id stringlengths 25 25 | question stringlengths 45 1.01k | chain stringlengths 75 4.11k | result stringclasses 5 values | result_float float64 -4,212 100B | question_without_options stringlengths 6 962 | options dict | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | rationale stringlengths 1 2.74k | category stringclasses 6 values |
|---|---|---|---|---|---|---|---|---|---|---|
math_qa__FtkqrOyAmGkgPGAT | What annual installment will discharge a debt of $100 due in 3 years at 10% simple interest?
Choices:
A) 25.6
B) 50.2
C) 30.3
D) 45
E) 56 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">100 * (1/10)</gadget>
<output>10</output>
<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<result>C</result> | C | 30.3 | What annual installment will discharge a debt of $100 due in 3 years at 10% simple interest? | {
"A": "25.6",
"B": "50.2",
"C": "30.3",
"D": "45",
"E": "56"
} | multiply(multiply(100, divide(10, const_100)), 3) | divide(n2,const_100)|multiply(n0,#0)|multiply(n1,#1) | let each installment be x [ x + ( x * 10 * 1 / 100 ) ] + [ x + ( x * 10 * 2 / 100 ) ] + x = 100 11 x / 10 + 12 x / 10 + x = 100 x = 30.3 answer is c | gain |
math_qa__CeZiTJZrg92ZkPUG | A boat can travel with aspeed of 20km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 125km downstream.
Select
A) 1 hr
B) 2 hrs
C) 3 hrs
D) 4 hrs
E) 5 hrs | <gadget id="calculator">20 + 5</gadget>
<output>25</output>
<gadget id="calculator">125 / 25</gadget>
<output>5</output>
<result>E</result> | E | 5 | A boat can travel with aspeed of 20km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 125km downstream. | {
"A": "1 hr",
"B": "2 hrs",
"C": "3 hrs",
"D": "4 hrs",
"E": "5 hrs"
} | divide(125, add(20, 5)) | add(n0,n1)|divide(n2,#0) | speed downstream = ( 20 + 5 ) km / hr = 25 km / hr . time taken to travel 125 km downstream = 125 / 25 hrs = 5 hrs . answer : e | physics |
math_qa__5xsaWG2E23viwl8Q | John bought 9.25m of cloth for $397.75. Find the cost price per metre. Choose the correct choice from the following choices
A) 46 B) 47 C) 58 D) 56 E) 43 | <gadget id="calculator">397.75 / 9.25</gadget>
<output>43</output>
<result>E</result> | E | 43 | John bought 9.25m of cloth for $397.75. Find the cost price per metre. | {
"A": "46",
"B": "47",
"C": "58",
"D": "56",
"E": "43"
} | divide(397.75, 9.25) | divide(n1,n0)| | "cloth bought by john = 9.25 m cost of 9.25 m = $ 397.75 cost per metre = 397.75 ÷ 9.25 the cost of the cloth per metre = $ 43 answers : e" | physics |
math_qa__1WUVTvQQJh53iQye | A sum fetched total simple interest of 4016.25 at the rate of 13 p.c.p.a. in 5 years. What is the sum? Choose the correct choice from the following answers:
A) 6178.85
B) 8032.5
C) 4462.5
D) 8900
E) none of these | <gadget id="calculator">100 * 4_016.25</gadget>
<output>401_625</output>
<gadget id="calculator">13 * 5</gadget>
<output>65</output>
<gadget id="calculator">401_625 / 65</gadget>
<output>80_325/13 = around 6_178.846154</output>
<result>A</result> | A | 6,178.85 | A sum fetched total simple interest of 4016.25 at the rate of 13 p.c.p.a. in 5 years. What is the sum? | {
"A": "6178.85",
"B": "8032.5",
"C": "4462.5",
"D": "8900",
"E": "none of these"
} | divide(multiply(const_100, 4016.25), multiply(13, 5)) | multiply(n0,const_100)|multiply(n1,n2)|divide(#0,#1)| | "let the sums be p . now , 65 % of p = 4016.25 or , p = 6178.85 answer a" | gain |
math_qa__SIPpWH8E6DwxaadF | I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways? Pick one
A) 12 mins B) 10 mins C) 19 mins D) 15 mins E) 20 mins | <gadget id="calculator">55 - 37</gadget>
<output>18</output>
<gadget id="calculator">37 / 2</gadget>
<output>37/2 = around 18.5</output>
<gadget id="calculator">18 + (37/2)</gadget>
<output>73/2 = around 36.5</output>
<gadget id="calculator">(73/2) - 18</gadget>
<output>37/2 = around 18.5</output>
<result>C</result> | C | 19 | I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways? | {
"A": "12 mins",
"B": "10 mins",
"C": "19 mins",
"D": "15 mins",
"E": "20 mins"
} | subtract(add(subtract(55, 37), divide(37, const_2)), subtract(55, 37)) | divide(n0,const_2)|subtract(n1,n0)|add(#0,#1)|subtract(#2,#1) | let the distance be x km . then , ( time taken to walk x km ) + ( time taken to ride x km ) = 37 min . ( time taken to walk 2 x km ) + ( time taken to ride 2 x km ) = 74 min . but , the time taken to walk 2 x km = 55 min . time taken to ride 2 x km = ( 74 - 55 ) min = 19 min . ans : c | physics |
math_qa__p890yExnZduxrPEI | The area of a parallelogram is 242sq m and its altitude is twice the corresponding base. Then the length of the base is? Pick.
A) 8 B) 9 C) 7 D) 11 E) 2 | <gadget id="calculator">242 / 2</gadget>
<output>121</output>
<gadget id="calculator">121 ** (1/2)</gadget>
<output>11</output>
<result>D</result> | D | 11 | The area of a parallelogram is 242sq m and its altitude is twice the corresponding base. Then the length of the base is? | {
"A": "8",
"B": "9",
"C": "7",
"D": "11",
"E": "2"
} | sqrt(divide(242, const_2)) | divide(n0,const_2)|sqrt(#0)| | "2 x * x = 242 = > x = 11 answer : d" | geometry |
math_qa__pVC63OOgPwHqWUiY | A part-time employee whose hourly wage was increased by 10 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced? Choose the correct choice from the following choices:
A) 9.09 B) 10 C) 11 D) 12 E) 13 | <gadget id="calculator">10 + 100</gadget>
<output>110</output>
<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) * 10</gadget>
<output>11</output>
<gadget id="calculator">1 / 11</gadget>
<output>1/11 = around 0.090909</output>
<gadget id="calculator">(1/11) * 100</gadget>
<output>100/11 = around 9.090909</output>
<result>A</result> | A | 9.09 | A part-time employee whose hourly wage was increased by 10 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced? | {
"A": "9.09",
"B": "10",
"C": "11",
"D": "12",
"E": "13"
} | multiply(divide(const_1, multiply(divide(add(10, const_100), const_100), const_10)), const_100) | add(n0,const_100)|divide(#0,const_100)|multiply(#1,const_10)|divide(const_1,#2)|multiply(#3,const_100) | let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.1 x now we need to find number of hours worked so that x * y = 1.1 x * z i . e z = x * y / 1.1 x = 1 / 1.1 y % decrease = ( y - 1 / 1.1 y ) / y * 100 = 1 - 1 / 1.1 * 100 = 9.09 % thus my answer is a . | general |
math_qa__f2sTkOyDrylnTFog | In the above number, A and B represent the tens and units digits, respectively. If the above number is divisible by 35, what is the greatest possible value of B x A?
Choose the correct choice:
A) 0 B) 10 C) 20 D) 30 E) 35 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">7 * 5</gadget>
<output>35</output>
<result>E</result> | E | 35 | In the above number, A and B represent the tens and units digits, respectively. If the above number is divisible by 35, what is the greatest possible value of B x A? | {
"A": "0",
"B": "10",
"C": "20",
"D": "30",
"E": "35"
} | multiply(add(const_3, const_4), add(const_2, const_3)) | add(const_3,const_4)|add(const_2,const_3)|multiply(#0,#1)| | "i also was confused when i was looking forabove number : d as far as i understood , 35 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 35 x 1 ( a = 3 , b = 5 respectively we have = 15 ) . but we do n ' t have this number in answer choices , move on . ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 35 x 3 = 105 ( a = 0 b = 5 respectively . hey ! that ' s 0 now . 35 x 5 = 175 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) . this is the greatest possible value of b x a . imo e ." | general |
math_qa__effQAwK4obPSVBtk | If 2x-y=4 then 6x-3y=?
Choices: A) 15 B) 12 C) 18 D) 10 E) 14 | <gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<result>B</result> | B | 12 | If 2x-y=4 then 6x-3y=? | {
"A": "15",
"B": "12",
"C": "18",
"D": "10",
"E": "14"
} | add(multiply(2, 3), 6) | multiply(n0,n3)|add(n2,#0) | 6 x - 3 y = 3 * ( 2 x - y ) = 3 * 4 = 12 answer : b | general |
math_qa__xybQHgLzJJEjtskP | Find 3486/189 Choose the most appropriate option:
A) 18.44 B) 18.48 C) 18.42 D) 18.49 E) 18.41 | <gadget id="calculator">3_486 / 189</gadget>
<output>166/9 = around 18.444444</output>
<result>A</result> | A | 18.44 | Find 3486/189 | {
"A": "18.44",
"B": "18.48",
"C": "18.42",
"D": "18.49",
"E": "18.41"
} | divide(3486, 189) | divide(n0,n1) | first we make the denominator 200 . i . e . , we are introducing an error of 11 which is 11189 = 11711189 = 117 th of the denominator . now 3486200 = 17.433486200 = 17.43 but this answer is less than actual answer . so we have to increase it by 1 / 17 th part of it . 117 × 17.43 ≃ 1117 × 17.43 ≃ 1 so final answer = 17.43 + 1 = 18.43 actual answer = 18.44 answer : a | general |
math_qa__vsQRtaQpmCRRDubY | Mary and Mike enter into a partnership by investing $600 and $400 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1000 more than Mike did, what was the profit made by their business in that year? Choose the correct choice from the following answers
A) $ 8500 B) $ 9500 C) $ 7000 D) $ 7500 E) $ 6500 | <gadget id="calculator">600 / 1_000</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">400 / 1_000</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(3/5) - (2/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/5) * (2/3)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">1_000 / (2/15)</gadget>
<output>7_500</output>
<result>D</result> | D | 7,500 | Mary and Mike enter into a partnership by investing $600 and $400 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1000 more than Mike did, what was the profit made by their business in that year? | {
"A": "$ 8500",
"B": "$ 9500",
"C": "$ 7000",
"D": "$ 7500",
"E": "$ 6500"
} | divide(1000, multiply(subtract(divide(600, const_1000), divide(400, const_1000)), subtract(const_1, divide(const_1, const_3)))) | divide(n0,const_1000)|divide(n1,const_1000)|divide(const_1,const_3)|subtract(#0,#1)|subtract(const_1,#2)|multiply(#3,#4)|divide(n2,#5)| | "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 6 : 4 . i . e . , 60 % of 2 x would go to mary and 40 % of 2 x would go to mike . hence , mary would get ( 60 - 40 ) % of 2 x more than mike or 20 % of 2 x = $ 1000 i . e . , ( 20 / 100 ) * 2 x = 1000 or 2 x = 5000 . hence , the profit made by the company during the year $ 3 x = $ 7500 . answer : d" | general |
math_qa__5T9W6HUvTcgi6jqQ | After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 80% full. If the original contents of the reservoir totaled 200 billion gallons, the reservoir was approximately what percentage full before the storm? Select: A) 45 % B) 48 % C) 50 % D) 58 % E) 65 % | <gadget id="calculator">120 + 200</gadget>
<output>320</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">320 / (4/5)</gadget>
<output>400</output>
<gadget id="calculator">200 / 400</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>C</result> | C | 50 | After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 80% full. If the original contents of the reservoir totaled 200 billion gallons, the reservoir was approximately what percentage full before the storm? | {
"A": "45 %",
"B": "48 %",
"C": "50 %",
"D": "58 %",
"E": "65 %"
} | multiply(divide(200, divide(add(120, 200), divide(80, const_100))), const_100) | add(n0,n2)|divide(n1,const_100)|divide(#0,#1)|divide(n2,#2)|multiply(#3,const_100)| | "when the storm deposited 120 billion gallons , volume of water in the reservoir = 200 + 120 = 320 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 320 / 0.8 = 400 billion gallons therefore percentage of reservoir that was full before the storm = ( 200 / 400 ) * 100 = 50 % option c" | general |
math_qa__GpaiJ43ME0IX3t9S | A classroom has 3 electric lamps. From a collocation of 10 electric bulbs of which 6 are good , 3 are selected at random and put in the lamps. Find the probability that the room is lighted. Choose the correct choice from the following choices
A) 1 / 6 B) 4 / 120 C) 29 / 30 D) 1 / 9 E) none of these | <gadget id="calculator">binomial(10, 3)</gadget>
<output>120</output>
<gadget id="calculator">10 - 6</gadget>
<output>4</output>
<gadget id="calculator">binomial(4, 3)</gadget>
<output>4</output>
<gadget id="calculator">120 - 4</gadget>
<output>116</output>
<gadget id="calculator">116 / 120</gadget>
<output>29/30 = around 0.966667</output>
<result>C</result> | C | 0.966667 | A classroom has 3 electric lamps. From a collocation of 10 electric bulbs of which 6 are good , 3 are selected at random and put in the lamps. Find the probability that the room is lighted. | {
"A": "1 / 6",
"B": "4 / 120",
"C": "29 / 30",
"D": "1 / 9",
"E": "none of these"
} | divide(subtract(choose(10, 3), choose(subtract(10, 6), 3)), choose(10, 3)) | choose(n1,n0)|subtract(n1,n2)|choose(#1,n0)|subtract(#0,#2)|divide(#3,#0) | explanation : out of 10 electric bulbs , 3 are selected in 10 c 3 ways . so , number of possible outcomes = t = 10 c 3 = 120 . the room is lighted i . e at least one fo the 3 bulbs chosen at random is a good bulb . wherever ' at least one ' is present , it is easier to do the problem using complement of the event ( i . e room is dark and all 3 bulbs are bad ) . p ( room is dark ) = f / t = p ( none of the bulbs is good ) = > 4 c 3 / 120 . [ since 4 bulbs are bad ] . p ( room is lighted ) = 1 - ( 4 c 3 / 120 ) . [ room is lighted if at least one bulb is good ] . or p ( at least one ) = 1 - ( 4 / 120 ) . = 29 / 30 . answer : c | probability |
math_qa__6f9YgLr9ZGSflJFR | If a population of women in a town is 90% of men . What is the population of men as a % of population of women ?
