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stringlengths 7
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math_qa__AuURD5X9bsjMchbw | If each side of a rectangle is increased by 100%, by what % the area increases? Pick one.
A) 100 % B) 200 % C) 250 % D) 300 % E) 400 % | <gadget id="calculator">100 / 100</gadget>
<output>1</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<result>D</result> | D | 300 | If each side of a rectangle is increased by 100%, by what % the area increases? | {
"A": "100 %",
"B": "200 %",
"C": "250 %",
"D": "300 %",
"E": "400 %"
} | multiply(subtract(power(multiply(divide(100, const_100), const_2), const_2), const_1), const_100) | divide(n0,const_100)|multiply(#0,const_2)|power(#1,const_2)|subtract(#2,const_1)|multiply(#3,const_100) | if length is l and width is b then area = l * b now new l and b is 2 l and 2 b respectively . so new area is = 4 * l * b % increase = 300 % answer : d | geometry |
math_qa__LxKDXPoR0lq4BaBx | A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water? Choose the correct choice from the following answers: A) 7 h B) 3 h C) 4 h D) 2 h E) 9 h | <gadget id="calculator">15 / 5</gadget>
<output>3</output>
<result>B</result> | B | 3 | A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water? | {
"A": "7 h",
"B": "3 h",
"C": "4 h",
"D": "2 h",
"E": "9 h"
} | divide(15, 5) | divide(n0,n1) | explanation : upstream speed = b - s downstream speed = b + s b - s = 15 / 5 = 3 km / h again b = 4 s therefore b - s = 3 = 3 s = > s = 1 and b = 4 km / h therefore b + s = 5 km / h therefore , time during downstream = 15 / 5 = 3 h answer : b | physics |
math_qa__P2pSNOmtfb64btMR | If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 16? Options
A) 1 / 4 B) 3 / 8 C) 1 / 2 D) 9 / 16 E) 3 / 4 | <gadget id="calculator">96 / 2</gadget>
<output>48</output>
<gadget id="calculator">96 / 16</gadget>
<output>6</output>
<gadget id="calculator">48 + 6</gadget>
<output>54</output>
<gadget id="calculator">54 / 96</gadget>
<output>9/16 = around 0.5625</output>
<result>D</result> | D | 0.5625 | If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 16? | {
"A": "1 / 4",
"B": "3 / 8",
"C": "1 / 2",
"D": "9 / 16",
"E": "3 / 4"
} | divide(add(divide(96, 2), divide(96, 16)), 96) | divide(n1,n3)|divide(n1,n4)|add(#0,#1)|divide(#2,n1)| | "i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 16 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 16 = not integer we can not forget multiples of 16 from 1 to 96 we have 6 numbers that are multiple of 16 therefore , 48 / 96 + 6 / 96 = 54 / 96 = 9 / 16 answer : d" | general |
math_qa__hxdkY184B8GJ4qUf | There was two trains from calcutta to kanyakumari one train is fast service travels with a speed 75km per hour another travels with a speed of 44km per hour the time taken to reach from calcutta to kanyakumari is 4hours less than the first train...find the distance b/w calcatta to kanyakumari Choose the correct choice from the following choices: A) 415.8 km B) 425.8 km C) 435.8 km D) 445.8 km E) 455.8 km | <gadget id="calculator">75 * 44</gadget>
<output>3_300</output>
<gadget id="calculator">4 * 3_300</gadget>
<output>13_200</output>
<gadget id="calculator">75 - 44</gadget>
<output>31</output>
<gadget id="calculator">13_200 / 31</gadget>
<output>13_200/31 = around 425.806452</output>
<result>B</result> | B | 425.8 | There was two trains from calcutta to kanyakumari one train is fast service travels with a speed 75km per hour another travels with a speed of 44km per hour the time taken to reach from calcutta to kanyakumari is 4hours less than the first train...find the distance b/w calcatta to kanyakumari | {
"A": "415.8 km",
"B": "425.8 km",
"C": "435.8 km",
"D": "445.8 km",
"E": "455.8 km"
} | divide(multiply(const_4, multiply(75, 44)), subtract(75, 44)) | multiply(n0,n1)|subtract(n0,n1)|multiply(#0,const_4)|divide(#2,#1) | let distance b / w calcutta to kanyakumari is = x km then eqn is x / 44 - x / 75 = 4 = > x * ( 75 - 44 ) = 4 * 75 * 44 = > x = 425.8 km answer : b | physics |
math_qa__UBETN5HlH5aRHU2n | In a group of 10 doctors, 3 doctors are only pediatricians; the others are surgeons or general practitioners - but not both. A team of 3 doctors is to be chosen which must have at least 1 pediatrician, how many different teams can be chosen? Pick one:
A) 85 B) 140 C) 60 D) 80 E) 75 | <gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>
<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">5_040 * 6</gadget>
<output>30_240</output>
<gadget id="calculator">3_628_800 / 30_240</gadget>
<output>120</output>
<gadget id="calculator">10 * 7</gadget>
<output>70</output>
<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<gadget id="calculator">120 - 35</gadget>
<output>85</output>
<result>A</result> | A | 85 | In a group of 10 doctors, 3 doctors are only pediatricians; the others are surgeons or general practitioners - but not both. A team of 3 doctors is to be chosen which must have at least 1 pediatrician, how many different teams can be chosen? | {
"A": "85",
"B": "140",
"C": "60",
"D": "80",
"E": "75"
} | subtract(divide(factorial(10), multiply(factorial(subtract(10, 3)), factorial(3))), divide(multiply(10, subtract(10, 3)), const_2)) | factorial(n0)|factorial(n1)|subtract(n0,n1)|factorial(#2)|multiply(n0,#2)|divide(#4,const_2)|multiply(#3,#1)|divide(#0,#6)|subtract(#7,#5) | the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 10 r = 3 so , total teams is 10 c 3 = 10 ! / ( 3 ! ( 10 - 3 ) ! ) = 120 , and n = 10 - 3 = 7 r = 3 for teams without a pediatrician is 7 c 3 = 7 ! / ( 3 ! ( 7 - 3 ) ! ) = 35 , so , teams with at least 1 pediatrician = 120 - 35 = 85 answer : a | other |
math_qa__u0nTPdHSaHCTYcFM | If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle? Choose the correct choice from the following options:
A) 76 B) 27 C) 19 D) 50 E) 11 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">21 - 12</gadget>
<output>9</output>
<gadget id="calculator">9 + 7</gadget>
<output>16</output>
<gadget id="calculator">9 + 16</gadget>
<output>25</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<result>D</result> | D | 50 | If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle? | {
"A": "76",
"B": "27",
"C": "19",
"D": "50",
"E": "11"
} | multiply(add(subtract(multiply(add(3, 4), 3), multiply(4, 3)), add(subtract(multiply(add(3, 4), 3), multiply(4, 3)), add(3, 4))), const_2) | add(n0,n1)|multiply(n0,n1)|multiply(n1,#0)|subtract(#2,#1)|add(#0,#3)|add(#4,#3)|multiply(#5,const_2)| | "let x and y be the length and breadth of the rectangle respectively . then , x - 4 = y + 3 or x - y = 7 - - - - ( i ) area of the rectangle = xy ; area of the square = ( x - 4 ) ( y + 3 ) ( x - 4 ) ( y + 3 ) = xy < = > 3 x - 4 y = 12 - - - - ( ii ) solving ( i ) and ( ii ) , we get x = 16 and y = 9 . perimeter of the rectangle = 2 ( x + y ) = [ 2 ( 16 + 9 ) ] cm = 50 cm . answer : d" | geometry |
math_qa__o5Tx676AVvpSjeQt | A football player scores 4 goals in his fifth match thus increasing his average goals score by 0.2. The total number of goals in his 5 matches would be
Choose the correct answer
A) 4 B) 6 C) 8 D) 10 E) 16 | <gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 0.2</gadget>
<output>4</output>
<gadget id="calculator">16 - 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<result>E</result> | E | 16 | A football player scores 4 goals in his fifth match thus increasing his average goals score by 0.2. The total number of goals in his 5 matches would be | {
"A": "4",
"B": "6",
"C": "8",
"D": "10",
"E": "16"
} | add(subtract(multiply(const_4, 4), multiply(multiply(const_4, 5), 0.2)), 4) | multiply(n0,const_4)|multiply(n2,const_4)|multiply(n1,#1)|subtract(#0,#2)|add(n0,#3)| | "while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer e = 16 goals if . . . . total goals = 16 goals 5 th game = 4 goals 1 st 4 games = 12 goals avg . for 1 st 4 games = 12 / 4 = 3 goal / game avg . for all 5 games = 6 / 5 = 3.2 goals / game this is an exact match for what we ' re told in the prompt , so answer e must be the answer ." | general |
math_qa__C7qFsTGxbWSn4YKO | If 8 men do a work in 80 days, in how many days will 20 men do it? Select the correct option:
A) 18 days
B) 32 days
C) 42 days
D) 48 days
E) 44 days | <gadget id="calculator">8 * 80</gadget>
<output>640</output>
<gadget id="calculator">640 / 20</gadget>
<output>32</output>
<result>B</result> | B | 32 | If 8 men do a work in 80 days, in how many days will 20 men do it? | {
"A": "18 days",
"B": "32 days",
"C": "42 days",
"D": "48 days",
"E": "44 days"
} | divide(multiply(8, 80), 20) | multiply(n0,n1)|divide(#0,n2)| | "8 * 80 = 20 * x x = 32 days answer : b" | physics |
math_qa__sMhg4IdQrpSdIsmy | In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 18 percent of revenues. The profits in 2009 were what percent of the profits in 2008? Pick:
A) 80 %
B) 105 %
C) 120 %
D) 144 %
E) 138 % | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">18 * (4/5)</gadget>
<output>72/5 = around 14.4</output>
<gadget id="calculator">(72/5) / 10</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">(36/25) * 100</gadget>
<output>144</output>
<result>D</result> | D | 144 | In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 18 percent of revenues. The profits in 2009 were what percent of the profits in 2008? | {
"A": "80 %",
"B": "105 %",
"C": "120 %",
"D": "144 %",
"E": "138 %"
} | multiply(divide(multiply(18, subtract(const_1, divide(20, const_100))), 10), const_100) | divide(n3,const_100)|subtract(const_1,#0)|multiply(n4,#1)|divide(#2,n1)|multiply(#3,const_100)| | "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,18 = 18 / 100 x = 80 * 18 / 100 x = 14.4 14.4 / 10 = 1,44 = 144 % , answer d" | gain |
math_qa__PzFoHH3IUHTAnlNr | A courtyard is 30 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is? Choose the correct choice:
A) 22877
B) 24000
C) 20000
D) 27999
E) 17799 | <gadget id="calculator">30 * 100</gadget>
<output>3_000</output>
<gadget id="calculator">16 * 100</gadget>
<output>1_600</output>
<gadget id="calculator">3_000 * 1_600</gadget>
<output>4_800_000</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">4_800_000 / 200</gadget>
<output>24_000</output>
<result>B</result> | B | 24,000 | A courtyard is 30 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is? | {
"A": "22877",
"B": "24000",
"C": "20000",
"D": "27999",
"E": "17799"
} | divide(multiply(multiply(30, const_100), multiply(16, const_100)), multiply(20, 10)) | multiply(n0,const_100)|multiply(n1,const_100)|multiply(n2,n3)|multiply(#0,#1)|divide(#3,#2)| | "number of bricks = courtyard area / 1 brick area = ( 3000 × 1600 / 20 × 10 ) = 24000 answer : b" | physics |
math_qa__QaUIXKgZxvKNKijQ | What Is The Smallest Positive Integer That Leaves A Remainder Of 1 When Divided By 2, Remainder Of 2 When Divided By 3, A Remainder Of 3 When Divided By 4, And A Remainder Of 9 When Divided By 10?
Pick one
A) 58 B) 59 C) 60 D) 61 E) 62 | <gadget id="calculator">lcm(2, 3)</gadget>
<output>6</output>
<gadget id="calculator">lcm(6, 4)</gadget>
<output>12</output>
<gadget id="calculator">lcm(12, 10)</gadget>
<output>60</output>
<gadget id="calculator">60 - 1</gadget>
<output>59</output>
<result>B</result> | B | 59 | What Is The Smallest Positive Integer That Leaves A Remainder Of 1 When Divided By 2, Remainder Of 2 When Divided By 3, A Remainder Of 3 When Divided By 4, And A Remainder Of 9 When Divided By 10? | {
"A": "58",
"B": "59",
"C": "60",
"D": "61",
"E": "62"
} | subtract(lcm(lcm(lcm(2, 3), 4), 10), const_1) | lcm(n1,n3)|lcm(n5,#0)|lcm(n7,#1)|subtract(#2,const_1) | remainder of 1 when divided by 2 : ( 2 - 1 = 1 ) remainder of 2 when divided by 3 : ( 3 - 2 = 1 ) remainder of 3 when divided by 4 : ( 4 - 3 = 1 ) remainder of 9 when divided by 10 : ( 2 - 1 = 1 ) so n + 1 should be divisible by 23 , 410 ( where n is desired number ) l . c . m . of 23 , 410 = 60 ( = n + 1 ) n = 59 answer : b | general |
math_qa__P2LS03Vx63GtXdPQ | Tim's garden is shaped like a square whose side is 28 meters. What's the length of the fence which surrounds the garden? Choose the correct option.
