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stringlengths 7
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math_qa__ZYYiahM3yFLrkrZJ | Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer R between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? Choices: A) 12 B) 15 C) 17 D) r = 18 E) 20 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<result>D</result> | D | 18 | Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer R between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? | {
"A": "12",
"B": "15",
"C": "17",
"D": "r = 18",
"E": "20"
} | multiply(multiply(const_3, const_2), 3) | multiply(const_2,const_3)|multiply(n0,#0) | since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 1112 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 1113 ) , ( 717 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 1517 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 1317 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 1819 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 2023 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) . | physics |
math_qa__lKTGxIaHaIUAnS3l | Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 2 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
Answers
A) 1 / 3 B) 1 / 2 C) 1 / 4 D) 1 E) 5 / 6 | <gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">(3/2) + 4</gadget>
<output>11/2 = around 5.5</output>
<gadget id="calculator">6 - (11/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) / 2</gadget>
<output>1/4 = around 0.25</output>
<result>C</result> | C | 0.25 | Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 2 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank. | {
"A": "1 / 3",
"B": "1 / 2",
"C": "1 / 4",
"D": "1",
"E": "5 / 6"
} | divide(subtract(add(3, 3), add(divide(3, 2), add(2, 2))), 2) | add(n1,n1)|add(n0,n0)|divide(n1,n0)|add(#1,#2)|subtract(#0,#3)|divide(#4,n0) | a + b = 2 ; a + c = 3 / 2 , b + c = 2 ; add then 2 * ( a + b + c ) = 4 + 3 / 2 = 11 / 2 a + b + c = 11 / 4 hrs c | physics |
math_qa__BYCBy53w3w8tT2mj | How many even number in the range between 8 to 100 inclusive are not divisible by 3
Choose one
A) 15
B) 30
C) 32
D) 33
E) 46 | <gadget id="calculator">100 - 8</gadget>
<output>92</output>
<gadget id="calculator">92 - 2</gadget>
<output>90</output>
<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<gadget id="calculator">100 - 2</gadget>
<output>98</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">98 - 12</gadget>
<output>86</output>
<gadget id="calculator">86 - 3</gadget>
<output>83</output>
<gadget id="calculator">83 - 3</gadget>
<output>80</output>
<gadget id="calculator">80 / 3</gadget>
<output>80/3 = around 26.666667</output>
<gadget id="calculator">(80/3) / 2</gadget>
<output>40/3 = around 13.333333</output>
<gadget id="calculator">45 - (40/3)</gadget>
<output>95/3 = around 31.666667</output>
<result>C</result> | C | 32 | How many even number in the range between 8 to 100 inclusive are not divisible by 3 | {
"A": "15",
"B": "30",
"C": "32",
"D": "33",
"E": "46"
} | subtract(divide(subtract(subtract(100, 8), const_2), const_2), divide(divide(subtract(subtract(subtract(subtract(100, const_2), multiply(3, const_4)), 3), 3), 3), const_2)) | multiply(n2,const_4)|subtract(n1,n0)|subtract(n1,const_2)|subtract(#1,const_2)|subtract(#2,#0)|divide(#3,const_2)|subtract(#4,n2)|subtract(#6,n2)|divide(#7,n2)|divide(#8,const_2)|subtract(#5,#9)| | "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 8,10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 47 . for 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 15 . hence , only divisible by 2 but not 3 = 47 - 15 = 32 . hence , answer c" | general |
math_qa__knHgxmE6vCPVmiYp | In a group of 100 people,50 like reading books,20 like both reading books and listening songs. How many like listening songs? Choices:
A) 40
B) 50
C) 70
D) 60
E) none | <gadget id="calculator">50 - 20</gadget>
<output>30</output>
<gadget id="calculator">20 + 30</gadget>
<output>50</output>
<gadget id="calculator">50 + 20</gadget>
<output>70</output>
<result>C</result> | C | 70 | In a group of 100 people,50 like reading books,20 like both reading books and listening songs. How many like listening songs? | {
"A": "40",
"B": "50",
"C": "70",
"D": "60",
"E": "none"
} | add(add(20, subtract(50, 20)), 20) | subtract(n1,n2)|add(n2,#0)|add(n2,#1) | make a venn diagram , and enter your data . let the number of people who like listening songs be x x + 20 + 30 = 100 x = 50 so number who like listening songs = 20 + 50 = 70 answer c | other |
math_qa__DdXAvhLIHCJ2r9gb | A man rows his boat 90 km downstream and 72 km upstream, taking 3 hours each time. Find the speed of the stream?
Choose the correct choice
A) 6 B) 5 C) 7 D) 3 E) 2 | <gadget id="calculator">90 / 3</gadget>
<output>30</output>
<gadget id="calculator">72 / 3</gadget>
<output>24</output>
<gadget id="calculator">30 - 24</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<result>D</result> | D | 3 | A man rows his boat 90 km downstream and 72 km upstream, taking 3 hours each time. Find the speed of the stream? | {
"A": "6",
"B": "5",
"C": "7",
"D": "3",
"E": "2"
} | divide(subtract(divide(90, 3), divide(72, 3)), const_2) | divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2)| | "speed downstream = d / t = 90 / 3 = 30 kmph speed upstream = d / t = 72 / ( 3 ) = 24 kmph the speed of the stream = ( 30 - 24 ) / 2 = 3 kmph answer : d" | physics |
math_qa__O1hoPoPWCivjK6jV | There are 97 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation? Select the correct option.
A) 29 B) 49 C) 39 D) 59 E) 69 | <gadget id="calculator">97 / 3</gadget>
<output>97/3 = around 32.333333</output>
<gadget id="calculator">floor(97/3)</gadget>
<output>32</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">97 / 5</gadget>
<output>97/5 = around 19.4</output>
<gadget id="calculator">floor(97/5)</gadget>
<output>19</output>
<gadget id="calculator">32 + 19</gadget>
<output>51</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">97 / 15</gadget>
<output>97/15 = around 6.466667</output>
<gadget id="calculator">floor(97/15)</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">51 - 12</gadget>
<output>39</output>
<result>C</result> | C | 39 | There are 97 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation? | {
"A": "29",
"B": "49",
"C": "39",
"D": "59",
"E": "69"
} | subtract(add(floor(divide(97, const_3)), floor(divide(97, add(const_1, const_4)))), multiply(floor(divide(97, multiply(const_3, add(const_1, const_4)))), const_2)) | add(const_1,const_4)|divide(n0,const_3)|divide(n0,#0)|floor(#1)|multiply(#0,const_3)|divide(n0,#4)|floor(#2)|add(#3,#6)|floor(#5)|multiply(#8,const_2)|subtract(#7,#9) | editing my solution : number of switches = 97 number of switches turned on by a : 3 , 6 , . . . 96 = 32 number of switches turned on by b : 5 , 10 , . . . . 95 = 19 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 32 - 6 ) + ( 19 - 6 ) = 39 answer : c | other |
math_qa__uNJXdDTjw9taQgVn | To fill a tank, 10 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ? Pick one:
A) 25 B) 50 C) 75 D) 100 E) 125 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">50 / 2</gadget>
<output>25</output>
<result>A</result> | A | 25 | To fill a tank, 10 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ? | {
"A": "25",
"B": "50",
"C": "75",
"D": "100",
"E": "125"
} | divide(multiply(10, add(const_4, const_1)), const_2) | add(const_1,const_4)|multiply(n0,#0)|divide(#1,const_2)| | "let the capacity of 1 bucket = x . then , the capacity of tank = 10 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 10 x ) / ( 2 x / 5 ) = ( 10 x ) x 5 / 2 x = 50 / 2 = 25 answer is a ." | physics |
math_qa__HgZzJhlVrKFJNmUA | If 30 oxen can plough 1/7th of a field in 2 days, how many days 18 oxen will take to do the remaining work? Pick:
A) 30 days
B) 20 days
C) 15 days
D) 18 days
E) 21 days | <gadget id="calculator">30 / 18</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">6 / 7</gadget>
<output>6/7 = around 0.857143</output>
<gadget id="calculator">(1/7) / (6/7)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) / 2</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(5/3) / (1/12)</gadget>
<output>20</output>
<result>B</result> | B | 20 | If 30 oxen can plough 1/7th of a field in 2 days, how many days 18 oxen will take to do the remaining work? | {
"A": "30 days",
"B": "20 days",
"C": "15 days",
"D": "18 days",
"E": "21 days"
} | divide(divide(30, 18), divide(divide(divide(1, 7), divide(subtract(7, const_1), 7)), 2)) | divide(n0,n4)|divide(n1,n2)|subtract(n2,const_1)|divide(#2,n2)|divide(#1,#3)|divide(#4,n3)|divide(#0,#5) | solution : we will use work equivalence method , 30 / 18 = ( 1 / 7 ) / ( 6 / 7 ) * x / 2 ; 5 / 3 = ( 1 / 6 ) * x / 2 ; or , x = 60 / 3 = 20 days . answer : option b | physics |
math_qa__QTGrDOhXJIsJDEvS | How many two-element subsets of {6,7,8,9} are there that do not contain the pair of elements 8 and 9?
Choose the correct choice
A) 5 B) 4 C) 3 D) 6 E) 7 | <gadget id="calculator">9 - 4</gadget>
<output>5</output>
<result>A</result> | A | 5 | How many two-element subsets of {6,7,8,9} are there that do not contain the pair of elements 8 and 9? | {
"A": "5",
"B": "4",
"C": "3",
"D": "6",
"E": "7"
} | subtract(9, const_4) | subtract(n3,const_4) | required subsets are = { 6,7 } , { 6,8 } , { 6,9 } , { 7,8 } , { 7,9 } = 5 answer : a | general |
math_qa__DdKyxKMwDJD8gDcV | One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 14 percent sugar by weight. The second solution was what percent sugar by weight? Pick one.
A) 74 % B) 64 % C) 42 % D) 28 % E) 26 % | <gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">100 * (7/50)</gadget>
<output>14</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">75 * (1/10)</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">14 - (15/2)</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">(13/2) / 25</gadget>
<output>13/50 = around 0.26</output>
<gadget id="calculator">(13/50) * 100</gadget>
<output>26</output>
<result>E</result> | E | 26 | One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 14 percent sugar by weight. The second solution was what percent sugar by weight? | {
"A": "74 %",
"B": "64 %",
"C": "42 %",
"D": "28 %",
"E": "26 %"
} | multiply(divide(subtract(multiply(const_100, divide(14, const_100)), multiply(subtract(const_100, multiply(divide(const_1, const_4), const_100)), divide(10, const_100))), multiply(divide(const_1, const_4), const_100)), const_100) | divide(n1,const_100)|divide(n0,const_100)|divide(const_1,const_4)|multiply(#0,const_100)|multiply(#2,const_100)|subtract(const_100,#4)|multiply(#1,#5)|subtract(#3,#6)|divide(#7,#4)|multiply(#8,const_100) | say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.14 - - > x = 0.26 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.14 - - > x = 0.26 . answer : e . | gain |
math_qa__xOHXb2dLBlR94LfK | There are 69 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there? Choose one
A) 2 B) 4 C) 8 D) 39 E) 32 | <gadget id="calculator">15 + 10</gadget>
<output>25</output>
<gadget id="calculator">25 + 5</gadget>
<output>30</output>
<gadget id="calculator">30 + 3</gadget>
<output>33</output>
<gadget id="calculator">69 - 33</gadget>
<output>36</output>
<gadget id="calculator">36 + 3</gadget>
<output>39</output>
<result>D</result> | D | 39 | There are 69 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there? | {
"A": "2",
"B": "4",
"C": "8",
"D": "39",
"E": "32"
} | add(subtract(69, add(add(add(15, 10), 5), 3)), 3) | add(n1,n2)|add(n3,#0)|add(n4,#1)|subtract(n0,#2)|add(n4,#3)| | "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 69 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 69 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 39 answer : d" | general |
math_qa__l0mcQJdufQOuDKMv | An employee’s annual salary was increased $25,000. If her new annual salary now equals $90,000, what was the percent increase?
Choose the correct choice from the following options.
