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1.01k
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float64 -4,212
100B
| question_without_options
stringlengths 6
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stringlengths 7
6.48k
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stringlengths 8
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math_qa__4DJjSWua0ZzW7NPJ | In Town X, 60 percent of the population are employed, and 15 percent of the population are employed males. What percent of the employed people in Town X are females? Choose the correct choice: A) 16 % B) 75 % C) 32 % D) 40 % E) 52 % | <gadget id="calculator">60 - 15</gadget>
<output>45</output>
<gadget id="calculator">45 / 60</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>
<result>B</result> | B | 75 | In Town X, 60 percent of the population are employed, and 15 percent of the population are employed males. What percent of the employed people in Town X are females? | {
"A": "16 %",
"B": "75 %",
"C": "32 %",
"D": "40 %",
"E": "52 %"
} | multiply(divide(subtract(60, 15), 60), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | "total employed people 60 % , out of which 15 are employed males , hence 45 % are employed females . ( employed females ) / ( total employed people ) = 45 / 60 = 3 / 4 = 75 % answer : b ." | gain |
math_qa__IkmFPmYE4NQtFfvE | According to a recent student poll, 5/6 out of 30 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking? Select the correct option: A) 1 / 14 B) 4 / 49 C) 2 / 7 D) 28 / 29 E) 13 / 14 | <gadget id="calculator">binomial(30, 2)</gadget>
<output>435</output>
<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">30 * (5/6)</gadget>
<output>25</output>
<gadget id="calculator">30 - 25</gadget>
<output>5</output>
<gadget id="calculator">binomial(5, 2)</gadget>
<output>10</output>
<gadget id="calculator">435 - 10</gadget>
<output>425</output>
<gadget id="calculator">425 / 435</gadget>
<output>85/87 = around 0.977011</output>
<result>D</result> | D | 0.965517 | According to a recent student poll, 5/6 out of 30 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking? | {
"A": "1 / 14",
"B": "4 / 49",
"C": "2 / 7",
"D": "28 / 29",
"E": "13 / 14"
} | divide(subtract(choose(30, const_2), choose(subtract(30, multiply(30, divide(5, 6))), const_2)), choose(30, const_2)) | choose(n2,const_2)|divide(n0,n1)|multiply(n2,#1)|subtract(n2,#2)|choose(#3,const_2)|subtract(#0,#4)|divide(#5,#0) | 25 students are interested , 5 are not interested prob = 1 - 5 c 2 / 30 c 2 = 1 - ( 5 * 4 / ( 30 * 29 ) ) = 1 - 20 / 580 = 1 - 1 / 29 = 28 / 29 answer : d | gain |
math_qa__P49LvxJ7VIK211qS | For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 80?
Select the correct option.
A) 24
B) 26
C) 20
D) 22
E) 18 | <gadget id="calculator">80 - 7</gadget>
<output>73</output>
<gadget id="calculator">73 / 4</gadget>
<output>73/4 = around 18.25</output>
<gadget id="calculator">floor(73/4)</gadget>
<output>18</output>
<gadget id="calculator">1 - 7</gadget>
<output>-6</output>
<gadget id="calculator">(-6) / 4</gadget>
<output>-3/2 = around -1.5</output>
<gadget id="calculator">floor(-3/2)</gadget>
<output>-2</output>
<gadget id="calculator">18 - (-2)</gadget>
<output>20</output>
<result>C</result> | C | 20 | For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 80? | {
"A": "24",
"B": "26",
"C": "20",
"D": "22",
"E": "18"
} | subtract(floor(divide(subtract(80, 7), 4)), floor(divide(subtract(1, 7), 4))) | subtract(n3,n1)|subtract(n2,n1)|divide(#0,n0)|divide(#1,n0)|floor(#2)|floor(#3)|subtract(#4,#5)| | "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 80 4 n < 73 n < 18 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 18 ) combining the two - 1.5 < n < 18.25 n = 1 to 18 ( 18 integers ) and n = - 1 and 0 so 20 integers . c is the answer" | general |
math_qa__wr8cB2s8bNq6m2wl | Three cubes of metal whose edges are 5, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
Choose the correct choice from the following answers: A) 28 B) 77 C) 17.3 D) 18 E) 99 | <gadget id="calculator">5 ** 3</gadget>
<output>125</output>
<gadget id="calculator">12 ** 3</gadget>
<output>1_728</output>
<gadget id="calculator">125 + 1_728</gadget>
<output>1_853</output>
<gadget id="calculator">15 ** 3</gadget>
<output>3_375</output>
<gadget id="calculator">1_853 + 3_375</gadget>
<output>5_228</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">5_228 ** (1/3)</gadget>
<output>5228**(1/3) = around 17.355822</output>
<result>C</result> | C | 17.3 | Three cubes of metal whose edges are 5, 12 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube? | {
"A": "28",
"B": "77",
"C": "17.3",
"D": "18",
"E": "99"
} | power(add(add(volume_cube(5), volume_cube(12)), volume_cube(15)), const_0_33) | volume_cube(n0)|volume_cube(n1)|volume_cube(n2)|add(#0,#1)|add(#3,#2)|power(#4,const_0_33)| | "53 + 123 + 153 = a 3 = > a = 17.3 answer : c" | physics |
math_qa__eDem3CitXX4vX3yD | A rectangular pig farm has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 1250 square feet, what is the total length of the fence, in feet?
Choose the correct choice.
A) 25 B) 50 C) 100 D) 150 E) 200 | <gadget id="calculator">1_250 / 2</gadget>
<output>625</output>
<gadget id="calculator">625 ** (1/2)</gadget>
<output>25</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<gadget id="calculator">2 * (25 + 50)</gadget>
<output>150</output>
<result>D</result> | D | 150 | A rectangular pig farm has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 1250 square feet, what is the total length of the fence, in feet? | {
"A": "25",
"B": "50",
"C": "100",
"D": "150",
"E": "200"
} | rectangle_perimeter(sqrt(divide(1250, const_2)), multiply(sqrt(divide(1250, const_2)), const_2)) | divide(n0,const_2)|sqrt(#0)|multiply(#1,const_2)|rectangle_perimeter(#2,#1) | two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 1250 ie x ^ 2 = 625 ie x = 25 l = 50 w = 25 total length of fence = 2 * 25 + 50 = 100 my answer is c | geometry |
math_qa__IfcNsG3NkzuzNZhu | The ratio of pens to pencils is 5 to 6. There are 6 more pencils than pens. How many pencils are there? Choose the most appropriate option.
A) 32
B) 36
C) 40
D) 44
E) 48 | <gadget id="calculator">6 * 5</gadget>
<output>30</output>
<gadget id="calculator">30 + 6</gadget>
<output>36</output>
<result>B</result> | B | 36 | The ratio of pens to pencils is 5 to 6. There are 6 more pencils than pens. How many pencils are there? | {
"A": "32",
"B": "36",
"C": "40",
"D": "44",
"E": "48"
} | add(multiply(6, 5), 6) | multiply(n0,n2)|add(n2,#0)| | "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 6 x = 6 the number of pencils is 36 . the answer is b ." | other |
math_qa__JcY649XjBwaTshB6 | There is a clock which shows false timing ie it shows 10 minutes less for each 1 hour....if the clock shows 12 noon now how many minutes will be lost when it shows 3 pm ? Choose the correct choice from the following answers:
A) 16 minutes
B) 26 minutes
C) 36 minutes
D) 46 minutes
E) 56 minutes | <gadget id="calculator">3 * 60</gadget>
<output>180</output>
<gadget id="calculator">60 - 10</gadget>
<output>50</output>
<gadget id="calculator">180 / 50</gadget>
<output>18/5 = around 3.6</output>
<gadget id="calculator">(18/5) - 3</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 60</gadget>
<output>36</output>
<result>C</result> | C | 36 | There is a clock which shows false timing ie it shows 10 minutes less for each 1 hour....if the clock shows 12 noon now how many minutes will be lost when it shows 3 pm ? | {
"A": "16 minutes",
"B": "26 minutes",
"C": "36 minutes",
"D": "46 minutes",
"E": "56 minutes"
} | multiply(subtract(divide(multiply(3, const_60), subtract(const_60, 10)), 3), const_60) | multiply(n3,const_60)|subtract(const_60,n0)|divide(#0,#1)|subtract(#2,n3)|multiply(#3,const_60) | for 1 hour , 10 minutes is slower , then for 06 miuntes - 1 minutes is slower 30 minutes - 5 minutes actual time false time 12 12 01 pm 12.50 pm ( 10 minutes slower ) 02 pm 01.40 pm ( 12.50 + 60 min - 10 minutes slower ) 03 pm 02.30 pm ( 01.40 + 60 min - 10 minutes slower ) 03.36 pm 03.00 pm ( 02.30 + 36 min - 6 minutes slower ) so , 36 minutes will be lost when it is showing 3.00 pm . and the actual time is 3.36 pm answer : c | physics |
math_qa__WM4g2n0qQMOKQwMF | In a box of 7 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective? Pick one:
A) 1 / 2
B) 1 / 5
C) 2 / 3
D) 2 / 7
E) 1 / 7 | <gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">120 / 12</gadget>
<output>10</output>
<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">7 - 3</gadget>
<output>4</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">24 * 6</gadget>
<output>144</output>
<gadget id="calculator">5_040 / 144</gadget>
<output>35</output>
<gadget id="calculator">10 / 35</gadget>
<output>2/7 = around 0.285714</output>
<result>D</result> | D | 0.285714 | In a box of 7 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective? | {
"A": "1 / 2",
"B": "1 / 5",
"C": "2 / 3",
"D": "2 / 7",
"E": "1 / 7"
} | divide(divide(factorial(subtract(7, 2)), multiply(factorial(subtract(subtract(7, 2), 3)), factorial(3))), divide(factorial(7), multiply(factorial(subtract(7, 3)), factorial(3)))) | factorial(n2)|factorial(n0)|subtract(n0,n1)|subtract(n0,n2)|factorial(#2)|factorial(#3)|subtract(#2,n2)|factorial(#6)|multiply(#5,#0)|divide(#1,#8)|multiply(#7,#0)|divide(#4,#10)|divide(#11,#9)| | "first , there are 5 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 7 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 5 c 3 / 7 c 3 = 10 / 35 = 2 / 7 answer is d" | general |
math_qa__zs6wQ2C75Lox5tap | The mean of 50 observations was 36. It was found later that an observation 90 was wrongly taken as 23. The corrected new mean is?
Options:
A) 37.3
B) 36.1
C) 36.5
D) 36.9
E) 36.3 | <gadget id="calculator">36 * 50</gadget>
<output>1_800</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 - 23</gadget>
<output>25</output>
<gadget id="calculator">1_800 + 25</gadget>
<output>1_825</output>
<gadget id="calculator">1_825 / 50</gadget>
<output>73/2 = around 36.5</output>
<result>A</result> | A | 37.3 | The mean of 50 observations was 36. It was found later that an observation 90 was wrongly taken as 23. The corrected new mean is? | {
"A": "37.3",
"B": "36.1",
"C": "36.5",
"D": "36.9",
"E": "36.3"
} | divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50) | multiply(n0,n1)|subtract(n0,const_2)|subtract(#1,n3)|add(#0,#2)|divide(#3,n0)| | "correct sum = ( 36 * 50 + 90 - 23 ) = 1867 . correct mean = 1825 / 50 = 37.3 answer : a" | general |
math_qa__Cu03G2MZ9MiBstLH | How many Kilograms of Pure water is to be added to 100 Kilograms of a 30% saline solution to make it a 10% saline solution. Choose the correct choice from the following answers: A) 100 B) 200 C) 300 D) 400 E) 500 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">30 / (1/10)</gadget>
<output>300</output>
<gadget id="calculator">300 - 100</gadget>
<output>200</output>
<result>B</result> | B | 200 | How many Kilograms of Pure water is to be added to 100 Kilograms of a 30% saline solution to make it a 10% saline solution. | {
"A": "100",
"B": "200",
"C": "300",
"D": "400",
"E": "500"
} | subtract(divide(multiply(divide(30, const_100), 100), divide(10, const_100)), 100) | divide(n1,const_100)|divide(n2,const_100)|multiply(n0,#0)|divide(#2,#1)|subtract(#3,n0) | let x be the weights , in kilograms , of pure water to be added . let y be the weight , in kilograms , of the 10 % solution . hence x + 100 = y x = 200 kilograms . answer b | other |
math_qa__HtRgSCYL1R23nLEu | There is a escalator and 2 persons move down it.A takes 50 steps and B takes 75 steps while the escalator is moving down.Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps.Find the no. of steps in the escalator while it is staionary? Options:
A) 60 B) 70 C) 80 D) 90 E) 100 | <gadget id="calculator">75 / 3</gadget>
<output>25</output>
<gadget id="calculator">75 + 25</gadget>
<output>100</output>
<result>E</result> | E | 100 | There is a escalator and 2 persons move down it.A takes 50 steps and B takes 75 steps while the escalator is moving down.Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps.Find the no. of steps in the escalator while it is staionary? | {
"A": "60",
"B": "70",
"C": "80",
"D": "90",
"E": "100"
} | add(75, divide(75, 3)) | divide(n2,n4)|add(n2,#0) | if a takes 1 step in one second , then b takes 3 steps in one second . if a takes t 1 seconds to take 50 steps , then b takes 150 steps in t 1 seconds . for b , to take 150 steps he requires t 1 seconds , then to take 75 steps he requires t 1 / 2 seconds . now use relative velocity l - v * t 1 = 50 ( for first person ) l - v * t 1 / 2 = 75 ( for second person ) s ( escalator w . r . t ground ) - s ( person w . r . t escalator ) = s 1 ( person w . r . t ground ) s , s , s 1 are the steps now put the v * t 1 from 1 into the second equation and u get l - ( l - 50 ) / 2 = 75 l + 50 = 150 l = 100 answer : e | general |
math_qa__gDNGnrUNOQTYJmg8 | At what price must an article costing Rs.57 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? Choose the correct choice.