Choose the correct choice from the following options.
A) 108 %
B) 105 %
C) 111 %
D) 112 %
E) 114 % | <gadget id="calculator">100 / 90</gadget>
<output>10/9 = around 1.111111</output>
<gadget id="calculator">(10/9) * 100</gadget>
<output>1_000/9 = around 111.111111</output>
<result>C</result> | C | 111 | If a population of women in a town is 90% of men . What is the population of men as a % of population of women ? | {
"A": "108 %",
"B": "105 %",
"C": "111 %",
"D": "112 %",
"E": "114 %"
} | multiply(divide(const_100, 90), const_100) | divide(const_100,n0)|multiply(#0,const_100) | we ' re told that the number of women in a town is equal to 90 % of the number of men in that town . if . . . . men = 10 women = 9 we ' re asked for the number of men , as a percentage of the number of women . m / w = 10 / 9 = 1 1 / 9 = 1.111111 = 111 % answer : c | gain |
math_qa__ehEvWXyyD44satTE | Two trains 135 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Choose the correct choice from the following answers: A) 7.18 B) 7.12 C) 7.3 D) 7.45 E) 7.51 | <gadget id="calculator">135 + 165</gadget>
<output>300</output>
<gadget id="calculator">80 + 65</gadget>
<output>145</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">145 * (5/18)</gadget>
<output>725/18 = around 40.277778</output>
<gadget id="calculator">300 / (725/18)</gadget>
<output>216/29 = around 7.448276</output>
<result>D</result> | D | 7.45 | Two trains 135 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? | {
"A": "7.18",
"B": "7.12",
"C": "7.3",
"D": "7.45",
"E": "7.51"
} | divide(add(135, 165), multiply(add(80, 65), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | "t = ( 135 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.45 answer : d" | physics |
math_qa__HFXP8PCsNGs060BV | 4 numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number . Choose the correct choice from the following choices.
A) 480 B) 239 C) 270 D) 282 E) 112 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 + 4</gadget>
<output>9</output>
<gadget id="calculator">9 + 5</gadget>
<output>14</output>
<gadget id="calculator">1_344 / 14</gadget>
<output>96</output>
<gadget id="calculator">96 * 5</gadget>
<output>480</output>
<result>A</result> | A | 480 | 4 numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number . | {
"A": "480",
"B": "239",
"C": "270",
"D": "282",
"E": "112"
} | multiply(divide(1344, add(add(add(2, 3), 4), 5)), 5) | add(n1,n2)|add(n0,#0)|add(n4,#1)|divide(n5,#2)|multiply(n4,#3) | answer : a | general |
math_qa__XIkdN2OWP65hZ2zR | Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is: Choose the correct choice from the following answers:
A) rs 200 B) rs 300 C) rs 400 D) rs 500 E) rs 600 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">4 / 7</gadget>
<output>4/7 = around 0.571429</output>
<gadget id="calculator">(4/7) * 700</gadget>
<output>400</output>
<result>C</result> | C | 400 | Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is: | {
"A": "rs 200",
"B": "rs 300",
"C": "rs 400",
"D": "rs 500",
"E": "rs 600"
} | multiply(divide(const_4, add(const_4, add(const_1, const_2))), 700) | add(const_1,const_2)|add(#0,const_4)|divide(const_4,#1)|multiply(n0,#2) | let c = x . then b = x / 2 and a = x / 4 a : b : c = 1 : 2 : 4 . c ' s share rs . [ ( 4 / 7 ) x 700 ) = 400 answer : c | general |
math_qa__LZz24YkuMPrx7Ygw | A is twice as good a workman as B and they took 8 days together to do the work B alone can do it in? Choose the correct choice from the following answers: A) 25 days B) 88 days C) 21 days D) 11 days E) 24 days | <gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<result>E</result> | E | 24 | A is twice as good a workman as B and they took 8 days together to do the work B alone can do it in? | {
"A": "25 days",
"B": "88 days",
"C": "21 days",
"D": "11 days",
"E": "24 days"
} | multiply(divide(multiply(8, add(const_2, const_1)), const_2), const_2) | add(const_1,const_2)|multiply(n0,#0)|divide(#1,const_2)|multiply(#2,const_2)| | "wc = 2 : 1 2 x + x = 1 / 8 x = 1 / 24 = > 24 days answer : e" | physics |
math_qa__5dqGsKPDLxUM8kzZ | Find the greatest number that will divide 150, 230 and 175 leaving 50, 5 and 25 as remainders respectively Choose the correct choice from the following choices.
A) 19
B) 17
C) 32
D) 9
E) 8 | <gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">12 + 20</gadget>
<output>32</output>
<result>C</result> | C | 32 | Find the greatest number that will divide 150, 230 and 175 leaving 50, 5 and 25 as remainders respectively | {
"A": "19",
"B": "17",
"C": "32",
"D": "9",
"E": "8"
} | add(const_12, multiply(5, const_4)) | multiply(n4,const_4)|add(#0,const_12) | explanation : answer will be hcf of ( 150 - 50 , 230 - 5 , 175 - 25 ) hcf of ( 100 , 225 , 150 ) = 32 option c | general |
math_qa__cHoSpkBkElUVEdUi | How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
Choose one:
A) 16.8 B) 17.8 C) 15.9 D) 13.2 E) 12.4 | <gadget id="calculator">110 + 170</gadget>
<output>280</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">280 / (50/3)</gadget>
<output>84/5 = around 16.8</output>
<result>A</result> | A | 16.8 | How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length? | {
"A": "16.8",
"B": "17.8",
"C": "15.9",
"D": "13.2",
"E": "12.4"
} | divide(add(110, 170), multiply(60, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | "d = 110 + 170 = 280 m s = 60 * 5 / 18 = 50 / 3 t = 280 * 3 / 50 = 16.8 sec answer a" | physics |
math_qa__iye1Yaq06mTbWf1c | in track last week , the boys ran 27 laps . the girls ran 9 more laps . each lap is a 3 - fourth of a mile . how many miles did the girls run ? Pick one
A) 24 miles B) 25 miles C) 26 miles D) 27 miles E) 28 miles | <gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">27 + 9</gadget>
<output>36</output>
<gadget id="calculator">(3/4) * 36</gadget>
<output>27</output>
<result>D</result> | D | 27 | in track last week , the boys ran 27 laps . the girls ran 9 more laps . each lap is a 3 - fourth of a mile . how many miles did the girls run ? | {
"A": "24 miles",
"B": "25 miles",
"C": "26 miles",
"D": "27 miles",
"E": "28 miles"
} | multiply(divide(3, const_4), add(27, 9)) | add(n0,n1)|divide(n2,const_4)|multiply(#0,#1) | the girls ran 27 + 9 = 36 laps . 36 x 3 / 4 = 108 / 4 , which reduces to 27 . the girls ran 27 miles correct answer d | general |
math_qa__MGuoJ6uqOYcnnslL | If Tim had lunch at $50.20 and he gave 20% tip, how much did he spend?
Choose one: A) $ 30.60 B) $ 60.60 C) $ 70.60 D) $ 40.60 E) $ 60.24 | <gadget id="calculator">50.2 * 20</gadget>
<output>1_004</output>
<gadget id="calculator">1_004 / 100</gadget>
<output>251/25 = around 10.04</output>
<gadget id="calculator">50.2 + (251/25)</gadget>
<output>60.24</output>
<result>E</result> | E | 60.24 | If Tim had lunch at $50.20 and he gave 20% tip, how much did he spend? | {
"A": "$ 30.60",
"B": "$ 60.60",
"C": "$ 70.60",
"D": "$ 40.60",
"E": "$ 60.24"
} | add(50.20, divide(multiply(50.20, 20), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)| | "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.20 = ( 20 / 100 ) * 50.20 = $ 10.04 total spent 50.20 + 10.04 = $ 60.24 correct answer e" | gain |
math_qa__il5GKVnQVXu3CDLq | If the operation € is defined for all x and y by the equation x € y = 2*x*y, then 8 € (4 € 5) =
Choose the correct choice from the following answers
A) 80 B) 120 C) 160 D) 640 E) 760 | <gadget id="calculator">2 * 8</gadget>
<output>16</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<gadget id="calculator">16 * 40</gadget>
<output>640</output>
<result>D</result> | D | 640 | If the operation € is defined for all x and y by the equation x € y = 2*x*y, then 8 € (4 € 5) = | {
"A": "80",
"B": "120",
"C": "160",
"D": "640",
"E": "760"
} | multiply(multiply(2, 8), multiply(multiply(2, 4), 5)) | multiply(n0,n1)|multiply(n0,n2)|multiply(n3,#1)|multiply(#0,#2)| | "working inside out , ( 4 € 5 ) = 2 * 4 * 5 = 40 8 € 40 = 2 * 8 * 40 = 640 hence , answer is d" | general |
math_qa__vkxHS8QmJ0qiFBqC | Every year an amount increases by 1/6th of itself. How much will it be after two years if its present value is Rs.64000? Choose the most appropriate option:
A) 87111
B) 81007
C) 81008
D) 81066
E) 81022 | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 64_000</gadget>
<output>32_000/3 = around 10_666.666667</output>
<gadget id="calculator">64_000 + (32_000/3)</gadget>
<output>224_000/3 = around 74_666.666667</output>
<gadget id="calculator">(1/6) * (224_000/3)</gadget>
<output>112_000/9 = around 12_444.444444</output>
<gadget id="calculator">(224_000/3) + (112_000/9)</gadget>
<output>784_000/9 = around 87_111.111111</output>
<result>A</result> | A | 87,111 | Every year an amount increases by 1/6th of itself. How much will it be after two years if its present value is Rs.64000? | {
"A": "87111",
"B": "81007",
"C": "81008",
"D": "81066",
"E": "81022"
} | add(add(64000, multiply(divide(1, 6), 64000)), multiply(divide(1, 6), add(64000, multiply(divide(1, 6), 64000)))) | divide(n0,n1)|multiply(n2,#0)|add(n2,#1)|multiply(#2,#0)|add(#2,#3)| | "64000 * 7 / 6 * 7 / 6 = 87111 answer : a" | general |
math_qa__y38ym0juqyGgq73R | A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 305 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day? Answers.
