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math_qa__AgabeOyX1qRtgCtS | In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (12, 0), (0, -3.5), (-12, 0)? Choose the most appropriate option
A) 84 B) 88 C) 112 D) 116 E) 120 | <gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">3.5 * 2</gadget>
<output>7</output>
<gadget id="calculator">(24 * 7) / 2</gadget>
<output>84</output>
<result>A</result> | A | 84 | In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (12, 0), (0, -3.5), (-12, 0)? | {
"A": "84",
"B": "88",
"C": "112",
"D": "116",
"E": "120"
} | rhombus_area(multiply(12, const_2), multiply(3.5, const_2)) | multiply(n2,const_2)|multiply(n1,const_2)|rhombus_area(#0,#1)| | "area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 12 + 12 = 24 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 24 * 7 = 84 a is the answer" | geometry |
math_qa__MNPwt9w9NXZwMgh6 | The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.7.2. The true discount is Options
A) rs . 72 B) rs . 36 C) rs . 54 D) rs . 60 E) none | <gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">7.2 / (3/25)</gadget>
<output>60</output>
<result>D</result> | D | 60 | The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.7.2. The true discount is | {
"A": "rs . 72",
"B": "rs . 36",
"C": "rs . 54",
"D": "rs . 60",
"E": "none"
} | divide(7.2, divide(12, const_100)) | divide(n1,const_100)|divide(n2,#0)| | "solution t . d = [ b . g x 100 / r x t ] = rs . ( 7.2 x 100 / 12 x 1 ) = rs . 60 . answer d" | gain |
math_qa__i3Hy1aRu07dQ3F2d | N is the greatest number which divides 1305, 4665 and 6905 and gives the same remainder in each case. What is the sum of the digits in N? Choose the most appropriate option: A) 23 B) 28 C) 4 D) 1 E) 25 | <gadget id="calculator">4_665 - 1_305</gadget>
<output>3_360</output>
<gadget id="calculator">6_905 - 4_665</gadget>
<output>2_240</output>
<gadget id="calculator">gcd(3_360, 2_240)</gadget>
<output>1_120</output>
<gadget id="calculator">6_905 - 1_305</gadget>
<output>5_600</output>
<gadget id="calculator">gcd(1_120, 5_600)</gadget>
<output>1_120</output>
<gadget id="calculator">1_120 / 10</gadget>
<output>112</output>
<gadget id="calculator">112 % 10</gadget>
<output>2</output>
<gadget id="calculator">112 - 2</gadget>
<output>110</output>
<gadget id="calculator">110 / 10</gadget>
<output>11</output>
<gadget id="calculator">11 % 10</gadget>
<output>1</output>
<gadget id="calculator">11 - 1</gadget>
<output>10</output>
<gadget id="calculator">10 / 10</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<result>C</result> | C | 4 | N is the greatest number which divides 1305, 4665 and 6905 and gives the same remainder in each case. What is the sum of the digits in N? | {
"A": "23",
"B": "28",
"C": "4",
"D": "1",
"E": "25"
} | add(add(divide(subtract(divide(subtract(divide(gcd(gcd(subtract(4665, 1305), subtract(6905, 4665)), subtract(6905, 1305)), const_10), reminder(divide(gcd(gcd(subtract(4665, 1305), subtract(6905, 4665)), subtract(6905, 1305)), const_10), const_10)), const_10), reminder(divide(subtract(divide(gcd(gcd(subtract(4665, 1305), subtract(6905, 4665)), subtract(6905, 1305)), const_10), reminder(divide(gcd(gcd(subtract(4665, 1305), subtract(6905, 4665)), subtract(6905, 1305)), const_10), const_10)), const_10), const_10)), const_10), reminder(divide(subtract(divide(gcd(gcd(subtract(4665, 1305), subtract(6905, 4665)), subtract(6905, 1305)), const_10), reminder(divide(gcd(gcd(subtract(4665, 1305), subtract(6905, 4665)), subtract(6905, 1305)), const_10), const_10)), const_10), const_10)), reminder(divide(gcd(gcd(subtract(4665, 1305), subtract(6905, 4665)), subtract(6905, 1305)), const_10), const_10)) | subtract(n1,n0)|subtract(n2,n1)|subtract(n2,n0)|gcd(#0,#1)|gcd(#3,#2)|divide(#4,const_10)|reminder(#5,const_10)|subtract(#5,#6)|divide(#7,const_10)|reminder(#8,const_10)|subtract(#8,#9)|divide(#10,const_10)|add(#11,#9)|add(#12,#6) | if the remainder is same in each case and remainder is not given , hcf of the differences of the numbers is the required greatest number 6905 - 1305 = 5600 6905 - 4665 = 2240 4665 - 1305 = 3360 hence , the greatest number which divides 1305 , 4665 and 6905 and gives the same remainder , n = hcf of 5600 , 2240 , 3360 = 1120 sum of digits in n = sum of digits in 1120 = 1 + 1 + 2 + 0 = 4 answer is c | general |
math_qa__iNbclcrtyHKgEtc7 | John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 2% and the mobile phone at a profit of 10%. Overall how much he make a profit. Choose the correct choice from the following answers: A) s . 90 B) s . 120 C) s . 200 D) s . 250 E) s . 500 | <gadget id="calculator">8_000 / 100</gadget>
<output>80</output>
<gadget id="calculator">10 * 80</gadget>
<output>800</output>
<gadget id="calculator">15_000 / 100</gadget>
<output>150</output>
<gadget id="calculator">2 * 150</gadget>
<output>300</output>
<gadget id="calculator">800 - 300</gadget>
<output>500</output>
<result>E</result> | E | 500 | John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 2% and the mobile phone at a profit of 10%. Overall how much he make a profit. | {
"A": "s . 90",
"B": "s . 120",
"C": "s . 200",
"D": "s . 250",
"E": "s . 500"
} | subtract(multiply(10, divide(8000, const_100)), multiply(2, divide(15000, const_100))) | divide(n1,const_100)|divide(n0,const_100)|multiply(n3,#0)|multiply(n2,#1)|subtract(#2,#3)| | "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 2 / 100 ) = 15000 - 300 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 300 + 800 = rs . 500 as this is positive , an overall profit of rs . 200 was made . e" | gain |
math_qa__kZhT66dhOXzrYjWo | mid intended to type a 7 - digit number , but the two 3 ' s he meant to type did not appear . what appeared instead was the 5 - digit number 52115 . how many different 7 - digit numbers could mid have meant to type ?
Select the correct option:
A) 10
B) 16
C) 21
D) 24
E) 27 | <gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">7 - 5</gadget>
<output>2</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">120 * 2</gadget>
<output>240</output>
<gadget id="calculator">5_040 / 240</gadget>
<output>21</output>
<result>C</result> | C | 21 | mid intended to type a 7 - digit number , but the two 3 ' s he meant to type did not appear . what appeared instead was the 5 - digit number 52115 . how many different 7 - digit numbers could mid have meant to type ? | {
"A": "10",
"B": "16",
"C": "21",
"D": "24",
"E": "27"
} | divide(factorial(7), multiply(factorial(5), factorial(subtract(7, 5)))) | factorial(n0)|factorial(n2)|subtract(n0,n2)|factorial(#2)|multiply(#1,#3)|divide(#0,#4) | should be 21 . mid intended to type a seven - digit number there are two possibilities for placing 2 3 s . case 1 : two 3 s were missed consecutively . i . e . he typed 33 and it came blank on screen . - 5 - 2 - 1 - 1 - 5 - in this arrangement we can fit 33 in 6 ways . ( six dashes , each dash represent one possible place for placing 33 ) case 2 : two 3 s are not together , i . e . they have one or more digits between them . - 5 - 2 - 1 - 1 - 5 - , in this arrangement if we place first 3 at first dash i . e . 35 - 2 - 1 - 1 - 5 - then the other 3 can fit into 5 places . if we place first 3 at second dash i . e . - 532 - 1 - 1 - 5 - then the other 3 can fit into 4 places . if we place first 3 at third dash i . e . - 5 - 231 - 1 - 5 - then the other 3 can fit into 3 places . if we place first 3 at fourth dash i . e . - 5 - 2 - 131 - 5 - then the other 3 can fit into 2 places . if we place first 3 at fifth dash i . e . - 5 - 2 - 1 - 135 - then the other 3 can fit into 1 place . so total 15 ways . case 2 + case 1 = 6 + 15 = 21 ways answer c | general |
math_qa__f40K3sRGEvT9KgkY | in a clothing store , there are 6 different colored neckties ( red , orange , yellow , green , blue , and indigo ) and 4 different colored shirts ( red , orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability that all of the boxes will contain a necktie and a shirt of the same color ? Options.
A) 719 / 720 B) 1 / 24 C) 2 / 233 D) 3 / 543 E) 1 / 720 | <gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<result>B</result> | B | 0.041667 | in a clothing store , there are 6 different colored neckties ( red , orange , yellow , green , blue , and indigo ) and 4 different colored shirts ( red , orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability that all of the boxes will contain a necktie and a shirt of the same color ? | {
"A": "719 / 720",
"B": "1 / 24",
"C": "2 / 233",
"D": "3 / 543",
"E": "1 / 720"
} | divide(const_1, factorial(4)) | factorial(n1)|divide(const_1,#0) | 4 ties and 4 shirts . . . red tie can take any of 4 shirts . . orange can take any of the remaining 3 shirts yellow any of remaining 2 . . and so on till last indigo chooses the 1 remaining . . total ways = 4 * 3 * 2 * 1 = 24 out of this 720 , only 1 way will have same colour tie and shirt . . prob = 1 / 720 b | general |
math_qa__aBfc9SwW1F0l5BRJ | a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 70000 , a receives : Choose the correct choice from the following options:
A) 14700
B) 24703
C) 29400
D) 33777
E) 34778 | <gadget id="calculator">4_000 + 5_000</gadget>
<output>9_000</output>
<gadget id="calculator">5_000 + 9_000</gadget>
<output>14_000</output>
<gadget id="calculator">50_000 - 14_000</gadget>
<output>36_000</output>
<gadget id="calculator">36_000 / 3</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 + 9_000</gadget>
<output>21_000</output>
<gadget id="calculator">21_000 * 70_000</gadget>
<output>1_470_000_000</output>
<gadget id="calculator">1_470_000_000 / 50_000</gadget>
<output>29_400</output>
<result>C</result> | C | 29,400 | a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 70000 , a receives : | {
"A": "14700",
"B": "24703",
"C": "29400",
"D": "33777",
"E": "34778"
} | divide(multiply(add(divide(subtract(50000, add(5000, add(4000, 5000))), const_3), add(4000, 5000)), 70000), 50000) | add(n1,n2)|add(n2,#0)|subtract(n0,#1)|divide(#2,const_3)|add(#0,#3)|multiply(n3,#4)|divide(#5,n0) | explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 70000 * 21 / 50 ) = rs . 29,400 . answer : c ) | general |
math_qa__2xQ5USI6Z7icO903 | A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability Q that you can still row the canoe?
Pick one.
A) 9 / 25 B) 10 / 25 C) 6 / 10 D) 2 / 3 E) 21 / 25 | <gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * (3/5)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(3/5) * (2/5)</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">(6/25) + (6/25)</gadget>
<output>12/25 = around 0.48</output>
<gadget id="calculator">(9/25) + (12/25)</gadget>
<output>21/25 = around 0.84</output>
<result>E</result> | E | 0.84 | A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability Q that you can still row the canoe? | {
"A": "9 / 25",
"B": "10 / 25",
"C": "6 / 10",
"D": "2 / 3",
"E": "21 / 25"
} | add(multiply(divide(3, 5), divide(3, 5)), add(multiply(divide(3, 5), divide(const_2, 5)), multiply(divide(3, 5), divide(const_2, 5)))) | divide(n0,n1)|divide(const_2,n1)|multiply(#0,#1)|multiply(#0,#0)|add(#2,#2)|add(#4,#3)| | "simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability q of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer : 1 – 4 / 25 = 21 / 25 . answer choice e ." | general |
math_qa__rbwqNvK0f4UCgXbO | John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make aprofit.
Options:
A) rs . 90 B) rs . 120 C) rs . 200 D) rs . 250 E) rs . 290 | <gadget id="calculator">8_000 / 100</gadget>
<output>80</output>
<gadget id="calculator">10 * 80</gadget>
<output>800</output>
<gadget id="calculator">15_000 / 100</gadget>
<output>150</output>
<gadget id="calculator">4 * 150</gadget>
<output>600</output>
<gadget id="calculator">800 - 600</gadget>
<output>200</output>
<result>C</result> | C | 200 | John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make aprofit. | {
"A": "rs . 90",
"B": "rs . 120",
"C": "rs . 200",
"D": "rs . 250",
"E": "rs . 290"
} | subtract(multiply(10, divide(8000, const_100)), multiply(4, divide(15000, const_100))) | divide(n1,const_100)|divide(n0,const_100)|multiply(n3,#0)|multiply(n2,#1)|subtract(#2,#3)| | "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . c" | gain |
math_qa__wjM9mhWCGDFvcymN | how much interest can a person get on rs . 7200 at 17.5 % p . a . simple interest for a period of two years and 6 months ? Select:
A) rs . 4150 B) rs . 3850 C) rs . 3770 D) rs . 3150 E) none of these | <gadget id="calculator">6 / 12</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) * 17.5</gadget>
<output>43.75</output>
<gadget id="calculator">43.75 / 100</gadget>
<output>0.4375</output>
<gadget id="calculator">7_200 * 0.4375</gadget>
<output>3_150</output>
<result>D</result> | D | 3,150 | how much interest can a person get on rs . 7200 at 17.5 % p . a . simple interest for a period of two years and 6 months ? | {
"A": "rs . 4150",
"B": "rs . 3850",
"C": "rs . 3770",
"D": "rs . 3150",
"E": "none of these"
} | multiply(7200, divide(multiply(add(const_2, divide(6, const_12)), 17.5), const_100)) | divide(n2,const_12)|add(#0,const_2)|multiply(n1,#1)|divide(#2,const_100)|multiply(n0,#3) | i = ( 7200 * 2.5 * 17.5 ) / 100 = ( 7200 * 5 * 35 ) / ( 100 * 2 * 2 ) = rs . 3150 answer : d | gain |
math_qa__OMYQfodPpUc6O9wH | Donovan took a math test and got 35 correct and 13 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth) Choose the correct answer.