A) 62.5 B) 69.5 C) 62.3 D) 62.1 E) 75 | <gadget id="calculator">57 * 25</gadget>
<output>1_425</output>
<gadget id="calculator">1_425 / 100</gadget>
<output>57/4 = around 14.25</output>
<gadget id="calculator">57 + (57/4)</gadget>
<output>285/4 = around 71.25</output>
<gadget id="calculator">(285/4) * 100</gadget>
<output>7_125</output>
<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">7_125 / 95</gadget>
<output>75</output>
<result>E</result> | E | 75 | At what price must an article costing Rs.57 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price? | {
"A": "62.5",
"B": "69.5",
"C": "62.3",
"D": "62.1",
"E": "75"
} | divide(multiply(add(57, divide(multiply(57, 25), const_100)), const_100), subtract(const_100, 5)) | multiply(n0,n2)|subtract(const_100,n1)|divide(#0,const_100)|add(n0,#2)|multiply(#3,const_100)|divide(#4,#1)| | "cp = 57 sp = 57 * ( 125 / 100 ) = 71.25 mp * ( 95 / 100 ) = 71.25 mp = 75 answer : e" | gain |
math_qa__JhmLTXbjbS2A6tIC | If 3^x*4^y = 59,049 and x – y = 10, then x = ? Choose the correct choice from the following choices.
A) 10 B) 11 C) 12 D) 13 E) 14 | <gadget id="calculator">10 * 1</gadget>
<output>10</output>
<result>A</result> | A | 10 | If 3^x*4^y = 59,049 and x – y = 10, then x = ? | {
"A": "10",
"B": "11",
"C": "12",
"D": "13",
"E": "14"
} | multiply(10, const_1) | multiply(n3,const_1)| | "since 59,049 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 10 and y = 0 , then x = 10 . the answer is a ." | general |
math_qa__YFYqOibtSfKzKftb | A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 18 seconds. What is the length of the train in meters? Options.
A) 180 meters
B) 1111 meters
C) 1777 meters
D) 1822 meters
E) none of these | <gadget id="calculator">100 - 64</gadget>
<output>36</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">10 * 18</gadget>
<output>180</output>
<result>A</result> | A | 180 | A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 18 seconds. What is the length of the train in meters? | {
"A": "180 meters",
"B": "1111 meters",
"C": "1777 meters",
"D": "1822 meters",
"E": "none of these"
} | multiply(multiply(subtract(100, 64), const_0_2778), 18) | subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(n2,#1)| | "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 18 seconds distance = speed * time 36000 * 18 / 3600 = 180 meters . a is the answer ." | physics |
math_qa__YrXpI1AjIcJktACF | From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 11 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?
Pick one:
A) 38 B) 39 C) 40 D) 41 E) 42 | <gadget id="calculator">100 + 11</gadget>
<output>111</output>
<gadget id="calculator">100 / 111</gadget>
<output>100/111 = around 0.900901</output>
<gadget id="calculator">(100/111) * 45</gadget>
<output>1_500/37 = around 40.540541</output>
<result>D</result> | D | 41 | From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 11 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ? | {
"A": "38",
"B": "39",
"C": "40",
"D": "41",
"E": "42"
} | multiply(divide(const_100, add(const_100, 11)), 45) | add(n4,const_100)|divide(const_100,#0)|multiply(n7,#1)| | "soln : - 11 x = 45 - - > 10 / 9 * x = 45 - - > x = 45 * 9 / 10 = 1500 / 37 = ~ 41 . answer : d ." | gain |
math_qa__skoDlvSlwjxgONQw | When you multiply a number by 4 and
then subtract 3, the result is the same as
if you first subtracted 7 from the same
number and then multiplied by 9. What
is the number? Choose the correct option:
A) 23 B) 13 C) 19 D) 12 E) 10 | <gadget id="calculator">9 * 7</gadget>
<output>63</output>
<gadget id="calculator">63 - 3</gadget>
<output>60</output>
<gadget id="calculator">9 - 4</gadget>
<output>5</output>
<gadget id="calculator">60 / 5</gadget>
<output>12</output>
<result>D</result> | D | 12 | When you multiply a number by 4 and
then subtract 3, the result is the same as
if you first subtracted 7 from the same
number and then multiplied by 9. What
is the number? | {
"A": "23",
"B": "13",
"C": "19",
"D": "12",
"E": "10"
} | divide(subtract(multiply(9, 7), 3), subtract(9, 4)) | multiply(n2,n3)|subtract(n3,n0)|subtract(#0,n1)|divide(#2,#1) | let x equal the number and then change the words into an equation and solve for x : 4 x – 3 = 9 ( x – 7 ) 4 x – 3 = 9 x – 63 60 = 5 x 12 = x correct answer d ) 12 | general |
math_qa__gddIsKiNtmdtAayz | A man can row his boat with the stream at 25 km/h and against the stream in 13 km/h. The man's rate is? Choose the correct choice from the following choices:
A) 1 kmph
B) 2 kmph
C) 6 kmph
D) 8 kmph
E) 3 kmph | <gadget id="calculator">25 - 13</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<result>C</result> | C | 6 | A man can row his boat with the stream at 25 km/h and against the stream in 13 km/h. The man's rate is? | {
"A": "1 kmph",
"B": "2 kmph",
"C": "6 kmph",
"D": "8 kmph",
"E": "3 kmph"
} | divide(subtract(25, 13), const_2) | subtract(n0,n1)|divide(#0,const_2)| | "ds = 25 us = 13 s = ? s = ( 25 - 13 ) / 2 = 6 kmph answer : c" | gain |
math_qa__ScxxWSocQ0QFhWoy | An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is: Choose the correct choice from the following answers
A) 2
B) 9
C) 8
D) 7
E) 4 | <gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">3 / 8</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">10 + 6</gadget>
<output>16</output>
<gadget id="calculator">(3/8) * 16</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">(5/8) * 16</gadget>
<output>10</output>
<gadget id="calculator">18 - 10</gadget>
<output>8</output>
<result>C</result> | C | 8 | An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 6 kg of the alloy so that the ratio of the metal may be 3 : 1 is: | {
"A": "2",
"B": "9",
"C": "8",
"D": "7",
"E": "4"
} | subtract(multiply(multiply(divide(3, add(5, 3)), add(const_10, 6)), 3), multiply(divide(5, add(5, 3)), add(const_10, 6))) | add(n2,const_10)|add(n0,n1)|divide(n1,#1)|divide(n0,#1)|multiply(#0,#2)|multiply(#0,#3)|multiply(n1,#4)|subtract(#6,#5) | explanation : in sixteen kg of alloy 10 kg of zinc and 6 kg copper is present to make the ratio 3 : 1 we must add 8 kg of zinc to make it 18 kg of zinc and 6 kg copper so answer is 8 . answer : c | other |
math_qa__XSR5LNR3z1J13GSd | What is the CP of Rs 100 stock at 5 discount, with 1/5% brokerage? Select the correct option: A) 96.9 B) 96.3 C) 95.2 D) 96.7 E) 96.21 | <gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">95 + (1/5)</gadget>
<output>476/5 = around 95.2</output>
<result>C</result> | C | 95.2 | What is the CP of Rs 100 stock at 5 discount, with 1/5% brokerage? | {
"A": "96.9",
"B": "96.3",
"C": "95.2",
"D": "96.7",
"E": "96.21"
} | add(subtract(100, 5), divide(1, 5)) | divide(n2,n3)|subtract(n0,n1)|add(#0,#1)| | "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 5 + 1 / 5 95.2 thus the cp is rs 95.2 . answer : c" | gain |
math_qa__2g3ek7tS1EAySUP5 | A monkey start climbing up a tree 21 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top. Choose the correct choice from the following choices.
A) 15 hrs B) 18 hrs C) 19 hrs D) 17 hrs E) 16 hrs | <gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">21 / 1</gadget>
<output>21</output>
<gadget id="calculator">21 - 2</gadget>
<output>19</output>
<result>C</result> | C | 19 | A monkey start climbing up a tree 21 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top. | {
"A": "15 hrs",
"B": "18 hrs",
"C": "19 hrs",
"D": "17 hrs",
"E": "16 hrs"
} | subtract(divide(21, subtract(3, 2)), 2) | subtract(n1,n2)|divide(n0,#0)|subtract(#1,n2)| | "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 18 hrs it wil be 18 ft . but since the height of the tree is 21 ft , so if the monkey hops up the tree in the next hr i . e 19 th hr then it reaches at the top of the tree . hence it takes 19 hrs for monkey to reach at the top answer : c" | physics |
math_qa__nxryREZKL4VlLCol | John makes $50 a week from his job. He earns a raise andnow makes $75 a week. What is the % increase?
Answers
A) 15 % B) 16.66 % C) 50 % D) 19 % E) 21 % | <gadget id="calculator">75 - 50</gadget>
<output>25</output>
<gadget id="calculator">25 / 50</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>C</result> | C | 50 | John makes $50 a week from his job. He earns a raise andnow makes $75 a week. What is the % increase? | {
"A": "15 %",
"B": "16.66 %",
"C": "50 %",
"D": "19 %",
"E": "21 %"
} | multiply(divide(subtract(75, 50), 50), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | "increase = ( 25 / 50 ) * 100 = ( 1 / 2 ) * 100 = 50 % . c" | gain |
math_qa__F24jJUu31X9AmS2O | Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.6400? Answers.
A) 8100 B) 3388 C) 7767 D) 2009 E) 22888 | <gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 6_400</gadget>
<output>800</output>
<gadget id="calculator">6_400 + 800</gadget>
<output>7_200</output>
<gadget id="calculator">(1/8) * 7_200</gadget>
<output>900</output>
<gadget id="calculator">7_200 + 900</gadget>
<output>8_100</output>
<result>A</result> | A | 8,100 | Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.6400? | {
"A": "8100",
"B": "3388",
"C": "7767",
"D": "2009",
"E": "22888"
} | add(add(6400, multiply(divide(1, 8), 6400)), multiply(divide(1, 8), add(6400, multiply(divide(1, 8), 6400)))) | divide(n0,n1)|multiply(n2,#0)|add(n2,#1)|multiply(#2,#0)|add(#2,#3)| | "6400 * 9 / 8 * 9 / 8 = 8100 answer : a" | general |
math_qa__tX7Wt8KP5CG2CMhi | By selling 16 pens for a rupee a woman loses 5%. How many for a rupee should he sell in order to gain 18%? Pick one
A) 12
B) 14
C) 45
D) 13
E) 65 | <gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">100 / 95</gadget>
<output>20/19 = around 1.052632</output>
<gadget id="calculator">(20/19) / 16</gadget>
<output>5/76 = around 0.065789</output>
<gadget id="calculator">(5/76) * 18</gadget>
<output>45/38 = around 1.184211</output>
<gadget id="calculator">(45/38) / 100</gadget>
<output>9/760 = around 0.011842</output>
<gadget id="calculator">(5/76) + (9/760)</gadget>
<output>59/760 = around 0.077632</output>
<gadget id="calculator">1 / (59/760)</gadget>
<output>760/59 = around 12.881356</output>
<result>D</result> | D | 13 | By selling 16 pens for a rupee a woman loses 5%. How many for a rupee should he sell in order to gain 18%? | {
"A": "12",
"B": "14",
"C": "45",
"D": "13",
"E": "65"
} | inverse(add(divide(divide(const_100, subtract(const_100, 5)), 16), divide(multiply(divide(divide(const_100, subtract(const_100, 5)), 16), 18), const_100))) | subtract(const_100,n1)|divide(const_100,#0)|divide(#1,n0)|multiply(n2,#2)|divide(#3,const_100)|add(#2,#4)|inverse(#5) | d 95 % - - - 16 118 % - - - ? 95 / 118 * 16 = 13 | gain |
math_qa__Iix37Zsjcl0yA9Kx | An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1200 sculptures are not on display, how many pieces of art does the gallery have? Answers.
A) 360
B) 2700
C) 540
D) 640
E) 720 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1_200 / (2/3)</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 / (2/3)</gadget>
<output>2_700</output>
<result>B</result> | B | 2,700 | An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1200 sculptures are not on display, how many pieces of art does the gallery have? | {
"A": "360",
"B": "2700",
"C": "540",
"D": "640",
"E": "720"
} | divide(divide(1200, subtract(1, divide(1, 3))), subtract(1, divide(1, 3))) | divide(n0,n1)|subtract(n0,#0)|divide(n6,#1)|divide(#2,#1)| | "too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1200 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1200 - - > { not on display } = 1800 . according to ( i ) 2 / 3 * { total } = 1800 - - > { total } = 2700 . answer : b ." | general |
math_qa__sa0Hd8dTMvWgmb3e | A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12600 after a year?