A) 400 B) 440 C) 550 D) 625 E) 700 | <gadget id="calculator">600 / 11</gadget>
<output>600/11 = around 54.545455</output>
<gadget id="calculator">(600/11) * 8</gadget>
<output>4_800/11 = around 436.363636</output>
<result>B</result> | B | 440 | A factory has three types of machines, each of which works at its own constant rate. If 7 Machine As and 11 Machine Bs can produce 305 widgets per hour, and if 8 Machine As and 22 Machine Cs can produce 600 widgets per hour, how many widgets could one machine A, one Machine B, and one Machine C produce in one 8-hour day? | {
"A": "400",
"B": "440",
"C": "550",
"D": "625",
"E": "700"
} | multiply(divide(600, 11), 8) | divide(n5,n1)|multiply(n3,#0) | let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 305 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 605 a + b + c = 55 per hour so for eight hrs = 55 * 8 = 440 = answer = b | physics |
math_qa__6Sx3jWCRVJZlxVCW | A chemical supply company has 60 liters of a 25% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution? Select: A) 12 B) 15 C) 20 D) 24 E) 30 | <gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">60 * 25</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 / 100</gadget>
<output>15</output>
<gadget id="calculator">30 - 15</gadget>
<output>15</output>
<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<result>E</result> | E | 30 | A chemical supply company has 60 liters of a 25% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution? | {
"A": "12",
"B": "15",
"C": "20",
"D": "24",
"E": "30"
} | multiply(subtract(divide(60, const_2), divide(multiply(60, 25), const_100)), const_2) | divide(n0,const_2)|multiply(n0,n1)|divide(#1,const_100)|subtract(#0,#2)|multiply(#3,const_2)| | "60 liters of a 25 % hno 3 solution means hno 3 = 15 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 15 + x = 50 % of ( 60 + x ) or x = 30 . hence , e" | gain |
math_qa__poxk7EmLvxlXKgg3 | In a 500 m race,the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m.Then,A wins by Choose the correct choice
A) 60 m B) 40 m C) 20 m D) 10 m E) 50 m | <gadget id="calculator">500 - 140</gadget>
<output>360</output>
<gadget id="calculator">360 * 4</gadget>
<output>1_440</output>
<gadget id="calculator">1_440 / 3</gadget>
<output>480</output>
<gadget id="calculator">500 - 480</gadget>
<output>20</output>
<result>C</result> | C | 20 | In a 500 m race,the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m.Then,A wins by | {
"A": "60 m",
"B": "40 m",
"C": "20 m",
"D": "10 m",
"E": "50 m"
} | subtract(500, divide(multiply(subtract(500, 140), 4), 3)) | subtract(n0,n3)|multiply(n2,#0)|divide(#1,n1)|subtract(n0,#2)| | "solution to reach the winning post a will have to cover a distance of ( 500 - 140 ) m , i . e , 360 m . while a covers 3 m , b covers 4 m . while a covers 360 m , b covers ( 4 / 3 x 360 ) m = 480 m thus , when a reaches the winning post , b covers 480 m and therefore remains 20 m behind . ∴ a wins by 20 m . answer c" | physics |
math_qa__v3Y5qZ8KTTkvGubK | Pipe A can fill a tank in 2 hours. Due to a leak at the bottom, it takes 3 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank? Select the correct option:
A) 10 B) 9 C) 7 D) 6 E) 5 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">6 / 1</gadget>
<output>6</output>
<result>D</result> | D | 6 | Pipe A can fill a tank in 2 hours. Due to a leak at the bottom, it takes 3 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank? | {
"A": "10",
"B": "9",
"C": "7",
"D": "6",
"E": "5"
} | divide(multiply(3, 2), subtract(3, 2)) | multiply(n0,n1)|subtract(n1,n0)|divide(#0,#1)| | "let the leak can empty the full tank in x hours 1 / 2 - 1 / x = 1 / 3 = > 1 / x = 1 / 2 - 1 / 3 = ( 3 - 2 ) / 6 = 1 / 6 = > x = 6 . answer : d" | physics |
math_qa__TsARV5BYTqgx8q1E | A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $752 in total compensation, how many total hours did he work that week?
Choose the correct choice from the following answers
A) 36
B) 40
C) 44
D) 48
E) 52 | <gadget id="calculator">16 * 40</gadget>
<output>640</output>
<gadget id="calculator">752 - 640</gadget>
<output>112</output>
<gadget id="calculator">100 + 75</gadget>
<output>175</output>
<gadget id="calculator">16 * 175</gadget>
<output>2_800</output>
<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>
<gadget id="calculator">112 / 28</gadget>
<output>4</output>
<gadget id="calculator">40 + 4</gadget>
<output>44</output>
<result>C</result> | C | 44 | A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $752 in total compensation, how many total hours did he work that week? | {
"A": "36",
"B": "40",
"C": "44",
"D": "48",
"E": "52"
} | add(40, divide(subtract(752, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100))) | add(n3,const_100)|multiply(n0,n1)|multiply(n0,#0)|subtract(n4,#1)|divide(#2,const_100)|divide(#3,#4)|add(n1,#5)| | "for 40 hrs = 40 * 16 = 640 excess = 752 - 640 = 112 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 112 / 28 = 28 / 7 = 4 total hrs = 40 + 4 = 44 answer c 44" | general |
math_qa__5SdjBwSTrtXQn9eD | If the weight of 12 meters long rod is 12.2 kg. What is the weight of 6 meters long rod ? Options:
A) 7.2 kg . B) 10.8 kg . C) 12.4 kg . D) 6.1 kg E) none | <gadget id="calculator">6 * 12.2</gadget>
<output>73.2</output>
<gadget id="calculator">73.2 / 12</gadget>
<output>6.1</output>
<result>D</result> | D | 6.1 | If the weight of 12 meters long rod is 12.2 kg. What is the weight of 6 meters long rod ? | {
"A": "7.2 kg .",
"B": "10.8 kg .",
"C": "12.4 kg .",
"D": "6.1 kg",
"E": "none"
} | divide(multiply(6, 12.2), 12) | multiply(n1,n2)|divide(#0,n0)| | "answer ∵ weight of 12 m long rod = 12.2 kg ∴ weight of 1 m long rod = 12.2 / 12 kg ∴ weight of 6 m long rod = 12.2 x 6 / 12 = 6.1 kg option : d" | physics |
math_qa__abIDaveiZFjeODfo | Find the fraction which has the same ratio to 2/5 that 3/7 has to 6/5
Choose the correct choice from the following answers
A) 2 / 4 B) 6 / 78 C) 4 / 7 D) 3 / 5 E) 1 / 7 | <gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">6 / 5</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(3/7) / (6/5)</gadget>
<output>5/14 = around 0.357143</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(5/14) * (2/5)</gadget>
<output>1/7 = around 0.142857</output>
<result>E</result> | E | 0.142857 | Find the fraction which has the same ratio to 2/5 that 3/7 has to 6/5 | {
"A": "2 / 4",
"B": "6 / 78",
"C": "4 / 7",
"D": "3 / 5",
"E": "1 / 7"
} | multiply(divide(divide(3, 7), divide(6, 5)), divide(2, 5)) | divide(n2,n3)|divide(n4,n5)|divide(n0,n1)|divide(#0,#1)|multiply(#3,#2)| | "p : 2 / 5 = 3 / 7 : 6 / 5 as the product of the means is equal to the product of the extremes . p * 6 / 5 = 2 / 5 * 3 / 7 p * 6 / 5 = 6 / 35 p = 1 / 7 = > p = 1 / 7 answer : e" | other |
math_qa__KiE5707VJW5dvwvR | David obtained 72, 60, 35, 62 and 84 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ? Select the correct option
A) 75
B) 62.6
C) 87
D) 165
E) 11 | <gadget id="calculator">72 + 60</gadget>
<output>132</output>
<gadget id="calculator">132 + 35</gadget>
<output>167</output>
<gadget id="calculator">167 + 62</gadget>
<output>229</output>
<gadget id="calculator">229 + 84</gadget>
<output>313</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">313 / 5</gadget>
<output>313/5 = around 62.6</output>
<result>B</result> | B | 62.6 | David obtained 72, 60, 35, 62 and 84 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ? | {
"A": "75",
"B": "62.6",
"C": "87",
"D": "165",
"E": "11"
} | divide(add(add(add(add(72, 60), 35), 62), 84), add(const_2, const_3)) | add(n0,n1)|add(const_2,const_3)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1) | explanation : average = ( 72 + 60 + 35 + 62 + 84 ) / 5 = 313 / 5 = 62.6 . answer : b | general |
math_qa__9ibD9ZBWbUfQ2Xi7 | Mohit sold an article for $12000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
Choose the correct choice from the following options:
A) 16000
B) 25000
C) 10000
D) 18000
E) 17000 | <gadget id="calculator">12_000 * 10</gadget>
<output>120_000</output>
<gadget id="calculator">120_000 / 100</gadget>
<output>1_200</output>
<gadget id="calculator">12_000 - 1_200</gadget>
<output>10_800</output>
<gadget id="calculator">100 + 8</gadget>
<output>108</output>
<gadget id="calculator">10_800 / 108</gadget>
<output>100</output>
<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<result>C</result> | C | 10,000 | Mohit sold an article for $12000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article? | {
"A": "16000",
"B": "25000",
"C": "10000",
"D": "18000",
"E": "17000"
} | multiply(divide(subtract(12000, divide(multiply(12000, 10), const_100)), add(const_100, 8)), const_100) | add(n2,const_100)|multiply(n0,n1)|divide(#1,const_100)|subtract(n0,#2)|divide(#3,#0)|multiply(#4,const_100)| | "let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 12000 - 10 / 100 ( 12000 ) = 12000 - 1200 = $ 10800 = > 1.08 x = 10800 = > x = 10000 c" | gain |
math_qa__f9XmhDmp8UKbpCF5 | A certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $1.80, what total number of pens and pencils did the customer purchase?
Choose the correct answer:
A) 6
B) 9
C) 10
D) 11
E) 12 | <gadget id="calculator">0.35 + 0.25</gadget>
<output>0.6</output>
<gadget id="calculator">1.8 / 0.6</gadget>
<output>3</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<result>A</result> | A | 6 | A certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $1.80, what total number of pens and pencils did the customer purchase? | {
"A": "6",
"B": "9",
"C": "10",
"D": "11",
"E": "12"
} | multiply(divide(1.80, add(0.35, 0.25)), const_2) | add(n0,n1)|divide(n2,#0)|multiply(#1,const_2)| | "answer : algebraically , the question looks like this : 2.5 = 0.35 x + 0.25 y there are three possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 and 3 pencils for $ 0.25 each . that ' s 3 pens and 3 pencils for a total of 6 pens and pencils . choice ( a ) is correct ." | other |
math_qa__bV4QVxjPxH9MQJ3X | What profit percent is made by selling an article at a certain price, if by selling at 1/2rd of that price, there would be a loss of 20%? Choose the correct answer
A) 20 % B) 29 % C) 60 % D) 27 % E) 28 % | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">80 / (1/2)</gadget>
<output>160</output>
<gadget id="calculator">160 - 100</gadget>
<output>60</output>
<result>C</result> | C | 60 | What profit percent is made by selling an article at a certain price, if by selling at 1/2rd of that price, there would be a loss of 20%? | {
"A": "20 %",
"B": "29 %",
"C": "60 %",
"D": "27 %",
"E": "28 %"
} | subtract(divide(subtract(const_100, 20), divide(1, 2)), const_100) | divide(n0,n1)|subtract(const_100,n2)|divide(#1,#0)|subtract(#2,const_100)| | "sp 2 = 1 / 2 sp 1 cp = 100 sp 2 = 80 1 / 2 sp 1 = 80 sp 1 = 160 100 - - - 160 = > 60 % answer : c" | gain |
math_qa__0dwgEejr6nXjJ3o7 | Williams works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 10 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked? Select.
A) 5 / 8 B) 7 / 8 C) 6 / 8 D) 2 / 9 E) 1 / 7 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">10 + 6</gadget>
<output>16</output>
<gadget id="calculator">10 / 16</gadget>
<output>5/8 = around 0.625</output>
<result>A</result> | A | 0.625 | Williams works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 10 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked? | {
"A": "5 / 8",
"B": "7 / 8",
"C": "6 / 8",
"D": "2 / 9",
"E": "1 / 7"
} | divide(10, add(10, subtract(add(const_3, const_4), const_1))) | add(const_3,const_4)|subtract(#0,const_1)|add(n0,#1)|divide(n0,#2)| | "first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 10 x total tips for all months = 6 * x + 10 x = 16 x tips for august / total tips for all months = 10 x / 16 x = 5 / 8 answer : a" | general |
math_qa__8Wa3hH1sqC4QVfHT | By selling an article at Rs.400, a profit of 25% is made. Find its cost price? Select
A) 228 B) 320 C) 287 D) 480 E) 811 | <gadget id="calculator">400 * 100</gadget>
<output>40_000</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">40_000 / 125</gadget>
<output>320</output>
<result>B</result> | B | 320 | By selling an article at Rs.400, a profit of 25% is made. Find its cost price? | {
"A": "228",
"B": "320",
"C": "287",
"D": "480",
"E": "811"
} | divide(multiply(400, const_100), add(const_100, 25)) | add(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)| | "sp = 400 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 400 * [ 100 / ( 100 + 25 ) ] = 400 * [ 100 / 125 ] = rs . 320 answer : b" | gain |
math_qa__yleP7x5XijIAQ9TA | A 9% stock yields 25%. The market value of the stock is: Choose the most appropriate option
A) rs 45 B) rs 25 C) rs 40 D) rs 39 E) rs 36 | <gadget id="calculator">100 / 25</gadget>
<output>4</output>
<gadget id="calculator">4 * 9</gadget>
<output>36</output>
<result>E</result> | E | 36 | A 9% stock yields 25%. The market value of the stock is: | {
"A": "rs 45",
"B": "rs 25",
"C": "rs 40",
"D": "rs 39",
"E": "rs 36"
} | multiply(divide(const_100, 25), 9) | divide(const_100,n1)|multiply(n0,#0)| | "explanation : for an income of rs . 25 , investment = rs . 100 . for an income of rs 9 , investment = rs . 100 / 25 x 9 = rs 36 market value of rs . 100 stock = rs 36 answer is e" | gain |
math_qa__sslH2TfJoOe3IpkX | Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 asquotient and the 15 as remainder?