A) 110 meters B) 111 meters C) 112 meters D) 113 meters E) 114 meters | <gadget id="calculator">4 * 28</gadget>
<output>112</output>
<result>C</result> | C | 112 | Tim's garden is shaped like a square whose side is 28 meters. What's the length of the fence which surrounds the garden? | {
"A": "110 meters",
"B": "111 meters",
"C": "112 meters",
"D": "113 meters",
"E": "114 meters"
} | square_perimeter(28) | square_perimeter(n0) | solution : all sides of the square are equal . the length of the fence is 4 times the side . p = 4 × 28 = 112 meters answer c | physics |
math_qa__Fiqr7p3IHVV4Ozld | Find the fraction which has the same ratio to 2/6 that 3/4 has to 1/2 Options: A) 1 / 2 B) 2 / 5 C) 6 / 8 D) 9 / 4 E) 7 / 5 | <gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(3/4) / (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">2 / 6</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(3/2) * (1/3)</gadget>
<output>1/2 = around 0.5</output>
<result>A</result> | A | 0.5 | Find the fraction which has the same ratio to 2/6 that 3/4 has to 1/2 | {
"A": "1 / 2",
"B": "2 / 5",
"C": "6 / 8",
"D": "9 / 4",
"E": "7 / 5"
} | multiply(divide(divide(3, 4), divide(1, 2)), divide(2, 6)) | divide(n2,n3)|divide(n4,n5)|divide(n0,n1)|divide(#0,#1)|multiply(#3,#2)| | "p : 2 / 6 = 3 / 4 : 1 / 2 as the product of the means is equal to the product of the extremes . p * 1 / 2 = 2 / 6 * 3 / 4 p * 1 / 2 = 6 / 24 p = 1 / 2 = > p = 1 / 2 answer : a" | other |
math_qa__jLt5HKkGG7NDJEbh | If 13 lions can kill 13 deers in 13 minutes how long will it take 100 lions to kill 100 deers? Choices:
A) 1 minutes B) 13 minute C) 100 minutes D) 10000 minutes E) 1000 minutes | <gadget id="calculator">13 / 13</gadget>
<output>1</output>
<gadget id="calculator">1 * 13</gadget>
<output>13</output>
<result>B</result> | B | 13 | If 13 lions can kill 13 deers in 13 minutes how long will it take 100 lions to kill 100 deers? | {
"A": "1 minutes",
"B": "13 minute",
"C": "100 minutes",
"D": "10000 minutes",
"E": "1000 minutes"
} | multiply(divide(13, 13), 13) | divide(n0,n0)|multiply(n0,#0)| | "we can try the logic of time and work , our work is to kill the deers so 13 ( lions ) * 13 ( min ) / 13 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 13 answer : b" | physics |
math_qa__X2P95PN0e1Fwaesh | If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $66, how much does one shirt cost?
Choose the correct option: A) $ 10 B) $ 12 C) $ 13.20 D) $ 15 E) $ 16.80 | <gadget id="calculator">66 * 3</gadget>
<output>198</output>
<gadget id="calculator">69 * 2</gadget>
<output>138</output>
<gadget id="calculator">198 - 138</gadget>
<output>60</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">9 - 4</gadget>
<output>5</output>
<gadget id="calculator">60 / 5</gadget>
<output>12</output>
<result>B</result> | B | 12 | If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $66, how much does one shirt cost? | {
"A": "$ 10",
"B": "$ 12",
"C": "$ 13.20",
"D": "$ 15",
"E": "$ 16.80"
} | divide(subtract(multiply(66, 3), multiply(69, 2)), subtract(multiply(3, 3), multiply(2, 2))) | multiply(n0,n5)|multiply(n1,n2)|multiply(n0,n0)|multiply(n1,n1)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)| | "let the price of one shirt be ss and of jeans be j : 3 j + 2 s = 69 2 j + 3 s = 66 subtracting the second from the first gives : j − s = 3 or j = s + 3 plug j in either of the equations and solve for s , which is $ 12 answer : b ." | general |
math_qa__xutZAMYTjmDkrTRf | Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 30 minutes earlier than usual. How much time did the man spend walking? Choose the correct option.
A) 45 minutes
B) 50 minutes
C) 40 minutes
D) 55 minutes
E) 35 minutes | <gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">60 - 15</gadget>
<output>45</output>
<result>A</result> | A | 45 | Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 30 minutes earlier than usual. How much time did the man spend walking? | {
"A": "45 minutes",
"B": "50 minutes",
"C": "40 minutes",
"D": "55 minutes",
"E": "35 minutes"
} | subtract(const_60, divide(30, const_2)) | divide(n0,const_2)|subtract(const_60,#0)| | "as they arrived 30 minutes earlier than usual , they saved 30 minutes on round trip from home to station ( home - station - home ) - - > 15 minutes in each direction ( home - station ) - - > wife meets husband 15 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 15 minutes = 45 minutes . answer : a" | physics |
math_qa__Zo8TQfUKe0BKb9SR | The speed of a car is 145 km in the first hour and 60 km in the second hour. What is the average speed of the car? Choose the correct choice from the following answers: A) 89 kmph B) 92 kmph C) 75 kmph D) 102.5 kmph E) 77 kmph | <gadget id="calculator">145 + 60</gadget>
<output>205</output>
<gadget id="calculator">205 / 2</gadget>
<output>205/2 = around 102.5</output>
<result>D</result> | D | 102.5 | The speed of a car is 145 km in the first hour and 60 km in the second hour. What is the average speed of the car? | {
"A": "89 kmph",
"B": "92 kmph",
"C": "75 kmph",
"D": "102.5 kmph",
"E": "77 kmph"
} | divide(add(145, 60), const_2) | add(n0,n1)|divide(#0,const_2)| | "s = ( 145 + 60 ) / 2 = 102.5 kmph d" | physics |
math_qa__CC7hPD8dnQp0zzBv | The greatest number which on dividing 1657 and 2037 leaves remainders 10 and 7 respectively, is:
Answers.
A) 123 B) 1 C) 235 D) 305 E) 505 | <gadget id="calculator">2_037 - 7</gadget>
<output>2_030</output>
<gadget id="calculator">1_657 - 10</gadget>
<output>1_647</output>
<gadget id="calculator">gcd(2_030, 1_647)</gadget>
<output>1</output>
<result>B</result> | B | 1 | The greatest number which on dividing 1657 and 2037 leaves remainders 10 and 7 respectively, is: | {
"A": "123",
"B": "1",
"C": "235",
"D": "305",
"E": "505"
} | gcd(subtract(2037, 7), subtract(1657, 10)) | subtract(n1,n3)|subtract(n0,n2)|gcd(#0,#1)| | "explanation : required number = h . c . f . of ( 1657 - 10 ) and ( 2037 - 7 ) = h . c . f . of 1647 and 2030 = 1 . answer : b" | general |
math_qa__xhpY7cqUpF8OwTMl | A grocer has 400 pounds of coffee in stock, 40 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated? Choose the correct choice from the following:
A) 28 % B) 30 % C) 32 % D) 34 % E) 44 % | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 400</gadget>
<output>160</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">100 * (3/5)</gadget>
<output>60</output>
<gadget id="calculator">160 + 60</gadget>
<output>220</output>
<gadget id="calculator">400 + 100</gadget>
<output>500</output>
<gadget id="calculator">220 / 500</gadget>
<output>11/25 = around 0.44</output>
<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>E</result> | E | 44 | A grocer has 400 pounds of coffee in stock, 40 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated? | {
"A": "28 %",
"B": "30 %",
"C": "32 %",
"D": "34 %",
"E": "44 %"
} | multiply(divide(add(multiply(divide(40, 100), 400), multiply(100, divide(60, 100))), add(400, 100)), 100) | add(n0,n2)|divide(n1,n2)|divide(n3,n2)|multiply(n0,#1)|multiply(n2,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,n2)| | "1 . 40 % of 400 = 160 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 220 pounds of decaffeinated out of 500 pounds , that means 220 / 500 * 100 % = 44 % . the correct answer is e ." | gain |
math_qa__F4XxDTEZ2eX0zMFg | If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 21?
Options: A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">21 / 4</gadget>
<output>21/4 = around 5.25</output>
<gadget id="calculator">floor(21/4)</gadget>
<output>5</output>
<result>E</result> | E | 5 | If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 21? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | floor(divide(21, subtract(5, const_1))) | subtract(n0,const_1)|divide(n1,#0)|floor(#1)| | "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 21 . then 4 n < 21 and n < 5.25 . the largest possible integer is n = 5 . the answer is e ." | general |
math_qa__tpNsfD7F4gOePBPV | The average runs of a cricket player of 13 innings was 22. How many runs must he make in his next innings so as to increase his average of runs by 5?
Answers: A) 92 B) 42 C) 64 D) 76 E) 84 | <gadget id="calculator">13 + 1</gadget>
<output>14</output>
<gadget id="calculator">22 + 5</gadget>
<output>27</output>
<gadget id="calculator">14 * 27</gadget>
<output>378</output>
<gadget id="calculator">22 * 13</gadget>
<output>286</output>
<gadget id="calculator">378 - 286</gadget>
<output>92</output>
<result>A</result> | A | 92 | The average runs of a cricket player of 13 innings was 22. How many runs must he make in his next innings so as to increase his average of runs by 5? | {
"A": "92",
"B": "42",
"C": "64",
"D": "76",
"E": "84"
} | subtract(multiply(add(13, const_1), add(22, 5)), multiply(22, 13)) | add(n0,const_1)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2) | explanation : average after 14 innings = 27 required number of runs = ( 27 * 14 ) – ( 22 * 13 ) = 378 – 286 = 92 answer a | general |
math_qa__xRp06efzHbqxEP19 | In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 20% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy? Choose the correct option: A) 22 % B) 23 % C) 24 % D) 25 % E) 27.5 % | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">22 / (4/5)</gadget>
<output>55/2 = around 27.5</output>
<result>E</result> | E | 27.5 | In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 20% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy? | {
"A": "22 %",
"B": "23 %",
"C": "24 %",
"D": "25 %",
"E": "27.5 %"
} | divide(22, divide(subtract(const_100, 20), const_100)) | subtract(const_100,n1)|divide(#0,const_100)|divide(n0,#1)| | "since 20 % of the customers who sample the candyare notcaught , then 80 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.80 = 0.22 ; { % of customers who sample candy } = 0.275 answer : e ." | gain |
math_qa__gjgXn97jfnAJy0di | 3 students appear at an examination of mathematics . the probability of their success are 1 / 2 , 1 / 4 , 1 / 5 respectively . find the probability of success of at least two . Select.
A) 1 / 60 B) 2 / 50 C) 9 / 40 D) 3 / 40 E) 4 / 50 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/2) * (1/4)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/8) * (1/5)</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">(1/2) * (1/5)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(1/10) * (3/4)</gadget>
<output>3/40 = around 0.075</output>
<gadget id="calculator">(3/40) + (1/10)</gadget>
<output>7/40 = around 0.175</output>
<gadget id="calculator">(1/4) * (1/5)</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/20) * (1/2)</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">(7/40) + (1/40)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/40) + (1/5)</gadget>
<output>9/40 = around 0.225</output>
<result>C</result> | C | 0.225 | 3 students appear at an examination of mathematics . the probability of their success are 1 / 2 , 1 / 4 , 1 / 5 respectively . find the probability of success of at least two . | {
"A": "1 / 60",
"B": "2 / 50",
"C": "9 / 40",
"D": "3 / 40",
"E": "4 / 50"
} | add(multiply(multiply(divide(1, 2), divide(1, 4)), divide(1, 5)), add(add(multiply(multiply(divide(1, 2), divide(1, 5)), subtract(1, divide(1, 4))), multiply(divide(1, 2), divide(1, 5))), multiply(multiply(divide(1, 4), divide(1, 5)), subtract(1, divide(1, 2))))) | divide(n1,n2)|divide(n1,n6)|divide(n1,n4)|multiply(#0,#1)|multiply(#2,#1)|multiply(#0,#2)|subtract(n1,#2)|subtract(n1,#0)|multiply(#3,#6)|multiply(#4,#7)|multiply(#1,#5)|add(#8,#3)|add(#11,#9)|add(#12,#10) | the probability of success of at least two students will involve the following possibilities . the first two students are successful , the last two students are successful , the first and third students are successful and all the three students are successful . therefore , the required probability = 1 / 2 x 1 / 4 x 4 / 5 + 1 / 4 x 1 / 5 x 1 / 2 + 1 / 2 x 1 / 5 x 3 / 4 + 1 / 2 x 1 / 4 x 1 / 5 = 9 / 40 answer : c | general |
math_qa__8Dw8s2NfgLcX9hXv | If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/2, then what is the value of abc/def ? Choices:
A) 27 / 4
B) 27 / 8
C) 3 / 4
D) 3 / 8
E) 1 / 4 | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<result>C</result> | C | 0.75 | If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/2, then what is the value of abc/def ? | {
"A": "27 / 4",
"B": "27 / 8",
"C": "3 / 4",
"D": "3 / 8",
"E": "1 / 4"
} | divide(multiply(3, 3), multiply(2, multiply(3, 2))) | multiply(n1,n1)|multiply(n1,n7)|multiply(n2,#1)|divide(#0,#2)| | "say a = 3 . then : a / b = 1 / 3 - - > b = 9 ; b / c = 2 - - > c = 9 / 2 ; c / d = 1 / 2 - - > d = 9 ; d / e = 3 - - > e = 3 ; e / f = 1 / 2 - - > f = 6 . abc / def = ( 3 * 9 * 9 / 2 ) / ( 9 * 3 * 6 ) = 3 / 4 . answer : c ." | general |
math_qa__XYqKwjtD2C7mlAnQ | The average of 7 consecutive numbers is 33. The highest of these numbers is: Select the correct option:
A) 28 B) 30 C) 33 D) 36 E) 28 | <gadget id="calculator">33 * 7</gadget>
<output>231</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">1 + 7</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">10 + 11</gadget>
<output>21</output>
<gadget id="calculator">231 - 21</gadget>
<output>210</output>
<gadget id="calculator">210 / 7</gadget>
<output>30</output>
<gadget id="calculator">30 + 6</gadget>
<output>36</output>
<result>D</result> | D | 36 | The average of 7 consecutive numbers is 33. The highest of these numbers is: | {
"A": "28",
"B": "30",
"C": "33",
"D": "36",
"E": "28"
} | add(divide(subtract(multiply(33, 7), add(add(add(add(const_1, add(add(add(add(add(const_1, const_2), const_1), const_1), const_1), const_1)), const_1), const_1), add(add(add(add(const_1, add(add(add(add(add(const_1, const_2), const_1), const_1), const_1), const_1)), const_1), const_1), const_1))), 7), add(add(add(add(const_1, const_2), const_1), const_1), const_1)) | add(const_1,const_2)|multiply(n0,n1)|add(#0,const_1)|add(#2,const_1)|add(#3,const_1)|add(#4,const_1)|add(#5,const_1)|add(#6,const_1)|add(#7,const_1)|add(#8,const_1)|add(#8,#9)|subtract(#1,#10)|divide(#11,n0)|add(#4,#12)| | "the average of 7 consecutive numbers will be the 4 th number which is given to be = 33 5 th number = 34 , 6 th number = 35 , 7 th number = 36 answer : d ." | general |
math_qa__N0sZuBvuWifEwzuV | In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/6. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life? Choose the correct answer: A) 116 B) 146 C) 152 D) 162 E) 170 | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 - (1/6)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">200 * (5/6)</gadget>
<output>500/3 = around 166.666667</output>
<gadget id="calculator">(500/3) * (5/6)</gadget>
<output>1_250/9 = around 138.888889</output>
<gadget id="calculator">(1_250/9) * (5/6)</gadget>
<output>3_125/27 = around 115.740741</output>
<result>A</result> | A | 116 | In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/6. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life? | {
"A": "116",
"B": "146",
"C": "152",
"D": "162",
"E": "170"
} | multiply(multiply(multiply(200, subtract(1, divide(1, 6))), subtract(1, divide(1, 6))), subtract(1, divide(1, 6))) | divide(n1,n2)|subtract(n1,#0)|multiply(n3,#1)|multiply(#2,#1)|multiply(#3,#1)| | "the probability of survival for each of the first 3 months of life is 1 - 1 / 6 = 5 / 6 , so of 200 newborn 200 * 5 / 6 * 5 / 6 * 5 / 6 = ~ 116 is expected to survive . answer : a ." | probability |
math_qa__PEsPUO4blGDg9Dhc | In what time will a train 50 m long cross an electric pole, it its speed be 144 km/hr?