A) 57.78 % B) 67.78 % C) 72.92 % D) 47.78 % E) 97.78 % | <gadget id="calculator">35 + 13</gadget>
<output>48</output>
<gadget id="calculator">35 / 48</gadget>
<output>35/48 = around 0.729167</output>
<gadget id="calculator">(35/48) * 100</gadget>
<output>875/12 = around 72.916667</output>
<result>C</result> | C | 72.92 | Donovan took a math test and got 35 correct and 13 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth) | {
"A": "57.78 %",
"B": "67.78 %",
"C": "72.92 %",
"D": "47.78 %",
"E": "97.78 %"
} | multiply(divide(35, add(35, 13)), const_100) | add(n0,n1)|divide(n0,#0)|multiply(#1,const_100) | 35 correct our of 48 total ( 35 + 13 ) 35 / 48 correct answer c | gain |
math_qa__w05DvMHpnfgNnVGO | The slant height of a cone is 14 cm and radius of the base is 12cm, find the curved surface of the cone.
Choose the correct choice from the following answers: A) 150 B) 170 C) 48 D) 528 E) 600 | <gadget id="calculator">pi * 12</gadget>
<output>12*pi = around 37.699112</output>
<gadget id="calculator">(12*pi) * 14</gadget>
<output>168*pi = around 527.787566</output>
<result>D</result> | D | 528 | The slant height of a cone is 14 cm and radius of the base is 12cm, find the curved surface of the cone. | {
"A": "150",
"B": "170",
"C": "48",
"D": "528",
"E": "600"
} | multiply(multiply(const_pi, 12), 14) | multiply(n1,const_pi)|multiply(n0,#0)| | "Ï€ * 12 * 14 = 528 answer : d" | geometry |
math_qa__Wb7SYQhKdEbiNmtr | Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 49, what is the measure of side XY?
Choose the correct choice from the following answers: A) 4 B) 4 √ 2 C) 14 D) 8 √ 2 E) can not be determined from the information provided | <gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>
<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>
<gadget id="calculator">7 * (sqrt(2))</gadget>
<output>7*sqrt(2) = around 9.899495</output>
<gadget id="calculator">(7*sqrt(2)) ** 2</gadget>
<output>98</output>
<gadget id="calculator">98 + 98</gadget>
<output>196</output>
<gadget id="calculator">196 ** (1/2)</gadget>
<output>14</output>
<result>C</result> | C | 14 | Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 49, what is the measure of side XY? | {
"A": "4",
"B": "4 √ 2",
"C": "14",
"D": "8 √ 2",
"E": "can not be determined from the information provided"
} | sqrt(add(power(multiply(sqrt(49), sqrt(const_2)), const_2), power(multiply(sqrt(49), sqrt(const_2)), const_2))) | sqrt(n0)|sqrt(const_2)|multiply(#0,#1)|power(#2,const_2)|add(#3,#3)|sqrt(#4) | ans c . . 14 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 4 or yz = 7 * \ sqrt { 2 } . . therefore hyp = xy = 14 | geometry |
math_qa__tRppMt7fSOi9iEKR | If the price of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumption of sugar by Pick one: A) 10 % B) 20 % C) 25 % D) 30 % E) none | <gadget id="calculator">1 * 6</gadget>
<output>6</output>
<gadget id="calculator">6 / 7.5</gadget>
<output>0.8</output>
<gadget id="calculator">1 - 0.8</gadget>
<output>0.2</output>
<gadget id="calculator">0.2 * 100</gadget>
<output>20</output>
<result>B</result> | B | 20 | If the price of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumption of sugar by | {
"A": "10 %",
"B": "20 %",
"C": "25 %",
"D": "30 %",
"E": "none"
} | multiply(subtract(const_1, divide(multiply(const_1, 6), 7.50)), const_100) | multiply(n0,const_1)|divide(#0,n1)|subtract(const_1,#1)|multiply(#2,const_100)| | "solution let the original consumption = 100 kg and new consumption = x kg . so , 100 x 6 = x × 7.50 x = 80 kg . reduction in consumption = 20 % . answer b" | general |
math_qa__2YbAgrNTakbYAY96 | In a lottery there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a blank? Choose the correct choice:
A) 2 / 3 B) 6 / 7 C) 5 / 7 D) 8 / 7 E) 4 / 3 | <gadget id="calculator">10 + 25</gadget>
<output>35</output>
<gadget id="calculator">25 / 35</gadget>
<output>5/7 = around 0.714286</output>
<result>C</result> | C | 0.714286 | In a lottery there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a blank? | {
"A": "2 / 3",
"B": "6 / 7",
"C": "5 / 7",
"D": "8 / 7",
"E": "4 / 3"
} | divide(25, add(10, 25)) | add(n0,n1)|divide(n1,#0) | total draws = prizes + blanks = 10 + 25 = 35 probability of getting a blank = 25 / 35 = 5 / 7 correct option is c | probability |
math_qa__hIYmRD0eGL3plqod | Walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in.
Choose the correct choice from the following: A) 12 min B) 25 min C) 40 min D) 48 min E) 52 min | <gadget id="calculator">45 / 60</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">2 + (3/4)</gadget>
<output>11/4 = around 2.75</output>
<gadget id="calculator">4 * (11/4)</gadget>
<output>11</output>
<gadget id="calculator">11 / 16.5</gadget>
<output>0.666667</output>
<gadget id="calculator">0.666667 * 60</gadget>
<output>40.00002</output>
<result>C</result> | C | 40 | Walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in. | {
"A": "12 min",
"B": "25 min",
"C": "40 min",
"D": "48 min",
"E": "52 min"
} | multiply(divide(multiply(4, add(2, divide(45, const_60))), 16.5), const_60) | divide(n2,const_60)|add(n1,#0)|multiply(n0,#1)|divide(#2,n3)|multiply(#3,const_60) | distance = speed * time 4 * 11 / 4 = 11 km new speed = 16.5 kmph therefore time = d / s = 11 / 16.5 = 40 min answer : c | physics |
math_qa__DNTmwBmVMespmuyv | If p and q are positive integers each greater than 1, and 15(p+1)=29(q+1), what is the least possible value of p+q? Choose the most appropriate option
A) 36 B) 42 C) 44 D) 46 E) none | <gadget id="calculator">29 + 15</gadget>
<output>44</output>
<gadget id="calculator">44 - 2</gadget>
<output>42</output>
<result>B</result> | B | 42 | If p and q are positive integers each greater than 1, and 15(p+1)=29(q+1), what is the least possible value of p+q? | {
"A": "36",
"B": "42",
"C": "44",
"D": "46",
"E": "none"
} | subtract(add(29, 15), const_2) | add(n1,n3)|subtract(#0,const_2) | 17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 29 , so the least value of p is 28 and the least positive value of q + 1 is 15 , so the least value of q is 14 - - > the least value of p + q is 28 + 14 = 42 . answer : b . | general |
math_qa__iMhQW5OH6RueNRPv | How many numbers from 10 to 50 are exactly divisible by 3?
Select.
A) 13 B) 15 C) 16 D) 17 E) 18 | <gadget id="calculator">50 / 3</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">floor(50/3)</gadget>
<output>16</output>
<gadget id="calculator">16 * 3</gadget>
<output>48</output>
<gadget id="calculator">10 / 3</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">floor(10/3)</gadget>
<output>3</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">48 - 12</gadget>
<output>36</output>
<gadget id="calculator">36 / 3</gadget>
<output>12</output>
<gadget id="calculator">12 + 1</gadget>
<output>13</output>
<result>A</result> | A | 13 | How many numbers from 10 to 50 are exactly divisible by 3? | {
"A": "13",
"B": "15",
"C": "16",
"D": "17",
"E": "18"
} | add(divide(subtract(multiply(floor(divide(50, 3)), 3), multiply(add(floor(divide(10, 3)), const_1), 3)), 3), const_1) | divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)| | "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits a )" | general |
math_qa__L68ESznj6wLk2ksA | The percentage profit earned by selling an article for Rs. 1820 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Choose the correct choice from the following choices
A) 3000 B) 1230 C) 2000 D) 5600 E) 1937.5 | <gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">1_820 + 1_280</gadget>
<output>3_100</output>
<gadget id="calculator">3_100 / 2</gadget>
<output>1_550</output>
<gadget id="calculator">(5/4) * 1_550</gadget>
<output>3_875/2 = around 1_937.5</output>
<result>E</result> | E | 1,937.5 | The percentage profit earned by selling an article for Rs. 1820 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit? | {
"A": "3000",
"B": "1230",
"C": "2000",
"D": "5600",
"E": "1937.5"
} | multiply(divide(add(const_100, 25), const_100), divide(add(1820, 1280), const_2)) | add(n2,const_100)|add(n0,n1)|divide(#0,const_100)|divide(#1,const_2)|multiply(#2,#3)| | "c . p . be rs . x . then , ( 1820 - x ) / x * 100 = ( x - 1280 ) / x * 100 1820 - x = x - 1280 2 x = 3100 = > x = 1550 required s . p . = 125 % of rs . 1550 = 125 / 100 * 1550 = rs . 1937.5 . answer e" | gain |
math_qa__cftWmZoFKxPmXSSe | If the remainder is 3 when positive integer n is divided by 18, what is the remainder when n is divided by 6? Choose the correct choice from the following choices:
A) 3
B) 1
C) 2
D) 3
E) 4 | <gadget id="calculator">18 / 6</gadget>
<output>3</output>
<result>A</result> | A | 3 | If the remainder is 3 when positive integer n is divided by 18, what is the remainder when n is divided by 6? | {
"A": "3",
"B": "1",
"C": "2",
"D": "3",
"E": "4"
} | divide(18, 6) | divide(n1,n2) | assume x is quotient here , n = 18 x + 3 - - - - - - - - - - ( 1 ) and n = 6 x + ? we can also write first term as n = ( 18 x + 6 ) = 6 ( 3 x + 1 ) + 3 ie 6 ( 3 x + 1 ) + 3 ie the first term is perfectly divisible by 6 . so , the remainder left is 3 . so , answer ( a ) is right choice . | general |
math_qa__G11JSX4hnqetVfMm | How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 7 can be used only once?
Choose the correct option.
A) 20
B) 150
C) 304
D) 310
E) 320 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">25 * 16</gadget>
<output>400</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<gadget id="calculator">400 - 100</gadget>
<output>300</output>
<result>C</result> | C | 304 | How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 7 can be used only once? | {
"A": "20",
"B": "150",
"C": "304",
"D": "310",
"E": "320"
} | subtract(multiply(multiply(add(4, const_1), add(4, const_1)), multiply(4, 4)), multiply(multiply(add(4, const_1), add(4, const_1)), 4)) | add(n0,const_1)|multiply(n0,n0)|multiply(#0,#0)|multiply(#2,#1)|multiply(#2,n0)|subtract(#3,#4)| | "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with seven 7 - s , 7 x 7 x 4 * 1 * 1 * 4 = 16 . thus there are 320 - 16 = 304 such numbers . answer : c ." | physics |
math_qa__Hr0wUoRwymRrD12R | Farm Tax is levied on the 40% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : Choose the correct choice from the following options.
A) 31.25 % B) 25 % C) 12.5 % D) 0.2083 % E) none | <gadget id="calculator">480 / 3_840</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 100</gadget>
<output>1_250</output>
<gadget id="calculator">1_250 / 40</gadget>
<output>125/4 = around 31.25</output>
<result>A</result> | A | 31.25 | Farm Tax is levied on the 40% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : | {
"A": "31.25 %",
"B": "25 %",
"C": "12.5 %",
"D": "0.2083 %",
"E": "none"
} | divide(multiply(multiply(divide(480, 3840), const_100), const_100), 40) | divide(n2,n1)|multiply(#0,const_100)|multiply(#1,const_100)|divide(#2,n0)| | "only trick n this question is to ignore 40 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 40 ) = 31.25 % and the answer is not there in the options . the correct answer is ( a ) ." | general |
math_qa__NFDdIdN1PZrLe1ex | The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.50 per metre. Choose the correct answer.