Choose the correct answer:
A) 3630 B) 3637 C) 3630 D) 3631 E) 3780 | <gadget id="calculator">6_300 + 4_200</gadget>
<output>10_500</output>
<gadget id="calculator">10_500 + 10_500</gadget>
<output>21_000</output>
<gadget id="calculator">6_300 / 21_000</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 12_600</gadget>
<output>3_780</output>
<result>E</result> | E | 3,780 | A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12600 after a year? | {
"A": "3630",
"B": "3637",
"C": "3630",
"D": "3631",
"E": "3780"
} | multiply(divide(6300, add(add(6300, 4200), 10500)), 12600) | add(n0,n1)|add(n2,#0)|divide(n0,#1)|multiply(n3,#2)| | "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12600 = 3780 answer : e" | gain |
math_qa__XqWAdeo0AQzukBLp | The distance from City A to City B is 180 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 120 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
Choose the correct choice.
A) 42
B) 45
C) 46
D) 48
E) 50 | <gadget id="calculator">180 / 30</gadget>
<output>6</output>
<gadget id="calculator">120 / 60</gadget>
<output>2</output>
<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<gadget id="calculator">180 / 4</gadget>
<output>45</output>
<result>B</result> | B | 45 | The distance from City A to City B is 180 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 120 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? | {
"A": "42",
"B": "45",
"C": "46",
"D": "48",
"E": "50"
} | divide(180, subtract(divide(180, 30), divide(120, const_60))) | divide(n0,n1)|divide(n2,const_60)|subtract(#0,#1)|divide(n0,#2)| | "the time it takes cara to drive to city b is 180 / 30 = 6 hours . dan needs to take less than 4 hours for the trip . dan needs to exceed a constant speed of 180 / 4 = 45 miles per hour . the answer is b ." | physics |
math_qa__9RBGrSZuTaaEwmMu | of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents c watch all of the shows ? Select
A) 150 B) 108 C) 42 D) 21 E) - 21 | <gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 600</gadget>
<output>210</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 600</gadget>
<output>300</output>
<gadget id="calculator">210 + 300</gadget>
<output>510</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 600</gadget>
<output>240</output>
<gadget id="calculator">510 + 240</gadget>
<output>750</output>
<gadget id="calculator">750 - 600</gadget>
<output>150</output>
<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">(9/50) * 600</gadget>
<output>108</output>
<gadget id="calculator">150 - 108</gadget>
<output>42</output>
<gadget id="calculator">42 / 2</gadget>
<output>21</output>
<result>D</result> | D | 21 | of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents c watch all of the shows ? | {
"A": "150",
"B": "108",
"C": "42",
"D": "21",
"E": "- 21"
} | divide(subtract(subtract(add(add(multiply(divide(35, const_100), 600), multiply(divide(50, const_100), 600)), multiply(divide(40, const_100), 600)), 600), multiply(divide(18, const_100), 600)), 2) | divide(n1,const_100)|divide(n3,const_100)|divide(n2,const_100)|divide(n5,const_100)|multiply(n0,#0)|multiply(n0,#1)|multiply(n0,#2)|multiply(n0,#3)|add(#4,#5)|add(#8,#6)|subtract(#9,n0)|subtract(#10,#7)|divide(#11,n6) | oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is 3.5 % of 600 , c is 21 . d is the correct answer | gain |
math_qa__5pF5QeCVJL0WpHvW | Find the lowest positive integer that can be divided by all the even numbers between 14 and 21.
Choices:
A) 4581 B) 5040 C) 3682 D) 1231 E) 1563 | <gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">lcm(10, 9)</gadget>
<output>90</output>
<gadget id="calculator">lcm(90, 7)</gadget>
<output>630</output>
<gadget id="calculator">630 * 8</gadget>
<output>5_040</output>
<result>B</result> | B | 5,040 | Find the lowest positive integer that can be divided by all the even numbers between 14 and 21. | {
"A": "4581",
"B": "5040",
"C": "3682",
"D": "1231",
"E": "1563"
} | multiply(lcm(lcm(const_10, add(add(divide(14, const_2), const_1), const_1)), divide(14, const_2)), add(divide(14, const_2), const_1)) | divide(n0,const_2)|add(#0,const_1)|add(#1,const_1)|lcm(#2,const_10)|lcm(#0,#3)|multiply(#1,#4) | the even numbers between 14 and 21 are 1416 , 1820 . find the lcm of these numbers lcm = 2 ^ 4 * 7 * 3 ^ 2 * 5 the answer is b ) | general |
math_qa__NhCZf6DhJJBPIPne | by combining number of small cubes, a larger cube is produced. the ratio between volume of larger cube and small cube is 1000:8 then how many small cubes are required to produce a larger cube? Choose the correct choice from the following choices.
A) 100 B) 2 C) 5 D) 125 E) 80 | <gadget id="calculator">1_000 / 8</gadget>
<output>125</output>
<result>D</result> | D | 125 | by combining number of small cubes, a larger cube is produced. the ratio between volume of larger cube and small cube is 1000:8 then how many small cubes are required to produce a larger cube? | {
"A": "100",
"B": "2",
"C": "5",
"D": "125",
"E": "80"
} | divide(1000, 8) | divide(n0,n1) | the ratio is a 13 : a 23 = 1000 : 8 then number small cubes requiered is 1000 / 8 = 125 so the answre is d | geometry |
math_qa__hp8bpu1erSNyiiJZ | Jacob is now 12 years younger than Michael. If 3 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years? Choose one
A) 3
B) 7
C) 15
D) 21
E) 13 | <gadget id="calculator">12 + 3</gadget>
<output>15</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">15 - 6</gadget>
<output>9</output>
<gadget id="calculator">4 + 9</gadget>
<output>13</output>
<result>E</result> | E | 13 | Jacob is now 12 years younger than Michael. If 3 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years? | {
"A": "3",
"B": "7",
"C": "15",
"D": "21",
"E": "13"
} | add(4, subtract(add(12, 3), multiply(const_2, 3))) | add(n0,n1)|multiply(n1,const_2)|subtract(#0,#1)|add(n2,#2)| | "jacob = x years , mike = x + 12 years 3 years from now , 2 ( x + 3 ) = x + 15 2 x + 6 = x + 15 x = 9 x + 4 = 13 years answer e" | general |
math_qa__SiaKHuoaSRm6yYxD | The length of the bridge, which a train 140 m long and traveling at 45 km/hr can cross in 30 sec is? Choose the correct choice from the following options: A) 235 B) 240 C) 245 D) 250 E) 255 | <gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 140</gadget>
<output>235</output>
<result>A</result> | A | 235 | The length of the bridge, which a train 140 m long and traveling at 45 km/hr can cross in 30 sec is? | {
"A": "235",
"B": "240",
"C": "245",
"D": "250",
"E": "255"
} | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 140) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 140 + x ) / 30 = 25 / 2 x = 235 m . answer : option a" | physics |
math_qa__8UDzfhIB1nZfQX29 | A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?
Choose the correct choice from the following answers:
A) 8 B) 12 C) 18 D) 24 E) 48 | <gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">8_000 / 2</gadget>
<output>4_000</output>
<gadget id="calculator">12 * 4_000</gadget>
<output>48_000</output>
<gadget id="calculator">48_000 / 1_000</gadget>
<output>48</output>
<result>E</result> | E | 48 | A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? | {
"A": "8",
"B": "12",
"C": "18",
"D": "24",
"E": "48"
} | divide(multiply(add(add(6, 4), 2), divide(8000, 2)), const_1000) | add(n4,n5)|divide(n0,n2)|add(n2,#0)|multiply(#2,#1)|divide(#3,const_1000) | in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 4,000 by that net inflow to get the minutes ) - 48 min . answer e . | physics |
math_qa__5RUXxrNVbkFelOBX | Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $124 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings? Choices
A) 600
B) 720
C) 1080
D) 1200
E) 1800 | <gadget id="calculator">124 - 120</gadget>
<output>4</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 / 120</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">120 / (1/15)</gadget>
<output>1_800</output>
<result>E</result> | E | 1,800 | Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $124 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings? | {
"A": "600",
"B": "720",
"C": "1080",
"D": "1200",
"E": "1800"
} | divide(120, divide(multiply(const_2, subtract(124, 120)), 120)) | subtract(n1,n0)|multiply(#0,const_2)|divide(#1,n0)|divide(n0,#2)| | "$ 120 for 2 years = $ 60 per year . extra $ 4 yearned with the compound interest is the percent yearned on percent . so , $ 4 is yearned on $ 60 , which means that the interest = 15 % . this on the other hand means that half of the savings = 60 * 15 = $ 900 . twice of that = $ 1,800 . answer : e ." | gain |
math_qa__SR3M4jFzXRXmwfh5 | ABCD is a square where AB =√6000. Let X be a point on AB and Y be a point on CD such that AX = CY . Compute the area of trapezoid AXYD. Select the correct option
A) 3008 B) 2002 C) 1008 D) 2016 E) 3000 | <gadget id="calculator">6_000 / 2</gadget>
<output>3_000</output>
<result>E</result> | E | 3,000 | ABCD is a square where AB =√6000. Let X be a point on AB and Y be a point on CD such that AX = CY . Compute the area of trapezoid AXYD. | {
"A": "3008",
"B": "2002",
"C": "1008",
"D": "2016",
"E": "3000"
} | divide(6000, const_2) | divide(n0,const_2)| | "note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 6000 / 2 = 3000 . correct answer e" | geometry |
math_qa__s7yvlWLkCaUNYEsJ | Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8410/-. Find out the amount that he borrowed. Answers.
A) s . 5266
B) s . 5269
C) s . 5461
D) s . 5218
E) s . 52192 | <gadget id="calculator">6 * 9</gadget>
<output>54</output>
<gadget id="calculator">54 / 100</gadget>
<output>27/50 = around 0.54</output>
<gadget id="calculator">1 + (27/50)</gadget>
<output>77/50 = around 1.54</output>
<gadget id="calculator">8_410 / (77/50)</gadget>
<output>420_500/77 = around 5_461.038961</output>
<result>C</result> | C | 5,461 | Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8410/-. Find out the amount that he borrowed. | {
"A": "s . 5266",
"B": "s . 5269",
"C": "s . 5461",
"D": "s . 5218",
"E": "s . 52192"
} | divide(8410, add(const_1, divide(multiply(6, 9), const_100))) | multiply(n0,n1)|divide(#0,const_100)|add(#1,const_1)|divide(n3,#2) | explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8410 = p + ( 54 p / 100 ) 8410 = ( 100 p + 54 p ) / 100 8410 = 154 p / 100 p = ( 8410 * 100 ) / 154 = rs . 5461.039 answer : c | gain |
math_qa__cPSUKcBtDHsRADOs | The perimeter of a semi circle is 108 cm then the radius is? Choices:
A) 17 B) 21 C) 19 D) 11 E) 12 | <gadget id="calculator">2 + pi</gadget>
<output>2 + pi = around 5.141593</output>
<gadget id="calculator">108 / (2 + pi)</gadget>
<output>108/(2 + pi) = around 21.005165</output>
<result>B</result> | B | 21 | The perimeter of a semi circle is 108 cm then the radius is? | {
"A": "17",
"B": "21",
"C": "19",
"D": "11",
"E": "12"
} | divide(108, add(const_2, const_pi)) | add(const_2,const_pi)|divide(n0,#0)| | "36 / 7 r = 108 = > r = 21 answer : b" | physics |
math_qa__jVuhLGjS9jZZHkDa | The length of a rectangle is one- sixth of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1296 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options: A) 560 sq . units B) 360 sq . units C) 260 sq . units D) 460 sq . units E) 160 sq . units | <gadget id="calculator">1_296 ** (1/2)</gadget>
<output>36</output>
<gadget id="calculator">36 * 10</gadget>
<output>360</output>
<result>B</result> | B | 360 | The length of a rectangle is one- sixth of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1296 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? | {
"A": "560 sq . units",
"B": "360 sq . units",
"C": "260 sq . units",
"D": "460 sq . units",
"E": "160 sq . units"
} | multiply(sqrt(1296), 10) | sqrt(n0)|multiply(n1,#0) | given that the area of the square = 1225 sq . units = > side of square = √ 1296 = 36 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 36 * 10 = 360 sq . units answer : b | geometry |
math_qa__RAPUfJpKhabpi6LD | The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 35 inclusive. Choose the correct choice from the following
A) 288
B) 364
C) 410
D) 424
E) 450 | <gadget id="calculator">35 + 1</gadget>
<output>36</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">18 ** 2</gadget>
<output>324</output>
<gadget id="calculator">13 - 2</gadget>
<output>11</output>
<gadget id="calculator">11 + 1</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">324 - 36</gadget>
<output>288</output>
<result>A</result> | A | 288 | The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 35 inclusive. | {
"A": "288",
"B": "364",
"C": "410",
"D": "424",
"E": "450"
} | subtract(power(divide(add(35, const_1), 2), 2), power(divide(add(subtract(13, 2), const_1), 2), 2)) | add(n2,const_1)|subtract(n1,n0)|add(#1,const_1)|divide(#0,n0)|divide(#2,n0)|power(#3,n0)|power(#4,n0)|subtract(#5,#6)| | "we ' re dealing with a sequence of consecutive odd integers : 13 to 35 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 13 + 35 = 48 2 ) now look at the ' next smallest ' and the ' next biggest ' : 15 + 33 = 48 now we have proof that there is no middle term . we have 6 bunches of 48 . 6 ( 48 ) = 288 a" | general |
math_qa__i2X7gHqWCCxT5L1d | The function F(n) is defined as the product of all the consecutive positive integers between 4 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is
Choose the most appropriate option
A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<result>D</result> | D | 4 | The function F(n) is defined as the product of all the consecutive positive integers between 4 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | power(2, 2) | power(n1,n1) | f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 4 answer : d | general |
math_qa__zbPLjcGnpZYAKK0k | In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
Select.