A) 15 % B) 162 ⁄ 3 % C) 20 % D) 38.46 % E) 24 % | <gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 * 1_000</gadget>
<output>90_000</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<gadget id="calculator">25 * 1_000</gadget>
<output>25_000</output>
<gadget id="calculator">90_000 - 25_000</gadget>
<output>65_000</output>
<gadget id="calculator">90_000 / 65_000</gadget>
<output>18/13 = around 1.384615</output>
<gadget id="calculator">(18/13) - 1</gadget>
<output>5/13 = around 0.384615</output>
<gadget id="calculator">(5/13) * 100</gadget>
<output>500/13 = around 38.461538</output>
<result>D</result> | D | 38.46 | An employee’s annual salary was increased $25,000. If her new annual salary now equals $90,000, what was the percent increase? | {
"A": "15 %",
"B": "162 ⁄ 3 %",
"C": "20 %",
"D": "38.46 %",
"E": "24 %"
} | multiply(subtract(divide(multiply(subtract(const_100, const_10), const_1000), subtract(multiply(subtract(const_100, const_10), const_1000), multiply(multiply(const_0_25, const_100), const_1000))), const_1), const_100) | multiply(const_0_25,const_100)|subtract(const_100,const_10)|multiply(#1,const_1000)|multiply(#0,const_1000)|subtract(#2,#3)|divide(#2,#4)|subtract(#5,const_1)|multiply(#6,const_100) | new annual salary = $ 90,000 salary increase = $ 25,000 . original salary = $ 90,000 - $ 25,000 . = $ 75,000 % increase = ( $ 25,000 / $ 65,000 ) * 100 = 38.46 % hence d . | general |
math_qa__BNZdAhYYMGyDiXyD | 30 men can do a work in 40 days. When should 15 men leave the work so that the entire work is completed in 40 days after they leave the work? Choose the correct choice from the following: A) 87 days B) 10 days C) 15 days D) 44 days E) 22 days | <gadget id="calculator">30 * 40</gadget>
<output>1_200</output>
<gadget id="calculator">40 * 15</gadget>
<output>600</output>
<gadget id="calculator">1_200 - 600</gadget>
<output>600</output>
<gadget id="calculator">600 / 40</gadget>
<output>15</output>
<result>C</result> | C | 15 | 30 men can do a work in 40 days. When should 15 men leave the work so that the entire work is completed in 40 days after they leave the work? | {
"A": "87 days",
"B": "10 days",
"C": "15 days",
"D": "44 days",
"E": "22 days"
} | divide(subtract(multiply(30, 40), multiply(40, 15)), 40) | multiply(n0,n1)|multiply(n1,n2)|subtract(#0,#1)|divide(#2,n1) | total work to be done = 30 * 40 = 1200 let 15 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 15 * 40 ) = 1200 40 p = 600 = > p = 15 days answer : c | physics |
math_qa__8SGNJS1Lp0P9oCon | A car averages 70 mph for the first 4 hours of a trip and averages 60 mph for each additional hour. The average speed for the entire trip was 65 mph. How many hours long is the trip? Select the correct option.
A) 8
B) 9
C) 10
D) 11
E) 12 | <gadget id="calculator">65 * 4</gadget>
<output>260</output>
<gadget id="calculator">70 * 4</gadget>
<output>280</output>
<gadget id="calculator">260 - 280</gadget>
<output>-20</output>
<gadget id="calculator">60 - 65</gadget>
<output>-5</output>
<gadget id="calculator">(-20) / (-5)</gadget>
<output>4</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<result>A</result> | A | 8 | A car averages 70 mph for the first 4 hours of a trip and averages 60 mph for each additional hour. The average speed for the entire trip was 65 mph. How many hours long is the trip? | {
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "12"
} | add(divide(subtract(multiply(65, 4), multiply(70, 4)), subtract(60, 65)), 4) | multiply(n3,n1)|multiply(n0,n1)|subtract(n2,n3)|subtract(#0,#1)|divide(#3,#2)|add(n1,#4)| | "let the time for which car averages 60 mph = t 65 * ( t + 4 ) = 70 * 4 + 60 t = > 5 t = 20 = > t = 4 total duration of the trip = 4 + 4 = 8 answer a" | general |
math_qa__0qxL0TVMzTmcVeQ7 | The speed of the boat in still water in 12 kmph. It can travel downstream through 39 kms in 3 hrs. In what time would it cover the same distance upstream?
Choose the correct choice from the following:
A) 3.5 hours B) 6 hours C) 4 hours D) 5 hours E) 6 hours | <gadget id="calculator">39 / 3</gadget>
<output>13</output>
<gadget id="calculator">13 - 12</gadget>
<output>1</output>
<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">39 / 11</gadget>
<output>39/11 = around 3.545455</output>
<result>A</result> | A | 3.5 | The speed of the boat in still water in 12 kmph. It can travel downstream through 39 kms in 3 hrs. In what time would it cover the same distance upstream? | {
"A": "3.5 hours",
"B": "6 hours",
"C": "4 hours",
"D": "5 hours",
"E": "6 hours"
} | divide(39, subtract(12, subtract(divide(39, 3), 12))) | divide(n1,n2)|subtract(#0,n0)|subtract(n0,#1)|divide(n1,#2)| | "still water = 12 km / hr downstream = 39 / 3 = 13 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 13 / 2 = 11 km / hr so time taken in upstream = 39 / 11 = 3.5 hrs answer : a" | physics |
math_qa__ZHYEVTnw6eVpxhlU | In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 14 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars? Choose the correct choice.
A) 320 $
B) 380 $
C) 525 $
D) 456 $
E) 480 $ | <gadget id="calculator">0.65 * 55</gadget>
<output>35.75</output>
<gadget id="calculator">35.75 * 14</gadget>
<output>500.5</output>
<result>C</result> | C | 525 | In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 14 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars? | {
"A": "320 $",
"B": "380 $",
"C": "525 $",
"D": "456 $",
"E": "480 $"
} | multiply(multiply(0.65, 55), 14) | multiply(n1,n3)|multiply(n2,#0)| | "total cost = ( 1.75 * 14 ) + ( 0.65 * 14 * 55 ) = 24.5 + 500.5 = > 525 hence answer will be ( c ) 525" | general |
math_qa__2rWiTDOIjARNulbI | In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 14 feet between each tree. How many trees can be planted if the road is 151 feet long?
Choose the correct choice:
A) 8
B) 9
C) 10
D) 11
E) 12 | <gadget id="calculator">151 - 1</gadget>
<output>150</output>
<gadget id="calculator">14 + 1</gadget>
<output>15</output>
<gadget id="calculator">150 / 15</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<result>D</result> | D | 11 | In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 14 feet between each tree. How many trees can be planted if the road is 151 feet long? | {
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "12"
} | add(divide(subtract(151, const_1), add(14, const_1)), const_1) | add(n0,const_1)|subtract(n1,const_1)|divide(#1,#0)|add(#2,const_1)| | "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 14 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 14 feet spaces will be t - 1 . then , the length of sidewalk required for 14 feet spaces will be 14 * ( t - 1 ) it is given that total lenght of sidewalk is 166 feet . or 14 ( t - 1 ) + t = 151 or 14 t - 14 + t = 151 or 15 t = 165 or t = 11 answer : - d" | geometry |
math_qa__DfNtGTyx2oXJyf6c | The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability Q that the next couple the maitre 'd seats will not order dessert? Choose the correct answer: A) 20 % B) 25 % C) 40 % D) 60 % E) 75 % | <gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 * 10</gadget>
<output>100</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(3/5) / (4/5)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>B</result> | B | 25 | The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability Q that the next couple the maitre 'd seats will not order dessert? | {
"A": "20 %",
"B": "25 %",
"C": "40 %",
"D": "60 %",
"E": "75 %"
} | multiply(subtract(const_1, divide(divide(60, multiply(multiply(const_2, const_5), multiply(const_2, const_5))), subtract(const_1, divide(20, multiply(multiply(const_2, const_5), multiply(const_2, const_5)))))), multiply(multiply(const_2, const_5), multiply(const_2, const_5))) | multiply(const_2,const_5)|multiply(#0,#0)|divide(n0,#1)|divide(n1,#1)|subtract(const_1,#3)|divide(#2,#4)|subtract(const_1,#5)|multiply(#1,#6)| | "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . q = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %" | probability |
math_qa__W9gHyUX2rkH0fHUR | The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
Pick
A) 23 B) 20 C) 12 D) 128 E) 171 | <gadget id="calculator">2 * 120</gadget>
<output>240</output>
<gadget id="calculator">289 - 240</gadget>
<output>49</output>
<gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>
<gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">4 * 120</gadget>
<output>480</output>
<gadget id="calculator">49 + 480</gadget>
<output>529</output>
<gadget id="calculator">529 ** (1/2)</gadget>
<output>23</output>
<result>A</result> | A | 23 | The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is: | {
"A": "23",
"B": "20",
"C": "12",
"D": "128",
"E": "171"
} | sqrt(add(power(sqrt(subtract(289, multiply(const_2, 120))), const_2), multiply(const_4, 120))) | multiply(n0,const_4)|multiply(n0,const_2)|subtract(n1,#1)|sqrt(#2)|power(#3,const_2)|add(#0,#4)|sqrt(#5)| | "let the numbers be x and y . then , xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . answer a" | general |
math_qa__VvYdpyNB4g9mXUCX | When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tammy is what percent greater than the quantifying chopped by Tom?. Choose the correct choice from the following answers
A) 44 %
B) 125 %
C) 105 %
D) 225 %
E) 400 % | <gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(3/2) - (2/3)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(5/6) / (2/3)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 100</gadget>
<output>125</output>
<result>B</result> | B | 125 | When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tammy is what percent greater than the quantifying chopped by Tom?. | {
"A": "44 %",
"B": "125 %",
"C": "105 %",
"D": "225 %",
"E": "400 %"
} | multiply(divide(subtract(divide(3, 2), divide(2, 3)), divide(2, 3)), const_100) | divide(n1,n0)|divide(n0,n1)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100) | tom chops 4 lbs in 6 minutes tammy chops 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : b | physics |
math_qa__J5BSOzoRVkLaHLM4 | According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 25, by how much does the temperature in degrees Celsius (C) increase? Pick: A) 9 B) 13.88 C) 47 D) 48 3 / 5 E) 59 | <gadget id="calculator">25 * 5</gadget>
<output>125</output>
<gadget id="calculator">125 / 9</gadget>
<output>125/9 = around 13.888889</output>
<result>B</result> | B | 13.88 | According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 25, by how much does the temperature in degrees Celsius (C) increase? | {
"A": "9",
"B": "13.88",
"C": "47",
"D": "48 3 / 5",
"E": "59"
} | divide(multiply(25, 5), 9) | multiply(n1,n3)|divide(#0,n0)| | "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 25 = 57 - - > c = 5 / 9 * 25 = 13.88 . increase = 13.88 degrees . answer : b ." | general |
math_qa__OnPjDwxpr0PK4njw | Kamal obtained 76, 60, 72, 65 and 82 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? Choose the correct choice from the following options.
A) 71
B) 69
C) 72
D) 75
E) none | <gadget id="calculator">76 + 60</gadget>
<output>136</output>
<gadget id="calculator">136 + 72</gadget>
<output>208</output>
<gadget id="calculator">208 + 65</gadget>
<output>273</output>
<gadget id="calculator">273 + 82</gadget>
<output>355</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">355 / 5</gadget>
<output>71</output>
<result>A</result> | A | 71 | Kamal obtained 76, 60, 72, 65 and 82 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? | {
"A": "71",
"B": "69",
"C": "72",
"D": "75",
"E": "none"
} | divide(add(add(add(add(76, 60), 72), 65), 82), add(const_1, const_4)) | add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | "sol . average = 76 + 60 + 72 + 65 + 82 / 5 ) = ( 355 / 5 ) = 71 . answer a" | general |
math_qa__QT1jm7LehgvZXai3 | A person buys an article at Rs.550. At what price should he sell the article so as to make a profit of 30%? Choose the correct choice from the following options.