A) 2399 B) 3888 C) 2999 D) 5940 E) 2888 | <gadget id="calculator">13.86 / pi</gadget>
<output>13.86/pi = around 4.411775</output>
<gadget id="calculator">(13.86/pi) ** (1/2)</gadget>
<output>3.72290209379726/sqrt(pi) = around 2.100423</output>
<gadget id="calculator">(3.72290209379726/sqrt(pi)) * 100</gadget>
<output>372.290209379726/sqrt(pi) = around 210.042258</output>
<gadget id="calculator">2 * pi * (372.290209379726/sqrt(pi))</gadget>
<output>744.580418759452*sqrt(pi) = around 1_319.734431</output>
<gadget id="calculator">(744.580418759452*sqrt(pi)) * 4.5</gadget>
<output>3350.61188441753*sqrt(pi) = around 5_938.804937</output>
<result>D</result> | D | 5,940 | The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.50 per metre. | {
"A": "2399",
"B": "3888",
"C": "2999",
"D": "5940",
"E": "2888"
} | multiply(circumface(multiply(sqrt(divide(13.86, const_pi)), const_100)), 4.50) | divide(n0,const_pi)|sqrt(#0)|multiply(#1,const_100)|circumface(#2)|multiply(#3,n1)| | "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.50 ) = rs . 5940 . answer : d ) 5940" | geometry |
math_qa__ni2UfeEcQ8rAQzdb | If the sides of a triangle are 26 cm, 25 cm and 10 cm, what is its area?
Choose the correct option:
A) 120
B) 110
C) 130
D) 140
E) 125 | <gadget id="calculator">25 * 10</gadget>
<output>250</output>
<gadget id="calculator">250 / 2</gadget>
<output>125</output>
<result>E</result> | E | 125 | If the sides of a triangle are 26 cm, 25 cm and 10 cm, what is its area? | {
"A": "120",
"B": "110",
"C": "130",
"D": "140",
"E": "125"
} | divide(multiply(25, 10), const_2) | multiply(n1,n2)|divide(#0,const_2)| | "the triangle with sides 26 cm , 25 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 25 * 10 = 125 cm 2 answer : option e" | geometry |
math_qa__EyR9SaegEFsMQon5 | (7.5 × 7.5 + 37.5 + 2.5 × 2.5) is equal to : Answers.
A) 30 B) 60 C) 80 D) 100 E) none of these | <gadget id="calculator">7.5 * 7.5</gadget>
<output>56.25</output>
<gadget id="calculator">2.5 * 2.5</gadget>
<output>6.25</output>
<gadget id="calculator">56.25 + 6.25</gadget>
<output>62.5</output>
<gadget id="calculator">62.5 + 37.5</gadget>
<output>100</output>
<result>D</result> | D | 100 | (7.5 × 7.5 + 37.5 + 2.5 × 2.5) is equal to : | {
"A": "30",
"B": "60",
"C": "80",
"D": "100",
"E": "none of these"
} | add(add(multiply(7.5, 7.5), multiply(2.5, 2.5)), 37.5) | multiply(n0,n0)|multiply(n3,n3)|add(#0,#1)|add(n2,#2) | solution given expression = ( 7.5 × 7.5 + 2 × 7.5 × 2.5 + 2.5 × 2.5 ) = ( a 2 + 2 ab + b 2 ) = ( a + b ) 2 = ( 7.5 + 2.5 ) 2 = 102 = 100 . answer d | general |
math_qa__A8mMr6qrpB6zHeem | A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra? Select the correct option: A) 90 B) 110 C) 120 D) 130 E) 220 | <gadget id="calculator">12 * 350</gadget>
<output>4_200</output>
<gadget id="calculator">3 * 1_000</gadget>
<output>3_000</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">3_000 + 300</gadget>
<output>3_300</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">3_300 + 20</gadget>
<output>3_320</output>
<gadget id="calculator">4_200 - 3_320</gadget>
<output>880</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">880 / 4</gadget>
<output>220</output>
<gadget id="calculator">350 - 220</gadget>
<output>130</output>
<gadget id="calculator">220 - 130</gadget>
<output>90</output>
<result>A</result> | A | 90 | A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra? | {
"A": "90",
"B": "110",
"C": "120",
"D": "130",
"E": "220"
} | subtract(divide(subtract(multiply(12, 350), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtract(12, 8)), subtract(350, divide(subtract(multiply(12, 350), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtract(12, 8)))) | multiply(n0,n2)|multiply(const_1000,const_3)|multiply(const_100,const_3)|multiply(const_10,const_2)|subtract(n0,n1)|add(#1,#2)|add(#5,#3)|subtract(#0,#6)|divide(#7,#4)|subtract(n2,#8)|subtract(#8,#9)| | "orchestra seats - a balcony seats - b a + b = 350 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 350 = 3320 - 2800 = 520 i . e . a = 130 and b = 350 - 130 = 220 more seats in balcony than orchestra = b - a = 220 - 130 = 90 answer : option a" | general |
math_qa__owy2BDPykVZvyADQ | If a - b = 3 and a2 + b2 = 29, find the value of ab. Choose the correct choice from the following options: A) 10 B) 12 C) 13 D) 15 E) 18 | <gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">29 - 9</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>A</result> | A | 10 | If a - b = 3 and a2 + b2 = 29, find the value of ab. | {
"A": "10",
"B": "12",
"C": "13",
"D": "15",
"E": "18"
} | divide(subtract(29, power(3, 2)), 2) | power(n0,n1)|subtract(n3,#0)|divide(#1,n1)| | "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 9 = 20 ab = 10 . answer : a" | general |
math_qa__IfAIbMSMSZT8T8XY | Each child has 4 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total?
Choose the correct choice from the following answers
A) 16 B) 12 C) 18 D) 22 E) 32 | <gadget id="calculator">4 * 8</gadget>
<output>32</output>
<result>E</result> | E | 32 | Each child has 4 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total? | {
"A": "16",
"B": "12",
"C": "18",
"D": "22",
"E": "32"
} | multiply(4, 8) | multiply(n0,n2)| | 4 * 8 = 32 . answer is e . | general |
math_qa__k0cKQtj7fNTqDPGR | Sandy had $140 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? Select the correct option:
A) $ 180 B) $ 200 C) $ 220 D) $ 240 E) $ 260 | <gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">140 / (7/10)</gadget>
<output>200</output>
<result>B</result> | B | 200 | Sandy had $140 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her? | {
"A": "$ 180",
"B": "$ 200",
"C": "$ 220",
"D": "$ 240",
"E": "$ 260"
} | divide(140, divide(subtract(const_100, 30), const_100)) | subtract(const_100,n1)|divide(#0,const_100)|divide(n0,#1) | let the money sandy took for shopping be x . 0.7 x = 140 x = 200 the answer is b . | gain |
math_qa__hJ97nLjiaarxHD7x | Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled? Choose the correct choice: A) 2 hours B) 4 hours C) 3 hours D) 5 hours E) 6 hours | <gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<result>C</result> | C | 3 | Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 1 minute each, how soon will the tank be filled? | {
"A": "2 hours",
"B": "4 hours",
"C": "3 hours",
"D": "5 hours",
"E": "6 hours"
} | add(add(1, 1), 1) | add(n3,n3)|add(n3,#0)| | "in three minute 1 / 20 + 1 / 30 - 1 / 15 = 1 / 60 part is filled 3 min - - - - - - - - 1 / 60 parts x min - - - - - - - - - 1 part ( full ) x = 180 min = 3 hours answer : c" | physics |
math_qa__trzMbMnZPXiqa2jg | The average of 5 quantities is 6. The average of 3 of them is 4. What is the average of remaining 2 numbers? Choose the most appropriate option: A) 9 B) 10 C) 8 D) 9.5 E) none of these | <gadget id="calculator">5 * 6</gadget>
<output>30</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">30 - 12</gadget>
<output>18</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<result>A</result> | A | 9 | The average of 5 quantities is 6. The average of 3 of them is 4. What is the average of remaining 2 numbers? | {
"A": "9",
"B": "10",
"C": "8",
"D": "9.5",
"E": "none of these"
} | divide(subtract(multiply(5, 6), multiply(3, 4)), 2) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4)| | answer : a | general |
math_qa__Vm9fkE0QWoJtmRyg | Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.40 at the candy store. What is John’s weekly allowance?
Options.
A) $ 1.50 B) $ 2.00 C) $ 2.50 D) $ 3.00 E) $ 3.50 | <gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(1/3) * (2/5)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(3/5) + (2/15)</gadget>
<output>11/15 = around 0.733333</output>
<gadget id="calculator">1 - (11/15)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">0.4 / (4/15)</gadget>
<output>1.5</output>
<result>A</result> | A | 1.5 | Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.40 at the candy store. What is John’s weekly allowance? | {
"A": "$ 1.50",
"B": "$ 2.00",
"C": "$ 2.50",
"D": "$ 3.00",
"E": "$ 3.50"
} | divide(0.40, subtract(const_1, add(divide(3, 5), multiply(divide(const_1, 3), subtract(const_1, divide(3, 5)))))) | divide(n0,n1)|divide(const_1,n0)|subtract(const_1,#0)|multiply(#1,#2)|add(#0,#3)|subtract(const_1,#4)|divide(n2,#5)| | "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 40 4 x / 15 = 40 x = 150 = $ 1.50 the answer is a ." | general |
math_qa__CH4jygQHxw6NRdOy | In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 32% of the boys and 32% of the girls passed, then the total percentage of failed candidates is? Choose the correct choice from the following.
A) 35.67 % B) 64.75 % C) 68.00 % D) 69.57 % E) none of these | <gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">2 * 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">32 / 100</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">2_000 - 900</gadget>
<output>1_100</output>
<gadget id="calculator">(8/25) * 1_100</gadget>
<output>352</output>
<gadget id="calculator">2_000 - 352</gadget>
<output>1_648</output>
<gadget id="calculator">(8/25) * 900</gadget>
<output>288</output>
<gadget id="calculator">1_648 - 288</gadget>
<output>1_360</output>
<gadget id="calculator">1_360 / 2_000</gadget>
<output>17/25 = around 0.68</output>
<gadget id="calculator">(17/25) * 100</gadget>
<output>68</output>
<result>C</result> | C | 68 | In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 32% of the boys and 32% of the girls passed, then the total percentage of failed candidates is? | {
"A": "35.67 %",
"B": "64.75 %",
"C": "68.00 %",
"D": "69.57 %",
"E": "none of these"
} | multiply(divide(subtract(subtract(multiply(const_2, multiply(const_100, const_10)), multiply(divide(32, const_100), subtract(multiply(const_2, multiply(const_100, const_10)), 900))), multiply(divide(32, const_100), 900)), multiply(const_2, multiply(const_100, const_10))), const_100) | divide(n2,const_100)|divide(n3,const_100)|multiply(const_10,const_100)|multiply(#2,const_2)|multiply(n1,#1)|subtract(#3,n1)|multiply(#0,#5)|subtract(#3,#6)|subtract(#7,#4)|divide(#8,#3)|multiply(#9,const_100)| | "girls = 900 , boys = 1100 passed = ( 32 % of 1100 ) + ( 32 % of 900 ) = 352 + 288 = 640 failed = 2000 - 640 = 1360 failed % = [ ( 1360 / 2000 ) x 100 ] % = 68 % . answer : c" | general |
math_qa__jhrcn07nbYJrZPvn | Find (7x + 5y ) / (x-2y) if x/2y = 3/2 ? Choose the correct choice from the following options.
A) 24 B) 25 C) 26 D) 27 E) 29 | <gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 2</gadget>
<output>3</output>
<gadget id="calculator">3 * 7</gadget>
<output>21</output>
<gadget id="calculator">21 + 5</gadget>
<output>26</output>
<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">26 / 1</gadget>
<output>26</output>
<result>C</result> | C | 26 | Find (7x + 5y ) / (x-2y) if x/2y = 3/2 ? | {
"A": "24",
"B": "25",
"C": "26",
"D": "27",
"E": "29"
} | divide(add(multiply(multiply(divide(3, 2), 2), 7), 5), subtract(multiply(divide(3, 2), 2), 2)) | divide(n4,n2)|multiply(n2,#0)|multiply(n0,#1)|subtract(#1,n2)|add(n1,#2)|divide(#4,#3)| | "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 5 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 5 y ) / ( 3 y - 2 y ) = > 26 y / y = 26 answer : c" | general |
math_qa__KK5kSQJTJoDEaeXu | When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students Answers:
A) 55
B) 56
C) 57
D) 58
E) 59 | <gadget id="calculator">59 + 1</gadget>
<output>60</output>
<gadget id="calculator">200 / 1_000</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">60 * (1/5)</gadget>
<output>12</output>
<gadget id="calculator">45 + 12</gadget>
<output>57</output>
<result>C</result> | C | 57 | When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students | {
"A": "55",
"B": "56",
"C": "57",
"D": "58",
"E": "59"
} | add(45, multiply(add(59, const_1), divide(200, const_1000))) | add(n1,const_1)|divide(n2,const_1000)|multiply(#0,#1)|add(n0,#2) | explanation : let the average weight of the 59 students be a . so the total weight of the 59 of them will be 59 * a . the questions states that when the weight of this student who left is added , the total weight of the class = 59 a + 45 when this student is also included , the average weight decreases by 0.2 kgs 59 a + 45 / 60 = a − 0.2 = > 59 a + 45 = 60 a - 12 = > 45 + 12 = 60 a - 59 a = > a = 57 answer : option c | general |
math_qa__3dgaI1vd6OGeWTaO | Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate J in miles per hour for the entire trip? Choose one
A) 26.7 B) j = 30.0 C) j = 40.0 D) j = 53.3 E) 60.0 | <gadget id="calculator">640 / 2</gadget>
<output>320</output>
<gadget id="calculator">320 / 80</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">640 / 16</gadget>
<output>40</output>
<result>C</result> | C | 40 | Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate J in miles per hour for the entire trip? | {
"A": "26.7",
"B": "j = 30.0",
"C": "j = 40.0",
"D": "j = 53.3",
"E": "60.0"
} | divide(640, add(add(multiply(divide(divide(640, const_2), 80), const_2), divide(divide(640, const_2), 80)), divide(divide(640, const_2), 80))) | divide(n0,const_2)|divide(#0,n1)|multiply(#1,const_2)|add(#1,#2)|add(#3,#1)|divide(n0,#4) | veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct . | physics |
math_qa__rTTJAqaPbBuZpfYZ | If f(x) = 12 - x^2/2 and f(2k) = 3k, what is one possible value for k?