Pick one:
A) 1245 B) 1567 C) 1678 D) 1335 E) 1635 | <gadget id="calculator">1_365 - 15</gadget>
<output>1_350</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_350 / 5</gadget>
<output>270</output>
<gadget id="calculator">270 * 6</gadget>
<output>1_620</output>
<result>E</result> | E | 1,635 | Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 asquotient and the 15 as remainder? | {
"A": "1245",
"B": "1567",
"C": "1678",
"D": "1335",
"E": "1635"
} | multiply(divide(subtract(1365, 15), subtract(6, const_1)), 6) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e" | general |
math_qa__xuS06yAMKGsnoLYV | ‘A’ completes a work in 12 days. ‘B’ completes the same work in 15 days. ‘A’ started working alone and after 3 days B joined him. How many days will they now take together to complete the remaining work? Answers
A) 5 B) 8 C) 6 D) 4 E) none of these | <gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/12) * 3</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">12 * 15</gadget>
<output>180</output>
<gadget id="calculator">3 ** 3</gadget>
<output>27</output>
<gadget id="calculator">180 / 27</gadget>
<output>20/3 = around 6.666667</output>
<gadget id="calculator">(3/4) * (20/3)</gadget>
<output>5</output>
<result>A</result> | A | 5 | ‘A’ completes a work in 12 days. ‘B’ completes the same work in 15 days. ‘A’ started working alone and after 3 days B joined him. How many days will they now take together to complete the remaining work? | {
"A": "5",
"B": "8",
"C": "6",
"D": "4",
"E": "none of these"
} | multiply(subtract(const_1, multiply(divide(const_1, 12), 3)), divide(multiply(12, 15), power(3, const_3))) | divide(const_1,n0)|multiply(n0,n1)|power(n2,const_3)|divide(#1,#2)|multiply(n2,#0)|subtract(const_1,#4)|multiply(#3,#5) | work done by ‘ a ’ in 3 days = 1 ⁄ 12 × 3 = 1 ⁄ 4 ∴ remaining work = 1 - 1 ⁄ 4 = 3 ⁄ 4 work done by a and b together = 12 × 15 / 27 = 20 / 3 ∴ remaining work done by a and b together in = 3 ⁄ 4 × 20 ⁄ 3 = 5 days answer a | physics |
math_qa__7KVEXSS2QRMChvch | In a coconut grove, (x + 2) trees yield 40 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x. Choose the correct choice from the following options: A) 3 B) 4 C) 5 D) 6 E) 7 | <gadget id="calculator">180 * 2</gadget>
<output>360</output>
<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">360 - 80</gadget>
<output>280</output>
<gadget id="calculator">40 + 120</gadget>
<output>160</output>
<gadget id="calculator">160 + 180</gadget>
<output>340</output>
<gadget id="calculator">100 * 3</gadget>
<output>300</output>
<gadget id="calculator">340 - 300</gadget>
<output>40</output>
<gadget id="calculator">280 / 40</gadget>
<output>7</output>
<result>E</result> | E | 7 | In a coconut grove, (x + 2) trees yield 40 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x. | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | divide(subtract(multiply(180, 2), multiply(40, 2)), subtract(add(add(40, 120), 180), multiply(100, const_3))) | add(n1,n2)|multiply(n0,n4)|multiply(n0,n1)|multiply(n5,const_3)|add(n4,#0)|subtract(#1,#2)|subtract(#4,#3)|divide(#5,#6)| | "( x + 2 ) × 40 + x × 120 + ( x − 2 ) × 180 / ( x + 2 ) + x + ( x − 2 ) = 100 ⇒ 340 x − 280 / 3 x = 100 ⇒ 40 x = 280 ⇒ x = 7 answer e" | general |
math_qa__2bmO2RLTcdkgpsRF | Rectangular tile each of size 25cm by 65cm must be laid horizontally on a rectangular floor of size 150cm by 390cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: Pick: A) 50 B) 40 C) 25 D) 36 E) 45 | <gadget id="calculator">150 * 390</gadget>
<output>58_500</output>
<gadget id="calculator">25 * 65</gadget>
<output>1_625</output>
<gadget id="calculator">58_500 / 1_625</gadget>
<output>36</output>
<result>D</result> | D | 36 | Rectangular tile each of size 25cm by 65cm must be laid horizontally on a rectangular floor of size 150cm by 390cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: | {
"A": "50",
"B": "40",
"C": "25",
"D": "36",
"E": "45"
} | divide(multiply(150, 390), multiply(25, 65)) | multiply(n2,n3)|multiply(n0,n1)|divide(#0,#1)| | "area of tile = 25 * 65 = 1625 area of floor = 150 * 390 = 58500 no of tiles = 58500 / 1625 = 36 so , the no of tile = 36 answer : d" | geometry |
math_qa__9UGCDp1R4cMjkEnh | Of the 3,600 employees of Company X, 1/6 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
Choose the correct choice
A) 13 % B) 22.2 % C) 20 % D) 12.5 % E) 11.1 % | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(1/6) * (3/4)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 - (1/6)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(1/8) + (5/6)</gadget>
<output>23/24 = around 0.958333</output>
<gadget id="calculator">(1/8) / (23/24)</gadget>
<output>3/23 = around 0.130435</output>
<gadget id="calculator">(3/23) * 100</gadget>
<output>300/23 = around 13.043478</output>
<result>A</result> | A | 13 | Of the 3,600 employees of Company X, 1/6 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical? | {
"A": "13 %",
"B": "22.2 %",
"C": "20 %",
"D": "12.5 %",
"E": "11.1 %"
} | multiply(divide(multiply(divide(1, 6), subtract(1, divide(1, 4))), add(multiply(divide(1, 6), subtract(1, divide(1, 4))), subtract(1, divide(1, 6)))), const_100) | divide(n1,n2)|divide(n3,n4)|subtract(n3,#1)|subtract(n3,#0)|multiply(#0,#2)|add(#4,#3)|divide(#4,#5)|multiply(#6,const_100)| | "welcome , just post the question and the choices let ' s see , the way i did it was 1 / 6 are clerical out of 3600 so 600 are clerical 600 reduced by 1 / 4 is 1200 * 1 / 4 so it reduced 150 people , so there is 450 clerical people left but since 150 people left , it also reduced from the total of 3600 so there are 3450 people total since 450 clerical left / 3450 people total you get ( a ) 13 % answer : a" | general |
math_qa__b9HAxmhJklx0rmg3 | The area of a triangle is with base 3m and height 6m? Select
A) 88 m 2 B) 9 m 2 C) 66 m 2 D) 77 m 2 E) 31 m 2 | <gadget id="calculator">(3 * 6) / 2</gadget>
<output>9</output>
<result>B</result> | B | 9 | The area of a triangle is with base 3m and height 6m? | {
"A": "88 m 2",
"B": "9 m 2",
"C": "66 m 2",
"D": "77 m 2",
"E": "31 m 2"
} | triangle_area(3, 6) | triangle_area(n0,n1)| | "1 / 2 * 3 * 6 = 9 m 2 answer : b" | geometry |
math_qa__I7BiW7ht3sKM402Y | In a stream running at 2kmph,a motor boat goes 6km upstream and back again to the starting point in 33 minutes.find the speed of the motorboat in still water. Choices:
A) 22 B) 24 C) 26 D) 28 E) none of them | <gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">33 / 60</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">12 / (11/20)</gadget>
<output>240/11 = around 21.818182</output>
<result>A</result> | A | 22 | In a stream running at 2kmph,a motor boat goes 6km upstream and back again to the starting point in 33 minutes.find the speed of the motorboat in still water. | {
"A": "22",
"B": "24",
"C": "26",
"D": "28",
"E": "none of them"
} | divide(add(6, 6), divide(33, const_60)) | add(n1,n1)|divide(n2,const_60)|divide(#0,#1) | let the speed of the motarboat in still water be x kmph . then , 6 / x + 2 + 6 / x - 2 = 33 / 60 11 x 2 - 240 x - 44 = 0 11 x 2 - 242 x + 2 x - 44 = 0 ( x - 22 ) ( 11 x + 2 ) = 0 x = 22 . answer is a | physics |
math_qa__UyRcuEYDvzdZkEGK | Ajay bought 15 kg of dal at the rate of Rs 14.50 per kg and 10 kg at the rate of Rs 13 per kg. He mixed the two and sold the mixture at the rate of Rs 15 per kg. What was his total gain in this transaction ? Choose the correct choice:
A) rs 1.10 B) rs 11 C) rs 16.50 D) rs 27.50 E) none of these | <gadget id="calculator">10 + 15</gadget>
<output>25</output>
<gadget id="calculator">15 * 25</gadget>
<output>375</output>
<gadget id="calculator">15 * 14.5</gadget>
<output>217.5</output>
<gadget id="calculator">10 * 13</gadget>
<output>130</output>
<gadget id="calculator">217.5 + 130</gadget>
<output>347.5</output>
<gadget id="calculator">375 - 347.5</gadget>
<output>27.5</output>
<result>D</result> | D | 27.5 | Ajay bought 15 kg of dal at the rate of Rs 14.50 per kg and 10 kg at the rate of Rs 13 per kg. He mixed the two and sold the mixture at the rate of Rs 15 per kg. What was his total gain in this transaction ? | {
"A": "rs 1.10",
"B": "rs 11",
"C": "rs 16.50",
"D": "rs 27.50",
"E": "none of these"
} | subtract(multiply(15, add(10, 15)), add(multiply(15, 14.5), multiply(10, 13))) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|multiply(n0,#0)|subtract(#4,#3) | explanation : cost price of 25 kg = rs . ( 15 x 14.50 + 10 x 13 ) = rs . 347.50 . sell price of 25 kg = rs . ( 25 x 15 ) = rs . 375 . profit = rs . ( 375 — 347.50 ) = rs . 27.50 . answer : d | gain |
math_qa__dxvrEQexbWT8UuWX | Shekar scored 76, 65, 82, 67 and 95 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks? Choose the correct option
A) 65 B) 77 C) 75 D) 85 E) 90 | <gadget id="calculator">76 + 65</gadget>
<output>141</output>
<gadget id="calculator">141 + 82</gadget>
<output>223</output>
<gadget id="calculator">223 + 67</gadget>
<output>290</output>
<gadget id="calculator">290 + 95</gadget>
<output>385</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">385 / 5</gadget>
<output>77</output>
<result>B</result> | B | 77 | Shekar scored 76, 65, 82, 67 and 95 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks? | {
"A": "65",
"B": "77",
"C": "75",
"D": "85",
"E": "90"
} | divide(add(add(add(add(76, 65), 82), 67), 95), add(const_1, const_4)) | add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1) | explanation : average = ( 76 + 65 + 82 + 67 + 95 ) / 5 = 385 / 5 = 77 hence average = 77 answer : b | general |
math_qa__nuhGA120DuG3fGdx | If in a race of 110m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by: Choose the correct option
A) 20 m B) 16 m C) 11 m D) 22 m E) 15 m | <gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">5 / 25</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 110</gadget>
<output>22</output>
<result>D</result> | D | 22 | If in a race of 110m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by: | {
"A": "20 m",
"B": "16 m",
"C": "11 m",
"D": "22 m",
"E": "15 m"
} | multiply(divide(subtract(25, 20), 25), 110) | subtract(n2,n1)|divide(#0,n2)|multiply(n0,#1)| | "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 110 * 5 ) / 25 = 22 m hence , a beats b by 22 m . answer d" | physics |
math_qa__wmvAEZyQV28hXBYR | A small company reduced its faculty by approximately 20 percent to 195 employees. What was the original number of employees? Choose the correct choice from the following answers:
A) 182 B) 208 C) 220 D) 224 E) 244 | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">195 / (4/5)</gadget>
<output>975/4 = around 243.75</output>
<result>E</result> | E | 244 | A small company reduced its faculty by approximately 20 percent to 195 employees. What was the original number of employees? | {
"A": "182",
"B": "208",
"C": "220",
"D": "224",
"E": "244"
} | divide(195, divide(subtract(const_100, 20), const_100)) | subtract(const_100,n0)|divide(#0,const_100)|divide(n1,#1)| | "if x is the original number of employees , then after 20 % reduction in employees number is . 80 x but we are given . 80 x = 195 x = 244 so the original number of employees is 244 correct answer - e" | gain |
math_qa__usgWsQOJCPmuTYdQ | the smallest number when increased by ` ` 3 ` ` is exactly divisible by 510 , 4590 , and 105 is : Choose the correct choice from the following.
A) 630 B) 633 C) 150 D) 140 E) 627 | <gadget id="calculator">4_590 / 510</gadget>
<output>9</output>
<gadget id="calculator">105 / 3</gadget>
<output>35</output>
<gadget id="calculator">9 * 35</gadget>
<output>315</output>
<gadget id="calculator">315 + 315</gadget>
<output>630</output>
<gadget id="calculator">630 - 3</gadget>
<output>627</output>
<result>E</result> | E | 627 | the smallest number when increased by ` ` 3 ` ` is exactly divisible by 510 , 4590 , and 105 is : | {
"A": "630",
"B": "633",
"C": "150",
"D": "140",
"E": "627"
} | subtract(add(multiply(divide(4590, 510), divide(105, 3)), multiply(divide(4590, 510), divide(105, 3))), const_3) | divide(n2,n1)|divide(n3,n0)|multiply(#0,#1)|add(#2,#2)|subtract(#3,const_3) | lcm = 630 630 - 3 = 627 answer : e | general |
math_qa__mFCY5t9pPZNqbmlj | If the perimeter of square region D and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of D Select the correct option
A) 25 : 16
B) 24 : 25
C) 5 : 6
D) 4 : 5
E) 4 : 9 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 / 4</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) ** 2</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">6 / (25/4)</gadget>
<output>24/25 = around 0.96</output>
<result>B</result> | B | 0.96 | If the perimeter of square region D and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of D | {
"A": "25 : 16",
"B": "24 : 25",
"C": "5 : 6",
"D": "4 : 5",
"E": "4 : 9"
} | divide(multiply(3, 2), power(divide(multiply(add(3, 2), const_2), const_4), const_2)) | add(n0,n1)|multiply(n0,n1)|multiply(#0,const_2)|divide(#2,const_4)|power(#3,const_2)|divide(#1,#4) | we know perimeter of a square ( pd ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pd = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b | geometry |
math_qa__H4FnIcj7YDrfoGQa | A waiter's salary consists of his salary and tips. During one week his tips were 5/3 of his salary. What fraction of his income came from tips ? Choose the correct choice from the following
A) 4 / 9 B) 5 / 4 C) 5 / 8 D) 5 / 9 E) 6 / 9 | <gadget id="calculator">5 / 3</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(5/3) + 1</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">(5/3) / (8/3)</gadget>
<output>5/8 = around 0.625</output>
<result>C</result> | C | 0.625 | A waiter's salary consists of his salary and tips. During one week his tips were 5/3 of his salary. What fraction of his income came from tips ? | {
"A": "4 / 9",
"B": "5 / 4",
"C": "5 / 8",
"D": "5 / 9",
"E": "6 / 9"
} | divide(divide(5, 3), add(divide(5, 3), const_1)) | divide(n0,n1)|add(#0,const_1)|divide(#0,#1)| | "income = salary ( s ) + tips = s + s * 5 / 3 = s * 8 / 3 tips = s * 8 / 3 fraction of his income came from tips = ( s * 5 / 3 ) / ( s * 8 / 3 ) = 5 / 8 answer : c" | general |
math_qa__8GdGL7cf8bBNgPbd | Rachel and Sarah spent $8 for gasoline, $15.65 for their lunch, and $5 apiece for gifts for Grandma.
