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25
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stringlengths 45
1.01k
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4.11k
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float64 -4,212
100B
| question_without_options
stringlengths 6
962
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dict | annotated_formula
stringlengths 7
6.48k
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stringlengths 8
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math_qa__WxEKYem619KbQ300 | A train is 310 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? Select the correct option:
A) 36 seconds B) 18 seconds C) 40 seconds D) 19 seconds E) 45 seconds | <gadget id="calculator">310 + 140</gadget>
<output>450</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">450 / (25/2)</gadget>
<output>36</output>
<result>A</result> | A | 36 | A train is 310 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? | {
"A": "36 seconds",
"B": "18 seconds",
"C": "40 seconds",
"D": "19 seconds",
"E": "45 seconds"
} | divide(add(310, 140), divide(multiply(45, const_1000), const_3600)) | add(n0,n2)|multiply(n1,const_1000)|divide(#1,const_3600)|divide(#0,#2)| | "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 310 + 140 = 500 meter time = distance / speed = 450 * ( 2 / 25 ) = 36 seconds answer : a" | physics |
math_qa__4JgeyG19pIty3u9Y | A 49 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? Choose the correct choice from the following answers: A) 12 B) 20 C) 88 D) 77 E) 14 | <gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) + 1</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">49 / (7/5)</gadget>
<output>35</output>
<gadget id="calculator">49 - 35</gadget>
<output>14</output>
<result>E</result> | E | 14 | A 49 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? | {
"A": "12",
"B": "20",
"C": "88",
"D": "77",
"E": "14"
} | subtract(49, divide(49, add(divide(2, 5), const_1))) | divide(n1,n2)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)| | "1 : 2 / 5 = 5 : 2 2 / 7 * 49 = 14 answer : e" | physics |
math_qa__IRxbL9d2HQaL7jRV | There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is: Choose one:
A) 5 B) 21 C) 33 D) 60 E) 6 | <gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">6 + 5</gadget>
<output>11</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">11 + 4</gadget>
<output>15</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">15 + 3</gadget>
<output>18</output>
<gadget id="calculator">18 + 2</gadget>
<output>20</output>
<result>B</result> | B | 21 | There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is: | {
"A": "5",
"B": "21",
"C": "33",
"D": "60",
"E": "6"
} | add(add(add(add(6, subtract(6, 1)), subtract(subtract(6, 1), 1)), subtract(subtract(subtract(6, 1), 1), 1)), 2) | subtract(n0,n1)|add(n0,#0)|subtract(#0,n1)|add(#1,#2)|subtract(#2,n1)|add(#3,#4)|add(n2,#5)| | "explanatory answer list down possibilities : from only 1 box all the way to all 6 if only one of the boxes has a green ball , it can be any of the 6 boxes . so , we have 6 possibilities . if two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes . 12 , 23 , 34 , 45 , 56 . if 3 of the boxes have green balls , there are 4 possibilities : 123 , 234 , 345 , 456 . if 4 boxes have green balls , there are 3 possibilities : 1234 , 2345 , 3456 . if 5 boxes have green balls , there are 2 possibilities : 12345 , 23456 . if all 6 boxes have green balls , there is just 1 possibility . total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21 . choice b" | general |
math_qa__0DHhD3qLIq2UEWB9 | The overall age of X and Y is 18 year greater than the overall age of Y and Z. Z is how many decades younger that X? Options.
A) 11
B) 15
C) 12
D) 17
E) 18 | <gadget id="calculator">18 / 1</gadget>
<output>18</output>
<result>E</result> | E | 18 | The overall age of X and Y is 18 year greater than the overall age of Y and Z. Z is how many decades younger that X? | {
"A": "11",
"B": "15",
"C": "12",
"D": "17",
"E": "18"
} | divide(18, const_1) | divide(n0,const_1)| | "e 18 ( x + y ) Γ’ β¬ β ( y + z ) = 18 x Γ’ β¬ β z = 18" | general |
math_qa__GCyX63DMZ4B8Wk0q | A boy rides his bicycle 10 km at an average sped of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately. Choose the correct option: A) 10.2 kmph B) 10.4 kmph C) 10.8 kmph D) 11.8 kmph E) none | <gadget id="calculator">10 + 12</gadget>
<output>22</output>
<gadget id="calculator">10 / 12</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(5/6) + (6/5)</gadget>
<output>61/30 = around 2.033333</output>
<gadget id="calculator">22 / (61/30)</gadget>
<output>660/61 = around 10.819672</output>
<result>C</result> | C | 10.8 | A boy rides his bicycle 10 km at an average sped of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately. | {
"A": "10.2 kmph",
"B": "10.4 kmph",
"C": "10.8 kmph",
"D": "11.8 kmph",
"E": "none"
} | divide(add(10, 12), add(divide(10, 12), divide(12, 10))) | add(n0,n1)|divide(n0,n1)|divide(n1,n0)|add(#1,#2)|divide(#0,#3) | sol . total distance travelled = ( 10 + 12 ) km / hr = 22 km / hr . total time taken = [ 10 / 12 + 12 / 10 ] hrs = 61 / 30 hrs β΄ average speed = [ 22 * 30 / 61 ] km / hr = 10.8 km / hr . answer c | general |
math_qa__YaF5lusVYnhI3KlX | (a/2)/(b/c)
In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression? Choices:
A) 8 / 2 B) 2 / 4 C) 1 / 8 D) 2 / 4 E) 4 / 6 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<result>A</result> | A | 4 | (a/2)/(b/c)
In the expression above, a, b, and c are different numbers and each is one of the numbers 1, 2, or 4. What is the largest possible value of the expression? | {
"A": "8 / 2",
"B": "2 / 4",
"C": "1 / 8",
"D": "2 / 4",
"E": "4 / 6"
} | divide(multiply(4, 2), 2) | multiply(n0,n3)|divide(#0,n0) | ( a / 2 ) / ( b / c ) = ( a * c ) / 2 b the expression will have the largest value when numerator ( a * c ) is the largest . = ( 2 * 4 ) / 2 * 1 = 8 / 2 answer a | general |
math_qa__vdUzjdmH7jJWAKLf | In a college the ratio of the numbers of boys to the girls is 8:5. If there are 190 girls, the total number of students in the college is? Pick one:
A) 562 B) 356 C) 452 D) 494 E) 512 | <gadget id="calculator">8 / 5</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) * 190</gadget>
<output>304</output>
<gadget id="calculator">304 + 190</gadget>
<output>494</output>
<result>D</result> | D | 494 | In a college the ratio of the numbers of boys to the girls is 8:5. If there are 190 girls, the total number of students in the college is? | {
"A": "562",
"B": "356",
"C": "452",
"D": "494",
"E": "512"
} | add(multiply(divide(8, 5), 190), 190) | divide(n0,n1)|multiply(n2,#0)|add(n2,#1)| | "let the number of boys and girls be 8 x and 5 x then , 5 x = 190 x = 38 total number of students = 13 x = 13 * 38 = 494 answer is d" | other |
math_qa__ToT1X1Qoj2YIQ59k | If the numerator of a fraction be increased by 15% and its denominator be diminished by 8%, the value of the fraction is 15/16. Find the original fraction ? Pick one.
A) 1 / 2 B) 3 / 5 C) 5 / 7 D) 9 / 11 E) 3 / 4 | <gadget id="calculator">100 - 8</gadget>
<output>92</output>
<gadget id="calculator">92 * 15</gadget>
<output>1_380</output>
<gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">115 * 16</gadget>
<output>1_840</output>
<gadget id="calculator">1_380 / 1_840</gadget>
<output>3/4 = around 0.75</output>
<result>E</result> | E | 0.75 | If the numerator of a fraction be increased by 15% and its denominator be diminished by 8%, the value of the fraction is 15/16. Find the original fraction ? | {
"A": "1 / 2",
"B": "3 / 5",
"C": "5 / 7",
"D": "9 / 11",
"E": "3 / 4"
} | divide(multiply(subtract(const_100, 8), 15), multiply(add(const_100, 15), 16)) | add(n0,const_100)|subtract(const_100,n1)|multiply(n2,#1)|multiply(n3,#0)|divide(#2,#3)| | "let the original fraction be x / y then , 115 % of x / 92 % of y = 15 / 16 115 x / 92 y = 15 / 16 x / y = 3 / 4 answer is e" | general |
math_qa__sZqtysPXcS6SKf6s | A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 5 Gallons of water and 10 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x? Select the correct option.
A) 37.5 B) 75 C) 100 D) 150 E) 175 | <gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">20 - 5</gadget>
<output>15</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">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(4/5) * (1/4)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(4/5) - (1/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">2 * (1/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(3/5) - (2/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">15 / (1/5)</gadget>
<output>75</output>
<result>B</result> | B | 75 | A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 5 Gallons of water and 10 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x? | {
"A": "37.5",
"B": "75",
"C": "100",
"D": "150",
"E": "175"
} | divide(subtract(multiply(10, const_2), 5), subtract(subtract(subtract(1, divide(20, const_100)), multiply(subtract(1, divide(20, const_100)), divide(1, const_4))), multiply(const_2, divide(20, const_100)))) | divide(n0,const_100)|divide(n4,const_4)|multiply(n2,const_2)|multiply(#0,const_2)|subtract(#2,n1)|subtract(n4,#0)|multiply(#1,#5)|subtract(#5,#6)|subtract(#7,#3)|divide(#4,#8)| | "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 10 gallons salt is added and 5 gallons of water is added . so salt now becomes - > ( 0.2 x + 10 ) and water - - > ( 0.6 x + 5 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 10 ) = ( 0.6 x + 5 ) / 2 = 0.4 x + 20 = 0.6 x + 5 = > 0.2 x = 15 solving , x = 75 answer : b" | general |
math_qa__TXjXjyIJKV2sgI90 | The tax on a commodity is diminished by 32% but its consumption is increased by 12%. Find the decrease percent in the revenue derived from it? Choose the correct choice from the following choices: A) 20 % B) 18 % C) 15 % D) 12 % E) 24 % | <gadget id="calculator">100 + 12</gadget>
<output>112</output>
<gadget id="calculator">100 - 32</gadget>
<output>68</output>
<gadget id="calculator">112 * 68</gadget>
<output>7_616</output>
<gadget id="calculator">7_616 / 100</gadget>
<output>1_904/25 = around 76.16</output>
<gadget id="calculator">100 - (1_904/25)</gadget>
<output>596/25 = around 23.84</output>
<result>E</result> | E | 24 | The tax on a commodity is diminished by 32% but its consumption is increased by 12%. Find the decrease percent in the revenue derived from it? | {
"A": "20 %",
"B": "18 %",
"C": "15 %",
"D": "12 %",
"E": "24 %"
} | subtract(const_100, divide(multiply(add(const_100, 12), subtract(const_100, 32)), const_100)) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)| | "100 * 100 = 10000 68 * 112 = 7616 10000 - - - - - - - 2384 100 - - - - - - - ? = 24 % answer : e" | general |
math_qa__VpAmAMtrS07rCwra | Of the 90 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 correct choice:
A) 10 B) 15 C) 20 D) 25 E) 35 | <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">90 - 55</gadget>
<output>35</output>
<result>E</result> | E | 35 | Of the 90 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": "35"
} | subtract(90, 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 ) = 90 - 50 - ( 40 - 35 ) = 90 - 55 = 35 answer e" | other |
math_qa__fRBlEvzobY0mOPkz | How many cuboids of length 5 m, width 6 m and height 3 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. Choose the correct answer: A) 4 B) 6 C) 10 D) 8 E) 11 | <gadget id="calculator">18 * 15</gadget>
<output>270</output>
<gadget id="calculator">270 * 2</gadget>
<output>540</output>
<gadget id="calculator">5 * 6</gadget>
<output>30</output>
<gadget id="calculator">30 * 3</gadget>
<output>90</output>
<gadget id="calculator">540 / 90</gadget>
<output>6</output>
<result>B</result> | B | 6 | How many cuboids of length 5 m, width 6 m and height 3 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. | {
"A": "4",
"B": "6",
"C": "10",
"D": "8",
"E": "11"
} | divide(multiply(multiply(18, 15), 2), multiply(multiply(5, 6), 3)) | multiply(n3,n4)|multiply(n0,n1)|multiply(n5,#0)|multiply(n2,#1)|divide(#2,#3)| | "( 18 Γ£ β 15 Γ£ β 12 ) / ( 5 Γ£ β 3 Γ£ β 2 ) = 6 answer is b ." | physics |
math_qa__DnK25eabPXNaqbzM | When x is multiplied by 3, the result is 26 more than the result of subtracting x from 26. What is the value of x?