Choose the correct option.
A) 2
B) 3
C) 4
D) 6
E) 8 | <gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<result>B</result> | B | 3 | If f(x) = 12 - x^2/2 and f(2k) = 3k, what is one possible value for k? | {
"A": "2",
"B": "3",
"C": "4",
"D": "6",
"E": "8"
} | add(divide(power(2, 2), 2), const_1) | power(n1,n1)|divide(#0,n1)|add(#1,const_1) | first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 4 or k = 3 . all the answers are positive , so we choose k = 3 . answer = b | general |
math_qa__9rvHRoCKJ4nW0xRC | Two numbers N and 14 have LCM = 56 and GCF = 12. Find N. Select the correct option
A) 48 B) 34 C) 44 D) 54 E) 64 | <gadget id="calculator">56 * 12</gadget>
<output>672</output>
<gadget id="calculator">672 / 14</gadget>
<output>48</output>
<result>A</result> | A | 48 | Two numbers N and 14 have LCM = 56 and GCF = 12. Find N. | {
"A": "48",
"B": "34",
"C": "44",
"D": "54",
"E": "64"
} | divide(multiply(56, 12), 14) | multiply(n1,n2)|divide(#0,n0)| | "the product of two integers is equal to the product of their lcm and gcf . hence . 14 × n = 56 × 12 n = 56 × 12 / 14 = 48 correct answer a" | physics |
math_qa__zJjgbp7KVvzvj9jG | Express a speed of 414 kmph in meters per second? Answers: A) 201 mps B) 114 mps C) 118 mps D) 115 mps E) 111 mps | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 414</gadget>
<output>115</output>
<result>D</result> | D | 115 | Express a speed of 414 kmph in meters per second? | {
"A": "201 mps",
"B": "114 mps",
"C": "118 mps",
"D": "115 mps",
"E": "111 mps"
} | multiply(const_0_2778, 414) | multiply(n0,const_0_2778)| | "414 * 5 / 18 = 115 mps answer : d" | physics |
math_qa__Kae52RDAdvqOh0gH | The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool? Choose the most appropriate option.
A) 1400
B) 1600
C) 1800
D) 1500
E) 2000 | <gadget id="calculator">100 / 100</gadget>
<output>1</output>
<gadget id="calculator">80 * 150</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 * 10</gadget>
<output>120_000</output>
<gadget id="calculator">1 * 120_000</gadget>
<output>120_000</output>
<gadget id="calculator">120_000 / 60</gadget>
<output>2_000</output>
<result>E</result> | E | 2,000 | The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool? | {
"A": "1400",
"B": "1600",
"C": "1800",
"D": "1500",
"E": "2000"
} | divide(multiply(divide(100, const_100), multiply(multiply(80, 150), 10)), 60) | divide(n4,const_100)|multiply(n1,n2)|multiply(n3,#1)|multiply(#0,#2)|divide(#3,n0)| | "volume of pool = 80 * 150 * 10 cu . ft , 100 % full = 60 * 100 * 10 * 1 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 80 * 150 * 10 * 1 / 60 min = 2000 min e" | gain |
math_qa__vpL6V3AUdlVIEO32 | There are 19 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?
Choose the correct choice from the following choices.
A) 1710
B) 1920
C) 2440
D) 2860
E) 3260 | <gadget id="calculator">19 - 1</gadget>
<output>18</output>
<gadget id="calculator">19 * 18</gadget>
<output>342</output>
<gadget id="calculator">342 * 10</gadget>
<output>3_420</output>
<gadget id="calculator">3_420 / 2</gadget>
<output>1_710</output>
<result>A</result> | A | 1,710 | There are 19 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season? | {
"A": "1710",
"B": "1920",
"C": "2440",
"D": "2860",
"E": "3260"
} | divide(multiply(multiply(19, subtract(19, const_1)), 10), const_2) | subtract(n0,const_1)|multiply(n0,#0)|multiply(n1,#1)|divide(#2,const_2)| | "the number of ways to choose two teams is 19 c 2 = 19 * 18 / 2 = 171 the total number of games in the season is 10 * 171 = 1710 . the answer is a ." | general |
math_qa__QDEAnOBu4XPuOMRp | In a family 11 people eat only vegetarian, 6 people eat only non veg., 9 people eat both veg and non veg.. How many people eat veg in the family? Select the correct option:
A) 20
B) 11
C) 9
D) 31
E) 21 | <gadget id="calculator">11 + 9</gadget>
<output>20</output>
<result>A</result> | A | 20 | In a family 11 people eat only vegetarian, 6 people eat only non veg., 9 people eat both veg and non veg.. How many people eat veg in the family? | {
"A": "20",
"B": "11",
"C": "9",
"D": "31",
"E": "21"
} | add(11, 9) | add(n0,n2)| | "total people eat veg = only veg + both veg and non veg total = 11 + 9 = 20 answer = a" | other |
math_qa__qZuGmKGkh3ZU2hFg | A cyclist climbs a hill with a length of 400 m with a speed of 7.2 km/h. When descending, the speed is two times greater. How much time is necessary for the cyclist to climb and descend the hill? Answers:
A) 30 seconds
B) 20 seconds
C) 40 seconds
D) 10 seconds
E) none | <gadget id="calculator">7.2 * 1_000</gadget>
<output>7_200</output>
<gadget id="calculator">7_200 / 3_600</gadget>
<output>2</output>
<gadget id="calculator">400 / 2</gadget>
<output>200</output>
<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<gadget id="calculator">100 + 200</gadget>
<output>300</output>
<gadget id="calculator">300 / 10</gadget>
<output>30</output>
<result>A</result> | A | 30 | A cyclist climbs a hill with a length of 400 m with a speed of 7.2 km/h. When descending, the speed is two times greater. How much time is necessary for the cyclist to climb and descend the hill? | {
"A": "30 seconds",
"B": "20 seconds",
"C": "40 seconds",
"D": "10 seconds",
"E": "none"
} | divide(add(divide(divide(400, divide(multiply(7.2, const_1000), const_3600)), const_2), divide(400, divide(multiply(7.2, const_1000), const_3600))), const_10) | multiply(n1,const_1000)|divide(#0,const_3600)|divide(n0,#1)|divide(#2,const_2)|add(#3,#2)|divide(#4,const_10) | 7.2 km = 7200 m . 1 h = 3600 s . the speed will be 7200 m / 3600 s = 2 m / s . the necessary time to climb will be 20 seconds . when descending , if the speed is two times greater , the necessary time will be two times smaller , so 10 seconds . the total necessary time is 20 s + 10 s = 30 seconds . answer a | general |
math_qa__jxuB7qudoiKFFDPD | The radius of a semi circle is 6.8 cm then its perimeter is? Choices: A) 32.7 B) 32.4 C) 22.4 D) 34.9 E) 35.1 | <gadget id="calculator">2 * pi * 6.8</gadget>
<output>13.6*pi = around 42.72566</output>
<gadget id="calculator">(13.6*pi) / 2</gadget>
<output>6.8*pi = around 21.36283</output>
<gadget id="calculator">6.8 * 2</gadget>
<output>13.6</output>
<gadget id="calculator">(6.8*pi) + 13.6</gadget>
<output>13.6 + 6.8*pi = around 34.96283</output>
<result>D</result> | D | 34.9 | The radius of a semi circle is 6.8 cm then its perimeter is? | {
"A": "32.7",
"B": "32.4",
"C": "22.4",
"D": "34.9",
"E": "35.1"
} | add(divide(circumface(6.8), const_2), multiply(6.8, const_2)) | circumface(n0)|multiply(n0,const_2)|divide(#0,const_2)|add(#2,#1)| | "36 / 7 r = 6.8 = 34.9 answer : d" | physics |
math_qa__TV0aJK6b32Vcx3qv | The ratio between the number of sheep and the number of horses at the Stewart farm is 6 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm? Pick one:
A) 18 B) 28 C) 48 D) 56 E) 60 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<gadget id="calculator">8 * 100</gadget>
<output>800</output>
<gadget id="calculator">80 + 800</gadget>
<output>880</output>
<gadget id="calculator">12 * 1_000</gadget>
<output>12_000</output>
<gadget id="calculator">880 + 12_000</gadget>
<output>12_880</output>
<gadget id="calculator">12_880 / 230</gadget>
<output>56</output>
<gadget id="calculator">56 / 7</gadget>
<output>8</output>
<gadget id="calculator">8 * 6</gadget>
<output>48</output>
<result>C</result> | C | 48 | The ratio between the number of sheep and the number of horses at the Stewart farm is 6 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm? | {
"A": "18",
"B": "28",
"C": "48",
"D": "56",
"E": "60"
} | multiply(divide(divide(add(add(multiply(multiply(const_4, const_2), const_10), multiply(multiply(const_4, const_2), const_100)), multiply(const_12, const_1000)), 230), 7), 6) | multiply(const_2,const_4)|multiply(const_1000,const_12)|multiply(#0,const_10)|multiply(#0,const_100)|add(#2,#3)|add(#4,#1)|divide(#5,n2)|divide(#6,n1)|multiply(n0,#7)| | "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 6 x = 6 * 8 = 48 . hence c ." | other |
math_qa__ZLfVXEZoMvhSShBL | The present age of the father is 4years more than 4 times the age of his son. 4 years hence, father's age will be 20 years more than twice the age of the son. Find the present age of the father?
Choose the correct choice from the following answers:
A) 25 B) 56 C) 45 D) 36 E) 44 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 20</gadget>
<output>28</output>
<gadget id="calculator">28 - 4</gadget>
<output>24</output>
<gadget id="calculator">24 - 4</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">40 + 4</gadget>
<output>44</output>
<result>E</result> | E | 44 | The present age of the father is 4years more than 4 times the age of his son. 4 years hence, father's age will be 20 years more than twice the age of the son. Find the present age of the father? | {
"A": "25",
"B": "56",
"C": "45",
"D": "36",
"E": "44"
} | add(multiply(divide(subtract(subtract(add(multiply(const_4, const_2), 20), 4), 4), const_2), 4), 4) | multiply(const_2,const_4)|add(n3,#0)|subtract(#1,n0)|subtract(#2,n0)|divide(#3,const_2)|multiply(n0,#4)|add(n0,#5) | let the son ' s present age be x years father ' s present age = ( 4 x + 4 ) 4 x + 4 + 4 = 2 ( x + 4 ) + 10 4 x + 8 = 2 x + 18 x = 5 father ' s present age = 4 x + 4 = 4 * 10 + 4 = 44 years answer is e | general |
math_qa__Wk6otbcBE5wuZanQ | A scuba diver descends at a rate of 60 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 3600feet below the sea level..how long will he take to reach the ship? Choose the correct choice from the following: A) 60 minutes B) 72 minutes C) 75 minutes D) 76 minutes E) 77 minutes | <gadget id="calculator">3_600 / 60</gadget>
<output>60</output>
<result>A</result> | A | 60 | A scuba diver descends at a rate of 60 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 3600feet below the sea level..how long will he take to reach the ship? | {
"A": "60 minutes",
"B": "72 minutes",
"C": "75 minutes",
"D": "76 minutes",
"E": "77 minutes"
} | divide(3600, 60) | divide(n1,n0) | time taken to reach = 3600 / 60 = 60 minutes answer : a | gain |
math_qa__ulsRvpHNXqx040Rk | In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 32. In the company, what is the maximum number of non-managers in a department that has 8 managers?
Pick one:
A) 35 B) 36 C) 37 D) 38 E) 39 | <gadget id="calculator">32 * 8</gadget>
<output>256</output>
<gadget id="calculator">256 / 7</gadget>
<output>256/7 = around 36.571429</output>
<gadget id="calculator">floor(256/7)</gadget>
<output>36</output>
<result>B</result> | B | 36 | In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 32. In the company, what is the maximum number of non-managers in a department that has 8 managers? | {
"A": "35",
"B": "36",
"C": "37",
"D": "38",
"E": "39"
} | floor(divide(multiply(32, 8), 7)) | multiply(n1,n2)|divide(#0,n0)|floor(#1)| | "8 / 7 * 32 = 36.6 the answer is b ." | general |
math_qa__ifDtGUlCWNsKdGKl | Two letters from the word KHANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant?