Grandma gave each of them $10. If the girls left home with a total of $50, how much do they have for
the return trip? Choose the correct option.
A) $ 36.35 B) $ 26.35 C) $ 16.35 D) $ 46.35 E) $ 56.35 | <gadget id="calculator">8 + 15.65</gadget>
<output>23.65</output>
<gadget id="calculator">5 + 23.65</gadget>
<output>28.65</output>
<gadget id="calculator">28.65 - 5</gadget>
<output>23.65</output>
<gadget id="calculator">50 - 23.65</gadget>
<output>26.35</output>
<gadget id="calculator">10 + 26.35</gadget>
<output>36.35</output>
<result>A</result> | A | 36.35 | Rachel and Sarah spent $8 for gasoline, $15.65 for their lunch, and $5 apiece for gifts for Grandma.
Grandma gave each of them $10. If the girls left home with a total of $50, how much do they have for
the return trip? | {
"A": "$ 36.35",
"B": "$ 26.35",
"C": "$ 16.35",
"D": "$ 46.35",
"E": "$ 56.35"
} | add(10, subtract(50, subtract(add(5, add(8, 15.65)), 5))) | add(n0,n1)|add(n2,#0)|subtract(#1,n2)|subtract(n4,#2)|add(n3,#3) | $ 50 + $ 20 = $ 70 what they left with plus $ 10 to each $ 8 + $ 15.65 + $ 10 = $ 33.65 what they spent ( gifts are $ 5 + $ 5 ) $ 70 - $ 33.65 = $ 36.35 left correct answer a | general |
math_qa__PIg7I4IrVFflY1VT | In the fifth grade at Parkway elementary school there are 420 students. 320 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer? Choices
A) 69 . B) 73 . C) 81 D) 65 E) 108 | <gadget id="calculator">420 - 320</gadget>
<output>100</output>
<gadget id="calculator">250 * 86</gadget>
<output>21_500</output>
<gadget id="calculator">21_500 / 100</gadget>
<output>215</output>
<gadget id="calculator">250 - 215</gadget>
<output>35</output>
<gadget id="calculator">100 - 35</gadget>
<output>65</output>
<result>D</result> | D | 65 | In the fifth grade at Parkway elementary school there are 420 students. 320 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer? | {
"A": "69 .",
"B": "73 .",
"C": "81",
"D": "65",
"E": "108"
} | subtract(subtract(420, 320), subtract(250, divide(multiply(250, 86), const_100))) | multiply(n2,n3)|subtract(n0,n1)|divide(#0,const_100)|subtract(n2,#2)|subtract(#1,#3)| | "total students = 420 boys = 320 , girls = 100 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 100 - 35 = 65 . correct option : d" | gain |
math_qa__g9gjEAj9Xn92AGKu | P and Q invested in a shop. The profits were divided in the ratio of 2 : 4 respectively. If P invested Rs. 500000, the amount invested by Q is:
Choose the correct choice:
A) 5000000
B) 4000000
C) 1000000
D) 6000000
E) none | <gadget id="calculator">500_000 / 2</gadget>
<output>250_000</output>
<gadget id="calculator">250_000 * 4</gadget>
<output>1_000_000</output>
<result>C</result> | C | 1,000,000 | P and Q invested in a shop. The profits were divided in the ratio of 2 : 4 respectively. If P invested Rs. 500000, the amount invested by Q is: | {
"A": "5000000",
"B": "4000000",
"C": "1000000",
"D": "6000000",
"E": "none"
} | multiply(divide(500000, 2), 4) | divide(n2,n0)|multiply(n1,#0)| | "suppose q invested rs . y . then , 500000 / y = 2 / 4 or y = [ 500000 x 4 / 2 ] = 1000000 . answer c" | gain |
math_qa__H0PoX4AGqNiVKR0y | If (m-8) is a factor of m^2-qm-24, then q= Choose the correct option.
A) 3 B) 5 C) 6 D) 11 E) 16 | <gadget id="calculator">24 / 8</gadget>
<output>3</output>
<gadget id="calculator">8 - 3</gadget>
<output>5</output>
<result>B</result> | B | 5 | If (m-8) is a factor of m^2-qm-24, then q= | {
"A": "3",
"B": "5",
"C": "6",
"D": "11",
"E": "16"
} | subtract(8, divide(24, 8)) | divide(n2,n0)|subtract(n0,#0)| | "( m - 8 ) ( m - a ) = m ^ 2 - qm - 24 a = - 3 q = 8 + a = 5 = b" | general |
math_qa__b2m2FQPsoIJxnJWg | Peter invests a sum of money and gets back an amount of $ 815 in 3 years . David invests an equal amount of money and gets an amount of $870 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ? Pick one:
A) 670 B) 650 C) 698 D) 744 E) 700 | <gadget id="calculator">870 - 815</gadget>
<output>55</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">(1/25) - (3/100)</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">55 / (1/100)</gadget>
<output>5_500</output>
<gadget id="calculator">5_500 * (3/100)</gadget>
<output>165</output>
<gadget id="calculator">815 - 165</gadget>
<output>650</output>
<result>B</result> | B | 650 | Peter invests a sum of money and gets back an amount of $ 815 in 3 years . David invests an equal amount of money and gets an amount of $870 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ? | {
"A": "670",
"B": "650",
"C": "698",
"D": "744",
"E": "700"
} | subtract(815, multiply(divide(subtract(870, 815), subtract(divide(4, const_100), divide(3, const_100))), divide(3, const_100))) | divide(n3,const_100)|divide(n1,const_100)|subtract(n2,n0)|subtract(#0,#1)|divide(#2,#3)|multiply(#4,#1)|subtract(n0,#5)| | "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 870 - 815 = 55 interest earned for 3 years = 55 * 3 = 165 amount invested = 815 - 165 = 650 answer : b" | gain |
math_qa__Q4fUZJrpQzE9tSlJ | In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ? Select the correct option:
A) 2 / 3 B) 5 / 8 C) 5 / 9 D) 3 / 7 E) 4 / 7 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(1/4) + (3/4)</gadget>
<output>1</output>
<gadget id="calculator">(1/2) + 1</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">1 + (3/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) / 4</gadget>
<output>5/8 = around 0.625</output>
<result>B</result> | B | 0.625 | In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ? | {
"A": "2 / 3",
"B": "5 / 8",
"C": "5 / 9",
"D": "3 / 7",
"E": "4 / 7"
} | divide(add(1, add(divide(1, const_2), add(divide(1, add(1, 3)), divide(3, add(1, 3))))), add(1, 3)) | add(n0,n1)|divide(n1,const_2)|divide(n1,#0)|divide(n0,#0)|add(#2,#3)|add(#4,#1)|add(n1,#5)|divide(#6,#0)| | "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b" | probability |
math_qa__LI9GaB7r5VMZAXvV | Half a number plus 5 is 13.What is the number?
Options: A) 8 B) 16 C) 10 D) 11 E) 12 | <gadget id="calculator">13 - 5</gadget>
<output>8</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<result>B</result> | B | 16 | Half a number plus 5 is 13.What is the number? | {
"A": "8",
"B": "16",
"C": "10",
"D": "11",
"E": "12"
} | multiply(subtract(13, 5), const_2) | subtract(n1,n0)|multiply(#0,const_2)| | "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 13 ( 1 / 2 ) x = 13 - 5 ( 1 / 2 ) x = 8 x = 16 correct answer is b" | general |
math_qa__niDQvmBYiJ0Dt3JX | a hare and a jackal are running a race . 3 leaps of the hare are equal to 4 leaps of the jackal . for every 6 leaps of the hare , the jackal takes 7 leaps . find the ratio of the speed of the hare to the speed of the jackal . Choose the correct answer: A) 64 : 25 B) 8 : 7 C) 5 : 8 D) 25 : 64 E) 6 : 7 | <gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">8 / 7</gadget>
<output>8/7 = around 1.142857</output>
<result>B</result> | B | 1.142857 | a hare and a jackal are running a race . 3 leaps of the hare are equal to 4 leaps of the jackal . for every 6 leaps of the hare , the jackal takes 7 leaps . find the ratio of the speed of the hare to the speed of the jackal . | {
"A": "64 : 25",
"B": "8 : 7",
"C": "5 : 8",
"D": "25 : 64",
"E": "6 : 7"
} | divide(add(const_4, const_4), 7) | add(const_4,const_4)|divide(#0,n3) | the hare takes 6 leaps and the jackal takes 7 leaps . 1 hare leap = 4 / 3 jackal leaps thus the hare ' s 6 leaps = 6 * ( 4 / 3 ) = 8 jackal leaps . the ratio of their speeds is 8 : 7 . the answer is b . | other |
math_qa__5sXsgsKttkAlApqH | On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. Choose the correct choice from the following answers: A) 10 B) 11 C) 12 D) 13 E) 15 | <gadget id="calculator">109 / 9</gadget>
<output>109/9 = around 12.111111</output>
<gadget id="calculator">floor(109/9)</gadget>
<output>12</output>
<result>C</result> | C | 12 | On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. | {
"A": "10",
"B": "11",
"C": "12",
"D": "13",
"E": "15"
} | floor(divide(109, 9)) | divide(n0,n1)|floor(#0)| | "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 c" | general |
math_qa__SSCvuzG3eStd5V90 | A, B and C enter into a partnership by investing $15000, $21000 and $27000 respectively. At the end of 8 months, B receives $1540 as his share. Find the share of A. Choose the correct choice from the following options:
A) $ 800 B) $ 900 C) $ 1000 D) $ 1100 E) $ 1200 | <gadget id="calculator">21_000 * 8</gadget>
<output>168_000</output>
<gadget id="calculator">168_000 / 100</gadget>
<output>1_680</output>
<gadget id="calculator">1_540 / 1_680</gadget>
<output>11/12 = around 0.916667</output>
<gadget id="calculator">15_000 * (11/12)</gadget>
<output>13_750</output>
<gadget id="calculator">13_750 * 8</gadget>
<output>110_000</output>
<gadget id="calculator">110_000 / 100</gadget>
<output>1_100</output>
<result>D</result> | D | 1,100 | A, B and C enter into a partnership by investing $15000, $21000 and $27000 respectively. At the end of 8 months, B receives $1540 as his share. Find the share of A. | {
"A": "$ 800",
"B": "$ 900",
"C": "$ 1000",
"D": "$ 1100",
"E": "$ 1200"
} | divide(multiply(multiply(15000, divide(1540, divide(multiply(21000, 8), const_100))), 8), const_100) | multiply(n1,n3)|divide(#0,const_100)|divide(n4,#1)|multiply(n0,#2)|multiply(n3,#3)|divide(#4,const_100)| | "the ratio of capital of a , b and c = 15000 : 21000 : 27000 = 5 : 7 : 9 a ' s share = ( 5 / 7 ) * 1540 = $ 1100 the answer is d ." | gain |
math_qa__5BI7b7ceExrxhJoG | When a number is divided by 6 &then multiply by 12 the answer is 15 what is the no.? Pick one
A) 4.5 B) 5 C) 5.6 D) 7.5 E) 6.5 | <gadget id="calculator">15 / 12</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 6</gadget>
<output>15/2 = around 7.5</output>
<result>D</result> | D | 7.5 | When a number is divided by 6 &then multiply by 12 the answer is 15 what is the no.? | {
"A": "4.5",
"B": "5",
"C": "5.6",
"D": "7.5",
"E": "6.5"
} | multiply(divide(15, 12), 6) | divide(n2,n1)|multiply(n0,#0)| | "if $ x $ is the number , x / 6 * 12 = 15 = > 2 x = 15 = > x = 7.5 d" | general |
math_qa__hpd09mANDBjR9aA5 | If the perimeter of square region Z and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of Z Choose the correct choice from the following.
