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__cFa44Zn2gDTa9Qsd | The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 45 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons? Choose the correct choice from the following choices.
A) 55 B) 56 C) 57 D) 58 E) 60 | <gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">21 * 5</gadget>
<output>105</output>
<gadget id="calculator">105 - 45</gadget>
<output>60</output>
<result>E</result> | E | 60 | The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 45 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons? | {
"A": "55",
"B": "56",
"C": "57",
"D": "58",
"E": "60"
} | subtract(multiply(add(20, const_1), 5), 45) | add(n0,const_1)|multiply(n2,#0)|subtract(#1,n1)| | "20 x + 45 = 21 ( x – 5 ) x = 60 answer : e" | general |
math_qa__7ILgSfpB46mxuvny | Q and F represent two distinct digits. If the number 457Q89F is divisible by 36, what is the value of (Q+F)?
Choices:
A) 9 B) 3 C) 12 D) 6 E) 10 | <gadget id="calculator">89 % 10</gadget>
<output>9</output>
<gadget id="calculator">457 % 10</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<gadget id="calculator">8 + 7</gadget>
<output>15</output>
<gadget id="calculator">15 - 9</gadget>
<output>6</output>
<gadget id="calculator">9 - 6</gadget>
<output>3</output>
<result>B</result> | B | 3 | Q and F represent two distinct digits. If the number 457Q89F is divisible by 36, what is the value of (Q+F)? | {
"A": "9",
"B": "3",
"C": "12",
"D": "6",
"E": "10"
} | subtract(reminder(89, const_10), subtract(add(add(reminder(457, const_10), const_1), reminder(457, const_10)), reminder(89, const_10))) | reminder(n1,const_10)|reminder(n0,const_10)|add(#1,const_1)|add(#2,#1)|subtract(#3,#0)|subtract(#0,#4) | a no . divisible by 36 means it is div by 49 . to be div by 4 last 2 digits to be multiple of 4 so , f could be either 2 or 6 only similarly for a number to be div by 9 its sum must be multiple of 9 first . filtering we find q could be either 1 , 47 only . to be divisible by 9 only 1 works . ( if we choose f = 6 then q have to be 6 but as per condition qf are distinct ) so q = 1 f = 2 ans : - 3 . b | general |
math_qa__9T2gqPNFvrN0Nine | the total population of dogs in a community is estimated to be 50 % male and 50 % female . the total number of black dogs is 20 % greater than the total number of male black dogs . if the total number of female dogs is 8 times more than the number of female black dogs what percentage of male dogs is black ? Select the correct option: A) 84.4 B) 70.2 C) 80.1 D) 60.8 E) 62.5 | <gadget id="calculator">20 / 50</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<result>E</result> | E | 62.5 | the total population of dogs in a community is estimated to be 50 % male and 50 % female . the total number of black dogs is 20 % greater than the total number of male black dogs . if the total number of female dogs is 8 times more than the number of female black dogs what percentage of male dogs is black ? | {
"A": "84.4",
"B": "70.2",
"C": "80.1",
"D": "60.8",
"E": "62.5"
} | multiply(subtract(const_1, divide(20, 50)), const_100) | divide(n2,n0)|subtract(const_1,#0)|multiply(#1,const_100) | since we are dealing in percentage let us pick 100 as the number of black male dogs . that means that the total number of black dogs is = 120 ( 20 % more ) , therefore the number of black female dogs is 20 . the total number of female dogs is 8 x the number of black female = 20 * 8 = 160 female dogs . male dogs are 50 % of the dogs , and because there are 160 female dogs , then there must also be 160 male dogs therefore percentage of male dogs that are black = 100 / 160 * 100 = 62.5 correct option is e | general |
math_qa__E8WbqwXYxtiZiYrJ | When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.3 centimeter. The actual diameter of the tissue, in centimeters, is
Choose the correct option:
A) 0.005 B) 0.002 C) 0.001 D) 0.0003 E) 0.0002 | <gadget id="calculator">0.3 / 1_000</gadget>
<output>0.0003</output>
<result>D</result> | D | 0.0003 | When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.3 centimeter. The actual diameter of the tissue, in centimeters, is | {
"A": "0.005",
"B": "0.002",
"C": "0.001",
"D": "0.0003",
"E": "0.0002"
} | divide(0.3, 1,000) | divide(n1,n0)| | "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.3 then x = 0.3 / 1000 = 0.0003 . the answer is d" | geometry |
math_qa__v9kWSdIsdqgSVWu8 | The ratio 25:50 expressed as percent equals to Choose one
A) 50 % B) 85 % C) 25 % D) 75 % E) none of above | <gadget id="calculator">25 / 50</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>A</result> | A | 50 | The ratio 25:50 expressed as percent equals to | {
"A": "50 %",
"B": "85 %",
"C": "25 %",
"D": "75 %",
"E": "none of above"
} | multiply(divide(25, 50), const_100) | divide(n0,n1)|multiply(#0,const_100)| | "explanation : actually it means 25 is what percent of 50 , which can be calculated as , ( 25 / 50 ) * 100 = 25 * 2 = 50 answer : option a" | general |
math_qa__SyNyqv5zeZ9fXBxL | A man is 22 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Pick: A) 23 years B) 22 years C) 21 years D) 20 years E) 19 years | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">22 - 2</gadget>
<output>20</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">20 / 1</gadget>
<output>20</output>
<result>D</result> | D | 20 | A man is 22 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son? | {
"A": "23 years",
"B": "22 years",
"C": "21 years",
"D": "20 years",
"E": "19 years"
} | divide(subtract(22, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | "let present age of the son = x years then , present age the man = ( x + 22 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 22 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 20 answer : d" | general |
math_qa__GNJT6pYWp2c4WRIg | 18 beavers, working together in a constant pace, can build a dam in 8 hours. How many hours will it take 36 beavers that work at the same pace, to build the same dam? Choose the most appropriate option.
A) 2 . B) 4 . C) 5 . D) 6 E) 8 . | <gadget id="calculator">8 * 18</gadget>
<output>144</output>
<gadget id="calculator">144 / 36</gadget>
<output>4</output>
<result>B</result> | B | 4 | 18 beavers, working together in a constant pace, can build a dam in 8 hours. How many hours will it take 36 beavers that work at the same pace, to build the same dam? | {
"A": "2 .",
"B": "4 .",
"C": "5 .",
"D": "6",
"E": "8 ."
} | divide(multiply(8, 18), 36) | multiply(n0,n1)|divide(#0,n2)| | "total work = 18 * 8 = 144 beaver hours 36 beaver * x = 144 beaver hours x = 144 / 36 = 4 answer : b" | physics |
math_qa__aGnhefvA4Ea4DrwK | A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/6 hours to fill the tank. The leak can drain all the water of the tank in? Choose the most appropriate option
A) 17 hr B) 19 hr C) 10 hr D) 24 hr E) 26 hr | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">12 + 1</gadget>
<output>13</output>
<gadget id="calculator">13 / 6</gadget>
<output>13/6 = around 2.166667</output>
<gadget id="calculator">1 / (13/6)</gadget>
<output>6/13 = around 0.461538</output>
<gadget id="calculator">(1/2) - (6/13)</gadget>
<output>1/26 = around 0.038462</output>
<gadget id="calculator">1 / (1/26)</gadget>
<output>26</output>
<result>E</result> | E | 26 | A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/6 hours to fill the tank. The leak can drain all the water of the tank in? | {
"A": "17 hr",
"B": "19 hr",
"C": "10 hr",
"D": "24 hr",
"E": "26 hr"
} | inverse(subtract(divide(1, 2), inverse(divide(add(multiply(2, 6), 1), 6)))) | divide(n2,n0)|multiply(n0,n3)|add(n2,#1)|divide(#2,n3)|inverse(#3)|subtract(#0,#4)|inverse(#5)| | "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 6 ) = 1 / 26 leak will empty the tank in 26 hrs . answer : e" | physics |
math_qa__0kGxWnN5AvAA1fzN | 10 people went to a hotel for combine dinner party 5 of them spent Rs. 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10. What was the total money spent by them. Answers
A) 1628.4
B) 1534
C) 1492
D) 240
E) none of these | <gadget id="calculator">5 * 20</gadget>
<output>100</output>
<gadget id="calculator">10 - 5</gadget>
<output>5</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 5</gadget>
<output>24</output>
<gadget id="calculator">24 * 10</gadget>
<output>240</output>
<result>D</result> | D | 240 | 10 people went to a hotel for combine dinner party 5 of them spent Rs. 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10. What was the total money spent by them. | {
"A": "1628.4",
"B": "1534",
"C": "1492",
"D": "240",
"E": "none of these"
} | multiply(divide(add(multiply(5, 20), multiply(subtract(10, 5), 4)), subtract(10, subtract(10, 5))), 10) | multiply(n1,n2)|subtract(n0,n1)|multiply(n3,#1)|subtract(n0,#1)|add(#0,#2)|divide(#4,#3)|multiply(n0,#5)| | "solution : let average expenditure of 10 people be x . then , 10 x = 20 * 5 + 5 * ( x + 4 ) ; or , 10 x = 20 * 5 + 5 x + 20 ; or , x = 24 ; so , total money spent = 24 * 10 = rs . 240 . answer : option d" | general |
math_qa__FxLIbYAeqYcMfK0B | A sum is divided among W, X and Y in such a way that for each rupee W gets, X gets 30 paisa and Y gets 20 paisa. If the share of W is RS. 10, what is the total amount? Select the correct option
A) 12 B) 13 C) 14 D) 15 E) 16 | <gadget id="calculator">20 / 10</gadget>
<output>2</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<result>D</result> | D | 15 | A sum is divided among W, X and Y in such a way that for each rupee W gets, X gets 30 paisa and Y gets 20 paisa. If the share of W is RS. 10, what is the total amount? | {
"A": "12",
"B": "13",
"C": "14",
"D": "15",
"E": "16"
} | divide(30, divide(20, 10)) | divide(n1,n2)|divide(n0,#0) | w : x : y = 100 : 30 : 20 20 : 6 : 4 20 - - - 10 30 - - - ? = > 15 answer : d | general |
math_qa__xksqPD2x3dVVQPPS | A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 4 new workers. How many different ways can she assign the new workers? Pick:
A) 1485 B) 2700 C) 3300 D) 4860 E) 5400 | <gadget id="calculator">12 / 4</gadget>
<output>3</output>
<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">factorial(12)</gadget>
<output>479_001_600</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">40_320 * 24</gadget>
<output>967_680</output>
<gadget id="calculator">479_001_600 / 967_680</gadget>
<output>495</output>
<gadget id="calculator">3 * 495</gadget>
<output>1_485</output>
<result>A</result> | A | 1,485 | A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 4 new workers. How many different ways can she assign the new workers? | {
"A": "1485",
"B": "2700",
"C": "3300",
"D": "4860",
"E": "5400"
} | multiply(divide(factorial(divide(12, 4)), const_2), divide(factorial(12), multiply(factorial(subtract(12, 4)), factorial(4)))) | divide(n0,n1)|factorial(n0)|factorial(n1)|subtract(n0,n1)|factorial(#0)|factorial(#3)|divide(#4,const_2)|multiply(#5,#2)|divide(#1,#7)|multiply(#6,#8) | whatever : my take selecting team of 4 out of 12 to assign to the shifts = 12 c 4 = 495 ways . now 4 out of 12 means total of 3 group possible . so putting them in shifts = counting methode : first , second , third , = 3 * 2 * 1 = 6 here alt and alt are the same : so 6 / 2 = 3 ways . total ways of selecting = ( selecting 4 out of 12 ) * arranging those teams in shifts = 495 * 3 = 1485 ans : a | physics |
math_qa__OKhOhESeCJMW3K8i | if the price of a book is first decreased by 30% and then increased by 20%, then the net change in the price will be : Choose the correct choice from the following answers:
A) 10
B) 16
C) 37
D) 29
E) 22 | <gadget id="calculator">100 * 30</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 100</gadget>
<output>30</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">100 * 20</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(7/10) * (6/5)</gadget>
<output>21/25 = around 0.84</output>
<gadget id="calculator">(21/25) * 100</gadget>
<output>84</output>
<gadget id="calculator">100 - 84</gadget>
<output>16</output>
<result>B</result> | B | 16 | if the price of a book is first decreased by 30% and then increased by 20%, then the net change in the price will be : | {
"A": "10",
"B": "16",
"C": "37",
"D": "29",
"E": "22"
} | subtract(const_100, multiply(multiply(divide(subtract(const_100, divide(multiply(const_100, 30), const_100)), const_100), divide(add(const_100, divide(multiply(const_100, 20), const_100)), const_100)), const_100)) | multiply(n0,const_100)|multiply(n1,const_100)|divide(#0,const_100)|divide(#1,const_100)|add(#3,const_100)|subtract(const_100,#2)|divide(#5,const_100)|divide(#4,const_100)|multiply(#6,#7)|multiply(#8,const_100)|subtract(const_100,#9)| | "explanation : let the original price be rs . 100 . decreased by 30 % = 70 then increased 20 % on rs 70 = 70 + 14 = 84 net change in price = 100 - 84 = 16 answer : b" | general |
math_qa__ca3lEanb1jKTsy4m | A man can do a piece of work in 10days, but with the help of his son, he can do it in 4 days. In what time can the son do it alone?
