <gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">45 * 20</gadget>
<output>900</output>
<result>C</result> | C | 900 | The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum Q of all the digits of the integers from 0 to 99 inclusive? | {
"A": "450",
"B": "810",
"C": "900",
"D": "1000",
"E": "1100"
} | multiply(divide(multiply(9, add(9, 1)), 2), multiply(2, const_10)) | add(n6,n3)|multiply(const_10,n7)|multiply(n6,#0)|divide(#2,n7)|multiply(#3,#1)| | "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just q = 900 : the answer is c ." | general |
math_qa__8AuwA4uoSdVbzYfk | A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 126.Find the number of notes of Rs.50 denomination. Choose the correct choice from the following options
A) 115 B) 121 C) 117 D) 119 E) 121 | <gadget id="calculator">500 * 126</gadget>
<output>63_000</output>
<gadget id="calculator">63_000 - 10_350</gadget>
<output>52_650</output>
<gadget id="calculator">500 - 50</gadget>
<output>450</output>
<gadget id="calculator">52_650 / 450</gadget>
<output>117</output>
<result>C</result> | C | 117 | A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 126.Find the number of notes of Rs.50 denomination. | {
"A": "115",
"B": "121",
"C": "117",
"D": "119",
"E": "121"
} | divide(subtract(multiply(500, 126), 10350), subtract(500, 50)) | multiply(n2,n3)|subtract(n2,n1)|subtract(#0,n0)|divide(#2,#1)| | "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 126 - x now , 50 * x + 500 * ( 126 - x ) = 10350 50 x + 63000 - 500 x = 10350 - 450 x = - 52650 x = 117 . no . of 50 rupees note = 117 . answer : option c" | general |
math_qa__wFKibg8CCJcZ47Ex | A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 33. Find the profit percentage? Pick one
A) 65 %
B) 50 %
C) 59 %
D) 40 %
E) 53 % | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">33 * 5</gadget>
<output>165</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<gadget id="calculator">165 - 100</gadget>
<output>65</output>
<result>A</result> | A | 65 | A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 33. Find the profit percentage? | {
"A": "65 %",
"B": "50 %",
"C": "59 %",
"D": "40 %",
"E": "53 %"
} | subtract(multiply(33, add(const_4, const_1)), multiply(25, const_4)) | add(const_1,const_4)|multiply(n1,const_4)|multiply(n3,#0)|subtract(#2,#1)| | "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 165 ( 33 * 5 ) profit percentage = ( 165 - 100 ) / 100 * 100 = 65 % answer : a" | gain |
math_qa__WzgHVn2lmLmb8VOU | 3 different containers contain 496 litres , 403 litres and 713 litres of mixtures of milk and water respectively . what biggest measure can measure all the different quantities exactly ? Choose the correct choice: A) 30 litres B) 31 litres C) 32 litres D) 33 litres E) 34 litres | <gadget id="calculator">12 + 3</gadget>
<output>15</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">15 + 16</gadget>
<output>31</output>
<result>B</result> | B | 31 | 3 different containers contain 496 litres , 403 litres and 713 litres of mixtures of milk and water respectively . what biggest measure can measure all the different quantities exactly ? | {
"A": "30 litres",
"B": "31 litres",
"C": "32 litres",
"D": "33 litres",
"E": "34 litres"
} | add(add(const_12, 3), multiply(multiply(multiply(const_2, const_2), const_2), const_2)) | add(n0,const_12)|multiply(const_2,const_2)|multiply(#1,const_2)|multiply(#2,const_2)|add(#0,#3) | 403 ) 713 ( 1 403 - - - - - - - - - 310 ) 403 ( 1 310 - - - - - - - - - - 93 ) 310 ( 3 279 - - - - - - - - 31 ) 93 ( 3 93 - - - - - - - x so answer is 31 litres . . . . . . answer : b | physics |
math_qa__aVtEjBcocb2rHtDE | 12 persons can complete the work in 18 days. after working for 6 days, 4 more persons added to complete the work fast. in how many more days they will complete the work? Choose the correct choice from the following answers: A) 10 days B) 9 days C) 8 days D) 7 days E) 6 days | <gadget id="calculator">18 - 6</gadget>
<output>12</output>
<gadget id="calculator">12 * 12</gadget>
<output>144</output>
<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">144 / 16</gadget>
<output>9</output>
<result>B</result> | B | 9 | 12 persons can complete the work in 18 days. after working for 6 days, 4 more persons added to complete the work fast. in how many more days they will complete the work? | {
"A": "10 days",
"B": "9 days",
"C": "8 days",
"D": "7 days",
"E": "6 days"
} | divide(multiply(subtract(18, 6), 12), add(12, 4)) | add(n0,n3)|subtract(n1,n2)|multiply(n0,#1)|divide(#2,#0) | total work 12 * 18 = 216 units after 6 days work finished 6 * 12 = 72 units remaining work 216 - 72 = 144 units remaing days = 144 ( 12 + 4 ) = 9 days answer : b | physics |
math_qa__kqBI8H8Kq9X6zGQr | There are 870 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female? Choices:
A) 75 B) 100 C) 125 D) 175 E) 145 | <gadget id="calculator">870 / 3</gadget>
<output>290</output>
<gadget id="calculator">290 * 4</gadget>
<output>1_160</output>
<gadget id="calculator">1_160 - 870</gadget>
<output>290</output>
<gadget id="calculator">290 / 2</gadget>
<output>145</output>
<result>E</result> | E | 145 | There are 870 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female? | {
"A": "75",
"B": "100",
"C": "125",
"D": "175",
"E": "145"
} | divide(subtract(multiply(divide(870, const_3), const_4), 870), const_2) | divide(n0,const_3)|multiply(#0,const_4)|subtract(#1,n0)|divide(#2,const_2)| | "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 870 . hence , we have m + f = 870 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 870 / 3 = 290 solving the three equations yields the solution f = 290 , m = 580 , and d = 290 . the number of female democratic participants equals half the female participants equals 290 / 2 = 145 . answer : e" | general |
math_qa__DSzlGG2DKtMeiciZ | is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 37, then how old is B? Choose the correct choice from the following: A) 7 B) 8 C) 9 D) 10 E) 14 | <gadget id="calculator">37 - 2</gadget>