Select the correct option.
A) 1.25 sec
B) 2.75 sec
C) 3.5 sec
D) 2.39 sec
E) 9.5 sec | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>
<gadget id="calculator">50 / 40</gadget>
<output>5/4 = around 1.25</output>
<result>A</result> | A | 1.25 | In what time will a train 50 m long cross an electric pole, it its speed be 144 km/hr? | {
"A": "1.25 sec",
"B": "2.75 sec",
"C": "3.5 sec",
"D": "2.39 sec",
"E": "9.5 sec"
} | divide(50, multiply(144, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | "speed = 144 * 5 / 18 = 40 m / sec time taken = 50 / 40 = 1.25 sec . answer : a" | physics |
math_qa__OgKVPWIO4bv5pQJU | A square carpet with an area 169 m2 must have 2 metres cut-off one of its edges in order to be a perfect fit for a rectangular room. What is the area of rectangular room?
Choose the correct choice from the following answers.
A) 180 m 2
B) 164 m 2
C) 152 m 2
D) 143 m 2
E) none of these | <gadget id="calculator">169 ** (1/2)</gadget>
<output>13</output>
<gadget id="calculator">13 - 2</gadget>
<output>11</output>
<gadget id="calculator">13 * 11</gadget>
<output>143</output>
<result>D</result> | D | 143 | A square carpet with an area 169 m2 must have 2 metres cut-off one of its edges in order to be a perfect fit for a rectangular room. What is the area of rectangular room? | {
"A": "180 m 2",
"B": "164 m 2",
"C": "152 m 2",
"D": "143 m 2",
"E": "none of these"
} | multiply(sqrt(169), subtract(sqrt(169), const_2)) | sqrt(n0)|subtract(#0,const_2)|multiply(#0,#1) | side of square carpet = √ area = √ 169 = 13 m after cutting of one side , measure of one side = 13 – 2 = 11 m and other side = 13 m ( remain same ) ∴ area of rectangular room = 13 × 11 = 143 m 2 answer d | geometry |
math_qa__UyJUzFgeOouBWilo | A number x is multiplied by 5, and this product is then divided by 7. If the positive square root of the result of these two operations equals x, what is the value of x if x≠0 ? Choose the correct choice from the following choices: A) 25 / 9 B) 9 / 5 C) 5 / 7 D) 3 / 5 E) 9 / 25 | <gadget id="calculator">5 / 7</gadget>
<output>5/7 = around 0.714286</output>
<result>C</result> | C | 0.714286 | A number x is multiplied by 5, and this product is then divided by 7. If the positive square root of the result of these two operations equals x, what is the value of x if x≠0 ? | {
"A": "25 / 9",
"B": "9 / 5",
"C": "5 / 7",
"D": "3 / 5",
"E": "9 / 25"
} | divide(5, 7) | divide(n0,n1)| | "sqrt ( 5 x / 7 ) to be perfect square x has to 5 / 7 ans : c" | general |
math_qa__LdfRoz6zAJ6Q630A | In a kilometer race, A beats B by 25 meters or 10 seconds. What time does A take to complete the race? Choose the correct choice from the following choices
A) 167 sec B) 190 sec C) 390 sec D) 716 sec E) 123 sec | <gadget id="calculator">1 * 1_000</gadget>
<output>1_000</output>
<gadget id="calculator">25 / 10</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">1_000 / (5/2)</gadget>
<output>400</output>
<gadget id="calculator">400 - 10</gadget>
<output>390</output>
<result>C</result> | C | 390 | In a kilometer race, A beats B by 25 meters or 10 seconds. What time does A take to complete the race? | {
"A": "167 sec",
"B": "190 sec",
"C": "390 sec",
"D": "716 sec",
"E": "123 sec"
} | subtract(divide(multiply(const_1, const_1000), divide(25, 10)), 10) | divide(n0,n1)|multiply(const_1,const_1000)|divide(#1,#0)|subtract(#2,n1)| | "time taken by b run 1000 meters = ( 1000 * 10 ) / 25 = 400 sec . time taken by a = 400 - 10 = 390 sec . answer : c" | physics |
math_qa__16VF7BevV0ClXvXz | Each week, Harry is paid x dollars per hour for the first 15 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
Choose one: A) 33 B) 36 C) 37 D) 38 E) 39 | <gadget id="calculator">40 + 2</gadget>
<output>42</output>
<gadget id="calculator">42 - 15</gadget>
<output>27</output>
<gadget id="calculator">27 / 1.5</gadget>
<output>18</output>
<gadget id="calculator">18 + 15</gadget>
<output>33</output>
<result>A</result> | A | 33 | Each week, Harry is paid x dollars per hour for the first 15 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? | {
"A": "33",
"B": "36",
"C": "37",
"D": "38",
"E": "39"
} | add(divide(subtract(add(40, 2), 15), 1.5), 15) | add(n2,n3)|subtract(#0,n0)|divide(#1,n1)|add(n0,#2) | 42 x = 15 x + 1.5 x ( h - 15 ) = = > 42 = 15 + 1.5 ( h - 15 ) = = > h - 15 = 27 / 1.5 = 18 = = > h = 33 answer is a | general |
math_qa__y6DLpTruAziTUtF3 | How many seconds will a train 100 meters long take to cross a bridge 160 meters long if the speed of the train is 36 kmph?
Choose the correct answer:
A) 26
B) 72
C) 25
D) 82
E) 27 | <gadget id="calculator">160 + 100</gadget>
<output>260</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">260 / 10</gadget>
<output>26</output>
<result>A</result> | A | 26 | How many seconds will a train 100 meters long take to cross a bridge 160 meters long if the speed of the train is 36 kmph? | {
"A": "26",
"B": "72",
"C": "25",
"D": "82",
"E": "27"
} | divide(add(160, 100), multiply(36, const_0_2778)) | add(n0,n1)|multiply(n2,const_0_2778)|divide(#0,#1)| | "explanation : d = 100 + 160 = 260 s = 36 * 5 / 18 = 10 mps t = 260 / 10 = 26 sec answer : option a" | physics |
math_qa__2D8AsniBxWx7nUcA | At a bank, the service charges for transactions were US Dollar 1 for every 5 transactions. The bank recently revised the charges to US Dollar 0.75 for every 3 transactions. By approximately what percent did the ratio of price to transactions increase from the previous charge? Pick.
A) 28 B) 24 C) 23 D) 22 E) 25 | <gadget id="calculator">0.75 / 3</gadget>
<output>0.25</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">0.25 / (1/5)</gadget>
<output>1.25</output>
<gadget id="calculator">1.25 * 100</gadget>
<output>125</output>
<gadget id="calculator">125 - 100</gadget>
<output>25</output>
<result>E</result> | E | 25 | At a bank, the service charges for transactions were US Dollar 1 for every 5 transactions. The bank recently revised the charges to US Dollar 0.75 for every 3 transactions. By approximately what percent did the ratio of price to transactions increase from the previous charge? | {
"A": "28",
"B": "24",
"C": "23",
"D": "22",
"E": "25"
} | subtract(multiply(divide(divide(0.75, 3), divide(1, 5)), const_100), const_100) | divide(n2,n3)|divide(n0,n1)|divide(#0,#1)|multiply(#2,const_100)|subtract(#3,const_100) | initial charge / transaction ratio = 1 / 5 = 3 / 15 revised charge / transaction ratio = . 75 / 3 = 3.75 / 15 answer : e | general |
math_qa__1SYk3CfOQxtZQgk4 | If m = 3^n, what is the greatest value of n for which m is a factor of 19! Choose the correct choice: A) 8 B) 10 C) 12 D) 14 E) 16 | <gadget id="calculator">19 / 3</gadget>
<output>19/3 = around 6.333333</output>
<gadget id="calculator">floor(19/3)</gadget>
<output>6</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">19 / 9</gadget>
<output>19/9 = around 2.111111</output>
<gadget id="calculator">floor(19/9)</gadget>
<output>2</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<result>A</result> | A | 8 | If m = 3^n, what is the greatest value of n for which m is a factor of 19! | {
"A": "8",
"B": "10",
"C": "12",
"D": "14",
"E": "16"
} | add(floor(divide(19, 3)), floor(divide(19, power(3, const_2)))) | divide(n1,n0)|power(n0,const_2)|divide(n1,#1)|floor(#0)|floor(#2)|add(#3,#4) | solution - consider multiples of 25 ! = > 3,6 , 9,12 , 15,18 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 - - - - count 3 ' s = 8 so answer is 8 answer : a | other |
math_qa__lzv6OOCnuee1vmff | A reduction of 15% in the price of oil enables a house wife to obtain 4kgs more for Rs.1200, what is the reduced price for kg?
Choices
A) 43 B) 55 C) 35 D) 45 E) 40 | <gadget id="calculator">1_200 * 15</gadget>
<output>18_000</output>
<gadget id="calculator">18_000 / 100</gadget>
<output>180</output>
<gadget id="calculator">180 / 4</gadget>
<output>45</output>
<result>D</result> | D | 45 | A reduction of 15% in the price of oil enables a house wife to obtain 4kgs more for Rs.1200, what is the reduced price for kg? | {
"A": "43",
"B": "55",
"C": "35",
"D": "45",
"E": "40"
} | divide(divide(multiply(1200, 15), const_100), 4) | multiply(n0,n2)|divide(#0,const_100)|divide(#1,n1)| | "1200 * ( 15 / 100 ) = 180 - - - - 4 ? - - - - 1 = > rs . 45 answer : d" | gain |
math_qa__Jn9eb4a26zs1p4u5 | How many real solutions does the equation x5 + 2x3 + 8x2 + 16 = 0 have?
Choose the correct choice from the following:
A) 0 B) 1 C) 2 D) 3 E) 5 | <gadget id="calculator">5 * 1</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<result>B</result> | B | 1 | How many real solutions does the equation x5 + 2x3 + 8x2 + 16 = 0 have? | {
"A": "0",
"B": "1",
"C": "2",
"D": "3",
"E": "5"
} | subtract(subtract(subtract(subtract(multiply(5, const_1), const_1), const_1), const_1), const_1) | multiply(n0,const_1)|subtract(#0,const_1)|subtract(#1,const_1)|subtract(#2,const_1)|subtract(#3,const_1) | note that x 5 + 2 x 3 + 8 x 2 + 16 = ( x 3 + 8 ) ( x 2 + 2 ) = ( x + 2 ) ( x 2 - 2 x + 4 ) ( x 2 + 2 ) . since the quadratic equations x 2 - 2 x + 4 = 0 and x 2 + 2 = 0 have no real solutions , the original equation has just one real solution , x = - 2 . correct answer b | general |
math_qa__p71g8BlmKaXFZY63 | A man is 20 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Choose the correct choice from the following choices
A) 23 years B) 22 years C) 21 years D) 20 years E) 18 years | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">20 - 2</gadget>
<output>18</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">18 / 1</gadget>
<output>18</output>
<result>E</result> | E | 18 | A man is 20 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son? | {
"A": "23 years",
"B": "22 years",
"C": "21 years",
"D": "20 years",
"E": "18 years"
} | divide(subtract(20, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | "let present age of the son = x years then , present age the man = ( x + 20 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 20 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 18 answer : e" | general |
math_qa__Oc10lU6MVDif6R2Q | Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 8 days. In how many days Peter complete the work separately.