A) 600 B) 715 C) 772 D) 662 E) 521 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">550 * (3/10)</gadget>
<output>165</output>
<gadget id="calculator">550 + 165</gadget>
<output>715</output>
<result>B</result> | B | 715 | A person buys an article at Rs.550. At what price should he sell the article so as to make a profit of 30%? | {
"A": "600",
"B": "715",
"C": "772",
"D": "662",
"E": "521"
} | add(550, multiply(550, divide(30, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | "cost price = rs . 550 profit = 30 % of 550 = rs . 165 selling price = cost price + profit = 550 + 165 = 715 answer : b" | gain |
math_qa__vAdBSzo28Cc3FOCA | an article with cost price of 280 is sold at 30% profit. what is the selling price? Answers
A) 198 B) 364 C) 369 D) 207 E) 210 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">280 * (3/10)</gadget>
<output>84</output>
<gadget id="calculator">280 + 84</gadget>
<output>364</output>
<result>B</result> | B | 364 | an article with cost price of 280 is sold at 30% profit. what is the selling price? | {
"A": "198",
"B": "364",
"C": "369",
"D": "207",
"E": "210"
} | add(280, multiply(280, divide(30, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | "sp = 1.30 * 280 = 364 answer : b" | gain |
math_qa__QtQIWrL3eCPtw75J | John can type a set of pages in 5 hours at a constant rate. If John types for 3 hours and Jack does the rest of the job, who works at 2/5 constant rate of John. How long will it take for Jack alone to do the rest of the job? Choose the correct choice from the following options: A) 1 hrs B) 3 hrs C) 4 hrs D) 5 hrs E) 7 hrs | <gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 * (2/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">3 / 5</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">(1/5) * (2/5)</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/5) / (2/25)</gadget>
<output>5</output>
<result>D</result> | D | 5 | John can type a set of pages in 5 hours at a constant rate. If John types for 3 hours and Jack does the rest of the job, who works at 2/5 constant rate of John. How long will it take for Jack alone to do the rest of the job? | {
"A": "1 hrs",
"B": "3 hrs",
"C": "4 hrs",
"D": "5 hrs",
"E": "7 hrs"
} | divide(multiply(const_1, divide(2, 5)), multiply(inverse(5), subtract(const_1, divide(3, 5)))) | divide(n2,n0)|divide(n1,n0)|inverse(n0)|multiply(#0,const_1)|subtract(const_1,#1)|multiply(#2,#4)|divide(#3,#5) | john will do 3 / 5 in 3 hrs , so john does 3 / 5 of the work . . therefore , jack will do the remaining 2 / 5 th work alone . . as the speed of jack is 2 / 5 rate of john , jack will do the 2 / 5 th work in same time that john takes to complete full job . . . ans 5 d | physics |
math_qa__lKuKk7m7GAmtJyOz | A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 30%, what should be the sale price of the mixed tea? Select the correct option
A) 23.75
B) 22
C) 20.8
D) 19.2
E) none of these | <gadget id="calculator">80 * 15</gadget>
<output>1_200</output>
<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">1_200 + 400</gadget>
<output>1_600</output>
<gadget id="calculator">80 + 20</gadget>
<output>100</output>
<gadget id="calculator">1_600 / 100</gadget>
<output>16</output>
<gadget id="calculator">16 * 30</gadget>
<output>480</output>
<gadget id="calculator">480 / 100</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">(24/5) + 16</gadget>
<output>104/5 = around 20.8</output>
<result>C</result> | C | 20.8 | A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 30%, what should be the sale price of the mixed tea? | {
"A": "23.75",
"B": "22",
"C": "20.8",
"D": "19.2",
"E": "none of these"
} | add(divide(multiply(divide(add(multiply(80, 15), multiply(20, 20)), add(80, 20)), 30), const_100), divide(add(multiply(80, 15), multiply(20, 20)), add(80, 20))) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n2)|add(#1,#2)|divide(#3,#0)|multiply(n4,#4)|divide(#5,const_100)|add(#6,#4)| | "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 30 ) / 100 × 16 = 20.8 answer c" | gain |
math_qa__WTJZVztY9c4z700w | Two persons A and B can complete a piece of work in 15 days and 30 days respectively. If they work together, what part of the work will be completed in 5 days? Choose the correct answer
A) 1 / 8 B) 1 / 3 C) 1 / 6 D) 1 / 2 E) 5 / 3 | <gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/15) + (1/30)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">5 * (1/10)</gadget>
<output>1/2 = around 0.5</output>
<result>D</result> | D | 0.5 | Two persons A and B can complete a piece of work in 15 days and 30 days respectively. If they work together, what part of the work will be completed in 5 days? | {
"A": "1 / 8",
"B": "1 / 3",
"C": "1 / 6",
"D": "1 / 2",
"E": "5 / 3"
} | multiply(5, add(divide(const_1, 15), divide(const_1, 30))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)| | "a ' s one day ' s work = 1 / 15 b ' s one day ' s work = 1 / 30 ( a + b ) ' s one day ' s work = 1 / 15 + 1 / 30 = 1 / 10 the part of the work completed in 5 days = 5 ( 1 / 10 ) = 1 / 2 . answer : d" | physics |
math_qa__YhpR7ZLxLquXLl14 | The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 50 minutes after it was poured was how many degrees Fahrenheit? Choose the correct choice from the following answers
A) 63.75 B) 75 C) 80 D) 85 E) 90 | <gadget id="calculator">60 / 10</gadget>
<output>6</output>
<gadget id="calculator">1 - 2</gadget>
<output>-1</output>
<gadget id="calculator">6 * (-1)</gadget>
<output>-6</output>
<gadget id="calculator">2 ** (-6)</gadget>
<output>1/64 = around 0.015625</output>
<gadget id="calculator">(1/64) * 120</gadget>
<output>15/8 = around 1.875</output>
<gadget id="calculator">(15/8) + 60</gadget>
<output>495/8 = around 61.875</output>
<result>A</result> | A | 63.75 | The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees Fahrenheit and a is a constant. Then the temperature of the coffee 50 minutes after it was poured was how many degrees Fahrenheit? | {
"A": "63.75",
"B": "75",
"C": "80",
"D": "85",
"E": "90"
} | add(multiply(power(2, multiply(divide(60, 10), subtract(const_1, 2))), 120), 60) | divide(n4,n0)|subtract(const_1,n3)|multiply(#0,#1)|power(n3,#2)|multiply(n1,#3)|add(n4,#4)| | "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 50 minutes after it was poured is : f = 120 ( 2 ^ - 50 / 10 ) + 60 f = 120 * 1 / 32 + 60 f = 15 / 4 + 60 f = 255 / 4 = 63.75 a" | general |
math_qa__VcExC6ssySdKcDy1 | Water boils at 212°F or 100°C and ice melts at 32°F or 0°C . If the temperature of a pot of water is 40°C, what is the temperature of the pot of water in °F? Options:
A) 85 ° f B) 92 ° f C) 96 ° f D) 99 ° f E) 104 ° f | <gadget id="calculator">212 - 32</gadget>
<output>180</output>
<gadget id="calculator">180 / 100</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">(9/5) * 40</gadget>
<output>72</output>
<gadget id="calculator">72 + 32</gadget>
<output>104</output>
<result>E</result> | E | 104 | Water boils at 212°F or 100°C and ice melts at 32°F or 0°C . If the temperature of a pot of water is 40°C, what is the temperature of the pot of water in °F? | {
"A": "85 ° f",
"B": "92 ° f",
"C": "96 ° f",
"D": "99 ° f",
"E": "104 ° f"
} | add(multiply(divide(subtract(212, 32), 100), 40), 32) | subtract(n0,n2)|divide(#0,n1)|multiply(n4,#1)|add(n2,#2)| | "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 40 ) / 5 + 32 = 104 ° f the answer is e ." | physics |
math_qa__4Qmzw6EjDrV3XOLx | The number of natural numbers n such that (n+1)^2/(n+7) is an integer, is ? Select.
A) 4 B) 5 C) 6 D) 7 E) 8 | <gadget id="calculator">7 - 3</gadget>
<output>4</output>
<result>A</result> | A | 4 | The number of natural numbers n such that (n+1)^2/(n+7) is an integer, is ? | {
"A": "4",
"B": "5",
"C": "6",
"D": "7",
"E": "8"
} | subtract(7, const_3) | subtract(n2,const_3) | we can use ( n + 1 ) ^ 2 greater than ( n + 7 ) which gives n > 2 , - 3 . . . . . . . . now there are four integers - 2 . - 1 , 01 in between - 3 and 2 . so answer is 4 . answer : a | general |
math_qa__5DuDtY7LGxMoN5f9 | total dinning bill of 8 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .
Pick:
A) 11.84 B) 12.84 C) 23.84 D) 19.11 E) 10.12 | <gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">139 * (11/10)</gadget>
<output>1_529/10 = around 152.9</output>
<gadget id="calculator">(1_529/10) / 8</gadget>
<output>1_529/80 = around 19.1125</output>
<result>D</result> | D | 19.11 | total dinning bill of 8 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared . | {
"A": "11.84",
"B": "12.84",
"C": "23.84",
"D": "19.11",
"E": "10.12"
} | divide(multiply(139.00, add(divide(const_1, 10), const_1)), 8) | divide(const_1,n2)|add(#0,const_1)|multiply(n1,#1)|divide(#2,n0)| | "dinner bill of 8 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 8 = $ 19.11 answer : d" | general |
math_qa__DvUXuFqAnqOWyxdJ | 3/4 of 1/2 of 2/5 of 5060 = ? Choose the correct choice from the following answers
A) 392 B) 759 C) 753 D) 493 E) 540 | <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>3/8 = around 0.375</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(3/8) * (2/5)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 5_060</gadget>
<output>759</output>
<result>B</result> | B | 759 | 3/4 of 1/2 of 2/5 of 5060 = ? | {
"A": "392",
"B": "759",
"C": "753",
"D": "493",
"E": "540"
} | multiply(multiply(multiply(divide(3, 4), divide(1, 2)), divide(2, 5)), 5060) | divide(n3,n5)|divide(n0,n1)|divide(n2,n3)|multiply(#1,#2)|multiply(#0,#3)|multiply(n6,#4)| | "b 759 ? = 5060 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 759" | general |
math_qa__LDg29q8I11Y3yDiC | The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average. Pick one: A) 40.2 B) 40.4 C) 40.6 D) 40.8 E) none of the above | <gadget id="calculator">40.2 * 10</gadget>
<output>402</output>
<gadget id="calculator">13 + 18</gadget>
<output>31</output>
<gadget id="calculator">402 + 31</gadget>
<output>433</output>
<gadget id="calculator">433 - 31</gadget>
<output>402</output>
<gadget id="calculator">402 / 10</gadget>
<output>201/5 = around 40.2</output>
<result>A</result> | A | 40.2 | The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average. | {
"A": "40.2",
"B": "40.4",
"C": "40.6",
"D": "40.8",
"E": "none of the above"
} | divide(subtract(add(multiply(40.2, 10), add(13, 18)), 31), 10) | add(n2,n3)|multiply(n0,n1)|add(#0,#1)|subtract(#2,n4)|divide(#3,n0) | sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 18 = 402 hence , new average = 402 ⁄ 10 = 40.2 answer a | general |
math_qa__fhFI0XpfabisOQi1 | $300 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is Pick: A) $ 100 B) $ 150 C) $ 125 D) $ 120 E) $ 250 | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">300 / (5/3)</gadget>
<output>180</output>
<gadget id="calculator">180 * (2/3)</gadget>
<output>120</output>
<result>D</result> | D | 120 | $300 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is | {
"A": "$ 100",
"B": "$ 150",
"C": "$ 125",
"D": "$ 120",
"E": "$ 250"
} | multiply(divide(300, add(divide(2, 3), const_1)), divide(2, 3)) | divide(n1,n2)|add(#0,const_1)|divide(n0,#1)|multiply(#2,#0)| | "a : ( b + c ) = 2 : 3 a ' s share = 300 * 2 / 5 = $ 120 answer is d" | general |
math_qa__dJvwMzFJrrDHPVOD | What is the CP of Rs 100 stock at 4 discount, with 1/5% brokerage? Select: A) 96.9 B) 96.3 C) 96.2 D) 96.7 E) 96.21 | <gadget id="calculator">100 - 4</gadget>
<output>96</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">96 + (1/5)</gadget>
<output>481/5 = around 96.2</output>
<result>C</result> | C | 96.2 | What is the CP of Rs 100 stock at 4 discount, with 1/5% brokerage? | {
"A": "96.9",
"B": "96.3",
"C": "96.2",
"D": "96.7",
"E": "96.21"
} | add(subtract(100, 4), divide(1, 5)) | divide(n2,n3)|subtract(n0,n1)|add(#0,#1) | explanation : use the formula , cp = 100 – discount + brokerage % cp = 100 - 4 + 1 / 5 96.2 thus the cp is rs 96.2 . answer : c | gain |
math_qa__DVCzcJXE0rmauXE7 | How many X ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?
Options: A) 3 B) 16 C) 28 D) 32 E) 56 | <gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<result>D</result> | D | 32 | How many X ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen? | {
"A": "3",
"B": "16",
"C": "28",
"D": "32",
"E": "56"
} | multiply(power(const_2, 3), 4) | power(const_2,n0)|multiply(n1,#0) | ways to select 3 people from 8 people ( 4 twins x 2 ) = 8 c 3 = 56 ways to select 1 twin + 1 people = 4 c 1 * 6 c 1 = 24 ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen x = 56 - 24 = 32 ans : d | general |
math_qa__vjSmM774MVecWoxB | in the game of dubblefud , yellow chips , blue chips and green chips are each worth 2 , 4 and 5 points respectively . in a certain selection of chips , the product of the point values of the chips is 16000 . if the number of blue chips in this selection equals the number of green chips , how many yellow chips are in the selection ? Choose the correct choice from the following answers: A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<gadget id="calculator">16_000 / 40</gadget>
<output>400</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">400 / 100</gadget>
<output>4</output>
<result>D</result> | D | 4 | in the game of dubblefud , yellow chips , blue chips and green chips are each worth 2 , 4 and 5 points respectively . in a certain selection of chips , the product of the point values of the chips is 16000 . if the number of blue chips in this selection equals the number of green chips , how many yellow chips are in the selection ? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | divide(divide(16000, multiply(multiply(2, 4), 5)), power(const_10, const_2)) | multiply(n0,n1)|power(const_10,const_2)|multiply(n2,#0)|divide(n3,#2)|divide(#3,#1) | this is equivalent to : - 2 x * 4 y * 5 z = 16000 y = z ( given ) 2 x * 4 y * 5 y = 16000 2 x * y ^ 2 = 16000 / 20 2 x * y ^ 2 = 800 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 4 as 2 * 4 * y ^ 2 = 800 y ^ 2 = 100 y = 10 number of yellow chips = 4 hence d | general |
math_qa__wD7drZRo91CGTadj | If the wheel is 18 cm then the number of revolutions to cover a distance of 1056 cm is? Choose the correct choice from the following options.