A) 75 cu . m
B) 750 cu . m
C) 7500 cu . m
D) 75000 cu . m
E) none of these | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1.5 * 1_000</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 * 10</gadget>
<output>15_000</output>
<gadget id="calculator">(1/20) * 15_000</gadget>
<output>750</output>
<result>B</result> | B | 750 | In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is: | {
"A": "75 cu . m",
"B": "750 cu . m",
"C": "7500 cu . m",
"D": "75000 cu . m",
"E": "none of these"
} | multiply(divide(5, const_100), multiply(multiply(1.5, const_1000), const_10)) | divide(n0,const_100)|multiply(n1,const_1000)|multiply(#1,const_10)|multiply(#0,#2) | solution area = ( 1.5 × 10000 ) m 2 = 45000 m 2 . depth = m = m . ∴ volume = ( area × depth ) = m 3 = 750 m 3 . answer b | physics |
math_qa__oibLzF1m5Px61cty | For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200? Select:
A) 48
B) 49
C) 50
D) 51
E) 52 | <gadget id="calculator">200 - 7</gadget>
<output>193</output>
<gadget id="calculator">193 / 4</gadget>
<output>193/4 = around 48.25</output>
<gadget id="calculator">floor(193/4)</gadget>
<output>48</output>
<gadget id="calculator">1 - 7</gadget>
<output>-6</output>
<gadget id="calculator">(-6) / 4</gadget>
<output>-3/2 = around -1.5</output>
<gadget id="calculator">floor(-3/2)</gadget>
<output>-2</output>
<gadget id="calculator">48 - (-2)</gadget>
<output>50</output>
<result>C</result> | C | 50 | For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200? | {
"A": "48",
"B": "49",
"C": "50",
"D": "51",
"E": "52"
} | subtract(floor(divide(subtract(200, 7), 4)), floor(divide(subtract(1, 7), 4))) | subtract(n3,n1)|subtract(n2,n1)|divide(#0,n0)|divide(#1,n0)|floor(#2)|floor(#3)|subtract(#4,#5) | from first constraint 4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 200 4 n < 193 n < 48 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 48 ) combining the two - 1.5 < n < 48.25 n = 1 to 48 ( 48 integers ) and n = - 1 and 0 so 50 integers . c is the answer | general |
math_qa__tYNNrNxcfLW0UsF6 | In the first 10 overs of a cricket game, the run rate was only 2.1. What should be the rate in the remaining 30 overs to reach the target of 282 runs? Select:
A) 6.25 B) 8.28 C) 6.11 D) 8.7 E) 8.11 | <gadget id="calculator">10 * 2.1</gadget>
<output>21</output>
<gadget id="calculator">282 - 21</gadget>
<output>261</output>
<gadget id="calculator">261 / 30</gadget>
<output>87/10 = around 8.7</output>
<result>D</result> | D | 8.7 | In the first 10 overs of a cricket game, the run rate was only 2.1. What should be the rate in the remaining 30 overs to reach the target of 282 runs? | {
"A": "6.25",
"B": "8.28",
"C": "6.11",
"D": "8.7",
"E": "8.11"
} | divide(subtract(282, multiply(10, 2.1)), 30) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | "required run rate = [ 282 - ( 2.1 * 10 ) ] / 30 = 261 / 30 = 8.70 answer : d" | gain |
math_qa__4YNmPDnjNb7tM4sM | A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 70% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?
Choices.
A) 1000 B) 1250 C) 1300 D) 1600 E) 1857.14 | <gadget id="calculator">300 * 100</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 30</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 + 300</gadget>
<output>1_300</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1_300 / (7/10)</gadget>
<output>13_000/7 = around 1_857.142857</output>
<result>E</result> | E | 1,857.14 | A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 70% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons? | {
"A": "1000",
"B": "1250",
"C": "1300",
"D": "1600",
"E": "1857.14"
} | divide(add(divide(multiply(300, const_100), 30), 300), divide(70, const_100)) | divide(n1,const_100)|multiply(n0,const_100)|divide(#1,n3)|add(n0,#2)|divide(#3,#0)| | "300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 70 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 70 = 1857.14 e is the answer" | general |
math_qa__C7LIypayVI4mW2Mf | A car takes 6 hours to cover a distance of 720 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Select the correct option.
A) 60
B) 50
C) 80
D) 70
E) 65 | <gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">720 / 9</gadget>
<output>80</output>
<result>C</result> | C | 80 | A car takes 6 hours to cover a distance of 720 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? | {
"A": "60",
"B": "50",
"C": "80",
"D": "70",
"E": "65"
} | divide(720, divide(multiply(6, 3), 2)) | multiply(n0,n2)|divide(#0,n3)|divide(n1,#1)| | "time = 6 distance = 720 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 720 / 9 = 80 kmph answer c ." | physics |
math_qa__GukhWF86NIZkfzOk | By selling 15 pencils for a rupee a man loses 15%. How many for a rupee should he sell in order to gain 15%? Choose the correct answer
A) 8 B) 9 C) 11 D) 89 E) 81 | <gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">1 / 85</gadget>
<output>1/85 = around 0.011765</output>
<gadget id="calculator">115 * (1/85)</gadget>
<output>23/17 = around 1.352941</output>
<gadget id="calculator">1 / (23/17)</gadget>
<output>17/23 = around 0.73913</output>
<gadget id="calculator">(17/23) * 15</gadget>
<output>255/23 = around 11.086957</output>
<result>C</result> | C | 11 | By selling 15 pencils for a rupee a man loses 15%. How many for a rupee should he sell in order to gain 15%? | {
"A": "8",
"B": "9",
"C": "11",
"D": "89",
"E": "81"
} | multiply(divide(const_1, multiply(add(const_100, 15), divide(const_1, subtract(const_100, 15)))), 15) | add(n2,const_100)|subtract(const_100,n1)|divide(const_1,#1)|multiply(#0,#2)|divide(const_1,#3)|multiply(n0,#4)| | "85 % - - - 15 115 % - - - ? 15 / 115 * 15 = 11 answer : c" | gain |
math_qa__r4cv6mqEq5COtY8p | The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $50 and other expenses per hous is $ 50, then what would be the minimum expenditure required to cover a distance of 500 Km?
Choose the correct answer:
A) 800 B) 950 C) 900 D) 1000 E) 1250 | <gadget id="calculator">500 / 50</gadget>
<output>10</output>
<gadget id="calculator">10 * 50</gadget>
<output>500</output>
<gadget id="calculator">500 + 500</gadget>
<output>1_000</output>
<result>D</result> | D | 1,000 | The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 50 kmph its consumption is 1 litre per hour. if each litre costs $50 and other expenses per hous is $ 50, then what would be the minimum expenditure required to cover a distance of 500 Km? | {
"A": "800",
"B": "950",
"C": "900",
"D": "1000",
"E": "1250"
} | add(multiply(divide(500, 50), 50), multiply(divide(500, 50), 50)) | divide(n4,n0)|multiply(n2,#0)|multiply(n3,#0)|add(#1,#2)| | "50 kmph consumption is 1 lt / hr so 500 km will take 10 hrs and the consumption is 10 lt for entire distance . 1 lt costs $ 50 so 10 lt costs $ 500 extra expenses for 1 hr - $ 50 10 hrs - $ 500 total expense - $ 500 + $ 500 = $ 1000 answer : d" | physics |
math_qa__GWZkNfdQMwZFubLC | A number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r. What is the greatest two digit prime saturated integer ? Choose the correct option
A) 99 B) 98 C) 97 D) 96 E) 95 | <gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">6 + 90</gadget>
<output>96</output>
<result>D</result> | D | 96 | A number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r. What is the greatest two digit prime saturated integer ? | {
"A": "99",
"B": "98",
"C": "97",
"D": "96",
"E": "95"
} | add(multiply(const_2, const_3), subtract(const_100, const_10)) | multiply(const_2,const_3)|subtract(const_100,const_10)|add(#0,#1) | clearly d a number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r . 96 has more number of smaller prime factor thats the clue ! ! = d | other |
math_qa__XUxkQPLXZcadqwv4 | If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 7000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college? Choose the correct choice from the following answers.
A) $ 28000 B) $ 15000 C) $ 12000 D) $ 10000 E) $ 9000 | <gadget id="calculator">7_000 * 2</gadget>
<output>14_000</output>
<gadget id="calculator">14_000 * 2</gadget>
<output>28_000</output>
<result>A</result> | A | 28,000 | If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 7000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college? | {
"A": "$ 28000",
"B": "$ 15000",
"C": "$ 12000",
"D": "$ 10000",
"E": "$ 9000"
} | multiply(multiply(7000, const_2), const_2) | multiply(n1,const_2)|multiply(#0,const_2)| | "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 7,000 * 2 ) * 2 = $ 28,000 ( after 9 years investment will become $ 7,000 * 2 = $ 14,000 and in another 9 years it ' ll become $ 14,000 * 2 = $ 28,000 ) . answer : a ." | general |
math_qa__wyGtPlRUkuBhqAjS | A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480? Choose the most appropriate option:
A) 228 B) 217 C) 100 D) 288 E) 772 | <gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">9 * 4</gadget>
<output>36</output>
<gadget id="calculator">18 + 36</gadget>
<output>54</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">54 + 20</gadget>
<output>74</output>
<gadget id="calculator">1_480 / 74</gadget>
<output>20</output>
<gadget id="calculator">5 * 20</gadget>
<output>100</output>
<result>C</result> | C | 100 | A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480? | {
"A": "228",
"B": "217",
"C": "100",
"D": "288",
"E": "772"
} | multiply(5, divide(1480, add(add(multiply(6, 3), multiply(9, 4)), multiply(4, 5)))) | multiply(n0,n3)|multiply(n1,n2)|multiply(n2,n5)|add(#0,#1)|add(#3,#2)|divide(n6,#4)|multiply(n5,#5)| | "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1480 74 x = 1480 = > x = 20 5 x = 100 rs . answer : c" | physics |
math_qa__JHc2XOstDt8QWmC6 | If the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? Choices: A) 14 B) 8 C) 12 D) 4 E) 18 | <gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<result>D</result> | D | 4 | If the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters? | {
"A": "14",
"B": "8",
"C": "12",
"D": "4",
"E": "18"
} | divide(power(4, const_2), 4) | power(n0,const_2)|divide(#0,n1)| | "let length of rectangle = l 4 ^ 2 = l * 4 = > l = 16 / 4 = 4 answer d" | geometry |
math_qa__NNCf4409S4Ynpbbj | What is the average (arithmetic mean) of the numbers 21, 22, 23, 23, 24, and 25?
Select the correct option:
A) 23.0
B) 22.5
C) 21
D) 24
E) 23 | <gadget id="calculator">21 + 23</gadget>
<output>44</output>
<gadget id="calculator">23 - 21</gadget>
<output>2</output>
<gadget id="calculator">2 / 21</gadget>
<output>2/21 = around 0.095238</output>
<gadget id="calculator">(2/21) + 1</gadget>
<output>23/21 = around 1.095238</output>
<gadget id="calculator">44 * (23/21)</gadget>
<output>1_012/21 = around 48.190476</output>
<gadget id="calculator">(1_012/21) / 2</gadget>
<output>506/21 = around 24.095238</output>
<gadget id="calculator">(506/21) / (23/21)</gadget>
<output>22</output>
<result>E</result> | E | 23 | What is the average (arithmetic mean) of the numbers 21, 22, 23, 23, 24, and 25? | {
"A": "23.0",
"B": "22.5",
"C": "21",
"D": "24",
"E": "23"
} | divide(divide(multiply(add(21, 23), add(divide(subtract(23, 21), 21), const_1)), const_2), add(divide(subtract(23, 21), 21), const_1)) | add(n0,n2)|subtract(n2,n0)|divide(#1,n0)|add(#2,const_1)|multiply(#0,#3)|divide(#4,const_2)|divide(#5,#3)| | "{ 21 , 22 , 23 , 23 , 24 , 25 } = { 23 - 2,23 - 1 , 23 , 23,23 + 1,23 + 2 } - - > the average = 23 . answer : e ." | general |
math_qa__9ndBImCy9QfZSSdF | A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet? Select.