A) 25 : 16 B) 24 : 25 C) 5 : 6 D) 4 : 5 E) 4 : 9 | <gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 / 2</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) ** 2</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">6 / (25/4)</gadget>
<output>24/25 = around 0.96</output>
<result>B</result> | B | 0.96 | If the perimeter of square region Z and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of Z | {
"A": "25 : 16",
"B": "24 : 25",
"C": "5 : 6",
"D": "4 : 5",
"E": "4 : 9"
} | divide(multiply(2, 3), power(divide(add(2, 3), const_2), const_2)) | add(n0,n1)|multiply(n0,n1)|divide(#0,const_2)|power(#2,const_2)|divide(#1,#3) | we know perimeter of a square ( pz ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pz = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b | geometry |
math_qa__yuQmoYz5jQrFl0eo | A, Band C can do a piece of work in 35 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days? Choose one:
A) 7 days B) 8 days C) 9 days D) 10 days E) 16 days | <gadget id="calculator">55 / 35</gadget>
<output>11/7 = around 1.571429</output>
<gadget id="calculator">55 / 20</gadget>
<output>11/4 = around 2.75</output>
<gadget id="calculator">(11/7) + (11/4)</gadget>
<output>121/28 = around 4.321429</output>
<gadget id="calculator">55 / 55</gadget>
<output>1</output>
<gadget id="calculator">(11/7) + 1</gadget>
<output>18/7 = around 2.571429</output>
<gadget id="calculator">(121/28) + (18/7)</gadget>
<output>193/28 = around 6.892857</output>
<gadget id="calculator">(193/28) / 2</gadget>
<output>193/56 = around 3.446429</output>
<gadget id="calculator">55 / (193/56)</gadget>
<output>3_080/193 = around 15.958549</output>
<result>E</result> | E | 16 | A, Band C can do a piece of work in 35 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days? | {
"A": "7 days",
"B": "8 days",
"C": "9 days",
"D": "10 days",
"E": "16 days"
} | divide(55, divide(add(add(divide(55, 35), divide(55, 20)), add(divide(55, 35), divide(55, 55))), const_2)) | divide(n2,n0)|divide(n2,n1)|divide(n2,n2)|add(#0,#1)|add(#0,#2)|add(#3,#4)|divide(#5,const_2)|divide(n2,#6)| | "( a + b ) ' s 1 day ' s work = 1 / 35 + 1 / 20 = 11 / 140 ( a + c ) ' s 1 day ' s work = 1 / 35 + 1 / 55 = 18 / 385 work done in 2 day ' s = 11 / 140 + 18 / 385 = 48 / 383 48 / 383 th work done in 2 days work done = 383 / 48 * 2 = 16 days ( approx ) answer : e" | physics |
math_qa__yb5RtHsyE24ExQ6t | Aram’s car was fined when he gave Joe and Peter a ride, so they decided to help Aram pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Aram pay?
Select the correct option.
A) $ 13 B) $ 15 C) $ 20 D) $ 28 E) $ 48 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 + 3</gadget>
<output>10</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/4) + (1/3)</gadget>
<output>7/12 = around 0.583333</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(7/12) + (1/2)</gadget>
<output>13/12 = around 1.083333</output>
<gadget id="calculator">(13/12) - 1</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">10 / (1/12)</gadget>
<output>120</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<result>C</result> | C | 20 | Aram’s car was fined when he gave Joe and Peter a ride, so they decided to help Aram pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Aram pay? | {
"A": "$ 13",
"B": "$ 15",
"C": "$ 20",
"D": "$ 28",
"E": "$ 48"
} | subtract(divide(add(add(3, 4), 3), subtract(add(add(divide(1, 4), divide(1, 3)), divide(1, 2)), 1)), const_100) | add(n0,n2)|divide(n1,n2)|divide(n1,n0)|divide(n1,n8)|add(n0,#0)|add(#1,#2)|add(#5,#3)|subtract(#6,n1)|divide(#4,#7)|subtract(#8,const_100) | as given aram ' payment is [ 1 ] [ / 2 ] * fine - 4 i . e total fine = 2 * ( sam ' s payment + 4 ) now , as everything looks integer , fine should be able to divide by 4 and 3 . because joe ' s contribution has 1 / 4 of the fine and peter ' s contribution has 1 / 3 of the fine so , that leads me to following : options , aram ' s pay , total fine ( f ) , f / 4 , f / 3 a ) , 13 , 34 , no i . e 34 / 4 , no i . e 34 / 3 b ) , 14 , 38 , no , no c ) , 20 , 48 , yes yes , no need to further go on as we have got f / 4 and f / 3 correct , just for confirmation we go further d ) , 28 , 64 , yes , no e ) , 48 , 104 , yes , no correct answer is c | general |
math_qa__iPlrs4UBLe765xTz | The mean of 50 observations was 36. It was found later that an observation 43 was wrongly taken as 23. The corrected new mean is
Choose the correct choice from the following options: A) 35.2 B) 36.1 C) 36.2 D) 36.4 E) none | <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>D</result> | D | 36.4 | The mean of 50 observations was 36. It was found later that an observation 43 was wrongly taken as 23. The corrected new mean is | {
"A": "35.2",
"B": "36.1",
"C": "36.2",
"D": "36.4",
"E": "none"
} | 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)| | "solution correct sum = ( 36 x 50 + 43 - 23 ) = 1820 . â ˆ ´ correct mean = 1820 / 50 = 36.4 . answer d" | general |
math_qa__5LSO06oO1Pc4z8fE | It is currently 7:16 PM. At what time in the morning was it exactly 19,443 minutes earlier? Choose the correct choice from the following answers:
A) 7 : 11 B) 7 : 13 C) 7 : 17 D) 7 : 19 E) 7 : 21 | <gadget id="calculator">16 - 3</gadget>
<output>13</output>
<gadget id="calculator">7 / 13</gadget>
<output>7/13 = around 0.538462</output>
<result>B</result> | B | 0.538462 | It is currently 7:16 PM. At what time in the morning was it exactly 19,443 minutes earlier? | {
"A": "7 : 11",
"B": "7 : 13",
"C": "7 : 17",
"D": "7 : 19",
"E": "7 : 21"
} | divide(7, subtract(16, const_3)) | subtract(n1,const_3)|divide(n0,#0) | converting 19,443 minutes to hours , we get 19,443 / 60 = 324 r 3 ; that is 324 hours and 3 minutes . all of the answers are during the same hour of the morning , thus the hours can be assumed to bring us into the 7 am hour evenly from 7 : 16 pm . thus 324 hours ago was 7 : 16 am . take an extra 3 minutes off , and it was 7 : 13 am . b | physics |
math_qa__qTnU4NDxj6itjuQs | 52 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
Choose the correct option
A) 30.33
B) 34.44
C) 26.1
D) 28.0
E) 21.0 | <gadget id="calculator">52 * 10</gadget>
<output>520</output>
<gadget id="calculator">780 - 520</gadget>
<output>260</output>
<gadget id="calculator">22 - 10</gadget>
<output>12</output>
<gadget id="calculator">260 / 12</gadget>
<output>65/3 = around 21.666667</output>
<gadget id="calculator">52 - (65/3)</gadget>
<output>91/3 = around 30.333333</output>
<result>A</result> | A | 30.33 | 52 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is : | {
"A": "30.33",
"B": "34.44",
"C": "26.1",
"D": "28.0",
"E": "21.0"
} | subtract(52, divide(subtract(780, multiply(52, 10)), subtract(22, 10))) | multiply(n0,n1)|subtract(n2,n1)|subtract(n3,#0)|divide(#2,#1)|subtract(n0,#3)| | "explanation : let the two parts be ( 52 - x ) and x . then , 10 ( 52 - x ) + 22 x = 780 = > 12 x = 260 = > x = 21.66 . bigger part = ( 52 - x ) = 30.33 . answer : a ) 30.33" | general |
math_qa__tBl8Tcqm8O6khTIy | The price of 2 sarees and 4 shirts is $1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? Select the correct option:
A) 3800 B) 3300 C) 2400 D) 4200 E) 1400 | <gadget id="calculator">2 * 1_600</gadget>
<output>3_200</output>
<gadget id="calculator">3_200 - 1_600</gadget>
<output>1_600</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">1_600 / 8</gadget>
<output>200</output>
<gadget id="calculator">200 * 12</gadget>
<output>2_400</output>
<result>C</result> | C | 2,400 | The price of 2 sarees and 4 shirts is $1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? | {
"A": "3800",
"B": "3300",
"C": "2400",
"D": "4200",
"E": "1400"
} | multiply(divide(subtract(multiply(2, 1600), 1600), subtract(multiply(2, 6), 4)), 12) | multiply(n0,n2)|multiply(n0,n4)|subtract(#0,n2)|subtract(#1,n1)|divide(#2,#3)|multiply(n5,#4) | c $ 2400 let the price of a saree and a shirt be $ x and $ y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = $ ( 12 x 200 ) = $ 2400 . | general |
math_qa__n5YbU3gdCYe1nok5 | On dividing 271 by a number, the quotient is 9 and the remainder is 1. Find the divisor? Choose the correct answer:
A) 12 B) 15 C) 16 D) 17 E) 30 | <gadget id="calculator">271 / 9</gadget>
<output>271/9 = around 30.111111</output>
<gadget id="calculator">floor(271/9)</gadget>
<output>30</output>
<result>E</result> | E | 30 | On dividing 271 by a number, the quotient is 9 and the remainder is 1. Find the divisor? | {
"A": "12",
"B": "15",
"C": "16",
"D": "17",
"E": "30"
} | floor(divide(271, 9)) | divide(n0,n1)|floor(#0)| | "d = ( d - r ) / q = ( 271 - 1 ) / 9 = 270 / 9 = 30 e )" | general |
math_qa__vqku7tD5MS0LOnzW | Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 12 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
Choose the correct choice from the following answers.
A) 4 B) 4.5 C) 6 D) 8 E) 6.5 | <gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">1 / 11</gadget>
<output>1/11 = around 0.090909</output>
<gadget id="calculator">12 + 2</gadget>
<output>14</output>
<gadget id="calculator">1 / 14</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">(1/11) + (1/14)</gadget>
<output>25/154 = around 0.162338</output>
<gadget id="calculator">1 / (25/154)</gadget>
<output>154/25 = around 6.16</output>
<result>C</result> | C | 6 | Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 12 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together? | {
"A": "4",
"B": "4.5",
"C": "6",
"D": "8",
"E": "6.5"
} | inverse(add(inverse(subtract(12, const_1)), inverse(add(12, 2)))) | add(n0,n1)|subtract(n1,const_1)|inverse(#1)|inverse(#0)|add(#2,#3)|inverse(#4)| | "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 6 no . of days when b works = 6 → 6 x + 6 y = 1 when b starts : no . of days when a works = 6.5 no . of days when b works = 5.5 → 6.5 x + 5.5 y = 1 solving the above two equations for xy x = 1 / 12 y = 1 / 12 → total work done by ab in a day = 1 / 12 + 1 / 12 = 2 / 12 = 1 / 6 → no . of days to complete the work when both work together = 6 answer : c" | physics |
math_qa__GVntJ1ztsa8twDoo | On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ? Choose the correct choice from the following options:
A) 0
B) 5
C) 8
D) 9
E) 4 | <gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">9 / 5</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">floor(9/5)</gadget>
<output>1</output>
<gadget id="calculator">(9/5) - 1</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 5</gadget>
<output>4</output>
<result>E</result> | E | 4 | On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ? | {
"A": "0",
"B": "5",
"C": "8",
"D": "9",
"E": "4"
} | multiply(subtract(divide(power(3, const_2), 5), floor(divide(power(3, const_2), 5))), 5) | power(n1,const_2)|divide(#0,n0)|floor(#1)|subtract(#1,#2)|multiply(n0,#3)| | "explanation : let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x ^ 2 = ( 5 k + 3 ) ^ 2 = ( 25 k ^ 2 + 30 k + 9 ) = 5 ( 5 k ^ 2 + 6 k + 1 ) + 4 on dividing x 2 by 5 , we get 4 as remainder . e )" | geometry |
math_qa__Juk74Ikab2jHQX5B | m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 15) both lie on the line defined by the equation x = (y/5) - (2/5), what is the value of p? Choose the correct choice
A) 1
B) 2
C) 3
D) 4
E) 5 | <gadget id="calculator">15 / 5</gadget>
<output>3</output>
<result>C</result> | C | 3 | m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 15) both lie on the line defined by the equation x = (y/5) - (2/5), what is the value of p? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | divide(15, 5) | divide(n0,n1)| | "x = ( y / 5 ) - ( 2 / 5 ) , and so y = 5 x + 2 . the slope is 5 . ( n + 15 - n ) / ( m + p - m ) = 5 p = 3 the answer is c ." | general |
math_qa__3huL9V8fZTLBTs4C | In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 7 : 7 : 8. If the shop carries 330 dogs and bunnies total in stock, how many dogs are there? Choose the correct choice:
A) 42 B) 66 C) 98 D) 112 E) 154 | <gadget id="calculator">7 + 8</gadget>
<output>15</output>
<gadget id="calculator">330 / 15</gadget>
<output>22</output>
<gadget id="calculator">22 * 7</gadget>
<output>154</output>
<result>E</result> | E | 154 | In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 7 : 7 : 8. If the shop carries 330 dogs and bunnies total in stock, how many dogs are there? | {
"A": "42",
"B": "66",
"C": "98",
"D": "112",
"E": "154"
} | multiply(divide(330, add(7, 8)), 7) | add(n0,n2)|divide(n3,#0)|multiply(n0,#1)| | "let us assume the number of dogs , cats and bunnies to be 7 x , 7 x and 8 x total dogs and bunnies = 15 x . and we are given that 15 x = 330 . hence x = 22 . dogs = 7 x = 7 * 22 = 154 ( option e )" | other |
math_qa__YAKOuuKKSzoc2CNg | The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ?