Select the correct option
A) 13 / 2 B) 17 / 3 C) 15 / 2 D) 20 / 3 E) 9 | <gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">10 - 4</gadget>
<output>6</output>
<gadget id="calculator">40 / 6</gadget>
<output>20/3 = around 6.666667</output>
<result>D</result> | D | 6.666667 | A man can do a piece of work in 10days, but with the help of his son, he can do it in 4 days. In what time can the son do it alone? | {
"A": "13 / 2",
"B": "17 / 3",
"C": "15 / 2",
"D": "20 / 3",
"E": "9"
} | divide(multiply(10, 4), subtract(10, 4)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | "son ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 10 ) = 3 / 20 the son alone can do the work in 20 / 3 days answer is d" | physics |
math_qa__EIlaa8ZjNVjX7u9w | The cash difference between the selling prices of an book at a profit of 2% and 4% is $3. The ratio of the two selling prices is:
Choose the correct choice from the following options: A) 55 : 23 B) 52 : 33 C) 51 : 52 D) 45 : 53 E) 51 : 34 | <gadget id="calculator">100 + 2</gadget>
<output>102</output>
<gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">102 / 104</gadget>
<output>51/52 = around 0.980769</output>
<result>C</result> | C | 0.980769 | The cash difference between the selling prices of an book at a profit of 2% and 4% is $3. The ratio of the two selling prices is: | {
"A": "55 : 23",
"B": "52 : 33",
"C": "51 : 52",
"D": "45 : 53",
"E": "51 : 34"
} | divide(add(const_100, 2), add(const_100, 4)) | add(n0,const_100)|add(n1,const_100)|divide(#0,#1)| | "let c . p . of the book be $ x . then , required ratio = 102 % of x / 104 % of x = 102 / 104 = 51 / 52 = 51 : 52 c" | gain |
math_qa__QpS3J9XAS2eVuyo8 | How long does a train 100 m long running at the speed of 75 km/hr takes to cross a bridge 135 m length?
Select the correct option
A) 11.3 sec B) 12.1 sec C) 13.1 sec D) 16.5 sec E) 12.7 sec | <gadget id="calculator">100 + 135</gadget>
<output>235</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">75 * (5/18)</gadget>
<output>125/6 = around 20.833333</output>
<gadget id="calculator">235 / (125/6)</gadget>
<output>282/25 = around 11.28</output>
<result>A</result> | A | 11.3 | How long does a train 100 m long running at the speed of 75 km/hr takes to cross a bridge 135 m length? | {
"A": "11.3 sec",
"B": "12.1 sec",
"C": "13.1 sec",
"D": "16.5 sec",
"E": "12.7 sec"
} | divide(add(100, 135), multiply(75, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | "speed = 75 * 5 / 18 = 20.8 m / sec total distance covered = 100 + 135 = 235 m . required time = 235 / 20.8 ' = 11.3 sec . answer : a" | physics |
math_qa__lAxStjE7y5OAX8u0 | A person buys an article at $1200. At what price should he sell the article so as to make a profit of 40%?
Choose the correct choice from the following options.
A) 1670 B) 1600 C) 1680 D) 1900 E) 1230 | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1_200 * (2/5)</gadget>
<output>480</output>
<gadget id="calculator">1_200 + 480</gadget>
<output>1_680</output>
<result>C</result> | C | 1,680 | A person buys an article at $1200. At what price should he sell the article so as to make a profit of 40%? | {
"A": "1670",
"B": "1600",
"C": "1680",
"D": "1900",
"E": "1230"
} | add(1200, multiply(1200, divide(40, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1) | c 1680 cost price = $ 1200 profit = 40 % of 1200 = $ 480 selling price = cost price + profit = 1200 + 480 = 1680 | gain |
math_qa__NOLYK7gLyL3hO1or | In the coordinate plane, points (x, 8) and (20, y) are on line k. If line k passes through the origin and has slope 1/4, then x * y =
Choose the most appropriate option:
A) 120
B) 100
C) 135
D) 140
E) 160 | <gadget id="calculator">20 * 4</gadget>
<output>80</output>
<gadget id="calculator">8 / 4</gadget>
<output>2</output>
<gadget id="calculator">80 * 2</gadget>
<output>160</output>
<result>E</result> | E | 160 | In the coordinate plane, points (x, 8) and (20, y) are on line k. If line k passes through the origin and has slope 1/4, then x * y = | {
"A": "120",
"B": "100",
"C": "135",
"D": "140",
"E": "160"
} | multiply(multiply(20, 4), divide(8, 4)) | divide(n0,n3)|multiply(n1,n3)|multiply(#0,#1) | line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 8 ) = ( 32 , 8 ) and ( 20 , y ) = ( 20,5 ) - - > x * y = 32 * 5 = 160 . answer : e | general |
math_qa__9n1RJIwaNw9bXejY | bill is golfing with 3 friends and can either buy generic golf tees that are packaged by the dozen or the higher quality aero flight tees that come by the pair . what is the minimum number of packages of aero flight tees bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome , if he will buy no more than 2 packages of the generic golf tees ?
Pick one:
A) 16
B) 10
C) 28
D) 4
E) 2 | <gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">4 * 20</gadget>
<output>80</output>
<gadget id="calculator">2 * 12</gadget>
<output>24</output>
<gadget id="calculator">80 - 24</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<result>C</result> | C | 28 | bill is golfing with 3 friends and can either buy generic golf tees that are packaged by the dozen or the higher quality aero flight tees that come by the pair . what is the minimum number of packages of aero flight tees bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome , if he will buy no more than 2 packages of the generic golf tees ? | {
"A": "16",
"B": "10",
"C": "28",
"D": "4",
"E": "2"
} | divide(subtract(multiply(add(3, const_1), 20), multiply(2, const_12)), const_2) | add(n0,const_1)|multiply(n2,const_12)|multiply(n1,#0)|subtract(#2,#1)|divide(#3,const_2) | at least 20 golf tees for each member of his foursome = total of at least 4 * 20 = 80 tees . 2 packages of the generic golf tees , that are packaged by the dozen = 2 * 12 = 24 tees . so , bill must by at least 16 aero tees . they come by the pair , hence he must by at least 56 / 2 = 28 packages of aero flight tees . answer : c . | general |
math_qa__N6M57vZfxXhFwmkw | A man's speed with the current is 20 kmph and speed of the current is 3 kmph. The Man's speed
against the current will be Choose the correct choice:
A) 11 kmph B) 12 kmph C) 14 kmph D) 17 kmph E) none of these | <gadget id="calculator">20 - 3</gadget>
<output>17</output>
<gadget id="calculator">17 - 3</gadget>
<output>14</output>
<result>C</result> | C | 14 | A man's speed with the current is 20 kmph and speed of the current is 3 kmph. The Man's speed
against the current will be | {
"A": "11 kmph",
"B": "12 kmph",
"C": "14 kmph",
"D": "17 kmph",
"E": "none of these"
} | subtract(subtract(20, 3), 3) | subtract(n0,n1)|subtract(#0,n1)| | "explanation : if you solved this question yourself , then trust me you have a all very clear with the basics of this chapter . if not then lets solve this together . speed with current is 20 , speed of the man + it is speed of the current speed in still water = 20 - 3 = 17 now speed against the current will be speed of the man - speed of the current = 17 - 3 = 14 kmph option c" | physics |
math_qa__W6M16NtBFmowMrOz | Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996? Choose the correct choice from the following
A) $ 24 million B) $ 120 million C) $ 144 million D) $ 240 million E) $ 888 million | <gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">388 * 6</gadget>
<output>2_328</output>
<gadget id="calculator">1.44 * 1_000</gadget>
<output>1_440</output>
<gadget id="calculator">2_328 - 1_440</gadget>
<output>888</output>
<result>E</result> | E | 888 | Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996? | {
"A": "$ 24 million",
"B": "$ 120 million",
"C": "$ 144 million",
"D": "$ 240 million",
"E": "$ 888 million"
} | subtract(multiply(388, divide(const_12, const_2)), multiply(1.44, const_1000)) | divide(const_12,const_2)|multiply(n0,const_1000)|multiply(n2,#0)|subtract(#2,#1)| | "convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 388 mill / 2 month i . e . $ 194 mill / month difference / month = 194 - 120 = 74 difference / year = $ 74 mill * 12 = $ 988 mill answer : e" | general |
math_qa__7G0WQDPsSRIW2Abi | 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 70% of the total school population of x students, what is x? Choose the correct choice from the following choices.
A) 113 B) 150 C) 225 D) 250 E) 500 | <gadget id="calculator">90 * 100</gadget>
<output>9_000</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">9_000 / (7/10)</gadget>
<output>90_000/7 = around 12_857.142857</output>
<gadget id="calculator">(90_000/7) ** (1/2)</gadget>
<output>300*sqrt(7)/7 = around 113.389342</output>
<result>A</result> | A | 113 | 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 70% of the total school population of x students, what is x? | {
"A": "113",
"B": "150",
"C": "225",
"D": "250",
"E": "500"
} | sqrt(divide(multiply(90, const_100), divide(70, const_100))) | divide(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)|sqrt(#2)| | "90 = x / 100 * 70 / 100 * x = > x ^ 2 = 9 * 10000 / 7 = > x = 113 a" | gain |
math_qa__CPa23vccgwSNrmx4 | Square A has an area of 25 square centimeters. Square B has a perimeter of 12 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? Choices: A) 9 / 25 B) 1 / 5 C) 16 / 25 D) 3 / 5 E) 6 / 25 | <gadget id="calculator">12 / 4</gadget>
<output>3</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">25 - 9</gadget>
<output>16</output>
<gadget id="calculator">16 / 25</gadget>
<output>16/25 = around 0.64</output>
<result>C</result> | C | 0.64 | Square A has an area of 25 square centimeters. Square B has a perimeter of 12 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B? | {
"A": "9 / 25",
"B": "1 / 5",
"C": "16 / 25",
"D": "3 / 5",
"E": "6 / 25"
} | divide(subtract(25, power(divide(12, const_4), const_2)), 25) | divide(n1,const_4)|power(#0,const_2)|subtract(n0,#1)|divide(#2,n0)| | "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 12 , then its side is 12 / 4 = 3 and the area is 3 ^ 2 = 9 empty space between the squares is 25 - 9 = 16 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 16 / 25 . answer : c" | geometry |
math_qa__DwQ5TwMUDVJJUViL | The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres? Choose the correct choice:
A) 40 B) 50 C) 60 D) 70 E) 80 | <gadget id="calculator">5_300 / 26.5</gadget>
<output>200</output>
<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<gadget id="calculator">2 * 20</gadget>
<output>40</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<result>C</result> | C | 60 | The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres? | {
"A": "40",
"B": "50",
"C": "60",
"D": "70",
"E": "80"
} | subtract(divide(divide(5300, 26.5), const_2), multiply(const_2, 20)) | divide(n2,n1)|multiply(n0,const_2)|divide(#0,const_2)|subtract(#2,#1) | let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 / 26.50 m = 200 m . 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m . answer : c | physics |
math_qa__GP3YqzzHxBdueKDy | Two trains 150 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? Choose the most appropriate option:
A) 7.18 B) 7.12 C) 7.16 D) 7.55 E) 7.82 | <gadget id="calculator">150 + 165</gadget>
<output>315</output>
<gadget id="calculator">80 + 65</gadget>
<output>145</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">145 * (5/18)</gadget>
<output>725/18 = around 40.277778</output>
<gadget id="calculator">315 / (725/18)</gadget>
<output>1_134/145 = around 7.82069</output>
<result>E</result> | E | 7.82 | Two trains 150 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? | {
"A": "7.18",
"B": "7.12",
"C": "7.16",
"D": "7.55",
"E": "7.82"
} | divide(add(150, 165), multiply(add(80, 65), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | "t = ( 150 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.82 answer : e" | physics |
math_qa__PXvX8Ov0y70dwQLP | A train running at the speed of 50 km/hr crosses a pole in 9 sec. What is the length of the train?
Choose the correct choice from the following answers
A) 125 m
B) 150 m
C) 187 m
D) 167 m
E) 197 m | <gadget id="calculator">50 * 1_000</gadget>
<output>50_000</output>
<gadget id="calculator">50_000 / 3_600</gadget>
<output>125/9 = around 13.888889</output>
<gadget id="calculator">(125/9) * 9</gadget>
<output>125</output>
<result>A</result> | A | 125 | A train running at the speed of 50 km/hr crosses a pole in 9 sec. What is the length of the train? | {
"A": "125 m",
"B": "150 m",
"C": "187 m",
"D": "167 m",
"E": "197 m"
} | multiply(divide(multiply(50, const_1000), const_3600), 9) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = 50 * 5 / 18 = 125 / 9 m / sec length of the train = speed * time = 125 / 9 * 9 = 125 m answer : a" | physics |
math_qa__v87zr7dAUfJ548NU | Two-third of a positive number and 25/216 of its reciprocal are equal. The number is: Choose the correct choice from the following
A) 5 / 12 B) 12 / 5 C) 25 / 144 D) 144 / 25 E) 146 / 25 | <gadget id="calculator">25 * 3</gadget>
<output>75</output>
<gadget id="calculator">216 * 2</gadget>
<output>432</output>
<gadget id="calculator">75 / 432</gadget>
<output>25/144 = around 0.173611</output>
<gadget id="calculator">(25/144) ** (1/2)</gadget>
<output>5/12 = around 0.416667</output>
<result>A</result> | A | 0.416667 | Two-third of a positive number and 25/216 of its reciprocal are equal. The number is: | {
"A": "5 / 12",
"B": "12 / 5",
"C": "25 / 144",
"D": "144 / 25",
"E": "146 / 25"
} | sqrt(divide(multiply(25, const_3), multiply(216, const_2))) | multiply(n0,const_3)|multiply(n1,const_2)|divide(#0,#1)|sqrt(#2)| | "let the number be x . then , 2 / 3 x = 25 / 216 * 1 / x x 2 = 25 / 216 * 3 / 2 = 25 / 144 x = 5 / 12 answer : a" | general |
math_qa__bouu2AiSC9mJaxlg | if 50% of (x-y) = 40% of (x+y) then what percent of x is y? Choose the correct choice from the following:
A) 2.5 % B) 11 % C) 5 % D) 15 % E) 25 % | <gadget id="calculator">50 - 40</gadget>
<output>10</output>
<gadget id="calculator">50 + 40</gadget>
<output>90</output>
<gadget id="calculator">10 / 90</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/9) * 100</gadget>
<output>100/9 = around 11.111111</output>
<result>B</result> | B | 11 | if 50% of (x-y) = 40% of (x+y) then what percent of x is y? | {
"A": "2.5 %",
"B": "11 %",
"C": "5 %",
"D": "15 %",
"E": "25 %"
} | multiply(divide(subtract(50, 40), add(50, 40)), const_100) | add(n0,n1)|subtract(n0,n1)|divide(#1,#0)|multiply(#2,const_100)| | "50 % of ( x - y ) = 40 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 40 / 100 ) ( x + y ) 5 ( x - y ) = 4 ( x + y ) x = 9 y x = 9 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 9 y ) x 100 ) = 11 % answer is b ." | general |
math_qa__UgXVrswlH57l6DD7 | A certain quantity of 60% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
Answers.