<output>35</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">35 / 5</gadget>
<output>7</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<result>E</result> | E | 14 | is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 37, then how old is B? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10",
"E": "14"
} | multiply(divide(subtract(37, const_2), add(const_3, const_2)), const_2) | add(const_2,const_3)|subtract(n0,const_2)|divide(#1,#0)|multiply(#2,const_2)| | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 37 5 x = 35 = > x = 7 hence , b ' s age = 2 x = 14 years . answer : e" | general |
math_qa__81QBcdmYrgLqPL67 | A batsman scored 150runs which included 5 boundaries and 5 sixes. What percent of his total score did he make by running between the wickets. Choices
A) 40 % B) 50 % C) 60 % D) 66.66 % E) 70 % | <gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 + 25</gadget>
<output>50</output>
<gadget id="calculator">150 - 50</gadget>
<output>100</output>
<gadget id="calculator">100 / 150</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 100</gadget>
<output>200/3 = around 66.666667</output>
<result>D</result> | D | 66.66 | A batsman scored 150runs which included 5 boundaries and 5 sixes. What percent of his total score did he make by running between the wickets. | {
"A": "40 %",
"B": "50 %",
"C": "60 %",
"D": "66.66 %",
"E": "70 %"
} | multiply(divide(subtract(150, add(multiply(5, 5), multiply(5, 5))), 150), const_100) | multiply(n1,n2)|multiply(n1,n2)|add(#0,#1)|subtract(n0,#2)|divide(#3,n0)|multiply(#4,const_100)| | "explanation : number of runs made by running = 150 - ( 5 x 4 + 5 x 6 ) = 150 - ( 50 ) = 100 now , we need to calculate 100 is what percent of 150 . = > 100 / 150 * 100 = 66.66 % option d" | general |
math_qa__isEbuLVZhbax3e8g | Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7380 km and comes back to the starting point. The total time taken by him is:
Pick: A) 914.2 hours B) 937.1 hours C) 915 hours D) 905 hours E) 915 hours | <gadget id="calculator">16 + 2</gadget>
<output>18</output>
<gadget id="calculator">7_380 / 18</gadget>
<output>410</output>
<gadget id="calculator">16 - 2</gadget>
<output>14</output>
<gadget id="calculator">7_380 / 14</gadget>
<output>3_690/7 = around 527.142857</output>
<gadget id="calculator">410 + (3_690/7)</gadget>
<output>6_560/7 = around 937.142857</output>
<result>B</result> | B | 937.1 | Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7380 km and comes back to the starting point. The total time taken by him is: | {
"A": "914.2 hours",
"B": "937.1 hours",
"C": "915 hours",
"D": "905 hours",
"E": "915 hours"
} | add(divide(7380, add(16, 2)), divide(7380, subtract(16, 2))) | add(n0,n1)|subtract(n0,n1)|divide(n2,#0)|divide(n2,#1)|add(#2,#3)| | "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7380 / 18 + 7380 / 14 = 410 + 527.1 = 937.1 hours answer : option b" | physics |
math_qa__JiGX9AChXCo7gHQR | A jar of 220 marbles is divided equally among a group of marble-players today. If 2 people joined the group in the future, each person would receive 1 marble less. How many people are there in the group today?
Choose the correct choice from the following options.
A) 20
B) 21
C) 22
D) 23
E) 24 | <gadget id="calculator">220 * 2</gadget>
<output>440</output>
<gadget id="calculator">440 * 4</gadget>
<output>1_760</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">1_760 + 4</gadget>
<output>1_764</output>
<gadget id="calculator">1_764 ** (1/2)</gadget>
<output>42</output>
<gadget id="calculator">42 - 2</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>A</result> | A | 20 | A jar of 220 marbles is divided equally among a group of marble-players today. If 2 people joined the group in the future, each person would receive 1 marble less. How many people are there in the group today? | {
"A": "20",
"B": "21",
"C": "22",
"D": "23",
"E": "24"
} | divide(subtract(sqrt(add(multiply(multiply(220, 2), const_4), power(2, 2))), 2), const_2) | multiply(n0,n1)|power(n1,n1)|multiply(#0,const_4)|add(#2,#1)|sqrt(#3)|subtract(#4,n1)|divide(#5,const_2) | 220 = 20 * 11 = 22 * 10 there are 20 people in the group today . the answer is a . | general |
math_qa__jduZap9aiLdlwsUu | A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train? Choose the correct option: A) 100 meter B) 170 meter C) 156 meter D) 168 meter E) 154 meter | <gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 6</gadget>
<output>100</output>
<result>A</result> | A | 100 | A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train? | {
"A": "100 meter",
"B": "170 meter",
"C": "156 meter",
"D": "168 meter",
"E": "154 meter"
} | multiply(divide(multiply(60, const_1000), const_3600), 6) | 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 ) * 6 = 100 meter answer : a" | physics |
math_qa__LoOXSyFHXrd1Xo4L | A chemist mixes one liter of pure water with x liters of a 60% salt solution, and the resulting mixture is a 20% salt solution. What is the value of x? Choose the correct choice.
A) 1 / 4 B) 1 / 3 C) 1 / 2 D) 1 E) 3 | <gadget id="calculator">60 - 20</gadget>
<output>40</output>
<gadget id="calculator">20 / 40</gadget>
<output>1/2 = around 0.5</output>
<result>C</result> | C | 0.5 | A chemist mixes one liter of pure water with x liters of a 60% salt solution, and the resulting mixture is a 20% salt solution. What is the value of x? | {
"A": "1 / 4",
"B": "1 / 3",
"C": "1 / 2",
"D": "1",
"E": "3"
} | divide(20, subtract(60, 20)) | subtract(n0,n1)|divide(n1,#0)| | "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 20 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 20 ) / ( 20 - 0 ) = 2 / 1 1 / x = 2 / 1 x = 1 / 2 answer : c" | gain |
math_qa__LOH7cF6QdZcK2c1S | If a and b are the roots of the equation x2 - 4x + 4 = 0, then the value of a2 + b2 is: Choose the correct choice from the following answers.