Choices:
A) 21
B) 24
C) 20
D) 25
E) 30 | <gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">12 * (1/20)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">8 / (2/5)</gadget>
<output>20</output>
<result>C</result> | C | 20 | Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 8 days. In how many days Peter complete the work separately. | {
"A": "21",
"B": "24",
"C": "20",
"D": "25",
"E": "30"
} | divide(8, subtract(const_1, multiply(12, divide(const_1, 20)))) | divide(const_1,n0)|multiply(n1,#0)|subtract(const_1,#1)|divide(n2,#2)| | "together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 8 days which means that the whole job ( 1 ) can be completed in x days . x = 8 / ( 8 / 20 ) = 20 c" | physics |
math_qa__8ygnl1JdV9IBQVdy | Jack rode his bicycle at an average speed of 5 mph for some time and then at an average speed of 15 mph for the rest of the journey. If he made no stops during the trip, and his average speed for the entire journey was 10 miles per hour, for what fraction of the total time did he ride at 15 mph? Choose the correct choice from the following choices.
A) 1 / 5 B) 1 / 3 C) 2 / 3 D) 2 / 5 E) 1 / 2 | <gadget id="calculator">15 / 15</gadget>
<output>1</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<result>E</result> | E | 0.5 | Jack rode his bicycle at an average speed of 5 mph for some time and then at an average speed of 15 mph for the rest of the journey. If he made no stops during the trip, and his average speed for the entire journey was 10 miles per hour, for what fraction of the total time did he ride at 15 mph? | {
"A": "1 / 5",
"B": "1 / 3",
"C": "2 / 3",
"D": "2 / 5",
"E": "1 / 2"
} | divide(divide(15, 15), const_2) | divide(n1,n1)|divide(#0,const_2) | we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . the average speed for the entire journey is 10 mph ; so , he rode at 5 mph and 15 mph for an equal duration of time . difference is 5 and 5 , respectively . 5 - - - - 10 - - - - 15 this shows that you can divide the entire journey into 2 equal parts . thus , 1 / 2 of the journey he rode at 10 mph , and 1 / 2 of the journey he rode at 15 mph . answer : e | physics |
math_qa__rYXK7vfgqY0ZvAv2 | The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 85 kg. What is the weight of the new person? Options: A) 75 kg B) 85 kg C) 95 kg D) 65 kg E) 105 kg | <gadget id="calculator">2.5 * 8</gadget>
<output>20</output>
<gadget id="calculator">20 + 85</gadget>
<output>105</output>
<result>E</result> | E | 105 | The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 85 kg. What is the weight of the new person? | {
"A": "75 kg",
"B": "85 kg",
"C": "95 kg",
"D": "65 kg",
"E": "105 kg"
} | add(multiply(2.5, 8), 85) | multiply(n0,n1)|add(n2,#0)| | "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 85 + 20 ) kg = 105 kg the answer is e ." | general |
math_qa__AyMpamzJDnU5jPdW | The average of 10numbers is 60. Out of 10numbers the average of first 6no. is 68, and last 6numbers is 75 then find 7th number? Choose the correct choice from the following options: A) 78 B) 65 C) 258 D) 62 E) 48 | <gadget id="calculator">6 * 68</gadget>
<output>408</output>
<gadget id="calculator">6 * 75</gadget>
<output>450</output>
<gadget id="calculator">408 + 450</gadget>
<output>858</output>
<gadget id="calculator">10 * 60</gadget>
<output>600</output>
<gadget id="calculator">858 - 600</gadget>
<output>258</output>
<result>C</result> | C | 258 | The average of 10numbers is 60. Out of 10numbers the average of first 6no. is 68, and last 6numbers is 75 then find 7th number? | {
"A": "78",
"B": "65",
"C": "258",
"D": "62",
"E": "48"
} | subtract(add(multiply(6, 68), multiply(6, 75)), multiply(10, 60)) | multiply(n3,n4)|multiply(n3,n6)|multiply(n0,n1)|add(#0,#1)|subtract(#3,#2)| | "7 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 68 + 6 * 75 - 10 * 60 = 258 answer is c" | general |
math_qa__svHtpEtA8KiO3m4F | For a certain exam,a score of 42 was 5 standard deviations below mean and a score of 67 was 2.5 standard deviations above mean.What was the mean score for the exam? Choose one.
A) 74 B) 76 C) 78 D) 58.67 E) 82.2 | <gadget id="calculator">42 * 2.5</gadget>
<output>105</output>
<gadget id="calculator">67 * 5</gadget>
<output>335</output>
<gadget id="calculator">105 + 335</gadget>
<output>440</output>
<gadget id="calculator">5 + 2.5</gadget>
<output>7.5</output>
<gadget id="calculator">440 / 7.5</gadget>
<output>58.666667</output>
<result>D</result> | D | 58.67 | For a certain exam,a score of 42 was 5 standard deviations below mean and a score of 67 was 2.5 standard deviations above mean.What was the mean score for the exam? | {
"A": "74",
"B": "76",
"C": "78",
"D": "58.67",
"E": "82.2"
} | divide(add(multiply(42, 2.5), multiply(67, 5)), add(5, 2.5)) | add(n1,n3)|multiply(n0,n3)|multiply(n1,n2)|add(#1,#2)|divide(#3,#0)| | "mean - 5 sd = 42 mean + 2.5 sd = 67 by solving above equations we get , sd ( absolute value ) = 3.33 mean = 58.67 ans . d" | general |
math_qa__gUmILBw6Rv5PhdJA | A cistern 4 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface? Choose the correct answer.
A) 28 B) 32 C) 36 D) 40 E) 44 | <gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">4 * (5/4)</gadget>
<output>5</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">16 + 10</gadget>
<output>26</output>
<gadget id="calculator">26 + 10</gadget>
<output>36</output>
<result>C</result> | C | 36 | A cistern 4 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface? | {
"A": "28",
"B": "32",
"C": "36",
"D": "40",
"E": "44"
} | add(add(multiply(4, 4), multiply(const_2, multiply(4, add(1, divide(25, const_100))))), multiply(const_2, multiply(4, add(1, divide(25, const_100))))) | divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|multiply(#3,const_2)|multiply(#4,const_2)|add(#1,#5)|add(#7,#6)| | "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 4 x 1.25 ) + 4 x 4 ] = 36 the answer is c ." | physics |
math_qa__RVGhoxcnBS27IGxw | Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $111 dollar, which she typically uses for gifts and charitable causes. What is Jill’s net monthly salary? Choices:
A) $ 2400 B) $ 3200 C) $ 6000 D) $ 6400 E) $ 3700 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">100 * 5</gadget>
<output>500</output>
<gadget id="calculator">30 + 20</gadget>
<output>50</output>
<gadget id="calculator">50 + 35</gadget>
<output>85</output>
<gadget id="calculator">100 - 85</gadget>
<output>15</output>
<gadget id="calculator">111 / 15</gadget>
<output>37/5 = around 7.4</output>
<gadget id="calculator">500 * (37/5)</gadget>
<output>3_700</output>
<result>E</result> | E | 3,700 | Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $111 dollar, which she typically uses for gifts and charitable causes. What is Jill’s net monthly salary? | {
"A": "$ 2400",
"B": "$ 3200",
"C": "$ 6000",
"D": "$ 6400",
"E": "$ 3700"
} | multiply(multiply(const_100, add(const_3, const_2)), divide(111, subtract(const_100, add(add(30, 20), 35)))) | add(n0,n1)|add(const_2,const_3)|add(n2,#0)|multiply(#1,const_100)|subtract(const_100,#2)|divide(n3,#4)|multiply(#5,#3)| | "let x be the monthly salary 15 % of 1 / 5 * x = 111 x = 3700 answer e" | gain |
math_qa__9yonVXAr7bqxnkXy | Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 4 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?
Answers
A) 6 B) 7 C) 8 D) 9 E) 10 | <gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/12) + (1/15)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 4</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 15</gadget>
<output>6</output>
<result>A</result> | A | 6 | Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 4 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off? | {
"A": "6",
"B": "7",
"C": "8",
"D": "9",
"E": "10"
} | multiply(subtract(const_1, multiply(add(divide(const_1, 12), divide(const_1, 15)), const_4)), 15) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(#2,const_4)|subtract(const_1,#3)|multiply(n1,#4) | let x be the total time it takes for the cistern to fill . 4 / 12 + x / 15 = 1 x / 15 = 2 / 3 x = 10 after the first pipe is turned off , it takes 6 more minutes to fill the cistern . the answer is a . | physics |
math_qa__KXhLSSOwV0fqNd2a | The edge of a cube is 5a cm. Find its surface? Choose the correct choice from the following answers
A) 150 a 2 cm 2
B) 170 a 2 cm 2
C) 125 a 2 cm 2
D) 175 a 2 cm 2
E) 120 a 2 cm 2 | <gadget id="calculator">6 * (5 ** 2)</gadget>
<output>150</output>
<result>A</result> | A | 150 | The edge of a cube is 5a cm. Find its surface? | {
"A": "150 a 2 cm 2",
"B": "170 a 2 cm 2",
"C": "125 a 2 cm 2",
"D": "175 a 2 cm 2",
"E": "120 a 2 cm 2"
} | surface_cube(5) | surface_cube(n0)| | "6 a 2 = 6 * 5 a * 5 a = 150 a 2 answer : a" | geometry |
math_qa__z1wuFSpzRYDqpjDn | 15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container Q? Options.
A) a : 45 B) b : 25 C) c : 37.5 D) d : 36 E) e : 42 | <gadget id="calculator">9 + 16</gadget>
<output>25</output>
<gadget id="calculator">9 / 25</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) ** (1/2)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">15 / (2/5)</gadget>
<output>75/2 = around 37.5</output>
<result>C</result> | C | 37.5 | 15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container Q? | {
"A": "a : 45",
"B": "b : 25",
"C": "c : 37.5",
"D": "d : 36",
"E": "e : 42"
} | divide(15, subtract(const_1, sqrt(divide(9, add(9, 16))))) | add(n2,n3)|divide(n2,#0)|sqrt(#1)|subtract(const_1,#2)|divide(n0,#3)| | "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ." | general |
math_qa__8B6Lh6QrhJu2iGkD | A retailer buys a radio for Rs 225. His overhead expenses are Rs 28. He sellis the radio for Rs 300. The profit percent of the retailer is Choose one.
A) 10 %
B) 50 %
C) 25 %
D) 52 %
E) 18.5 % | <gadget id="calculator">225 + 28</gadget>
<output>253</output>
<gadget id="calculator">300 / 253</gadget>
<output>300/253 = around 1.185771</output>
<gadget id="calculator">(300/253) * 100</gadget>
<output>30_000/253 = around 118.577075</output>
<gadget id="calculator">(30_000/253) - 100</gadget>
<output>4_700/253 = around 18.577075</output>
<result>E</result> | E | 18.5 | A retailer buys a radio for Rs 225. His overhead expenses are Rs 28. He sellis the radio for Rs 300. The profit percent of the retailer is | {
"A": "10 %",
"B": "50 %",
"C": "25 %",
"D": "52 %",
"E": "18.5 %"
} | subtract(multiply(divide(300, add(225, 28)), const_100), const_100) | add(n0,n1)|divide(n2,#0)|multiply(#1,const_100)|subtract(#2,const_100)| | "explanation : cost price = ( 225 + 28 ) = 253 sell price = 300 gain = ( 47 / 253 ) * 100 = 18.5 % . answer : e" | gain |
math_qa__FzLnX67z90Y3KPaX | Two parallel sides of a trapezium are 4 cm and 5 cm respectively. The perpendicular distance between the parallel sides is 6 cm. Find the area of the trapezium. Choose the correct choice from the following choices:
A) 24 cm 2
B) 25 cm 2
C) 26 cm 2
D) 27 cm 2
E) 28 cm 2 | <gadget id="calculator">4 + 5</gadget>
<output>9</output>
<gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">(9/2) * 6</gadget>
<output>27</output>
<result>D</result> | D | 27 | Two parallel sides of a trapezium are 4 cm and 5 cm respectively. The perpendicular distance between the parallel sides is 6 cm. Find the area of the trapezium. | {
"A": "24 cm 2",
"B": "25 cm 2",
"C": "26 cm 2",
"D": "27 cm 2",
"E": "28 cm 2"
} | multiply(divide(add(4, 5), const_2), 6) | add(n0,n1)|divide(#0,const_2)|multiply(n2,#1) | area of trapezium when height and two parallel sides are given = 1 / 2 × h × ( a + b ) = 1 / 2 x 6 x ( 4 + 5 ) = 27 cm 2 answer d | physics |
math_qa__5gtMnZq1Fvn1zl6D | A ring x of diameter 16 inches is placed inside another ring y of diameter of 18 inches. How much fraction of the ring x surface is not covered by the ring y?