A) 1 / 4 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 5 / 7 | <gadget id="calculator">35 - 25</gadget>
<output>10</output>
<gadget id="calculator">60 - 35</gadget>
<output>25</output>
<gadget id="calculator">10 / 25</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) + 1</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">1 / (7/5)</gadget>
<output>5/7 = around 0.714286</output>
<result>E</result> | E | 0.714286 | A certain quantity of 60% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced? | {
"A": "1 / 4",
"B": "1 / 3",
"C": "1 / 2",
"D": "2 / 3",
"E": "5 / 7"
} | inverse(add(divide(subtract(35, 25), subtract(60, 35)), const_1)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)|add(#2,const_1)|inverse(#3)| | "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 60 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 60 ml and 25 ml is 35 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 35 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 25 % . therefore , 25 out of 35 is 5 / 7 and e is the answer ." | other |
math_qa__m4lyRcJKKhoFYbf4 | Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team T. If team A's average speed was 5 mph greater than team T's, what was team T's average mph? Choose the most appropriate option: A) 12 B) 15 C) 18 D) 20 E) 25 | <gadget id="calculator">300 / 5</gadget>
<output>60</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<result>D</result> | D | 20 | Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team T. If team A's average speed was 5 mph greater than team T's, what was team T's average mph? | {
"A": "12",
"B": "15",
"C": "18",
"D": "20",
"E": "25"
} | divide(divide(300, 5), 3) | divide(n0,n2)|divide(#0,n1)| | "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team t ' s speed was s . then team t ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team t . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team t is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ." | physics |
math_qa__h2LQDRFBg5ILXaOk | A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is: Choose the correct option: A) 4 mph B) 2.5 mph C) 3 mph D) 2 mph E) none of these | <gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">100 * 4</gadget>
<output>400</output>
<gadget id="calculator">90 / 60</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">36 / (3/2)</gadget>
<output>24</output>
<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<gadget id="calculator">48 ** 2</gadget>
<output>2_304</output>
<gadget id="calculator">400 + 2_304</gadget>
<output>2_704</output>
<gadget id="calculator">2_704 ** (1/2)</gadget>
<output>52</output>
<gadget id="calculator">52 - 48</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<result>D</result> | D | 2 | A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is: | {
"A": "4 mph",
"B": "2.5 mph",
"C": "3 mph",
"D": "2 mph",
"E": "none of these"
} | divide(subtract(sqrt(add(multiply(power(10, const_2), const_4), power(multiply(divide(36, divide(90, const_60)), const_2), const_2))), multiply(divide(36, divide(90, const_60)), const_2)), const_2) | divide(n0,const_60)|power(n2,const_2)|divide(n1,#0)|multiply(#1,const_4)|multiply(#2,const_2)|power(#4,const_2)|add(#3,#5)|sqrt(#6)|subtract(#7,#4)|divide(#8,const_2) | explanation : speed of the boat in still water = 10 mph let speed of the stream be x mph then , speed downstream = ( 10 + x ) mph speed upstream = ( 10 - x ) mph time taken to travel 36 miles upstream - time taken to travel 36 miles downstream = 90 / 60 hours = > 36 / ( 10 − x ) − 36 / ( 10 + x ) = 3 / 2 = > 12 / ( 10 − x ) − 12 / ( 10 + x ) = 1 / 2 = > 24 ( 10 + x ) − 24 ( 10 − x ) = ( 10 + x ) ( 10 − x ) = > 240 + 24 x − 240 + 24 x = ( 100 − x 2 ) = > 48 x = 100 − x 2 = > x 2 + 48 x − 100 = 0 = > ( x + 50 ) ( x − 2 ) = 0 = > x = - 50 or 2 . answer : option d | physics |
math_qa__kGc98Hy2RNmWRgE9 | ) A cube is painted blue on all of its surfaces. It is then cut in to 27 smaller cubes of equal size. Find how many smaller cubes have no color?
Choose the correct choice from the following options:
A) 1 B) 3 C) 8 D) 5 E) 7 | <gadget id="calculator">27 / 3</gadget>
<output>9</output>
<gadget id="calculator">9 / 3</gadget>
<output>3</output>
<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">1 ** 3</gadget>
<output>1</output>
<result>A</result> | A | 1 | ) A cube is painted blue on all of its surfaces. It is then cut in to 27 smaller cubes of equal size. Find how many smaller cubes have no color? | {
"A": "1",
"B": "3",
"C": "8",
"D": "5",
"E": "7"
} | volume_cube(subtract(divide(divide(27, const_3), const_3), const_2)) | divide(n0,const_3)|divide(#0,const_3)|subtract(#1,const_2)|volume_cube(#2) | if the cube is cut in to 27 smaller cubes , then number of separations made = n = 3 ( since 3 × 3 × 3 = 27 ) . number of smaller cubes with no color = ( n – 2 ) 3 = ( 3 – 2 ) 3 = 13 = 1 answer : a | geometry |
math_qa__CKg9ZS1eoH54xFRr | A rectangular field has to be fenced on three sides leaving a side of 25 feet uncovered. If the area of the field is 880 sq. feet, how many feet of fencing will be required?
Select the correct option:
A) 75.4 feet B) 98.4 feet C) 95.4 feet D) 85.4 feet E) 92.4 feet | <gadget id="calculator">880 / 25</gadget>
<output>176/5 = around 35.2</output>
<gadget id="calculator">2 * (25 + (176/5))</gadget>
<output>602/5 = around 120.4</output>
<gadget id="calculator">(602/5) - 25</gadget>
<output>477/5 = around 95.4</output>
<result>C</result> | C | 95.4 | A rectangular field has to be fenced on three sides leaving a side of 25 feet uncovered. If the area of the field is 880 sq. feet, how many feet of fencing will be required? | {
"A": "75.4 feet",
"B": "98.4 feet",
"C": "95.4 feet",
"D": "85.4 feet",
"E": "92.4 feet"
} | subtract(rectangle_perimeter(25, divide(880, 25)), 25) | divide(n1,n0)|rectangle_perimeter(n0,#0)|subtract(#1,n0)| | "area of the field = 880 sq . feet . length of the adjacent sides are 25 feet and 880 / 25 = 35.2 feet . required length of the fencing = 25 + 35.2 + 35.2 = 95.4 feet answer : c" | geometry |
math_qa__jvZLLZez9EjTfJzT | x+(1/x) = 2.5 find x^2 + (1/x^2)
Pick one
A) 2.25 B) 3.25 C) 4.25 D) 5.25 E) 6.25 | <gadget id="calculator">2.5 ** 2</gadget>
<output>6.25</output>
<gadget id="calculator">6.25 - 2</gadget>
<output>4.25</output>
<result>C</result> | C | 4.25 | x+(1/x) = 2.5 find x^2 + (1/x^2) | {
"A": "2.25",
"B": "3.25",
"C": "4.25",
"D": "5.25",
"E": "6.25"
} | subtract(power(2.5, 2), 2) | power(n1,n2)|subtract(#0,n2)| | "squaring on both sides ( x + 1 / x ) ^ 2 = 2.5 ^ 2 x ^ 2 + 1 / x ^ 2 = 6.25 - 2 x ^ 2 + 1 / x ^ 2 = 4.25 answer : c" | general |
math_qa__zpjT3PQV0G2bKwtj | A = {0, 1, -3, 6, -8, -10}
B = {-1, 2, -4, 7, 6, -9}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab < 0? Options:
A) 1 / 4 B) 1 / 3 C) 5 / 13 D) 5 / 12 E) 1 / 2 | <gadget id="calculator">3 / 6</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * (1/2)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">2 / 6</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * (1/2)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/4) + (1/6)</gadget>
<output>5/12 = around 0.416667</output>
<result>D</result> | D | 0.416667 | A = {0, 1, -3, 6, -8, -10}
B = {-1, 2, -4, 7, 6, -9}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab < 0? | {
"A": "1 / 4",
"B": "1 / 3",
"C": "5 / 13",
"D": "5 / 12",
"E": "1 / 2"
} | add(multiply(divide(3, 6), divide(3, 6)), multiply(divide(2, 6), divide(const_3, 6))) | divide(n2,n3)|divide(n7,n3)|divide(const_3,n3)|multiply(#0,#0)|multiply(#1,#2)|add(#3,#4) | for the product of 2 numbers to be negative either of them must be positive or negative : p ( positive , negative ) = 2 / 6 * 3 / 6 = 6 / 36 ; p ( negative , positive ) = 3 / 6 * 3 / 6 = 9 / 36 p = 6 / 36 + 9 / 36 p = 15 / 36 p = 5 / 12 answer : d | general |
math_qa__ch9gOJejJ8Jx1mxM | Which number need to add to 172835 to get a number exactly divisible by 136? Choose the correct answer.
A) 27
B) 25
C) 26
D) 21
E) 24 | <gadget id="calculator">172_835 / 136</gadget>
<output>172_835/136 = around 1_270.845588</output>
<gadget id="calculator">floor(172_835/136)</gadget>
<output>1_270</output>
<gadget id="calculator">1_270 + 1</gadget>
<output>1_271</output>
<gadget id="calculator">1_271 - (172_835/136)</gadget>
<output>21/136 = around 0.154412</output>
<gadget id="calculator">136 * (21/136)</gadget>
<output>21</output>
<result>D</result> | D | 21 | Which number need to add to 172835 to get a number exactly divisible by 136? | {
"A": "27",
"B": "25",
"C": "26",
"D": "21",
"E": "24"
} | multiply(136, subtract(add(floor(divide(172835, 136)), const_1), divide(172835, 136))) | divide(n0,n1)|floor(#0)|add(#1,const_1)|subtract(#2,#0)|multiply(n1,#3)| | "172835 / 136 = 1270 and reminder = 115 . 136 - 115 = 21 so , the next number divisible by 115 is 21 places in front of 172835 which means 21 + 172835 = 172856 21 should be added to 172835 d" | general |
math_qa__8S5setKfZJ2dFHdd | A boy swims downstream 91 km and upstream 21 km taking 7 hours each time, what is the speed of the boy in still water? Choose the correct choice from the following choices: A) 6 B) 7 C) 8 D) 9 E) 10 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">91 / 7</gadget>
<output>13</output>
<gadget id="calculator">21 / 7</gadget>
<output>3</output>
<gadget id="calculator">13 + 3</gadget>
<output>16</output>
<gadget id="calculator">(1/2) * 16</gadget>
<output>8</output>
<result>C</result> | C | 8 | A boy swims downstream 91 km and upstream 21 km taking 7 hours each time, what is the speed of the boy in still water? | {
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "10"
} | multiply(divide(const_1, const_2), add(divide(91, 7), divide(21, 7))) | divide(n0,n2)|divide(n1,n2)|divide(const_1,const_2)|add(#0,#1)|multiply(#3,#2) | 91 - - - 7 ds = 13 ? - - - - 1 21 - - - - 7 us = 3 ? - - - - 1 m = ? m = ( 13 + 3 ) / 2 = 8 answer : c | physics |
math_qa__56Rvr9j6Eme8F96t | the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 10 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? Choose the correct choice:
A) 10 B) 15 C) 20 D) 15 / 2 E) 24 | <gadget id="calculator">10 - 4</gadget>
<output>6</output>
<gadget id="calculator">5 / 60</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">6 * (1/12)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) / 4</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 60</gadget>
<output>15/2 = around 7.5</output>
<result>D</result> | D | 7.5 | the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 10 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? | {
"A": "10",
"B": "15",
"C": "20",
"D": "15 / 2",
"E": "24"
} | multiply(divide(multiply(subtract(10, 4), divide(5, const_60)), 4), const_60) | divide(n2,const_60)|subtract(n1,n0)|multiply(#0,#1)|divide(#2,n0)|multiply(#3,const_60) | after passing the hiker the cyclist travels for 5 minutes at a rate of 10 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 6 miles . in those 5 mins the hiker travels a distance of 1 / 2 miles . so the hiker still has to cover 1 / 2 miles to meet the waiting cyclist . the hiker will need 15 / 2 mins to cover the remaining 1 / 2 miles . so the answer is d . | physics |
math_qa__nHjn2vNakJoqbhOr | Find the amount on Rs.9000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
Choices.