A) 2.15 pm
B) 1.15 pm
C) 4.15 pm
D) 3.15 pm
E) 12.15 pm | <gadget id="calculator">390 + 35</gadget>
<output>425</output>
<gadget id="calculator">65 + 35</gadget>
<output>100</output>
<gadget id="calculator">425 / 100</gadget>
<output>17/4 = around 4.25</output>
<gadget id="calculator">(17/4) + 10</gadget>
<output>57/4 = around 14.25</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">(57/4) - 12</gadget>
<output>9/4 = around 2.25</output>
<result>A</result> | A | 2.15 | A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet? | {
"A": "2.15 pm",
"B": "1.15 pm",
"C": "4.15 pm",
"D": "3.15 pm",
"E": "12.15 pm"
} | subtract(add(divide(add(390, 35), add(65, 35)), 10), add(10, const_2)) | add(n0,n4)|add(n2,n4)|add(n1,const_2)|divide(#0,#1)|add(n1,#3)|subtract(#4,#2) | suppose they meet x hours after 10 a . m . then , ( distance moved by first in x hrs ) + [ distance moved by second in ( x - 1 ) hrs ] = 390 . 65 x + 35 ( x - 1 ) = 390 = > 100 x = 425 = > x = 17 / 4 so , they meet 4 hrs . 15 min . after 10 a . m i . e . , at 2.15 p . m . answer a | physics |
math_qa__NMSDkvvBXgqg6Mem | In a group of cows and chickens, the number of legs was 16 more than twice the number of heads. The number of cows was: Select the correct option: A) 8 B) 7 C) 10 D) 12 E) 14 | <gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>A</result> | A | 8 | In a group of cows and chickens, the number of legs was 16 more than twice the number of heads. The number of cows was: | {
"A": "8",
"B": "7",
"C": "10",
"D": "12",
"E": "14"
} | divide(16, subtract(const_4, const_2)) | subtract(const_4,const_2)|divide(n0,#0)| | "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 16 more than twice the number of heads . therefore , 2 × ( x + y ) + 16 = 4 x + 2 y . or , 2 x + 2 y + 16 = 4 x + 2 y . or , 2 x + 16 = 4 x [ subtracting 2 y from both sides ] . or , 16 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 16 = 2 x . or , x = 8 [ dividing by 2 on both sides ] . therefore , the number of cows = 7 . correct answer : a ) 8" | general |
math_qa__7r0D8Dgy9Uqiu8ju | A is a working partner and B is a sleeping partner in the business. A puts in Rs.5000 and B Rs.1000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is? Choose the most appropriate option: A) 1978 B) 2707 C) 7728 D) 8160 E) 7291 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">9_600 * (9/10)</gadget>
<output>8_640</output>
<gadget id="calculator">5_000 + 1_000</gadget>
<output>6_000</output>
<gadget id="calculator">1_000 / 6_000</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">8_640 * (1/6)</gadget>
<output>1_440</output>
<gadget id="calculator">9_600 - 1_440</gadget>
<output>8_160</output>
<result>D</result> | D | 8,160 | A is a working partner and B is a sleeping partner in the business. A puts in Rs.5000 and B Rs.1000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is? | {
"A": "1978",
"B": "2707",
"C": "7728",
"D": "8160",
"E": "7291"
} | subtract(9600, multiply(multiply(9600, subtract(const_1, divide(10, const_100))), divide(1000, add(5000, 1000)))) | add(n0,n1)|divide(n2,const_100)|divide(n1,#0)|subtract(const_1,#1)|multiply(n3,#3)|multiply(#2,#4)|subtract(n3,#5)| | "5000 : 1000 = > 5 : 1 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 5 / 6 = 7200 + 960 = 8160 answer : d" | gain |
math_qa__UflINMAjxpazW2F0 | How much 90% of 40 is greater than 80% of 30? Choose the correct choice from the following.
A) 12 B) 14 C) 16 D) 17 E) 18 | <gadget id="calculator">90 * 40</gadget>
<output>3_600</output>
<gadget id="calculator">3_600 / 100</gadget>
<output>36</output>
<gadget id="calculator">80 * 30</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 / 100</gadget>
<output>24</output>
<gadget id="calculator">36 - 24</gadget>
<output>12</output>
<result>A</result> | A | 12 | How much 90% of 40 is greater than 80% of 30? | {
"A": "12",
"B": "14",
"C": "16",
"D": "17",
"E": "18"
} | subtract(divide(multiply(90, 40), const_100), divide(multiply(80, 30), const_100)) | multiply(n0,n1)|multiply(n2,n3)|divide(#0,const_100)|divide(#1,const_100)|subtract(#2,#3)| | "( 90 / 100 ) * 40 – ( 80 / 100 ) * 30 36 - 24 = 12 answer : a" | gain |
math_qa__eCkyvBAJ5u66JZiz | In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 3 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture. Select
A) 2 / 1
B) 4 / 1
C) 2 / 3
D) 3 / 4
E) 3 / 1 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">45 / 5</gadget>
<output>9</output>
<gadget id="calculator">45 - 9</gadget>
<output>36</output>
<gadget id="calculator">9 + 3</gadget>
<output>12</output>
<gadget id="calculator">36 / 12</gadget>
<output>3</output>
<result>E</result> | E | 3 | In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 3 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture. | {
"A": "2 / 1",
"B": "4 / 1",
"C": "2 / 3",
"D": "3 / 4",
"E": "3 / 1"
} | divide(subtract(45, divide(45, add(4, 1))), add(divide(45, add(4, 1)), 3)) | add(n1,n2)|divide(n0,#0)|add(n3,#1)|subtract(n0,#1)|divide(#3,#2)| | "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 3 ) = 36 / 12 = 3 / 1 . answer : e ." | general |
math_qa__lbsKh0Fimr2Cl1jO | The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned? Select: A) 19828.29 B) 19828.2 C) 19828.8 D) 19828.88 E) 19828.21 | <gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">1 + (2/25)</gadget>
<output>27/25 = around 1.08</output>
<gadget id="calculator">(27/25) ** 2</gadget>
<output>729/625 = around 1.1664</output>
<gadget id="calculator">(729/625) - 1</gadget>
<output>104/625 = around 0.1664</output>
<gadget id="calculator">2_828.8 / (104/625)</gadget>
<output>17_000</output>
<gadget id="calculator">17_000 + 2_828.8</gadget>
<output>19_828.8</output>
<result>C</result> | C | 19,828.8 | The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned? | {
"A": "19828.29",
"B": "19828.2",
"C": "19828.8",
"D": "19828.88",
"E": "19828.21"
} | add(divide(2828.80, subtract(power(add(const_1, divide(8, const_100)), const_2), const_1)), 2828.80) | divide(n0,const_100)|add(#0,const_1)|power(#1,const_2)|subtract(#2,const_1)|divide(n1,#3)|add(n1,#4)| | "let the sum be rs . p p { [ 1 + 8 / 100 ] 2 - 1 } = 2828.80 p ( 8 / 100 ) ( 2 + 8 / 100 ) = 2828.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 2828.80 / ( 0.08 ) ( 2.08 ) = 1360 / 0.08 = 17000 principal + interest = rs . 19828.80 answer : c" | gain |
math_qa__TtBSYaaehAUAzCWF | A man took loan from a bank at the rate of 13% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was? Choose the correct option
A) rs . 1846 B) rs . 18846 C) rs . 13846 D) rs . 2000 E) rs . 14846 | <gadget id="calculator">5_400 * 100</gadget>
<output>540_000</output>
<gadget id="calculator">540_000 / 3</gadget>
<output>180_000</output>
<gadget id="calculator">180_000 / 13</gadget>
<output>180_000/13 = around 13_846.153846</output>
<result>C</result> | C | 13,846 | A man took loan from a bank at the rate of 13% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was? | {
"A": "rs . 1846",
"B": "rs . 18846",
"C": "rs . 13846",
"D": "rs . 2000",
"E": "rs . 14846"
} | divide(divide(multiply(5400, const_100), 3), 13) | multiply(n2,const_100)|divide(#0,n1)|divide(#1,n0)| | "principal = ( 100 * 5400 ) / ( 13 * 3 ) = rs . 13846 answer : c" | gain |
math_qa__y3gKwEiU8jcgoCMM | A sum amounts to Rs.4410 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal? Select:
A) rs . 4000 B) rs . 5000 C) rs . 4500 D) rs . 4800 E) rs . 5800 | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) + 1</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">4_410 / (441/400)</gadget>
<output>4_000</output>
<result>A</result> | A | 4,000 | A sum amounts to Rs.4410 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal? | {
"A": "rs . 4000",
"B": "rs . 5000",
"C": "rs . 4500",
"D": "rs . 4800",
"E": "rs . 5800"
} | divide(4410, power(add(divide(5, const_100), const_1), const_2)) | divide(n2,const_100)|add(#0,const_1)|power(#1,const_2)|divide(n0,#2) | ci = 4410 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 4410 = p [ 21 / 20 ] ^ 2 4410 [ 20 / 21 ] ^ 2 4000 answer : a | gain |
math_qa__t9N9COqN5BXGnc7Y | How much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a mixture worth Rs.32/3 a litre? Select
A) 10 litres B) 12 litres C) 15 litres D) 18 litres E) 21 litres | <gadget id="calculator">32 / 3</gadget>
<output>32/3 = around 10.666667</output>
<gadget id="calculator">20 / 1.5</gadget>
<output>13.333333</output>
<gadget id="calculator">13.333333 - (32/3)</gadget>
<output>2.666666</output>
<gadget id="calculator">(32/3) / 2.666666</gadget>
<output>4.000001</output>
<gadget id="calculator">60 / 4.000001</gadget>
<output>14.999996</output>
<result>C</result> | C | 15 | How much water must be added to 60 litres of milk at 1.5 litres for Rs. 20 So as to have a mixture worth Rs.32/3 a litre? | {
"A": "10 litres",
"B": "12 litres",
"C": "15 litres",
"D": "18 litres",
"E": "21 litres"
} | divide(60, divide(divide(32, 3), subtract(divide(20, 1.5), divide(32, 3)))) | divide(n3,n4)|divide(n2,n1)|subtract(#1,#0)|divide(#0,#2)|divide(n0,#3) | c . p . of 1 litre of milk = rs . 20 × 2 / 3 = rs . 40 / 3 . c . p . of 1 litre of water = rs 0 . mean price = rs . 32 / 3 . by the rule of alligation , we have : c . p of 1 litre c . p of 1 litre of water of milk ( 0 ) ( rs . 40 / 3 ) \ / mean price ( rs . 32 / 3 ) / \ 40 / 3 − 32 / 3 32 / ( 3 − 0 ) 8 / 3 32 / 3 the ratio of water and milk = 8 / 3 : 32 / 3 . = 8 : 32 = 1 : 4 . thus , quantity of water to be added to 60 litres of milk : = ( 1 / 4 ) × 60 litres . = 15 litres . answer : c | general |
math_qa__dVsUIPeXJA5v9dq9 | A cricket bat is sold for $850, making a profit of $255. The profit percentage would be Choose the correct choice from the following answers
A) 24 % B) 25 % C) 30 % D) 36 % E) 43 % | <gadget id="calculator">850 - 255</gadget>
<output>595</output>
<gadget id="calculator">255 / 595</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(3/7) * 100</gadget>
<output>300/7 = around 42.857143</output>
<result>E</result> | E | 43 | A cricket bat is sold for $850, making a profit of $255. The profit percentage would be | {
"A": "24 %",
"B": "25 %",
"C": "30 %",
"D": "36 %",
"E": "43 %"
} | multiply(divide(255, subtract(850, 255)), const_100) | subtract(n0,n1)|divide(n1,#0)|multiply(#1,const_100)| | "255 / ( 850 - 255 ) = 255 / 595 = 51 / 119 = 43 % . answer : e ." | gain |
math_qa__uDGb4YTsBxgu7DQ4 | A car covers a distance of 624 km in 2 3/5 hours. Find its speed?
Select the correct option.
A) 104 kmph B) 194 kmph C) 109 kmph D) 174 kmph E) 240 kmph | <gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">2 + (3/5)</gadget>
<output>13/5 = around 2.6</output>
<gadget id="calculator">624 / (13/5)</gadget>
<output>240</output>
<result>E</result> | E | 240 | A car covers a distance of 624 km in 2 3/5 hours. Find its speed? | {
"A": "104 kmph",
"B": "194 kmph",
"C": "109 kmph",
"D": "174 kmph",
"E": "240 kmph"
} | divide(624, add(2, divide(3, 5))) | divide(n2,n3)|add(n1,#0)|divide(n0,#1) | 624 / 2 3 / 5 = 240 kmph answer : e | physics |
math_qa__ZQ8KAJH6jxXogceZ | Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 30 square meters. What is the area that is covered with three layers of wallpaper? Pick one: A) 5 square meters B) 36 square meters C) 42 square meters D) 45 square meters E) 120 square meters | <gadget id="calculator">300 - 180</gadget>
<output>120</output>
<gadget id="calculator">120 - 30</gadget>
<output>90</output>
<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<result>D</result> | D | 45 | Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 30 square meters. What is the area that is covered with three layers of wallpaper? | {
"A": "5 square meters",
"B": "36 square meters",
"C": "42 square meters",
"D": "45 square meters",
"E": "120 square meters"
} | divide(subtract(subtract(300, 180), 30), const_2) | subtract(n0,n1)|subtract(#0,n2)|divide(#1,const_2)| | "300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 30 = 90 sq m of the wallpaper overlaps in three layers . 90 sq m makes two extra layers hence the area over which it makes two extra layers is 45 sq m . answer ( d ) ." | geometry |
math_qa__1QeTeLLHoPuu2hIZ | If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $40. If Greg buys 7 shirts, 2 trousers and 2 ties, the total cost is $60. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties?
Choose the correct option.