A) 18 B) 26 C) 14 D) 12 E) 9.3 | <gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">1 * 10</gadget>
<output>10</output>
<gadget id="calculator">300 + 10</gadget>
<output>310</output>
<gadget id="calculator">310 + 4</gadget>
<output>314</output>
<gadget id="calculator">314 / 100</gadget>
<output>157/50 = around 3.14</output>
<gadget id="calculator">2 * (157/50)</gadget>
<output>157/25 = around 6.28</output>
<gadget id="calculator">(157/25) * 18</gadget>
<output>2_826/25 = around 113.04</output>
<gadget id="calculator">1_056 / (2_826/25)</gadget>
<output>4_400/471 = around 9.341826</output>
<result>E</result> | E | 9.3 | If the wheel is 18 cm then the number of revolutions to cover a distance of 1056 cm is? | {
"A": "18",
"B": "26",
"C": "14",
"D": "12",
"E": "9.3"
} | divide(1056, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 18)) | multiply(const_100,const_3)|multiply(const_1,const_10)|add(#0,#1)|add(#2,const_4)|divide(#3,const_100)|multiply(#4,const_2)|multiply(n0,#5)|divide(n1,#6)| | "2 * 22 / 7 * 18 * x = 1056 = > x = 9.3 answer : e" | physics |
math_qa__LiA3a0VWckB4MDFX | If a large pizza has a radius that is 60% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza? Select the correct option
A) 30 % B) 60 % C) 98 % D) 120 % E) 156 % | <gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) ** 2</gadget>
<output>64/25 = around 2.56</output>
<gadget id="calculator">(64/25) - 1</gadget>
<output>39/25 = around 1.56</output>
<gadget id="calculator">(39/25) * 100</gadget>
<output>156</output>
<result>E</result> | E | 156 | If a large pizza has a radius that is 60% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza? | {
"A": "30 %",
"B": "60 %",
"C": "98 %",
"D": "120 %",
"E": "156 %"
} | multiply(subtract(power(add(const_1, divide(60, const_100)), const_2), const_1), const_100) | divide(n0,const_100)|add(#0,const_1)|power(#1,const_2)|subtract(#2,const_1)|multiply(#3,const_100)| | "let the radius of medium pizza be r . then the radius of large pizza is 1.6 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.6 * r ) ^ 2 = 2.56 * pi * r ^ 2 , an increase of 156 % . the answer is e ." | gain |
math_qa__Hr9ziXbRvGe8Baky | If a - b = 3 and a(power 2) + b(power 2) = 25, find the value of ab. Choose the most appropriate option
A) 5 B) 8 C) 4 D) 10 E) 3 | <gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">25 - 9</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>B</result> | B | 8 | If a - b = 3 and a(power 2) + b(power 2) = 25, find the value of ab. | {
"A": "5",
"B": "8",
"C": "4",
"D": "10",
"E": "3"
} | divide(subtract(25, power(3, 2)), 2) | power(n0,n1)|subtract(n3,#0)|divide(#1,n1) | 2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 25 - 9 = 16 ab = 8 . answer is b . | general |
math_qa__BATHoEaZr4I7eIxJ | A car takes 6 hours to cover a distance of 144 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Choose the correct answer:
A) 50 kmph B) 60 kmph C) 65 kmph D) 16 kmph E) none | <gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">144 / 9</gadget>
<output>16</output>
<result>D</result> | D | 16 | A car takes 6 hours to cover a distance of 144 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? | {
"A": "50 kmph",
"B": "60 kmph",
"C": "65 kmph",
"D": "16 kmph",
"E": "none"
} | divide(144, divide(multiply(6, 3), 2)) | multiply(n0,n2)|divide(#0,n3)|divide(n1,#1)| | "time = 6 distence = 144 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 144 / 9 = 16 kmph d )" | physics |
math_qa__9lLg6jQnFF2VlSTl | How long will it take a train travelling at 78kmph to pass an electric pole if the train is 110 meters in lenght? Choose the correct choice from the following answers: A) 2.07 B) 3.07 C) 5.07 D) 4.07 E) 2 | <gadget id="calculator">110 / 1_000</gadget>
<output>11/100 = around 0.11</output>
<gadget id="calculator">(11/100) / 78</gadget>
<output>11/7_800 = around 0.00141</output>
<gadget id="calculator">(11/7_800) * 3_600</gadget>
<output>66/13 = around 5.076923</output>
<result>C</result> | C | 5.07 | How long will it take a train travelling at 78kmph to pass an electric pole if the train is 110 meters in lenght? | {
"A": "2.07",
"B": "3.07",
"C": "5.07",
"D": "4.07",
"E": "2"
} | multiply(divide(divide(110, const_1000), 78), const_3600) | divide(n1,const_1000)|divide(#0,n0)|multiply(#1,const_3600) | sol . speed = [ 78 x 5 / 18 ] m / sec = 21.7 m / sec . time taken = ( 110 / 21.7 ) sec = 5.07 sec . answer c | physics |
math_qa__veRY0fnyBv9hmCLL | The cash realised on selling a 14% stock is Rs.106.25, brokerage being 1/4% is Choose the correct choice from the following: A) 123 B) 106 C) 100 D) 156 E) 240 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">106.25 - (1/4)</gadget>
<output>106</output>
<result>B</result> | B | 106 | The cash realised on selling a 14% stock is Rs.106.25, brokerage being 1/4% is | {
"A": "123",
"B": "106",
"C": "100",
"D": "156",
"E": "240"
} | subtract(106.25, divide(1, 4)) | divide(n2,n3)|subtract(n1,#0) | explanation : cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b | general |
math_qa__cI9p4FU19ZevgshH | If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 54kmh, what was the average speed of the car for the entire trip? Choose the correct choice from the following choices.
A) 36 kmh B) 40 kmh C) 41 kmh D) 44 kmh E) 50 kmh | <gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/80) + (1/24)</gadget>
<output>13/240 = around 0.054167</output>
<gadget id="calculator">1 / 54</gadget>
<output>1/54 = around 0.018519</output>
<gadget id="calculator">(13/240) + (1/54)</gadget>
<output>157/2_160 = around 0.072685</output>
<gadget id="calculator">3 / (157/2_160)</gadget>
<output>6_480/157 = around 41.273885</output>
<result>C</result> | C | 41 | If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 54kmh, what was the average speed of the car for the entire trip? | {
"A": "36 kmh",
"B": "40 kmh",
"C": "41 kmh",
"D": "44 kmh",
"E": "50 kmh"
} | divide(const_3, add(add(divide(const_1, 80), divide(const_1, 24)), divide(const_1, 54))) | divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|add(#3,#2)|divide(const_3,#4)| | "assume d / 3 = 2160 ( this number is convenient because it is divisible by 80 , 24 and 54 ) so : 2160 = 80 * t 1 = 27 hrs 2160 = 24 * t 2 = 90 hrs 2160 = 54 * t 3 = 40 hrs t = t 1 + t 2 + t 3 = 157 hrs d = rt ( 240 * 3 ) = r * 157 r = 41.27 answer : c" | physics |
math_qa__IVuJeXY4FJDrC4lh | Rice weighing 25/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces) Choose the correct choice from the following options:
A) 22
B) 25
C) 28
D) 31
E) 34 | <gadget id="calculator">25 / 4</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">(25/4) * 16</gadget>
<output>100</output>
<gadget id="calculator">100 / 4</gadget>
<output>25</output>
<result>B</result> | B | 25 | Rice weighing 25/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces) | {
"A": "22",
"B": "25",
"C": "28",
"D": "31",
"E": "34"
} | divide(multiply(divide(25, 4), 16), 4) | divide(n0,n1)|multiply(n4,#0)|divide(#1,n2)| | "25 / 4 ÷ 4 = 25 / 16 pounds in each container 25 / 16 pounds * 16 ounces / pound = 25 ounces in each container the answer is b ." | general |
math_qa__855HW93qKrqierrR | A towel, when bleached, lost 20% of its length and 20% of its breadth. What is the percentage decrease in area? Choose the correct choice from the following options:
A) 24 %
B) 36 %
C) 32 %
D) 54 %
E) 64 % | <gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 * 80</gadget>
<output>6_400</output>
<gadget id="calculator">10_000 - 6_400</gadget>
<output>3_600</output>
<gadget id="calculator">3_600 / 100</gadget>
<output>36</output>
<result>B</result> | B | 36 | A towel, when bleached, lost 20% of its length and 20% of its breadth. What is the percentage decrease in area? | {
"A": "24 %",
"B": "36 %",
"C": "32 %",
"D": "54 %",
"E": "64 %"
} | divide(subtract(multiply(const_100, const_100), multiply(subtract(const_100, 20), subtract(const_100, 20))), const_100) | multiply(const_100,const_100)|subtract(const_100,n0)|subtract(const_100,n1)|multiply(#1,#2)|subtract(#0,#3)|divide(#4,const_100)| | "percentage change in area = ( − 20 − 20 + ( 20 × 20 ) / 100 ) % = − 36 % i . e . , area is decreased by 36 % answer : b" | gain |
math_qa__7ozA0TNGs7gVaoj7 | a business finds that their ratio of spending to income is 5 to 9 . their total profit is $ 48000 . what is their total income ?
Select the correct option
A) $ 90000 B) $ 108000 C) $ 119000 D) $ 126000 E) $ 140000 | <gadget id="calculator">9 - 5</gadget>
<output>4</output>
<gadget id="calculator">48_000 / 4</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 * 9</gadget>
<output>108_000</output>
<result>B</result> | B | 108,000 | a business finds that their ratio of spending to income is 5 to 9 . their total profit is $ 48000 . what is their total income ? | {
"A": "$ 90000",
"B": "$ 108000",
"C": "$ 119000",
"D": "$ 126000",
"E": "$ 140000"
} | multiply(divide(48000, subtract(9, 5)), 9) | subtract(n1,n0)|divide(n2,#0)|multiply(n1,#1) | let x equal the amount of spending , and y equal the amount of income . we know that x = 5 / 9 y we also know that x = y - 48000 therefore we can simplify to : y - 48000 = 5 / 9 y we isolate y , and get : 4 / 9 y = 48000 and to solve for y , we get : y = 48000 answer : b | other |
math_qa__vmCtmryFQOM40Qgg | 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 1/10. For a group of 300 newborn members of the population, approximately how many would be expected to survive the first 3 months of life? Options.