Choose the correct answer:
A) - 4
B) - 2
C) 11
D) 13
E) 22 | <gadget id="calculator">26 + 26</gadget>
<output>52</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">52 / 4</gadget>
<output>13</output>
<result>D</result> | D | 13 | When x is multiplied by 3, the result is 26 more than the result of subtracting x from 26. What is the value of x? | {
"A": "- 4",
"B": "- 2",
"C": "11",
"D": "13",
"E": "22"
} | divide(add(26, 26), add(3, const_1)) | add(n1,n2)|add(const_1,n0)|divide(#0,#1)| | "the equation that can be formed is : 3 x - 26 = 26 - x or , 4 x = 52 or , x = 13 . d answer ." | general |
math_qa__56PwOYd1SE73Pim1 | A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 90 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally. Choose the correct choice from the following answers: A) 180 B) 130 C) 140 D) 160 E) 288 | <gadget id="calculator">8 * 90</gadget>
<output>720</output>
<gadget id="calculator">13 - 8</gadget>
<output>5</output>
<gadget id="calculator">720 / 5</gadget>
<output>144</output>
<gadget id="calculator">144 * 2</gadget>
<output>288</output>
<result>E</result> | E | 288 | A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 90 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally. | {
"A": "180",
"B": "130",
"C": "140",
"D": "160",
"E": "288"
} | multiply(divide(multiply(8, 90), subtract(13, 8)), const_2) | multiply(n0,n1)|subtract(n2,n1)|divide(#0,#1)|multiply(#2,const_2)| | "white : yellow = x : ( x + 90 ) = 8 : 13 - - > 13 x = 8 x + 720 - - > x = 144 . the total # of balls originally x + x = 144 + 144 = 288 . answer : e ." | general |
math_qa__N2dZFH2y342YUbZv | If two girls starting from same point, walking in the opposite directions with 5km/hr and 10km/hr as average speeds respectively. Then the distance between them after 5 hours is? Choose the correct option
A) 45 B) 55 C) 65 D) 75 E) 85 | <gadget id="calculator">5 + 10</gadget>
<output>15</output>
<gadget id="calculator">15 * 5</gadget>
<output>75</output>
<result>D</result> | D | 75 | If two girls starting from same point, walking in the opposite directions with 5km/hr and 10km/hr as average speeds respectively. Then the distance between them after 5 hours is? | {
"A": "45",
"B": "55",
"C": "65",
"D": "75",
"E": "85"
} | multiply(add(5, 10), 5) | add(n0,n1)|multiply(n2,#0)| | "explanation : total distance = distance traveled by person a + distance traveled by person b = ( 5 Γ£ β 5 ) + ( 10 Γ£ β 5 ) = 25 + 50 = 75 km answer : d" | physics |
math_qa__kmkgFZqm3XDBrsIP | The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 2028 sq m, then what is the breadth of the rectangular plot? Choose the most appropriate option: A) 11 B) 17 C) 26 D) 101 E) 1322 | <gadget id="calculator">2_028 / 3</gadget>
<output>676</output>
<gadget id="calculator">676 ** (1/2)</gadget>
<output>26</output>
<result>C</result> | C | 26 | The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 2028 sq m, then what is the breadth of the rectangular plot? | {
"A": "11",
"B": "17",
"C": "26",
"D": "101",
"E": "1322"
} | sqrt(divide(2028, const_3)) | divide(n0,const_3)|sqrt(#0)| | "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 2028 3 b 2 = 2028 b 2 = 676 = 26 ( b > 0 ) b = 26 m . answer : c" | geometry |
math_qa__pXGGrhsEk7jGkJjl | find the least number which when divided by 5 , 67 , and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder
Choose the correct choice from the following: A) 1683 B) 1684 C) 1685 D) 1582 E) 1584 | <gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">lcm(5, 6)</gadget>
<output>30</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">lcm(30, 7)</gadget>
<output>210</output>
<gadget id="calculator">lcm(210, 8)</gadget>
<output>840</output>
<gadget id="calculator">840 * 2</gadget>
<output>1_680</output>
<gadget id="calculator">1_680 + 3</gadget>
<output>1_683</output>
<result>A</result> | A | 1,683 | find the least number which when divided by 5 , 67 , and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder | {
"A": "1683",
"B": "1684",
"C": "1685",
"D": "1582",
"E": "1584"
} | add(multiply(lcm(lcm(lcm(5, multiply(const_2, const_3)), add(const_3, const_4)), 8), const_2), 3) | add(const_3,const_4)|multiply(const_2,const_3)|lcm(n0,#1)|lcm(#0,#2)|lcm(n2,#3)|multiply(#4,const_2)|add(n3,#5) | explanation : l . c . m . of 5,6 , 7,8 = 840 . required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . required number = ( 840 x 2 + 3 ) = 1683 answer is a | general |
math_qa__O9Jd5KN5v8Bo4sbJ | Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/6, 1/2 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem? Options.
A) 1 / 32 B) 7 / 8 C) 9 / 64 D) 5 / 64 E) 3 / 64 | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/6) * (1/2)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(1/12) * (3/8)</gadget>
<output>1/32 = around 0.03125</output>
<result>A</result> | A | 0.03125 | Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/6, 1/2 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem? | {
"A": "1 / 32",
"B": "7 / 8",
"C": "9 / 64",
"D": "5 / 64",
"E": "3 / 64"
} | multiply(multiply(divide(1, 6), divide(1, 2)), subtract(1, divide(5, 8))) | divide(n0,n1)|divide(n2,n3)|divide(n4,n5)|multiply(#0,#1)|subtract(n0,#2)|multiply(#3,#4)| | "p ( xavier will solve ) = 1 / 6 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 6 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 32 . ans . a ." | general |
math_qa__9R4u1uFxWpBTW7CV | A sum fetched total simple interest of 4016.25 at the rate of 11 p.c.p.a. in 5 years. What is the sum? Select the correct option
A) 8925
B) 8032.5
C) 7302.3
D) 8900
E) none of these | <gadget id="calculator">100 * 4_016.25</gadget>
<output>401_625</output>
<gadget id="calculator">11 * 5</gadget>
<output>55</output>
<gadget id="calculator">401_625 / 55</gadget>
<output>80_325/11 = around 7_302.272727</output>
<result>C</result> | C | 7,302.3 | A sum fetched total simple interest of 4016.25 at the rate of 11 p.c.p.a. in 5 years. What is the sum? | {
"A": "8925",
"B": "8032.5",
"C": "7302.3",
"D": "8900",
"E": "none of these"
} | divide(multiply(const_100, 4016.25), multiply(11, 5)) | multiply(n0,const_100)|multiply(n1,n2)|divide(#0,#1)| | "let the sums be p . now , 55 % of p = 4016.25 or , p = 7302.3 answer c" | gain |
math_qa__noRXg268oXbtNFWP | What is the CP of Rs 100 stock at 8 discount, with 1/5% brokerage? Select the correct option:
A) 92.9 B) 96.3 C) 92.2 D) 96.7 E) 92.8 | <gadget id="calculator">100 - 8</gadget>
<output>92</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">92 + (1/5)</gadget>
<output>461/5 = around 92.2</output>
<result>C</result> | C | 92.2 | What is the CP of Rs 100 stock at 8 discount, with 1/5% brokerage? | {
"A": "92.9",
"B": "96.3",
"C": "92.2",
"D": "96.7",
"E": "92.8"
} | add(subtract(100, 8), divide(1, 5)) | divide(n2,n3)|subtract(n0,n1)|add(#0,#1)| | "explanation : use the formula , cp = 100 Γ’ β¬ β discount + brokerage % cp = 100 - 8 + 1 / 5 92.2 thus the cp is rs 92.2 . answer : c" | gain |
math_qa__TPoqm7NTHZmn5hiQ | Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 27 kg of zinc has been consumed in it?
Choose the correct answer: A) 58 kg B) 60 kg C) 64 kg D) 70 kg E) none | <gadget id="calculator">11 / 9</gadget>
<output>11/9 = around 1.222222</output>
<gadget id="calculator">(11/9) * 27</gadget>
<output>33</output>
<gadget id="calculator">33 + 27</gadget>
<output>60</output>
<result>B</result> | B | 60 | Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 27 kg of zinc has been consumed in it? | {
"A": "58 kg",
"B": "60 kg",
"C": "64 kg",
"D": "70 kg",
"E": "none"
} | add(multiply(divide(11, 9), 27), 27) | divide(n1,n0)|multiply(n2,#0)|add(n2,#1)| | "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 27 kg zinc , mixture , melted = [ 20 / 9 x 27 ] kg = 60 kg . answer b" | general |
math_qa__5bk9DdGVbqplgqXq | If x is an integer such that 3 < x < 10, 5 < x < 18, 9 > x > β2, 8 > x > 0, and x + 1 < 9, then x is
Select the correct option.
A) 3 B) 5 C) 7 D) 9 E) 11 | <gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<result>C</result> | C | 7 | If x is an integer such that 3 < x < 10, 5 < x < 18, 9 > x > β2, 8 > x > 0, and x + 1 < 9, then x is | {
"A": "3",
"B": "5",
"C": "7",
"D": "9",
"E": "11"
} | subtract(subtract(9, 1), 1) | subtract(n4,n8)|subtract(#0,n8)| | "3 < x < 10 , 6 < x < 18 , - 2 < x < 9 0 < x < 8 x < 8 from above : 6 < x < 8 - - > x = 7 . answer : c ." | general |
math_qa__gCrsbFey8eTBfa0r | If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. The second smallest prime factor of p(12)+11 is Choices.
A) 2 B) 11 C) 13 D) 17 E) 211 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">11 * 7</gadget>
<output>77</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">77 * 5</gadget>
<output>385</output>
<gadget id="calculator">385 * 3</gadget>
<output>1_155</output>
<gadget id="calculator">1_155 * 2</gadget>
<output>2_310</output>
<gadget id="calculator">2_310 + 11</gadget>
<output>2_321</output>
<gadget id="calculator">2_321 / 11</gadget>
<output>211</output>
<result>E</result> | E | 211 | If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. The second smallest prime factor of p(12)+11 is | {
"A": "2",
"B": "11",
"C": "13",
"D": "17",
"E": "211"
} | divide(add(multiply(multiply(multiply(multiply(11, add(const_4, const_3)), add(const_4, const_1)), const_3), const_2), 11), 11) | add(const_1,const_4)|add(const_3,const_4)|multiply(n2,#1)|multiply(#0,#2)|multiply(#3,const_3)|multiply(#4,const_2)|add(n2,#5)|divide(#6,n2) | p ( 12 ) + 11 = 2 β 3 β 5 β 7 β 11 + 11 = 11 ( 2 β 3 β 5 β 7 + 1 ) = 11 β 211 . both 11 and 211 are primes : 11 is the smallest prime of p ( 12 ) + 11 and 211 is the second smallest prime of p ( 12 ) + 11 . answer : e . | general |
math_qa__SX8EnEcW1xfZoYyW | In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 140 marks, the no of questions he attempts correctly is : Choices:
A) 35 B) 38 C) 90 D) 88 E) 40 | <gadget id="calculator">140 + 60</gadget>
<output>200</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">200 / 5</gadget>
<output>40</output>
<result>E</result> | E | 40 | In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 140 marks, the no of questions he attempts correctly is : | {
"A": "35",
"B": "38",
"C": "90",
"D": "88",
"E": "40"
} | divide(add(140, 60), add(4, 1)) | add(n2,n3)|add(n0,n1)|divide(#0,#1)| | "let the number of correct answers be x . number of incorrect answers = ( 60 β x ) . 4 x β ( 60 β x ) = 140 = > 5 x = 200 = > x = 40 answer : e" | physics |
math_qa__JRapD3iJqPLIqUTf | The average (arithmetic mean) of 4 different integers is 70. If the largest integer is 90, what is the least possible value of the smallest integer?
Options.
A) 1 B) 19 C) 29 D) 13 E) 33 | <gadget id="calculator">70 * 4</gadget>
<output>280</output>
<gadget id="calculator">280 - 90</gadget>
<output>190</output>
<gadget id="calculator">90 - 1</gadget>
<output>89</output>
<gadget id="calculator">190 - 89</gadget>
<output>101</output>
<gadget id="calculator">90 - 2</gadget>
<output>88</output>
<gadget id="calculator">101 - 88</gadget>
<output>13</output>
<result>D</result> | D | 13 | The average (arithmetic mean) of 4 different integers is 70. If the largest integer is 90, what is the least possible value of the smallest integer? | {
"A": "1",
"B": "19",
"C": "29",
"D": "13",
"E": "33"
} | subtract(subtract(subtract(multiply(70, 4), 90), subtract(90, const_1)), subtract(90, const_2)) | multiply(n0,n1)|subtract(n2,const_1)|subtract(n2,const_2)|subtract(#0,n2)|subtract(#3,#1)|subtract(#4,#2)| | "total of integers = 70 * 4 = 280 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 280 - ( 90 + 89 + 88 ) = 280 - 267 = 13 answer : d" | general |
math_qa__gkCiayBjZNs5QxNd | P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?