A) $ 50 B) $ 64 C) $ 75 D) $ 96 E) can not be determined | <gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<result>A</result> | A | 50 | If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $40. If Greg buys 7 shirts, 2 trousers and 2 ties, the total cost is $60. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties? | {
"A": "$ 50",
"B": "$ 64",
"C": "$ 75",
"D": "$ 96",
"E": "can not be determined"
} | divide(add(60, 40), 2) | add(n3,n7)|divide(#0,n2)| | "solution : 3 x + 4 y + 2 z = 40 7 x + 2 y + 2 z = 60 adding both the equations = 10 x + 6 y + 4 z = 100 5 x + 3 y + 2 z = 50 ans a" | general |
math_qa__iRTDrSX1yt3CXxye | the heights of 3 individuals are in the ratio 4 : 5 : 6 . if the sum of the heights of the heaviest and the lightest boy is 150 cm more than the height of the third boy , what is the weight of the lightest boy ? Select the correct option
A) 120 cm B) 150 cm C) 160 cm D) 190 cm E) of these | <gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">10 - 5</gadget>
<output>5</output>
<gadget id="calculator">150 / 5</gadget>
<output>30</output>
<gadget id="calculator">30 * 4</gadget>
<output>120</output>
<result>A</result> | A | 120 | the heights of 3 individuals are in the ratio 4 : 5 : 6 . if the sum of the heights of the heaviest and the lightest boy is 150 cm more than the height of the third boy , what is the weight of the lightest boy ? | {
"A": "120 cm",
"B": "150 cm",
"C": "160 cm",
"D": "190 cm",
"E": "of these"
} | multiply(divide(150, subtract(add(4, 6), 5)), 4) | add(n1,n3)|subtract(#0,n2)|divide(n4,#1)|multiply(n1,#2) | let the heights of the three boys be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 150 = > 5 k = 150 = > k = 30 therefore the height of the lightest boy = 4 k = 4 ( 30 ) = 120 cm . answer : a | general |
math_qa__LPlNdqHKYvy44Jgf | The sale price of a trolley bag including the sale tax is Rs. 1190. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is: Choices: A) rs 800 B) rs 820 C) rs 860 D) rs 850 E) none of these | <gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">1_190 * (3/25)</gadget>
<output>714/5 = around 142.8</output>
<gadget id="calculator">1_190 - (714/5)</gadget>
<output>5_236/5 = around 1_047.2</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5_236/5) / (5/4)</gadget>
<output>20_944/25 = around 837.76</output>
<result>D</result> | D | 850 | The sale price of a trolley bag including the sale tax is Rs. 1190. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is: | {
"A": "rs 800",
"B": "rs 820",
"C": "rs 860",
"D": "rs 850",
"E": "none of these"
} | divide(subtract(1190, multiply(1190, divide(12, const_100))), add(divide(25, const_100), const_1)) | divide(n1,const_100)|divide(n2,const_100)|add(#1,const_1)|multiply(n0,#0)|subtract(n0,#3)|divide(#4,#2)| | "explanation : 112 % of s . p . = 1190 s . p . = rs . ( 1190 x 100 / 112 ) = rs . 1062.50 . c . p . = rs ( 100 / 125 x 1062.50 ) = rs 850 answer : d" | gain |
math_qa__oM5Em9pvN0ykqzfS | Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 74 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?
Pick: A) 3 B) 4 C) 5 D) 6 E) 8 | <gadget id="calculator">74 + 6</gadget>
<output>80</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">80 / 10</gadget>
<output>8</output>
<result>E</result> | E | 8 | Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 74 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "8"
} | divide(add(74, 6), add(4, 6)) | add(n0,n2)|add(n1,n2)|divide(#0,#1)| | "total distance = 74 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 70 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 70 / 10 = 7 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 7 = 28 + 4 = 32 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 32 / 4 = 8 hrs . . . answer e" | physics |
math_qa__MchOCRq1ETtNGMOB | the two sides of a triangle are 32 and 68. the area is 960 sq.cm. find the third side of triangle? Choose the correct choice from the following answers.
A) 45 B) 50 C) 60 D) 70 E) 80 | <gadget id="calculator">68 + 32</gadget>
<output>100</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">68 * 32</gadget>
<output>2_176</output>
<gadget id="calculator">2_176 ** 2</gadget>
<output>4_734_976</output>
<gadget id="calculator">960 ** 2</gadget>
<output>921_600</output>
<gadget id="calculator">921_600 * 4</gadget>
<output>3_686_400</output>
<gadget id="calculator">4_734_976 - 3_686_400</gadget>
<output>1_048_576</output>
<gadget id="calculator">1_048_576 ** (1/2)</gadget>
<output>1_024</output>
<gadget id="calculator">1_024 + 2_176</gadget>
<output>3_200</output>
<gadget id="calculator">3_200 / 2</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 * 4</gadget>
<output>6_400</output>
<gadget id="calculator">10_000 - 6_400</gadget>
<output>3_600</output>
<gadget id="calculator">3_600 ** (1/2)</gadget>
<output>60</output>
<gadget id="calculator">60 + 100</gadget>
<output>160</output>
<gadget id="calculator">160 / 2</gadget>
<output>80</output>
<gadget id="calculator">80 * 2</gadget>
<output>160</output>
<gadget id="calculator">160 - 100</gadget>
<output>60</output>
<result>C</result> | C | 60 | the two sides of a triangle are 32 and 68. the area is 960 sq.cm. find the third side of triangle? | {
"A": "45",
"B": "50",
"C": "60",
"D": "70",
"E": "80"
} | subtract(multiply(divide(add(sqrt(subtract(power(add(68, 32), const_2), multiply(divide(add(sqrt(subtract(power(multiply(68, 32), const_2), multiply(power(960, const_2), const_4))), multiply(68, 32)), const_2), const_4))), add(68, 32)), const_2), const_2), add(68, 32)) | add(n0,n1)|multiply(n0,n1)|power(n2,const_2)|multiply(#2,const_4)|power(#0,const_2)|power(#1,const_2)|subtract(#5,#3)|sqrt(#6)|add(#1,#7)|divide(#8,const_2)|multiply(#9,const_4)|subtract(#4,#10)|sqrt(#11)|add(#0,#12)|divide(#13,const_2)|multiply(#14,const_2)|subtract(#15,#0) | we see 68 ^ 2 - 32 ^ 2 = ( 68 + 32 ) * ( 68 - 32 ) = 100 * 36 = 60 ^ 2 now ( 1 / 2 ) * 60 * 32 = 960 ( match with given options ) ( i . e area of a right angled triangle whose sides are 32 , 60,68 ) third side = 60 answer : c | geometry |
math_qa__IlNc7wyK1whPp9Oo | From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 40 percent. What percent of the stock’s 2007 starting price was the price of the stock at the end of 2009? Choices:
A) 80
B) 126
C) 95
D) 100
E) 108 | <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">100 * (6/5)</gadget>
<output>120</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">120 * (3/4)</gadget>
<output>90</output>
<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">140 / 100</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">90 * (7/5)</gadget>
<output>126</output>
<result>B</result> | B | 126 | From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 40 percent. What percent of the stock’s 2007 starting price was the price of the stock at the end of 2009? | {
"A": "80",
"B": "126",
"C": "95",
"D": "100",
"E": "108"
} | multiply(multiply(multiply(const_100, divide(add(const_100, 20), const_100)), divide(subtract(const_100, 25), const_100)), divide(add(const_100, 40), const_100)) | add(n5,const_100)|add(n1,const_100)|subtract(const_100,n3)|divide(#0,const_100)|divide(#2,const_100)|divide(#1,const_100)|multiply(#5,const_100)|multiply(#4,#6)|multiply(#3,#7)| | "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 40 % = 90 * 1.2 = 126 thus ratio = 126 / 100 = 1.26 ( in % terms = 126 % ) . thus b is the correct answer ." | gain |
math_qa__eMaakRXOwS50ObsE | John makes $50 a week from his job. He earns a raise and now makes $70 a week. What is the % increase? Choose the correct choice from the following options
A) 16 % B) 16.66 % C) 18 % D) 21 % E) 40 % | <gadget id="calculator">70 - 50</gadget>
<output>20</output>
<gadget id="calculator">20 / 50</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>E</result> | E | 40 | John makes $50 a week from his job. He earns a raise and now makes $70 a week. What is the % increase? | {
"A": "16 %",
"B": "16.66 %",
"C": "18 %",
"D": "21 %",
"E": "40 %"
} | multiply(divide(subtract(70, 50), 50), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | "increase = ( 20 / 50 ) * 100 = 40 % . e" | gain |
math_qa__7oUQvx4LcejfxcIY | on a game show , there are 3 tables . each table has 3 boxes ( one zonk ! , one cash prize , and one grand prize ) . the contestant can choose one box from each table for a total of 3 boxes . if any of the boxes are a zonk ! , the contestant loses everything . what is the probability of getting no zonk ! from any of the 3 boxes chosen ?
Select
A) 1 / 5
B) 1 / 3
C) 8 / 27
D) 1 / 27
E) 7 / 8 | <gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">3 ** 3</gadget>
<output>27</output>
<gadget id="calculator">8 / 27</gadget>
<output>8/27 = around 0.296296</output>
<result>C</result> | C | 0.296296 | on a game show , there are 3 tables . each table has 3 boxes ( one zonk ! , one cash prize , and one grand prize ) . the contestant can choose one box from each table for a total of 3 boxes . if any of the boxes are a zonk ! , the contestant loses everything . what is the probability of getting no zonk ! from any of the 3 boxes chosen ? | {
"A": "1 / 5",
"B": "1 / 3",
"C": "8 / 27",
"D": "1 / 27",
"E": "7 / 8"
} | divide(power(const_2, 3), power(3, const_3)) | power(const_2,n0)|power(n0,const_3)|divide(#0,#1) | no zonk ! : 1 st box = no zonk ! = 2 / 3 2 nd box = no zonk ! = 2 / 3 3 rd box = no zonk ! = 2 / 3 ( 2 / 3 ) ( 2 / 3 ) ( 2 / 3 ) = 8 / 27 8 / 27 is the probability of no zonk ! , so . . . answer : c | general |
math_qa__igDQlGaw3cBIAetL | The average weight of A, B and C is 42 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is: Choose the correct choice from the following answers:
A) 33 kg
B) 31 kg
C) 32 kg
D) 40 kg
E) 37 kg | <gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">43 * 2</gadget>
<output>86</output>
<gadget id="calculator">80 + 86</gadget>
<output>166</output>
<gadget id="calculator">42 * 3</gadget>
<output>126</output>
<gadget id="calculator">166 - 126</gadget>
<output>40</output>
<result>D</result> | D | 40 | The average weight of A, B and C is 42 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is: | {
"A": "33 kg",
"B": "31 kg",
"C": "32 kg",
"D": "40 kg",
"E": "37 kg"
} | subtract(add(multiply(40, const_2), multiply(43, const_2)), multiply(42, const_3)) | multiply(n1,const_2)|multiply(n2,const_2)|multiply(n0,const_3)|add(#0,#1)|subtract(#3,#2)| | "let a , b , c represent their respective weights . then , we have : a + b + c = ( 42 x 3 ) = 126 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 40 . b ' s weight = 40 kg . d" | general |
math_qa__E5homimBdTBUhkrR | Dividing by 3⁄8 and then multiplying by 5⁄9 is the same as dividing by what number? Choose the correct option
A) 31 ⁄ 5 B) 16 ⁄ 5 C) 20 ⁄ 9 D) 40 / 27 E) 5 ⁄ 16 | <gadget id="calculator">8 / 3</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">5 / 9</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">(8/3) * (5/9)</gadget>
<output>40/27 = around 1.481481</output>
<result>D</result> | D | 1.481481 | Dividing by 3⁄8 and then multiplying by 5⁄9 is the same as dividing by what number? | {
"A": "31 ⁄ 5",
"B": "16 ⁄ 5",
"C": "20 ⁄ 9",
"D": "40 / 27",
"E": "5 ⁄ 16"
} | multiply(divide(8, 3), divide(5, 9)) | divide(n1,n0)|divide(n2,n3)|multiply(#0,#1) | say x / 3 / 8 * 5 / 9 = x * 8 / 3 * 5 / 9 = x * 40 / 27 d | general |
math_qa__WoAvjhcXRfrJjvGR | How many integers n greater than and less than 100 are there such that,if the digits of n are reversed, the resulting integer is n+9 ? Answers:
A) 5
B) 6
C) 7
D) 8
E) 9 | <gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">10 - 2</gadget>
<output>8</output>
<result>D</result> | D | 8 | How many integers n greater than and less than 100 are there such that,if the digits of n are reversed, the resulting integer is n+9 ? | {
"A": "5",
"B": "6",
"C": "7",
"D": "8",
"E": "9"
} | subtract(divide(100, const_10), const_2) | divide(n0,const_10)|subtract(#0,const_2) | ( 10 x + y ) = ( 10 y + x ) + 9 = > 9 x - 9 y = 9 = > x - y = 1 and only 8 numbers satisfy this condition and the numbers are 21,32 , 43,54 , 65,76 , 87,98 answer : d | general |
math_qa__YWXmpX155YdlppHz | A runs twice as fast as B and gives B a start of 50m.How long should the racecourse be so that A and B might reach in the same time? Pick: A) 75 m . B) 80 m . C) 150 m . D) 100 m . E) none of the above | <gadget id="calculator">50 * 2</gadget>
<output>100</output>
<result>D</result> | D | 100 | A runs twice as fast as B and gives B a start of 50m.How long should the racecourse be so that A and B might reach in the same time? | {
"A": "75 m .",
"B": "80 m .",
"C": "150 m .",
"D": "100 m .",
"E": "none of the above"
} | multiply(50, const_2) | multiply(n0,const_2)| | "ratio of speeds of a and b is 2 : 1 b is 50 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 50 m is 50 / 1 = 50 m so the total time taken by a and b to reach = 2 * 50 = 100 m answer : d" | physics |
math_qa__1s7CIY9BkBXxIih7 | What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 12%? Choose the correct choice from the following
A) 20 % B) 25 % C) 13 1 / 30 % D) 32 % E) 13 % | <gadget id="calculator">100 - 12</gadget>
<output>88</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">88 / (2/3)</gadget>
<output>132</output>
<gadget id="calculator">132 - 100</gadget>
<output>32</output>
<result>D</result> | D | 32 | What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 12%? | {
"A": "20 %",
"B": "25 %",
"C": "13 1 / 30 %",
"D": "32 %",
"E": "13 %"
} | subtract(divide(subtract(const_100, 12), divide(2, 3)), const_100) | divide(n0,n1)|subtract(const_100,n2)|divide(#1,#0)|subtract(#2,const_100)| | "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 88 2 / 3 sp 1 = 88 sp 1 = 132 100 - - - 32 = > 32 % answer : d" | gain |
math_qa__yZBJqlLRlG8FotIt | Reeya obtained 65, 67, 76, 80 and 95 out of 100 in different subjects, What will be the average
Choose the correct option
A) 76.6
B) 75
C) 80
D) 85
E) 90 | <gadget id="calculator">65 + 67</gadget>
<output>132</output>
<gadget id="calculator">132 + 76</gadget>
<output>208</output>
<gadget id="calculator">208 + 80</gadget>
<output>288</output>
<gadget id="calculator">288 + 95</gadget>
<output>383</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">383 / 5</gadget>
<output>383/5 = around 76.6</output>
<result>A</result> | A | 76.6 | Reeya obtained 65, 67, 76, 80 and 95 out of 100 in different subjects, What will be the average | {
"A": "76.6",
"B": "75",
"C": "80",
"D": "85",
"E": "90"
} | divide(add(add(add(add(65, 67), 76), 80), 95), add(const_4, const_1)) | add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1) | explanation : ( 65 + 67 + 76 + 80 + 95 / 5 ) = 76.6 option a | general |
math_qa__RUM7Wl0j2UKM61QT | An ant walks an average of 600 meters in 12 minutes. A beetle walks 15% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?