A) 36 B) 24 C) 17 D) 8 E) 5 | <gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 - 16</gadget>
<output>0</output>
<gadget id="calculator">0 ** (1/2)</gadget>
<output>0</output>
<gadget id="calculator">4 - 0</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 0</gadget>
<output>4</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<result>D</result> | D | 8 | If a and b are the roots of the equation x2 - 4x + 4 = 0, then the value of a2 + b2 is: | {
"A": "36",
"B": "24",
"C": "17",
"D": "8",
"E": "5"
} | add(power(divide(subtract(4, sqrt(subtract(power(4, 2), multiply(const_4, 4)))), 2), 2), power(divide(add(4, sqrt(subtract(power(4, 2), multiply(const_4, 4)))), 2), 2)) | multiply(n1,const_4)|power(n1,n0)|subtract(#1,#0)|sqrt(#2)|add(n1,#3)|subtract(n1,#3)|divide(#5,n0)|divide(#4,n0)|power(#6,n0)|power(#7,n0)|add(#8,#9)| | "sol . ( b ) the sum of roots = a + b = 4 product of roots = ab = 4 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 16 - 8 = 8 answer d" | general |
math_qa__37enC4eRUhCqaOaR | If (m-8) is a factor of m^2-sm-24, then s= Choose the correct answer:
A) 3 B) 5 C) 6 D) 11 E) 16 | <gadget id="calculator">24 / 8</gadget>
<output>3</output>
<gadget id="calculator">8 - 3</gadget>
<output>5</output>
<result>B</result> | B | 5 | If (m-8) is a factor of m^2-sm-24, then s= | {
"A": "3",
"B": "5",
"C": "6",
"D": "11",
"E": "16"
} | subtract(8, divide(24, 8)) | divide(n2,n0)|subtract(n0,#0)| | "( m - 8 ) ( m - a ) = m ^ 2 - sm - 24 a = - 3 s = 8 + a = 5 = d = b" | general |
math_qa__aN6cdHlGIAfz7aGv | a dice has one of the first 4 prime number on each its 6 sides , with no two sides having the same number . the dice is rolled 10 times and the results added . the addition is most likely to be closet to Select the correct option
A) 41
B) 43
C) 60
D) 68
E) 70 | <gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">10 + 7</gadget>
<output>17</output>
<gadget id="calculator">7 + 4</gadget>
<output>11</output>
<gadget id="calculator">17 + 11</gadget>
<output>28</output>
<gadget id="calculator">2 + 11</gadget>
<output>13</output>
<gadget id="calculator">28 + 13</gadget>
<output>41</output>
<result>B</result> | B | 43 | a dice has one of the first 4 prime number on each its 6 sides , with no two sides having the same number . the dice is rolled 10 times and the results added . the addition is most likely to be closet to | {
"A": "41",
"B": "43",
"C": "60",
"D": "68",
"E": "70"
} | add(add(add(add(add(const_2, divide(6, const_2)), add(const_2, const_3)), add(const_3, const_4)), add(add(const_3, const_4), const_4)), add(const_2, add(add(const_3, const_4), const_4))) | add(const_2,const_3)|add(const_3,const_4)|divide(n1,const_2)|add(#2,const_2)|add(#1,const_4)|add(#3,#0)|add(#4,const_2)|add(#5,#1)|add(#7,#4)|add(#8,#6) | if die is rolled then avg score = ( 2 + 3 + 5 + 7 ) / 4 = 41 / 4 so , most likely sum for 10 times = 41 / 4 * 10 = 43 answer : b | general |
math_qa__uecD21VCS9LmJynt | Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.7%, what fraction of the products was checked by worker y?
Choose the correct answer
A) 2 / 3 B) 5 / 6 C) 7 / 8 D) 4 / 5 E) 5 / 8 | <gadget id="calculator">0.7 - 0.5</gadget>
<output>0.2</output>
<gadget id="calculator">0.8 - 0.5</gadget>
<output>0.3</output>
<gadget id="calculator">0.2 / 0.3</gadget>
<output>0.666667</output>
<result>A</result> | A | 0.666667 | Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.7%, what fraction of the products was checked by worker y? | {
"A": "2 / 3",
"B": "5 / 6",
"C": "7 / 8",
"D": "4 / 5",
"E": "5 / 8"
} | divide(subtract(0.7, 0.5), subtract(0.8, 0.5)) | subtract(n2,n0)|subtract(n1,n0)|divide(#0,#1) | x : 0.5 % is 0.2 % - points from 0.7 % . y : 0.8 % is 0.1 % - points from 0.7 % . therefore the ratio of products checked by y : x is 2 : 1 . thus , worker y checked 2 / 3 of the products . the answer is a . | general |
math_qa__RkoX6LfF7K6Arpi9 | If A is thrice as fast as B and together can do a work in 18 days. In how many days A alone can do the work? Choices:
A) 36 B) 42 C) 24 D) 54 E) 45 | <gadget id="calculator">18 * 4</gadget>
<output>72</output>
<gadget id="calculator">3 / 72</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">1 / (1/24)</gadget>
<output>24</output>
<result>C</result> | C | 24 | If A is thrice as fast as B and together can do a work in 18 days. In how many days A alone can do the work? | {
"A": "36",
"B": "42",
"C": "24",
"D": "54",
"E": "45"
} | inverse(divide(const_3, multiply(18, const_4))) | multiply(n0,const_4)|divide(const_3,#0)|inverse(#1)| | "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 18 = 3 + 1 / 3 x = 4 / 3 x = 1 / 18 x = 18 * 4 / 3 = 24 answer : c" | physics |
math_qa__4kJ1vpIzHl5r2Mzw | What is the average of first 21 multiples of 4 ? Choose the correct choice.
A) 44 B) 77 C) 79 D) 81 E) 82 | <gadget id="calculator">21 + 1</gadget>
<output>22</output>
<gadget id="calculator">21 * 22</gadget>
<output>462</output>
<gadget id="calculator">462 / 2</gadget>
<output>231</output>
<gadget id="calculator">231 / 21</gadget>
<output>11</output>
<gadget id="calculator">11 * 4</gadget>
<output>44</output>
<result>A</result> | A | 44 | What is the average of first 21 multiples of 4 ? | {
"A": "44",
"B": "77",
"C": "79",
"D": "81",
"E": "82"
} | multiply(divide(divide(multiply(21, add(21, const_1)), const_2), 21), 4) | add(n0,const_1)|multiply(n0,#0)|divide(#1,const_2)|divide(#2,n0)|multiply(n1,#3)| | "required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 4 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 44 a" | general |
math_qa__nd8ekrsaZMMMoOcp | A factory produces 3400 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? Select the correct option
A) 575 toys B) 375 toys C) 680 toys D) 475 toys E) 675 toys | <gadget id="calculator">3_400 / 5</gadget>
<output>680</output>
<result>C</result> | C | 680 | A factory produces 3400 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? | {
"A": "575 toys",
"B": "375 toys",
"C": "680 toys",
"D": "475 toys",
"E": "675 toys"
} | divide(3400, 5) | divide(n0,n1)| | "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 3400 / 5 = 680 toys correct answer c" | physics |
math_qa__x4CeTINGMNFwA6PJ | If the cost price is 99% of selling price then what is the profit percentage.
Pick.
A) 1 B) 1.11 C) 1.01 D) 1.1 E) 1.21 | <gadget id="calculator">100 - 99</gadget>
<output>1</output>
<gadget id="calculator">1 / 99</gadget>
<output>1/99 = around 0.010101</output>
<gadget id="calculator">(1/99) * 100</gadget>
<output>100/99 = around 1.010101</output>
<result>C</result> | C | 1.01 | If the cost price is 99% of selling price then what is the profit percentage. | {
"A": "1",
"B": "1.11",
"C": "1.01",
"D": "1.1",
"E": "1.21"
} | multiply(divide(subtract(const_100, 99), 99), const_100) | subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)| | "selling price = rs 100 : then cost price = rs 99 : profit = rs 1 . profit = { ( 1 / 99 ) * 100 } % = 1.01 % answer is c ." | gain |
math_qa__T3ZboxpxBhZXUntE | g(a) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(y) is divisible by 4^11, what is the smallest possible value for a? Choose the correct choice from the following
A) 22 B) 24 C) 28 D) 32 E) 44 | <gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">2 * 11</gadget>
<output>22</output>
<gadget id="calculator">22 + 2</gadget>
<output>24</output>
<result>B</result> | B | 24 | g(a) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(y) is divisible by 4^11, what is the smallest possible value for a? | {
"A": "22",
"B": "24",
"C": "28",
"D": "32",
"E": "44"
} | add(multiply(divide(4, const_2), 11), const_2) | divide(n3,const_2)|multiply(n10,#0)|add(#1,const_2) | g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b | general |
math_qa__F2B9ql2HdU6gMHG0 | J is 25% less than P and 20% less than T. T is w% less than P. What is the value of w? Choices.