Choose one
A) 13 / 15 B) 12 / 4 C) 16 / 17 D) 22 / 16 E) 17 / 81 | <gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">pi * (9 ** 2)</gadget>
<output>81*pi = around 254.469005</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">pi * (8 ** 2)</gadget>
<output>64*pi = around 201.06193</output>
<gadget id="calculator">(81*pi) - (64*pi)</gadget>
<output>17*pi = around 53.407075</output>
<gadget id="calculator">(17*pi) / (81*pi)</gadget>
<output>17/81 = around 0.209877</output>
<result>E</result> | E | 0.209877 | A ring x of diameter 16 inches is placed inside another ring y of diameter of 18 inches. How much fraction of the ring x surface is not covered by the ring y? | {
"A": "13 / 15",
"B": "12 / 4",
"C": "16 / 17",
"D": "22 / 16",
"E": "17 / 81"
} | divide(subtract(circle_area(divide(18, const_2)), circle_area(divide(16, const_2))), circle_area(divide(18, const_2))) | divide(n1,const_2)|divide(n0,const_2)|circle_area(#0)|circle_area(#1)|subtract(#2,#3)|divide(#4,#2) | the questions asks us to find the surface which is not covered by the ring x i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the ring x = pi * r ^ 2 , where r = 8 = > pi * 64 area of the ring y = pi * 81 surface not covered by the ring x = pi * 81 - pi * 64 = pi * 17 fraction of ring y ' s surface is not covered by a ring x = pi * 17 / total area of the ring y = > pi * 17 / pi * 81 17 / 81 answer e | geometry |
math_qa__GuSz5pOxBZsTD3Qs | the smallest number which when diminished by 3 is divisible by 21 , 2836 and 45 is . . . Choose the correct choice from the following
A) 829 B) 869 C) 859 D) 4320 E) 427 | <gadget id="calculator">21 * 45</gadget>
<output>945</output>
<gadget id="calculator">945 / 2</gadget>
<output>945/2 = around 472.5</output>
<gadget id="calculator">45 - 10</gadget>
<output>35</output>
<gadget id="calculator">(945/2) - 35</gadget>
<output>875/2 = around 437.5</output>
<result>E</result> | E | 427 | the smallest number which when diminished by 3 is divisible by 21 , 2836 and 45 is . . . | {
"A": "829",
"B": "869",
"C": "859",
"D": "4320",
"E": "427"
} | subtract(divide(multiply(21, 45), const_2), subtract(45, const_10)) | multiply(n1,n3)|subtract(n3,const_10)|divide(#0,const_2)|subtract(#2,#1) | 427 answer : e | general |
math_qa__BHPCw840iAZ1bK4u | If 45% of z is 96% of y and y is 75% of x, what percent of x is z? Answers
A) 200
B) 160
C) 100
D) 65
E) 50 | <gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">96 / 100</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">(9/20) / (24/25)</gadget>
<output>15/32 = around 0.46875</output>
<gadget id="calculator">(3/4) / (15/32)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) * 100</gadget>
<output>160</output>
<result>B</result> | B | 160 | If 45% of z is 96% of y and y is 75% of x, what percent of x is z? | {
"A": "200",
"B": "160",
"C": "100",
"D": "65",
"E": "50"
} | multiply(divide(divide(75, const_100), divide(divide(45, const_100), divide(96, const_100))), const_100) | divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|divide(#1,#2)|divide(#0,#3)|multiply(#4,const_100)| | "( 45 / 100 ) z = ( 96 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 96 / 100 ) * ( 3 / 4 ) x i . e . z = ( 96 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1.6 ) x = ( 160 / 100 ) x i . e . z is 160 % of x answer : option b" | gain |
math_qa__XlunwLTg0TlvBrjR | The area of a triangle is with base 4.5m and height 6m?
Select the correct option:
A) 11 m 2 B) 10 m 2 C) 13.5 m 2 D) 19 m 2 E) 12.5 m 2 | <gadget id="calculator">(4.5 * 6) / 2</gadget>
<output>13.5</output>
<result>C</result> | C | 13.5 | The area of a triangle is with base 4.5m and height 6m? | {
"A": "11 m 2",
"B": "10 m 2",
"C": "13.5 m 2",
"D": "19 m 2",
"E": "12.5 m 2"
} | triangle_area(4.5, 6) | triangle_area(n0,n1)| | "1 / 2 * 4.5 * 6 = 13.5 m 2 answer : c" | geometry |
math_qa__3JmyLDVgWR9iJBkn | If (5^15)(9^8)=3(15^x), what is the value of x? Select the correct option.
A) 7 B) 9 C) 11 D) 13 E) 15 | <gadget id="calculator">5 ** 15</gadget>
<output>30_517_578_125</output>
<gadget id="calculator">9 ** 8</gadget>
<output>43_046_721</output>
<gadget id="calculator">30_517_578_125 * 43_046_721</gadget>
<output>1_313_681_671_142_578_125</output>
<gadget id="calculator">1_313_681_671_142_578_125 / 3</gadget>
<output>437_893_890_380_859_375</output>
<gadget id="calculator">log(437_893_890_380_859_375)</gadget>
<output>log(437893890380859375) = around 40.620753</output>
<gadget id="calculator">log(15)</gadget>
<output>log(15) = around 2.70805</output>
<gadget id="calculator">log(437893890380859375) / log(15)</gadget>
<output>log(437893890380859375)/log(15) = around 15</output>
<result>E</result> | E | 15 | If (5^15)(9^8)=3(15^x), what is the value of x? | {
"A": "7",
"B": "9",
"C": "11",
"D": "13",
"E": "15"
} | divide(log(divide(multiply(power(5, 15), power(9, 8)), 3)), log(15)) | log(n5)|power(n0,n1)|power(n2,n3)|multiply(#1,#2)|divide(#3,n4)|log(#4)|divide(#5,#0)| | "( 5 ^ 15 ) ( 9 ^ 8 ) = 3 ( 15 ^ x ) = > 5 ^ 15 * 3 ^ 16 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 15 * 3 ^ 16 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 15 answer e" | general |
math_qa__OAI3YQRrnPu0Une6 | A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 830 in 4 years. The sum is? Choose the correct choice from the following:
A) s . 738 B) s . 638 C) s . 650 D) s . 810 E) s . 735 | <gadget id="calculator">830 - 825</gadget>
<output>5</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">15 / 4</gadget>
<output>15/4 = around 3.75</output>
<gadget id="calculator">825 - (15/4)</gadget>
<output>3_285/4 = around 821.25</output>
<result>D</result> | D | 810 | A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 830 in 4 years. The sum is? | {
"A": "s . 738",
"B": "s . 638",
"C": "s . 650",
"D": "s . 810",
"E": "s . 735"
} | subtract(825, divide(multiply(subtract(830, 825), 3), 4)) | subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)| | "s . i . for 1 year = ( 830 - 825 ) = rs . 5 s . i . for 3 years = 5 * 3 = rs . 15 principal = ( 825 - 15 ) = rs . 810 . answer : d" | gain |
math_qa__MKlzXkHLBD3rKwOS | At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts? Choose the correct choice
A) 18 B) 30 C) 42 D) 68 E) 70 | <gadget id="calculator">70 * 300</gadget>
<output>21_000</output>
<gadget id="calculator">21_000 / 100</gadget>
<output>210</output>
<gadget id="calculator">300 - 210</gadget>
<output>90</output>
<gadget id="calculator">90 - 45</gadget>
<output>45</output>
<gadget id="calculator">45 * 100</gadget>
<output>4_500</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">4_500 / 60</gadget>
<output>75</output>
<gadget id="calculator">75 * 40</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 100</gadget>
<output>30</output>
<result>B</result> | B | 30 | At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 45 males did not bring gifts to the party, how many females did bring gifts? | {
"A": "18",
"B": "30",
"C": "42",
"D": "68",
"E": "70"
} | divide(multiply(divide(multiply(subtract(subtract(300, divide(multiply(70, 300), const_100)), 45), const_100), subtract(const_100, 40)), 40), const_100) | multiply(n0,n1)|subtract(const_100,n2)|divide(#0,const_100)|subtract(n0,#2)|subtract(#3,n3)|multiply(#4,const_100)|divide(#5,#1)|multiply(n2,#6)|divide(#7,const_100)| | "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 48 are males , so remaining 90 - 45 = 50 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 45 , 100 % = 45 * 100 / 60 = 75 . . ans 40 % of 75 = 30 b" | gain |
math_qa__F5anCfzb2BF1WD6H | After playing 40 games, the Lesley basketball team had won 50% of the games. The additional games played gave the team a 20% total winning average. How many additional games must the team have won to obtain this average? Select:
A) 2
B) 15
C) 7
D) 10
E) 9 | <gadget id="calculator">50 - 20</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<result>B</result> | B | 15 | After playing 40 games, the Lesley basketball team had won 50% of the games. The additional games played gave the team a 20% total winning average. How many additional games must the team have won to obtain this average? | {
"A": "2",
"B": "15",
"C": "7",
"D": "10",
"E": "9"
} | divide(subtract(50, 20), const_2) | subtract(n1,n2)|divide(#0,const_2) | explanation : identify the parts , set up equation , and solve . number of games initially won by the team : 50 % * 40 = 20 additional games won by the team leaving a 20 % average . ( let x represent the unknown number of additional games won . ) therefore , the total number of games played is 40 + x , and the total number of games won is 20 + x . this gives the equation as : 20 % * ( 40 + x ) = 20 + x solve : let ' s get rid of the percent sign 20 / 100 * ( 40 + x ) = 20 + x 1 / 5 * ( 40 + x ) = 20 + x get rid of the fraction : 5 [ 1 / 5 * ( 40 + x ) ] = 5 ( 20 + x ) 1 * ( 40 + x ) = 100 + 5 x 40 + x = 100 + 5 x ( 40 - 100 ) + x = ( 100 - 100 ) + 5 x - 60 + x = 5 x - 60 + ( x - x ) + 5 x - x - 60 = 4 x 15 = x answer : b | general |
math_qa__KimqxDL1ogrd6Apq | A water tank is four-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely? Pick: A) 6 B) 9 C) 10 D) 12 E) 15 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/6) - (1/10)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(4/5) / (1/15)</gadget>
<output>12</output>
<result>D</result> | D | 12 | A water tank is four-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely? | {
"A": "6",
"B": "9",
"C": "10",
"D": "12",
"E": "15"
} | divide(divide(const_4, add(const_2, const_3)), subtract(inverse(6), inverse(10))) | add(const_2,const_3)|inverse(n1)|inverse(n0)|divide(const_4,#0)|subtract(#1,#2)|divide(#3,#4) | the combined rate of filling / emptying the tank = 1 / 10 - 1 / 6 = - 1 / 15 since the rate is negative , the tank will be emptied . a full tank would take 15 minutes to empty . since the tank is only four - fifths full , the time is ( 4 / 5 ) * 15 = 12 minutes the answer is d . | physics |
math_qa__SCuhnykFQ1G6CA7c | mr . smith calculated the average of 10 3 digit numbers . but due to a mistake he reversed the digits of a number and thus his average increased by 19.8 the difference between the unit digit and hundreds digit of that number is : Choose the correct choice from the following answers:
A) 2 B) 6 C) 5 D) 3 E) 4 | <gadget id="calculator">10 * 19.8</gadget>
<output>198</output>
<gadget id="calculator">100 - 1</gadget>
<output>99</output>
<gadget id="calculator">198 / 99</gadget>
<output>2</output>
<result>A</result> | A | 2 | mr . smith calculated the average of 10 3 digit numbers . but due to a mistake he reversed the digits of a number and thus his average increased by 19.8 the difference between the unit digit and hundreds digit of that number is : | {
"A": "2",
"B": "6",
"C": "5",
"D": "3",
"E": "4"
} | divide(multiply(10, 19.8), subtract(const_100, const_1)) | multiply(n0,n2)|subtract(const_100,const_1)|divide(#0,#1) | since the average increased by 29.7 and there were a total of 10 numbers , it means the incorrect number was 198 greater than the correct number . say , the correct number was abc ( where a , b and c are the digits of the 3 digit number ) then the incorrect number was cba . 100 c + 10 b + a - ( 100 a + 10 b + c ) = 198 99 c - 99 a = 99 ( c - a ) = 198 198 = 99 * 2 = 99 ( c - a ) so c - a = 2 answer ( a ) | general |
math_qa__iUUHtagceK7brT8c | A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 4 years ago? Choose the most appropriate option: A) 8 B) 10 C) 12 D) 14 E) 16 | <gadget id="calculator">6 + 8</gadget>
<output>14</output>
<gadget id="calculator">14 - 4</gadget>
<output>10</output>
<result>B</result> | B | 10 | A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 4 years ago? | {
"A": "8",
"B": "10",
"C": "12",
"D": "14",
"E": "16"
} | subtract(add(6, 8), 4) | add(n1,n2)|subtract(#0,n4)| | "let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 4 years ago ? i . e . d - 4 = 14 - 4 = 10 years answer : b" | general |
math_qa__li2nJ921RNwsm3pz | Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 24 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red?
Choose the correct answer: A) 64 B) 72 C) 86 D) 98 E) 101 | <gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 ** 3</gadget>
<output>125</output>
<gadget id="calculator">125 - 24</gadget>
<output>101</output>
<result>E</result> | E | 101 | Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 24 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red? | {
"A": "64",
"B": "72",
"C": "86",
"D": "98",
"E": "101"
} | subtract(power(add(const_1, add(const_1, const_3)), const_3), 24) | add(const_1,const_3)|add(#0,const_1)|power(#1,const_3)|subtract(#2,n0)| | "use the options . the options which after getting added to 24 shows a cube of a number could be right . here 64 + 24 = 88 72 + 24 = 96 86 + 24 = 110 98 + 24 = 122 101 + 24 = 125 - - - ( 5 * 5 * 5 ) so we have 101 as the answer ! e" | geometry |
math_qa__rjm1J1heQtYCvEDI | In a certain pond, 30 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
Pick one.