Choose the correct answer: A) 5 days B) 10 days C) 14 days D) 22 days E) 26 days | <gadget id="calculator">4 / 20</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/20) + (1/12)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(4/5) / (2/15)</gadget>
<output>6</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<result>B</result> | B | 10 | P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last? | {
"A": "5 days",
"B": "10 days",
"C": "14 days",
"D": "22 days",
"E": "26 days"
} | add(4, divide(subtract(const_1, divide(4, 20)), add(inverse(20), inverse(12)))) | divide(n2,n0)|inverse(n0)|inverse(n1)|add(#1,#2)|subtract(const_1,#0)|divide(#4,#3)|add(n2,#5)| | "explanation : work done by p in 1 day = 1 / 20 work done by q in 1 day = 1 / 12 work done by p in 4 days = 4 Γ ( 1 / 20 ) = 1 / 5 remaining work = 1 β 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 20 + 1 / 12 = 8 / 60 = 2 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 2 / 15 ) = 6 total days = 4 + 6 = 10 answer : option b" | physics |
math_qa__26laNEmf0yonGEtm | if in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr). Choose the correct choice from the following answers
A) 18 kmph B) 15.5 kmph C) 12.5 kmph D) 13.5 kmph E) 22.5 kmph | <gadget id="calculator">16 + 9</gadget>
<output>25</output>
<gadget id="calculator">25 / 2</gadget>
<output>25/2 = around 12.5</output>
<result>C</result> | C | 12.5 | if in one hour, a canoe rows at 16 km/hr downstream and 9 km/hr upstream, Calculate the speed of a boat in still water (in km/hr). | {
"A": "18 kmph",
"B": "15.5 kmph",
"C": "12.5 kmph",
"D": "13.5 kmph",
"E": "22.5 kmph"
} | divide(add(16, 9), const_2) | add(n0,n1)|divide(#0,const_2) | speed in still water = ( 16 + 9 ) 1 / 2 kmph = 12.5 kmph . answer : c | physics |
math_qa__YudiV8LQAXAfTiwg | A rectangular lawn 55m by 35m has two roads each 4m wide running in the middle of it. One parallel to the length and the other parallel to breadth. The cost of graveling the roads at 75 paise per sq meter is? Choices:
A) rs . 259
B) rs . 252
C) rs . 258
D) rs . 251
E) rs . 252 | <gadget id="calculator">55 + 35</gadget>
<output>90</output>
<gadget id="calculator">90 - 4</gadget>
<output>86</output>
<gadget id="calculator">86 * 4</gadget>
<output>344</output>
<gadget id="calculator">344 * 75</gadget>
<output>25_800</output>
<gadget id="calculator">25_800 / 100</gadget>
<output>258</output>
<result>C</result> | C | 258 | A rectangular lawn 55m by 35m has two roads each 4m wide running in the middle of it. One parallel to the length and the other parallel to breadth. The cost of graveling the roads at 75 paise per sq meter is? | {
"A": "rs . 259",
"B": "rs . 252",
"C": "rs . 258",
"D": "rs . 251",
"E": "rs . 252"
} | divide(multiply(multiply(subtract(add(55, 35), 4), 4), 75), const_100) | add(n0,n1)|subtract(#0,n2)|multiply(#1,n2)|multiply(n3,#2)|divide(#3,const_100)| | "area of cross roads = 55 * 4 + 35 * 4 - 4 * 4 = 344 sq m cost of graveling = 344 * ( 75 / 100 ) = rs . 258 answer : c" | physics |
math_qa__BfY3rgqGSVdrjz3G | a salesman ` s commission is 5 % on all sales upto rs . 10000 and 4 % on all sales exceeding this . he remits rs . 31100 to his parent company after deducing his commission . find the total sales . Choose the correct choice from the following options
A) 32500 B) 2500 C) 22500 D) 30000 E) 40000 | <gadget id="calculator">31_100 + 100</gadget>
<output>31_200</output>
<gadget id="calculator">100 / 4</gadget>
<output>25</output>
<gadget id="calculator">31_200 * 25</gadget>
<output>780_000</output>
<gadget id="calculator">12 + 12</gadget>
<output>24</output>
<gadget id="calculator">780_000 / 24</gadget>
<output>32_500</output>
<result>A</result> | A | 32,500 | a salesman ` s commission is 5 % on all sales upto rs . 10000 and 4 % on all sales exceeding this . he remits rs . 31100 to his parent company after deducing his commission . find the total sales . | {
"A": "32500",
"B": "2500",
"C": "22500",
"D": "30000",
"E": "40000"
} | divide(multiply(add(31100, const_100), divide(const_100, const_4)), add(const_12, const_12)) | add(n3,const_100)|add(const_12,const_12)|divide(const_100,const_4)|multiply(#0,#2)|divide(#3,#1) | let his total sales be rs . x . now ( total sales ) β ( commission ) = rs . 31100 x - [ ( 5 % of 10000 + 4 % of ( x - 10000 ) ] = 31100 x - [ ( ( 5 / 100 ) * 10000 + ( 4 / 100 ) * ( x - 10000 ) ] = 31100 ο³ x - 500 - ( ( x - 10000 ) / 25 ) = 31100 ο³ x - ( x / 25 ) = 31200 ο³ 24 x / 25 = 31200 ο³ x = [ ( 31200 * 25 ) / 24 ) = 32500 . total sales = rs . 32500 answer a | general |
math_qa__HwGBNqUhKNzXBbmc | Approximately how many revolutions will be made by a car tire with a 15-inch diameter if the car travels 1β2 mile? Options.
A) 669 B) 660 C) 360 D) 720 E) 1,440 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 / 10</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) + 1</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) / 10</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">(4/25) + 4</gadget>
<output>104/25 = around 4.16</output>
<gadget id="calculator">(104/25) / 10</gadget>
<output>52/125 = around 0.416</output>
<gadget id="calculator">(52/125) + 1</gadget>
<output>177/125 = around 1.416</output>
<gadget id="calculator">(177/125) / 10</gadget>
<output>177/1_250 = around 0.1416</output>
<gadget id="calculator">(177/1_250) + 3</gadget>
<output>3_927/1_250 = around 3.1416</output>
<gadget id="calculator">(3_927/1_250) * 15</gadget>
<output>11_781/250 = around 47.124</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">60 + 3</gadget>
<output>63</output>
<gadget id="calculator">63 * 10</gadget>
<output>630</output>
<gadget id="calculator">630 + 3</gadget>
<output>633</output>
<gadget id="calculator">633 * 10</gadget>
<output>6_330</output>
<gadget id="calculator">6_330 + 3</gadget>
<output>6_333</output>
<gadget id="calculator">6_333 + 2</gadget>
<output>6_335</output>
<gadget id="calculator">6_335 * 10</gadget>
<output>63_350</output>
<gadget id="calculator">(11_781/250) / 63_350</gadget>
<output>1_683/2_262_500 = around 0.000744</output>
<gadget id="calculator">(1/2) / (1_683/2_262_500)</gadget>
<output>1_131_250/1_683 = around 672.162805</output>
<result>A</result> | A | 669 | Approximately how many revolutions will be made by a car tire with a 15-inch diameter if the car travels 1β2 mile? | {
"A": "669",
"B": "660",
"C": "360",
"D": "720",
"E": "1,440"
} | divide(divide(1, 2), divide(multiply(add(divide(add(divide(add(divide(add(divide(multiply(const_3, const_2), const_10), const_1), const_10), const_4), const_10), const_1), const_10), const_3), 15), multiply(add(add(multiply(add(multiply(add(multiply(multiply(const_3, const_2), const_10), const_3), const_10), const_3), const_10), const_3), const_2), const_10))) | divide(n1,n2)|multiply(const_2,const_3)|divide(#1,const_10)|multiply(#1,const_10)|add(#2,const_1)|add(#3,const_3)|divide(#4,const_10)|multiply(#5,const_10)|add(#6,const_4)|add(#7,const_3)|divide(#8,const_10)|multiply(#9,const_10)|add(#10,const_1)|add(#11,const_3)|add(#13,const_2)|divide(#12,const_10)|add(#15,const_3)|multiply(#14,const_10)|multiply(n0,#16)|divide(#18,#17)|divide(#0,#19) | diameter of car tire = 15 inches radius of car tire = 7.5 inches = 7.5 * 2.54 cm = 19.05 cm circumference of the car tire = 2 * pi * 19.05 = 2 * 3.14 * 19.05 = 119.63 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 119.63 = 668.73 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer a | general |
math_qa__hqIDTkdEpIC6rFj2 | 16 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? Choices: A) 190 B) 200 C) 210 D) 220 E) 240 | <gadget id="calculator">16 - 1</gadget>
<output>15</output>
<gadget id="calculator">16 * 15</gadget>
<output>240</output>
<result>E</result> | E | 240 | 16 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? | {
"A": "190",
"B": "200",
"C": "210",
"D": "220",
"E": "240"
} | multiply(16, subtract(16, const_1)) | subtract(n0,const_1)|multiply(n0,#0) | 2 * 16 c 2 = 2 * 120 = 240 the answer is e . | general |
math_qa__sdtrjbMnSDcie748 | The grade point average of one third of the classroom is 30; the grade point average of the rest is 33. What is the grade point average of the whole class? Choose the correct choice from the following answers.
A) 44
B) 41
C) 38
D) 35
E) 32 | <gadget id="calculator">33 / 3</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">30 / 3</gadget>
<output>10</output>
<gadget id="calculator">22 + 10</gadget>
<output>32</output>
<result>E</result> | E | 32 | The grade point average of one third of the classroom is 30; the grade point average of the rest is 33. What is the grade point average of the whole class? | {
"A": "44",
"B": "41",
"C": "38",
"D": "35",
"E": "32"
} | add(multiply(divide(33, const_3), const_2), divide(30, const_3)) | divide(n0,const_3)|divide(n1,const_3)|multiply(#1,const_2)|add(#0,#2)| | "let n = total students in class total points for 1 / 3 class = 30 n / 3 = 10 n total points for 2 / 3 class = 33 * 2 n / 3 = 22 n total points for whole class = 10 n + 22 n = 32 n 32 n total class points / n total students = 32 grade point average for total class answer : e" | general |
math_qa__YA0Kh84WvQfKWj4K | In a rectangular axis system, what is the area of a parallelogram with the coordinates: (4,4), (7,4), (5,9), (8,9) ? Choices:
A) 21 .
B) 28 .
C) 5 .
D) 49 .
E) 52 . | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<result>C</result> | C | 5 | In a rectangular axis system, what is the area of a parallelogram with the coordinates: (4,4), (7,4), (5,9), (8,9) ? | {
"A": "21 .",
"B": "28 .",
"C": "5 .",
"D": "49 .",
"E": "52 ."
} | add(const_3, const_2) | add(const_2,const_3) | delta x will give us the dimension of one side of the parallelogram = 5 - 4 = 1 unit delta y will give us the dimension of the other side of parallelogram = 9 - 4 = 5 unit area of parallelogram = 1 * 5 = 5 answer is c | geometry |
math_qa__qCnBN5GAPsK5aGeW | Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel? Choose the most appropriate option:
A) 54 B) 66 C) 80 D) 36 E) 96 | <gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">18 / 6</gadget>
<output>3</output>
<gadget id="calculator">18 * 3</gadget>
<output>54</output>
<result>A</result> | A | 54 | Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel? | {
"A": "54",
"B": "66",
"C": "80",
"D": "36",
"E": "96"
} | multiply(18, divide(divide(36, 2), 6)) | divide(n1,n3)|divide(#0,n0)|multiply(n2,#1)| | "a 54 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 18 mph = 54 miles" | physics |
math_qa__XbddRomVPexcVG97 | Average expenditure of a person for the first 3 days of a week is Rs. 360 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is: Choices.
A) 350
B) 370
C) 390
D) 400
E) none | <gadget id="calculator">420 - 360</gadget>
<output>60</output>
<gadget id="calculator">4 * 60</gadget>
<output>240</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">240 / 7</gadget>
<output>240/7 = around 34.285714</output>
<gadget id="calculator">360 + (240/7)</gadget>
<output>2_760/7 = around 394.285714</output>
<result>D</result> | D | 400 | Average expenditure of a person for the first 3 days of a week is Rs. 360 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is: | {
"A": "350",
"B": "370",
"C": "390",
"D": "400",
"E": "none"
} | add(360, divide(multiply(4, subtract(420, 360)), add(3, 4))) | add(n0,n2)|subtract(n3,n1)|multiply(n2,#1)|divide(#2,#0)|add(n1,#3)| | "explanation : assumed mean = rs . 360 total excess than assumed mean = 4 Γ ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 360 + rs . 40 = rs . 400 correct option : d" | general |
math_qa__dT2KiqabkTJWt64P | What approximate value will come in place of the question mark(?) in the below question?
(47% of 1442 - 36% of 1412) + 63 = ? Answers
A) 237 B) 278 C) 278 D) 252 E) 271 | <gadget id="calculator">10 + 4</gadget>
<output>14</output>
<gadget id="calculator">14 + 4</gadget>
<output>18</output>
<gadget id="calculator">18 + 1</gadget>
<output>19</output>
<gadget id="calculator">36 + 10</gadget>
<output>46</output>
<gadget id="calculator">46 + 12</gadget>
<output>58</output>
<gadget id="calculator">58 / 100</gadget>
<output>29/50 = around 0.58</output>
<gadget id="calculator">19 + (29/50)</gadget>
<output>979/50 = around 19.58</output>
<gadget id="calculator">47 / 100</gadget>
<output>47/100 = around 0.47</output>
<gadget id="calculator">(47/100) * 1_442</gadget>
<output>33_887/50 = around 677.74</output>
<gadget id="calculator">36 / 100</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) * 1_412</gadget>
<output>12_708/25 = around 508.32</output>
<gadget id="calculator">(33_887/50) - (12_708/25)</gadget>
<output>8_471/50 = around 169.42</output>
<gadget id="calculator">63 + (8_471/50)</gadget>
<output>11_621/50 = around 232.42</output>
<gadget id="calculator">(979/50) + (11_621/50)</gadget>
<output>252</output>
<result>D</result> | D | 252 | What approximate value will come in place of the question mark(?) in the below question?
(47% of 1442 - 36% of 1412) + 63 = ? | {
"A": "237",
"B": "278",
"C": "278",
"D": "252",
"E": "271"
} | add(add(add(add(add(const_10, const_4), const_4), const_1), divide(add(add(36, const_10), const_12), const_100)), add(63, subtract(multiply(divide(47, const_100), 1442), multiply(divide(36, const_100), 1412)))) | add(const_10,const_4)|add(n2,const_10)|divide(n0,const_100)|divide(n2,const_100)|add(#0,const_4)|add(#1,const_12)|multiply(n1,#2)|multiply(n3,#3)|add(#4,const_1)|divide(#5,const_100)|subtract(#6,#7)|add(#8,#9)|add(n4,#10)|add(#11,#12) | explanation : since there are 5 cups of each kind , prepared with milk or tea leaves added first , are identical hence , total number of different people ways of presenting the cups to the expert is 10 ! / ( 5 ! x 5 ! ) = 252 answer : d ) 252 | general |
math_qa__lQAZZGaVDLH5EPiX | Multiplication of 2 numbers is 9375 and the quotient, when the larger one is divided by the smalleris 15. Find the sum of the numbers? Choose one
A) 200 B) 300 C) 400 D) 500 E) 600 | <gadget id="calculator">9_375 / 15</gadget>
<output>625</output>
<gadget id="calculator">625 ** (1/2)</gadget>
<output>25</output>
<gadget id="calculator">9_375 / 25</gadget>
<output>375</output>
<gadget id="calculator">25 + 375</gadget>
<output>400</output>
<result>C</result> | C | 400 | Multiplication of 2 numbers is 9375 and the quotient, when the larger one is divided by the smalleris 15. Find the sum of the numbers? | {
"A": "200",
"B": "300",
"C": "400",
"D": "500",
"E": "600"
} | add(sqrt(divide(9375, 15)), divide(9375, sqrt(divide(9375, 15)))) | divide(n1,n2)|sqrt(#0)|divide(n1,#1)|add(#2,#1) | let the numbers be x and y . then , xy = 9375 and x = 15 . y xy = 9375 ( x / y ) 15 y 2 = 625 . y = 25 . x = 15 y = ( 15 x 25 ) = 375 . sum of the numbers = x + y = 375 + 25 = 400 . c | general |
math_qa__AbaNoVwMvwLj7uaJ | A person distributed 20% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income? Select.