A) 219 B) 246 C) 252 D) 262 E) 270 | <gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">300 * (9/10)</gadget>
<output>270</output>
<gadget id="calculator">270 * (9/10)</gadget>
<output>243</output>
<gadget id="calculator">243 * (9/10)</gadget>
<output>2_187/10 = around 218.7</output>
<result>A</result> | A | 219 | 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 1/10. For a group of 300 newborn members of the population, approximately how many would be expected to survive the first 3 months of life? | {
"A": "219",
"B": "246",
"C": "252",
"D": "262",
"E": "270"
} | multiply(multiply(multiply(300, subtract(1, divide(1, 10))), subtract(1, divide(1, 10))), subtract(1, divide(1, 10))) | divide(n1,n2)|subtract(n1,#0)|multiply(n3,#1)|multiply(#2,#1)|multiply(#3,#1)| | "number of newborns that can die in first month = 1 / 10 * 300 = 30 survived = 270 number of newborns that can die in second month = 1 / 10 * 270 = 27 survived = 243 number of newborns that can die in third month = 1 / 10 * 243 = 24 survived = 219 answer : a" | probability |
math_qa__bnAdz5RrgiFl5enU | What is the perimeter, in meters, of a rectangular garden 12 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide? Choose the most appropriate option:
A) 48
B) 56
C) 60
D) 56
E) 192 | <gadget id="calculator">16 * 12</gadget>
<output>192</output>
<gadget id="calculator">192 / 12</gadget>
<output>16</output>
<gadget id="calculator">2 * (16 + 12)</gadget>
<output>56</output>
<result>D</result> | D | 56 | What is the perimeter, in meters, of a rectangular garden 12 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide? | {
"A": "48",
"B": "56",
"C": "60",
"D": "56",
"E": "192"
} | rectangle_perimeter(divide(rectangle_area(16, 12), 12), 12) | rectangle_area(n1,n2)|divide(#0,n0)|rectangle_perimeter(n0,#1)| | "say length of garden is l meters . then ( l * 12 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 16 meters . perimeter of garden = 2 * ( 16 + 12 ) = 56 meter . answer is d" | geometry |
math_qa__qDGagu9bFPdtrQOD | How many seconds will a train 100 meters long take to cross a bridge 200 meters long if the speed of the train is 36 kmph? Choose the correct answer:
A) 22 sec B) 27 sec C) 30 sec D) 24 sec E) 11 sec | <gadget id="calculator">200 + 100</gadget>
<output>300</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">300 / 10</gadget>
<output>30</output>
<result>C</result> | C | 30 | How many seconds will a train 100 meters long take to cross a bridge 200 meters long if the speed of the train is 36 kmph? | {
"A": "22 sec",
"B": "27 sec",
"C": "30 sec",
"D": "24 sec",
"E": "11 sec"
} | divide(add(200, 100), multiply(36, const_0_2778)) | add(n0,n1)|multiply(n2,const_0_2778)|divide(#0,#1)| | "explanation : d = 100 + 200 = 300 s = 36 * 5 / 18 = 10 mps t = 300 / 10 = 10 sec answer : option c" | physics |
math_qa__1NbTwltXlD1na20m | In a bag, there are 5 green, 6 black and 7 red pens. One pen is picked up randomly. What is the probability that it is neither red nor green? Pick
A) 5 / 18
B) 7 / 18
C) 1 / 3
D) 1 / 2
E) 1 / 5 | <gadget id="calculator">5 + 6</gadget>
<output>11</output>
<gadget id="calculator">11 + 7</gadget>
<output>18</output>
<gadget id="calculator">6 / 18</gadget>
<output>1/3 = around 0.333333</output>
<result>C</result> | C | 0.333333 | In a bag, there are 5 green, 6 black and 7 red pens. One pen is picked up randomly. What is the probability that it is neither red nor green? | {
"A": "5 / 18",
"B": "7 / 18",
"C": "1 / 3",
"D": "1 / 2",
"E": "1 / 5"
} | divide(6, add(add(5, 6), 7)) | add(n0,n1)|add(n2,#0)|divide(n1,#1) | explanation : neither red nor green means the pen drawn is black . total number of outcomes = ( 5 + 6 + 7 ) = 18 . number of favourable outcomes = 6 = number of black pens . hence , probability of the event = 6 / 18 = 1 / 3 . answer : c | other |
math_qa__Q9Y5fjxe2hgfyFYv | The marks obtained by Polly and Sandy are in the ratio 5:6 and those obtained by Sandy and Willy are in the ratio of 9:7. The marks obtained by Polly and Willy are in the ratio of...? Choose the correct choice from the following answers:
A) 9 : 8 B) 11 : 10 C) 13 : 12 D) 15 : 14 E) 17 : 16 | <gadget id="calculator">5 * 9</gadget>
<output>45</output>
<gadget id="calculator">6 * 7</gadget>
<output>42</output>
<gadget id="calculator">45 / 42</gadget>
<output>15/14 = around 1.071429</output>
<result>D</result> | D | 1.071429 | The marks obtained by Polly and Sandy are in the ratio 5:6 and those obtained by Sandy and Willy are in the ratio of 9:7. The marks obtained by Polly and Willy are in the ratio of...? | {
"A": "9 : 8",
"B": "11 : 10",
"C": "13 : 12",
"D": "15 : 14",
"E": "17 : 16"
} | divide(multiply(5, 9), multiply(6, 7)) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1) | polly : sandy = 5 : 6 = 15 : 18 sandy : willy = 9 : 7 = 18 : 14 polly : sandy : willy = 15 : 18 : 14 polly : willy = 15 : 14 the answer is d . | other |
math_qa__PC3IofDFBCJ6CLkh | X can finish a work in 36 days. Y can finish the same work in 24 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work? Choose the correct choice from the following answers:
A) 12 B) 13 C) 16 D) 17 E) 18 | <gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">12 * (1/24)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">(1/2) / (1/36)</gadget>
<output>18</output>
<result>E</result> | E | 18 | X can finish a work in 36 days. Y can finish the same work in 24 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work? | {
"A": "12",
"B": "13",
"C": "16",
"D": "17",
"E": "18"
} | divide(subtract(const_1, multiply(12, divide(const_1, 24))), divide(const_1, 36)) | divide(const_1,n1)|divide(const_1,n0)|multiply(n2,#0)|subtract(const_1,#2)|divide(#3,#1)| | "work done by x in 1 day = 1 / 36 work done by y in 1 day = 1 / 24 work done by y in 12 days = 12 / 24 = 1 / 2 remaining work = 1 – 1 / 2 = 1 / 2 number of days in which x can finish the remaining work = ( 1 / 2 ) / ( 1 / 36 ) = 18 e" | physics |
math_qa__fWkj3MFKHASGyR0d | Two cars started at the same time, from the same point, driving along the same road. The rate of the first car is 50 mph and the rate of the second car is 60 mph. How long will it take for the distance between the two cars to be 30 miles? Choose the correct answer
A) 1 hrs B) 2 hrs C) 3 hrs D) 4 hrs E) 5 hrs | <gadget id="calculator">60 - 50</gadget>
<output>10</output>
<gadget id="calculator">30 / 10</gadget>
<output>3</output>
<result>C</result> | C | 3 | Two cars started at the same time, from the same point, driving along the same road. The rate of the first car is 50 mph and the rate of the second car is 60 mph. How long will it take for the distance between the two cars to be 30 miles? | {
"A": "1 hrs",
"B": "2 hrs",
"C": "3 hrs",
"D": "4 hrs",
"E": "5 hrs"
} | divide(30, subtract(60, 50)) | subtract(n1,n0)|divide(n2,#0) | car 1 50 50 50 total = 150 car 2 60 60 60 total = 180 differece = 30 miles after 3 hrs . answer : c | physics |
math_qa__nxrtnjfw03c5Qubv | A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long? Choices.
A) 65 B) 80 C) 85 D) 82 E) 89 | <gadget id="calculator">240 + 650</gadget>
<output>890</output>
<gadget id="calculator">240 / 24</gadget>
<output>10</output>
<gadget id="calculator">890 / 10</gadget>
<output>89</output>
<result>E</result> | E | 89 | A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long? | {
"A": "65",
"B": "80",
"C": "85",
"D": "82",
"E": "89"
} | divide(add(240, 650), speed(240, 24)) | add(n0,n2)|speed(n0,n1)|divide(#0,#1) | speed = ( 240 / 24 ) m / sec = 10 m / sec . therefore , required time = ( 240 + 650 ) / 10 sec = 89 sec . answer is e . | physics |
math_qa__myGXyrCr2z5btQER | A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A? Choose the correct choice from the following choices:
A) 40 %
B) 45 %
C) 50 %
D) 60 %
E) 55 % | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<result>D</result> | D | 60 | A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A? | {
"A": "40 %",
"B": "45 %",
"C": "50 %",
"D": "60 %",
"E": "55 %"
} | multiply(divide(const_3, add(const_3, const_2)), const_100) | add(const_2,const_3)|divide(const_3,#0)|multiply(#1,const_100)| | "another method to solve this question using equations : 1 kg of brand a will have 400 g millet and 600 g sunflower . 1 kg of brand b will gave 650 g millet and 350 g sunflower . suppose , x kg of brand a and y kg of brand b are in the mixture . then total weight of millet = 400 x + 650 y g total weight of mixture = 1000 x + 1000 y g given that millet is 500 % hence ( 400 x + 650 y ) / ( 1000 x + 1000 y ) = 1 / 2 or , 800 x + 1300 y = 1000 x + 1000 y or 300 y = 200 x or , x / y = 3 / 2 % of brand a = ( 3 / ( 3 + 2 ) ) * 100 = 60 % hence answer is d" | gain |
math_qa__AzL803OlKjnDPBLi | A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.360 in all. For how many days was he absent? Select the correct option.
A) 8 B) 12 C) 15 D) 17 E) 19 | <gadget id="calculator">7.5 * 30</gadget>
<output>225</output>
<gadget id="calculator">225 + 360</gadget>
<output>585</output>
<gadget id="calculator">7.5 + 25</gadget>
<output>32.5</output>
<gadget id="calculator">585 / 32.5</gadget>
<output>18</output>
<gadget id="calculator">30 - 18</gadget>
<output>12</output>
<result>B</result> | B | 12 | A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.360 in all. For how many days was he absent? | {
"A": "8",
"B": "12",
"C": "15",
"D": "17",
"E": "19"
} | subtract(30, divide(add(multiply(7.50, 30), 360), add(7.50, 25))) | add(n1,n2)|multiply(n0,n2)|add(n3,#1)|divide(#2,#0)|subtract(n0,#3)| | "30 * 25 = 750 360 - - - - - - - - - - - 380 25 + 7.50 = 32.5 390 / 32.5 = 12 b" | physics |
math_qa__UxIk3GDmWBzFr9Yq | When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ? Choose the correct choice from the following choices
A) 349 B) 300 C) 500 D) 450 E) 250 | <gadget id="calculator">10 + 12</gadget>
<output>22</output>
<gadget id="calculator">22 + 4</gadget>
<output>26</output>
<gadget id="calculator">13 * 26</gadget>
<output>338</output>
<gadget id="calculator">338 + 11</gadget>
<output>349</output>
<result>A</result> | A | 349 | When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ? | {
"A": "349",
"B": "300",
"C": "500",
"D": "450",
"E": "250"
} | add(multiply(13, add(add(const_10, const_12), const_4)), 11) | add(const_10,const_12)|add(#0,const_4)|multiply(n0,#1)|add(n1,#2) | x = 13 p + 11 and x = 17 q + 9 13 p + 11 = 17 q + 9 17 q - 13 p = 2 q = 2 + 13 p / 17 least value of p which q = 2 + 13 p / 17 = > 26 x = ( 13 * 26 + 11 ) = 349 answer a | general |
math_qa__umpdUAVDBLuepGmr | A football player scores 3 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 choice from the following.
A) 4 B) 6 C) 8 D) 11 E) 12 | <gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 0.2</gadget>
<output>4</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">8 + 3</gadget>
<output>11</output>
<result>D</result> | D | 11 | A football player scores 3 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": "11",
"E": "12"
} | add(subtract(multiply(const_4, 3), multiply(multiply(const_4, 5), 0.2)), 3) | 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 go higher or lower with your next test . here , i ' ll start with answer d = 11 goals if . . . . total goals = 11 goals 5 th game = 3 goals 1 st 4 games = 8 goals avg . for 4 games = 8 / 4 = 2 goals / game avg . for all 5 games = 6 / 5 = 2.2 goals / game 2.2 * 5 = 11 so answer d | general |
math_qa__CYLc20gn9rcRKJql | 350 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees Options:
A) 10 B) 12 C) 14 D) 16 E) 17 | <gadget id="calculator">26 - 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">350 / 25</gadget>
<output>14</output>
<result>C</result> | C | 14 | 350 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees | {
"A": "10",
"B": "12",
"C": "14",
"D": "16",
"E": "17"
} | divide(350, add(subtract(26, 2), const_1)) | subtract(n1,n2)|add(#0,const_1)|divide(n0,#1)| | "26 trees have 25 gaps between them , required distance ( 350 / 25 ) = 14 c" | physics |
math_qa__suMBMCovHOuqeNj8 | The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years? Choose the correct choice from the following answers
A) 4300 B) 4500 C) 5120 D) 5230 E) 5366 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">8_000 * (1/5)</gadget>
<output>1_600</output>
<gadget id="calculator">8_000 - 1_600</gadget>
<output>6_400</output>
<gadget id="calculator">6_400 * (1/5)</gadget>
<output>1_280</output>
<gadget id="calculator">6_400 - 1_280</gadget>
<output>5_120</output>
<result>C</result> | C | 5,120 | The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years? | {
"A": "4300",
"B": "4500",
"C": "5120",
"D": "5230",
"E": "5366"
} | subtract(subtract(8000, multiply(8000, divide(20, const_100))), multiply(subtract(8000, multiply(8000, divide(20, const_100))), divide(20, const_100))) | divide(n1,const_100)|multiply(n0,#0)|subtract(n0,#1)|multiply(#0,#2)|subtract(#2,#3)| | "formula : ( after = 100 denominator ago = 100 numerator ) 8000 × 80 / 100 × 80 / 100 = 5120 c" | gain |
math_qa__dvuLU4iwZpuxFrMd | A man buys an item at Rs. 600 and sells it at the loss of 20 percent. Then what is the selling price of that item Choose the correct answer
A) rs . 480 B) rs . 760 C) rs . 860 D) rs . 960 E) none of these | <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">600 * (4/5)</gadget>
<output>480</output>
<result>A</result> | A | 480 | A man buys an item at Rs. 600 and sells it at the loss of 20 percent. Then what is the selling price of that item | {
"A": "rs . 480",
"B": "rs . 760",
"C": "rs . 860",
"D": "rs . 960",
"E": "none of these"
} | multiply(600, subtract(const_1, divide(20, const_100))) | divide(n1,const_100)|subtract(const_1,#0)|multiply(n0,#1)| | "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 600 = 80 / 100 * 600 = 480 option a" | gain |
math_qa__UEPYwmV8axZEASh4 | Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.8 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect? Pick
A) 1 / 6 B) 1 / 2 C) 5 / 8 D) 5 / 6 E) 15 / 16 | <gadget id="calculator">0.75 - 0.5</gadget>
<output>0.25</output>
<gadget id="calculator">0.8 - 0.5</gadget>
<output>0.3</output>
<gadget id="calculator">0.25 / 0.3</gadget>
<output>0.833333</output>
<result>D</result> | D | 0.833333 | Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.8 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect? | {
"A": "1 / 6",
"B": "1 / 2",
"C": "5 / 8",
"D": "5 / 6",
"E": "15 / 16"
} | divide(subtract(0.75, 0.5), subtract(0.8, 0.5)) | subtract(n2,n0)|subtract(n1,n0)|divide(#0,#1)| | "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.8 ( x ) + 0.5 ( 1 - x ) = 0.75 0.3 x = 0.75 - 0.5 x = 0.25 / 0.3 x = 5 / 6 therefore the answer is d : 5 / 6 ." | gain |
math_qa__UsSg8QTKuThfEvbg | If k is an integer and 0.00010101 x 10^k is greater than 10, what is the least possible value of k? Choose the correct option:
A) 3 B) 4 C) 5 D) 6 E) 7 | <gadget id="calculator">10 / 0.000101</gadget>
<output>99_009.90099</output>
<gadget id="calculator">log(99_009.90099)</gadget>
<output>11.502975</output>
<gadget id="calculator">log(10)</gadget>
<output>log(10) = around 2.302585</output>
<gadget id="calculator">11.502975 / log(10)</gadget>
<output>11.502975/log(10) = around 4.995679</output>
<result>C</result> | C | 5 | If k is an integer and 0.00010101 x 10^k is greater than 10, what is the least possible value of k? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | divide(log(divide(10, 0.00010101)), log(10)) | divide(n2,n0)|log(n1)|log(#0)|divide(#2,#1)| | "0.00010101 * 10 ^ k > 10 we need to move the decimal point to the right 5 places to get 10.101 this is equivalent to multiplying by 10 ^ 5 . the answer is c ." | general |
math_qa__ks1aLrQJAnmtKYCZ | What least number must be subtracted from 42398 so that remaining no.is divisible by 15 Select the correct option: A) 3 B) 5 C) 6 D) 8 E) 9 | <gadget id="calculator">42_398 / 15</gadget>
<output>42_398/15 = around 2_826.533333</output>
<gadget id="calculator">floor(42_398/15)</gadget>
<output>2_826</output>
<gadget id="calculator">2_826 * 15</gadget>
<output>42_390</output>
<gadget id="calculator">42_398 - 42_390</gadget>
<output>8</output>
<result>D</result> | D | 8 | What least number must be subtracted from 42398 so that remaining no.is divisible by 15 | {
"A": "3",
"B": "5",
"C": "6",
"D": "8",
"E": "9"
} | subtract(42398, multiply(floor(divide(42398, 15)), 15)) | divide(n0,n1)|floor(#0)|multiply(n1,#1)|subtract(n0,#2)| | "explanation : on dividing 42398 by 15 we get the remainder 8 , so 8 should be subtracted option d" | general |
math_qa__RufoQXVSOPMFV7tR | A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Select:
A) 14 years
B) 18 years
C) 20 years
D) 22 years
E) 17 years | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">24 - 2</gadget>
<output>22</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">22 / 1</gadget>
<output>22</output>
<result>D</result> | D | 22 | A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: | {
"A": "14 years",
"B": "18 years",
"C": "20 years",
"D": "22 years",
"E": "17 years"
} | divide(subtract(24, 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 the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 x = 22 . answer d" | general |
math_qa__dr0EBdRRMt4IJfBW | Pat, kate and mark charged a total of 180 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate.