A) 93.5 B) 90 C) 6.75 D) 6.25 E) 2 | <gadget id="calculator">25 * 25</gadget>
<output>625</output>
<gadget id="calculator">625 / 100</gadget>
<output>25/4 = around 6.25</output>
<result>D</result> | D | 6.25 | J is 25% less than P and 20% less than T. T is w% less than P. What is the value of w? | {
"A": "93.5",
"B": "90",
"C": "6.75",
"D": "6.25",
"E": "2"
} | divide(multiply(25, 25), const_100) | multiply(n0,n0)|divide(#0,const_100)| | "usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( w / 100 ) ] * p i . e . 100 - w = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . w = 6.25 answer : option d" | gain |
math_qa__lSD1BtuCaqRIXb7i | How many litres of pure acid are there in 4 litres of a 35% solution Choices:
A) 1.5 B) 1.6 C) 1.7 D) 1.8 E) 1.4 | <gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 4</gadget>
<output>7/5 = around 1.4</output>
<result>E</result> | E | 1.4 | How many litres of pure acid are there in 4 litres of a 35% solution | {
"A": "1.5",
"B": "1.6",
"C": "1.7",
"D": "1.8",
"E": "1.4"
} | multiply(divide(35, const_100), 4) | divide(n1,const_100)|multiply(n0,#0)| | explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 8 * 20 / 100 = 1.4 answer : option e | gain |
math_qa__KkVbxrUDjaaC1iLj | Last year Department Store X had a sales total for December that was 7 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year? Choose the correct answer
A) 1 / 4 B) 4 / 15 C) 1 / 3 D) 7 / 18 E) 4 / 5 | <gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">11 + 7</gadget>
<output>18</output>
<gadget id="calculator">7 / 18</gadget>
<output>7/18 = around 0.388889</output>
<result>D</result> | D | 0.388889 | Last year Department Store X had a sales total for December that was 7 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year? | {
"A": "1 / 4",
"B": "4 / 15",
"C": "1 / 3",
"D": "7 / 18",
"E": "4 / 5"
} | divide(7, add(subtract(const_12, const_1), 7)) | subtract(const_12,const_1)|add(n0,#0)|divide(n0,#1)| | "let avg for 11 mos . = 10 therefore , dec = 70 year total = 11 * 10 + 70 = 180 answer = 70 / 180 = 7 / 18 = d" | general |
math_qa__rIXnQDuNV6VKr0c4 | A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
Choices
A) 1 : 2 B) 2 : 5 C) 6 ' ' 2 D) 3 : 1 E) 4 : 7 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">3 / 1</gadget>
<output>3</output>
<result>D</result> | D | 3 | A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is: | {
"A": "1 : 2",
"B": "2 : 5",
"C": "6 ' ' 2",
"D": "3 : 1",
"E": "4 : 7"
} | divide(add(const_1, const_2), subtract(const_2, const_1)) | add(const_1,const_2)|subtract(const_2,const_1)|divide(#0,#1) | explanation : let speed upstream = x hen , speed downstream = 2 x speed in still water = 2 x + x / 2 speed of the stream = 2 x - x / 2 speed in still water : speed of the stream = 3 x / 2 : x / 2 = 3 : 1 answer : d | physics |
math_qa__uOod5tMTf8wZVC6l | The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is? Choose the correct choice from the following choices:
A) 9
B) 11
C) 15
D) 12
E) 20 | <gadget id="calculator">15 * 15</gadget>
<output>225</output>
<gadget id="calculator">5 * 14</gadget>
<output>70</output>
<gadget id="calculator">9 * 16</gadget>
<output>144</output>
<gadget id="calculator">70 + 144</gadget>
<output>214</output>
<gadget id="calculator">225 - 214</gadget>
<output>11</output>
<result>B</result> | B | 11 | The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is? | {
"A": "9",
"B": "11",
"C": "15",
"D": "12",
"E": "20"
} | subtract(multiply(15, 15), add(multiply(5, 14), multiply(9, 16))) | multiply(n0,n0)|multiply(n2,n3)|multiply(n4,n5)|add(#1,#2)|subtract(#0,#3)| | "age of the 15 th student = 15 * 15 - ( 14 * 5 + 16 * 9 ) = 225 - 214 = 11 years answer is b" | general |
math_qa__M6IihFCroQ7Odwle | A shopkeeper sold an article at $100 with 10% profit. Then find its cost price? Choose one:
A) $ 120
B) $ 100
C) $ 91
D) $ 72
E) $ 69 | <gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">100 / 110</gadget>
<output>10/11 = around 0.909091</output>
<gadget id="calculator">100 * (10/11)</gadget>
<output>1_000/11 = around 90.909091</output>
<result>C</result> | C | 91 | A shopkeeper sold an article at $100 with 10% profit. Then find its cost price? | {
"A": "$ 120",
"B": "$ 100",
"C": "$ 91",
"D": "$ 72",
"E": "$ 69"
} | multiply(100, divide(100, add(100, 10))) | add(n1,n0)|divide(n0,#0)|multiply(n0,#1)| | "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 110 = $ 91 ( approximately ) answer is c" | gain |
math_qa__PXRSnsKtWTV4Szww | A glass was filled with 12 ounces of water, and 0.03 ounce of the water evaporated each day during a 22-day period. What percent of the original amount of water evaporated during this period?
Pick one:
A) 5.002 % B) 5.5 % C) 0.5 % D) 5 % E) 20 % | <gadget id="calculator">0.03 * 22</gadget>
<output>0.66</output>
<gadget id="calculator">0.66 / 12</gadget>
<output>0.055</output>
<gadget id="calculator">0.055 * 100</gadget>
<output>5.5</output>
<result>B</result> | B | 5.5 | A glass was filled with 12 ounces of water, and 0.03 ounce of the water evaporated each day during a 22-day period. What percent of the original amount of water evaporated during this period? | {
"A": "5.002 %",
"B": "5.5 %",
"C": "0.5 %",
"D": "5 %",
"E": "20 %"
} | multiply(divide(multiply(0.03, 22), 12), const_100) | multiply(n1,n2)|divide(#0,n0)|multiply(#1,const_100)| | "in 22 days 22 * 0.03 = 0.66 ounces of water evaporated , which is 0.66 / 12 â ˆ — 100 = 5.5 of the original amount of water . answer : b ." | gain |
math_qa__lZbXKo9m3yBf1ecv | Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $38 of gas? Choose the correct option.