A) 452000 B) 562000 C) 800000 D) 500000 E) 652000 | <gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">60 + 30</gadget>
<output>90</output>
<gadget id="calculator">90 + 5</gadget>
<output>95</output>
<gadget id="calculator">100 - 95</gadget>
<output>5</output>
<gadget id="calculator">40_000 / 5</gadget>
<output>8_000</output>
<gadget id="calculator">8_000 * 100</gadget>
<output>800_000</output>
<result>C</result> | C | 800,000 | A person distributed 20% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $40000. Find his total income? | {
"A": "452000",
"B": "562000",
"C": "800000",
"D": "500000",
"E": "652000"
} | multiply(divide(40000, subtract(const_100, add(add(multiply(20, 3), 30), 5))), const_100) | multiply(n0,n1)|add(n2,#0)|add(n3,#1)|subtract(const_100,#2)|divide(n4,#3)|multiply(#4,const_100)| | "3 children got = 3 * 20 % = 60 % wife got = 30 % orphan house = 5 % total = 60 + 30 + 5 = 95 % remaining = 100 - 95 = 5 % 5 % = 40000 100 % = 40000 * 100 / 5 = $ 800000 answer is c" | gain |
math_qa__E5LxfdcT7NvKdN9c | A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is Select the correct option.
A) 7 / 19
B) 6 / 19
C) 5 / 19
D) 4 / 19
E) none of these | <gadget id="calculator">20 - 4</gadget>
<output>16</output>
<gadget id="calculator">binomial(16, 2)</gadget>
<output>120</output>
<gadget id="calculator">binomial(20, 2)</gadget>
<output>190</output>
<gadget id="calculator">120 / 190</gadget>
<output>12/19 = around 0.631579</output>
<gadget id="calculator">1 - (12/19)</gadget>
<output>7/19 = around 0.368421</output>
<result>A</result> | A | 0.368421 | A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is | {
"A": "7 / 19",
"B": "6 / 19",
"C": "5 / 19",
"D": "4 / 19",
"E": "none of these"
} | subtract(const_1, divide(choose(subtract(20, 4), const_2), choose(20, const_2))) | choose(n0,const_2)|subtract(n0,n1)|choose(#1,const_2)|divide(#2,#0)|subtract(const_1,#3)| | "explanation : please remember that maximum portability is 1 . so we can get total probability of non defective bulbs and subtract it form 1 to get total probability of defective bulbs . so here we go , total cases of non defective bulbs 16 c 2 = 16 β 15 / 2 β 1 = 120 total cases = 20 c 2 = 20 β 19 / 2 β 1 = 190 probability = 120 / 190 = 12 / 19 p of at least one defective = 1 β 12 / 19 = 7 / 19 option a" | probability |
math_qa__oNdOn2lxB2GrHWAt | After decreasing 24% in the price of an article costs Rs.988. Find the actual cost of an article? Choose the correct option:
A) 1667 B) 6789 C) 1300 D) 6151 E) 1421 | <gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>
<gadget id="calculator">988 / (19/25)</gadget>
<output>1_300</output>
<result>C</result> | C | 1,300 | After decreasing 24% in the price of an article costs Rs.988. Find the actual cost of an article? | {
"A": "1667",
"B": "6789",
"C": "1300",
"D": "6151",
"E": "1421"
} | divide(988, subtract(const_1, divide(24, const_100))) | divide(n0,const_100)|subtract(const_1,#0)|divide(n1,#1)| | "cp * ( 76 / 100 ) = 988 cp = 13 * 100 = > cp = 1300 answer : c" | gain |
math_qa__B229yOx9FeNTru49 | Of the votes cast on a certain proposal, 58 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)
Options: A) 230 B) 245 C) 260 D) 275 E) 290 | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) - (2/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">58 / (1/5)</gadget>
<output>290</output>
<result>E</result> | E | 290 | Of the votes cast on a certain proposal, 58 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.) | {
"A": "230",
"B": "245",
"C": "260",
"D": "275",
"E": "290"
} | divide(58, subtract(subtract(const_1, divide(40, const_100)), divide(40, const_100))) | divide(n1,const_100)|subtract(const_1,#0)|subtract(#1,#0)|divide(n0,#2)| | "let x be the total number of votes cast . 0.6 x = 0.4 x + 58 0.2 x = 58 x = 290 the answer is e ." | gain |
math_qa__Wy85rIfajexQKa72 | The S.I. on a certain sum of money for 3 years at 10% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? Choose one:
A) 2197 B) 1267 C) 1750 D) 2267 E) 1400 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">4_000 * (121/100)</gadget>
<output>4_840</output>
<gadget id="calculator">4_840 - 4_000</gadget>
<output>840</output>
<gadget id="calculator">840 / 2</gadget>
<output>420</output>
<gadget id="calculator">3 * (1/10)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">420 / (3/10)</gadget>
<output>1_400</output>
<result>E</result> | E | 1,400 | The S.I. on a certain sum of money for 3 years at 10% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is? | {
"A": "2197",
"B": "1267",
"C": "1750",
"D": "2267",
"E": "1400"
} | divide(divide(subtract(multiply(4000, power(add(const_1, divide(10, const_100)), 2)), 4000), 2), multiply(3, divide(10, const_100))) | divide(n4,const_100)|divide(n1,const_100)|add(#0,const_1)|multiply(n0,#1)|power(#2,n3)|multiply(n2,#4)|subtract(#5,n2)|divide(#6,n3)|divide(#7,#3)| | "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 10 ) = rs . 1400 answer : e" | gain |
math_qa__BrPBdsa0rKYOx15g | For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.45 β 6.45*? Answers
A) 0.45 B) 0.5 C) 6.45 D) 0.25 E) 6.0 | <gadget id="calculator">floor(6.45)</gadget>
<output>6</output>
<gadget id="calculator">6.45 - 6</gadget>
<output>0.45</output>
<result>A</result> | A | 0.45 | For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.45 β 6.45*? | {
"A": "0.45",
"B": "0.5",
"C": "6.45",
"D": "0.25",
"E": "6.0"
} | subtract(6.45, floor(6.45)) | floor(n0)|subtract(n0,#0)| | "since z * is defined as the greatest positive even integer less than or equal to z , then 6.45 * = 6 ( the greatest positive even integer less than or equal to 6.45 is 6 ) . hence , 6.45 β 6.45 * = 6.45 - 6 = 0.45 answer : a ." | general |
math_qa__mkbLzdk5iumZqlUA | Find the total number of prime factors in the expression (4)^11 x (7)^7 x (11)^2 Pick:
A) 31 B) 22 C) 25 D) 27 E) 29 | <gadget id="calculator">2 * 11</gadget>
<output>22</output>
<gadget id="calculator">22 + 7</gadget>
<output>29</output>
<gadget id="calculator">29 + 2</gadget>
<output>31</output>
<result>A</result> | A | 31 | Find the total number of prime factors in the expression (4)^11 x (7)^7 x (11)^2 | {
"A": "31",
"B": "22",
"C": "25",
"D": "27",
"E": "29"
} | add(add(multiply(2, 11), 7), 2) | multiply(n1,n5)|add(n3,#0)|add(n5,#1)| | "( 4 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 7 x 11 ^ 2 = 2 ^ 22 x 7 ^ 7 x 11 ^ 2 total number of prime factors = ( 22 + 7 + 2 ) = 31 . answer is a ." | general |
math_qa__qWyDhUSkSCRzkzDH | At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 48 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 45 cents? Pick one:
A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">48 * 10</gadget>
<output>480</output>
<gadget id="calculator">45 * 10</gadget>
<output>450</output>
<gadget id="calculator">480 - 450</gadget>
<output>30</output>
<gadget id="calculator">60 - 45</gadget>
<output>15</output>
<gadget id="calculator">30 / 15</gadget>
<output>2</output>
<result>B</result> | B | 2 | At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 48 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 45 cents? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | divide(subtract(multiply(48, 10), multiply(45, 10)), subtract(60, 45)) | multiply(n2,n4)|multiply(n2,n5)|subtract(n1,n5)|subtract(#0,#1)|divide(#3,#2)| | "let number of apples = a number of oranges = b a + b = 10 - - - 1 . 48 = ( . 4 a + . 6 b ) / 10 = > 48 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 6 b = 4 let the number of oranges put back = c 45 * ( 10 - c ) = 40 * 6 + 60 ( 4 - c ) = > c = 2 answer b" | general |
math_qa__LMJltkZtOTIDkN0B | A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area Q covered by the two roads? Choose the correct choice from the following options
A) 400 B) 1550 C) 1575 D) 1600 E) 1625 | <gadget id="calculator">200 * 5</gadget>
<output>1_000</output>
<gadget id="calculator">120 * 5</gadget>
<output>600</output>
<gadget id="calculator">1_000 + 600</gadget>
<output>1_600</output>
<result>C</result> | C | 1,575 | A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area Q covered by the two roads? | {
"A": "400",
"B": "1550",
"C": "1575",
"D": "1600",
"E": "1625"
} | add(rectangle_area(200, 5), rectangle_area(120, 5)) | rectangle_area(n0,n2)|rectangle_area(n1,n2)|add(#0,#1)| | "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads q = 1000 + 600 - 25 = 1575 answer : option c" | geometry |
math_qa__mwYxHU5UlaaPHdpw | Find the surface area of a 8 cm x 6 cm x 2 cm brick. Choose the correct choice.
A) 112 cu cm B) 136 cu cm C) 164 cu cm D) 180 cu cm E) 152 cu cm | <gadget id="calculator">2 * (2 * 6 + 6 * 8 + 2 * 8)</gadget>
<output>152</output>
<result>E</result> | E | 152 | Find the surface area of a 8 cm x 6 cm x 2 cm brick. | {
"A": "112 cu cm",
"B": "136 cu cm",
"C": "164 cu cm",
"D": "180 cu cm",
"E": "152 cu cm"
} | surface_rectangular_prism(2, 6, 8) | surface_rectangular_prism(n0,n1,n2)| | "sol . surface area = [ 2 ( 8 x 6 + 6 x 2 + 8 x 2 ) ] = ( 2 x 76 ) = 152 cu cm answer e" | geometry |
math_qa__yqOwpqIHcYdepGpq | A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 15% while buying and by 20% while selling. What is his percentage profit? Choose the correct choice from the following answers
A) 10.22 % B) 20.22 % C) 21.22 % D) 43.75 % E) ca n ' t be calculated | <gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">115 - 80</gadget>
<output>35</output>
<gadget id="calculator">35 * 100</gadget>
<output>3_500</output>
<gadget id="calculator">3_500 / 80</gadget>
<output>175/4 = around 43.75</output>
<result>D</result> | D | 43.75 | A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 15% while buying and by 20% while selling. What is his percentage profit? | {
"A": "10.22 %",
"B": "20.22 %",
"C": "21.22 %",
"D": "43.75 %",
"E": "ca n ' t be calculated"
} | divide(multiply(subtract(add(const_100, 15), subtract(const_100, 20)), const_100), subtract(const_100, 20)) | add(n0,const_100)|subtract(const_100,n1)|subtract(#0,#1)|multiply(#2,const_100)|divide(#3,#1)| | "the owner buys 100 kg but actually gets 115 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 115 - 80 ) / 80 * 100 = ~ 43.75 % answer : d ." | gain |
math_qa__PYFYtMisBoleTZVO | A field is 90 metre long and 50 metre broad. A 25 metre long, 20 metre broad and 4 metre deep tank dug in the field and the earth taken out is spread evenly over the remaining field. How much the level of field will rise? Choose the correct choice from the following choices
A) 0.5 metre B) 0.3 metre C) 0.8 metre D) 0.6 metre E) 0.7 metre | <gadget id="calculator">25 * 20</gadget>
<output>500</output>
<gadget id="calculator">500 * 4</gadget>
<output>2_000</output>
<gadget id="calculator">90 * 50</gadget>
<output>4_500</output>
<gadget id="calculator">4_500 - 500</gadget>
<output>4_000</output>
<gadget id="calculator">2_000 / 4_000</gadget>
<output>1/2 = around 0.5</output>
<result>A</result> | A | 0.5 | A field is 90 metre long and 50 metre broad. A 25 metre long, 20 metre broad and 4 metre deep tank dug in the field and the earth taken out is spread evenly over the remaining field. How much the level of field will rise? | {
"A": "0.5 metre",
"B": "0.3 metre",
"C": "0.8 metre",
"D": "0.6 metre",
"E": "0.7 metre"
} | divide(multiply(multiply(25, 20), 4), subtract(multiply(90, 50), multiply(25, 20))) | multiply(n2,n3)|multiply(n0,n1)|multiply(n4,#0)|subtract(#1,#0)|divide(#2,#3) | area of field = 90 x 50 = 4500 m 2 area of field dug out = 25 x 20 = 500 m 2 therefore , area of remaining field = 4500 m 2 - 500 m 2 = 4000 m 2 volume of the earth dug out = 25 x 20 x 4 = 2000 m 3 therefore , field will rise by 2000 / 4000 = 0.5 metre answer a | physics |
math_qa__aobnQydFN7JkLaUU | The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? Select the correct option
A) 11.73 B) 12 C) 13.8 D) 14 E) 15.87 | <gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">207 * 85</gadget>
<output>17_595</output>
<gadget id="calculator">17_595 / 100</gadget>
<output>3_519/20 = around 175.95</output>
<gadget id="calculator">(3_519/20) / 15</gadget>
<output>1_173/100 = around 11.73</output>
<result>B</result> | B | 12 | The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity? | {
"A": "11.73",
"B": "12",
"C": "13.8",
"D": "14",
"E": "15.87"
} | divide(divide(multiply(207, subtract(const_100, 15)), const_100), 15) | subtract(const_100,n2)|multiply(n1,#0)|divide(#1,const_100)|divide(#2,n0)| | "x - > price without gratuity 207 = x + 0.15 x = > x = 207 / 1.15 = 180 so average price per person , excluding the gratuity = 180 / 15 = 12 the answer is b ." | general |
math_qa__XKEDHLgeIspXeugI | A soft drink company had 6000 small and 15000 big bottles in storage. If 11% of small 12% of big bottles have been sold, then the total bottles remaining in storage is
Choose the correct choice from the following options.