Answers:
A) 18 B) 36 C) 72 D) 90 E) 100 | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">3 + 6</gadget>
<output>9</output>
<gadget id="calculator">180 / 9</gadget>
<output>20</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">20 * 5</gadget>
<output>100</output>
<result>E</result> | E | 100 | Pat, kate and mark charged a total of 180 hours to a certain project . If pat charged twice as much time to the project as kate and 1/3 as much times as mark, how many more hours did mark charge to the project than kate. | {
"A": "18",
"B": "36",
"C": "72",
"D": "90",
"E": "100"
} | multiply(divide(180, add(add(1, const_2), multiply(const_2, 3))), subtract(multiply(const_2, 3), 1)) | add(n1,const_2)|multiply(n2,const_2)|add(#0,#1)|subtract(#1,n1)|divide(n0,#2)|multiply(#4,#3) | let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 180 - total hours charged for , x = 20 . mat charged 6 x - x or 5 x for more hours than kate , or for 100 hours . e is correct | general |
math_qa__DfJLSIjwsO0Bzdah | One tap, working alone at its maximum constant rate, can fill a certain sink in 287 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 283 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to Choose the correct choice from the following.
A) 142 seconds B) 150 seconds C) 177 seconds D) 200 seconds E) 270 seconds | <gadget id="calculator">1 / 287</gadget>
<output>1/287 = around 0.003484</output>
<gadget id="calculator">1 / 283</gadget>
<output>1/283 = around 0.003534</output>
<gadget id="calculator">(1/287) + (1/283)</gadget>
<output>570/81_221 = around 0.007018</output>
<gadget id="calculator">1 / (570/81_221)</gadget>
<output>81_221/570 = around 142.492982</output>
<result>A</result> | A | 142 | One tap, working alone at its maximum constant rate, can fill a certain sink in 287 seconds. A second tap, working alone at its maximum constant rate, can fill the same sink in 283 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the sink is closest to | {
"A": "142 seconds",
"B": "150 seconds",
"C": "177 seconds",
"D": "200 seconds",
"E": "270 seconds"
} | divide(const_1, add(divide(const_1, 287), divide(const_1, 283))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2) | tap 1 : 283 secs tap 2 : 287 secs considering the average of these 2 taps : 285 secs . so 1 tap can fill the tank in 285 secs , so 2 taps can fill the tank in 285 / 2 = 142.5 secs . closest answer is a . | physics |
math_qa__WCE494AG3Me4wyr7 | Of the 85 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool? Choose the most appropriate option
A) 10 B) 15 C) 20 D) 25 E) 30 | <gadget id="calculator">50 - 35</gadget>
<output>15</output>
<gadget id="calculator">40 - 35</gadget>
<output>5</output>
<gadget id="calculator">15 + 5</gadget>
<output>20</output>
<gadget id="calculator">20 + 35</gadget>
<output>55</output>
<gadget id="calculator">85 - 55</gadget>
<output>30</output>
<result>E</result> | E | 30 | Of the 85 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool? | {
"A": "10",
"B": "15",
"C": "20",
"D": "25",
"E": "30"
} | subtract(85, add(add(subtract(50, 35), subtract(40, 35)), 35)) | subtract(n1,n3)|subtract(n2,n3)|add(#0,#1)|add(n3,#2)|subtract(n0,#3)| | "neither car nor garage = total - garage - ( swim - common ) = 85 - 50 - ( 40 - 35 ) = 85 - 55 = 30 answer e" | other |
math_qa__96AHVgukCKm8djV0 | A train running at the speed of 240 km/hr crosses a pole in 21 seconds. What is the length of the train? Pick one.
A) 1300 m B) 1350 m C) 1400 m D) 1450 m E) 1500 m | <gadget id="calculator">240 * 1_000</gadget>
<output>240_000</output>
<gadget id="calculator">240_000 / 3_600</gadget>
<output>200/3 = around 66.666667</output>
<gadget id="calculator">(200/3) * 21</gadget>
<output>1_400</output>
<result>C</result> | C | 1,400 | A train running at the speed of 240 km/hr crosses a pole in 21 seconds. What is the length of the train? | {
"A": "1300 m",
"B": "1350 m",
"C": "1400 m",
"D": "1450 m",
"E": "1500 m"
} | multiply(divide(multiply(240, const_1000), const_3600), 21) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = ( 240 * 5 / 18 ) m / sec = ( 200 / 3 ) m / sec length of the train = ( speed x time ) = ( 200 / 3 * 21 ) m = 1400 m . answer : c" | physics |
math_qa__1gMYxuHg7iM9rETA | The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits M of the larger integer? Choose the correct choice from the following answers:
A) m = 2 B) m = 5 C) m = 8 D) 10 E) 11 | <gadget id="calculator">1_000 / 10</gadget>
<output>100</output>
<gadget id="calculator">100 + 1</gadget>
<output>101</output>
<gadget id="calculator">101 ** 2</gadget>
<output>10_201</output>
<gadget id="calculator">101 - 2</gadget>
<output>99</output>
<gadget id="calculator">99 ** 2</gadget>
<output>9_801</output>
<gadget id="calculator">10_201 - 9_801</gadget>
<output>400</output>
<gadget id="calculator">400 ** (1/2)</gadget>
<output>20</output>
<gadget id="calculator">20 / 10</gadget>
<output>2</output>
<result>A</result> | A | 2 | The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits M of the larger integer? | {
"A": "m = 2",
"B": "m = 5",
"C": "m = 8",
"D": "10",
"E": "11"
} | divide(sqrt(subtract(power(add(divide(1000, const_10), const_1), const_2), power(subtract(add(divide(1000, const_10), const_1), const_2), const_2))), const_10) | divide(n0,const_10)|add(#0,const_1)|power(#1,const_2)|subtract(#1,const_2)|power(#3,const_2)|subtract(#2,#4)|sqrt(#5)|divide(#6,const_10) | really hard . but let ' s start with few concepts : 1 . square of an odd integer will be odd . 2 . difference of odd and odd will be even . 3 . any odd integer can be expressed as difference of two squares . 4 . an even integer can be expressed as difference of two squares only if that even integer is a multiple of 4 . assume two odd integers to be ( 2 x - 1 ) and ( 2 x + 1 ) . difference of their squares = ( 2 x + 1 ) ^ 2 - ( 2 x - 1 ) ^ 2 = 4 x ^ 2 + 1 + 4 x - ( 4 x ^ 2 + 1 - 4 x ) = 4 x ^ 2 + 1 + 4 x - 4 x ^ 2 - 1 + 4 x = 8 x now root of 8 x needs to be an integer such that it is equal to the sum of the digits of the two odd integers . 8 = 2 ^ 3 , so x needs to be such that itcompletesa perfect square . if we find x , we can find the value of 2 x + 1 ( larger integer ) and then sum of its digits . let ' s check the options , starting with c . for sum to be 8 , few possibilities are : 17 , 35 , 53 , 71 if we take 17 , the pair is 15 and 17 , meaning x = 8 . 8 x = 64 root of 64 = 4 but 4 is not equal to 1 + 5 + 1 + 7 . reject . if we take 35 , the pair is 33 and 35 , meaning x = 17 . 8 x = 8 * 17 reject since perfect square is not possible . if we take 53 , the pair is 51 and 53 , meaning x = 26 . 8 x = 8 * 26 reject since perfect square is not possible . if we take 71 , the pair is 69 and 71 , meaning x = 35 . 8 x = 8 * 35 reject since perfect square is not possible . i tried each option and the possibilities and then got lost . then , it occurred to me that i was only checking 2 - digit integers . what about 3 - digits ? starting with option a , only 2 - digit odd integer whose sum is 2 is 101 . if we take 101 , the pair is 99 and 101 , meaning x = 50 . 8 x = 8 * 50 = 400 root of 400 = 20 which is indeed equal to 9 + 9 + 1 + 1 . answer ( a ) . | general |
math_qa__7KqEsqdYCNCU9BMi | If f(x) = 2x + 3, & g(x) = (x - 3)/2, then what is the value of, fo(fo(go(go(fo(fo(go(go................(fo(fo(go(gof(x) )))).....)))))) ? Choices
A) 3 B) 2 C) 9 D) 7 E) 1 | <gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">12 + 2</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>D</result> | D | 7 | If f(x) = 2x + 3, & g(x) = (x - 3)/2, then what is the value of, fo(fo(go(go(fo(fo(go(go................(fo(fo(go(gof(x) )))).....)))))) ? | {
"A": "3",
"B": "2",
"C": "9",
"D": "7",
"E": "1"
} | divide(add(multiply(const_4, 3), 2), 2) | multiply(n1,const_4)|add(n0,#0)|divide(#1,n0) | f ( x ) = 2 x + 3 g ( x ) = ( x - 3 ) / 2 gof ( x ) = 2 x + 3 − 32 = x 2 x + 3 − 32 = x gogof ( x ) = x − 32 x − 32 fogogof ( x ) = 2 ( x − 32 ) + 32 ( x − 32 ) + 3 = 2 x − 6 + 622 x − 6 + 62 = x fofogogof ( x ) = 2 x + 3 this means , when we apply two times g ( x ) and two time f ( x ) on f ( x ) we get f ( x ) . this pattern continues , hence the answer is option ( d ) . | general |
math_qa__aH851k7aNOrplmav | The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? Choices:
A) 76 m B) 178 m C) 225 m D) 187 m E) 176 m | <gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 150</gadget>
<output>225</output>
<result>C</result> | C | 225 | The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? | {
"A": "76 m",
"B": "178 m",
"C": "225 m",
"D": "187 m",
"E": "176 m"
} | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 150) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 150 + x ) / 30 = 25 / 2 = > 2 ( 150 + x ) = 750 = > x = 225 m . answer : c" | physics |
math_qa__pyirfMQyhI2K5GZL | Find the number which is nearest to 3105 and is exactly divisible by 21 Choose the correct option: A) 1208 B) 3108 C) 241 D) 217 E) 3147 | <gadget id="calculator">3_105 % 21</gadget>
<output>18</output>
<gadget id="calculator">21 - 18</gadget>
<output>3</output>
<gadget id="calculator">3_105 + 3</gadget>
<output>3_108</output>
<result>B</result> | B | 3,108 | Find the number which is nearest to 3105 and is exactly divisible by 21 | {
"A": "1208",
"B": "3108",
"C": "241",
"D": "217",
"E": "3147"
} | add(3105, subtract(21, reminder(3105, 21))) | reminder(n0,n1)|subtract(n1,#0)|add(n0,#1)| | "on dividing 3105 by 21 , we get 18 as remainder . number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . answer b 3108" | general |
math_qa__FxjliSLX78tMkYQ5 | The ratio of pens to pencils is 5 to 6. There are 5 more pencils than pens. How many pencils are there? Choose the correct choice
A) 24 B) 30 C) 36 D) 42 E) 48 | <gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 + 5</gadget>
<output>30</output>
<result>B</result> | B | 30 | The ratio of pens to pencils is 5 to 6. There are 5 more pencils than pens. How many pencils are there? | {
"A": "24",
"B": "30",
"C": "36",
"D": "42",
"E": "48"
} | add(multiply(5, 5), 5) | multiply(n0,n2)|add(n2,#0)| | "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 5 x = 5 the number of pencils is 30 . the answer is b ." | other |
math_qa__C1fvHcUlOzc6zvDF | if length of a room is three times of its breadth and its area is 12 sq.m.what is perimeter of room?