A) 212
B) 256
C) 304
D) 372
E) 460 | <gadget id="calculator">38 * 32</gadget>
<output>1_216</output>
<gadget id="calculator">1_216 / 4</gadget>
<output>304</output>
<result>C</result> | C | 304 | Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $38 of gas? | {
"A": "212",
"B": "256",
"C": "304",
"D": "372",
"E": "460"
} | divide(multiply(38, 32), 4) | multiply(n0,n2)|divide(#0,n1)| | "38 / 4 = 9.5 gallons 9.5 * 32 = 304 miles the answer is c ." | physics |
math_qa__cOa1McY0eKcd4RWT | If x+y=20, x-y=10, for integers of x and y, x=? Choose the correct choice from the following answers: A) 15 B) 20 C) 25 D) 13 E) 42 | <gadget id="calculator">20 + 10</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<result>A</result> | A | 15 | If x+y=20, x-y=10, for integers of x and y, x=? | {
"A": "15",
"B": "20",
"C": "25",
"D": "13",
"E": "42"
} | divide(add(20, 10), const_2) | add(n0,n1)|divide(#0,const_2)| | "x + y = 20 x - y = 10 2 x = 30 x = 15 answer is a" | general |
math_qa__H4bIDJonm7vq6MCS | molly ' s age in 18 years will be 5 times her age 6 years ago . what is molly ' s present age ? Choose one:
A) 8 B) 9 C) 10 D) 12 E) 14 | <gadget id="calculator">18 - 6</gadget>
<output>12</output>
<result>D</result> | D | 12 | molly ' s age in 18 years will be 5 times her age 6 years ago . what is molly ' s present age ? | {
"A": "8",
"B": "9",
"C": "10",
"D": "12",
"E": "14"
} | subtract(18, 6) | subtract(n0,n2) | let x be molly ' s present age . x + 18 = 5 ( x - 6 ) x = 12 the answer is d . | general |
math_qa__wp0PMOag0hYXtbxY | in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3200 circuit boards where 64 fail inspection ?
Choose the correct choice from the following options: A) 72 B) 192 C) 456 D) 256 E) 264 | <gadget id="calculator">3_200 - 64</gadget>
<output>3_136</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">3_136 * (1/8)</gadget>
<output>392</output>
<gadget id="calculator">392 + 64</gadget>
<output>456</output>
<result>C</result> | C | 456 | in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3200 circuit boards where 64 fail inspection ? | {
"A": "72",
"B": "192",
"C": "456",
"D": "256",
"E": "264"
} | add(multiply(subtract(3200, 64), divide(1, 8)), 64) | divide(n0,n1)|subtract(n2,n3)|multiply(#0,#1)|add(n3,#2) | total of 3,200 boards . all that fail verification are indeed faulty . so the 64 are indeed faulty . 1 / 8 those that pass are also faulty . from the 3,200 we know 64 fail . so 3,136 must pass . of these 1 / 8 are faulty . 3,136 divided by 8 gives you 392 . what one must do now is to add to the 392 which were not detected the actually detected faulty ones , namely the 64 . total faulty : 456 . answer : c | other |
math_qa__tbfTJ6lv9QcfOvp6 | The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 90/kg. how much did a kg of coffee cost in june ?
Pick
A) 50 B) 60 C) 80 D) 90 E) 120 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(1/5) + 1</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(4/5) * (6/5)</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">90 / (24/25)</gadget>
<output>375/4 = around 93.75</output>
<result>D</result> | D | 90 | The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 90/kg. how much did a kg of coffee cost in june ? | {
"A": "50",
"B": "60",
"C": "80",
"D": "90",
"E": "120"
} | divide(90, multiply(subtract(const_1, divide(20, const_100)), add(divide(20, const_100), const_1))) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|divide(n2,#4)| | "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 900 gm ) of tea and 1 / 2 kg ( 900 gm ) of coffee ( equal quantities ) = 90 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 90 = > x = 90 thus proved . . . option d ." | general |
math_qa__p8Wm9YnULfVJzrim | A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? Choose the most appropriate option:
A) 108 % B) 300 % C) 100 % D) 180 % E) 200 % | <gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(3/4) / (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 100</gadget>
<output>150</output>
<gadget id="calculator">150 - 50</gadget>
<output>100</output>
<result>C</result> | C | 100 | A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? | {
"A": "108 %",
"B": "300 %",
"C": "100 %",
"D": "180 %",
"E": "200 %"
} | subtract(multiply(divide(divide(3, 4), divide(50, const_100)), const_100), 50) | divide(n0,n1)|divide(n2,const_100)|divide(#0,#1)|multiply(#2,const_100)|subtract(#3,n2) | mp = 100 cp = 75 sp = 150 - - - - - - 75 - - - - 75 100 - - - - ? = > 100 % answer : c | gain |
math_qa__Avy3c91HlFGCkmI6 | 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 24. What is half of that number? Choose the correct choice from the following answers: A) 670 B) 750 C) 945 D) 375 E) 315 | <gadget id="calculator">4 / 15</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">5 / 7</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">(4/15) * (5/7)</gadget>
<output>4/21 = around 0.190476</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">4 / 9</gadget>
<output>4/9 = around 0.444444</output>
<gadget id="calculator">(2/5) * (4/9)</gadget>
<output>8/45 = around 0.177778</output>
<gadget id="calculator">(4/21) - (8/45)</gadget>
<output>4/315 = around 0.012698</output>
<gadget id="calculator">24 / (4/315)</gadget>
<output>1_890</output>
<gadget id="calculator">1_890 / 2</gadget>
<output>945</output>
<result>C</result> | C | 945 | 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 24. What is half of that number? | {
"A": "670",
"B": "750",
"C": "945",
"D": "375",
"E": "315"
} | divide(divide(24, subtract(multiply(divide(4, 15), divide(5, 7)), multiply(divide(2, 5), divide(4, 9)))), 2) | divide(n0,n1)|divide(n2,n3)|divide(n6,n2)|divide(n0,n5)|multiply(#0,#1)|multiply(#2,#3)|subtract(#4,#5)|divide(n8,#6)|divide(#7,n6)| | "let no . be x 4 / 15 * 5 / 7 * x - 4 / 9 * 2 / 5 * x = 8 by further solving 20 x / 105 - 8 x / 45 = 8 4 x / 315 = 24 x = 1890 we have to find x / 2 = 1890 / 2 = 945 answer : c" | general |
math_qa__TvsK5OuCDWN8EIMV | A driver just filled the car's gas tank with 54 liters of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If the car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance? Select