Choose the correct option: A) 25 / 28 B) 27 / 28 C) 30 / 28 D) 40 / 28 E) 50 / 28 | <gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">binomial(8, 2)</gadget>
<output>28</output>
<gadget id="calculator">1 / 28</gadget>
<output>1/28 = around 0.035714</output>
<gadget id="calculator">1 - (1/28)</gadget>
<output>27/28 = around 0.964286</output>
<result>B</result> | B | 0.964286 | Two letters from the word KHANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant? | {
"A": "25 / 28",
"B": "27 / 28",
"C": "30 / 28",
"D": "40 / 28",
"E": "50 / 28"
} | negate_prob(divide(const_1, choose(multiply(const_2, const_4), const_2))) | multiply(const_2,const_4)|choose(#0,const_2)|divide(const_1,#1)|negate_prob(#2) | there are 6 consonants and 2 vowels in khantkar . probability that at least one of the selected letters is a consonant = 1 - ( probability of both vowels ) probability of both vowels = 2 c 2 / 8 c 2 = 1 / 28 so , answer is 1 - 1 / 28 = 27 / 28 answer : b | probability |
math_qa__ZMl8wG6yPl4y9dMd | A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 30 pints of Perfect Pink paint? Choose the correct choice from the following choices:
A) 9 B) 16 C) 15 D) 25 1 / 3 E) 28 1 / 2 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">6 / 12</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">30 * (1/2)</gadget>
<output>15</output>
<result>C</result> | C | 15 | A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 30 pints of Perfect Pink paint? | {
"A": "9",
"B": "16",
"C": "15",
"D": "25 1 / 3",
"E": "28 1 / 2"
} | multiply(30, divide(multiply(3, 2), multiply(4, 3))) | multiply(n0,n2)|multiply(n0,n1)|divide(#0,#1)|multiply(n4,#2) | 3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 30 pints will require 9 / 17 * 30 = 15 pints . . c | general |
math_qa__TRPcDzM7oQ7iqAbX | there are 3 vessels of equal capacity . vessel a contains milk and water in the ratio 4 : 3 ; vessel b contains milk and water in the ratio 2 : 1 and vessel c contains milk and water in the ratio 3 : 2 . if the mixture in all the 3 vessels is mixed up . what will be the ratio of water to milk ?
Choose the correct choice from the following options: A) 9 : 6 B) 3 : 2 C) 118 : 126 D) 122 : 193 E) 201 : 132 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(2/5) + (1/3)</gadget>
<output>11/15 = around 0.733333</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(11/15) + (3/7)</gadget>
<output>122/105 = around 1.161905</output>
<gadget id="calculator">(11/15) / (122/105)</gadget>
<output>77/122 = around 0.631148</output>
<result>D</result> | D | 0.632124 | there are 3 vessels of equal capacity . vessel a contains milk and water in the ratio 4 : 3 ; vessel b contains milk and water in the ratio 2 : 1 and vessel c contains milk and water in the ratio 3 : 2 . if the mixture in all the 3 vessels is mixed up . what will be the ratio of water to milk ? | {
"A": "9 : 6",
"B": "3 : 2",
"C": "118 : 126",
"D": "122 : 193",
"E": "201 : 132"
} | divide(add(divide(2, add(3, 2)), divide(1, add(2, 1))), add(add(divide(2, add(3, 2)), divide(1, add(2, 1))), divide(3, add(4, 3)))) | add(n0,n3)|add(n3,n4)|add(n0,n1)|divide(n3,#0)|divide(n4,#1)|divide(n0,#2)|add(#3,#4)|add(#6,#5)|divide(#6,#7) | 4 : 3 = > 4 x + 3 x = 7 x 2 : 1 = > 2 y + 1 y = 3 y 3 : 2 = > 3 z + 2 z = 5 z 7 x = 3 y = 5 z take lcm of 7 , 3,5 = 105 or simply ; x = 3 * 5 = 15 y = 7 * 5 = 35 z = 3 * 7 = 21 so , ratio of water : milk = ( 3 x + y + 2 z ) / ( 4 x + 2 y + 3 z ) = 122 / 193 ans : d | general |
math_qa__ywWLf3HdD5UnQ7lL | Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 5625 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period. Choices
A) 2304 B) 2305 C) 2309 D) 2310 E) 2311 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) ** 4</gadget>
<output>625/256 = around 2.441406</output>
<gadget id="calculator">5_625 / (625/256)</gadget>
<output>2_304</output>
<result>A</result> | A | 2,304 | Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 5625 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period. | {
"A": "2304",
"B": "2305",
"C": "2309",
"D": "2310",
"E": "2311"
} | divide(5625, power(add(divide(1, 4), 1), 4)) | divide(n1,n0)|add(n1,#0)|power(#1,n0)|divide(n3,#2)| | "trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate b , c , d , e the answer to be a again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 2304 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 2304 = 5625 hence , correct answer = a" | general |
math_qa__pJISSRRXzBa2MyDl | The time it took car P to travel 800 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour? Pick one:
A) 43 B) 58 C) 60 D) 70 E) 80 | <gadget id="calculator">-10</gadget>
<output>-10</output>
<gadget id="calculator">(-10) ** 2</gadget>
<output>100</output>
<gadget id="calculator">800 * 10</gadget>
<output>8_000</output>
<gadget id="calculator">8_000 / 2</gadget>
<output>4_000</output>
<gadget id="calculator">-4_000</gadget>
<output>-4_000</output>
<gadget id="calculator">4 * (-4_000)</gadget>
<output>-16_000</output>
<gadget id="calculator">100 - (-16_000)</gadget>
<output>16_100</output>
<gadget id="calculator">16_100 ** (1/2)</gadget>
<output>10*sqrt(161) = around 126.885775</output>
<gadget id="calculator">(-10) + (10*sqrt(161))</gadget>
<output>-10 + 10*sqrt(161) = around 116.885775</output>
<gadget id="calculator">(-10 + 10*sqrt(161)) / 2</gadget>
<output>-5 + 5*sqrt(161) = around 58.442888</output>
<result>B</result> | B | 58 | The time it took car P to travel 800 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour? | {
"A": "43",
"B": "58",
"C": "60",
"D": "70",
"E": "80"
} | divide(add(negate(10), sqrt(subtract(power(negate(10), 2), multiply(const_4, negate(divide(multiply(800, 10), 2)))))), 2) | multiply(n0,n2)|negate(n2)|divide(#0,n1)|power(#1,n1)|negate(#2)|multiply(#4,const_4)|subtract(#3,#5)|sqrt(#6)|add(#1,#7)|divide(#8,n1)| | "let speed of car r be = x then speed of car p = x + 10 a / q , ( 800 / x ) - ( 800 / ( x + 10 ) ) = 2 solving for x = 58 miles \ hr . b" | physics |
math_qa__FocWuNgesT64gKFs | A man can do a piece of work in 5 days, but with the help of his son, he can do it in 4 days. In what time can the son do it alone? Choose the correct choice from the following options.
A) 15 B) 17 C) 20 D) 8 E) 9 | <gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">20 / 1</gadget>
<output>20</output>
<result>C</result> | C | 20 | A man can do a piece of work in 5 days, but with the help of his son, he can do it in 4 days. In what time can the son do it alone? | {
"A": "15",
"B": "17",
"C": "20",
"D": "8",
"E": "9"
} | divide(multiply(5, 4), subtract(5, 4)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | "son ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 5 ) = 1 / 20 the son alone can do the work in 20 days answer is c" | physics |
math_qa__2dBehpQr8S0OUB11 | A train running at the speed of 60 km/hr crosses a pole in 27 seconds. Find the length of the train? Select the correct option:
A) 150 meter B) 876 meter C) 167 meter D) 450 meter E) 169 meter | <gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 27</gadget>
<output>450</output>
<result>D</result> | D | 450 | A train running at the speed of 60 km/hr crosses a pole in 27 seconds. Find the length of the train? | {
"A": "150 meter",
"B": "876 meter",
"C": "167 meter",
"D": "450 meter",
"E": "169 meter"
} | multiply(divide(multiply(60, const_1000), const_3600), 27) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 27 = 450 meter answer : d" | physics |
math_qa__jZv2Pi9OTr3hyba5 | What is the largest 4 digit number exactly divisible by 88 Choose the correct choice from the following answers: A) 9900 B) 9999 C) 9988 D) 9944 E) 9966 | <gadget id="calculator">10 ** 4</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 88</gadget>
<output>1_250/11 = around 113.636364</output>
<gadget id="calculator">floor(1_250/11)</gadget>
<output>113</output>
<gadget id="calculator">113 * 88</gadget>
<output>9_944</output>
<result>D</result> | D | 9,944 | What is the largest 4 digit number exactly divisible by 88 | {
"A": "9900",
"B": "9999",
"C": "9988",
"D": "9944",
"E": "9966"
} | multiply(floor(divide(power(const_10, 4), 88)), 88) | power(const_10,n0)|divide(#0,n1)|floor(#1)|multiply(n1,#2)| | "explanation : largest 4 digit number is 9999 after doing 9999 ÷ 88 we get remainder 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 answer : option d" | general |
math_qa__qCeEApCSvxzxapEE | Find the area of the quadrilateral of one of its diagonals is 22 cm and its off sets 9 cm and 6 cm? Choose the correct choice from the following options.
A) 188 cm 2 B) 165 cm 2 C) 168 cm 2 D) 198 cm 2 E) 987 cm 2 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">6 + 9</gadget>
<output>15</output>
<gadget id="calculator">(1/2) * 15</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) * 22</gadget>
<output>165</output>
<result>B</result> | B | 165 | Find the area of the quadrilateral of one of its diagonals is 22 cm and its off sets 9 cm and 6 cm? | {
"A": "188 cm 2",
"B": "165 cm 2",
"C": "168 cm 2",
"D": "198 cm 2",
"E": "987 cm 2"
} | multiply(multiply(divide(const_1, const_2), add(6, 9)), 22) | add(n1,n2)|divide(const_1,const_2)|multiply(#0,#1)|multiply(n0,#2)| | "1 / 2 * 22 ( 9 + 6 ) = 165 cm 2 answer : b" | geometry |
math_qa__g6c7I0X8C5QuEHbV | A work which could be finished in 8 days was finished 3 days earlier after 10 more men joined. The number of men employed was? Choose the correct choice from the following choices: A) 22 B) 30 C) 88 D) 71 E) 11 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">8 - 6</gadget>
<output>2</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<result>B</result> | B | 30 | A work which could be finished in 8 days was finished 3 days earlier after 10 more men joined. The number of men employed was? | {
"A": "22",
"B": "30",
"C": "88",
"D": "71",
"E": "11"
} | divide(multiply(multiply(3, const_2), 10), subtract(8, multiply(3, const_2))) | multiply(n1,const_2)|multiply(n2,#0)|subtract(n0,#0)|divide(#1,#2)| | "x - - - - - - - 8 ( x + 10 ) - - - - 6 x * 8 = ( x + 10 ) 6 x = 30 \ answer : b" | physics |
math_qa__c8ECbSKko7U0kk0v | A certain protective additive increases from 25 days to 30 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive? Select: A) 25 % B) 20 % C) 50 % D) 66 2 / 3 % E) 75 % | <gadget id="calculator">30 - 25</gadget>
<output>5</output>
<gadget id="calculator">5 / 25</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>B</result> | B | 20 | A certain protective additive increases from 25 days to 30 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive? | {
"A": "25 %",
"B": "20 %",
"C": "50 %",
"D": "66 2 / 3 %",
"E": "75 %"
} | multiply(divide(subtract(30, 25), 25), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 30 − 25 / 25 ∗ 100 = 20 answer : b ." | general |
math_qa__txxw0Fy4PZmrEznV | A copy machine, working at a constant rate, makes 40 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
Choose one
A) 90 B) 2,700 C) 4,500 D) 5,400 E) 2,850 | <gadget id="calculator">40 + 55</gadget>
<output>95</output>
<gadget id="calculator">95 * 60</gadget>
<output>5_700</output>
<gadget id="calculator">5_700 / 2</gadget>
<output>2_850</output>
<result>E</result> | E | 2,850 | A copy machine, working at a constant rate, makes 40 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ? | {
"A": "90",
"B": "2,700",
"C": "4,500",
"D": "5,400",
"E": "2,850"
} | divide(multiply(add(40, 55), const_60), const_2) | add(n0,n1)|multiply(#0,const_60)|divide(#1,const_2) | together the two machines make 40 + 55 = 95 copies per minute . so , in half an hour they will make 95 * 30 = 2,850 copies . answer : e . | physics |
math_qa__hxfhvmPV2VF2H8E9 | Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 2x units of product P in 6 days? Choose the correct choice from the following answers
A) 24 B) 18 C) 16 D) 12 E) 8 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">6 / 6</gadget>
<output>1</output>
<gadget id="calculator">8 * 1</gadget>
<output>8</output>
<result>E</result> | E | 8 | Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 2x units of product P in 6 days? | {
"A": "24",
"B": "18",
"C": "16",
"D": "12",
"E": "8"
} | multiply(multiply(4, 2), divide(6, 6)) | divide(n1,n3)|multiply(n0,n2)|multiply(#0,#1)| | "4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 2 x units in 4 days therefore , we need to get to 2 x / 4 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 2 x done in 6 days . 2 x / 6 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 2 x / 6 y = 2 x / 6 * 24 / x cancel 6 with 24 , and x with x and get - > 8 . answer choice e" | general |
math_qa__rzbVjOXTYC218r6X | Product of two natural numbers is 19. Then, the sum of reciprocals of their squares is
Options: A) 290 / 289 B) 1 / 289 C) 290 / 90 D) 362 / 361 E) none of these | <gadget id="calculator">1 / 1</gadget>
<output>1</output>
<gadget id="calculator">1 ** 2</gadget>
<output>1</output>
<gadget id="calculator">1 / 19</gadget>
<output>1/19 = around 0.052632</output>
<gadget id="calculator">(1/19) ** 2</gadget>
<output>1/361 = around 0.00277</output>
<gadget id="calculator">1 + (1/361)</gadget>
<output>362/361 = around 1.00277</output>
<result>D</result> | D | 1.00277 | Product of two natural numbers is 19. Then, the sum of reciprocals of their squares is | {
"A": "290 / 289",
"B": "1 / 289",
"C": "290 / 90",
"D": "362 / 361",
"E": "none of these"
} | add(power(divide(const_1, const_1), const_2), power(divide(const_1, 19), const_2)) | divide(const_1,const_1)|divide(const_1,n0)|power(#0,const_2)|power(#1,const_2)|add(#2,#3) | explanation : if the numbers are a , b , then ab = 19 , as 17 is a prime number , so a = 1 , b = 19 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 19 ( 2 ) = 362 / 361 option d | general |
math_qa__gTig7k5dAKCVFEhz | A train 630 m long, running with a speed of 63 km/hr will pass a tree in? Choose the correct choice from the following answers
A) 35
B) 36
C) 37
D) 38
E) 39 | <gadget id="calculator">63 * 1_000</gadget>
<output>63_000</output>
<gadget id="calculator">630 / 63_000</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">(1/100) * 3_600</gadget>
<output>36</output>
<result>B</result> | B | 36 | A train 630 m long, running with a speed of 63 km/hr will pass a tree in? | {
"A": "35",
"B": "36",
"C": "37",
"D": "38",
"E": "39"
} | multiply(divide(630, multiply(63, const_1000)), const_3600) | multiply(n1,const_1000)|divide(n0,#0)|multiply(#1,const_3600)| | "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 630 * 2 / 35 = 36 sec answer : option b" | physics |
math_qa__VWfq6yiU2S7wmu30 | A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many U apples did each person get before 45 people joined the feast? Choose the correct choice:
A) 20 . B) 21 . C) 22 . D) 23 . E) 24 . | <gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 2</gadget>
<output>22</output>
<gadget id="calculator">1_430 / 22</gadget>
<output>65</output>
<gadget id="calculator">65 + 45</gadget>
<output>110</output>
<gadget id="calculator">1_430 / 110</gadget>
<output>13</output>
<gadget id="calculator">13 + 9</gadget>
<output>22</output>
<result>C</result> | C | 22 | A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many U apples did each person get before 45 people joined the feast? | {
"A": "20 .",
"B": "21 .",
"C": "22 .",
"D": "23 .",
"E": "24 ."