Choices.
A) 148
B) 152
C) 156
D) 144
E) none | <gadget id="calculator">37 + 39</gadget>
<output>76</output>
<gadget id="calculator">76 + 2</gadget>
<output>78</output>
<gadget id="calculator">78 / 2</gadget>
<output>39</output>
<gadget id="calculator">152 / 39</gadget>
<output>152/39 = around 3.897436</output>
<gadget id="calculator">39 * (152/39)</gadget>
<output>152</output>
<result>C</result> | C | 156 | The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ? | {
"A": "148",
"B": "152",
"C": "156",
"D": "144",
"E": "none"
} | multiply(39, divide(152, divide(add(add(37, 39), const_2), const_2))) | add(n0,n1)|add(#0,const_2)|divide(#1,const_2)|divide(n2,#2)|multiply(n1,#3)| | "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 152 . so , total number of ducks and frogs in the pond , = 2 * 152 = 304 . therefore , number of frogs , = ( 304 * 39 ) / 76 = 156 . answer : option c" | general |
math_qa__tSSAl1nLmrwuVynY | The side of a square is increased by 30% then how much % does its area increases? Choose the correct answer: A) 52.65 B) 69 C) 50.75 D) 42.75 E) 52.75 | <gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">130 ** 2</gadget>
<output>16_900</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">16_900 - 10_000</gadget>
<output>6_900</output>
<gadget id="calculator">6_900 * 100</gadget>
<output>690_000</output>
<gadget id="calculator">690_000 / 10_000</gadget>
<output>69</output>
<result>B</result> | B | 69 | The side of a square is increased by 30% then how much % does its area increases? | {
"A": "52.65",
"B": "69",
"C": "50.75",
"D": "42.75",
"E": "52.75"
} | divide(multiply(subtract(square_area(add(const_100, 30)), square_area(const_100)), const_100), square_area(const_100)) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)| | "a = 100 a 2 = 10000 a = 130 a 2 = 16900 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 6900 100 - - - - - - - ? = > 69 % answer : b" | geometry |
math_qa__F2PbqwejswNY0La6 | The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24/96 = 1/4
The positive integer y is less than 20 and the connection between y and 6 is equal to 1/1. How many possible values of y are there? Choices
A) 7
B) 8
C) 9
D) 10
E) 11 | <gadget id="calculator">20 - 1</gadget>
<output>19</output>
<gadget id="calculator">19 - 12</gadget>
<output>7</output>
<result>A</result> | A | 7 | The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24/96 = 1/4
The positive integer y is less than 20 and the connection between y and 6 is equal to 1/1. How many possible values of y are there? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10",
"E": "11"
} | subtract(subtract(20, const_1), 12) | subtract(n12,const_1)|subtract(#0,n1) | since “ connection ” between y and 6 is 1 / 1 then lcm ( 6 , y ) = 6 y , which means that 6 and y are co - prime ( they do not share any common factor but 1 ) , because if the had any common factor but 1 then lcm ( 6 , y ) would be less than 6 y . so , we should check how many integers less than 20 are co - prime with 6 , which can be rephrased as how many integers less than 20 are not divisible by 2 or 3 ( 6 = 2 * 3 ) . there are ( 18 - 2 ) / 2 + 1 = 9 multiples of 2 in the range from 0 to 20 , not inclusive ; there are ( 18 - 3 ) / 3 + 1 = 6 multiples of 3 in the range from 0 to 20 , not inclusive ; there are 3 multiples of 6 in the range from 0 to 20 , not inclusive ( 6 , 12 , 18 ) - overlap of the above two sets ; total multiples of 2 or 6 in the range from 0 to 20 , not inclusive is 9 + 6 - 3 = 12 ; total integers in the range from 0 to 20 , not inclusive is 19 ; hence , there are total of 19 - 12 = 7 numbers which have no common factor with 6 other than 1 : 1 , 5 , 7 , 11 , 13 , 17 and 19 . answer : a . | general |
math_qa__N8AuL1xpymQYPBr6 | The probability of two events A and B are 0.15 and 0.40 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________ Answers: A) 0.45 B) 0.4 C) 0.5 D) 0.05 E) 0.6 | <gadget id="calculator">0.15 + 0.4</gadget>
<output>0.55</output>
<gadget id="calculator">0.55 - 0.15</gadget>
<output>0.4</output>
<gadget id="calculator">1 - 0.4</gadget>
<output>0.6</output>
<result>E</result> | E | 0.6 | The probability of two events A and B are 0.15 and 0.40 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________ | {
"A": "0.45",
"B": "0.4",
"C": "0.5",
"D": "0.05",
"E": "0.6"
} | subtract(const_1, subtract(add(0.15, 0.40), 0.15)) | add(n0,n1)|subtract(#0,n2)|subtract(const_1,#1)| | "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 15 + . 40 - . 15 = . 40 but the probability of neither a nor b = 1 - . 40 = 0.60 answer : e" | other |
math_qa__KaqOLYThI8EIr2zK | (0.8)(power 3) - (0.5)(power 3)/ (0.8)(power 2) + 0.40 + (0.5)(power 2) is: Choose the correct choice from the following answers:
A) 0.6
B) 0.5
C) 0.35
D) 0.3
E) none of them | <gadget id="calculator">0.8 ** 3</gadget>
<output>0.512</output>
<gadget id="calculator">0.5 ** 3</gadget>
<output>0.125</output>
<gadget id="calculator">0.512 - 0.125</gadget>
<output>0.387</output>
<gadget id="calculator">0.8 ** 2</gadget>
<output>0.64</output>
<gadget id="calculator">0.64 + 0.4</gadget>
<output>1.04</output>
<gadget id="calculator">0.5 ** 2</gadget>
<output>0.25</output>
<gadget id="calculator">1.04 + 0.25</gadget>
<output>1.29</output>
<gadget id="calculator">0.387 / 1.29</gadget>
<output>0.3</output>
<result>D</result> | D | 0.3 | (0.8)(power 3) - (0.5)(power 3)/ (0.8)(power 2) + 0.40 + (0.5)(power 2) is: | {
"A": "0.6",
"B": "0.5",
"C": "0.35",
"D": "0.3",
"E": "none of them"
} | divide(subtract(power(0.8, 3), power(0.5, 3)), add(add(power(0.8, 2), 0.40), power(0.5, 2))) | power(n0,n1)|power(n2,n1)|power(n0,n5)|power(n2,n5)|add(n6,#2)|subtract(#0,#1)|add(#4,#3)|divide(#5,#6)| | "given expression = ( 0.8 ) ( power 3 ) - ( 0.5 ) ( power 3 ) / ( 0.8 ) ( power 2 ) + ( 0.8 x 0.5 ) + ( 0.5 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.8 - 0.5 ) = 0.30 answer is d ." | general |
math_qa__MjPsuReFnCkOc4t1 | If the length of the sides of two cubes are in the ratio 7:1, what is the ratio of their total surface area? Choose the correct option: A) 7 : 1 B) 14 : 1 C) 21 : 1 D) 42 : 1 E) 49 : 1 | <gadget id="calculator">7 * 7</gadget>
<output>49</output>
<result>E</result> | E | 49 | If the length of the sides of two cubes are in the ratio 7:1, what is the ratio of their total surface area? | {
"A": "7 : 1",
"B": "14 : 1",
"C": "21 : 1",
"D": "42 : 1",
"E": "49 : 1"
} | multiply(7, 7) | multiply(n0,n0)| | "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 7 x ) ^ 2 = 294 x ^ 2 . the ratio of surface areas is 49 : 1 . the answer is e ." | geometry |
math_qa__Y5SyQr4UEFKV16bN | When a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $110.60, what was the total value of the item?
Choose the correct option
A) $ 2160 B) $ 2370 C) $ 2580 D) $ 2790 E) $ 2950 | <gadget id="calculator">7 / 100</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">110.6 / (7/100)</gadget>
<output>1_580</output>
<gadget id="calculator">1_000 + 1_580</gadget>
<output>2_580</output>
<result>C</result> | C | 2,580 | When a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $110.60, what was the total value of the item? | {
"A": "$ 2160",
"B": "$ 2370",
"C": "$ 2580",
"D": "$ 2790",
"E": "$ 2950"
} | add(1,000, divide(110.60, divide(7, const_100))) | divide(n0,const_100)|divide(n2,#0)|add(#1,n1)| | "let x be the value of the item . 0.07 * ( x - 1000 ) = 110.60 x = 2580 the answer is c ." | general |
math_qa__QICCfb9EzYEauhIR | On a trip covering 400 km, a bicyclist travels the first 100 km at 20 km per hour and the remainder of the distance at 15 km per hour. What is the average speed, in km per hour, for the entire trip?
Choose the correct choice from the following answers.
A) 15.5
B) 16.0
C) 16.5
D) 17.0
E) 17.5 | <gadget id="calculator">100 / 20</gadget>
<output>5</output>
<gadget id="calculator">400 - 100</gadget>
<output>300</output>
<gadget id="calculator">300 / 15</gadget>
<output>20</output>
<gadget id="calculator">5 + 20</gadget>
<output>25</output>
<gadget id="calculator">400 / 25</gadget>
<output>16</output>
<result>B</result> | B | 16 | On a trip covering 400 km, a bicyclist travels the first 100 km at 20 km per hour and the remainder of the distance at 15 km per hour. What is the average speed, in km per hour, for the entire trip? | {
"A": "15.5",
"B": "16.0",
"C": "16.5",
"D": "17.0",
"E": "17.5"
} | speed(400, add(divide(100, 20), divide(subtract(400, 100), 15))) | divide(n1,n2)|subtract(n0,n1)|divide(#1,n3)|add(#0,#2)|speed(n0,#3) | time 1 = 100 / 20 = 5 hours time 2 = 300 / 15 = 20 hours total time = 25 hours average speed = 400 / 25 = 16 km / hr the answer is b . | physics |
math_qa__xxC7AcK7FHqqZOQK | eighteen years ago , a father was 3 times as old as his son . now the father is only twice as old his son . then the sum of the present ages of the son and the father is : Choose the correct choice from the following answers:
A) 53
B) 108
C) 77
D) 107
E) 109 | <gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 * 3</gadget>
<output>54</output>
<gadget id="calculator">54 - 18</gadget>
<output>36</output>
<gadget id="calculator">36 * 2</gadget>
<output>72</output>
<gadget id="calculator">36 + 72</gadget>
<output>108</output>
<result>D</result> | D | 107 | eighteen years ago , a father was 3 times as old as his son . now the father is only twice as old his son . then the sum of the present ages of the son and the father is : | {
"A": "53",
"B": "108",
"C": "77",
"D": "107",
"E": "109"
} | add(subtract(multiply(multiply(add(const_3, const_3), 3), 3), multiply(add(const_3, const_3), 3)), multiply(subtract(multiply(multiply(add(const_3, const_3), 3), 3), multiply(add(const_3, const_3), 3)), const_2)) | add(const_3,const_3)|multiply(n0,#0)|multiply(n0,#1)|subtract(#2,#1)|multiply(#3,const_2)|add(#4,#3) | explanation : let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 18 ) = 3 ( x - 18 ) = > x = 36 required sum = ( 2 x + x ) = 108 years . answer : option d | general |
math_qa__QBOukmlLzHmcLj8U | The area of a parallelogram is 128sq m.Then the area of a triangle formed by its diagonal is ----------?