A) 15360 B) 16010 C) 15060 D) 14930 E) 18540 | <gadget id="calculator">6_000 + 15_000</gadget>
<output>21_000</output>
<gadget id="calculator">11 / 100</gadget>
<output>11/100 = around 0.11</output>
<gadget id="calculator">6_000 * (11/100)</gadget>
<output>660</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) * 15_000</gadget>
<output>1_800</output>
<gadget id="calculator">660 + 1_800</gadget>
<output>2_460</output>
<gadget id="calculator">21_000 - 2_460</gadget>
<output>18_540</output>
<result>E</result> | E | 18,540 | A soft drink company had 6000 small and 15000 big bottles in storage. If 11% of small 12% of big bottles have been sold, then the total bottles remaining in storage is | {
"A": "15360",
"B": "16010",
"C": "15060",
"D": "14930",
"E": "18540"
} | subtract(add(6000, 15000), add(multiply(6000, divide(11, const_100)), multiply(divide(12, const_100), 15000))) | add(n0,n1)|divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(n1,#2)|add(#3,#4)|subtract(#0,#5)| | "6000 + 15000 - ( 0.11 * 6000 + 0.12 * 15000 ) = 18540 . answer : e ." | general |
math_qa__Mjsa5lfvSUJxrDnb | A sum of money at simple interest amounts to Rs. 840 in 3 years and to Rs. 854 in 4 years. The sum is: Choose the correct choice from the following
A) 647 B) 798 C) 654 D) 847 E) 976 | <gadget id="calculator">854 - 840</gadget>
<output>14</output>
<gadget id="calculator">14 * 3</gadget>
<output>42</output>
<gadget id="calculator">42 / 4</gadget>
<output>21/2 = around 10.5</output>
<gadget id="calculator">840 - (21/2)</gadget>
<output>1_659/2 = around 829.5</output>
<result>B</result> | B | 798 | A sum of money at simple interest amounts to Rs. 840 in 3 years and to Rs. 854 in 4 years. The sum is: | {
"A": "647",
"B": "798",
"C": "654",
"D": "847",
"E": "976"
} | subtract(840, divide(multiply(subtract(854, 840), 3), 4)) | subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)| | "s . i . for 1 year = rs . ( 854 - 840 ) = rs . 14 . s . i . for 3 years = rs . ( 14 x 3 ) = rs . 42 . principal = rs . ( 840 - 42 ) = rs . 798 . answer : b" | gain |
math_qa__bQm4epBXZ1UGel3a | Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 51 minutes, for how many kilometers total did she hike east? Select: A) 3.625 B) 3 C) 4.5 D) 4 E) 3.5 | <gadget id="calculator">51 / 12</gadget>
<output>17/4 = around 4.25</output>
<gadget id="calculator">(17/4) - 2.75</gadget>
<output>1.5</output>
<gadget id="calculator">1.5 / 2</gadget>
<output>0.75</output>
<gadget id="calculator">0.75 + 2.75</gadget>
<output>3.5</output>
<result>E</result> | E | 3.5 | Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 51 minutes, for how many kilometers total did she hike east? | {
"A": "3.625",
"B": "3",
"C": "4.5",
"D": "4",
"E": "3.5"
} | add(divide(subtract(divide(51, 12), 2.75), const_2), 2.75) | divide(n2,n0)|subtract(#0,n1)|divide(#1,const_2)|add(n1,#2)| | "set up two r x t = d cases . 1 . 1 / 12 km / min x t = 2.75 from which t = 33 mins . we know total journey time now is 51 + 33 = 84 . the rate is the same ie 1 / 12 km / min . set up second r x t = d case . 1 / 12 km / min x 84 = 7 km now the total journey would be halved as distance would be same in each direction . 7 / 2 = 3.5 e ." | physics |
math_qa__y1SycBot3XfK3eWD | If Sharon's weekly salary increased by 16 percent, she would earn $348 per week. If instead, her weekly salary were to increase by 25 percent, how much would she earn per week? Choose the correct choice from the following options
A) $ 374 B) $ 382 C) $ 385 D) $ 392 E) $ 375 | <gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">1 + (4/25)</gadget>
<output>29/25 = around 1.16</output>
<gadget id="calculator">348 / (29/25)</gadget>
<output>300</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 300</gadget>
<output>75</output>
<gadget id="calculator">300 + 75</gadget>
<output>375</output>
<result>E</result> | E | 375 | If Sharon's weekly salary increased by 16 percent, she would earn $348 per week. If instead, her weekly salary were to increase by 25 percent, how much would she earn per week? | {
"A": "$ 374",
"B": "$ 382",
"C": "$ 385",
"D": "$ 392",
"E": "$ 375"
} | add(divide(348, add(const_1, divide(16, const_100))), multiply(divide(25, const_100), divide(348, add(const_1, divide(16, const_100))))) | divide(n0,const_100)|divide(n2,const_100)|add(#0,const_1)|divide(n1,#2)|multiply(#1,#3)|add(#3,#4)| | "( 348 / 116 ) 125 = 375 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 125 = 375 ( 300 + 75 ) answer e" | general |
math_qa__efJwilv5yZld77uM | A certain hospital has a policy that for every 50 patients there should be 2 doctors. If the number of patients visiting the hospital every day is 400, how many doctors are there in the hospital? Pick
A) 4 B) 16 C) 5 D) 14 E) 11 | <gadget id="calculator">400 / 50</gadget>
<output>8</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<result>B</result> | B | 16 | A certain hospital has a policy that for every 50 patients there should be 2 doctors. If the number of patients visiting the hospital every day is 400, how many doctors are there in the hospital? | {
"A": "4",
"B": "16",
"C": "5",
"D": "14",
"E": "11"
} | multiply(divide(400, 50), 2) | divide(n2,n0)|multiply(n1,#0) | 2 / 50 = x / 400 x = 16 answer is b | physics |
math_qa__Evlq0VOU8KnujL6i | 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 2553, how much was it in the beginning?
Choose the correct choice from the following: A) 2988 B) 2776 C) 4400 D) 2871 E) 3162 | <gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">(19/20) * (17/20)</gadget>
<output>323/400 = around 0.8075</output>
<gadget id="calculator">2_553 / (323/400)</gadget>
<output>1_021_200/323 = around 3_161.609907</output>
<gadget id="calculator">floor(1_021_200/323)</gadget>
<output>3_161</output>
<result>E</result> | E | 3,162 | 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 2553, how much was it in the beginning? | {
"A": "2988",
"B": "2776",
"C": "4400",
"D": "2871",
"E": "3162"
} | floor(divide(2553, multiply(divide(subtract(const_100, 5), const_100), divide(subtract(const_100, 15), const_100)))) | subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|divide(n2,#4)|floor(#5)| | "x * ( 95 / 100 ) * ( 85 / 100 ) = 2553 x = 3162 answer : e" | general |
math_qa__ow8K5Jgtza6aYYE4 | A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: Options:
A) 49 m 2 B) 50 m 2 C) 52 m 2 D) 62 m 2 E) 55 m 2 | <gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 8</gadget>
<output>10</output>
<gadget id="calculator">(5/4) * 4</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">2 * 15</gadget>
<output>30</output>
<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<gadget id="calculator">30 + 32</gadget>
<output>62</output>
<result>D</result> | D | 62 | A cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: | {
"A": "49 m 2",
"B": "50 m 2",
"C": "52 m 2",
"D": "62 m 2",
"E": "55 m 2"
} | add(multiply(const_2, add(multiply(add(divide(25, const_100), 1), 8), multiply(add(divide(25, const_100), 1), 4))), multiply(8, 4)) | divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|add(#3,#4)|multiply(#5,const_2)|add(#6,#1)| | "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 8 x 1.25 + 4 x 1.25 ) + 8 x 4 ] m 2 = 62 m 2 . answer : d" | physics |
math_qa__8RzzQJfgy8MLa59w | In measuring the sides of a rectangle, one side is taken 12% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. Choose the correct answer:
A) 3.5 %
B) 6.4 %
C) 3 %
D) 5 %
E) 2.6 % | <gadget id="calculator">12 - 5</gadget>
<output>7</output>
<gadget id="calculator">12 * 5</gadget>
<output>60</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">7 - (3/5)</gadget>
<output>32/5 = around 6.4</output>
<result>B</result> | B | 6.4 | In measuring the sides of a rectangle, one side is taken 12% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements. | {
"A": "3.5 %",
"B": "6.4 %",
"C": "3 %",
"D": "5 %",
"E": "2.6 %"
} | subtract(subtract(12, 5), divide(multiply(12, 5), const_100)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,const_100)|subtract(#1,#2)| | "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 112 * 95 = 10,640 , which is 6.4 % greater than the actual area . answer : b ." | geometry |
math_qa__6QT7W4io3MTOuXq9 | In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 7720 votes were polled, then how many valid votes did B get? Choose the correct answer
A) 1888 B) 2999 C) 2834 D) 2509 E) 2991 | <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">(4/5) * 7_720</gadget>
<output>6_176</output>
<gadget id="calculator">15 * 7_720</gadget>
<output>115_800</output>
<gadget id="calculator">115_800 / 100</gadget>
<output>1_158</output>
<gadget id="calculator">6_176 - 1_158</gadget>
<output>5_018</output>
<gadget id="calculator">5_018 / 2</gadget>
<output>2_509</output>
<result>D</result> | D | 2,509 | In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 7720 votes were polled, then how many valid votes did B get? | {
"A": "1888",
"B": "2999",
"C": "2834",
"D": "2509",
"E": "2991"
} | divide(subtract(multiply(subtract(const_1, divide(20, const_100)), 7720), divide(multiply(15, 7720), const_100)), const_2) | divide(n1,const_100)|multiply(n0,n2)|divide(#1,const_100)|subtract(const_1,#0)|multiply(n2,#3)|subtract(#4,#2)|divide(#5,const_2) | let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 7720 32.5 k = 32.5 k / 100 k * 7720 = 2509 the number of valid votes polled in favour of b is 2834 . answer : d | general |
math_qa__R0b7IfBS7Fi8Z7DT | 3 candidates in an election and received 3000, 5000 and 15000 votes respectively. What % of the total votes did the winningcandidate got in that election? Select the correct option:
A) 65.21 % B) 50.16 % C) 57 % D) 60 % E) 65.24 % | <gadget id="calculator">3_000 + 5_000</gadget>
<output>8_000</output>
<gadget id="calculator">8_000 + 15_000</gadget>
<output>23_000</output>
<gadget id="calculator">15_000 / 23_000</gadget>
<output>15/23 = around 0.652174</output>
<gadget id="calculator">(15/23) * 100</gadget>
<output>1_500/23 = around 65.217391</output>
<result>A</result> | A | 65.21 | 3 candidates in an election and received 3000, 5000 and 15000 votes respectively. What % of the total votes did the winningcandidate got in that election? | {
"A": "65.21 %",
"B": "50.16 %",
"C": "57 %",
"D": "60 %",
"E": "65.24 %"
} | multiply(divide(15000, add(add(3000, 5000), 15000)), const_100) | add(n1,n2)|add(n3,#0)|divide(n3,#1)|multiply(#2,const_100)| | "total number of votes polled = ( 3000 + 5000 + 15000 ) = 23000 so , required percentage = 15000 / 23000 * 100 = 65.21 % a" | gain |
math_qa__U3Gl6WSmRHw0ZwJf | Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 16 more photos than Claire. How many photos has Claire taken?
Choose the correct choice from the following.
A) 6 B) 8 C) 10 D) 12 E) 14 | <gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>B</result> | B | 8 | Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 16 more photos than Claire. How many photos has Claire taken? | {
"A": "6",
"B": "8",
"C": "10",
"D": "12",
"E": "14"
} | divide(16, subtract(3, const_1)) | subtract(n0,const_1)|divide(n1,#0)| | "l = r l = 3 c r = c + 16 3 c = c + 16 c = 8 the answer is b ." | general |
math_qa__Vnsdxdy86binCUqP | In the fifth grade at Parkway elementary school there are 420 students. 296 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer? Choose the correct choice:
A) 69 . B) 73 . C) 81 D) 91 E) 89 | <gadget id="calculator">420 - 296</gadget>
<output>124</output>
<gadget id="calculator">250 * 86</gadget>
<output>21_500</output>
<gadget id="calculator">21_500 / 100</gadget>
<output>215</output>
<gadget id="calculator">250 - 215</gadget>
<output>35</output>
<gadget id="calculator">124 - 35</gadget>
<output>89</output>
<result>E</result> | E | 89 | In the fifth grade at Parkway elementary school there are 420 students. 296 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer? | {
"A": "69 .",
"B": "73 .",
"C": "81",
"D": "91",
"E": "89"
} | subtract(subtract(420, 296), subtract(250, divide(multiply(250, 86), const_100))) | multiply(n2,n3)|subtract(n0,n1)|divide(#0,const_100)|subtract(n2,#2)|subtract(#1,#3)| | "total students = 420 boys = 296 , girls = 124 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 124 - 35 = 89 . correct option : e" | gain |
math_qa__FxhVFQ8gdCTDtmlx | The percentage increase in the area of a rectangle, if each of its sides is increased by 20%
Choose one.