} | add(divide(1430, add(divide(1430, add(add(const_10, const_10), const_2)), 45)), 9) | add(const_10,const_10)|add(#0,const_2)|divide(n0,#1)|add(n1,#2)|divide(n0,#3)|add(n2,#4)| | "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons u = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c" | general |
math_qa__dRISq3TGoTGw4Hdv | What is the smallest number which when increased by 3 is divisible by 18, 70, 100 and 21?
Choices:
A) 5037
B) 5447
C) 5867
D) 6297
E) 6617 | <gadget id="calculator">lcm(18, 70)</gadget>
<output>630</output>
<gadget id="calculator">lcm(100, 21)</gadget>
<output>2_100</output>
<gadget id="calculator">lcm(630, 2_100)</gadget>
<output>6_300</output>
<gadget id="calculator">6_300 + 3</gadget>
<output>6_303</output>
<result>D</result> | D | 6,297 | What is the smallest number which when increased by 3 is divisible by 18, 70, 100 and 21? | {
"A": "5037",
"B": "5447",
"C": "5867",
"D": "6297",
"E": "6617"
} | add(lcm(lcm(18, 70), lcm(100, 21)), 3) | lcm(n1,n2)|lcm(n3,n4)|lcm(#0,#1)|add(n0,#2)| | "when increased by 3 , the number must include at least 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 = 6300 the answer is d ." | general |
math_qa__7X6AK834Mg9dB5A4 | If A(k)=(2k+1)^K, and k=0, what is the value of A(A(A(k)))? Choices: A) 343 B) 199 C) 121 D) 69 E) 249 | <gadget id="calculator">2 * 0</gadget>
<output>0</output>
<gadget id="calculator">1 + 0</gadget>
<output>1</output>
<gadget id="calculator">1 ** 0</gadget>
<output>1</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">3 ** 1</gadget>
<output>3</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">7 ** 3</gadget>
<output>343</output>
<result>A</result> | A | 343 | If A(k)=(2k+1)^K, and k=0, what is the value of A(A(A(k)))? | {
"A": "343",
"B": "199",
"C": "121",
"D": "69",
"E": "249"
} | power(add(multiply(2, power(add(multiply(2, power(add(1, multiply(2, 0)), 0)), 1), 1)), 1), power(add(multiply(2, power(add(1, multiply(2, 0)), 0)), 1), 1)) | multiply(n0,n2)|add(n1,#0)|power(#1,n2)|multiply(n0,#2)|add(n1,#3)|power(#4,n1)|multiply(n0,#5)|add(n1,#6)|power(#7,#5) | a ( a ( a ( 0 ) ) ) = a ( a ( 1 ) ) = a ( 3 ) = ( 6 + 1 ) ^ 3 = 343 . thus , the answer is a . | general |
math_qa__38PyvCjqHXkAxsWd | The cricket team of 11members is 27yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ? Select the correct option: A) 21 B) 22 C) 23 D) 25 E) 24 | <gadget id="calculator">27 + 3</gadget>
<output>30</output>
<gadget id="calculator">30 + 27</gadget>
<output>57</output>
<gadget id="calculator">11 - 2</gadget>
<output>9</output>
<gadget id="calculator">57 - 9</gadget>
<output>48</output>
<gadget id="calculator">11 - 9</gadget>
<output>2</output>
<gadget id="calculator">48 / 2</gadget>
<output>24</output>
<result>E</result> | E | 24 | The cricket team of 11members is 27yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ? | {
"A": "21",
"B": "22",
"C": "23",
"D": "25",
"E": "24"
} | divide(subtract(add(add(27, 3), 27), subtract(11, 2)), subtract(11, subtract(11, 2))) | add(n1,n2)|subtract(n0,n3)|add(n1,#0)|subtract(n0,#1)|subtract(#2,#1)|divide(#4,#3)| | "let the average age of the whole team be x years . 11 x - ( 27 + 30 ) = 9 ( x - 1 ) = > 11 x - 9 x = 48 = > 2 x = 48 = > x = 24 . so , average age of the team is 24 years . e" | general |
math_qa__kfVZm3zWdlnb6KNs | The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 12 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament? Choices:
A) 6
B) 7
C) 8
D) 9
E) 10 | <gadget id="calculator">40 - 12</gadget>
<output>28</output>
<gadget id="calculator">20 - 5</gadget>
<output>15</output>
<gadget id="calculator">28 - 15</gadget>
<output>13</output>
<gadget id="calculator">13 / 2</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">floor(13/2)</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<result>B</result> | B | 7 | The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 12 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament? | {
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "10"
} | add(floor(divide(subtract(subtract(40, 12), subtract(20, 5)), const_2)), 1) | subtract(n6,n4)|subtract(n3,n5)|subtract(#0,#1)|divide(#2,const_2)|floor(#3)|add(#4,n1)| | "to get 40 points as end of season we need another 28 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 hence option b - 7" | general |
math_qa__EQVo2dlVcMwGrarE | If x is an integer and 3.134 × 10^x is less than 31,000 what is the greatest possible value for x? Choices:
A) 7 B) 6 C) 5 D) 4 E) 3 | <gadget id="calculator">31_000 / 3.134</gadget>
<output>9_891.512444</output>
<gadget id="calculator">log(9_891.512444)</gadget>
<output>9.199432</output>
<gadget id="calculator">log(10)</gadget>
<output>log(10) = around 2.302585</output>
<gadget id="calculator">9.199432 / log(10)</gadget>
<output>9.199432/log(10) = around 3.995263</output>
<gadget id="calculator">floor(9.199432/log(10))</gadget>
<output>3</output>
<result>E</result> | E | 3 | If x is an integer and 3.134 × 10^x is less than 31,000 what is the greatest possible value for x? | {
"A": "7",
"B": "6",
"C": "5",
"D": "4",
"E": "3"
} | floor(divide(log(divide(31,000, 3.134)), log(10))) | divide(n2,n0)|log(n1)|log(#0)|divide(#2,#1)|floor(#3)| | "if x = 4 3.134 × 10 ^ 4 = 31340 > 31000 so , x = 3 answer : e" | general |
math_qa__iuGeuULel0o5VhnT | In a river flowing at 2 km/hr, a boat travels 40 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time. Choose the correct choice from the following answers.
A) 10 hours B) 12 hours C) 14 hours D) 15 hours E) none of these | <gadget id="calculator">6 - 2</gadget>
<output>4</output>
<gadget id="calculator">40 / 4</gadget>
<output>10</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">40 / 8</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<result>D</result> | D | 15 | In a river flowing at 2 km/hr, a boat travels 40 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time. | {
"A": "10 hours",
"B": "12 hours",
"C": "14 hours",
"D": "15 hours",
"E": "none of these"
} | add(divide(40, subtract(6, 2)), divide(40, add(6, 2))) | add(n0,n2)|subtract(n2,n0)|divide(n1,#1)|divide(n1,#0)|add(#2,#3)| | "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 40 km total time taken = time taken downstream + time taken upstream = ( 40 / 8 ) + ( 40 / 4 ) = 15 d" | general |
math_qa__IVizBoy38vU8B60q | A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be
Choices.
A) 45 min B) 60 min C) 55 min D) 70 min E) 80 min | <gadget id="calculator">50 / 60</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">48 * (5/6)</gadget>
<output>40</output>
<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">40 / (2/3)</gadget>
<output>60</output>
<result>B</result> | B | 60 | A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be | {
"A": "45 min",
"B": "60 min",
"C": "55 min",
"D": "70 min",
"E": "80 min"
} | divide(multiply(48, divide(50, const_60)), divide(40, const_60)) | divide(n0,const_60)|divide(n2,const_60)|multiply(n1,#0)|divide(#2,#1)| | "time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph answer : b ." | physics |
math_qa__2s2nGQi1LVYNcRTv | Ifaequals the sum of the even integers from 2 to 100, inclusive, andbequals the sum of the odd integers from 1 to 99, inclusive, what is the value of a - b ? Choose the most appropriate option
A) 1
B) 50
C) 19
D) 20
E) 21 | <gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">50 + 1</gadget>
<output>51</output>
<gadget id="calculator">50 * 51</gadget>
<output>2_550</output>
<gadget id="calculator">99 + 1</gadget>
<output>100</output>
<gadget id="calculator">99 - 1</gadget>
<output>98</output>
<gadget id="calculator">98 / 2</gadget>
<output>49</output>
<gadget id="calculator">49 + 1</gadget>
<output>50</output>
<gadget id="calculator">50 * 50</gadget>
<output>2_500</output>
<gadget id="calculator">2_550 - 2_500</gadget>
<output>50</output>
<result>B</result> | B | 50 | Ifaequals the sum of the even integers from 2 to 100, inclusive, andbequals the sum of the odd integers from 1 to 99, inclusive, what is the value of a - b ? | {
"A": "1",
"B": "50",
"C": "19",
"D": "20",
"E": "21"
} | subtract(multiply(divide(100, 2), add(divide(100, 2), 1)), multiply(divide(add(99, 1), 2), add(divide(subtract(99, 1), 2), 1))) | add(n2,n3)|divide(n1,n0)|subtract(n3,n2)|add(n2,#1)|divide(#2,n0)|divide(#0,n0)|add(n2,#4)|multiply(#3,#1)|multiply(#6,#5)|subtract(#7,#8)| | "this is a solution from beatthegmat : even numbers : ( 100 - 2 ) / 2 + 1 = 50 even integers . ( 100 + 2 ) / 2 = 51 is the average of the even set . sum = avg * ( # of elements ) = 51 * 50 = 2550 = a odd numbers : ( 99 - 1 ) / 2 + 1 = 50 odd integers . ( 99 + 1 ) / 2 = 50 is the average of the odd set . sum = avg * ( # of elements ) = 50 * 50 = 2500 = b a - b = 2550 - 2500 = 50 . ( b )" | general |
math_qa__pGwaEBcrA5xrT8l4 | the sum of 4 consecutive numbers is 102 . the greatest among these 3 number is : Choose the correct option: A) 26 B) 28 C) 29 D) 30 E) 27 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">102 - 6</gadget>
<output>96</output>
<gadget id="calculator">96 / 4</gadget>
<output>24</output>
<gadget id="calculator">24 + 3</gadget>
<output>27</output>
<result>E</result> | E | 27 | the sum of 4 consecutive numbers is 102 . the greatest among these 3 number is : | {
"A": "26",
"B": "28",
"C": "29",
"D": "30",
"E": "27"
} | add(divide(subtract(102, add(add(const_1, const_2), 3)), 4), 3) | add(const_1,const_2)|add(n2,#0)|subtract(n1,#1)|divide(#2,n0)|add(n2,#3) | let the numbers be x , x + 1 , x + 2 and x + 3 then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 102 4 x = 96 x = 24 greatest number , ( x + 3 ) = 27 answer : e | physics |
math_qa__6gfeBLAtJva6QOzJ | the sum of all possible two digit numbers formed from 3 different one digit natural numbers when divided by the sum of the original 3 numbers is equal to ? Choose the correct choice from the following options.