Choose the correct choice from the following
A) 128 m B) 64 m C) 64 m ^ 2 D) 128 m ^ 2 E) none | <gadget id="calculator">128 / 2</gadget>
<output>64</output>
<result>B</result> | B | 64 | The area of a parallelogram is 128sq m.Then the area of a triangle formed by its diagonal is ----------? | {
"A": "128 m",
"B": "64 m",
"C": "64 m ^ 2",
"D": "128 m ^ 2",
"E": "none"
} | divide(128, const_2) | divide(n0,const_2) | b * h / 2 = 128 / 2 = 64 m . ans : ( b ) | geometry |
math_qa__NUMbRQpuhQQhg42F | A person crosses a 1080 m long street in 14 minutes. What is his speed in km per hour? Choose the correct choice from the following choices:
A) 4.1 B) 4.5 C) 4.6 D) 5.4 E) 5.5 | <gadget id="calculator">1_080 / 1_000</gadget>
<output>27/25 = around 1.08</output>
<gadget id="calculator">14 * 60</gadget>
<output>840</output>
<gadget id="calculator">840 / 3_600</gadget>
<output>7/30 = around 0.233333</output>
<gadget id="calculator">(27/25) / (7/30)</gadget>
<output>162/35 = around 4.628571</output>
<result>C</result> | C | 4.6 | A person crosses a 1080 m long street in 14 minutes. What is his speed in km per hour? | {
"A": "4.1",
"B": "4.5",
"C": "4.6",
"D": "5.4",
"E": "5.5"
} | divide(divide(1080, const_1000), divide(multiply(14, const_60), const_3600)) | divide(n0,const_1000)|multiply(n1,const_60)|divide(#1,const_3600)|divide(#0,#2)| | "speed = 1080 / ( 12 x 60 ) m / sec = 1.3 m / sec . converting m / sec to km / hr = 1.3 x ( 18 / 5 ) km / hr = 4.6 km / hr . answer : c" | physics |
math_qa__U6MHQNBF3wM5ia1b | If x is a prime number, and x-1 is the median of the set {x-1, 3x+3, 2x-4}, then what is the average (arithmetic mean) of the set? Options
A) 2 B) 5 / 3 C) 3 D) 10 / 3 E) 14 / 3 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 3</gadget>
<output>9</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">10 / 3</gadget>
<output>10/3 = around 3.333333</output>
<result>D</result> | D | 3.333333 | If x is a prime number, and x-1 is the median of the set {x-1, 3x+3, 2x-4}, then what is the average (arithmetic mean) of the set? | {
"A": "2",
"B": "5 / 3",
"C": "3",
"D": "10 / 3",
"E": "14 / 3"
} | divide(add(add(multiply(3, 2), 3), subtract(2, 1)), 3) | multiply(n2,n4)|subtract(n4,n0)|add(n2,#0)|add(#2,#1)|divide(#3,n2) | if x is a prime number , and x - 1 is the median of the set { x - 1 , 3 x + 3 , 2 x - 4 } , then what is the average ( arithmetic mean ) of the set ? a . 2 b . 5 / 3 c . 3 d . 10 / 3 e . 14 / 3 solution : x - 1 is the median of the set , implies if we arrange the set in ascending order , the set would be [ 2 x - 4 , x - 1 , 3 x + 3 ] . this means that : 2 x - 4 < x - 2 < 3 x + 3 solving inequality gives x > - 2 and x < 3 . since x is prime number and the only prime number < 3 is 2 , so put x = 2 . hence set becomes : [ 0 , 1 , 9 ] and avg = 10 / 3 . d | general |
math_qa__5zHyC2SYGbbW06LG | The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. Options
A) 179
B) 208
C) 210
D) 223
E) 229 | <gadget id="calculator">60 * 46</gadget>
<output>2_760</output>
<gadget id="calculator">46 - 2</gadget>
<output>44</output>
<gadget id="calculator">58 * 44</gadget>
<output>2_552</output>
<gadget id="calculator">2_760 - 2_552</gadget>
<output>208</output>
<gadget id="calculator">150 + 208</gadget>
<output>358</output>
<gadget id="calculator">358 / 2</gadget>
<output>179</output>
<result>A</result> | A | 179 | The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. | {
"A": "179",
"B": "208",
"C": "210",
"D": "223",
"E": "229"
} | divide(add(150, subtract(multiply(60, 46), multiply(58, subtract(46, const_2)))), const_2) | multiply(n0,n1)|subtract(n1,const_2)|multiply(n3,#1)|subtract(#0,#2)|add(n2,#3)|divide(#4,const_2)| | "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 – 2552 = 208 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 208 2 x = 358 x = 179 runs answer a" | general |
math_qa__5TiNmvgLKggB3fwW | The radius of a semicircle is 7. What is the approximate perimeter of the semicircle? Choose the correct option: A) 36 B) 25 C) 15 D) 28 E) 37 | <gadget id="calculator">2 * pi * 7</gadget>
<output>14*pi = around 43.982297</output>
<gadget id="calculator">(14*pi) / 2</gadget>
<output>7*pi = around 21.991149</output>
<gadget id="calculator">7 + 7</gadget>
<output>14</output>
<gadget id="calculator">(7*pi) + 14</gadget>
<output>14 + 7*pi = around 35.991149</output>
<result>A</result> | A | 36 | The radius of a semicircle is 7. What is the approximate perimeter of the semicircle? | {
"A": "36",
"B": "25",
"C": "15",
"D": "28",
"E": "37"
} | add(divide(circumface(7), const_2), add(7, 7)) | add(n0,n0)|circumface(n0)|divide(#1,const_2)|add(#0,#2) | perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 7 + 2 * 7 = 35.98 approximately 36 answer a | geometry |
math_qa__ezXBZzfZPVtLx4GE | A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, one boggies were detached. The train now crosses a telegraph post in Choose one:
A) 16.5 sec B) 12 sec C) 15 sec D) 20 sec E) none of these | <gadget id="calculator">12 * 15</gadget>
<output>180</output>
<gadget id="calculator">180 - 15</gadget>
<output>165</output>
<gadget id="calculator">180 / 18</gadget>
<output>10</output>
<gadget id="calculator">165 / 10</gadget>
<output>33/2 = around 16.5</output>
<result>A</result> | A | 16.5 | A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 18 seconds. Due to some problem, one boggies were detached. The train now crosses a telegraph post in | {
"A": "16.5 sec",
"B": "12 sec",
"C": "15 sec",
"D": "20 sec",
"E": "none of these"
} | divide(subtract(multiply(12, 15), 15), divide(multiply(12, 15), 18)) | multiply(n0,n1)|divide(#0,n2)|subtract(#0,n1)|divide(#2,#1) | length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â „ 18 = 10 m / s now , length of train = 11 ã — 15 = 165 m â ˆ ´ required time = 165 â „ 10 = 16.5 sec . answer a | physics |
math_qa__lAQupfLk36HQlEJw | If a sum of money doubles itself in 8 years at simple interest, the ratepercent per annum is Pick one: A) 12 B) 12.5 C) 13 D) 13.5 E) 14 | <gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">2 / (2/25)</gadget>
<output>25</output>
<gadget id="calculator">25 / 2</gadget>
<output>25/2 = around 12.5</output>
<result>B</result> | B | 12.5 | If a sum of money doubles itself in 8 years at simple interest, the ratepercent per annum is | {
"A": "12",
"B": "12.5",
"C": "13",
"D": "13.5",
"E": "14"
} | divide(divide(const_2, divide(8, const_100)), const_2) | divide(n0,const_100)|divide(const_2,#0)|divide(#1,const_2) | explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 8 ) = 12.5 option b | gain |
math_qa__tz8Eh5KzaNMfKk76 | Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 2 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?
Choose the correct choice
A) 1.5 B) 2.5 C) 3.75 D) 5 E) 7.5 | <gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">6 / 4</gadget>
<output>3/2 = around 1.5</output>
<result>A</result> | A | 1.5 | Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 2 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top? | {
"A": "1.5",
"B": "2.5",
"C": "3.75",
"D": "5",
"E": "7.5"
} | divide(divide(multiply(add(4, 2), 2), 2), 4) | add(n0,n1)|multiply(n2,#0)|divide(#1,n1)|divide(#2,n0)| | "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 2 km / hour x / 3 = 2 x = 6 km the average speed while climbing = distance / time = 6 / 4 = 1.5 km / h the answer is a ." | physics |
math_qa__8wA7Fpc4VK8eNdi8 | The average (arithmetic mean) of 4 positive integers is 30. If the average of 2 of these integers is 15, what is the greatest possible value that one of the other 2 integers can have?
Select.
A) 55 B) 89 C) 100 D) 109 E) 115 | <gadget id="calculator">30 * 4</gadget>
<output>120</output>
<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<gadget id="calculator">120 - 30</gadget>
<output>90</output>
<result>B</result> | B | 89 | The average (arithmetic mean) of 4 positive integers is 30. If the average of 2 of these integers is 15, what is the greatest possible value that one of the other 2 integers can have? | {
"A": "55",
"B": "89",
"C": "100",
"D": "109",
"E": "115"
} | subtract(multiply(30, 4), multiply(15, 2)) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)| | "a + b + c + d = 120 a + b = 30 c + d = 90 greatest possible = 89 ( just less than 1 ) answer = b" | general |
math_qa__Xgc2hGs1UrE7mg48 | The length of the bridge, which a train 135 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Choose the correct answer
A) 76 m B) 178 m C) 240 m D) 187 m E) 176 m | <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 - 135</gadget>
<output>240</output>
<result>C</result> | C | 240 | The length of the bridge, which a train 135 metres long and travelling at 45 km/hr can cross in 30 seconds, is? | {
"A": "76 m",
"B": "178 m",
"C": "240 m",
"D": "187 m",
"E": "176 m"
} | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 135) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 135 + x ) / 30 = 25 / 2 = > 2 ( 135 + x ) = 750 = > x = 240 m . answer : c" | physics |
math_qa__9ebicQauYkFDEZrG | Jancy had 100 currency notes in all, some of which are of Rs 70 denomination and the remaining of Rs 50 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did she have in the denomination of Rs 50?
Choose the correct choice:
A) 103
B) 102
C) 100
D) 105
E) 106 | <gadget id="calculator">5_000 / 50</gadget>
<output>100</output>
<result>C</result> | C | 100 | Jancy had 100 currency notes in all, some of which are of Rs 70 denomination and the remaining of Rs 50 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did she have in the denomination of Rs 50? | {
"A": "103",
"B": "102",
"C": "100",
"D": "105",
"E": "106"
} | divide(5000, 50) | divide(n3,n2) | let the number of 50 - rupee notes = x then , the number of 70 - rupee notes = ( 100 – x ) 50 x + 70 ( 100 – x ) = 5000 : x = 100 answer : c | general |
math_qa__AxfCIC5fNX55QLgh | A line that passes through (–1, –4) and (4, k) has a slope = k. What is the value of k? Choose the correct choice:
A) 3 / 4 B) 1 C) 4 / 3 D) 2 E) 7 / 2 | <gadget id="calculator">4 / 4</gadget>
<output>1</output>
<result>B</result> | B | 1 | A line that passes through (–1, –4) and (4, k) has a slope = k. What is the value of k? | {
"A": "3 / 4",
"B": "1",
"C": "4 / 3",
"D": "2",
"E": "7 / 2"
} | divide(4, 4) | divide(n1,n2)| | "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 4 + 1 ) = > 5 k = k + 4 = > k = 1 ans b it is !" | general |
math_qa__sgVn40mvbkON6cWC | A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 25% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save? Select the correct option:
A) 20 % B) 25 % C) 28.5 % D) 30 % E) 32 % | <gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 + 100</gadget>
<output>225</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">225 - 200</gadget>
<output>25</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>B</result> | B | 25 | A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 25% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save? | {
"A": "20 %",
"B": "25 %",
"C": "28.5 %",
"D": "30 %",
"E": "32 %"
} | multiply(divide(subtract(add(add(100, 25), 100), multiply(2, 100)), 100), 100) | add(n0,n1)|multiply(n1,n2)|add(n1,#0)|subtract(#2,#1)|divide(#3,n1)|multiply(#4,n1)| | "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.25 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 25 % income the savings increased by 100 % . or s = . 25 i or s = 25 % of income b is the answer" | general |
math_qa__aPiB3IbwI1FKK8Ay | P and Q can complete a work in 80 days and 48 days respectively. P alone started the work and Q joined him after 16 days till the completion of the work. How long did the work last?
Choose the most appropriate option.
A) 5 days B) 10 days C) 14 days D) 22 days E) 40 days | <gadget id="calculator">16 / 80</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">1 / 48</gadget>
<output>1/48 = around 0.020833</output>
<gadget id="calculator">(1/80) + (1/48)</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(4/5) / (1/30)</gadget>
<output>24</output>
<gadget id="calculator">16 + 24</gadget>
<output>40</output>
<result>E</result> | E | 40 | P and Q can complete a work in 80 days and 48 days respectively. P alone started the work and Q joined him after 16 days till the completion of the work. How long did the work last? | {
"A": "5 days",
"B": "10 days",
"C": "14 days",
"D": "22 days",
"E": "40 days"
} | add(16, divide(subtract(const_1, divide(16, 80)), add(inverse(80), inverse(48)))) | divide(n2,n0)|inverse(n0)|inverse(n1)|add(#1,#2)|subtract(const_1,#0)|divide(#4,#3)|add(n2,#5) | explanation : work done by p in 1 day = 1 / 80 work done by q in 1 day = 1 / 48 work done by p in 16 days = 16 ã — ( 1 / 80 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 80 + 1 / 48 = 1 / 30 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 1 / 30 ) = 24 total days = 16 + 24 = 40 answer : option e | physics |
math_qa__vpwFdXcznr9hfT1k | Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is Options
A) 4 : 9 B) 4 : 3 C) 4 : 12 D) 4 : 8 E) 4 : 5 | <gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>
<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<result>B</result> | B | 1.333333 | Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is | {
"A": "4 : 9",
"B": "4 : 3",
"C": "4 : 12",
"D": "4 : 8",
"E": "4 : 5"
} | divide(sqrt(16), sqrt(9)) | sqrt(n1)|sqrt(n0)|divide(#0,#1)| | "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 16 : 9 = 4 : 3 . answer : b" | physics |
math_qa__cM6IBBqx7DIeGMfF | A meal cost $ 34.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be: Choose one:
A) 40 - 42
B) 39 - 41
C) 38 - 40
D) 37 - 39
E) 36 - 37 | <gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">34.5 * (3/20)</gadget>
<output>5.175</output>
<gadget id="calculator">5.175 + 34.5</gadget>
<output>39.675</output>
<result>C</result> | C | 38 | A meal cost $ 34.50 and there was no tax. If the tip was more than 10 pc but less than 15pc of the price, then the total amount paid should be: | {
"A": "40 - 42",
"B": "39 - 41",
"C": "38 - 40",
"D": "37 - 39",
"E": "36 - 37"
} | add(multiply(34.5, divide(15, const_100)), 34.5) | divide(n2,const_100)|multiply(n0,#0)|add(n0,#1) | 10 % ( 34.5 ) = 3.45 15 % ( 34.5 ) = 5.175 total amount could have been 34.5 + 3.45 and 34.5 + 5.175 = > could have been between 37.95 and 39.675 = > approximately between 38 and 40 answer is c . | general |
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