A) 5568 B) 9828 C) 5460 D) 5635 E) 6734 | <gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">9_000 * 104</gadget>
<output>936_000</output>
<gadget id="calculator">936_000 / 100</gadget>
<output>9_360</output>
<gadget id="calculator">100 + 5</gadget>
<output>105</output>
<gadget id="calculator">9_360 * 105</gadget>
<output>982_800</output>
<gadget id="calculator">982_800 / 100</gadget>
<output>9_828</output>
<result>B</result> | B | 9,828 | Find the amount on Rs.9000 in 2 years, the rate of interest being 4% per first year and 5% for the second year? | {
"A": "5568",
"B": "9828",
"C": "5460",
"D": "5635",
"E": "6734"
} | divide(multiply(divide(multiply(9000, add(const_100, 4)), const_100), add(const_100, 5)), const_100) | add(n3,const_100)|add(n2,const_100)|multiply(n0,#1)|divide(#2,const_100)|multiply(#0,#3)|divide(#4,const_100)| | "9000 * 104 / 100 * 105 / 100 = > 9828 answer : b" | gain |
math_qa__oW02NdwjkEJiYxtT | How many even integers n, such that 20<=n<=180 are of the form 3k+4, where k is any natural number? Choose the correct choice from the following answers:
A) 24 B) 27 C) 30 D) 33 E) 36 | <gadget id="calculator">180 - 2</gadget>
<output>178</output>
<gadget id="calculator">20 + 2</gadget>
<output>22</output>
<gadget id="calculator">178 - 22</gadget>
<output>156</output>
<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">156 / 6</gadget>
<output>26</output>
<gadget id="calculator">26 + 1</gadget>
<output>27</output>
<result>B</result> | B | 27 | How many even integers n, such that 20<=n<=180 are of the form 3k+4, where k is any natural number? | {
"A": "24",
"B": "27",
"C": "30",
"D": "33",
"E": "36"
} | add(divide(subtract(subtract(180, const_2), add(20, const_2)), add(const_2, const_4)), const_1) | add(n0,const_2)|add(const_2,const_4)|subtract(n1,const_2)|subtract(#2,#0)|divide(#3,#1)|add(#4,const_1) | the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 278 = 16 + 6 ( 27 ) there are 27 numbers in the list . the answer is b . | general |
math_qa__sQBBLsxXk9Dx6EXd | Two numbers N and 12 have LCM = 48 and GCF = 8. Find N. Choose the correct choice from the following answers.
A) 24
B) 34
C) 44
D) 54
E) 32 | <gadget id="calculator">48 * 8</gadget>
<output>384</output>
<gadget id="calculator">384 / 12</gadget>
<output>32</output>
<result>E</result> | E | 32 | Two numbers N and 12 have LCM = 48 and GCF = 8. Find N. | {
"A": "24",
"B": "34",
"C": "44",
"D": "54",
"E": "32"
} | divide(multiply(48, 8), 12) | multiply(n1,n2)|divide(#0,n0)| | "the product of two integers is equal to the product of their lcm and gcf . hence . 12 × n = 48 × 8 n = 48 × 8 / 12 = 32 correct answer e" | physics |
math_qa__WWBKCW2lXa0Bt9rV | In a hostel, the number of students decreased by 9% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year? Choose the correct choice from the following answers:
A) 19 % B) 15 % C) 25 % D) 40 % E) 8.4 % | <gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">100 - 9</gadget>
<output>91</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">91 * 120</gadget>
<output>10_920</output>
<gadget id="calculator">10_000 / 10_920</gadget>
<output>250/273 = around 0.915751</output>
<gadget id="calculator">1 - (250/273)</gadget>
<output>23/273 = around 0.084249</output>
<gadget id="calculator">(23/273) * 100</gadget>
<output>2_300/273 = around 8.424908</output>
<result>E</result> | E | 8.4 | In a hostel, the number of students decreased by 9% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year? | {
"A": "19 %",
"B": "15 %",
"C": "25 %",
"D": "40 %",
"E": "8.4 %"
} | multiply(subtract(const_1, divide(multiply(const_100, const_100), multiply(subtract(const_100, 9), add(const_100, 20)))), const_100) | add(n1,const_100)|multiply(const_100,const_100)|subtract(const_100,n0)|multiply(#0,#2)|divide(#1,#3)|subtract(const_1,#4)|multiply(#5,const_100)| | "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.91 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.91 * 1.2 ) = > f ( new ) = 0.915 f therefore the new cost of food must be 91.5 % of the old cost , or the cost of food must decrease by 8.4 % ( option e )" | general |
math_qa__2yMCBLKGZPhWlHdh | A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average of 4375 items per month over the whole? Options
A) 4500
B) 4600
C) 4680
D) 4710
E) none | <gadget id="calculator">9 + 3</gadget>
<output>12</output>
<gadget id="calculator">4_375 * 12</gadget>
<output>52_500</output>
<gadget id="calculator">4_000 * 3</gadget>
<output>12_000</output>
<gadget id="calculator">52_500 - 12_000</gadget>
<output>40_500</output>
<gadget id="calculator">40_500 / 9</gadget>
<output>4_500</output>
<result>A</result> | A | 4,500 | A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average of 4375 items per month over the whole? | {
"A": "4500",
"B": "4600",
"C": "4680",
"D": "4710",
"E": "none"
} | divide(subtract(multiply(4375, add(9, 3)), multiply(4000, 3)), 9) | add(n1,n2)|multiply(n0,n1)|multiply(n3,#0)|subtract(#2,#1)|divide(#3,n2) | sol . required average = ( 4375 x 12 ) - ( 4000 x 3 ) / 9 ⇔ 52500 - 12000 / 9 ⇔ 40500 / 9 = 4500 . answer a | general |
math_qa__FJYrhcpKO1KluZo1 | Pat, kate and mark charged a total of 144 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
Choices.
A) 18 B) 36 C) 80 D) 90 E) 108 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">3 + 6</gadget>
<output>9</output>
<gadget id="calculator">144 / 9</gadget>
<output>16</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">16 * 5</gadget>
<output>80</output>
<result>C</result> | C | 80 | Pat, kate and mark charged a total of 144 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate. | {
"A": "18",
"B": "36",
"C": "80",
"D": "90",
"E": "108"
} | multiply(divide(144, add(add(1, const_2), multiply(const_2, 3))), subtract(multiply(const_2, 3), 1)) | add(n1,const_2)|multiply(n2,const_2)|add(#0,#1)|subtract(#1,n1)|divide(n0,#2)|multiply(#4,#3)| | "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 144 - total hours charged for , x = 16 . mat charged 6 x - x or 5 x for more hours than kate , or for 80 hours . c is correct" | general |
math_qa__UXaSueDRX9lvkkBd | Divide $5000 among X,Y in the ratio 2:8. How many $ that X get?
Choose the correct answer:
A) $ 1000 B) $ 1050 C) $ 1100 D) $ 1150 E) $ 1200 | <gadget id="calculator">4 * 1_000</gadget>
<output>4_000</output>
<gadget id="calculator">5_000 - 4_000</gadget>
<output>1_000</output>
<result>A</result> | A | 1,000 | Divide $5000 among X,Y in the ratio 2:8. How many $ that X get? | {
"A": "$ 1000",
"B": "$ 1050",
"C": "$ 1100",
"D": "$ 1150",
"E": "$ 1200"
} | subtract(5000, multiply(const_4, const_1000)) | multiply(const_1000,const_4)|subtract(n0,#0) | sum of ratio terms = 2 + 8 = 10 x = 5000 * 2 / 10 = $ 1000 answer is a | general |
math_qa__Ljvbw9IroRyNubJv | a teacher gave the same test to 3 history classes : u , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 80 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ? Pick:
A) 74 B) 75 C) 76 D) 77 E) 78 | <gadget id="calculator">65 * 4</gadget>
<output>260</output>
<gadget id="calculator">80 * 6</gadget>
<output>480</output>
<gadget id="calculator">260 + 480</gadget>
<output>740</output>
<gadget id="calculator">77 * 5</gadget>
<output>385</output>
<gadget id="calculator">740 + 385</gadget>
<output>1_125</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">1_125 / 15</gadget>
<output>75</output>
<result>B</result> | B | 75 | a teacher gave the same test to 3 history classes : u , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 80 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ? | {
"A": "74",
"B": "75",
"C": "76",
"D": "77",
"E": "78"
} | divide(add(add(multiply(65, 4), multiply(80, 6)), multiply(77, 5)), add(add(4, 6), 5)) | add(n5,n6)|multiply(n2,n5)|multiply(n3,n6)|multiply(n4,n7)|add(#1,#2)|add(n7,#0)|add(#4,#3)|divide(#6,#5) | ans : b ( 75 ) lets say class u indeed has 4 children , b has 6 children and c has 5 children . now , if the average of class u is 65 , hence total marks awarded in the class = 65 * 4 = 260 similarly , class b = 80 * 6 = 480 class c = 77 * 5 = 385 total marks provided = u + b + c = 260 + 480 + 385 = 1125 avg . marks = 1125 / 15 ( total no . of students ) = 75 = b | general |
math_qa__g4B9AnjaqDBYbuFR | A cube of edge 15cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?
Select the correct option: A) 6 cm B) 8.25 cm C) 11.25 cm D) 15.12 cm E) 20.62 cm | <gadget id="calculator">15 ** 3</gadget>
<output>3_375</output>
<gadget id="calculator">20 * 15</gadget>
<output>300</output>
<gadget id="calculator">3_375 / 300</gadget>
<output>45/4 = around 11.25</output>
<result>C</result> | C | 11.25 | A cube of edge 15cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level? | {
"A": "6 cm",
"B": "8.25 cm",
"C": "11.25 cm",
"D": "15.12 cm",
"E": "20.62 cm"
} | divide(volume_cube(15), multiply(20, 15)) | multiply(n1,n2)|volume_cube(n0)|divide(#1,#0)| | "increase in volume = volume of the cube = 15 * 15 * 15 cm ^ 3 rise in water level = volume / area = 15 * 15 * 15 / 20 * 15 = 11.25 cm answer is c" | geometry |
math_qa__aVdj5dvfVChwnzVW | What are the last two digits of 63*35*37*82*71*41*53?
Choices:
A) 10 B) 30 C) 40 D) 70 E) 80 | <gadget id="calculator">82 - 2</gadget>
<output>80</output>
<result>E</result> | E | 80 | What are the last two digits of 63*35*37*82*71*41*53? | {
"A": "10",
"B": "30",
"C": "40",
"D": "70",
"E": "80"
} | subtract(82, const_2) | subtract(n3,const_2) | we know that to find the last two digits , we need to find the remainder we get when we divide the product by 100 . remainder of ( 63 * 35 * 37 * 82 * 71 * 41 ) / 100 note that we can simplify this expression by canceling out the 5 and 2 in the numerator and denominator . but before we do that , here is an important note : note : we can not just cancel off the common terms in the numerator and denominator to get the remainder . but , if we want to cancel off to simplify the question , we can do it , provided we remember to multiply it back again . so say , we want to find the remainder when 14 is divided by 10 i . e . 14 / 10 ( remainder 4 ) . but we cancel off the common 2 to get 7 / 5 . the remainder here will be 2 which is not the same as the remainder obtained by dividing 14 by 10 . but if we multiply 2 back by 2 ( the number we canceled off ) , the remainder will become 2 * 2 = 4 which is correct . take another example to reinforce this – what is the remainder when 85 is divided by 20 ? it is 5 . we might rephrase it as – what is the remainder when 17 is divided by 4 ( cancel off 5 from the numerator and the denominator ) . the remainder in this case is 1 . we multiply the 5 back to 1 to get the remainder as 5 which is correct . so keeping this very important point in mind , let ’ s go ahead and cancel the common 5 and 2 . we need the remainder of ( 63 * 7 * 37 * 41 * 71 * 41 * 5 * 2 ) / 10 * 5 * 2 remainder of ( 63 * 7 * 37 * 41 * 71 * 41 ) / 10 now using concept 2 , let ’ s write the numbers in form of multiples of 10 remainder of ( 60 + 3 ) * 7 * ( 30 + 7 ) * ( 40 + 1 ) * ( 70 + 1 ) * ( 40 + 1 ) / 10 remainder of 3 * 7 * 7 * 1 * 1 * 1 / 10 remainder of 147 / 10 = 7 now remember , we had canceled off 10 so to get the actual remainder so we need to multiply by 10 : 7 * 10 = 70 . when 63 * 35 * 37 * 82 * 71 * 41 is divided by 100 , the remainder is 70 . so the last two digits of 63 * 35 * 37 * 82 * 71 * 41 must be 80 . answer ( e ) | general |
math_qa__TfQD1y0i4bBdeQen | The population of a city increases by 5% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years? Pick: A) 9 % B) 9.27 % C) 27 % D) 12.48 % E) none of these | <gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">104 * 4</gadget>
<output>416</output>
<gadget id="calculator">416 / 100</gadget>
<output>104/25 = around 4.16</output>
<gadget id="calculator">(104/25) + 4</gadget>
<output>204/25 = around 8.16</output>
<gadget id="calculator">100 + (204/25)</gadget>
<output>2_704/25 = around 108.16</output>
<gadget id="calculator">(2_704/25) * 4</gadget>
<output>10_816/25 = around 432.64</output>
<gadget id="calculator">(10_816/25) / 100</gadget>
<output>2_704/625 = around 4.3264</output>
<gadget id="calculator">(2_704/625) + (204/25)</gadget>
<output>7_804/625 = around 12.4864</output>
<result>D</result> | D | 12.48 | The population of a city increases by 5% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years? | {
"A": "9 %",
"B": "9.27 %",
"C": "27 %",
"D": "12.48 %",
"E": "none of these"
} | add(divide(multiply(add(const_100, add(divide(multiply(add(const_100, subtract(5, 1)), subtract(5, 1)), const_100), subtract(5, 1))), subtract(5, 1)), const_100), add(divide(multiply(add(const_100, subtract(5, 1)), subtract(5, 1)), const_100), subtract(5, 1))) | subtract(n0,n1)|add(#0,const_100)|multiply(#1,#0)|divide(#2,const_100)|add(#3,#0)|add(#4,const_100)|multiply(#5,#0)|divide(#6,const_100)|add(#4,#7)| | "actual increase in population = 4 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 4 / 100 ) ^ 3 = 112.4864 ∴ required percentage = 12.48 % answer : d" | general |
math_qa__mrokqEEeea3LpigP | The sum of the present age of Henry and Jill is 33. What is their present ages if 6 years ago Henry was twice the age of Jill?