A) 14 B) 16 C) 18 D) 20 E) 22 | <gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">30 + 3</gadget>
<output>33</output>
<gadget id="calculator">33 / 3</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<result>E</result> | E | 22 | the sum of all possible two digit numbers formed from 3 different one digit natural numbers when divided by the sum of the original 3 numbers is equal to ? | {
"A": "14",
"B": "16",
"C": "18",
"D": "20",
"E": "22"
} | multiply(divide(add(multiply(3, const_10), const_3), 3), const_2) | multiply(n0,const_10)|add(#0,const_3)|divide(#1,n0)|multiply(#2,const_2) | let the one digit numbers x , y , z sum of all possible two digit numbers = ( 10 x + y ) + ( 10 x + z ) + ( 10 y + x ) + ( 10 y + z ) + ( 10 z + x ) + ( 10 z + y ) = 22 ( x + y + z ) therefore sum of all possible two digit numbers when divided by sum of one digit numbers gives 22 . answer e | general |
math_qa__ZBLRrlq46oI0JBfj | If a man lost 10% by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 32%? Answers
A) 13.25 B) 14.36 C) 15.85 D) 12.27 E) 11.25 | <gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 * 18</gadget>
<output>1_620</output>
<gadget id="calculator">100 + 32</gadget>
<output>132</output>
<gadget id="calculator">1_620 / 132</gadget>
<output>135/11 = around 12.272727</output>
<result>D</result> | D | 12.27 | If a man lost 10% by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 32%? | {
"A": "13.25",
"B": "14.36",
"C": "15.85",
"D": "12.27",
"E": "11.25"
} | divide(multiply(subtract(const_100, 10), 18), add(const_100, 32)) | add(n2,const_100)|subtract(const_100,n0)|multiply(n1,#1)|divide(#2,#0)| | "90 % - - - - 18 132 % - - - - ? 90 / 132 * 18 = 12.27 answer : d" | gain |
math_qa__Zg6a064G0DFGy53W | Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate Z in miles per hour for the entire trip? Choose one:
A) 26.7 B) z = 30.0 C) z = 40.0 D) z = 53.3 E) 60.0 | <gadget id="calculator">640 / 2</gadget>
<output>320</output>
<gadget id="calculator">320 / 80</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">640 / 16</gadget>
<output>40</output>
<result>C</result> | C | 40 | Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate Z in miles per hour for the entire trip? | {
"A": "26.7",
"B": "z = 30.0",
"C": "z = 40.0",
"D": "z = 53.3",
"E": "60.0"
} | divide(640, add(add(multiply(divide(divide(640, const_2), 80), const_2), divide(divide(640, const_2), 80)), divide(divide(640, const_2), 80))) | divide(n0,const_2)|divide(#0,n1)|multiply(#1,const_2)|add(#1,#2)|add(#3,#1)|divide(n0,#4)| | "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ." | physics |
math_qa__cjmW42lLeX9ezSbB | John is going with 10 friends on a trip to Sidney for spring break. Airfare and hotel costs a total of $12100.00 for the group of 11 friends. How much does each person have to pay for their hotel and airfare? Answers:
A) $ 1010 B) $ 1100 C) $ 1110 D) $ 1101 E) $ 1200 | <gadget id="calculator">12_100 / 11</gadget>
<output>1_100</output>
<result>B</result> | B | 1,100 | John is going with 10 friends on a trip to Sidney for spring break. Airfare and hotel costs a total of $12100.00 for the group of 11 friends. How much does each person have to pay for their hotel and airfare? | {
"A": "$ 1010",
"B": "$ 1100",
"C": "$ 1110",
"D": "$ 1101",
"E": "$ 1200"
} | divide(12100, 11) | divide(n1,n2) | answer = b the total cost of the trip ( $ 12100.00 ) divided by 11 equals $ 1100.00 . | general |
math_qa__gxIIYJt2uM0Jl0du | A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what R percent of the list price is the lowest possible sale price? Choices:
A) 20 B) 25 C) 30 D) 40 E) 50 | <gadget id="calculator">80 / 2</gadget>
<output>40</output>
<result>D</result> | D | 40 | A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what R percent of the list price is the lowest possible sale price? | {
"A": "20",
"B": "25",
"C": "30",
"D": "40",
"E": "50"
} | divide(80, const_2) | divide(n3,const_2) | let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which r is 40 % of 80 hence , d is the answer | general |
math_qa__Cq8DJMoXpK9lmnzr | Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.7 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect? Select the correct option.
A) 1 / 6 B) 1 / 2 C) 5 / 8 D) 5 / 4 E) 15 / 16 | <gadget id="calculator">0.75 - 0.5</gadget>
<output>0.25</output>
<gadget id="calculator">0.7 - 0.5</gadget>
<output>0.2</output>
<gadget id="calculator">0.25 / 0.2</gadget>
<output>1.25</output>
<result>D</result> | D | 1.25 | Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.7 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect? | {
"A": "1 / 6",
"B": "1 / 2",
"C": "5 / 8",
"D": "5 / 4",
"E": "15 / 16"
} | divide(subtract(0.75, 0.5), subtract(0.7, 0.5)) | subtract(n2,n0)|subtract(n1,n0)|divide(#0,#1) | x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.7 ( x ) + 0.5 ( 1 - x ) = 0.75 0.2 x = 0.75 - 0.5 x = 0.25 / 0.2 x = 5 / 4 therefore the answer is d : 5 / 4 . | gain |
math_qa__XMDEFxRrasHUrEWX | The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Select: A) 978 B) 789 C) 999 D) 778 E) 787 | <gadget id="calculator">3_136 ** (1/2)</gadget>
<output>56</output>
<gadget id="calculator">56 * 4</gadget>
<output>224</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">224 - 2</gadget>
<output>222</output>
<gadget id="calculator">222 * 1.5</gadget>
<output>333</output>
<gadget id="calculator">333 * 3</gadget>
<output>999</output>
<result>C</result> | C | 999 | The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? | {
"A": "978",
"B": "789",
"C": "999",
"D": "778",
"E": "787"
} | multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, const_1)), 1.5), const_3) | multiply(const_1,const_2)|sqrt(n0)|multiply(#1,const_4)|subtract(#2,#0)|multiply(n2,#3)|multiply(#4,const_3) | a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999 answer : c | physics |
math_qa__gV6y9iRqCXGmsNfZ | A firm is comprised of partners and associates in a ratio of 2:63. If 50 more associates were hired, the ratio of partners to associates would be 1:34. How many partners are currently in the firm? Choices.
A) 5 B) 10 C) 12 D) 20 E) 25 | <gadget id="calculator">34 * 2</gadget>
<output>68</output>
<gadget id="calculator">68 - 63</gadget>
<output>5</output>
<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<result>D</result> | D | 20 | A firm is comprised of partners and associates in a ratio of 2:63. If 50 more associates were hired, the ratio of partners to associates would be 1:34. How many partners are currently in the firm? | {
"A": "5",
"B": "10",
"C": "12",
"D": "20",
"E": "25"
} | multiply(divide(50, subtract(multiply(34, 2), 63)), 2) | multiply(n0,n4)|subtract(#0,n1)|divide(n2,#1)|multiply(n0,#2) | the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 10 of the increase in 50 associates . the ratio changed from 20 : 630 to 20 : 680 . thus the number of partners is 20 . the answer is d . | other |
math_qa__DkZwVe6Va077ztVV | A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 42 liters of drink A to convert it to drink B? Choose the correct choice from the following choices
A) 7 B) 9 C) 12 D) 14 E) 18 | <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) * 42</gadget>
<output>24</output>
<gadget id="calculator">24 * 4</gadget>
<output>96</output>
<gadget id="calculator">96 / 3</gadget>
<output>32</output>
<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(3/7) * 42</gadget>
<output>18</output>
<gadget id="calculator">32 - 18</gadget>
<output>14</output>
<result>D</result> | D | 14 | A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 42 liters of drink A to convert it to drink B? | {
"A": "7",
"B": "9",
"C": "12",
"D": "14",
"E": "18"
} | subtract(divide(multiply(multiply(divide(4, add(4, 3)), 42), 4), 3), multiply(divide(3, add(4, 3)), 42)) | add(n0,n1)|divide(n0,#0)|divide(n1,#0)|multiply(n4,#1)|multiply(n4,#2)|multiply(n0,#3)|divide(#5,n1)|subtract(#6,#4) | in 42 liters of drink a , there are 24 liters of milk and 18 liters of juice . with 24 liters of milk , we need a total of 32 liters of juice to make drink b . we need to add 14 liters of juice . the answer is d . | general |
math_qa__plnMV6bZkrk0ORPv | The ratio between the number of sheep and the number of horses at the Stewar farm is 5 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form?? Choose the correct choice from the following options: A) 18 B) 28 C) 40 D) 56 E) 58 | <gadget id="calculator">12_880 / 230</gadget>
<output>56</output>
<gadget id="calculator">56 / 7</gadget>
<output>8</output>
<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<result>C</result> | C | 40 | The ratio between the number of sheep and the number of horses at the Stewar farm is 5 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form?? | {
"A": "18",
"B": "28",
"C": "40",
"D": "56",
"E": "58"
} | multiply(divide(divide(12880, 230), 7), 5) | divide(n3,n2)|divide(#0,n1)|multiply(n0,#1)| | "et no of sheep and horses are 5 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 5 * 8 ) = 40 answer : c" | other |
math_qa__Icu0C3pfYLDG61iq | Working alone, Tom finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Tom alone cleans the entire house in 6 hours. How many hours will it take Nick and Tom to clean the entire house if they work together? Choose the correct choice from the following answers
A) 1.5 B) 2 C) 2.4 D) 3 E) 3.6 | <gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">18 / 5</gadget>
<output>18/5 = around 3.6</output>
<result>E</result> | E | 3.6 | Working alone, Tom finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Tom alone cleans the entire house in 6 hours. How many hours will it take Nick and Tom to clean the entire house if they work together? | {
"A": "1.5",
"B": "2",
"C": "2.4",
"D": "3",
"E": "3.6"
} | divide(multiply(6, const_3), add(const_3, const_2)) | add(const_2,const_3)|multiply(n0,const_3)|divide(#1,#0) | answer is 3.6 hours . tom does the complete house in 6 hours while nick does it in 9 hours . 1 / ( 1 / 6 + 1 / 9 ) = 3.6 answer is e | physics |
math_qa__WIlvTuFJi14qHJ0x | Of the people who responded to a market survey, 360 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 9 to 1, how many people responded to the survey?
Choose the correct choice from the following answers
A) 80 B) 160 C) 240 D) 360 E) 400 | <gadget id="calculator">360 / 9</gadget>
<output>40</output>
<gadget id="calculator">40 + 360</gadget>
<output>400</output>
<result>E</result> | E | 400 | Of the people who responded to a market survey, 360 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 9 to 1, how many people responded to the survey? | {
"A": "80",
"B": "160",
"C": "240",
"D": "360",
"E": "400"
} | add(divide(360, 9), 360) | divide(n0,n1)|add(n0,#0)| | "ratio = 9 : 1 = > 9 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 360 = > 9 x = 360 = > x = 40 hence total no . of respondents = 360 + 40 = 400 hence e is the answer ." | other |
math_qa__uGE7fnx0epjMeqtU | 90 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine? Choose the correct choice from the following answers.
A) 80 litres B) 90 litres C) 120 litres D) 180 litres E) none of these | <gadget id="calculator">800 * 600</gadget>
<output>480_000</output>
<gadget id="calculator">90 / 480_000</gadget>
<output>3/16_000 = around 0.000188</output>
<gadget id="calculator">800 * (3/16_000)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1_200 * (3/20)</gadget>
<output>180</output>
<result>D</result> | D | 180 | 90 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine? | {
"A": "80 litres",
"B": "90 litres",
"C": "120 litres",
"D": "180 litres",
"E": "none of these"
} | multiply(1200, multiply(800, divide(90, multiply(800, 600)))) | multiply(n1,n2)|divide(n0,#0)|multiply(n2,#1)|multiply(n4,#2)| | "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 90 = 120 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 120 = 180 litres . answer d" | physics |
math_qa__w9uFs8I4kjz17MG0 | machine – a produces 40 % of the total output and machine - b produces 60 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - a and one unit of 50 units produced by machine - b prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ?
Options: A) a . 0.156 B) b . 0.01506 C) c . 0.0156 D) d . 0.0001566 E) e . 0.00001566 | <gadget id="calculator">1_000 * 60</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 40</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 / 50</gadget>
<output>30</output>
<gadget id="calculator">30 + 9</gadget>
<output>39</output>
<gadget id="calculator">1_500 + 1_000</gadget>
<output>2_500</output>
<gadget id="calculator">39 / 2_500</gadget>
<output>39/2_500 = around 0.0156</output>
<result>C</result> | C | 0.0156 | machine – a produces 40 % of the total output and machine - b produces 60 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - a and one unit of 50 units produced by machine - b prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ? | {
"A": "a . 0.156",
"B": "b . 0.01506",
"C": "c . 0.0156",
"D": "d . 0.0001566",
"E": "e . 0.00001566"
} | divide(add(divide(divide(multiply(1000, 60), 40), 50), 9), add(divide(multiply(1000, 60), 40), 1000)) | multiply(n1,n3)|divide(#0,n0)|add(n3,#1)|divide(#1,n4)|add(n2,#3)|divide(#4,#2) | let total production be 10000 units . . . . a produces 4000 units and 36 units are defective b produces 6000 units and 120 units are defective so , out of total 10,000 units 156 units are defective . . . so the required probability = 156 / 10000 = > 0.0156 answer will be ( c ) | general |
math_qa__6uhhnY8wFznXsgNS | A 470 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? Choose the most appropriate option.
A) 41.1 sec B) 64.8 sec C) 31.8 sec D) 50.4 sec E) none of the above | <gadget id="calculator">470 + 520</gadget>
<output>990</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">55 * (5/18)</gadget>
<output>275/18 = around 15.277778</output>
<gadget id="calculator">990 / (275/18)</gadget>
<output>324/5 = around 64.8</output>
<result>B</result> | B | 64.8 | A 470 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? | {
"A": "41.1 sec",
"B": "64.8 sec",
"C": "31.8 sec",
"D": "50.4 sec",
"E": "none of the above"
} | divide(add(470, 520), multiply(55, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 470 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 990 m time = distance / speed = 990 x 18 / ( 5 x 55 ) = 64.8 sec ans is : b" | physics |
math_qa__V97a9jx1poQhwpge | The ratio between the number of sheep and the number of horses at the Stewar farm is 7 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form?? Options.