A) 33 B) 37 C) 44 D) 99 E) 277 | <gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * (6/5)</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>
<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>C</result> | C | 44 | The percentage increase in the area of a rectangle, if each of its sides is increased by 20% | {
"A": "33",
"B": "37",
"C": "44",
"D": "99",
"E": "277"
} | multiply(subtract(multiply(divide(add(const_100, 20), const_100), divide(add(const_100, 20), const_100)), const_1), const_100) | add(n0,const_100)|divide(#0,const_100)|multiply(#1,#1)|subtract(#2,const_1)|multiply(#3,const_100)| | "explanation : let original length = x metres and original breadth = y metres . original area = xy increased length = and increased breadth = new area = the difference between the original area and new area is : increase % = = 44 % ] answer : c ) 44 %" | geometry |
math_qa__T66qDuYdY7SshHMn | A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 69 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 Pick one:
A) 2000 B) 2100 C) 2200 D) 2300 E) 2400 | <gadget id="calculator">69 / 3</gadget>
<output>23</output>
<gadget id="calculator">23 * 100</gadget>
<output>2_300</output>
<result>D</result> | D | 2,300 | A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 69 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480 | {
"A": "2000",
"B": "2100",
"C": "2200",
"D": "2300",
"E": "2400"
} | multiply(divide(69, 3), const_100) | divide(n2,n0)|multiply(#0,const_100)| | "1 percent for 3 years = 69 1 percent for 1 year = 23 = > 100 percent = 2300 answer : d" | gain |
math_qa__4NtdeDoGmhDCk6dW | A train 200 m long running at 54 kmph crosses a platform in 25 sec. What is the length of the platform? Pick:
A) 175
B) 266
C) 350
D) 277
E) 232 | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">54 * (5/18)</gadget>
<output>15</output>
<gadget id="calculator">25 * 15</gadget>
<output>375</output>
<gadget id="calculator">375 - 200</gadget>
<output>175</output>
<result>A</result> | A | 175 | A train 200 m long running at 54 kmph crosses a platform in 25 sec. What is the length of the platform? | {
"A": "175",
"B": "266",
"C": "350",
"D": "277",
"E": "232"
} | subtract(multiply(25, multiply(54, const_0_2778)), 200) | multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0) | length of the platform = 54 * 5 / 18 * 25 = 375 β 200 = 175 answer : a | physics |
math_qa__uyjlppd5vSMVJVPh | A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5.4 hours, then the distance covered at 40 kmph is
Choose the correct choice from the following.
A) 130 km B) 120 km C) 100 km D) 140 km E) 148 | <gadget id="calculator">60 * 5.4</gadget>
<output>324</output>
<gadget id="calculator">324 - 250</gadget>
<output>74</output>
<gadget id="calculator">40 - 60</gadget>
<output>-20</output>
<gadget id="calculator">-(-20)</gadget>
<output>20</output>
<gadget id="calculator">74 / 20</gadget>
<output>37/10 = around 3.7</output>
<gadget id="calculator">(37/10) * 40</gadget>
<output>148</output>
<result>E</result> | E | 148 | A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5.4 hours, then the distance covered at 40 kmph is | {
"A": "130 km",
"B": "120 km",
"C": "100 km",
"D": "140 km",
"E": "148"
} | multiply(divide(subtract(multiply(60, 5.4), 250), negate(subtract(40, 60))), 40) | multiply(n2,n3)|subtract(n1,n2)|negate(#1)|subtract(#0,n0)|divide(#3,#2)|multiply(n1,#4) | let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 5.4 or , x / 40 + ( 250 - x ) / 60 = 5.4 or , ( 3 x + 500 - 2 x ) / / 120 = 5.4 or 500 + x = 648 x = 148 answer : e | physics |
math_qa__d4j2VxK0fUMET9bH | The population of a bacteria colony doubles every day. If it was started 11 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? Choose one:
A) 512 B) 768 C) 1024 D) 2048 E) 4096 | <gadget id="calculator">11 + 1</gadget>
<output>12</output>
<gadget id="calculator">2 ** 12</gadget>
<output>4_096</output>
<gadget id="calculator">4_096 - 1</gadget>
<output>4_095</output>
<result>E</result> | E | 4,096 | The population of a bacteria colony doubles every day. If it was started 11 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? | {
"A": "512",
"B": "768",
"C": "1024",
"D": "2048",
"E": "4096"
} | subtract(power(2, add(11, const_1)), const_1) | add(n0,const_1)|power(n1,#0)|subtract(#1,const_1)| | "2 ^ 11 ( 2 ) = 2 ^ 12 = 4096 the answer is e ." | physics |
math_qa__b6x7p0U6TJ3whBBI | The unit digit in the product 7858*1086*4582*9783 is? Choices:
A) 0 B) 1 C) 8 D) 3 E) 4 | <gadget id="calculator">7_858 * 1_086</gadget>
<output>8_533_788</output>
<gadget id="calculator">8_533_788 * 4_582</gadget>
<output>39_101_816_616</output>
<gadget id="calculator">39_101_816_616 * 9_783</gadget>
<output>382_533_071_954_328</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">382_533_071_954_328 - 8</gadget>
<output>382_533_071_954_320</output>
<gadget id="calculator">382_533_071_954_328 - 382_533_071_954_320</gadget>
<output>8</output>
<result>C</result> | C | 8 | The unit digit in the product 7858*1086*4582*9783 is? | {
"A": "0",
"B": "1",
"C": "8",
"D": "3",
"E": "4"
} | subtract(multiply(multiply(multiply(7858, 1086), 4582), 9783), subtract(multiply(multiply(multiply(7858, 1086), 4582), 9783), add(const_4, const_4))) | add(const_4,const_4)|multiply(n0,n1)|multiply(n2,#1)|multiply(n3,#2)|subtract(#3,#0)|subtract(#3,#4)| | "unit digit in the given product = unit digit in 8 * 6 * 2 * 3 = 8 answer is c" | general |
math_qa__JHlHxOlTU63x8krQ | A train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds. Its length is : Options:
A) 200 m
B) 400 m
C) 500 m
D) 700 m
E) none of the above | <gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">500 * 1</gadget>
<output>500</output>
<result>C</result> | C | 500 | A train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds. Its length is : | {
"A": "200 m",
"B": "400 m",
"C": "500 m",
"D": "700 m",
"E": "none of the above"
} | multiply(500, subtract(const_2, const_1)) | subtract(const_2,const_1)|multiply(n1,#0)| | sol . let the length of the train be x metres and its speed be y m / sec . then , x / y = 20 β y = x / 20 β΄ ( x + 500 ) / 40 = x / 20 β x = 500 m . answer c | physics |
math_qa__zo0vsCmu3VN9Ef0u | Yesterday's closing prices of 1,980 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday? Select
A) 484
B) 1080
C) 1,100
D) 1,320
E) 1,694 | <gadget id="calculator">20 * 100</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 - 10</gadget>
<output>1_990</output>
<gadget id="calculator">1_990 - 10</gadget>
<output>1_980</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) + 1</gadget>
<output>11/5 = around 2.2</output>
<gadget id="calculator">1_980 / (11/5)</gadget>
<output>900</output>
<gadget id="calculator">900 * (6/5)</gadget>
<output>1_080</output>
<result>B</result> | B | 1,080 | Yesterday's closing prices of 1,980 different stocks listed on a certain stock exchange were all different from today's closing prices. The number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price. How many of the stocks closed at a higher price today than yesterday? | {
"A": "484",
"B": "1080",
"C": "1,100",
"D": "1,320",
"E": "1,694"
} | multiply(divide(subtract(subtract(multiply(20, const_100), const_10), const_10), add(add(const_1, divide(20, const_100)), const_1)), add(const_1, divide(20, const_100))) | divide(n1,const_100)|multiply(n1,const_100)|add(#0,const_1)|subtract(#1,const_10)|add(#2,const_1)|subtract(#3,const_10)|divide(#5,#4)|multiply(#2,#6) | lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1980 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1080 . b is my answer . | gain |
math_qa__XMFSIzNjUGbhuk03 | 20 - 8 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ? Choose the correct choice from the following answers: A) 15 % B) 20 % C) 25 % D) 54 % E) 75 % | <gadget id="calculator">20 + 8</gadget>
<output>28</output>
<gadget id="calculator">100 - 28</gadget>
<output>72</output>
<gadget id="calculator">20 + 5</gadget>
<output>25</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">72 * (3/4)</gadget>
<output>54</output>
<result>D</result> | D | 54 | 20 - 8 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ? | {
"A": "15 %",
"B": "20 %",
"C": "25 %",
"D": "54 %",
"E": "75 %"
} | multiply(subtract(const_100, add(20, 8)), divide(subtract(const_100, add(20, 5)), const_100)) | add(n0,n4)|add(n0,n1)|subtract(const_100,#0)|subtract(const_100,#1)|divide(#2,const_100)|multiply(#4,#3) | initially 72 % and 28 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) β 72 so , the required % is [ ( 3 / 4 ) β 72 / 100 ] β 100 = 54 % answer : d | general |
math_qa__cD7F22r8UlIDIyQY | A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 3300 in all from both of them as interest. The rate of interest per annum is? Select the correct option.
A) 16 % B) 12 % C) 74 % D) 10 % E) 15 % | <gadget id="calculator">5_000 * 2</gadget>
<output>10_000</output>
<gadget id="calculator">3_000 * 4</gadget>
<output>12_000</output>
<gadget id="calculator">10_000 + 12_000</gadget>
<output>22_000</output>
<gadget id="calculator">3_300 / 22_000</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 100</gadget>
<output>15</output>
<result>E</result> | E | 15 | A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 3300 in all from both of them as interest. The rate of interest per annum is? | {
"A": "16 %",
"B": "12 %",
"C": "74 %",
"D": "10 %",
"E": "15 %"
} | multiply(divide(3300, add(multiply(5000, 2), multiply(3000, 4))), const_100) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|divide(n4,#2)|multiply(#3,const_100)| | "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 3300 100 r + 120 r = 3300 r = 15 % answer : e" | gain |
math_qa__mmStRO6TM8XSbLXw | In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs? Pick one:
A) 6.25 B) 7.25 C) 7.75 D) 7.35 E) 8.25 | <gadget id="calculator">10 * 3.2</gadget>
<output>32</output>
<gadget id="calculator">282 - 32</gadget>
<output>250</output>
<gadget id="calculator">250 / 40</gadget>
<output>25/4 = around 6.25</output>
<result>A</result> | A | 6.25 | In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs? | {
"A": "6.25",
"B": "7.25",
"C": "7.75",
"D": "7.35",
"E": "8.25"
} | divide(subtract(282, multiply(10, 3.2)), 40) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | "runs scored in the first 10 overs = 10 Γ 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 40 run rate needed = 25040 = 6.25 answer : a" | gain |
math_qa__ClO3geLT3x2L93Pp | What is the unitβs digit of 7^6 Choose one.
A) 1 B) 3 C) 5 D) 7 E) 9 | <gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">49 % 10</gadget>
<output>9</output>
<result>E</result> | E | 9 | What is the unitβs digit of 7^6 | {
"A": "1",
"B": "3",
"C": "5",
"D": "7",
"E": "9"
} | reminder(power(7, const_2), const_10) | power(n0,const_2)|reminder(#0,const_10)| | "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 7 ^ 6 = 9 answer e" | general |
math_qa__FViOSLQiZ5J1SdU8 | A can finish a work in 4 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day? Choose the most appropriate option.