A) 750 B) 625 C) 1,250 D) 2,500 E) 10,000 | <gadget id="calculator">2 / 50</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">30 / (1/25)</gadget>
<output>750</output>
<result>A</result> | A | 750 | In a certain pond, 30 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? | {
"A": "750",
"B": "625",
"C": "1,250",
"D": "2,500",
"E": "10,000"
} | divide(30, divide(2, 50)) | divide(n2,n1)|divide(n0,#0)| | "this is a rather straight forward ratio problem . 1 . 30 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 30 / x thus , x = 750 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . a" | gain |
math_qa__PIhBSoZIA0vvqwxQ | in an examination , there are 100 questions divided into 3 groups a , b and c such that each group contains at least one question . each question in group a carries 1 mark , each question in group b carries 2 marks and each question in group c carries 3 marks . it is known that the questions in group a together carry at least 60 % of the total marks . if group b contains 23 questions , then how many questions are there in group c ? Choose the correct answer
A) 1
B) 2
C) 3
D) 4
E) 5 | <gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 / (3/5)</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(5/3) - 1</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">100 - 23</gadget>
<output>77</output>
<gadget id="calculator">(2/3) * 77</gadget>
<output>154/3 = around 51.333333</output>
<gadget id="calculator">2 * 23</gadget>
<output>46</output>
<gadget id="calculator">(154/3) - 46</gadget>
<output>16/3 = around 5.333333</output>
<gadget id="calculator">3 + (2/3)</gadget>
<output>11/3 = around 3.666667</output>
<gadget id="calculator">(16/3) / (11/3)</gadget>
<output>16/11 = around 1.454545</output>
<gadget id="calculator">floor(16/11)</gadget>
<output>1</output>
<result>A</result> | A | 1 | in an examination , there are 100 questions divided into 3 groups a , b and c such that each group contains at least one question . each question in group a carries 1 mark , each question in group b carries 2 marks and each question in group c carries 3 marks . it is known that the questions in group a together carry at least 60 % of the total marks . if group b contains 23 questions , then how many questions are there in group c ? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | floor(divide(subtract(multiply(subtract(inverse(divide(60, const_100)), const_1), subtract(100, 23)), multiply(2, 23)), add(3, subtract(inverse(divide(60, const_100)), const_1)))) | divide(n5,const_100)|multiply(n3,n6)|subtract(n0,n6)|inverse(#0)|subtract(#3,const_1)|add(n1,#4)|multiply(#4,#2)|subtract(#6,#1)|divide(#7,#5)|floor(#8) | explanation : since group b contains 23 questions , the marks associated with this group are 46 . now , check for option ( 1 ) , if group ( c ) has one question , the marks associated with this group will be 3 . thus total marks will be 49 . total number of questions = 100 , group ( a ) will have 76 questions , the corresponding weightage being 76 marks . answer : a | general |
math_qa__t81GVmX0oBR6vKww | A and B finish the job in 15 days.while A,B and C can finish it in 5 days . C alone will finish the job in Choose the correct option:
A) 4.50 days
B) 3.50 days
C) 6.0 days
D) 7.5 days
E) 5.50 days | <gadget id="calculator">5 * 15</gadget>
<output>75</output>
<gadget id="calculator">15 - 5</gadget>
<output>10</output>
<gadget id="calculator">75 / 10</gadget>
<output>15/2 = around 7.5</output>
<result>D</result> | D | 7.5 | A and B finish the job in 15 days.while A,B and C can finish it in 5 days . C alone will finish the job in | {
"A": "4.50 days",
"B": "3.50 days",
"C": "6.0 days",
"D": "7.5 days",
"E": "5.50 days"
} | divide(multiply(5, 15), subtract(15, 5)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | "explanation : 5 = ( 15 * x ) / ( 15 + x ) 75 + 5 x = 15 x 10 x = 75 x = 7.5 answer : option d" | physics |
math_qa__whsGdOoHlSVSJkJk | Calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days, Choose the correct choice from the following options.
A) 6 days
B) 3 days
C) 4 days
D) 2 days
E) 5 days | <gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">20 * 35</gadget>
<output>700</output>
<gadget id="calculator">25 * 7</gadget>
<output>175</output>
<gadget id="calculator">700 / 175</gadget>
<output>4</output>
<result>C</result> | C | 4 | Calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days, | {
"A": "6 days",
"B": "3 days",
"C": "4 days",
"D": "2 days",
"E": "5 days"
} | divide(multiply(multiply(5, 4), 35), multiply(25, 7)) | multiply(n2,n4)|multiply(n0,n3)|multiply(n1,#0)|divide(#2,#1)| | "the length of wall painted by one boy in one day = 25 / 5 * 1 / 4 = 1.25 m no . of days required to paint 50 m cloth by 8 boys = 35 / 7 * 1 / 1.25 = 4 days . c" | physics |
math_qa__EPTuJg7x9mB3ajXi | How many diagonals does a 61-sided convex polygon have? Answers
A) 1182
B) 1769
C) 2456
D) 3538
E) 4209 | <gadget id="calculator">factorial(61)</gadget>
<output>507_580_213_877_224_798_800_856_812_176_625_227_226_004_528_988_036_003_099_405_939_480_985_600_000_000_000_000</output>
<gadget id="calculator">61 - 2</gadget>
<output>59</output>
<gadget id="calculator">factorial(59)</gadget>
<output>138_683_118_545_689_835_737_939_019_720_389_406_345_902_876_772_687_432_540_821_294_940_160_000_000_000_000</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">138_683_118_545_689_835_737_939_019_720_389_406_345_902_876_772_687_432_540_821_294_940_160_000_000_000_000 * 2</gadget>
<output>277_366_237_091_379_671_475_878_039_440_778_812_691_805_753_545_374_865_081_642_589_880_320_000_000_000_000</output>
<gadget id="calculator">507_580_213_877_224_798_800_856_812_176_625_227_226_004_528_988_036_003_099_405_939_480_985_600_000_000_000_000 / 277_366_237_091_379_671_475_878_039_440_778_812_691_805_753_545_374_865_081_642_589_880_320_000_000_000_000</gadget>
<output>1_830</output>
<result>B</result> | B | 1,769 | How many diagonals does a 61-sided convex polygon have? | {
"A": "1182",
"B": "1769",
"C": "2456",
"D": "3538",
"E": "4209"
} | divide(factorial(61), multiply(factorial(subtract(61, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)| | "a 61 - sided convex polygon has 61 vertices . if we examine a single vertex , we can see that we can connect it with 58 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 61 vertices can be connected with 58 vertices to create a diagonal then the total number of diagonals would be ( 61 ) ( 58 ) = 3538 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3538 by 2 to get 1769 . the answer is b ." | general |
math_qa__VUZ7z6qeJ9rgYCGU | What is (16^7+16) / 16? Choose the correct choice:
A) 15467118 B) 16777217 C) 17827343 D) 18047455 E) 19357579 | <gadget id="calculator">16 ** 7</gadget>
<output>268_435_456</output>
<gadget id="calculator">268_435_456 + 16</gadget>
<output>268_435_472</output>
<gadget id="calculator">268_435_472 / 16</gadget>
<output>16_777_217</output>
<result>B</result> | B | 16,777,217 | What is (16^7+16) / 16? | {
"A": "15467118",
"B": "16777217",
"C": "17827343",
"D": "18047455",
"E": "19357579"
} | divide(add(power(16, 7), 16), 16) | power(n0,n1)|add(n0,#0)|divide(#1,n0)| | "( 16 ^ 7 + 16 ) / 16 = 16 * ( 16 ^ 6 + 1 ) / 16 = 16 ^ 6 + 1 clearly this is a number which ends with a 7 in the units place . the answer is b ." | general |
math_qa__TywXZ4sRFNa90st4 | If the sum of a number and its square is 240, what is the number? Choose the correct choice from the following answers:
A) 15
B) 77
C) 25
D) 87
E) 171 | <gadget id="calculator">240 ** (1/2)</gadget>
<output>4*sqrt(15) = around 15.491933</output>
<gadget id="calculator">floor(4*sqrt(15))</gadget>
<output>15</output>
<result>A</result> | A | 15 | If the sum of a number and its square is 240, what is the number? | {
"A": "15",
"B": "77",
"C": "25",
"D": "87",
"E": "171"
} | floor(sqrt(240)) | sqrt(n0)|floor(#0)| | "explanation : let the integer be x . then , x + x 2 = 240 x 2 + x - 240 = 0 ( x + 16 ) ( x – 15 ) = 0 x = 15 answer : a" | geometry |
math_qa__rdahVZPAOOg7xIDm | Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 6 minutes more to walk to work than to ride his bike to work, then x equals? Choose the correct choice from the following answers: A) 4 B) 7 C) 9 D) 15 E) 20 | <gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<result>C</result> | C | 9 | Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 6 minutes more to walk to work than to ride his bike to work, then x equals? | {
"A": "4",
"B": "7",
"C": "9",
"D": "15",
"E": "20"
} | divide(multiply(6, const_3), const_2) | multiply(n2,const_3)|divide(#0,const_2)| | "please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 360 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 360 - - - - > 40 x = 360 - - > x = 9 . option c" | physics |
math_qa__qo7mCjYhsf5WOarR | Two family reunions are happening at the Leela hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 50 people attend the Oates reunion and 62 people attend the Hall reunion, how many people attend both reunions? Choose the most appropriate option:
A) 2
B) 5
C) 12
D) 16
E) 22 | <gadget id="calculator">62 - 50</gadget>
<output>12</output>
<result>C</result> | C | 12 | Two family reunions are happening at the Leela hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 50 people attend the Oates reunion and 62 people attend the Hall reunion, how many people attend both reunions? | {
"A": "2",
"B": "5",
"C": "12",
"D": "16",
"E": "22"
} | subtract(62, 50) | subtract(n2,n1) | no of people in oates reunion = 50 no of people in hall reunion = 62 attending both = x all guests attend at least one . therefore , 100 = 50 + 62 - ( both ) both = 12 answer c | other |
math_qa__4hqgkSflPgM7K6xm | Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 1600 then loss of Pyarelal? Choose one.
A) 600 B) 700 C) 840 D) 940 E) 1440 | <gadget id="calculator">9 * 1_600</gadget>
<output>14_400</output>
<gadget id="calculator">1 + 9</gadget>
<output>10</output>
<gadget id="calculator">14_400 / 10</gadget>
<output>1_440</output>
<result>E</result> | E | 1,440 | Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 1600 then loss of Pyarelal? | {
"A": "600",
"B": "700",
"C": "840",
"D": "940",
"E": "1440"
} | divide(multiply(9, 1600), add(1, 9)) | add(n0,n1)|multiply(n1,n2)|divide(#1,#0)| | "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1600 , loss of pyarelal = 1600 * 9 x / 10 x = 1440 answer : e" | gain |
math_qa__oOojDs95o8kmVRoR | Following an increase in prices, the price of a candy box was 10 pounds and the price of a can of soda was 9 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised? Choose the correct choice from the following.
A) 11 .
B) 12 .
C) 13 .
D) 14 .