Choose the correct choice from the following answers: A) 2.215 . B) 2.55 C) 2.775 . D) 3.2 . E) 3.5 . | <gadget id="calculator">600 / 1_000</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">12 / 60</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(3/5) / (1/5)</gadget>
<output>3</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">3 * (17/20)</gadget>
<output>51/20 = around 2.55</output>
<result>B</result> | B | 2.55 | An ant walks an average of 600 meters in 12 minutes. A beetle walks 15% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h? | {
"A": "2.215 .",
"B": "2.55",
"C": "2.775 .",
"D": "3.2 .",
"E": "3.5 ."
} | multiply(divide(divide(600, const_1000), divide(12, const_60)), subtract(const_1, divide(15, const_100))) | divide(n0,const_1000)|divide(n1,const_60)|divide(n2,const_100)|divide(#0,#1)|subtract(const_1,#2)|multiply(#3,#4)| | "the ant walks an average of 600 meters in 12 minutes 600 meters in 1 / 5 hours the beetle walks 15 % less distance = 600 - 90 = 510 meters in 12 minutes 0.510 km in 12 / 60 = 1 / 5 hours speed = 0.510 * 5 = 2.55 km / h correct answer b = 2.55" | general |
math_qa__x0BYGc3kTnTNLWj1 | An aeroplane covers a certain distance of 450 Kmph in 4 hours. to cover the same distance in 3 2/3 hours, it Must travel at a speed of Options:
A) 440
B) 490
C) 640
D) 740
E) 250 | <gadget id="calculator">450 * 4</gadget>
<output>1_800</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 + 2</gadget>
<output>11</output>
<gadget id="calculator">11 / 3</gadget>
<output>11/3 = around 3.666667</output>
<gadget id="calculator">1_800 / (11/3)</gadget>
<output>5_400/11 = around 490.909091</output>
<result>B</result> | B | 490 | An aeroplane covers a certain distance of 450 Kmph in 4 hours. to cover the same distance in 3 2/3 hours, it Must travel at a speed of | {
"A": "440",
"B": "490",
"C": "640",
"D": "740",
"E": "250"
} | divide(multiply(450, 4), divide(add(multiply(3, 3), 2), 3)) | multiply(n0,n1)|multiply(n2,n4)|add(n3,#1)|divide(#2,n4)|divide(#0,#3)| | "speed of aeroplane = 450 kmph distance travelled in 4 hours = 450 * 4 = 1800 km speed of aeroplane to acver 1800 km in 11 / 3 = 1800 * 3 / 11 = 490 km answer b ." | physics |
math_qa__ZKKdQKJOalIVdyK1 | a 12 month project had a total budget of $ 42000 . after 8 months , the project had spent $ 23700 . at this point , how much was the project under budget ? Pick.
A) $ 4100 B) $ 4300 C) $ 4500 D) $ 4700 E) $ 4900 | <gadget id="calculator">23_700 / 8</gadget>
<output>5_925/2 = around 2_962.5</output>
<gadget id="calculator">(5_925/2) * 12</gadget>
<output>35_550</output>
<gadget id="calculator">42_000 - 35_550</gadget>
<output>6_450</output>
<gadget id="calculator">6_450 / 12</gadget>
<output>1_075/2 = around 537.5</output>
<gadget id="calculator">(1_075/2) * 8</gadget>
<output>4_300</output>
<result>B</result> | B | 4,300 | a 12 month project had a total budget of $ 42000 . after 8 months , the project had spent $ 23700 . at this point , how much was the project under budget ? | {
"A": "$ 4100",
"B": "$ 4300",
"C": "$ 4500",
"D": "$ 4700",
"E": "$ 4900"
} | multiply(divide(subtract(42000, multiply(divide(23700, 8), 12)), 12), 8) | divide(n3,n2)|multiply(n0,#0)|subtract(n1,#1)|divide(#2,n0)|multiply(n2,#3) | each month , the project should spend $ 42,000 / 12 = $ 3500 . in 8 months , the project should spend 8 * $ 3500 = $ 28,000 . the project is under budget by $ 28,000 - $ 23,700 = $ 4300 . the answer is b . | general |
math_qa__Mg7xOVrNuNuweHuq | A is the average (arithmetic mean) of the first 7 positive multiples of 4 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 answers
A) 2 B) 4 C) 6 D) 8 E) 10 | <gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>D</result> | D | 8 | A is the average (arithmetic mean) of the first 7 positive multiples of 4 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": "2",
"B": "4",
"C": "6",
"D": "8",
"E": "10"
} | divide(multiply(4, const_4), 2) | multiply(n1,const_4)|divide(#0,n3)| | "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 = 16 , which also equals b . b is the second positive multiple of n , thus n = 16 / 2 = 8 . the answer is d ." | general |
math_qa__2MoxiNJSpuRNRsLL | A cistern 8 m long and 6 m wide contains water up to a breadth of 1 m 85 cm. Find the total area of the wet surface. Choose the correct answer:
A) 102 m sqaure B) 100 m sqaure C) 152 m sqaure D) 164 m sqaure E) none of these | <gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">(17/20) + 1</gadget>
<output>37/20 = around 1.85</output>
<gadget id="calculator">(37/20) * 6</gadget>
<output>111/10 = around 11.1</output>
<gadget id="calculator">(37/20) * 8</gadget>
<output>74/5 = around 14.8</output>
<gadget id="calculator">(111/10) + (74/5)</gadget>
<output>259/10 = around 25.9</output>
<gadget id="calculator">2 * (259/10)</gadget>
<output>259/5 = around 51.8</output>
<gadget id="calculator">6 * 8</gadget>
<output>48</output>
<gadget id="calculator">(259/5) + 48</gadget>
<output>499/5 = around 99.8</output>
<result>B</result> | B | 100 | A cistern 8 m long and 6 m wide contains water up to a breadth of 1 m 85 cm. Find the total area of the wet surface. | {
"A": "102 m sqaure",
"B": "100 m sqaure",
"C": "152 m sqaure",
"D": "164 m sqaure",
"E": "none of these"
} | add(multiply(const_2, add(multiply(add(divide(85, const_100), 1), 6), multiply(add(divide(85, const_100), 1), 8))), multiply(6, 8)) | divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|add(#3,#4)|multiply(#5,const_2)|add(#6,#1)| | "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 6 * 1.85 + 8 * 1.85 ) ] + 8 * 6 = 100 m square option b" | physics |
math_qa__qC54qJmDAvkyuj0r | The ratio of buses to cars on River Road is 1 to 13. If there are 60 fewer buses than cars on River Road, how many cars are on River Road? Choose the correct choice from the following answers.
A) 65 B) 60 C) 55 D) 40 E) 45 | <gadget id="calculator">13 - 1</gadget>
<output>12</output>
<gadget id="calculator">60 / 12</gadget>
<output>5</output>
<gadget id="calculator">5 * 13</gadget>
<output>65</output>
<result>A</result> | A | 65 | The ratio of buses to cars on River Road is 1 to 13. If there are 60 fewer buses than cars on River Road, how many cars are on River Road? | {
"A": "65",
"B": "60",
"C": "55",
"D": "40",
"E": "45"
} | multiply(divide(60, subtract(13, 1)), 13) | subtract(n1,n0)|divide(n2,#0)|multiply(n1,#1)| | "b / c = 1 / 13 c - b = 60 . . . . . . . . . > b = c - 60 ( c - 60 ) / c = 1 / 13 testing answers . clearly eliminate bcde put c = 65 . . . . . . . . . > ( 65 - 60 ) / 65 = 5 / 65 = 1 / 13 answer : a" | other |
math_qa__BzJieVEG5bYFQOc8 | If A takes x days to do a work then B takes 2x days to do the same work then with in how many day's A will alone complete this work ? Options.
A) 27
B) 23
C) 24
D) 25
E) 26 | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">9 * 4</gadget>
<output>36</output>
<gadget id="calculator">9 + 4</gadget>
<output>13</output>
<gadget id="calculator">36 - 13</gadget>
<output>23</output>
<gadget id="calculator">23 + 4</gadget>
<output>27</output>
<result>A</result> | A | 27 | If A takes x days to do a work then B takes 2x days to do the same work then with in how many day's A will alone complete this work ? | {
"A": "27",
"B": "23",
"C": "24",
"D": "25",
"E": "26"
} | add(subtract(multiply(multiply(const_3, const_3), multiply(2, const_2)), add(multiply(const_3, const_3), multiply(2, const_2))), multiply(2, const_2)) | multiply(n0,const_2)|multiply(const_3,const_3)|add(#1,#0)|multiply(#1,#0)|subtract(#3,#2)|add(#0,#4) | 1 / x + 1 / 2 x = 1 / 18 = > 3 / 2 x = 1 / 18 = > x = 27 days . hence , a alone can finish the work in 27 days . answer : a | physics |
math_qa__IO54YE9WhkSjelac | 62 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? Choose the correct choice from the following answers
A) 64 B) 128 C) 152 D) 154 E) 256 | <gadget id="calculator">62 ** (1/3)</gadget>
<output>62**(1/3) = around 3.957892</output>
<gadget id="calculator">(62**(1/3)) + 2</gadget>
<output>2 + 62**(1/3) = around 5.957892</output>
<gadget id="calculator">(2 + 62**(1/3)) ** 3</gadget>
<output>(2 + 62**(1/3))**3 = around 211.484135</output>
<gadget id="calculator">((2 + 62**(1/3))**3) - 62</gadget>
<output>-62 + (2 + 62**(1/3))**3 = around 149.484135</output>
<result>D</result> | D | 154 | 62 small identical cubes are used to form a large cube. How many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? | {
"A": "64",
"B": "128",
"C": "152",
"D": "154",
"E": "256"
} | subtract(volume_cube(add(cube_edge_by_volume(62), const_2)), 62) | cube_edge_by_volume(n0)|add(#0,const_2)|volume_cube(#1)|subtract(#2,n0)| | "62 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 62 = 154 hence , d is the answer ." | geometry |
math_qa__HRIlJs4u3TG5ny68 | If you throw two dice at a same time.
Can you find the probability of getting sum as 10 of the two numbers shown ? Choices: A) 1 / 16 B) 2 / 14 C) 1 / 12 D) 1 / 19 E) 1 / 17 | <gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">(1/36) + (1/36)</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/18) + (1/36)</gadget>
<output>1/12 = around 0.083333</output>
<result>C</result> | C | 0.083333 | If you throw two dice at a same time.