A) 18 B) 28 C) 32 D) 56 E) 58 | <gadget id="calculator">12_880 / 230</gadget>
<output>56</output>
<gadget id="calculator">56 / 7</gadget>
<output>8</output>
<gadget id="calculator">8 * 7</gadget>
<output>56</output>
<result>D</result> | D | 56 | The ratio between the number of sheep and the number of horses at the Stewar farm is 7 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form?? | {
"A": "18",
"B": "28",
"C": "32",
"D": "56",
"E": "58"
} | multiply(divide(divide(12880, 230), 7), 7) | divide(n3,n2)|divide(#0,n1)|multiply(n0,#1)| | "et no of sheep and horses are 7 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 7 * 8 ) = 56 answer : d" | other |
math_qa__qBx2nVZuWxBVfGec | Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 9 times as heavy as water?
Answers:
A) 3 : 2 B) 1 : 2 C) 4 : 1 D) 5 : 2 E) 4 : 3 | <gadget id="calculator">9 - 5</gadget>
<output>4</output>
<gadget id="calculator">10 - 9</gadget>
<output>1</output>
<gadget id="calculator">4 / 1</gadget>
<output>4</output>
<result>C</result> | C | 4 | Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 9 times as heavy as water? | {
"A": "3 : 2",
"B": "1 : 2",
"C": "4 : 1",
"D": "5 : 2",
"E": "4 : 3"
} | divide(subtract(9, 5), subtract(10, 9)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)| | "g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 9 w 10 + 5 x = 9 ( x + 1 ) x = 1 / 4 ratio of gold with copper = 1 : 1 / 4 = 4 : 1 answer is c" | general |
math_qa__BA4mhGdxqpV74xzA | Veena ranks 73rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination? Choose the correct answer: A) 88 B) 108 C) 110 D) 90 E) 93 | <gadget id="calculator">182 - 22</gadget>
<output>160</output>
<gadget id="calculator">73 - 1</gadget>
<output>72</output>
<gadget id="calculator">160 - 72</gadget>
<output>88</output>
<gadget id="calculator">88 - 4</gadget>
<output>84</output>
<result>A</result> | A | 88 | Veena ranks 73rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination? | {
"A": "88",
"B": "108",
"C": "110",
"D": "90",
"E": "93"
} | subtract(subtract(subtract(182, 22), subtract(73, const_1)), const_4) | subtract(n1,n2)|subtract(n0,const_1)|subtract(#0,#1)|subtract(#2,const_4)| | "total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 73 + 1 = 88 answer : a" | other |
math_qa__w22ACiV9ZKXhzRhe | Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 12% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit? Choose the correct choice from the following answers:
A) 117 % B) 120 % C) 121 % D) 133 % E) 140 % | <gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) / 2</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">1 + (3/50)</gadget>
<output>53/50 = around 1.06</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">(53/50) ** 5</gadget>
<output>418_195_493/312_500_000 = around 1.338226</output>
<gadget id="calculator">(418_195_493/312_500_000) * 100</gadget>
<output>418_195_493/3_125_000 = around 133.822558</output>
<result>D</result> | D | 133 | Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 12% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit? | {
"A": "117 %",
"B": "120 %",
"C": "121 %",
"D": "133 %",
"E": "140 %"
} | multiply(power(add(1, divide(divide(12, const_100), const_2)), add(const_2, const_3)), const_100) | add(const_2,const_3)|divide(n2,const_100)|divide(#1,const_2)|add(#2,n0)|power(#3,#0)|multiply(#4,const_100)| | "since michelle earns 12 % interest compounded semiannually , then she earns 6 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 6 % * 5 = 30 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 30 % , only answer choice d fits . answer : d" | gain |
math_qa__FwDQNzZBzPcuueCm | Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took P.E. as an elective, 1/3 of the students took Theatre as an elective, and all of the other students took Music. In this year, 1/3 of the students who took P.E. and 1/4 of the students who took Theatre left school, other students did not leave, and no fresh student come in. What fraction of all students took P.E. or Music? Pick one:
A) 2 / 3
B) 1 / 4
C) 7 / 9
D) 1 / 5
E) 8 / 11 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/2) + (1/3)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">1 - (5/6)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * (1/2)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/6) + (1/3)</gadget>
<output>1/2 = around 0.5</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">(3/4) * (1/3)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/2) + (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(1/2) / (3/4)</gadget>
<output>2/3 = around 0.666667</output>
<result>A</result> | A | 0.666667 | Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took P.E. as an elective, 1/3 of the students took Theatre as an elective, and all of the other students took Music. In this year, 1/3 of the students who took P.E. and 1/4 of the students who took Theatre left school, other students did not leave, and no fresh student come in. What fraction of all students took P.E. or Music? | {
"A": "2 / 3",
"B": "1 / 4",
"C": "7 / 9",
"D": "1 / 5",
"E": "8 / 11"
} | divide(add(subtract(const_1, add(divide(1, 2), divide(1, 3))), multiply(subtract(const_1, divide(1, 3)), divide(1, 2))), add(add(subtract(const_1, add(divide(1, 2), divide(1, 3))), multiply(subtract(const_1, divide(1, 3)), divide(1, 2))), multiply(subtract(const_1, divide(1, 4)), divide(1, 3)))) | divide(n0,n1)|divide(n0,n3)|divide(n0,n7)|add(#0,#1)|subtract(const_1,#1)|subtract(const_1,#2)|multiply(#0,#4)|multiply(#1,#5)|subtract(const_1,#3)|add(#6,#8)|add(#9,#7)|divide(#9,#10) | lets pick smart numbers . total number of students : 12 p . e . ( 1 / 2 ) : 6 theatre ( 1 / 3 ) : 4 music ( 1 / 6 ) : 2 after leaving school p . e . : 4 theatre : 3 music : 2 new total number of students : 9 p . e . and music : 6 answer 2 / 3 or a | general |
math_qa__0NH4Xqpr99TzKgrV | What is the compound interest paid on a sum of Rs.1500 for the period of 2 years at 10% per annum.
Choose the correct choice:
A) 230 B) 175 C) 225 D) 315 E) none of these | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">1_500 * (121/100)</gadget>
<output>1_815</output>
<gadget id="calculator">1_815 - 1_500</gadget>
<output>315</output>
<result>D</result> | D | 315 | What is the compound interest paid on a sum of Rs.1500 for the period of 2 years at 10% per annum. | {
"A": "230",
"B": "175",
"C": "225",
"D": "315",
"E": "none of these"
} | subtract(multiply(1500, power(add(const_1, divide(10, const_100)), 2)), 1500) | divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|subtract(#3,n0)| | "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 1500 = 1500 * ( 21 / 100 ) = 315 answer d" | gain |
math_qa__UGvxXx2NOjemWlll | If Sharon's weekly salary increased by 20 percent, she would earn $600 per week. If instead, her weekly salary were to increase by 15 percent, how much would she earn per week? Choose the correct choice from the following answers
A) rs . 575
B) rs . 600
C) rs . 625
D) rs . 485
E) rs . 590 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">600 / (6/5)</gadget>
<output>500</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 500</gadget>
<output>75</output>
<gadget id="calculator">500 + 75</gadget>
<output>575</output>
<result>A</result> | A | 575 | If Sharon's weekly salary increased by 20 percent, she would earn $600 per week. If instead, her weekly salary were to increase by 15 percent, how much would she earn per week? | {
"A": "rs . 575",
"B": "rs . 600",
"C": "rs . 625",
"D": "rs . 485",
"E": "rs . 590"
} | add(divide(600, add(const_1, divide(20, const_100))), multiply(divide(15, const_100), divide(600, add(const_1, divide(20, const_100))))) | divide(n0,const_100)|divide(n2,const_100)|add(#0,const_1)|divide(n1,#2)|multiply(#1,#3)|add(#3,#4)| | "soln : - ( 600 / 120 ) 115 = 575 in this case long division does not take much time . ( 5 / 1 ) 115 = rs . 575 answer : a" | general |
math_qa__uGk42pIMHSgYB65J | Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 3 hours. How long would it take Taimour to paint the fence alone? Choose the correct answer.
A) 6 hours B) 9 hours C) 14 hours D) 24 hours E) 32 hours | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<result>B</result> | B | 9 | Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 3 hours. How long would it take Taimour to paint the fence alone? | {
"A": "6 hours",
"B": "9 hours",
"C": "14 hours",
"D": "24 hours",
"E": "32 hours"
} | multiply(3, const_3) | multiply(n1,const_3)| | "i believe the answer is b . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 3 = > 1 / 9 working alone taimour can do the job in 1 = 1 / 9 * hours = > 9 answer b" | physics |
math_qa__HVnvy3lKmzARoHQC | A man is walking at the rate of 9 km/hr crosses a bridge in 15 minutes. The length of the bridge is Choose the correct choice from the following answers
A) 1000 meters B) 1050 meters C) 2200 meters D) 2250 meters E) none of these | <gadget id="calculator">15 / 60</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">9 * (1/4)</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">(9/4) * 1_000</gadget>
<output>2_250</output>
<result>D</result> | D | 2,250 | A man is walking at the rate of 9 km/hr crosses a bridge in 15 minutes. The length of the bridge is | {
"A": "1000 meters",
"B": "1050 meters",
"C": "2200 meters",
"D": "2250 meters",
"E": "none of these"
} | multiply(multiply(9, divide(15, const_60)), const_1000) | divide(n1,const_60)|multiply(n0,#0)|multiply(#1,const_1000)| | "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 9 â ˆ — 5 / 18 = 5 / 2 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 5 / 2 â ˆ — 900 = 2250 meter option d" | gain |
math_qa__I9QWhJsODIpZTYzz | Patrick purchased 80 pencils and sold them at a loss equal to the selling price of 30 pencils. The cost of 80 pencils is how many times the selling price of 80 pencils? Answers
A) 0.75 B) 0.8 C) 1.375 D) 1.4 E) 1.85 | <gadget id="calculator">80 + 30</gadget>
<output>110</output>
<gadget id="calculator">80 / 110</gadget>
<output>8/11 = around 0.727273</output>
<gadget id="calculator">1 / (8/11)</gadget>
<output>11/8 = around 1.375</output>
<result>C</result> | C | 1.375 | Patrick purchased 80 pencils and sold them at a loss equal to the selling price of 30 pencils. The cost of 80 pencils is how many times the selling price of 80 pencils? | {
"A": "0.75",
"B": "0.8",
"C": "1.375",
"D": "1.4",
"E": "1.85"
} | inverse(divide(80, add(80, 30))) | add(n0,n1)|divide(n0,#0)|inverse(#1) | say the cost price of 80 pencils was $ 80 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 80 - 80 p = 30 p - - > p = 8 / 11 . ( cost price ) / ( selling price ) = 1 / ( 8 / 11 ) = 11 / 8 = 1.375 . answer : c . | general |
math_qa__S0ouJyII6RWP40ch | A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered? Choose the correct choice from the following choices: A) 70 % B) 60 % C) 30 % D) 10 % E) 20 % | <gadget id="calculator">100 + 23.5</gadget>
<output>123.5</output>
<gadget id="calculator">123.5 * 100</gadget>
<output>12_350</output>
<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">12_350 / 95</gadget>
<output>130</output>
<gadget id="calculator">130 - 100</gadget>
<output>30</output>
<result>C</result> | C | 30 | A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered? | {
"A": "70 %",
"B": "60 %",
"C": "30 %",
"D": "10 %",
"E": "20 %"
} | subtract(divide(multiply(add(const_100, 23.5), const_100), subtract(const_100, 5)), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,const_100)|divide(#2,#1)|subtract(#3,const_100)| | "explanation : let c . p . be rs . 100 . then , s . p . = rs . 123.50 let marked price be rs . x . then , 95 / 100 x = 123.50 x = 12350 / 95 = rs . 130 now , s . p . = rs . 130 , c . p . = rs . 100 profit % = 30 % . answer c" | gain |
math_qa__NSY5GSGXWJtyGjt5 | the hiker walking at a constant rate of 7 miles per hour is passed by a cyclist traveling in the same direction along the same path at 28 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up?
Answers
A) 10 B) 15 C) 20 D) 25 E) 30 | <gadget id="calculator">28 - 7</gadget>
<output>21</output>
<gadget id="calculator">5 / 60</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">21 * (1/12)</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">(7/4) / 7</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 60</gadget>
<output>15</output>
<result>B</result> | B | 15 | the hiker walking at a constant rate of 7 miles per hour is passed by a cyclist traveling in the same direction along the same path at 28 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? | {
"A": "10",
"B": "15",
"C": "20",
"D": "25",
"E": "30"
} | multiply(divide(multiply(subtract(28, 7), divide(5, const_60)), 7), const_60) | divide(n2,const_60)|subtract(n1,n0)|multiply(#0,#1)|divide(#2,n0)|multiply(#3,const_60)| | "for the 5 minutes the cyclist continues to overtake the hiker , she is going at 21 miles per hour faster than the hiker . once the cyclist stops , the hiker is going at 7 miles per hour while the cyclist is at rest so the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds . 21 / 7 * 5 or 15 minutes answer is ( b )" | physics |
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