E) 14.5 | <gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">1_000 / 125</gadget>
<output>8</output>
<gadget id="calculator">9 * 100</gadget>
<output>900</output>
<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">900 / 150</gadget>
<output>6</output>
<gadget id="calculator">8 + 6</gadget>
<output>14</output>
<result>D</result> | D | 14 | Following an increase in prices, the price of a candy box was 10 pounds and the price of a can of soda was 9 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised? | {
"A": "11 .",
"B": "12 .",
"C": "13 .",
"D": "14 .",
"E": "14.5"
} | add(divide(multiply(10, const_100), add(const_100, 25)), divide(multiply(9, const_100), add(const_100, 50))) | add(n2,const_100)|add(n3,const_100)|multiply(n0,const_100)|multiply(n1,const_100)|divide(#2,#0)|divide(#3,#1)|add(#4,#5)| | "price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 9 / 1.5 = 6 total price = 8 + 6 = 14 d is the answer" | general |
math_qa__djsftUPDVqxe7hJh | In a factory, an average of 65 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 60 sets/day . The average production per day for day last 5days is ? Choose the correct choice from the following answers:
A) 20 B) 35 C) 48 D) 50 E) 59 | <gadget id="calculator">25 + 5</gadget>
<output>30</output>
<gadget id="calculator">30 * 60</gadget>
<output>1_800</output>
<gadget id="calculator">25 * 65</gadget>
<output>1_625</output>
<gadget id="calculator">1_800 - 1_625</gadget>
<output>175</output>
<gadget id="calculator">175 / 5</gadget>
<output>35</output>
<result>B</result> | B | 35 | In a factory, an average of 65 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 60 sets/day . The average production per day for day last 5days is ? | {
"A": "20",
"B": "35",
"C": "48",
"D": "50",
"E": "59"
} | divide(subtract(multiply(add(25, 5), 60), multiply(25, 65)), 5) | add(n1,n2)|multiply(n0,n1)|multiply(n3,#0)|subtract(#2,#1)|divide(#3,n2)| | "production during these 5 days = total production in a month - production in first 25 days . = 30 x 60 - 25 x 65 = 175 ∴ average for last 5 days = 175 / 5 = 35 aswer : b" | general |
math_qa__YzrpEBFDPWc1NLeD | How many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
Answers: A) 50 B) 60 C) 70 D) 80 E) 90 | <gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">10 * 8</gadget>
<output>80</output>
<result>D</result> | D | 80 | How many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99? | {
"A": "50",
"B": "60",
"C": "70",
"D": "80",
"E": "90"
} | multiply(const_10, subtract(const_10, const_2)) | subtract(const_10,const_2)|multiply(#0,const_10) | kk is 3 - digit integer . any 3 digit integer can be expressed as 100 a + 10 b + c 100 a + 10 b + c . now , we are told that ( 100 a + 10 b + c ) + 99 = 100 c + 10 b + a ( 100 a + 10 b + c ) + 99 = 100 c + 10 b + a - - > 99 c − 99 a = 9999 c − 99 a = 99 - - > c − a = 1 c − a = 1 - - > there are 8 pairs of cc and aa possible such that their difference to be 1 : ( 9,8 ) , ( 8,7 ) , . . . , and ( 2,1 ) ( note that aa can not be 0 as kk is 3 - digit integer and its hundreds digit , aa , is more than or equal to 1 ) . also , bb , tens digit of kk , could tale 10 values ( 0 , 1 , . . . , 9 ) so there are total of 8 * 10 = 80 such numbers possible . example : 102 - 201 ; 112 - 211 ; 122 - 221 ; . . . 899 - 998 . answer : d . | general |
math_qa__hEuZxPbudUoey8to | If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction? Choose the correct choice from the following choices
A) 9
B) 8
C) 7
D) 6
E) 5 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<result>E</result> | E | 5 | If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction? | {
"A": "9",
"B": "8",
"C": "7",
"D": "6",
"E": "5"
} | add(const_2, const_3) | add(const_2,const_3)| | "0 . [ u ] 225 [ / u = 0.225225225 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e" | general |
math_qa__C03JQE4hdbCsXvU4 | If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction. Choose the correct choice from the following choices: A) 1 / 12 B) 1 / 8 C) 1 / 6 D) 1 / 4 E) 1 / 2 | <gadget id="calculator">2 / 15</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">20 + 100</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(6/5) / (3/4)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(2/15) / (8/5)</gadget>
<output>1/12 = around 0.083333</output>
<result>A</result> | A | 0.083333 | If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction. | {
"A": "1 / 12",
"B": "1 / 8",
"C": "1 / 6",
"D": "1 / 4",
"E": "1 / 2"
} | divide(divide(2, 15), divide(divide(add(20, const_100), const_100), divide(subtract(const_100, 25), const_100))) | add(n0,const_100)|divide(n2,n3)|subtract(const_100,n1)|divide(#0,const_100)|divide(#2,const_100)|divide(#3,#4)|divide(#1,#5) | x * ( 120 / 100 ) - - - - - - - - - - - - - - - - = 2 / 15 y * ( 75 / 100 ) x / y = 1 / 12 answer : a | general |
math_qa__AdIRQEsV2dKKqzas | Jerry went to a shop and bought things worth Rs. 30, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Choose the correct choice from the following choices
A) 19 B) 19.7 C) 21.3 D) 21.5 E) 24.7 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">100 / 6</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(3/10) * (50/3)</gadget>
<output>5</output>
<gadget id="calculator">5 + (3/10)</gadget>
<output>53/10 = around 5.3</output>
<gadget id="calculator">30 - (53/10)</gadget>
<output>247/10 = around 24.7</output>
<result>E</result> | E | 24.7 | Jerry went to a shop and bought things worth Rs. 30, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? | {
"A": "19",
"B": "19.7",
"C": "21.3",
"D": "21.5",
"E": "24.7"
} | subtract(30, add(multiply(divide(30, const_100), divide(const_100, 6)), divide(30, const_100))) | divide(n1,const_100)|divide(const_100,n2)|multiply(#0,#1)|add(#0,#2)|subtract(n0,#3)| | "total cost of the items he purchased = rs . 30 given that out of this rs . 30 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 30 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 30 − 0.3 − x ) = 30 ⇒ ( 30 − 0.3 − x ) = 5 ⇒ x = 30 − 0.3 − 5 = 24.7 e )" | gain |
math_qa__86SAhWo0TB5sHSlX | How many different ways can 2 students be seated in a row of 6 desks, so that there is always at least one empty desk between the students? Select
A) 2
B) 3
C) 4
D) 20
E) 12 | <gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">factorial(5) / factorial(5 - 2)</gadget>
<output>20</output>
<result>D</result> | D | 20 | How many different ways can 2 students be seated in a row of 6 desks, so that there is always at least one empty desk between the students? | {
"A": "2",
"B": "3",
"C": "4",
"D": "20",
"E": "12"
} | permutation(subtract(6, const_1), 2) | subtract(n1,const_1)|permutation(#0,n0)| | "10 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 10 x 2 = 20 d" | probability |
math_qa__XGpGO4YZWENAhqV1 | If 75 percent of a class answered the first question on a certain test correctly, 35 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly? Choices
A) 10 % B) ( 8 ) 20 % C) 30 % D) 50 % E) 65 % | <gadget id="calculator">75 + 35</gadget>
<output>110</output>
<gadget id="calculator">110 + 20</gadget>
<output>130</output>
<gadget id="calculator">130 - 100</gadget>
<output>30</output>
<result>C</result> | C | 30 | If 75 percent of a class answered the first question on a certain test correctly, 35 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly? | {
"A": "10 %",
"B": "( 8 ) 20 %",
"C": "30 %",
"D": "50 %",
"E": "65 %"
} | subtract(add(add(75, 35), 20), const_100) | add(n0,n1)|add(n2,#0)|subtract(#1,const_100)| | "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 35 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 110 x = 30 ans : c" | other |
math_qa__fiPFoJqwan4u0WUT | Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 30 kg of fresh grapes?
Choose one:
A) 3.75 kg B) 2.4 kg C) 2.5 kg D) 10 kg E) none of these | <gadget id="calculator">100 - 90</gadget>
<output>10</output>
<gadget id="calculator">10 * 30</gadget>
<output>300</output>
<gadget id="calculator">300 / 100</gadget>
<output>3</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">3 / 80</gadget>
<output>3/80 = around 0.0375</output>
<gadget id="calculator">(3/80) * 100</gadget>
<output>15/4 = around 3.75</output>
<result>A</result> | A | 3.75 | Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 30 kg of fresh grapes? | {
"A": "3.75 kg",
"B": "2.4 kg",
"C": "2.5 kg",
"D": "10 kg",
"E": "none of these"
} | multiply(divide(divide(multiply(subtract(const_100, 90), 30), const_100), subtract(const_100, 20)), const_100) | subtract(const_100,n0)|subtract(const_100,n1)|multiply(n2,#0)|divide(#2,const_100)|divide(#3,#1)|multiply(#4,const_100)| | "the weight of non - water in 30 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 30 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 3.75 answer : a" | gain |
math_qa__YqNTaFnUeRWnti4d | 4!/(4-3)!=? Choices:
A) 24 B) 34 C) 35 D) 36 E) 39 | <gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">factorial(1)</gadget>
<output>1</output>
<gadget id="calculator">24 / 1</gadget>
<output>24</output>
<result>A</result> | A | 24 | 4!/(4-3)!=? | {
"A": "24",
"B": "34",
"C": "35",
"D": "36",
"E": "39"
} | divide(factorial(4), factorial(subtract(4, 3))) | factorial(n0)|subtract(n0,n2)|factorial(#1)|divide(#0,#2)| | 4 ! / ( 4 - 3 ) ! = 4 ! / 1 ! = 4 * 3 * 2 = 24 . hence , the correct answer is a . | general |
math_qa__YJbbYKDWPysT2MRq | Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 1.5 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top? Choose the correct choice from the following answers.
A) 1.065 B) 1.125 C) 1.225 D) 1.375 E) 1.425 | <gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 1.5</gadget>
<output>9</output>
<gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">(9/2) / 4</gadget>
<output>9/8 = around 1.125</output>
<result>B</result> | B | 1.125 | Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 1.5 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top? | {
"A": "1.065",
"B": "1.125",
"C": "1.225",
"D": "1.375",
"E": "1.425"
} | divide(divide(multiply(add(4, 2), 1.5), 2), 4) | add(n0,n1)|multiply(n2,#0)|divide(#1,n1)|divide(#2,n0)| | "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 1.5 km / hour x / 3 = 1.5 x = 4.5 km the average speed while climbing = distance / time = 4.5 / 4 = 1.125 km / h the answer is b ." | physics |
math_qa__Y2HsuhEJDBGQAF5B | Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 11/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos? Choose the correct answer:
A) 11 / 21
B) 14 / 31
C) 7 / 15
D) 17 / 35
E) 1 / 2 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>
<result>A</result> | A | 0.52381 | Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 11/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos? | {
"A": "11 / 21",
"B": "14 / 31",
"C": "7 / 15",
"D": "17 / 35",
"E": "1 / 2"
} | divide(add(3, 2), const_10) | add(n0,n1)|divide(#0,const_10)| | "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 11 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 11 / 5 = 11 - - > total time for both of them would be 10 + 11 = 21 - - > deluxe / total = 11 / 21 . answer : a ." | general |
math_qa__mK8AEHwc8DZcLRTv | After decreasing 24% in the price of an article costs Rs.608. Find the actual cost of an article? Select
A) 128
B) 277
C) 800
D) 2688
E) 1991 | <gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>
<gadget id="calculator">608 / (19/25)</gadget>
<output>800</output>
<result>C</result> | C | 800 | After decreasing 24% in the price of an article costs Rs.608. Find the actual cost of an article? | {
"A": "128",
"B": "277",
"C": "800",
"D": "2688",
"E": "1991"
} | divide(608, subtract(const_1, divide(24, const_100))) | divide(n0,const_100)|subtract(const_1,#0)|divide(n1,#1)| | "cp * ( 76 / 100 ) = 608 cp = 8 * 100 = > cp = 800 answer : c" | gain |
math_qa__PDNOfzTsZ7y85axn | In a zoo there are 30 penguins, 22 zebras, and 8 tigers with some zookeepers. If the total number of heads are 132 less than the number of feet, the number of zookeepers is
Choose one
A) 12 B) 14 C) 16 D) 18 E) 22 | <gadget id="calculator">30 * 2</gadget>
<output>60</output>
<gadget id="calculator">22 * 4</gadget>
<output>88</output>
<gadget id="calculator">60 + 88</gadget>
<output>148</output>
<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<gadget id="calculator">148 + 32</gadget>
<output>180</output>
<gadget id="calculator">180 - 132</gadget>
<output>48</output>
<gadget id="calculator">60 - 48</gadget>
<output>12</output>
<result>A</result> | A | 12 | In a zoo there are 30 penguins, 22 zebras, and 8 tigers with some zookeepers. If the total number of heads are 132 less than the number of feet, the number of zookeepers is | {
"A": "12",
"B": "14",
"C": "16",
"D": "18",
"E": "22"
} | subtract(multiply(30, const_2), subtract(add(add(multiply(30, const_2), multiply(22, const_4)), multiply(8, const_4)), 132)) | multiply(n0,const_2)|multiply(n1,const_4)|multiply(n2,const_4)|add(#0,#1)|add(#3,#2)|subtract(#4,n3)|subtract(#0,#5) | explanation : let number of zookeepers be x . then , total number of feet = 2 x 30 + 4 x 22 + 4 x 8 + 2 x = 2 x + 180 . total number of heads = 30 + 22 + 8 + x = 60 + x . therefore ( 2 x + 180 ) - 132 = ( 60 + x ) + or x = 12 . answer : a | general |
math_qa__jAxl5Z8spOJhdPL5 | What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal) Choose the correct choice from the following choices:
A) 3
B) 4
C) 5
D) 6
E) 7 | <gadget id="calculator">21 / 3</gadget>
<output>7</output>
<result>E</result> | E | 7 | What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal) | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | divide(21, const_3) | divide(n0,const_3) | since no flowers are to be left out , then the number of bouquets must be a factor of both 21 and 91 . for example , we can not have 2 bouquets since we can not divide 91 red tulips into 2 bouquets without one tulip left over . only answer choice which is a factor of 91 is e ( 7 ) . answer : e . | general |
math_qa__2CNX1NmYULP34TMv | What least number must be added to 1049, so that the sum is completely divisible by 25 ? Choose the correct choice from the following answers.
A) 2 B) 4 C) 6 D) 8 E) 1 | <gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">40 + 2</gadget>
<output>42</output>
<gadget id="calculator">42 * 25</gadget>
<output>1_050</output>
<gadget id="calculator">1_050 - 1_049</gadget>
<output>1</output>
<result>E</result> | E | 1 | What least number must be added to 1049, so that the sum is completely divisible by 25 ? | {
"A": "2",
"B": "4",
"C": "6",
"D": "8",
"E": "1"
} | subtract(multiply(add(multiply(const_4, const_10), const_2), 25), 1049) | multiply(const_10,const_4)|add(#0,const_2)|multiply(n1,#1)|subtract(#2,n0) | if we divide 1049 by 25 remainder is 24 25 - 24 = 1 answer : e | general |
math_qa__Fancd8nfWJBMSDUN | man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? Choose the correct choice from the following answers: A) 12 B) 22 C) 30 D) 88 E) 13 | <gadget id="calculator">25 + 35</gadget>
<output>60</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<result>C</result> | C | 30 | man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? | {
"A": "12",
"B": "22",
"C": "30",
"D": "88",
"E": "13"
} | divide(add(25, 35), const_2) | add(n0,n1)|divide(#0,const_2)| | "us = 25 ds = 35 m = ( 35 + 25 ) / 2 = 30 answer : c" | physics |
math_qa__aogQ8aDidLYniCLJ | The diagonals of a rhombus are 30 cm and 12 cm. Find its area?