A) 1.5
B) 2
C) 2.4
D) 2.7
E) 3 | <gadget id="calculator">54 * 5</gadget>
<output>270</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">270 / 90</gadget>
<output>3</output>
<result>E</result> | E | 3 | A driver just filled the car's gas tank with 54 liters of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If the car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance? | {
"A": "1.5",
"B": "2",
"C": "2.4",
"D": "2.7",
"E": "3"
} | divide(multiply(54, 5), subtract(const_100, 10)) | multiply(n0,n1)|subtract(const_100,n3)|divide(#0,#1)| | "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 54 ) + x = 0.1 ( 54 + x ) 0.9 x = 5.4 - 2.7 = 2.7 x = 3 liters the answer is e ." | general |
math_qa__qUOZaUceVkJDQNYU | 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? Choose the correct choice from the following options
A) 25 B) 30 C) 50 D) 55 E) 60 | <gadget id="calculator">20 / 40</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>C</result> | C | 50 | 20% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair? | {
"A": "25",
"B": "30",
"C": "50",
"D": "55",
"E": "60"
} | multiply(divide(20, 40), const_100) | divide(n0,n1)|multiply(#0,const_100) | 20 % of employees are women with fair hair . 40 % of fair - haired employees are women . so , 20 % * employees = 40 % * fair haired employees ( because both are equal to the number of fair haired women employees ) ( 1 / 2 ) * employees = fair haired employees answer ( c ) | gain |
math_qa__YIfXS7AOfiijIu8F | Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $10,000 and the marginal cost is $250, and the total cost is $16,000, what is the value of n? Pick:
A) 10 B) 24 C) 60 D) 70 E) 85 | <gadget id="calculator">250 / 10</gadget>
<output>25</output>
<result>B</result> | B | 24 | Marginal cost is the cost of increasing the quantity produced (or purchased) by one unit. If the fixed cost for n products is $10,000 and the marginal cost is $250, and the total cost is $16,000, what is the value of n? | {
"A": "10",
"B": "24",
"C": "60",
"D": "70",
"E": "85"
} | divide(250, const_10) | divide(n1,const_10)| | "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 10,000 + n * $ 250 - - > n = 24 . answer : b ." | general |
math_qa__XUiHj2Lde8VZWbdB | In a sports club with 30 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis? Choose the correct choice from the following choices:
A) 3 B) 5 C) 6 D) 7 E) 8 | <gadget id="calculator">17 + 19</gadget>
<output>36</output>
<gadget id="calculator">36 + 2</gadget>
<output>38</output>
<gadget id="calculator">38 - 30</gadget>
<output>8</output>
<result>E</result> | E | 8 | In a sports club with 30 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis? | {
"A": "3",
"B": "5",
"C": "6",
"D": "7",
"E": "8"
} | subtract(add(add(17, 19), 2), 30) | add(n1,n2)|add(n3,#0)|subtract(#1,n0)| | "17 + 19 = 36 but where as total number is 30 - 2 = 28 therefore answer is 36 - 28 = 8 hence answer is e" | other |
math_qa__o1ZvLLN872O3aqq5 | A boy want to make a cuboid of dimension 5m, 6m, 7m from small cubes of .04 m3. Later he realized he can make same cuboid by making it hollow. Then it takes some cubes less. What is the no. of these cubes?
Choose the correct choice from the following options: A) 2150 B) 2250 C) 2350 D) 2850 E) 3250 | <gadget id="calculator">5 * 6</gadget>
<output>30</output>
<gadget id="calculator">30 * 7</gadget>
<output>210</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">210 / (1/25)</gadget>
<output>5_250</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">20 * 6</gadget>
<output>120</output>
<gadget id="calculator">120 / (1/25)</gadget>
<output>3_000</output>
<gadget id="calculator">5_250 - 3_000</gadget>
<output>2_250</output>
<result>B</result> | B | 2,250 | A boy want to make a cuboid of dimension 5m, 6m, 7m from small cubes of .04 m3. Later he realized he can make same cuboid by making it hollow. Then it takes some cubes less. What is the no. of these cubes? | {
"A": "2150",
"B": "2250",
"C": "2350",
"D": "2850",
"E": "3250"
} | subtract(divide(multiply(multiply(5, 6), 7), divide(4, const_100)), divide(multiply(multiply(subtract(5, const_1), subtract(6, const_1)), subtract(7, const_1)), divide(4, const_100))) | divide(n3,const_100)|multiply(n0,n1)|subtract(n0,const_1)|subtract(n1,const_1)|subtract(n2,const_1)|multiply(n2,#1)|multiply(#2,#3)|divide(#5,#0)|multiply(#6,#4)|divide(#8,#0)|subtract(#7,#9) | volume of cuboid = 5 * 6 * 7 = 210 m 3 volume of inner cuboid = ( 5 - 1 ) * ( 6 - 1 ) * ( 7 - 1 ) = 120 m 3 therefore , volume of hollow cuboid = 210 - 120 = 90 m 3 no of cubes required = 90 / . 04 = 2250 cubes answer : b | physics |
math_qa__ViChmJs1qEMGx48U | A fill pipe can fill 1/2 of cistern in 10 minutes. In how many minutes, it can fill 1/2 of the cistern? Choose the correct choice from the following:
A) 1 min B) 4 min C) 6 min D) 10 min E) 25 min | <gadget id="calculator">10 / 1</gadget>
<output>10</output>
<result>D</result> | D | 10 | A fill pipe can fill 1/2 of cistern in 10 minutes. In how many minutes, it can fill 1/2 of the cistern? | {
"A": "1 min",
"B": "4 min",
"C": "6 min",
"D": "10 min",
"E": "25 min"
} | divide(10, 1) | divide(n2,n0)| | "required time = 10 * 2 * 1 / 2 = 10 minutes answer is d" | physics |
math_qa__DndYcuSBZCDuM3V7 | The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Choose the correct choice from the following.
A) 100 kg B) 102.5 kg C) 85 kg D) data inadequate E) none of these | <gadget id="calculator">10 * 3.5</gadget>
<output>35</output>
<gadget id="calculator">35 + 65</gadget>
<output>100</output>
<result>A</result> | A | 100 | The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person? | {
"A": "100 kg",
"B": "102.5 kg",
"C": "85 kg",
"D": "data inadequate",
"E": "none of these"
} | add(multiply(10, 3.5), 65) | multiply(n0,n1)|add(n2,#0)| | "explanation : total weight increased = ( 10 x 3.5 ) kg = 35 kg . weight of new person = ( 65 + 35 ) kg = 100 kg . answer : a" | general |
math_qa__BLW5SnJK2LvPC7RK | The average marks of 10 students in a class is 100. But a student mark is wrongly noted as 90 instead of 10 then find the correct average marks?
Choices.