Choose the correct choice:
A) and 20
B) and 24
C) and 22
D) and 29
E) of these | <gadget id="calculator">33 + 6</gadget>
<output>39</output>
<gadget id="calculator">39 / 3</gadget>
<output>13</output>
<gadget id="calculator">33 - 13</gadget>
<output>20</output>
<result>A</result> | A | 20 | The sum of the present age of Henry and Jill is 33. What is their present ages if 6 years ago Henry was twice the age of Jill? | {
"A": "and 20",
"B": "and 24",
"C": "and 22",
"D": "and 29",
"E": "of these"
} | subtract(33, divide(add(33, 6), const_3)) | add(n0,n1)|divide(#0,const_3)|subtract(n0,#1)| | "let the age of jill 6 years ago be x , age of henry be 2 x x + 6 + 2 x + 6 = 33 x = 7 present ages will be 13 and 20 answer : a" | general |
math_qa__UX1ZY7J6WnylZgS0 | In a division sum, the remainder is 5 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder. The dividend is:
Select.
A) 72 B) 76 C) 100 D) 113 E) 112 | <gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">15 + 3</gadget>
<output>18</output>
<gadget id="calculator">18 / 3</gadget>
<output>6</output>
<gadget id="calculator">18 * 6</gadget>
<output>108</output>
<gadget id="calculator">108 + 5</gadget>
<output>113</output>
<result>D</result> | D | 113 | In a division sum, the remainder is 5 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder. The dividend is: | {
"A": "72",
"B": "76",
"C": "100",
"D": "113",
"E": "112"
} | add(multiply(add(multiply(5, const_3), 3), divide(add(multiply(5, const_3), 3), 3)), 5) | multiply(n0,const_3)|add(n2,#0)|divide(#1,n1)|multiply(#1,#2)|add(n0,#3)| | "diver = ( 5 * 3 ) + 3 = 18 3 * quotient = 18 quotient = 6 dividend = ( divisor * quotient ) + remainder dividend = ( 18 * 6 ) + 5 = 113 d" | general |
math_qa__lkT0V0ennjpcW7ej | What is the sum of the multiples of 4 between 34 and 135 inclusive? Pick one
A) 2000
B) 2100
C) 2150
D) 2200
E) 2500 | <gadget id="calculator">135 - 3</gadget>
<output>132</output>
<gadget id="calculator">34 + 2</gadget>
<output>36</output>
<gadget id="calculator">132 + 36</gadget>
<output>168</output>
<gadget id="calculator">168 / 2</gadget>
<output>84</output>
<gadget id="calculator">132 - 36</gadget>
<output>96</output>
<gadget id="calculator">96 / 4</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">84 * 25</gadget>
<output>2_100</output>
<result>B</result> | B | 2,100 | What is the sum of the multiples of 4 between 34 and 135 inclusive? | {
"A": "2000",
"B": "2100",
"C": "2150",
"D": "2200",
"E": "2500"
} | multiply(divide(add(subtract(135, const_3), add(34, const_2)), const_2), add(divide(subtract(subtract(135, const_3), add(34, const_2)), 4), const_1)) | add(n1,const_2)|subtract(n2,const_3)|add(#0,#1)|subtract(#1,#0)|divide(#3,n0)|divide(#2,const_2)|add(#4,const_1)|multiply(#6,#5) | the fastest way in an ap is to find the average and multiply with total integers . . between 34 and 135 , the smallest multiple of 4 is 36 and largest = 132 . . average = ( 36 + 132 ) / 2 = 84 . . total numbers = ( 132 - 36 ) / 4 + 1 = 24 + 1 = 25 . . sum = 25 * 84 = 2100 ans b | general |
math_qa__BWehoB1bZO9KLN4K | The area of a rectangular plot is 21 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth? Choose the correct answer
A) 10 metres B) 5 metres C) 11 metres D) data inadequate E) none of these | <gadget id="calculator">21 - 10</gadget>
<output>11</output>
<result>C</result> | C | 11 | The area of a rectangular plot is 21 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth? | {
"A": "10 metres",
"B": "5 metres",
"C": "11 metres",
"D": "data inadequate",
"E": "none of these"
} | subtract(21, 10) | subtract(n0,n1)| | "l × b = 21 × b ∴ l = 21 m and l – b = 10 ∴ b = 21 – 10 = 11 m answer c" | geometry |
math_qa__l5EtNSfPYcdn2pxj | A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 3600 interest. The principal amount borrowed by him was. Pick one.
A) rs 10000 B) rs 15000 C) rs 16000 D) rs 17000 E) none of these | <gadget id="calculator">3_600 * 100</gadget>
<output>360_000</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">360_000 / 36</gadget>
<output>10_000</output>
<result>A</result> | A | 10,000 | A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 3600 interest. The principal amount borrowed by him was. | {
"A": "rs 10000",
"B": "rs 15000",
"C": "rs 16000",
"D": "rs 17000",
"E": "none of these"
} | divide(multiply(3600, const_100), multiply(12, 3)) | multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)| | "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 3600 â ˆ — 100 / 12 â ˆ — 3 = rs 10000 option a" | gain |
math_qa__1acLMNLBEFe9eLl4 | (3x + 2) (2x - 3) = ax^2 + kx + n . What is the value of a - n + k ? Options: A) 5 B) 7 C) 9 D) 10 E) 11 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">4 - 9</gadget>
<output>-5</output>
<gadget id="calculator">12 + (-5)</gadget>
<output>7</output>
<result>B</result> | B | 7 | (3x + 2) (2x - 3) = ax^2 + kx + n . What is the value of a - n + k ? | {
"A": "5",
"B": "7",
"C": "9",
"D": "10",
"E": "11"
} | add(add(multiply(3, 2), multiply(3, 2)), subtract(multiply(2, 2), multiply(3, 3))) | multiply(n0,n1)|multiply(n1,n3)|multiply(n1,n1)|multiply(n0,n3)|add(#0,#1)|subtract(#2,#3)|add(#4,#5)| | "expanding we have 6 x ^ 2 - 9 x + 4 x - 6 6 x ^ 2 - 5 x - 6 taking coefficients , a = 6 , k = - 5 , n = - 6 therefore a - n + k = 6 - ( - 6 ) - 5 = 12 - 5 = 7 the answer is b ." | general |
math_qa__ZNCd6IBrwRzGoNvQ | A vendor sells 50 percent of the apples he had and throws away 20 percent of the remainder. The next day, the vendor sells 50 percent of the remaining apples and throws away the rest. In total, what percent of his apples does the vendor throw away? Answers:
A) 30 B) 35 C) 40 D) 45 E) 50 | <gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 50</gadget>
<output>10</output>
<gadget id="calculator">50 - 10</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">20 + 10</gadget>
<output>30</output>
<result>A</result> | A | 30 | A vendor sells 50 percent of the apples he had and throws away 20 percent of the remainder. The next day, the vendor sells 50 percent of the remaining apples and throws away the rest. In total, what percent of his apples does the vendor throw away? | {
"A": "30",
"B": "35",
"C": "40",
"D": "45",
"E": "50"
} | add(divide(subtract(subtract(const_100, 50), multiply(divide(20, const_100), subtract(const_100, 50))), const_2), multiply(divide(20, const_100), subtract(const_100, 50))) | divide(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|subtract(#1,#2)|divide(#3,const_2)|add(#4,#2)| | "let x be the original number of apples . on day one , the vendor throws away ( 0.2 ) ( 0.5 ) x = 0.1 x . the remaining apples are ( 0.8 ) ( 0.5 ) x = 0.4 x . on day two , the vendor throws away ( 0.5 ) ( 0.4 ) x = 0.2 x . the vendor throws away a total of 0.1 x + 0.2 x = 0.3 x . the vendor throws away 30 percent of the apples . the answer is a ." | general |
math_qa__LuQFhXPExwsSokTF | A can do a piece of work in 12 days and B alone can do it in 14 days. How much time will both take to finish the work ? Pick.
A) 3.2222
B) 5
C) 6.46
D) 8.3333
E) 9 | <gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / 14</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">(1/12) + (1/14)</gadget>
<output>13/84 = around 0.154762</output>
<gadget id="calculator">1 / (13/84)</gadget>
<output>84/13 = around 6.461538</output>
<result>C</result> | C | 6.46 | A can do a piece of work in 12 days and B alone can do it in 14 days. How much time will both take to finish the work ? | {
"A": "3.2222",
"B": "5",
"C": "6.46",
"D": "8.3333",
"E": "9"
} | divide(const_1, add(divide(const_1, 12), divide(const_1, 14))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2) | this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 12 x 14 / ( 12 + 14 ) = 150 / 25 = 6.46 days answer : c | physics |
math_qa__wg0In9NBkCCrIZy7 | A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ? Choose the most appropriate option
A) 1 / 3 B) 2 / 3 C) 2 / 5 D) 3 / 5 E) 4 / 5 | <gadget id="calculator">40 - 26</gadget>
<output>14</output>
<gadget id="calculator">40 - 19</gadget>
<output>21</output>
<gadget id="calculator">14 / 21</gadget>
<output>2/3 = around 0.666667</output>
<result>B</result> | B | 0.666667 | A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ? | {
"A": "1 / 3",
"B": "2 / 3",
"C": "2 / 5",
"D": "3 / 5",
"E": "4 / 5"
} | divide(subtract(40, 26), subtract(40, 19)) | subtract(n0,n2)|subtract(n0,n1)|divide(#0,#1) | let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 2 / 3 . hence , b is the correct answer . | gain |
math_qa__IKV4BeTkk9A7wHMc | X^Y + Y^X =2408
Find the values of X ? Choose one:
A) 2407 B) 2408 C) 2409 D) 2405 E) 32 | <gadget id="calculator">2_408 - 1</gadget>
<output>2_407</output>
<result>A</result> | A | 2,407 | X^Y + Y^X =2408
Find the values of X ? | {
"A": "2407",
"B": "2408",
"C": "2409",
"D": "2405",
"E": "32"
} | subtract(2408, const_1) | subtract(n0,const_1) | 2407 ^ 1 + 1 ^ 2407 = 2408 answer : a | general |
math_qa__VSvnOkIWmz7oHEjx | The speed of a boat in still water in 20 km/hr and the rate of current is 6 km/hr. The distance travelled downstream in 12 minutes is: Choose the correct option.
A) 10.6 B) 5.2 C) 10.8 D) 5.4 E) 5.0 | <gadget id="calculator">20 + 6</gadget>
<output>26</output>
<gadget id="calculator">12 / 60</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">26 * (1/5)</gadget>
<output>26/5 = around 5.2</output>
<result>B</result> | B | 5.2 | The speed of a boat in still water in 20 km/hr and the rate of current is 6 km/hr. The distance travelled downstream in 12 minutes is: | {
"A": "10.6",
"B": "5.2",
"C": "10.8",
"D": "5.4",
"E": "5.0"
} | multiply(add(20, 6), divide(12, const_60)) | add(n0,n1)|divide(n2,const_60)|multiply(#0,#1)| | "speed downstream = ( 20 + 6 ) = 26 kmph time = 24 minutes = 12 / 60 hour = 1 / 5 hour distance travelled = time × speed = 1 / 5 × 26 = 5.20 km answer is b ." | physics |
math_qa__CUfy72ZFt3uohskJ | 15 litres of mixture contains 20% alcohol and the rest water. If 5litres of water be mixed with it, the percentage of alcohol in the new mixture would be? Choose the correct option
A) 16.67 % B) 23 % C) 15 % D) 19.75 % E) 21.23 % | <gadget id="calculator">15 + 5</gadget>
<output>20</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 15</gadget>
<output>12</output>
<gadget id="calculator">12 + 5</gadget>
<output>17</output>
<gadget id="calculator">20 - 17</gadget>
<output>3</output>
<gadget id="calculator">3 / 20</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 100</gadget>
<output>15</output>
<result>C</result> | C | 15 | 15 litres of mixture contains 20% alcohol and the rest water. If 5litres of water be mixed with it, the percentage of alcohol in the new mixture would be? | {
"A": "16.67 %",
"B": "23 %",
"C": "15 %",
"D": "19.75 %",
"E": "21.23 %"
} | multiply(divide(subtract(add(15, 5), add(multiply(divide(subtract(const_100, 20), const_100), 15), 5)), add(15, 5)), const_100) | add(n0,n2)|subtract(const_100,n1)|divide(#1,const_100)|multiply(n0,#2)|add(n2,#3)|subtract(#0,#4)|divide(#5,#0)|multiply(#6,const_100)| | "alcohol in the 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 5 = 20 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 20 = 15 % answer is c" | gain |
math_qa__hwdOYKl4OT0rU2tG | Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1111. Find the cost of each ice-cream cup? Choose the correct choice from the following.