Choose the correct choice from the following choices: A) 176 B) 190 C) 180 D) 278 E) 292 | <gadget id="calculator">(30 * 12) / 2</gadget>
<output>180</output>
<result>C</result> | C | 180 | The diagonals of a rhombus are 30 cm and 12 cm. Find its area? | {
"A": "176",
"B": "190",
"C": "180",
"D": "278",
"E": "292"
} | rhombus_area(30, 12) | rhombus_area(n0,n1)| | "1 / 2 * 30 * 12 = 180 answer : c" | geometry |
math_qa__HKNqZuOmtQ5BKvTk | If the cost price of 50 articles is equal to the selling price of 30 articles, then the gain or loss percent is? Select:
A) 16 B) 127 C) 12 D) 18 E) 67 | <gadget id="calculator">100 * 30</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 50</gadget>
<output>60</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">100 * (2/3)</gadget>
<output>200/3 = around 66.666667</output>
<result>E</result> | E | 67 | If the cost price of 50 articles is equal to the selling price of 30 articles, then the gain or loss percent is? | {
"A": "16",
"B": "127",
"C": "12",
"D": "18",
"E": "67"
} | multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 30), 50)), divide(multiply(const_100, 30), 50))) | multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)|divide(#2,#1)|multiply(#3,const_100)| | "percentage of profit = 20 / 30 * 100 = 67 % answer : e" | gain |
math_qa__WGFETo5FCzobrbKx | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent W of the distribution is less than m +d ? Answers:
A) 16 % B) 32 % C) 48 % D) 84 % E) 92 % | <gadget id="calculator">100 - 68</gadget>
<output>32</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<gadget id="calculator">100 - 16</gadget>
<output>84</output>
<result>D</result> | D | 84 | A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent W of the distribution is less than m +d ? | {
"A": "16 %",
"B": "32 %",
"C": "48 %",
"D": "84 %",
"E": "92 %"
} | subtract(const_100, divide(subtract(const_100, 68), const_2)) | subtract(const_100,n0)|divide(#0,const_2)|subtract(const_100,#1)| | "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , w = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d ." | general |
math_qa__ogE83oEPDU66Ch6m | A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey? Choose the correct choice from the following answers
A) 3.1 kmph B) 5 kmph C) 6 kmph D) 4 kmph E) 7 kmph | <gadget id="calculator">4.5 - 2.5</gadget>
<output>2</output>
<gadget id="calculator">4.5 + 2</gadget>
<output>6.5</output>
<gadget id="calculator">6.5 / 2</gadget>
<output>3.25</output>
<result>A</result> | A | 3.1 | A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey? | {
"A": "3.1 kmph",
"B": "5 kmph",
"C": "6 kmph",
"D": "4 kmph",
"E": "7 kmph"
} | divide(add(4.5, subtract(4.5, 2.5)), const_2) | subtract(n0,n1)|add(n0,#0)|divide(#1,const_2) | explanation : speed of man = 4.5 kmph speed of stream = 2.5 kmph speed in downstream = 7 kmph speed in upstream = 2 kmph average speed = ( 2 x 7 x 2 ) / 9 = 3.1 kmph . answer : a | general |
math_qa__ahGjuq2pzmpkPsRG | If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals? Select.
A) 4 : 3 B) 4 : 8 C) 4 : 1 D) 4 : 2 E) 4 : 7 | <gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<result>A</result> | A | 1.333333 | If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals? | {
"A": "4 : 3",
"B": "4 : 8",
"C": "4 : 1",
"D": "4 : 2",
"E": "4 : 7"
} | divide(4, 3) | divide(n0,n1)| | "a 1 : a 2 = 4 : 3 d 1 : d 2 = 4 : 3 answer : a" | geometry |
math_qa__gJ6lIaP5jaG1bFLI | The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 37 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add? Choices: A) 17 litres B) 24.67 litres C) 11 litres D) 24.07 litres E) 38.67 litres | <gadget id="calculator">37 * 1_399.45</gadget>
<output>51_779.65</output>
<gadget id="calculator">37 * 262.85</gadget>
<output>9_725.45</output>
<gadget id="calculator">51_779.65 - 9_725.45</gadget>
<output>42_054.2</output>
<gadget id="calculator">3_104.35 - 1_399.45</gadget>
<output>1_704.9</output>
<gadget id="calculator">42_054.2 / 1_704.9</gadget>
<output>24.666667</output>
<result>B</result> | B | 24.67 | The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 37 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add? | {
"A": "17 litres",
"B": "24.67 litres",
"C": "11 litres",
"D": "24.07 litres",
"E": "38.67 litres"
} | divide(subtract(multiply(37, 1399.45), multiply(37, 262.85)), subtract(3104.35, 1399.45)) | multiply(n0,n3)|multiply(n1,n3)|subtract(n2,n0)|subtract(#0,#1)|divide(#3,#2)| | "262.85 ( 37 ) + 3 , 104.35 x = 1 , 399.45 ( 37 + x ) solve the equation . 262.85 ( 37 ) + 3 , 104.35 x = 1 , 399.45 ( 37 + x ) 9725.45 + 3 , 104.35 x = 51779.65 + 1 , 399.45 x 9725.45 + 1 , 704.9 x = 51779.65 1 , 704.9 x = 42054.2 x ≈ 24.67 answer is b ." | general |
math_qa__e2XOqhU95Yfotnd0 | Two equilateral triangle of side 12cm are placed one on top another, such a 6 pionted star is formed if the six vertices lie on a circle what is the area of the circle not enclosed by the Star? Choose the correct choice from the following choices: A) 21 B) 88937 C) 269 D) 279 E) 2701 | <gadget id="calculator">3 ** (1/2)</gadget>
<output>sqrt(3) = around 1.732051</output>
<gadget id="calculator">(sqrt(3)) / 2</gadget>
<output>sqrt(3)/2 = around 0.866025</output>
<gadget id="calculator">(sqrt(3)/2) * 12</gadget>
<output>6*sqrt(3) = around 10.392305</output>
<gadget id="calculator">(6*sqrt(3)) * 2</gadget>
<output>12*sqrt(3) = around 20.78461</output>
<result>A</result> | A | 21 | Two equilateral triangle of side 12cm are placed one on top another, such a 6 pionted star is formed if the six vertices lie on a circle what is the area of the circle not enclosed by the Star? | {
"A": "21",
"B": "88937",
"C": "269",
"D": "279",
"E": "2701"
} | multiply(multiply(divide(sqrt(const_3), const_2), 12), const_2) | sqrt(const_3)|divide(#0,const_2)|multiply(n0,#1)|multiply(#2,const_2) | answer : a | geometry |
math_qa__S0R4jNBy5S8pp9N9 | The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years while that of girls is 15.4 years. What is the ratio of boys to girls in the class?
Select: A) 1 : 2 B) 3 : 4 C) 3 : 5 D) 2 : 3 E) none of these | <gadget id="calculator">15.8 - 15.4</gadget>
<output>0.4</output>
<gadget id="calculator">16.4 - 15.8</gadget>
<output>0.6</output>
<gadget id="calculator">0.4 / 0.6</gadget>
<output>0.666667</output>
<result>D</result> | D | 0.666667 | The average age of a class is 15.8 years. The average age of boys in the class is 16.4 years while that of girls is 15.4 years. What is the ratio of boys to girls in the class? | {
"A": "1 : 2",
"B": "3 : 4",
"C": "3 : 5",
"D": "2 : 3",
"E": "none of these"
} | divide(subtract(15.8, 15.4), subtract(16.4, 15.8)) | subtract(n0,n2)|subtract(n1,n0)|divide(#0,#1) | let x = number of girls y = number of boys sum of girls ages / x = 15.4 sum of boys ages / y = 16.4 the sum of the girls ' ages is 15.4 x , and boys ' sum is 16.4 y ( sum of girls ages + sum of boys ages ) / ( x + y ) = 15.8 ( 15.4 x + 16.4 y ) / ( x + y ) = 15.8 15.4 x + 16.4 y = 15.8 ( x + y ) 15.4 x + 16.4 y = 15.8 x + 15.8 y 0.6 y = 0.4 x 0.6 y / x = 0.4 y / x = 0.4 / 0.6 y / x = 2 / 3 which is the ratio of boys to girls answer : d | general |
math_qa__VPDf6bPtPu2tBkM0 | Subtracting 7% of A from A is equivalent to multiplying A by how much ?
Options.
A) 0.93 B) 9.4 C) 0.094 D) 94 E) none | <gadget id="calculator">100 - 7</gadget>
<output>93</output>
<gadget id="calculator">93 / 100</gadget>
<output>93/100 = around 0.93</output>
<result>A</result> | A | 0.93 | Subtracting 7% of A from A is equivalent to multiplying A by how much ? | {
"A": "0.93",
"B": "9.4",
"C": "0.094",
"D": "94",
"E": "none"
} | divide(subtract(const_100, 7), const_100) | subtract(const_100,n0)|divide(#0,const_100)| | "answer let a - 7 % of a = ab . ⇒ ( 93 x a ) / 100 = ab ∴ b = 0.93 correct option : a" | general |
math_qa__ouJG6wqvPa6p9Gu4 | A children's gift store sells gift certificates in denominations of $3 and $5. The store sold 'm' $3 certificates and 'n' $5 certificates worth $93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take? Choose the correct choice from the following answers
A) 5 B) 7 C) 6 D) 31 E) 18 | <gadget id="calculator">93 / 3</gadget>
<output>31</output>
<gadget id="calculator">31 / 5</gadget>
<output>31/5 = around 6.2</output>
<gadget id="calculator">floor(31/5)</gadget>
<output>6</output>
<result>C</result> | C | 6 | A children's gift store sells gift certificates in denominations of $3 and $5. The store sold 'm' $3 certificates and 'n' $5 certificates worth $93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take? | {
"A": "5",
"B": "7",
"C": "6",
"D": "31",
"E": "18"
} | floor(divide(divide(93, 3), 5)) | divide(n4,n0)|divide(#0,n1)|floor(#1) | explanatory answer step 1 : key data 1 . total value of all certificates sold = $ 93 . 2 . certificates sold were in denominations of $ 3 and $ 5 . 3 . both ' m ' and ' n ' are natural numbers . step 2 : approach the value of all certificates sold , 93 is divisible by 3 . so , a maximum of 31 $ 3 certificates and no $ 5 certificates could have been sold . however , the question states that both ' m ' and ' n ' are natural numbers . hence , at least 1 $ 5 certificate should have been sold . let us reduce the number of $ 3 certificates from theoretical maximum count of 31 by say ' x ' and correspondingly increase $ 5 certificates by ' y ' . evidently , 3 x = 5 y because the value of $ 3 certificates reduced should be the same as the value of $ 5 certificates increased . it means that x has to be a multiple of 5 and y has to be a multiple of 3 . or $ 3 certificates reduce in steps of 5 certificates . step 3 : list down possibilities the following combinations are possible 1 . m = 26 , n = 3 2 . m = 21 , n = 6 3 . m = 16 , n = 9 4 . m = 11 , n = 12 5 . m = 6 , n = 15 6 . m = 1 , n = 18 an alternative way to think of the same concept - replacing five $ 3 certificates with three $ 5 certificates leads to no change in the overall value of certficates sold and gives us a new combination each time . we need to see how many such combinations are possible . answer c | physics |
math_qa__Z2SAIxUbdUyj4aHp | How long will a boy take to run round a square field of side 45 meters, if he runs at the rate of 9km/hr? Answers: A) 72 sec B) 45 sec C) 1 min D) 32 sec E) 25 sec | <gadget id="calculator">45 * 4</gadget>
<output>180</output>
<gadget id="calculator">1_000 / 3_600</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">9 * (5/18)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">180 / (5/2)</gadget>
<output>72</output>
<result>A</result> | A | 72 | How long will a boy take to run round a square field of side 45 meters, if he runs at the rate of 9km/hr? | {
"A": "72 sec",
"B": "45 sec",
"C": "1 min",
"D": "32 sec",
"E": "25 sec"
} | divide(multiply(45, const_4), multiply(9, divide(const_1000, const_3600))) | divide(const_1000,const_3600)|multiply(n0,const_4)|multiply(n1,#0)|divide(#1,#2)| | "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 45 * 4 = 180 m time taken = 180 * 2 / 5 = 72 sec answer is a" | gain |
math_qa__C8YHOguvst8S3PZd | Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 8 miles per hour, what is his average rate for the entire trip in miles per minute?
Choose the correct choice from the following choices:
A) 1 / 7
B) 2 / 15
C) 3 / 15
D) 1 / 4
E) 3 / 8 | <gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">2 / 8</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 60</gadget>
<output>15</output>
<gadget id="calculator">2 / 10</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 60</gadget>
<output>12</output>
<gadget id="calculator">15 + 12</gadget>
<output>27</output>
<gadget id="calculator">4 / 27</gadget>
<output>4/27 = around 0.148148</output>
<result>A</result> | A | 0.142857 | Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hour and swims at a rate of 8 miles per hour, what is his average rate for the entire trip in miles per minute? | {
"A": "1 / 7",
"B": "2 / 15",
"C": "3 / 15",
"D": "1 / 4",
"E": "3 / 8"
} | divide(add(2, 2), add(multiply(divide(2, 8), const_60), multiply(divide(2, 10), const_60))) | add(n0,n0)|divide(n0,n2)|divide(n0,n1)|multiply(#1,const_60)|multiply(#2,const_60)|add(#3,#4)|divide(#0,#5)| | "dan travels 4 miles round trip . running part : ( 2 / 10 = 1 / 5 * 60 = 12 minutes ) swimming part : ( 2 / 8 = 1 / 4 * 60 = 15 minutes ) 4 miles in ( 12 + 15 ) minutes 4 / 27 = 1 / 7 mile per minute answer : 1 / 7 mile per minute a" | physics |
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