A) 1 / 4 B) 1 / 6 C) 1 / 7 D) 3 / 4 E) none of these | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>
<result>D</result> | D | 0.75 | A can finish a work in 4 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day? | {
"A": "1 / 4",
"B": "1 / 6",
"C": "1 / 7",
"D": "3 / 4",
"E": "none of these"
} | add(divide(const_1, 4), multiply(divide(const_1, 4), const_2)) | divide(const_1,n0)|multiply(#0,const_2)|add(#0,#1) | explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 4 b ' s 1 day work = 1 / 2 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 4 + 1 / 2 ) = 3 / 4 so in one day 3 / 4 work will be done answer : d | physics |
math_qa__PgNF4T7bqFIidmmh | A rectangular lawn of dimensions 100 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m? Choose the correct choice: A) 3820 B) 930 C) 9309 D) 4500 E) 8302 | <gadget id="calculator">100 + 60</gadget>
<output>160</output>
<gadget id="calculator">160 - 10</gadget>
<output>150</output>
<gadget id="calculator">150 * 10</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 * 3</gadget>
<output>4_500</output>
<result>D</result> | D | 4,500 | A rectangular lawn of dimensions 100 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m? | {
"A": "3820",
"B": "930",
"C": "9309",
"D": "4500",
"E": "8302"
} | multiply(multiply(subtract(add(100, 60), 10), 10), 3) | add(n0,n1)|subtract(#0,n2)|multiply(n2,#1)|multiply(n3,#2)| | "explanation : area = ( l + b β d ) d ( 100 + 60 β 10 ) 10 = > 1500 m 2 1500 * 3 = rs . 4500 answer : option d" | geometry |
math_qa__mayDi8bxZKvfDm2V | Find avrg speed if a man travels at speed of 18km/hr up and 24km/hr dawn at an altitude of 300m. Answers
A) 25.8 B) 26.8 C) 27.8 D) 20.5 E) 21.8 | <gadget id="calculator">2 * 18</gadget>
<output>36</output>
<gadget id="calculator">36 * 24</gadget>
<output>864</output>
<gadget id="calculator">18 + 24</gadget>
<output>42</output>
<gadget id="calculator">864 / 42</gadget>
<output>144/7 = around 20.571429</output>
<result>D</result> | D | 20.5 | Find avrg speed if a man travels at speed of 18km/hr up and 24km/hr dawn at an altitude of 300m. | {
"A": "25.8",
"B": "26.8",
"C": "27.8",
"D": "20.5",
"E": "21.8"
} | divide(multiply(multiply(const_2, 18), 24), add(18, 24)) | add(n0,n1)|multiply(n0,const_2)|multiply(n1,#1)|divide(#2,#0)| | "avg speed = 2 * x * y / ( x + y ) = 2 * 18 * 24 / ( 18 + 24 ) = 20.5 answer : d" | physics |
math_qa__dIhYowcGwXf0ZNTb | Nitin ranks 27th in a class of 89 students. What is rank from the last ? Pick one
A) 63 B) 65 C) 67 D) 87 E) 89 | <gadget id="calculator">89 - 27</gadget>
<output>62</output>
<result>A</result> | A | 63 | Nitin ranks 27th in a class of 89 students. What is rank from the last ? | {
"A": "63",
"B": "65",
"C": "67",
"D": "87",
"E": "89"
} | subtract(89, 27) | subtract(n1,n0)| | "explanation : number students behind the nitin in rank = ( 89 - 27 ) = 62 nitin is 63 th from the last answer : a ) 63" | other |
math_qa__YkuNCyx1JAoPMaHe | The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 424 different signs. If the company used 422 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 424 signs? Choices
A) 246 B) 248 C) 1692 D) 15,128 E) 30,256 | <gadget id="calculator">424 - 422</gadget>
<output>2</output>
<gadget id="calculator">422 * 2</gadget>
<output>844</output>
<gadget id="calculator">844 * 2</gadget>
<output>1_688</output>
<result>C</result> | C | 1,692 | The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 424 different signs. If the company used 422 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 424 signs? | {
"A": "246",
"B": "248",
"C": "1692",
"D": "15,128",
"E": "30,256"
} | multiply(multiply(422, subtract(424, 422)), subtract(424, 422)) | subtract(n1,n2)|multiply(n2,#0)|multiply(#1,#0)| | "# of 2 - letter codes possible from 424 different signs = 424 * 424 . # of 2 - letter codes possible from 422 different signs = 422 * 422 . the difference = 424 ^ 2 - 422 ^ 2 = ( 424 - 422 ) ( 424 + 422 ) = 1692 . answer : c ." | general |
math_qa__Qpdfy8EbzhgjeeCR | Thin rectangular slab of potato was cut into two pieces for an osmosis lab. One piece is 50mm greater than the other. If the original uncut slab is 600mm, what is the length of the other piece of the potato after it is cut. Options:
A) 550 B) 275 C) 50 D) 300 E) 250 | <gadget id="calculator">600 - 50</gadget>
<output>550</output>
<gadget id="calculator">550 / 2</gadget>
<output>275</output>
<result>B</result> | B | 275 | Thin rectangular slab of potato was cut into two pieces for an osmosis lab. One piece is 50mm greater than the other. If the original uncut slab is 600mm, what is the length of the other piece of the potato after it is cut. | {
"A": "550",
"B": "275",
"C": "50",
"D": "300",
"E": "250"
} | divide(subtract(600, 50), const_2) | subtract(n1,n0)|divide(#0,const_2) | piece one as p 1 , and piece two as p 2 . p 2 + 50 = p 1 as eq . a p 1 + p 2 = 600 as eq . b substitute eq . a into eq . b , resulting in ( p 2 + 50 ) + p 2 = 600 mm . group like terms , p 2 + p 2 = 600 - 50 ( 2 * p 2 / 2 ) = 550 / 2 solves to p 2 = 275 . ansewr is b . | geometry |
math_qa__7MDJxkH5IJ2Ifl8e | A alone can complete a work in 16 days and B alone can do in 12 days. StarΖng with A, they work on
alternate days. The total work will be completed in Choose the correct choice from the following:
A) 1314
B) 1312
C) 1334
D) 1344
E) none of these | <gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">(1/12) + (1/16)</gadget>
<output>7/48 = around 0.145833</output>
<gadget id="calculator">1 / (7/48)</gadget>
<output>48/7 = around 6.857143</output>
<gadget id="calculator">(48/7) * 2</gadget>
<output>96/7 = around 13.714286</output>
<gadget id="calculator">100 * (96/7)</gadget>
<output>9_600/7 = around 1_371.428571</output>
<result>C</result> | C | 1,334 | A alone can complete a work in 16 days and B alone can do in 12 days. StarΖng with A, they work on
alternate days. The total work will be completed in | {
"A": "1314",
"B": "1312",
"C": "1334",
"D": "1344",
"E": "none of these"
} | multiply(const_100, multiply(inverse(add(inverse(12), inverse(16))), const_2)) | inverse(n1)|inverse(n0)|add(#0,#1)|inverse(#2)|multiply(#3,const_2)|multiply(#4,const_100) | explana Ι΅ on : a ' s 1 day work = 1 / 16 b ' s 1 day work = 1 / 12 as they are working on alternate day ' s so their 2 days work = ( 1 / 16 ) + ( 1 / 12 ) = 7 / 48 [ here is a small technique , total work done will be 1 , right , then mul Ι΅ ply numerator Ι΅ ll denominator , as 7 * 6 = 42 , 7 * 7 = 49 , as 7 * 7 is more than 48 , so we will consider 7 * 6 , means 6 pairs ] work done in 6 pairs = 6 * ( 7 / 48 ) = 7 / 8 remaining work = 1 - 7 / 8 = 1 / 8 on 13 th day it will a turn , then remaining work = ( 1 / 8 ) - ( 1 / 16 ) = 1 / 16 on 14 th day it is b turn , 1 / 12 work done by b in 1 day 1 / 16 work will be done in ( 12 * 1 / 16 ) = 3 / 4 day so total days = 1334 answer : c | physics |
math_qa__xq2SDqnhtd9nlKV1 | A cistern which could be filled in 6 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
Choose the correct choice from the following answers: A) 76 hrs B) 99 hrs C) 15 hrs D) 90 hrs E) 11 hrs | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/6) - (1/10)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / (1/15)</gadget>
<output>15</output>
<result>C</result> | C | 15 | A cistern which could be filled in 6 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it? | {
"A": "76 hrs",
"B": "99 hrs",
"C": "15 hrs",
"D": "90 hrs",
"E": "11 hrs"
} | inverse(subtract(divide(const_1, 6), divide(const_1, const_10))) | divide(const_1,n0)|divide(const_1,const_10)|subtract(#0,#1)|inverse(#2)| | "1 / 6 - 1 / x = 1 / 10 = > 15 hrs answer : c" | physics |
math_qa__8UbKl3mY93XGZlQH | On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 28 miles on Saturday and Sunday, how many miles did Bill run on Sunday? Choose the correct option:
A) 5 B) 6 C) 7 D) 8 E) 9 | <gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">4 + 8</gadget>
<output>12</output>
<gadget id="calculator">28 - 12</gadget>
<output>16</output>
<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<result>D</result> | D | 8 | On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 28 miles on Saturday and Sunday, how many miles did Bill run on Sunday? | {
"A": "5",
"B": "6",
"C": "7",
"D": "8",
"E": "9"
} | add(divide(subtract(28, add(4, multiply(const_2, 4))), 4), 4) | multiply(n0,const_2)|add(n0,#0)|subtract(n1,#1)|divide(#2,n0)|add(n0,#3)| | "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 28 . . 4 x + 12 = 28 . . x = 4 . . ans = x + 4 = 4 + 4 = 8 aswer d" | general |
math_qa__SLZ8rkmMc50BQSeF | Bhanu spends 30% of his income on petrol on scooter 14% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent?
Choose one:
A) 98 B) 140 C) 62 D) 797 E) 123 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">300 / (3/10)</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 300</gadget>
<output>700</output>
<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">700 * (7/50)</gadget>
<output>98</output>
<result>A</result> | A | 98 | Bhanu spends 30% of his income on petrol on scooter 14% of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on house rent? | {
"A": "98",
"B": "140",
"C": "62",
"D": "797",
"E": "123"
} | multiply(subtract(divide(300, divide(30, const_100)), 300), divide(14, const_100)) | divide(n1,const_100)|divide(n0,const_100)|divide(n2,#1)|subtract(#2,n2)|multiply(#0,#3)| | "given 30 % ( income ) = 300 β β income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 14 % ( 700 ) = rs . 98 answer : a" | gain |
math_qa__XRzDOMI8y5vXyklR | A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the distance in km? Choose the correct choice
A) 36
B) 38
C) 40
D) 42
E) 45 | <gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">2 * (2/3)</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">3 * (2/3)</gadget>
<output>2</output>
<gadget id="calculator">(4/3) + 2</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">(10/3) / 1</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">2 * (10/3)</gadget>
<output>20/3 = around 6.666667</output>
<gadget id="calculator">(20/3) + (4/3)</gadget>
<output>8</output>
<gadget id="calculator">8 / (2/3)</gadget>
<output>12</output>
<gadget id="calculator">12 * (10/3)</gadget>
<output>40</output>
<result>C</result> | C | 40 | A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the distance in km? | {
"A": "36",
"B": "38",
"C": "40",
"D": "42",
"E": "45"
} | multiply(divide(add(multiply(2, divide(add(multiply(2, divide(40, const_60)), multiply(3, divide(40, const_60))), subtract(3, 2))), multiply(2, divide(40, const_60))), divide(40, const_60)), divide(add(multiply(2, divide(40, const_60)), multiply(3, divide(40, const_60))), subtract(3, 2))) | divide(n1,const_60)|subtract(n0,n2)|multiply(n2,#0)|multiply(n0,#0)|add(#2,#3)|divide(#4,#1)|multiply(n2,#5)|add(#6,#2)|divide(#7,#0)|multiply(#8,#5) | explanation : speed = 2 v 1 v 2 / v 1 β v 2 = 2 Γ 3 Γ 23 β 2 = 12 km / h = hr distance = vt 1 ( 1 + v / v 1 ) = 12 Γ 40 / 60 ( 1 + 12 / 3 ) = 40 km answer is c | physics |
math_qa__1EcAycaA0NbNjVuG | A student got 72% in math and 84% in history. To get an overall average of 75%, how much should the student get in the third subject? Choices
A) 65 % B) 67 % C) 69 % D) 71 % E) 73 % | <gadget id="calculator">3 * 75</gadget>
<output>225</output>
<gadget id="calculator">72 + 84</gadget>
<output>156</output>
<gadget id="calculator">225 - 156</gadget>
<output>69</output>
<result>C</result> | C | 69 | A student got 72% in math and 84% in history. To get an overall average of 75%, how much should the student get in the third subject? | {
"A": "65 %",
"B": "67 %",
"C": "69 %",
"D": "71 %",
"E": "73 %"
} | subtract(multiply(const_3, 75), add(72, 84)) | add(n0,n1)|multiply(n2,const_3)|subtract(#1,#0)| | "72 + 84 + x = 3 * 75 x = 69 the answer is c ." | general |
math_qa__z8zeEvkezBoW9T9s | What is the sum R of all 3 digit numbers that leave a remainder of '2' when divided by 3?
Choose the correct choice:
A) 897
B) 164850
C) 164749
D) 149700
E) 156720 | <gadget id="calculator">10 ** 3</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 / 10</gadget>
<output>100</output>
<gadget id="calculator">100 - 2</gadget>
<output>98</output>
<gadget id="calculator">98 / 3</gadget>
<output>98/3 = around 32.666667</output>
<gadget id="calculator">floor(98/3)</gadget>
<output>32</output>
<gadget id="calculator">32 + 1</gadget>
<output>33</output>
<gadget id="calculator">33 * 3</gadget>
<output>99</output>
<gadget id="calculator">99 + 2</gadget>
<output>101</output>
<gadget id="calculator">1_000 - 101</gadget>
<output>899</output>
<gadget id="calculator">899 / 3</gadget>
<output>899/3 = around 299.666667</output>
<gadget id="calculator">floor(899/3)</gadget>
<output>299</output>
<gadget id="calculator">299 * 3</gadget>
<output>897</output>
<gadget id="calculator">897 + 101</gadget>
<output>998</output>
<gadget id="calculator">101 + 998</gadget>
<output>1_099</output>
<gadget id="calculator">1_099 * 299</gadget>
<output>328_601</output>
<gadget id="calculator">328_601 / 2</gadget>
<output>328_601/2 = around 164_300.5</output>
<result>B</result> | B | 164,850 | What is the sum R of all 3 digit numbers that leave a remainder of '2' when divided by 3? | {
"A": "897",
"B": "164850",
"C": "164749",
"D": "149700",
"E": "156720"
} | divide(multiply(add(add(multiply(add(floor(divide(subtract(divide(power(const_10, 3), const_10), 2), 3)), const_1), 3), 2), add(multiply(floor(divide(subtract(power(const_10, 3), add(multiply(add(floor(divide(subtract(divide(power(const_10, 3), const_10), 2), 3)), const_1), 3), 2)), 3)), 3), add(multiply(add(floor(divide(subtract(divide(power(const_10, 3), const_10), 2), 3)), const_1), 3), 2))), floor(divide(subtract(power(const_10, 3), add(multiply(add(floor(divide(subtract(divide(power(const_10, 3), const_10), 2), 3)), const_1), 3), 2)), 3))), const_2) | power(const_10,n0)|divide(#0,const_10)|subtract(#1,n1)|divide(#2,n0)|floor(#3)|add(#4,const_1)|multiply(n0,#5)|add(n1,#6)|subtract(#0,#7)|divide(#8,n0)|floor(#9)|multiply(n0,#10)|add(#7,#11)|add(#7,#12)|multiply(#13,#10)|divide(#14,const_2) | the series is = > 101 + . . . 998 number of terms = > 300 sum = > 300 / 2 * [ 101 + 998 ] hence sum r = > 164850 i . e . option b | general |
math_qa__KhcvdxqJXSsYM115 | Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs.12 per square metre.