A) 25 B) 66 C) 77 D) 50 E) 91 | <gadget id="calculator">16 * 6</gadget>
<output>96</output>
<gadget id="calculator">1_111 - 96</gadget>
<output>1_015</output>
<gadget id="calculator">5 * 45</gadget>
<output>225</output>
<gadget id="calculator">1_015 - 225</gadget>
<output>790</output>
<gadget id="calculator">7 * 70</gadget>
<output>490</output>
<gadget id="calculator">790 - 490</gadget>
<output>300</output>
<gadget id="calculator">300 / 6</gadget>
<output>50</output>
<result>D</result> | D | 50 | Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1111. Find the cost of each ice-cream cup? | {
"A": "25",
"B": "66",
"C": "77",
"D": "50",
"E": "91"
} | divide(subtract(subtract(subtract(1111, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6) | multiply(n0,n3)|multiply(n1,n5)|multiply(n2,n6)|subtract(n7,#0)|subtract(#3,#1)|subtract(#4,#2)|divide(#5,n3)| | "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1111 96 + 225 + 490 + 6 x = 1111 6 x = 300 = > x = 50 . answer : d" | general |
math_qa__jZbJgwIsIIc9xX2o | the average of 3 numbers is 48 . the average of two of these numbers is 56 % . what is the third number ? Answers.
A) 64 B) 32 C) 46 D) 75 E) 47 | <gadget id="calculator">3 * 48</gadget>
<output>144</output>
<gadget id="calculator">2 * 56</gadget>
<output>112</output>
<gadget id="calculator">144 - 112</gadget>
<output>32</output>
<result>B</result> | B | 32 | the average of 3 numbers is 48 . the average of two of these numbers is 56 % . what is the third number ? | {
"A": "64",
"B": "32",
"C": "46",
"D": "75",
"E": "47"
} | subtract(multiply(3, 48), multiply(const_2, 56)) | multiply(n0,n1)|multiply(n2,const_2)|subtract(#0,#1) | b 32 the total of three numbers must be 48 x 3 = 144 . the total of two numbers must be 56 x 2 = 112 . therefore , 144 - 112 = 32 . | general |
math_qa__7IskPbIvAwMBBRTk | By selling an article for $180, a person gains $30. What is the gain %?
Pick one:
A) 25 %
B) 30 %
C) 50 %
D) 20 %
E) 10 % | <gadget id="calculator">30 * 100</gadget>
<output>3_000</output>
<gadget id="calculator">180 - 30</gadget>
<output>150</output>
<gadget id="calculator">3_000 / 150</gadget>
<output>20</output>
<result>D</result> | D | 20 | By selling an article for $180, a person gains $30. What is the gain %? | {
"A": "25 %",
"B": "30 %",
"C": "50 %",
"D": "20 %",
"E": "10 %"
} | divide(multiply(30, const_100), subtract(180, 30)) | multiply(n1,const_100)|subtract(n0,n1)|divide(#0,#1)| | "s . p . = $ 180 gain = $ 30 c . p . = 180 - 30 = 150 gain % = 30 / 150 * 100 = 20 % answer is d" | gain |
math_qa__rLdAoz4GziaVMLDz | Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 6 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is? Choose the correct choice:
A) 13 : 1
B) 13 : 3
C) 13 : 8
D) 13 : 5
E) 13 : 2 | <gadget id="calculator">62.5 * 2</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">87.5 * 6</gadget>
<output>525</output>
<gadget id="calculator">525 / 100</gadget>
<output>21/4 = around 5.25</output>
<gadget id="calculator">(5/4) + (21/4)</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">2 - (5/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">6 - (21/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) + (3/4)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(13/2) / (3/2)</gadget>
<output>13/3 = around 4.333333</output>
<result>B</result> | B | 4.333333 | Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 6 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is? | {
"A": "13 : 1",
"B": "13 : 3",
"C": "13 : 8",
"D": "13 : 5",
"E": "13 : 2"
} | divide(add(divide(multiply(62.5, 2), const_100), divide(multiply(87.5, 6), const_100)), add(subtract(2, divide(multiply(62.5, 2), const_100)), subtract(6, divide(multiply(87.5, 6), const_100)))) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,const_100)|divide(#1,const_100)|add(#2,#3)|subtract(n2,#2)|subtract(n3,#3)|add(#5,#6)|divide(#4,#7) | quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 6 = 21 / 4 litres quantity of alcohol in the mixture formed = 5 / 4 + 21 / 4 = 13 / 2 = 6.5 litres as 8 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 6.5 : 1.5 = 13 : 3 . answer : b | other |
math_qa__KwyPJTY7z24liArN | What is 2/5 of 5/9 of 1/2? Choose the correct answer
A) 1 / 4 B) 1 / 9 C) 9 / 16 D) 5 / 8 E) 16 / 9 | <gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">5 / 9</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(5/9) * (1/2)</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(2/5) * (5/18)</gadget>
<output>1/9 = around 0.111111</output>
<result>B</result> | B | 0.111111 | What is 2/5 of 5/9 of 1/2? | {
"A": "1 / 4",
"B": "1 / 9",
"C": "9 / 16",
"D": "5 / 8",
"E": "16 / 9"
} | multiply(divide(2, 5), multiply(divide(5, 9), divide(1, 2))) | divide(n0,n1)|divide(n1,n3)|divide(n4,n0)|multiply(#1,#2)|multiply(#0,#3)| | "2 / 5 * 5 / 9 * 1 / 2 = 1 / 9 answer : b" | general |
math_qa__Sp2RGwS79T9e914t | John completes a piece of work in 10 days, Rose completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is? Choose one.
A) 5 days B) 8 days C) 10 days D) 12 days E) 14 days | <gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">(1/10) + (1/40)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / (1/8)</gadget>
<output>8</output>
<result>B</result> | B | 8 | John completes a piece of work in 10 days, Rose completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is? | {
"A": "5 days",
"B": "8 days",
"C": "10 days",
"D": "12 days",
"E": "14 days"
} | divide(const_1, add(divide(const_1, 10), divide(const_1, 40))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)| | "if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 10 × 40 / 50 = 8 days b )" | physics |
math_qa__CSk9tZFfdUVMw7OW | at a time A,do 20% less work than B.if A do any work in 15/2 hour,then in how many hour B will finish work? Pick one.
A) 5 hour B) 11 / 2 hour C) 6 hour D) 13 / 2 hour E) 8 hour | <gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(15/2) * (4/5)</gadget>
<output>6</output>
<result>C</result> | C | 6 | at a time A,do 20% less work than B.if A do any work in 15/2 hour,then in how many hour B will finish work? | {
"A": "5 hour",
"B": "11 / 2 hour",
"C": "6 hour",
"D": "13 / 2 hour",
"E": "8 hour"
} | multiply(divide(15, 2), subtract(const_1, divide(20, const_100))) | divide(n1,n2)|divide(n0,const_100)|subtract(const_1,#1)|multiply(#0,#2) | let b will finish a work in x hour . then , in x hour a , 80 / 100 = 4 / 5 work do ratio of work done by a and b = inverse ratio of time taken 4 / 5 : 1 = 2 / 15 : 1 / x 4 / 5 * 1 / x = 1 * 2 / 15 = 4 / 5 x = 2 / 15 ; x = 6 . time = 6 hour answer c | physics |
math_qa__pZbqiLwaSsDCpBvf | Worker A takes 8 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 option:
A) 20 / 9 B) 40 / 9 C) 50 / 9 D) 60 / 9 E) 80 / 9 | <gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/8) + (1/10)</gadget>
<output>9/40 = around 0.225</output>
<gadget id="calculator">1 / (9/40)</gadget>
<output>40/9 = around 4.444444</output>
<result>B</result> | B | 4.444444 | Worker A takes 8 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": "80 / 9"
} | divide(const_1, add(divide(const_1, 8), 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 / 8 one day work of b = 1 / 10 so one day work of a and b together = 1 / 8 + 1 / 10 = 9 / 40 so total days required = 40 / 9 answer : b" | physics |
math_qa__5lKAHLS4nSf3VXtJ | 106 × 106 + 94 × 94 = ? Choose the correct choice from the following: A) 20072 B) 20062 C) 10072 D) 20172 E) 10272 | <gadget id="calculator">106 ** 2</gadget>
<output>11_236</output>
<gadget id="calculator">11_236 - 106</gadget>
<output>11_130</output>
<gadget id="calculator">94 ** 2</gadget>
<output>8_836</output>
<gadget id="calculator">8_836 - 94</gadget>
<output>8_742</output>
<gadget id="calculator">11_130 + 8_742</gadget>
<output>19_872</output>
<result>A</result> | A | 20,072 | 106 × 106 + 94 × 94 = ? | {
"A": "20072",
"B": "20062",
"C": "10072",
"D": "20172",
"E": "10272"
} | add(subtract(power(106, const_2), 106), subtract(power(94, const_2), 94)) | power(n0,const_2)|power(n2,const_2)|subtract(#0,n0)|subtract(#1,n2)|add(#2,#3)| | "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1062 + 942 = ( 100 + 6 ) 2 + ( 100 â ˆ ’ 6 ) 2 = 2 ( 1002 + 62 ) = 2 ( 10000 + 36 ) = 20072 . answer : option a" | general |
math_qa__KotxZ5ydsOzlPi62 | In an office, totally there are 6400 employees and 65% of the total employees are males. 25% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years? Pick: A) 1040 B) 2080 C) 3120 D) 4160 E) none of these | <gadget id="calculator">6_400 * 65</gadget>
<output>416_000</output>
<gadget id="calculator">416_000 / 100</gadget>
<output>4_160</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">4_160 * (3/4)</gadget>
<output>3_120</output>
<result>C</result> | C | 3,120 | In an office, totally there are 6400 employees and 65% of the total employees are males. 25% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years? | {
"A": "1040",
"B": "2080",
"C": "3120",
"D": "4160",
"E": "none of these"
} | multiply(divide(multiply(6400, 65), const_100), divide(subtract(const_100, 25), const_100)) | multiply(n0,n1)|subtract(const_100,n2)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)| | "number of male employees = 6400 * 65 / 100 = 4160 required number of male employees who are less than 50 years old = 4160 * ( 100 - 25 ) % = 4160 * 75 / 100 = 3120 . answer : c" | general |
math_qa__6q3z9zdEZxW87HBZ | The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 75 percent of a, and m equals b decreased by 80 percent of b, what is the value of m/x? Choose the correct answer:
A) 1 / 7
B) 3 / 4
C) 4 / 5
D) 5 / 4
E) 3 / 2 | <gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">100 + 75</gadget>
<output>175</output>
<gadget id="calculator">20 / 175</gadget>
<output>4/35 = around 0.114286</output>
<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(4/35) * (5/4)</gadget>
<output>1/7 = around 0.142857</output>
<result>A</result> | A | 0.142857 | The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 75 percent of a, and m equals b decreased by 80 percent of b, what is the value of m/x? | {
"A": "1 / 7",
"B": "3 / 4",
"C": "4 / 5",
"D": "5 / 4",
"E": "3 / 2"
} | multiply(divide(subtract(const_100, 80), add(const_100, 75)), divide(5, 4)) | add(n2,const_100)|divide(n1,n0)|subtract(const_100,n3)|divide(#2,#0)|multiply(#3,#1)| | "a / b = 4 / 5 m / x = ( 1 / 5 ) * 5 / ( 7 / 4 ) * 4 = 1 / 7 the answer is a ." | general |
math_qa__9617kjdBv1hzIrFU | 9. The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is Options.
A) 41 B) 42 C) 32 D) 37 E) 39 | <gadget id="calculator">lcm(3, 5)</gadget>
<output>15</output>
<gadget id="calculator">lcm(15, 7)</gadget>
<output>105</output>
<gadget id="calculator">lcm(105, 8)</gadget>
<output>840</output>
<gadget id="calculator">28_523 % 840</gadget>
<output>803</output>
<gadget id="calculator">840 - 803</gadget>
<output>37</output>
<result>D</result> | D | 37 | 9. The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is | {
"A": "41",
"B": "42",
"C": "32",
"D": "37",
"E": "39"
} | subtract(lcm(lcm(lcm(3, 5), 7), 8), reminder(28523, lcm(lcm(lcm(3, 5), 7), 8))) | lcm(n2,n3)|lcm(n4,#0)|lcm(n5,#1)|reminder(n1,#2)|subtract(#2,#3) | lcm of 3 , 5 , 7 and 8 = 840 28523 ÷ 840 = 33 remainder = 803 hence the least number which should be added = 840 - 803 = 37 answer : option d | general |
math_qa__ZOD28HJwr7n6t6sl | The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1250 resolutions? Choose the correct option.
A) 1277 m B) 1760 m C) 1278 m D) 1288 m E) 1378 v | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 + 1</gadget>
<output>22</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">(22/7) * 22.4</gadget>
<output>70.4</output>
<gadget id="calculator">70.4 * 2</gadget>
<output>140.8</output>
<gadget id="calculator">140.8 * 1_250</gadget>
<output>176_000</output>
<gadget id="calculator">176_000 / 100</gadget>
<output>1_760</output>
<result>B</result> | B | 1,760 | The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 1250 resolutions? | {
"A": "1277 m",
"B": "1760 m",
"C": "1278 m",
"D": "1288 m",
"E": "1378 v"
} | divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 1250), const_100) | add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)| | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1250 resolutions . = 1250 * 2 * 22 / 7 * 22.4 = 176000 cm = 1760 m answer : b" | physics |
math_qa__YN4jsbYAGnpUcKS5 | The salary of a worker is first increased by 10% and afterwards reduced by 10%. What is the net change in the worker's salary?