Select the correct option
A) 14 m B) 18 m C) 24 m D) 16 m E) none of the above | <gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">4 ** (1/2)</gadget>
<output>2</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">2 * (2 + 6)</gadget>
<output>16</output>
<result>D</result> | D | 16 | if length of a room is three times of its breadth and its area is 12 sq.m.what is perimeter of room? | {
"A": "14 m",
"B": "18 m",
"C": "24 m",
"D": "16 m",
"E": "none of the above"
} | rectangle_perimeter(sqrt(divide(12, const_3)), multiply(sqrt(divide(12, const_3)), const_3)) | divide(n0,const_3)|sqrt(#0)|multiply(#1,const_3)|rectangle_perimeter(#2,#1) | let breadth = x m . and length = 3 x m . x * 3 x = 12 , x ^ 2 = 4 , x = 2 . length = 6 m , breadth = 2 m . perimeter = 2 * ( 6 + 2 ) = 16 m answer d | physics |
math_qa__Hg8JMuh7VczKCNJb | p is 3 times as old as q . in 11 years , p will be twice as old as q . how old was p 3 years ago ?
Choices.
A) 21 B) 24 C) 27 D) 30 E) 33 | <gadget id="calculator">3 * 11</gadget>
<output>33</output>
<gadget id="calculator">33 - 3</gadget>
<output>30</output>
<result>D</result> | D | 30 | p is 3 times as old as q . in 11 years , p will be twice as old as q . how old was p 3 years ago ? | {
"A": "21",
"B": "24",
"C": "27",
"D": "30",
"E": "33"
} | subtract(multiply(3, 11), 3) | multiply(n0,n1)|subtract(#0,n0) | p = 3 q so q = p / 3 p + 11 = 2 ( q + 11 ) = 2 ( p / 3 + 11 ) p / 3 = 11 p = 33 three years ago , p was 30 . the answer is d . | general |
math_qa__MrLSfFRLGJ84zY9R | In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 13 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? Choices.
A) 3 B) 4 C) 5 D) 6 E) 7 | <gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">12 * 1</gadget>
<output>12</output>
<gadget id="calculator">12 + 13</gadget>
<output>25</output>
<gadget id="calculator">25 + 2</gadget>
<output>27</output>
<gadget id="calculator">40 - 27</gadget>
<output>13</output>
<gadget id="calculator">13 - 1</gadget>
<output>12</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">13 * 2</gadget>
<output>26</output>
<gadget id="calculator">12 + 26</gadget>
<output>38</output>
<gadget id="calculator">36 + 38</gadget>
<output>74</output>
<gadget id="calculator">80 - 74</gadget>
<output>6</output>
<result>D</result> | D | 6 | In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 13 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | subtract(multiply(40, 2), add(multiply(subtract(subtract(40, add(add(multiply(12, 1), 13), 2)), 1), 3), add(multiply(12, 1), multiply(13, 2)))) | multiply(n0,n1)|multiply(n2,n3)|multiply(n1,n4)|add(#1,#2)|add(n4,#1)|add(n1,#4)|subtract(n0,#5)|subtract(#6,n3)|multiply(n6,#7)|add(#3,#8)|subtract(#0,#9)| | "the class borrowed a total of 40 * 2 = 80 books . the 27 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 13 * 2 = 38 . to maximize the number of books borrowed by 1 student , let ' s assume that 12 students borrowed 3 books and 1 student borrowed the rest . 80 - 38 - 3 * 12 = 6 the maximum number of books borrowed by any student is 6 . the answer is d ." | general |
math_qa__fWCIKpujwDnFYgLH | On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 3 cups of tea. Last week Mo drank a total of 26 cups of tea and hot chocolate together. If during that week Mo drank 10 more tea cups than hot chocolate cups, then how many rainy days were there last week? Choices
A) 0
B) 1
C) 4
D) 5
E) 6 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">26 + 10</gadget>
<output>36</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">18 / 3</gadget>
<output>6</output>
<gadget id="calculator">7 - 6</gadget>
<output>1</output>
<result>B</result> | B | 1 | On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 3 cups of tea. Last week Mo drank a total of 26 cups of tea and hot chocolate together. If during that week Mo drank 10 more tea cups than hot chocolate cups, then how many rainy days were there last week? | {
"A": "0",
"B": "1",
"C": "4",
"D": "5",
"E": "6"
} | subtract(add(const_4, 3), divide(divide(add(26, 10), const_2), 3)) | add(n0,const_4)|add(n1,n2)|divide(#1,const_2)|divide(#2,n0)|subtract(#0,#3)| | "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 26 t - c = 10 - > t = 18 . c = 8 . mo drinks 3 cups of tea a day then number of days that are not rainy = 18 / 3 = 6 so number of rainy days = 7 - 6 = 1 b is the answer ." | general |
math_qa__9NfjMlXf6yhIascA | The mean of 50 observations was 36. It was found later that an observation 45 was wrongly taken as 23. The corrected new mean is? Options.
A) 36.7
B) 36.4
C) 36.5
D) 36.9
E) 36.3 | <gadget id="calculator">36 * 50</gadget>
<output>1_800</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 - 23</gadget>
<output>25</output>
<gadget id="calculator">1_800 + 25</gadget>
<output>1_825</output>
<gadget id="calculator">1_825 / 50</gadget>
<output>73/2 = around 36.5</output>
<result>B</result> | B | 36.4 | The mean of 50 observations was 36. It was found later that an observation 45 was wrongly taken as 23. The corrected new mean is? | {
"A": "36.7",
"B": "36.4",
"C": "36.5",
"D": "36.9",
"E": "36.3"
} | divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50) | multiply(n0,n1)|subtract(n0,const_2)|subtract(#1,n3)|add(#0,#2)|divide(#3,n0)| | "correct sum = ( 36 * 50 + 45 - 23 ) = 1822 . correct mean = 1822 / 50 = 36.4 answer : b" | general |
math_qa__sB8Xbde3NdDizimN | Pipe A can fill a tank in 4 hours. Due to a leak at the bottom, it takes 6 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank? Choices:
A) 12
B) 67
C) 95
D) 36
E) 66 | <gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">6 - 4</gadget>
<output>2</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<result>A</result> | A | 12 | Pipe A can fill a tank in 4 hours. Due to a leak at the bottom, it takes 6 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank? | {
"A": "12",
"B": "67",
"C": "95",
"D": "36",
"E": "66"
} | divide(multiply(6, 4), subtract(6, 4)) | multiply(n0,n1)|subtract(n1,n0)|divide(#0,#1)| | "let the leak can empty the full tank in x hours 1 / 4 - 1 / x = 1 / 6 = > 1 / x = 1 / 4 - 1 / 6 = ( 3 - 2 ) / 12 = 1 / 12 = > x = 12 . answer : a" | physics |
math_qa__sZsjoMoUCJG3KKJr | An individual deposited 20% of 25% of 30% of what he had into his account with a bank. If he deposited Rs.750, how much was he having initially with him before depositing? Choose the correct choice from the following answers: A) rs . 500000 B) rs . 50000 C) rs . 5000 D) rs . 15000 E) rs . 6000 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/5) * (1/4)</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(3/10) * (1/20)</gadget>
<output>3/200 = around 0.015</output>
<gadget id="calculator">750 / (3/200)</gadget>
<output>50_000</output>
<result>B</result> | B | 50,000 | An individual deposited 20% of 25% of 30% of what he had into his account with a bank. If he deposited Rs.750, how much was he having initially with him before depositing? | {
"A": "rs . 500000",
"B": "rs . 50000",
"C": "rs . 5000",
"D": "rs . 15000",
"E": "rs . 6000"
} | divide(750, multiply(divide(30, const_100), multiply(divide(20, const_100), divide(25, const_100)))) | divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|multiply(#1,#2)|multiply(#0,#3)|divide(n3,#4) | let x amount he has then 20 % of 25 % of 30 % of x = 750 so x = 50000 answer : b | general |
math_qa__PisoyZzsxdQX1GDf | In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many R cents does a liter of kerosene cost? [One dollar has 100 cents.] Choices.
A) 0.33 B) 0.44 C) 0.55 D) 44 E) 55 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">8 / (1/2)</gadget>
<output>16</output>
<gadget id="calculator">16 / 12</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">0.33 * 100</gadget>
<output>33</output>
<gadget id="calculator">(4/3) * 33</gadget>
<output>44</output>
<result>D</result> | D | 44 | In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many R cents does a liter of kerosene cost? [One dollar has 100 cents.] | {
"A": "0.33",
"B": "0.44",
"C": "0.55",
"D": "44",
"E": "55"
} | multiply(divide(divide(8, divide(const_1, const_2)), const_12), multiply(0.33, 100)) | divide(const_1,const_2)|multiply(n1,n2)|divide(n0,#0)|divide(#2,const_12)|multiply(#3,#1)| | "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer r = 44 . d" | general |
math_qa__jeb7VfjnHnUDJ5Vx | Dacid obtained 96, 98, 99, 100 and 98 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Choose the correct choice from the following answers
A) 79
B) 99
C) 88
D) 88
E) 98 | <gadget id="calculator">96 + 98</gadget>
<output>194</output>
<gadget id="calculator">194 + 99</gadget>
<output>293</output>
<gadget id="calculator">293 + 100</gadget>
<output>393</output>
<gadget id="calculator">393 + 98</gadget>
<output>491</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">491 / 5</gadget>
<output>491/5 = around 98.2</output>
<result>E</result> | E | 98 | Dacid obtained 96, 98, 99, 100 and 98 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? | {
"A": "79",
"B": "99",
"C": "88",
"D": "88",
"E": "98"
} | divide(add(add(add(add(96, 98), 99), 100), 98), divide(const_10, const_2)) | add(n0,n1)|divide(const_10,const_2)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | "average = ( 96 + 98 + 99 + 100 + 98 ) / 5 = 491 / 5 = 98 . answer : e" | general |
math_qa__3xSUMpW3lAbz3NU4 | A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 1/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
Choose the correct choice from the following answers: A) 7 / 16 B) 7 / 15 C) 10 / 21 D) 17 / 35 E) 1 / 10 | <gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 10</gadget>
<output>6</output>
<gadget id="calculator">10 - 6</gadget>
<output>4</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 6</gadget>
<output>1</output>
<gadget id="calculator">4 * 1</gadget>
<output>4</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">36 + 4</gadget>
<output>40</output>
<gadget id="calculator">4 / 40</gadget>
<output>1/10 = around 0.1</output>
<result>E</result> | E | 0.1 | A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 1/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups? | {
"A": "7 / 16",
"B": "7 / 15",
"C": "10 / 21",
"D": "17 / 35",
"E": "1 / 10"
} | divide(multiply(subtract(const_10, multiply(divide(3, 5), const_10)), multiply(divide(1, 6), multiply(divide(3, 5), const_10))), add(multiply(multiply(divide(3, 5), const_10), multiply(divide(3, 5), const_10)), multiply(subtract(const_10, multiply(divide(3, 5), const_10)), multiply(divide(1, 6), multiply(divide(3, 5), const_10))))) | divide(n2,n3)|divide(n0,n1)|multiply(#1,const_10)|multiply(#0,#2)|multiply(#2,#2)|subtract(const_10,#2)|multiply(#3,#5)|add(#4,#6)|divide(#6,#7)| | "let the total # of cups be 10 . # of small cups sold 3 / 5 * 10 = 6 ; # of large cups sold 10 - 6 = 4 ; let the price of small cup be $ 6 , then the price of larges cup would be 1 / 6 * 6 = $ 1 ; revenue from small cups : 6 * $ 6 = $ 36 ; revenue from large cups cups : 4 * $ 1 = $ 4 ; fraction of total revenue from large cups : 4 / ( 36 + 4 ) = 1 / 10 . answer : e ." | general |
math_qa__cytTNyPGaxX7my7a | An exam consists of 7 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes? Choose the correct answer:
A) 1 / 16
B) 37 / 256
C) 1 / 2
D) 219 / 256
E) 15 / 16 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 7</gadget>
<output>1/128 = around 0.007812</output>
<gadget id="calculator">7 * (1/128)</gadget>
<output>7/128 = around 0.054688</output>
<gadget id="calculator">(1/128) + (7/128)</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 * (1/128)</gadget>
<output>21/128 = around 0.164062</output>
<gadget id="calculator">(1/16) + (21/128)</gadget>
<output>29/128 = around 0.226562</output>
<gadget id="calculator">1 - (29/128)</gadget>
<output>99/128 = around 0.773438</output>
<gadget id="calculator">(99/128) / 10</gadget>
<output>99/1_280 = around 0.077344</output>
<gadget id="calculator">(99/1_280) + (99/128)</gadget>
<output>1_089/1_280 = around 0.850781</output>
<result>D</result> | D | 0.855469 | An exam consists of 7 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes? | {
"A": "1 / 16",
"B": "37 / 256",
"C": "1 / 2",
"D": "219 / 256",
"E": "15 / 16"
} | add(divide(subtract(const_1, add(add(power(divide(const_1, const_2), 7), multiply(7, power(divide(const_1, const_2), 7))), multiply(multiply(7, const_3), power(divide(const_1, const_2), 7)))), const_10), subtract(const_1, add(add(power(divide(const_1, const_2), 7), multiply(7, power(divide(const_1, const_2), 7))), multiply(multiply(7, const_3), power(divide(const_1, const_2), 7))))) | divide(const_1,const_2)|multiply(n0,const_3)|power(#0,n0)|multiply(n0,#2)|multiply(#1,#2)|add(#3,#2)|add(#5,#4)|subtract(const_1,#6)|divide(#7,const_10)|add(#8,#7) | if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 219 / 256 . d | general |
math_qa__qeVlmBy3MvG9rlLB | What is difference between biggest and smallest fraction among 2/3, 3/4, 4/5 and 5/7
Select: A) 2 / 15 B) 3 / 5 C) 1 / 6 D) 1 / 7 E) none of these | <gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(4/5) - (2/3)</gadget>
<output>2/15 = around 0.133333</output>
<result>A</result> | A | 0.133333 | What is difference between biggest and smallest fraction among 2/3, 3/4, 4/5 and 5/7 | {
"A": "2 / 15",
"B": "3 / 5",
"C": "1 / 6",
"D": "1 / 7",
"E": "none of these"
} | subtract(divide(4, 5), divide(2, 3)) | divide(n3,n5)|divide(n0,n1)|subtract(#0,#1) | explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 7 = . 71 so biggest is 4 / 5 and smallest is 2 / 3 their difference is 4 / 5 - 2 / 3 = 2 / 15 option a | general |
math_qa__U7gDlFNaylu7kHG5 | Last year Department Store X had a sales total for December that was 5 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year? Choose the most appropriate option.