A) 78 B) 82 C) 92 D) 91 E) 85 | <gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 90</gadget>
<output>910</output>
<gadget id="calculator">910 + 10</gadget>
<output>920</output>
<gadget id="calculator">920 / 10</gadget>
<output>92</output>
<result>C</result> | C | 92 | The average marks of 10 students in a class is 100. But a student mark is wrongly noted as 90 instead of 10 then find the correct average marks? | {
"A": "78",
"B": "82",
"C": "92",
"D": "91",
"E": "85"
} | divide(add(subtract(multiply(100, 10), 90), 10), 10) | multiply(n0,n1)|subtract(#0,n2)|add(n3,#1)|divide(#2,n0)| | "correct avg marks = 100 + ( 10 - 90 ) / 10 avg = 100 - 8 = 92 answer is c" | general |
math_qa__5Ejb9XO6ULCaBhn3 | What will be remainder when (67^67 + 67) is divided by 68 ?
Choose the correct choice from the following choices: A) 65 B) 66 C) 67 D) 71 E) 72 | <gadget id="calculator">67 - 68</gadget>
<output>-1</output>
<gadget id="calculator">(-1) ** 67</gadget>
<output>-1</output>
<gadget id="calculator">67 + (-1)</gadget>
<output>66</output>
<result>B</result> | B | 66 | What will be remainder when (67^67 + 67) is divided by 68 ? | {
"A": "65",
"B": "66",
"C": "67",
"D": "71",
"E": "72"
} | add(67, power(subtract(67, 68), 67)) | subtract(n0,n3)|power(#0,n0)|add(n0,#1) | ( xn + 1 ) will be divisible by ( x + 1 ) only when n is odd . ( 67 ^ 67 + 1 ) will be divisible by ( 67 + 1 ) ( 67 ^ 67 + 1 ) + 66 , when divided by 68 will give 66 as remainder . b ) | general |
math_qa__VI7OaPjLGkVtoOAe | A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? Choose the correct option.
A) s . 50 B) s . 46 C) s . 49 D) s . 41 E) s . 42 | <gadget id="calculator">1_000 * 25</gadget>
<output>25_000</output>
<gadget id="calculator">25_000 / 100</gadget>
<output>250</output>
<gadget id="calculator">250 / 5</gadget>
<output>50</output>
<result>A</result> | A | 50 | A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1000, what is the reduced price for kg? | {
"A": "s . 50",
"B": "s . 46",
"C": "s . 49",
"D": "s . 41",
"E": "s . 42"
} | divide(divide(multiply(1000, 25), const_100), 5) | multiply(n0,n2)|divide(#0,const_100)|divide(#1,n1)| | "1000 * ( 25 / 100 ) = 250 - - - - 5 ? - - - - 1 = > rs . 50 answer : a" | gain |
math_qa__AfxglIySfJwrQ4Uz | The perimeters of 2 squares are 60cm and 48cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares? Select the correct option:
A) 20 cm B) 28 cm C) 36 cm D) 48 cm E) 40 cm | <gadget id="calculator">60 / 4</gadget>
<output>15</output>
<gadget id="calculator">15 ** 2</gadget>
<output>225</output>
<gadget id="calculator">48 / 4</gadget>
<output>12</output>
<gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">225 - 144</gadget>
<output>81</output>
<gadget id="calculator">81 ** (1/2)</gadget>
<output>9</output>
<gadget id="calculator">4 * 9</gadget>
<output>36</output>
<result>C</result> | C | 36 | The perimeters of 2 squares are 60cm and 48cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares? | {
"A": "20 cm",
"B": "28 cm",
"C": "36 cm",
"D": "48 cm",
"E": "40 cm"
} | square_perimeter(sqrt(subtract(square_area(divide(60, const_4)), square_area(divide(48, const_4))))) | divide(n1,const_4)|divide(n2,const_4)|square_area(#0)|square_area(#1)|subtract(#2,#3)|sqrt(#4)|square_perimeter(#5) | side of the 1 st square = 60 / 4 = 15 cm side of the 2 nd square = 48 / 4 = 12 cm area of the 3 rd square = 15 ^ 2 - 12 ^ 2 = 81 cm ^ 2 side of the 3 rd square = 9 cm required perimeter = 9 * 4 = 36 cm answer is c | geometry |
math_qa__TdtSBgxNM5zYwAEA | The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $300, by what percent is the price to be reduced?
Choose the correct answer
A) 10 % B) 15 % C) 20 % D) 60 % E) 30 % | <gadget id="calculator">300 / 500</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<result>D</result> | D | 60 | The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $300, by what percent is the price to be reduced? | {
"A": "10 %",
"B": "15 %",
"C": "20 %",
"D": "60 %",
"E": "30 %"
} | multiply(divide(300, 500), const_100) | divide(n1,n0)|multiply(#0,const_100) | price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 300 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 300 ) * 100 / 500 = 60 % answer : option d | gain |
math_qa__JSf9TCitHEPZPs2S | ----------------YES---------NO----UNSURE Subject M----500--------200-----100 Subject R----400--------100-----300 A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 170 students answered yes only for subject M, how many of the students did not answer yes for either subject?
Answers: A) 100 B) 230 C) 300 D) 400 E) 500 | <gadget id="calculator">500 - 170</gadget>
<output>330</output>
<gadget id="calculator">170 + 330</gadget>
<output>500</output>
<gadget id="calculator">400 - 330</gadget>
<output>70</output>
<gadget id="calculator">500 + 70</gadget>
<output>570</output>
<gadget id="calculator">800 - 570</gadget>
<output>230</output>
<result>B</result> | B | 230 | ----------------YES---------NO----UNSURE Subject M----500--------200-----100 Subject R----400--------100-----300 A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 170 students answered yes only for subject M, how many of the students did not answer yes for either subject? | {
"A": "100",
"B": "230",
"C": "300",
"D": "400",
"E": "500"
} | subtract(800, add(add(170, subtract(500, 170)), subtract(400, subtract(500, 170)))) | subtract(n0,n7)|add(n7,#0)|subtract(n3,#0)|add(#1,#2)|subtract(n6,#3) | since 170 students answered yes only for subject m , then the remaining 330 students who answered yes for subject m , also answered yes for subject r . so , 330 students answered yes for both subjects . if 320 students answered yes for both subjects , then 400 - 330 = 70 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 70 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 70 + 300 ) = 230 students did not answer yes for either subject . answer : b . | general |
math_qa__YwXFq42PGFkS6vCD | A man can do a piece of work in 10days, but with the help of his son, he can finish it in 5days. In what time can the son do it alone? Select: A) 5 B) 8 C) 7 D) 10 E) 15 | <gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">10 - 5</gadget>
<output>5</output>
<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<result>D</result> | D | 10 | A man can do a piece of work in 10days, but with the help of his son, he can finish it in 5days. In what time can the son do it alone? | {
"A": "5",
"B": "8",
"C": "7",
"D": "10",
"E": "15"
} | divide(multiply(10, 5), subtract(10, 5)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | "son ' s 1 day work = 1 / 5 - 1 / 10 = 1 / 10 son alone can do the work in 10 days answer is d" | physics |
math_qa__lNdKGjz5oooHbkkg | Find large number from below question The difference of two numbers is 750. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder Choose the correct choice from the following answers.