Options:
A) 1 % increase
B) 1 % decrease
C) 2 % increase
D) 2 % decrease
E) no change | <gadget id="calculator">10 + 100</gadget>
<output>110</output>
<gadget id="calculator">110 * 10</gadget>
<output>1_100</output>
<gadget id="calculator">1_100 / 100</gadget>
<output>11</output>
<gadget id="calculator">110 - 11</gadget>
<output>99</output>
<gadget id="calculator">100 - 99</gadget>
<output>1</output>
<result>B</result> | B | 1 | The salary of a worker is first increased by 10% and afterwards reduced by 10%. What is the net change in the worker's salary? | {
"A": "1 % increase",
"B": "1 % decrease",
"C": "2 % increase",
"D": "2 % decrease",
"E": "no change"
} | subtract(const_100, subtract(add(10, const_100), divide(multiply(add(10, const_100), 10), const_100))) | add(n0,const_100)|multiply(n0,#0)|divide(#1,const_100)|subtract(#0,#2)|subtract(const_100,#3)| | "let x be the original salary . the final salary is 0.9 ( 1.1 x ) = 0.99 x the answer is b ." | gain |
math_qa__kLhRCsFPLhNZmgXG | Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1051. Find the cost of each ice-cream cup? Choose the most appropriate option:
A) 25 B) 40 C) 77 D) 99 E) 91 | <gadget id="calculator">16 * 6</gadget>
<output>96</output>
<gadget id="calculator">1_051 - 96</gadget>
<output>955</output>
<gadget id="calculator">5 * 45</gadget>
<output>225</output>
<gadget id="calculator">955 - 225</gadget>
<output>730</output>
<gadget id="calculator">7 * 70</gadget>
<output>490</output>
<gadget id="calculator">730 - 490</gadget>
<output>240</output>
<gadget id="calculator">240 / 6</gadget>
<output>40</output>
<result>B</result> | B | 40 | Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1051. Find the cost of each ice-cream cup? | {
"A": "25",
"B": "40",
"C": "77",
"D": "99",
"E": "91"
} | divide(subtract(subtract(subtract(1051, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6) | multiply(n0,n3)|multiply(n1,n5)|multiply(n2,n6)|subtract(n7,#0)|subtract(#3,#1)|subtract(#4,#2)|divide(#5,n3)| | "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1051 96 + 225 + 490 + 6 x = 1051 6 x = 240 = > x = 40 . answer : b" | general |
math_qa__cEBdYX1IXzFiYAd5 | the cost of painting the 4 walls of a room is rs . 350 . the cost of painting a room 3 times in length , breadth and height will be : Pick.
A) rs . 1050 B) rs . 1400 C) rs . 3150 D) rs . 4200 E) none | <gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">350 * 9</gadget>
<output>3_150</output>
<result>C</result> | C | 3,150 | the cost of painting the 4 walls of a room is rs . 350 . the cost of painting a room 3 times in length , breadth and height will be : | {
"A": "rs . 1050",
"B": "rs . 1400",
"C": "rs . 3150",
"D": "rs . 4200",
"E": "none"
} | multiply(350, power(3, const_2)) | power(n2,const_2)|multiply(n1,#0) | explanation : area of 4 walls of the room = [ 2 ( l + b ) × h ] m 2 area of 4 walls of new room = [ 2 ( 3 l + 3 b ) × 3 h ] m 2 = 9 [ 2 ( l + b ) × h ] m 2 cost of painting the 4 walls of new room = rs . ( 9 × 350 ) = rs . 3150 correct option : c | general |
math_qa__8SVwxzg2Han0femz | A number is doubled and 5 is added. If the resultant is trebled, it becomes 123. What is that number?
Choose the correct choice from the following answers.
A) 12 B) 29 C) 27 D) 18 E) 99 | <gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">123 - 15</gadget>
<output>108</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">108 / 6</gadget>
<output>18</output>
<result>D</result> | D | 18 | A number is doubled and 5 is added. If the resultant is trebled, it becomes 123. What is that number? | {
"A": "12",
"B": "29",
"C": "27",
"D": "18",
"E": "99"
} | divide(subtract(123, multiply(const_3, 5)), multiply(const_3, const_2)) | multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)| | "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 123 6 x + 15 = 123 6 x = 108 x = 18 answer : d" | general |
math_qa__vXaRuIxo5F6bTius | A certain number when divided by 899 leaves the remainder 63. Find the remainder when the same number is divided by 29.
Pick: A) 5 B) 4 C) 1 D) 0 E) can not be determined | <gadget id="calculator">63 % 29</gadget>
<output>5</output>
<result>A</result> | A | 5 | A certain number when divided by 899 leaves the remainder 63. Find the remainder when the same number is divided by 29. | {
"A": "5",
"B": "4",
"C": "1",
"D": "0",
"E": "can not be determined"
} | reminder(63, 29) | reminder(n1,n2)| | "sol . ( a ) number = 899 q + 63 , where q is quotient = 31 × 29 q + ( 58 + 5 ) = 29 [ 31 q + 2 ] + 5 ∴ remainder = 5 answer a" | general |
math_qa__wM3ASEmxEgwLqbwP | Kelsey travelled for 10 hours. He covered the first half of the distance at 25 kmph and remaining half of the distance at 40 kmph. Find the distance travelled by Kelsey? Answers:
A) 583 km B) 400 km C) 670 km D) 360 km E) 234 km | <gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/40) + (1/10)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">25 / (1/8)</gadget>
<output>200</output>
<gadget id="calculator">200 * 2</gadget>
<output>400</output>
<result>B</result> | B | 400 | Kelsey travelled for 10 hours. He covered the first half of the distance at 25 kmph and remaining half of the distance at 40 kmph. Find the distance travelled by Kelsey? | {
"A": "583 km",
"B": "400 km",
"C": "670 km",
"D": "360 km",
"E": "234 km"
} | multiply(divide(25, add(divide(const_1, 40), divide(const_1, 10))), const_2) | divide(const_1,n2)|divide(const_1,n0)|add(#0,#1)|divide(n1,#2)|multiply(#3,const_2) | let the distance travelled be x km . total time = ( x / 2 ) / 25 + ( x / 2 ) / 40 = 10 = > x / 50 + x / 80 = 10 = > ( 8 x + 5 x ) / 400 = 10 = > x = 400 km answer : b | physics |
math_qa__MKxzsQshyrF4y5Q6 | A gambler has won 40% of his 30 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
Choose the correct choice from the following answers.
A) 20 B) 25 C) 30 D) 35 E) 40 | <gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">30 * (3/5)</gadget>
<output>18</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">30 * (2/5)</gadget>
<output>12</output>
<gadget id="calculator">18 - 12</gadget>
<output>6</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) - (3/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">6 / (1/5)</gadget>
<output>30</output>
<result>C</result> | C | 30 | A gambler has won 40% of his 30 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week? | {
"A": "20",
"B": "25",
"C": "30",
"D": "35",
"E": "40"
} | divide(subtract(multiply(30, divide(60, const_100)), multiply(30, divide(40, const_100))), subtract(divide(80, const_100), divide(60, const_100))) | divide(n3,const_100)|divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|multiply(n1,#1)|subtract(#2,#0)|subtract(#3,#4)|divide(#6,#5)| | "let x be the number of additional games the gambler needs to play . 0.4 ( 30 ) + 0.8 x = 0.6 ( x + 30 ) 0.2 x = 6 x = 30 the answer is c ." | gain |
math_qa__AIONbbAxGtoEDEnJ | The length of the rectangular field is double its width. Inside the field there is square shaped pond 5m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field? Options:
A) 54 B) 32 C) 75 D) 20 E) 11 | <gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">25 * 8</gadget>
<output>200</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">200 / (1/2)</gadget>
<output>400</output>
<gadget id="calculator">400 ** (1/2)</gadget>
<output>20</output>
<result>D</result> | D | 20 | The length of the rectangular field is double its width. Inside the field there is square shaped pond 5m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field? | {
"A": "54",
"B": "32",
"C": "75",
"D": "20",
"E": "11"
} | sqrt(divide(multiply(square_area(5), 8), inverse(const_2))) | inverse(const_2)|square_area(n0)|multiply(n2,#1)|divide(#2,#0)|sqrt(#3) | a / 8 = 5 * 5 = > a = 5 * 5 * 8 x * 2 x = 5 * 5 * 8 x = 10 = > 2 x = 20 answer : d | geometry |
math_qa__pgOCCknUaLB7bOCr | If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area? Choose the correct choice:
A) 30
B) 40
C) 50
D) 60
E) 70 | <gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) - 1</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>C</result> | C | 50 | If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area? | {
"A": "30",
"B": "40",
"C": "50",
"D": "60",
"E": "70"
} | multiply(subtract(divide(const_3, const_2), const_1), const_100) | divide(const_3,const_2)|subtract(#0,const_1)|multiply(#1,const_100) | length is halved . i . e . , length is decreased by 50 % breadth is tripled i . e . , breadth is increased by 200 % formula for change in area is : = ( - x + y - xy / 100 ) % = ( − 50 + 200 − 50 × 200 / 100 ) % = 50 % i . e . , area is increased by 50 % answer is c . | geometry |
math_qa__BAMYs1RVYpli83wu | The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8587 for a computer table, then what was the cost price of the computer table? Choose the most appropriate option
A) 6925 B) 6887 C) 6728 D) 6725 E) 2871 | <gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 + (6/25)</gadget>
<output>31/25 = around 1.24</output>
<gadget id="calculator">8_587 / (31/25)</gadget>
<output>6_925</output>
<result>A</result> | A | 6,925 | The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8587 for a computer table, then what was the cost price of the computer table? | {
"A": "6925",
"B": "6887",
"C": "6728",
"D": "6725",
"E": "2871"
} | divide(8587, add(const_1, divide(24, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | ": cp = sp * ( 100 / ( 100 + profit % ) ) = 8587 ( 100 / 124 ) = rs . 6925 . answer : a" | gain |
math_qa__84weJcxoXxUrYznh | In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 90 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election? Choose one:
A) 2 %
B) 5 %
C) 8 %
D) 10 %
E) 20 % | <gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 2</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) * 3</gadget>
<output>27/10 = around 2.7</output>
<gadget id="calculator">(3/10) + (27/10)</gadget>
<output>3</output>
<gadget id="calculator">3 - (27/10)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">2 - (3/10)</gadget>
<output>17/10 = around 1.7</output>
<gadget id="calculator">(3/10) + (17/10)</gadget>
<output>2</output>
<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>E</result> | E | 20 | In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 90 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election? | {
"A": "2 %",
"B": "5 %",
"C": "8 %",
"D": "10 %",
"E": "20 %"
} | multiply(divide(subtract(add(multiply(divide(15, const_100), 2), multiply(divide(90, const_100), 3)), add(subtract(3, multiply(divide(90, const_100), 3)), subtract(2, multiply(divide(15, const_100), 2)))), add(3, 2)), const_100) | add(n0,n1)|divide(n3,const_100)|divide(n2,const_100)|multiply(n1,#1)|multiply(n0,#2)|add(#3,#4)|subtract(n0,#4)|subtract(n1,#3)|add(#6,#7)|subtract(#5,#8)|divide(#9,#0)|multiply(#10,const_100)| | "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 90 % of republicans ( which is ( 60 * 0.9 ) = 54 ) and 15 % of democrats ( 40 * 0.15 = 6 ) voted for candidate x , means that out of total of 100 voters ; 60 ( 54 + 6 ) voters voted for candidate x and 40 voted for candidate y . thus we can infer that candidate x is expected to win the election by 20 ( 60 - 40 ) votes . therefore candidate x is expected to win the election by ( 20 / 100 ) votes which is equivalent to 20 % . i think the answer is e ." | other |
math_qa__NhMc3z8xelzqjsUb | Sandy bought 65 books for $1280 from one shop and 55 books for $880 from another shop. What is the average price that Sandy paid per book? Choose the correct choice from the following choices.