Can you find the probability of getting sum as 10 of the two numbers shown ? | {
"A": "1 / 16",
"B": "2 / 14",
"C": "1 / 12",
"D": "1 / 19",
"E": "1 / 17"
} | add(add(divide(const_1, power(const_6, const_2)), divide(const_1, power(const_6, const_2))), divide(const_1, power(const_6, const_2))) | power(const_6,const_2)|divide(const_1,#0)|add(#1,#1)|add(#2,#1) | c 1 / 12 all possible cases can be 36 ( 6 * 6 ) case we need : [ ( 4,6 ) , ( 5,5 ) , ( 6,4 ) ] = 3 probability = > 3 / 36 = 1 / 12 | probability |
math_qa__Ax8pIJ4jsmWaH26Z | Can N and can В are both right circular cylinders. The radius of can N is twice the radius of can B, while the height of can N is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can N with the same brand of gasoline? Choose one
A) $ 1 B) $ 2 C) $ 4 D) $ 8 E) $ 16 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<result>E</result> | E | 16 | Can N and can В are both right circular cylinders. The radius of can N is twice the radius of can B, while the height of can N is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can N with the same brand of gasoline? | {
"A": "$ 1",
"B": "$ 2",
"C": "$ 4",
"D": "$ 8",
"E": "$ 16"
} | multiply(multiply(4, const_2), divide(power(const_2, const_2), const_2)) | multiply(n0,const_2)|power(const_2,const_2)|divide(#1,const_2)|multiply(#2,#0) | let x be the radius of b and 2 h be the height of b . therefore , radius of n = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e | geometry |
math_qa__JLbJuNiwoNiaR4HA | If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? Choose the correct choice from the following answers
A) 120 cm 2 B) 765 cm 2 C) 216 cm 2 D) 270 cm 2 E) 275 cm 2 | <gadget id="calculator">36 * 15</gadget>
<output>540</output>
<gadget id="calculator">540 / 2</gadget>
<output>270</output>
<result>D</result> | D | 270 | If the sides of a triangle are 39 cm, 36 cm and 15 cm, what is its area? | {
"A": "120 cm 2",
"B": "765 cm 2",
"C": "216 cm 2",
"D": "270 cm 2",
"E": "275 cm 2"
} | divide(multiply(36, 15), const_2) | multiply(n1,n2)|divide(#0,const_2)| | "the triangle with sides 39 cm , 36 cm and 15 cm is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : d" | geometry |
math_qa__CFHfNCR3mwrJGeM4 | What is the dividend. divisor 19, the quotient is 7 and the remainder is 6 Choose the correct choice from the following options:
A) 136 B) 137 C) 138 D) 139 E) 140 | <gadget id="calculator">19 * 7</gadget>
<output>133</output>
<gadget id="calculator">133 + 6</gadget>
<output>139</output>
<result>D</result> | D | 139 | What is the dividend. divisor 19, the quotient is 7 and the remainder is 6 | {
"A": "136",
"B": "137",
"C": "138",
"D": "139",
"E": "140"
} | add(multiply(19, 7), 6) | multiply(n0,n1)|add(n2,#0)| | "d = d * q + r d = 19 * 7 + 6 d = 133 + 6 d = 139" | general |
math_qa__YQqjxqRjX6DgjaMo | Some persons can do a piece of work in 20 days. Two times the number of these people will do half of that work in? Select the correct option: A) 3 B) 4 C) 5 D) 6 E) 8 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">20 * (1/2)</gadget>
<output>10</output>
<gadget id="calculator">10 * (1/2)</gadget>
<output>5</output>
<result>C</result> | C | 5 | Some persons can do a piece of work in 20 days. Two times the number of these people will do half of that work in? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "8"
} | multiply(multiply(20, divide(const_1, const_2)), divide(const_1, const_2)) | divide(const_1,const_2)|multiply(n0,#0)|multiply(#0,#1)| | "20 / ( 2 * 2 ) = 5 days answer : c" | physics |
math_qa__Lo2eXRzXjh9kldxu | If paint costs $3.20 per quart, and a quart covers 1200 square feet, how much will it cost to paint the outside of a cube 10 feet on each edge?
Pick one: A) $ 1.60 B) $ 16.00 C) $ 96.00 D) $ 108.00 E) $ 196.00 | <gadget id="calculator">3.2 / 1_200</gadget>
<output>0.002667</output>
<gadget id="calculator">6 * (10 ** 2)</gadget>
<output>600</output>
<gadget id="calculator">0.002667 * 600</gadget>
<output>1.6002</output>
<result>A</result> | A | 1.6 | If paint costs $3.20 per quart, and a quart covers 1200 square feet, how much will it cost to paint the outside of a cube 10 feet on each edge? | {
"A": "$ 1.60",
"B": "$ 16.00",
"C": "$ 96.00",
"D": "$ 108.00",
"E": "$ 196.00"
} | multiply(divide(3.2, 1200), surface_cube(10)) | divide(n0,n1)|surface_cube(n2)|multiply(#0,#1) | total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 1200 = 0.5 cost will be 0.5 * 3.2 = $ 1.6 ans : a | geometry |
math_qa__YoJ48s9YyPpzuROT | The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 33 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel? Select the correct option:
A) 20 ft
B) 25 ft
C) 750 ft
D) 900 ft
E) 1650 ft | <gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">30 * 5</gadget>
<output>150</output>
<gadget id="calculator">150 / 3</gadget>
<output>50</output>
<gadget id="calculator">50 + 5</gadget>
<output>55</output>
<gadget id="calculator">30 * 55</gadget>
<output>1_650</output>
<result>E</result> | E | 1,650 | The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 33 ft long. What is the distance traveled by the cart, when the front wheel has done five more revolutions than the rear wheel? | {
"A": "20 ft",
"B": "25 ft",
"C": "750 ft",
"D": "900 ft",
"E": "1650 ft"
} | multiply(30, add(divide(multiply(30, divide(const_10, const_2)), const_3), divide(const_10, const_2))) | divide(const_10,const_2)|multiply(n0,#0)|divide(#1,const_3)|add(#2,#0)|multiply(n0,#3) | point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 33 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 50 . sub x = 50 either in ( x + 5 ) * 30 or in x * 33 to get the distance , which is 1650 . so the correct choice is e . | physics |
math_qa__DOs9I9iH7yTXBrcE | If 50% of (x-y) = 20% of (x+y), then what percent of x is y? Choose the correct choice from the following options
A) 50.5 % B) 42.8 % C) 22.2 % D) 33.3 % E) 25 % | <gadget id="calculator">50 - 20</gadget>
<output>30</output>
<gadget id="calculator">50 + 20</gadget>
<output>70</output>
<gadget id="calculator">30 / 70</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(3/7) * 100</gadget>
<output>300/7 = around 42.857143</output>
<result>B</result> | B | 42.8 | If 50% of (x-y) = 20% of (x+y), then what percent of x is y? | {
"A": "50.5 %",
"B": "42.8 %",
"C": "22.2 %",
"D": "33.3 %",
"E": "25 %"
} | multiply(divide(subtract(50, 20), add(50, 20)), const_100) | add(n0,n1)|subtract(n0,n1)|divide(#1,#0)|multiply(#2,const_100)| | "50 % of ( x - y ) = 20 % of ( x + y ) 50 / 100 ( x - y ) = 20 / 100 ( x + y ) 3 x = 7 y required percentage = y / x * 100 = 3 y / 7 y * 100 = 42.85 % answer is b" | general |
math_qa__TsBd3VTkHsGC0Pl6 | Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 34% ryegrass, what percent of the weight of the mixture is from mixture X?
Choose one:
A) 25 %
B) 40 %
C) 50 %
D) 60 %
E) 75 % | <gadget id="calculator">25 + 1</gadget>
<output>26</output>
<gadget id="calculator">34 - 26</gadget>
<output>8</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">26 / 100</gadget>
<output>13/50 = around 0.26</output>
<gadget id="calculator">(2/5) - (13/50)</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">8 / (7/50)</gadget>
<output>400/7 = around 57.142857</output>
<result>D</result> | D | 60 | Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 34% ryegrass, what percent of the weight of the mixture is from mixture X? | {
"A": "25 %",
"B": "40 %",
"C": "50 %",
"D": "60 %",
"E": "75 %"
} | divide(subtract(34, add(25, const_1)), subtract(divide(40, const_100), divide(add(25, const_1), const_100))) | add(n2,const_1)|divide(n0,const_100)|divide(#0,const_100)|subtract(n4,#0)|subtract(#1,#2)|divide(#3,#4)| | "34 % is 9 % - points above 25 % and 6 % - points below 40 % . thus the ratio of mixture y to mixture x is 2 : 3 . the percent of mixture x is 3 / 5 = 60 % . the answer is d ." | gain |
math_qa__YZqzB1jIkkzFRyr0 | In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with centre B) is drawn. If the circle cuts AB and BC at P and Q respectively, then AP : QC is equal to Pick.
A) 1 : 1 B) 3 : 2 C) 4 : 1 D) 3 : 8 E) 2 : 5 | <gadget id="calculator">8 * 6</gadget>
<output>48</output>
<gadget id="calculator">48 / 10</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">6 - (24/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">8 - (24/5)</gadget>
<output>16/5 = around 3.2</output>
<gadget id="calculator">(6/5) / (16/5)</gadget>
<output>3/8 = around 0.375</output>
<result>D</result> | D | 0.375 | In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with centre B) is drawn. If the circle cuts AB and BC at P and Q respectively, then AP : QC is equal to | {
"A": "1 : 1",
"B": "3 : 2",
"C": "4 : 1",
"D": "3 : 8",
"E": "2 : 5"
} | divide(subtract(6, divide(multiply(8, 6), 10)), subtract(8, divide(multiply(8, 6), 10))) | multiply(n0,n1)|divide(#0,n2)|subtract(n0,#1)|subtract(n1,#1)|divide(#2,#3) | explanation : triangle abc and triangle adb are similar , ac / ab = bc / bd 10 / 6 = 8 / r r = 24 / 5 bp = bq = bd = r = 24 / 5 ap = ab - r = 6 - 24 / 5 = 6 / 5 cq = bc - r = 8 - 24 / 5 = 16 / 5 ap : cq = 6 / 16 = 3 : 8 answer : d | geometry |
math_qa__9V2e1eXhVrod1cUg | Find the mean proportional between 49 & 81? Answers:
A) 59 B) 61 C) 63 D) 65 E) 67 | <gadget id="calculator">49 + 81</gadget>
<output>130</output>
<gadget id="calculator">130 / 2</gadget>
<output>65</output>
<result>C</result> | C | 63 | Find the mean proportional between 49 & 81? | {
"A": "59",
"B": "61",
"C": "63",
"D": "65",
"E": "67"
} | divide(add(49, 81), const_2) | add(n0,n1)|divide(#0,const_2) | formula = √ a × b a = 49 and b = 81 √ 49 × 81 = 7 × 9 = 63 c | general |
math_qa__4TeDmiNaNTz8ZJUx | How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once? Select the correct option.
A) 20 B) 150 C) 225 D) 300 E) 320 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">25 * 16</gadget>
<output>400</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<gadget id="calculator">400 - 100</gadget>
<output>300</output>
<result>D</result> | D | 300 | How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once? | {
"A": "20",
"B": "150",
"C": "225",
"D": "300",
"E": "320"
} | subtract(multiply(multiply(add(4, const_1), add(4, const_1)), multiply(4, 4)), multiply(multiply(add(4, const_1), add(4, const_1)), 4)) | add(n0,const_1)|multiply(n0,n0)|multiply(#0,#0)|multiply(#2,#1)|multiply(#2,n0)|subtract(#3,#4)| | "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 4 = 20 . thus there are 320 - 20 = 300 such numbers . answer : d ." | physics |
math_qa__3XGGWLg8tGqRVQRI | In one hour, a boat goes 9 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:
Select the correct option
A) 2
B) 4
C) 7
D) 12
E) 15 | <gadget id="calculator">9 + 5</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>C</result> | C | 7 | In one hour, a boat goes 9 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is: | {
"A": "2",
"B": "4",
"C": "7",
"D": "12",
"E": "15"
} | divide(add(9, 5), const_2) | add(n0,n1)|divide(#0,const_2)| | "sol . speed in still water = 1 / 2 ( 9 + 5 ) kmph = 7 kmph . answer c" | physics |
math_qa__HXgabYAINvn4MNQJ | A 70 cm long wire is to be cut into two pieces so that one piece will be 2/3th of the other, how many centimeters will the shorter piece be? Choose the correct choice from the following choices
A) 35 B) 20 C) 28 D) 36 E) 30 | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">70 / (5/3)</gadget>
<output>42</output>
<gadget id="calculator">70 - 42</gadget>
<output>28</output>
<result>C</result> | C | 28 | A 70 cm long wire is to be cut into two pieces so that one piece will be 2/3th of the other, how many centimeters will the shorter piece be? | {
"A": "35",
"B": "20",
"C": "28",
"D": "36",
"E": "30"
} | subtract(70, divide(70, add(divide(2, 3), const_1))) | divide(n1,n2)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)| | "1 : 2 / 3 = 3 : 2 2 / 5 * 70 = 28 answer : c" | physics |
math_qa__D4USNEFWFnHUddho | 165 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4? Select the correct option:
A) 66 liters B) 32 liters C) 41 liters D) 50 liters E) 34 liters | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">165 / 5</gadget>
<output>33</output>
<gadget id="calculator">33 * 2</gadget>
<output>66</output>
<result>A</result> | A | 66 | 165 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4? | {
"A": "66 liters",
"B": "32 liters",
"C": "41 liters",
"D": "50 liters",
"E": "34 liters"
} | multiply(divide(165, add(3, 2)), 2) | add(n1,n2)|divide(n0,#0)|multiply(n2,#1)| | "milk = 3 / 5 * 165 = 99 liters water = 66 liters 99 : ( 66 + p ) = 3 : 4 198 + 3 p = 396 = > p = 66 66 liters of water are to be added for the ratio become 3 : 4 . answer : a" | general |
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