A) 1345 B) 1250 C) 897 D) 900 E) 1635 | <gadget id="calculator">750 - 15</gadget>
<output>735</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">735 / 5</gadget>
<output>147</output>
<gadget id="calculator">147 * 6</gadget>
<output>882</output>
<result>C</result> | C | 897 | Find large number from below question The difference of two numbers is 750. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder | {
"A": "1345",
"B": "1250",
"C": "897",
"D": "900",
"E": "1635"
} | multiply(divide(subtract(750, 15), subtract(6, const_1)), 6) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | "let the smaller number be x . then larger number = ( x + 1365 ) . x + 750 = 6 x + 15 5 x = 735 x = 147 large number = 147 + 1365 = 897 c" | general |
math_qa__3kw4CcOMlAmT3plQ | A man, a woman and a boy can together complete a piece of work in 4 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work? Choose the correct choice from the following answers
A) 36 days B) 32 days C) 34 days D) 42 days E) 49 days | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/6) + (1/18)</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">(1/4) - (2/9)</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">1 / (1/36)</gadget>
<output>36</output>
<result>A</result> | A | 36 | A man, a woman and a boy can together complete a piece of work in 4 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work? | {
"A": "36 days",
"B": "32 days",
"C": "34 days",
"D": "42 days",
"E": "49 days"
} | inverse(subtract(inverse(4), add(inverse(6), inverse(18)))) | 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 / 4 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 woman ’ s 1 day ’ s work = 1 / 4 – 2 / 9 = 1 / 36 therefore , the woman alone can finish the work in 36 days . answer : option a" | physics |
math_qa__nEdBkUDUmfTQ4M9F | The price of lunch for 15 people was $210.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity? Choose the correct choice.
A) $ 11.73 B) $ 12.72 C) $ 13.80 D) $ 14.00 E) $ 15.87 | <gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">210 / 115</gadget>
<output>42/23 = around 1.826087</output>
<gadget id="calculator">(42/23) * 100</gadget>
<output>4_200/23 = around 182.608696</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(4_200/23) * (1/15)</gadget>
<output>280/23 = around 12.173913</output>
<result>B</result> | B | 12.72 | The price of lunch for 15 people was $210.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity? | {
"A": "$ 11.73",
"B": "$ 12.72",
"C": "$ 13.80",
"D": "$ 14.00",
"E": "$ 15.87"
} | multiply(multiply(divide(210.00, add(const_100, 15)), const_100), divide(const_1, 15)) | add(n0,const_100)|divide(const_1,n0)|divide(n1,#0)|multiply(#2,const_100)|multiply(#1,#3)| | "take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 210 is for 115 then we have to calculate for 100 for 115 210 for 100 x so by cross multiplication we get 115 x = 100 * 210 = > x = 100 * 210 / 110 by simplifying we get x as 190.90 which is the price of lunch before gratuity so the gratuity is 19.10 so as the question ask the average price person excluding gratuity is 190.90 / 15 = 12.72 so our answer is b )" | general |
math_qa__u4kBeiY8AlAzmhCH | 82
a7
+ 6b
____
190
If a and b represent positive single digits in the correctly worked computation above, what is the value of a + 2b ? Select.
A) 2 B) 6 C) 9 D) 11 E) 12 | <gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">190 - 60</gadget>
<output>130</output>
<gadget id="calculator">130 - 82</gadget>
<output>48</output>
<gadget id="calculator">48 - 7</gadget>
<output>41</output>
<gadget id="calculator">41 / 10</gadget>
<output>41/10 = around 4.1</output>
<gadget id="calculator">floor(41/10)</gadget>
<output>4</output>
<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">41 - 40</gadget>
<output>1</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<result>B</result> | B | 6 | 82
a7
+ 6b
____
190
If a and b represent positive single digits in the correctly worked computation above, what is the value of a + 2b ? | {
"A": "2",
"B": "6",
"C": "9",
"D": "11",
"E": "12"
} | add(multiply(subtract(subtract(subtract(subtract(190, multiply(6, const_10)), 82), 7), multiply(floor(divide(subtract(subtract(subtract(190, multiply(6, const_10)), 82), 7), const_10)), const_10)), 2), floor(divide(subtract(subtract(subtract(190, multiply(6, const_10)), 82), 7), const_10))) | multiply(n2,const_10)|subtract(n3,#0)|subtract(#1,n0)|subtract(#2,n1)|divide(#3,const_10)|floor(#4)|multiply(#5,const_10)|subtract(#3,#6)|multiply(n4,#7)|add(#5,#8) | adding the digits in unit ' s place , 2 + 7 + b = 10 ( since a and b are positive single digits ) = > b = 1 now adding the digits in ten ' s place , 8 + a + 6 + 1 = 19 ( 1 has been carried over from unit ' s place addition ) = > a = 4 a + 2 b = 4 + 2 * 1 = 6 answer b | physics |
math_qa__UnQQpV7feJ8nmOse | The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i
Choices
A) 70 B) 72 C) 75 D) 78 E) 80 | <gadget id="calculator">85 * 6</gadget>
<output>510</output>
<gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">510 + 240</gadget>
<output>750</output>
<gadget id="calculator">750 + 30</gadget>
<output>780</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">780 / 10</gadget>
<output>78</output>
<result>D</result> | D | 78 | The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income i | {
"A": "70",
"B": "72",
"C": "75",
"D": "78",
"E": "80"
} | divide(add(add(multiply(85, 6), multiply(60, 4)), 30), add(6, 4)) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|add(n4,#3)|divide(#4,#0)| | "income of 6 months = ( 6 × 85 ) – debt = 510 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 780 average monthly income = 780 ÷ 10 = 78 answer d" | general |
math_qa__aJhSgdzHosPJUIoH | In a certain alphabet, 13 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line? Choose the correct choice from the following: A) 3 B) 8 C) 14 D) 20 E) 28 | <gadget id="calculator">13 + 24</gadget>
<output>37</output>
<gadget id="calculator">40 - 37</gadget>
<output>3</output>
<result>A</result> | A | 3 | In a certain alphabet, 13 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line? | {
"A": "3",
"B": "8",
"C": "14",
"D": "20",
"E": "28"
} | subtract(40, add(13, 24)) | add(n0,n1)|subtract(n2,#0)| | "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 13 + 24 = 37 ; next , we find the total # of letters without line : 40 - 37 = 3 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 3 - 0 = 3 . a" | other |
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