A) $ 12
B) $ 14
C) $ 16
D) $ 18
E) $ 20 | <gadget id="calculator">1_280 + 880</gadget>
<output>2_160</output>
<gadget id="calculator">65 + 55</gadget>
<output>120</output>
<gadget id="calculator">2_160 / 120</gadget>
<output>18</output>
<result>D</result> | D | 18 | Sandy bought 65 books for $1280 from one shop and 55 books for $880 from another shop. What is the average price that Sandy paid per book? | {
"A": "$ 12",
"B": "$ 14",
"C": "$ 16",
"D": "$ 18",
"E": "$ 20"
} | divide(add(1280, 880), add(65, 55)) | add(n1,n3)|add(n0,n2)|divide(#0,#1)| | "average price per book = ( 1280 + 880 ) / ( 65 + 55 ) = 2160 / 120 = $ 18 the answer is d ." | general |
math_qa__YuOV8lYoH7rEfDPd | each of the integers from 0 to 8 , inclusive , is written on a separate slip of blank paper and the 10 slips are dropped into hat . if the slips are then drawn one at a time without replacement , how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10 ? Options: A) 8 B) 9 C) 7 D) 6 E) 5 | <gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">1 + 6</gadget>
<output>7</output>
<result>C</result> | C | 7 | each of the integers from 0 to 8 , inclusive , is written on a separate slip of blank paper and the 10 slips are dropped into hat . if the slips are then drawn one at a time without replacement , how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10 ? | {
"A": "8",
"B": "9",
"C": "7",
"D": "6",
"E": "5"
} | add(const_1, subtract(8, const_2)) | subtract(n1,const_2)|add(#0,const_1) | you should consider the worst case scenario : if you pick numbers 0 , 1 , 2 , 3 , 4 and 5 then no two numbers out of these 6 add up to 10 . now , the next , 7 th number whatever it ' ll be ( 6,7 , or 8 ) will guarantee that two number will add up to 10 . so , 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10 answer : c | gain |
math_qa__Uj7mOLaKV41dl7gr | An ore contains 25% of an alloy that has 90% iron. Other than this, in the remaining 75% of the ore, there is no iron. How many kilograms of the ore are needed to obtain 60 kg of pure iron? Choices:
A) 250 kg
B) 275 kg
C) 300 kg
D) 266.66 kg
E) none | <gadget id="calculator">100 * 60</gadget>
<output>6_000</output>
<gadget id="calculator">25 * 90</gadget>
<output>2_250</output>
<gadget id="calculator">2_250 / 100</gadget>
<output>45/2 = around 22.5</output>
<gadget id="calculator">6_000 / (45/2)</gadget>
<output>800/3 = around 266.666667</output>
<result>D</result> | D | 266.66 | An ore contains 25% of an alloy that has 90% iron. Other than this, in the remaining 75% of the ore, there is no iron. How many kilograms of the ore are needed to obtain 60 kg of pure iron? | {
"A": "250 kg",
"B": "275 kg",
"C": "300 kg",
"D": "266.66 kg",
"E": "none"
} | divide(multiply(const_100, 60), divide(multiply(25, 90), const_100)) | multiply(n3,const_100)|multiply(n0,n1)|divide(#1,const_100)|divide(#0,#2) | solution : let there is 100 kg of ore . 25 % ore contains 90 % off iron that means 25 kg contains ; 25 * 90 / 100 = 22.5 kg iron . 22.5 kg iron contains 100 kg of ore . then , 1 kg of iron contains = 25 / 100 kg ore ; hence , 60 kg iron contains = 100 * 60 / 22.5 = 266.66 kg ore . answer : option d | other |
math_qa__Jwi8O1I1fzN8QSPs | Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 8 as quotient and the 15 as remainder
Choose the correct choice from the following choices
A) 1235 B) 1557.9 C) 1378 D) 1635 E) 1489 | <gadget id="calculator">1_365 - 15</gadget>
<output>1_350</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">1_350 / 7</gadget>
<output>1_350/7 = around 192.857143</output>
<gadget id="calculator">(1_350/7) * 8</gadget>
<output>10_800/7 = around 1_542.857143</output>
<result>B</result> | B | 1,557.9 | Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 8 as quotient and the 15 as remainder | {
"A": "1235",
"B": "1557.9",
"C": "1378",
"D": "1635",
"E": "1489"
} | multiply(divide(subtract(1365, 15), subtract(8, const_1)), 8) | 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 + 1365 = 8 x + 15 7 x = 1350 x = 192.9 large number = 192.9 + 1365 = 1557.9 b" | general |
math_qa__bKtKCvJKGzrxLkWu | A is the average (arithmetic mean) of the first 7 positive multiples of 6 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n? Choose the correct choice from the following
A) 8 B) 10 C) 12 D) 16 E) 24 | <gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<result>C</result> | C | 12 | A is the average (arithmetic mean) of the first 7 positive multiples of 6 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n? | {
"A": "8",
"B": "10",
"C": "12",
"D": "16",
"E": "24"
} | divide(multiply(6, const_4), const_2) | multiply(n1,const_4)|divide(#0,const_2) | if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 24 , which also equals b . b is the second positive multiple of n , thus n = 24 / 2 = 12 . the answer is c . | general |
math_qa__vEv8jPcRmyXGrXbZ | Cereal A is 11% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 3% sugar, what should be the ratio of Cereal A to Cereal B, by weight? Pick: A) 2 : 9 B) 3 : 7 C) 2 : 5 D) 1 : 8 E) 1 : 5 | <gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">11 - 3</gadget>
<output>8</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<result>D</result> | D | 0.125 | Cereal A is 11% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 3% sugar, what should be the ratio of Cereal A to Cereal B, by weight? | {
"A": "2 : 9",
"B": "3 : 7",
"C": "2 : 5",
"D": "1 : 8",
"E": "1 : 5"
} | divide(subtract(3, 2), subtract(11, 3)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)| | "2 % is 1 % - points below 3 % and 11 % is 8 % - points above 3 % . the ratio of a : b should be 1 : 8 . the answer is d ." | general |
math_qa__7pCaPMaKYYpSkSYX | In a class of 20 students, 2 students did not borrow any books from the library, 10 students each borrowed 1 book, 5 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? Select: A) 12 B) 13 C) 14 D) 15 E) 16 | <gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">10 * 1</gadget>
<output>10</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">15 + 2</gadget>
<output>17</output>
<gadget id="calculator">20 - 17</gadget>
<output>3</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">6 + 20</gadget>
<output>26</output>
<gadget id="calculator">40 - 26</gadget>
<output>14</output>
<result>C</result> | C | 14 | In a class of 20 students, 2 students did not borrow any books from the library, 10 students each borrowed 1 book, 5 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? | {
"A": "12",
"B": "13",
"C": "14",
"D": "15",
"E": "16"
} | subtract(multiply(20, 2), add(multiply(subtract(subtract(20, add(add(multiply(10, 1), 5), 2)), 1), 3), add(multiply(10, 1), multiply(5, 2)))) | multiply(n0,n1)|multiply(n2,n3)|multiply(n1,n4)|add(#1,#2)|add(n4,#1)|add(n1,#4)|subtract(n0,#5)|subtract(#6,n3)|multiply(n6,#7)|add(#3,#8)|subtract(#0,#9)| | "the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 10 * 1 + 5 * 2 = 20 books . the 3 students who borrowed at least three books borrowed 40 - 20 = 20 books . if 2 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 20 - 6 = 14 books . the answer is c ." | general |
math_qa__SXf38ZR8yzHdtAGI | A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations G are possible?
Choose the correct choice from the following answers:
A) 3 B) 4 C) 5 D) 6 E) g = 8 | <gadget id="calculator">240 / 30</gadget>
<output>8</output>
<result>E</result> | E | 8 | A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations G are possible? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "g = 8"
} | divide(240, 30) | divide(n0,n2)| | "the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10 , 24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . . e" | general |
math_qa__itv9VzuMY0x7jAar | The reciprocal of the hcf and lcm of two are 1/15 and 1/312 .if one of the number is 24 then other no. is Options.
A) 126 B) 136 C) 146 D) 156 E) 195 | <gadget id="calculator">15 * 312</gadget>
<output>4_680</output>
<gadget id="calculator">4_680 / 24</gadget>
<output>195</output>
<result>E</result> | E | 195 | The reciprocal of the hcf and lcm of two are 1/15 and 1/312 .if one of the number is 24 then other no. is | {
"A": "126",
"B": "136",
"C": "146",
"D": "156",
"E": "195"
} | divide(multiply(15, 312), 24) | multiply(n1,n3)|divide(#0,n4)| | "reciprocal of the hcf and lcm of two are 1 / 15 and 1 / 312 so , hcf = 15 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 15 * 312 / 24 = 195 answer : e" | physics |
math_qa__M9HUqnjhVbI3G16l | X and Y start a business with Rs.3000 and Rs.6000 respectively. Hoe should they share their profits at the end of one year?
Choose one:
A) 3 : 1
B) 2 : 1
C) 1 : 2
D) 1 : 3
E) 1 : 4 | <gadget id="calculator">3_000 / 6_000</gadget>
<output>1/2 = around 0.5</output>
<result>C</result> | C | 0.5 | X and Y start a business with Rs.3000 and Rs.6000 respectively. Hoe should they share their profits at the end of one year? | {
"A": "3 : 1",
"B": "2 : 1",
"C": "1 : 2",
"D": "1 : 3",
"E": "1 : 4"
} | divide(3000, 6000) | divide(n0,n1) | explanation : they should share the profits in the ratio of their investments . the ratio of the investments made by x and y = 3000 : 6000 = > 1 : 2 answer : c | gain |
math_qa__PSzQ8NezEvxYRQZ1 | In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 60 liters and they are all empty, how much money total will it cost to fuel all cars? Pick:
A) 320 $ B) 389 $ C) 420 $ D) 450 $ E) 489 $ | <gadget id="calculator">0.65 * 60</gadget>
<output>39</output>
<gadget id="calculator">39 * 12</gadget>
<output>468</output>
<result>E</result> | E | 489 | In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 60 liters and they are all empty, how much money total will it cost to fuel all cars? | {
"A": "320 $",
"B": "389 $",
"C": "420 $",
"D": "450 $",
"E": "489 $"
} | multiply(multiply(0.65, 60), 12) | multiply(n1,n3)|multiply(n2,#0) | total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 60 ) = 489 hence answer will be ( e ) | general |
math_qa__I6pY73jYNnIsjP0U | Set X consists of 10 integers and has median of 10 and a range of 10. What is the value of the greatest possible integer that can be present in the set? Choose the correct choice from the following answers: A) 32 B) 37 C) c . 40 D) 20 E) 50 | <gadget id="calculator">10 + 10</gadget>
<output>20</output>
<result>D</result> | D | 20 | Set X consists of 10 integers and has median of 10 and a range of 10. What is the value of the greatest possible integer that can be present in the set? | {
"A": "32",
"B": "37",
"C": "c . 40",
"D": "20",
"E": "50"
} | add(10, 10) | add(n1,n2)| | "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 this is possible . hence it is the greatest such number . answer ( d )" | general |
math_qa__eOCia4cCUAdPFGTs | A student chose a number, multiplied it by 2, then subtracted 140 from the result and got 102. What was the number he chose? Choose the correct choice:
A) 90 B) 100 C) 120 D) 160 E) 121 | <gadget id="calculator">102 + 140</gadget>
<output>242</output>
<gadget id="calculator">242 / 2</gadget>
<output>121</output>
<result>E</result> | E | 121 | A student chose a number, multiplied it by 2, then subtracted 140 from the result and got 102. What was the number he chose? | {
"A": "90",
"B": "100",
"C": "120",
"D": "160",
"E": "121"
} | divide(add(102, 140), 2) | add(n1,n2)|divide(#0,n0)| | "solution : let x be the number he chose , then 2 * x * 140 = 102 2 x = 242 x = 121 correct answer e" | general |
math_qa__Wi7xzexhHOhmEVQc | A can do a work in 15 days and B in 20 days. If they work on it together for 6 days, then the fraction of the work that is left is
Options.
A) 8 / 17 B) 7 / 15 C) 3 / 10 D) 8 / 15 E) 1 / 4 | <gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">(7/60) * 6</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>
<result>C</result> | C | 0.3 | A can do a work in 15 days and B in 20 days. If they work on it together for 6 days, then the fraction of the work that is left is | {
"A": "8 / 17",
"B": "7 / 15",
"C": "3 / 10",
"D": "8 / 15",
"E": "1 / 4"
} | subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 6)) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)|subtract(const_1,#3)| | "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 6 = 210 remaining work is 300 - 210 = 90 remaining fraction of work is = 90 / 300 = 3 / 10 answer c" | physics |
math_qa__qYtE1MzW1PocDU8A | A certain quantity is measured on two different scales, the P-scale and the S-scale, that are related linearly. Measurements on the P-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the P-scale corresponds to a measurement of 100 on the S-scale?
Choose the correct choice from the following answers:
A) 20 B) 36 C) 48 D) 60 E) 84 | <gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 30</gadget>
<output>7/3 = around 2.333333</output>
<gadget id="calculator">24 - 6</gadget>
<output>18</output>
<gadget id="calculator">(7/3) * 18</gadget>
<output>42</output>
<gadget id="calculator">42 + 6</gadget>
<output>48</output>
<result>C</result> | C | 48 | A certain quantity is measured on two different scales, the P-scale and the S-scale, that are related linearly. Measurements on the P-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the P-scale corresponds to a measurement of 100 on the S-scale? | {
"A": "20",
"B": "36",
"C": "48",
"D": "60",
"E": "84"
} | add(multiply(divide(subtract(100, 30), 30), subtract(24, 6)), 6) | subtract(n4,n2)|subtract(n1,n0)|divide(#0,n2)|multiply(#2,#1)|add(n0,#3) | first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that p increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , p will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c | general |
math_qa__fb0LivHmpXMaw9zn | Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A? Choose the correct choice from the following answers
A) 2500
B) 2550
C) 5050
D) 6275
E) 11325 | <gadget id="calculator">102 - 2</gadget>
<output>100</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 / 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">100 * 25</gadget>
<output>2_500</output>
<result>A</result> | A | 2,500 | Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A? | {
"A": "2500",
"B": "2550",
"C": "5050",
"D": "6275",
"E": "11325"
} | multiply(subtract(102, 2), add(divide(subtract(50, 2), const_2), const_1)) | subtract(n1,n0)|subtract(n2,n0)|divide(#0,const_2)|add(#2,const_1)|multiply(#3,#1)| | "set a contains 2,4 , 6 . . . 50 set b contains 102 , 104 , 106 . . . 150 number of terms in each set = 25 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 25 = 2500 answer a" | general |
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