A) 1 / 4
B) 4 / 15
C) 1 / 3
D) 5 / 16
E) 4 / 5 | <gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">11 + 5</gadget>
<output>16</output>
<gadget id="calculator">5 / 16</gadget>
<output>5/16 = around 0.3125</output>
<result>D</result> | D | 0.3125 | Last year Department Store X had a sales total for December that was 5 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year? | {
"A": "1 / 4",
"B": "4 / 15",
"C": "1 / 3",
"D": "5 / 16",
"E": "4 / 5"
} | divide(5, add(subtract(const_12, const_1), 5)) | subtract(const_12,const_1)|add(n0,#0)|divide(n0,#1)| | "let avg for 11 mos . = 10 therefore , dec = 50 year total = 11 * 10 + 50 = 160 answer = 50 / 160 = 5 / 16 = d" | general |
math_qa__AJD8Tb1qCem5nuRE | A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth.The percentage of decrease in area is : Choose one:
A) 13 % B) 14 % C) 18 % D) 20 % E) 28 % | <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">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(4/5) * (9/10)</gadget>
<output>18/25 = around 0.72</output>
<gadget id="calculator">1 - (18/25)</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">(7/25) * 100</gadget>
<output>28</output>
<result>E</result> | E | 28 | A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth.The percentage of decrease in area is : | {
"A": "13 %",
"B": "14 %",
"C": "18 %",
"D": "20 %",
"E": "28 %"
} | multiply(subtract(const_1, multiply(divide(subtract(const_100, 20), const_100), divide(subtract(const_100, 10), const_100))), const_100) | subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|subtract(const_1,#4)|multiply(#5,const_100) | let original length = x and original breadth = y . decrease in area = xy - ( 80 / 100 * x * 90 / 100 * y ) = ( xy - 18 / 25 * xy ) = 7 / 25 * xy . decrease % = ( 7 / 25 * xy * 1 / xy * 100 ) % = 28 % . answer is e | gain |
math_qa__uycWO1lyQrwT84MB | At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years? Choose the correct choice
A) 4 %
B) 74 %
C) 64 %
D) 74 %
E) 94 % | <gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<result>A</result> | A | 4 | At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years? | {
"A": "4 %",
"B": "74 %",
"C": "64 %",
"D": "74 %",
"E": "94 %"
} | divide(multiply(divide(2, 5), const_100), 10) | divide(n0,n1)|multiply(#0,const_100)|divide(#1,n2) | let sum = x . then , s . i . = 2 x / 5 , time = 10 years . rate = ( 100 * 2 x ) / ( x * 5 * 10 ) = 4 % answer : a | gain |
math_qa__yLAupbDYzgYTGXnJ | A cycle is bought for Rs.900 and sold for Rs.1125, find the gain percent?
Choices.
A) 27 % B) 20 % C) 80 % D) 30 % E) 25 % | <gadget id="calculator">1_125 - 900</gadget>
<output>225</output>
<gadget id="calculator">225 / 900</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>E</result> | E | 25 | A cycle is bought for Rs.900 and sold for Rs.1125, find the gain percent? | {
"A": "27 %",
"B": "20 %",
"C": "80 %",
"D": "30 %",
"E": "25 %"
} | multiply(divide(subtract(1125, 900), 900), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | "900 - - - - 225 100 - - - - ? = > 25 % answer : e" | gain |
math_qa__iAvaKPk4QXUDOdrk | The vertex of a rectangle are (1, 0), (5, 0), (1, 2) and (5, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L? Answers: A) 3 B) 6 C) 1 / 3 D) 1 / 2 E) 1 / 6 | <gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<result>C</result> | C | 0.333333 | The vertex of a rectangle are (1, 0), (5, 0), (1, 2) and (5, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L? | {
"A": "3",
"B": "6",
"C": "1 / 3",
"D": "1 / 2",
"E": "1 / 6"
} | divide(1, divide(add(subtract(5, 1), 2), 2)) | subtract(n2,n0)|add(#0,n5)|divide(#1,n5)|divide(n0,#2)| | "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 3 , 1 ) . the slope of a line passing through ( 0,0 ) and ( 3 , 1 ) is 1 / 3 . the answer is c ." | general |
math_qa__lowozUw7uk6pugYC | A 140 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? Choose the correct choice from the following options
A) 41.1 sec B) 20.2 sec C) 31.8 sec D) 43.2 sec E) none of the above | <gadget id="calculator">140 + 520</gadget>
<output>660</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">55 * (5/18)</gadget>
<output>275/18 = around 15.277778</output>
<gadget id="calculator">660 / (275/18)</gadget>
<output>216/5 = around 43.2</output>
<result>D</result> | D | 43.2 | A 140 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? | {
"A": "41.1 sec",
"B": "20.2 sec",
"C": "31.8 sec",
"D": "43.2 sec",
"E": "none of the above"
} | divide(add(140, 520), multiply(55, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1) | speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 140 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 660 m time = distance / speed = 660 x 18 / ( 5 x 55 ) = 43.2 sec ans is : d | physics |
math_qa__NWOrlAgJfQ1HSKMA | How long will a boy take to run round a square field of side 50 meters, if he runs at the rate of 9km/hr? Pick one.
A) 80 sec
B) 45 sec
C) 1 min
D) 32 sec
E) 25 sec | <gadget id="calculator">50 * 4</gadget>
<output>200</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">200 / (5/2)</gadget>
<output>80</output>
<result>A</result> | A | 80 | How long will a boy take to run round a square field of side 50 meters, if he runs at the rate of 9km/hr? | {
"A": "80 sec",
"B": "45 sec",
"C": "1 min",
"D": "32 sec",
"E": "25 sec"
} | divide(multiply(50, 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 = 50 * 4 = 200 m time taken = 200 * 2 / 5 = 80 sec answer is a" | gain |
math_qa__51Fmzc5IdNFgKDsN | If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 28, what is the common ratio of the G.P? Choose the correct answer.
A) 3 B) 1 / 3 C) 2 D) 9 E) 1 / 9 | <gadget id="calculator">28 - 1</gadget>
<output>27</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">27 ** (1/3)</gadget>
<output>3</output>
<result>A</result> | A | 3 | If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 28, what is the common ratio of the G.P? | {
"A": "3",
"B": "1 / 3",
"C": "2",
"D": "9",
"E": "1 / 9"
} | power(subtract(28, const_1), divide(const_1, 3)) | divide(const_1,n1)|subtract(n2,const_1)|power(#1,#0)| | "28 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 28 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 28 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 27 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 27 = r ^ 3 r = 3 a" | other |
math_qa__iUp59LinwM2MYg4F | 19 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? Choose the correct option:
A) 32
B) 87
C) 38
D) 99
E) 77 | <gadget id="calculator">21 * 8</gadget>
<output>168</output>
<gadget id="calculator">19 * 3</gadget>
<output>57</output>
<gadget id="calculator">168 * 57</gadget>
<output>9_576</output>
<gadget id="calculator">21 * 2</gadget>
<output>42</output>
<gadget id="calculator">42 * 6</gadget>
<output>252</output>
<gadget id="calculator">9_576 / 252</gadget>
<output>38</output>
<gadget id="calculator">floor(38)</gadget>
<output>38</output>
<gadget id="calculator">38 + 1</gadget>
<output>39</output>
<result>C</result> | C | 38 | 19 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? | {
"A": "32",
"B": "87",
"C": "38",
"D": "99",
"E": "77"
} | add(floor(divide(multiply(multiply(21, 8), multiply(19, 3)), multiply(multiply(21, 2), 6))), const_1) | multiply(n1,n2)|multiply(n0,n5)|multiply(n4,n6)|multiply(#0,#1)|multiply(n3,#2)|divide(#3,#4)|floor(#5)|add(#6,const_1)| | "3 w = 2 m 19 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 19 * 21 * 8 = 14 * x * 6 x = 38 answer : c" | physics |
math_qa__Qh0nDRun23p1Ni9N | The length of the bridge, which a train 135 m long and traveling at 45 km/hr can cross in 30 sec is? Choose the correct choice from the following:
A) 235
B) 240
C) 245
D) 250
E) 255 | <gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 135</gadget>
<output>240</output>
<result>B</result> | B | 240 | The length of the bridge, which a train 135 m long and traveling at 45 km/hr can cross in 30 sec is? | {
"A": "235",
"B": "240",
"C": "245",
"D": "250",
"E": "255"
} | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 135) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 135 + x ) / 30 = 25 / 2 x = 240 m . answer : option b" | physics |
math_qa__oKjjrVygfXUGFXj3 | If a 10 percent deposit that has been paid toward the purchase of a certain product is $80, how much more remains to be paid? Choices:
A) $ 640
B) $ 680
C) $ 720
D) $ 760
E) $ 800 | <gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">80 * 10</gadget>
<output>800</output>
<gadget id="calculator">800 - 80</gadget>
<output>720</output>
<result>C</result> | C | 720 | If a 10 percent deposit that has been paid toward the purchase of a certain product is $80, how much more remains to be paid? | {
"A": "$ 640",
"B": "$ 680",
"C": "$ 720",
"D": "$ 760",
"E": "$ 800"
} | subtract(multiply(80, divide(const_100, 10)), 80) | divide(const_100,n0)|multiply(n1,#0)|subtract(#1,n1)| | "90 % remains to be paid so the remaining amount is 9 * 80 = $ 720 . the answer is c ." | general |
math_qa__GnOkz93s1VudmNU4 | Mike needs 30% to pass. If he scored 212 marks and falls short by 22 marks, what was the maximum marks he could have got? Choose the correct choice from the following choices:
A) 343
B) 777
C) 780
D) 867
E) 232 | <gadget id="calculator">212 + 22</gadget>
<output>234</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">234 / (3/10)</gadget>
<output>780</output>
<result>C</result> | C | 780 | Mike needs 30% to pass. If he scored 212 marks and falls short by 22 marks, what was the maximum marks he could have got? | {
"A": "343",
"B": "777",
"C": "780",
"D": "867",
"E": "232"
} | divide(add(212, 22), divide(30, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1)| | "if mike had scored 22 marks more , he could have scored 30 % therefore , mike required 212 + 22 = 234 marks let the maximum marks be m . then 30 % of m = 234 ( 30 / 100 ) × m = 234 m = ( 234 × 100 ) / 30 m = 23400 / 30 m = 780 answer : c" | gain |
math_qa__AE2aCz3UiAWfrUvR | If shares of two persons in profits are Rs.400 and Rs.500 then ratio of their capitals is
Choices
A) 3 : 4
B) 4 : 5
C) 4 : 3
D) 1 : 3
E) 1 : 2 | <gadget id="calculator">400 / 500</gadget>
<output>4/5 = around 0.8</output>
<result>B</result> | B | 0.8 | If shares of two persons in profits are Rs.400 and Rs.500 then ratio of their capitals is | {
"A": "3 : 4",
"B": "4 : 5",
"C": "4 : 3",
"D": "1 : 3",
"E": "1 : 2"
} | divide(400, 500) | divide(n0,n1)| | "profit = time * capital so 400 : 500 = 4 : 5 answer : b" | other |
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