Answers:
A) 1824 B) 1854 C) 1872 D) 1888 E) 1999 | <gadget id="calculator">13 * 12</gadget>
<output>156</output>
<gadget id="calculator">156 * 12</gadget>
<output>1_872</output>
<result>C</result> | C | 1,872 | Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of Rs.12 per square metre. | {
"A": "1824",
"B": "1854",
"C": "1872",
"D": "1888",
"E": "1999"
} | multiply(multiply(13, 12), 12) | multiply(n0,n3)|multiply(n3,#0) | explanation : area of the carpet = area of the room = ( 13 Γ 9 ) m 2 = 117 m 2 . length of the carpet = ( area / width ) = 117 Γ ( 4 / 3 ) m = 156 m . therefore cost of carpeting = ( 156 Γ 12 ) = rs . 1872 answer : option c | physics |
math_qa__6nSEMVZpKks76jh2 | Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 25-ounce cans or 15-ounce cans of chili paste. If the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs, then how many larger cans are required to fulfill its weekly needs? Choose the most appropriate option
A) 60 B) 70 C) 80 D) 100 E) 45 | <gadget id="calculator">15 + 30</gadget>
<output>45</output>
<result>E</result> | E | 45 | Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 25-ounce cans or 15-ounce cans of chili paste. If the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs, then how many larger cans are required to fulfill its weekly needs? | {
"A": "60",
"B": "70",
"C": "80",
"D": "100",
"E": "45"
} | add(15, 30) | add(n1,n2) | let x be the number of 25 ounce cans . therefore ( x + 30 ) is the number of 15 ounce cans . total volume is same , therefore 25 x = 15 ( x + 30 ) 10 x = 450 x = 45 ans - e | general |
math_qa__bo8jRc9VYIm1foS3 | Express a speed of 54 kmph in meters per second? Choose the correct choice:
A) 10 mps B) 76 mps C) 15 mps D) 97 mps E) 16 mps | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 54</gadget>
<output>15</output>
<result>C</result> | C | 15 | Express a speed of 54 kmph in meters per second? | {
"A": "10 mps",
"B": "76 mps",
"C": "15 mps",
"D": "97 mps",
"E": "16 mps"
} | multiply(const_0_2778, 54) | multiply(n0,const_0_2778)| | "54 * 5 / 18 = 15 mps answer : c" | physics |
math_qa__zC4UnlT8n3OlWzaI | The cash difference between the selling prices of an article at a profit of 8% and 6% is Rs 3. The ratio of two selling prices is Choose the correct option:
A) 51 : 52 B) 52 : 53 C) 53 : 54 D) 54 : 53 E) none of these | <gadget id="calculator">100 + 8</gadget>
<output>108</output>
<gadget id="calculator">100 + 6</gadget>
<output>106</output>
<gadget id="calculator">108 / 106</gadget>
<output>54/53 = around 1.018868</output>
<result>D</result> | D | 1.018868 | The cash difference between the selling prices of an article at a profit of 8% and 6% is Rs 3. The ratio of two selling prices is | {
"A": "51 : 52",
"B": "52 : 53",
"C": "53 : 54",
"D": "54 : 53",
"E": "none of these"
} | divide(add(const_100, 8), add(const_100, 6)) | add(n0,const_100)|add(n1,const_100)|divide(#0,#1)| | "explanation : let the cost price of article is rs . x required ratio = ( 108 % of x ) / ( 106 % of x ) = 108 / 106 = 54 / 53 = 54 : 53 . answer : d" | gain |
math_qa__gwe4fdrcSNSzWTLE | The tax on a commodity is diminished by 16% and its consumption increased by 15%. The effect on revenue is? Select
A) 2 % B) 3.8 % C) 3.4 % D) 3.6 % E) 1 % | <gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">1 - (4/25)</gadget>
<output>21/25 = around 0.84</output>
<gadget id="calculator">(23/20) * (21/25)</gadget>
<output>483/500 = around 0.966</output>
<gadget id="calculator">(483/500) * 100</gadget>
<output>483/5 = around 96.6</output>
<gadget id="calculator">100 - (483/5)</gadget>
<output>17/5 = around 3.4</output>
<result>C</result> | C | 3.4 | The tax on a commodity is diminished by 16% and its consumption increased by 15%. The effect on revenue is? | {
"A": "2 %",
"B": "3.8 %",
"C": "3.4 %",
"D": "3.6 %",
"E": "1 %"
} | subtract(const_100, multiply(multiply(add(const_1, divide(15, const_100)), subtract(const_1, divide(16, const_100))), const_100)) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5) | 100 * 100 = 10000 84 * 115 = 9660 - - - - - - - - - - - 10000 - - - - - - - - - - - 340 100 - - - - - - - - - - - ? = > 3.4 % decrease answer : c | general |
math_qa__FhTfZaTpkpa9N5qf | The maximum number of student amoung them 2010 pens and 1050 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : Choose the correct choice from the following options:
A) 90
B) 60
C) 30
D) 1911
E) none of these | <gadget id="calculator">gcd(2_010, 1_050)</gadget>
<output>30</output>
<result>C</result> | C | 30 | The maximum number of student amoung them 2010 pens and 1050 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : | {
"A": "90",
"B": "60",
"C": "30",
"D": "1911",
"E": "none of these"
} | gcd(2010, 1050) | gcd(n0,n1)| | "solution required number of student = h . c . f of 2010 and 1050 = 30 . answer c" | general |
math_qa__GepirIUMSWyF8FIm | two quarts containing 2 β 3 water and 1 β 3 formula are mixed with 3 quarts containing 3 β 8 water and 5 β 8 formula . approximately what percent of the combined 5 - quart mixture is water ? Answers.
A) 40 % B) 45 % C) 50 % D) 55 % E) 60 % | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 2</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">3 / 8</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/8) * 3</gadget>
<output>9/8 = around 1.125</output>
<gadget id="calculator">(4/3) + (9/8)</gadget>
<output>59/24 = around 2.458333</output>
<gadget id="calculator">(59/24) / 5</gadget>
<output>59/120 = around 0.491667</output>
<gadget id="calculator">(59/120) * 100</gadget>
<output>295/6 = around 49.166667</output>
<result>C</result> | C | 50 | two quarts containing 2 β 3 water and 1 β 3 formula are mixed with 3 quarts containing 3 β 8 water and 5 β 8 formula . approximately what percent of the combined 5 - quart mixture is water ? | {
"A": "40 %",
"B": "45 %",
"C": "50 %",
"D": "55 %",
"E": "60 %"
} | multiply(divide(add(multiply(divide(2, 3), 2), multiply(divide(3, 8), 3)), 5), const_100) | divide(n0,n1)|divide(n1,n6)|multiply(n0,#0)|multiply(n1,#1)|add(#2,#3)|divide(#4,n7)|multiply(#5,const_100) | since we are asking of water in the end , lets concentrate on water only . . a solution has 2 quarts with fraction of water = 2 / 3 , almost 67 % . . b solution has 3 quarts with fraction of water = 3 / 8 almost 37 % . . so the ratio a : b = 2 : 3 . . . the average will therefore be closer to b % and will be 2 / ( 2 + 3 ) of { 67 - 37 } away from b . . 2 / ( 2 + 3 ) of { 67 - 37 } = 2 / 5 * 30 = 12 . . so 37 + 12 = 49 nearly 50 % answer : c | general |
math_qa__eXqQFx0Hkym9cEBl | A cricketer scored 134 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
Choose the correct choice from the following answers
A) 55.22 % B) 54.54 % C) 63 % D) 70 % E) none of these | <gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">48 + 12</gadget>
<output>60</output>
<gadget id="calculator">134 - 60</gadget>
<output>74</output>
<gadget id="calculator">74 / 134</gadget>
<output>37/67 = around 0.552239</output>
<gadget id="calculator">(37/67) * 100</gadget>
<output>3_700/67 = around 55.223881</output>
<result>A</result> | A | 55.22 | A cricketer scored 134 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets. | {
"A": "55.22 %",
"B": "54.54 %",
"C": "63 %",
"D": "70 %",
"E": "none of these"
} | multiply(divide(subtract(134, add(multiply(12, const_4), multiply(2, multiply(2, const_3)))), 134), const_100) | multiply(n1,const_4)|multiply(n2,const_3)|multiply(n2,#1)|add(#0,#2)|subtract(n0,#3)|divide(#4,n0)|multiply(#5,const_100)| | "explanation : number of runs made by running = 134 - ( 12 x 4 + 2 x 6 ) = 134 - ( 60 ) = 74 now , we need to calculate 72 is what percent of 134 . = > 74 / 134 * 100 = 55.22 % answer : a" | general |
math_qa__CgLyU7HiduhCa0Ni | A worker makes a toy in every 2h. If he works for 80h, then how many toys will he make ?
Choose the correct choice from the following choices: A) 40 B) 54 C) 45 D) 39 E) none | <gadget id="calculator">80 / 2</gadget>
<output>40</output>
<result>A</result> | A | 40 | A worker makes a toy in every 2h. If he works for 80h, then how many toys will he make ? | {
"A": "40",
"B": "54",
"C": "45",
"D": "39",
"E": "none"
} | divide(80, 2) | divide(n1,n0)| | "answer let number of toys be n . more hours , more toys ( direct proportion ) 2 : 80 : : 1 : n β n = 80 / 2 = 40 toys correct option : a" | physics |
math_qa__jYiRfF0bKAkmnT3q | Bhavan travelled for 20 hours. He covered the first half of the distance at 50 kmph and remaining half of the distance at 40 kmph. Find the distance travelled by Bhavan? Choose the correct choice from the following options:
A) 888.89
B) 788.89
C) 899.89
D) 688.89
E) 899.99 | <gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 50</gadget>
<output>500</output>
<gadget id="calculator">10 * 40</gadget>
<output>400</output>
<gadget id="calculator">500 + 400</gadget>
<output>900</output>
<result>A</result> | A | 888.89 | Bhavan travelled for 20 hours. He covered the first half of the distance at 50 kmph and remaining half of the distance at 40 kmph. Find the distance travelled by Bhavan? | {
"A": "888.89",
"B": "788.89",
"C": "899.89",
"D": "688.89",
"E": "899.99"
} | add(multiply(divide(20, const_2), 50), multiply(divide(20, const_2), 40)) | divide(n0,const_2)|multiply(n1,#0)|multiply(n2,#0)|add(#1,#2) | let the distance travelled be x km . total time = ( x / 2 ) / 50 + ( x / 2 ) / 40 = 20 = > x / 100 + x / 80 = 20 = > ( 4 x + 5 x ) / 400 = 20 = > x = 888.89 km answer : a | physics |
math_qa__fL1kOJ8jN1ZR94Qr | ? x 40 = 173 x 240 Answers:
A) 545 B) 685 C) 1038 D) 495 E) 534 | <gadget id="calculator">173 * 240</gadget>
<output>41_520</output>
<gadget id="calculator">41_520 / 40</gadget>
<output>1_038</output>
<result>C</result> | C | 1,038 | ? x 40 = 173 x 240 | {
"A": "545",
"B": "685",
"C": "1038",
"D": "495",
"E": "534"
} | divide(multiply(173, 240), 40) | multiply(n1,n2)|divide(#0,n0)| | "let y x 40 = 173 x 240 then y = ( 173 x 240 ) / 40 = 1038 answer : c" | general |
math_qa__fNe4LLEtprPweHrR | Rose made a part payment of $300 toward buying a brand new car, which represents 5% of the total cost of the car, how much remains to be paid? Choose the correct choice:
A) $ 5700
B) $ 5500
C) $ 5800
D) $ 5200
E) $ 5880 | <gadget id="calculator">300 * 100</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 5</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 - 300</gadget>
<output>5_700</output>
<result>A</result> | A | 5,700 | Rose made a part payment of $300 toward buying a brand new car, which represents 5% of the total cost of the car, how much remains to be paid? | {
"A": "$ 5700",
"B": "$ 5500",
"C": "$ 5800",
"D": "$ 5200",
"E": "$ 5880"
} | subtract(divide(multiply(300, const_100), 5), 300) | multiply(n0,const_100)|divide(#0,n1)|subtract(#1,n0) | explanation : let ' s start with what the total price of the car would be . if 5 % is equal to $ 300 then 100 % equals $ x . we just have to multiply $ 300 by 20 to get total amount = $ 6000 . out of this amount we then need to deduct the amount already paid which was $ 300 so we have $ 6000 - $ 300 = $ 5700 answer : option a | general |
math_qa__y9pLNBKAl2n5nnxT | A pump can fill a tank with water in 2 hours. Because of a leak, it took 2x1/3 hours to fill the tank. The leak can drain all the water of the tank in
Choices.
A) 5 hours B) 7 hours C) 8 hours D) 14 hours E) 18 hours | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">7 / 3</gadget>
<output>7/3 = around 2.333333</output>
<gadget id="calculator">1 / (7/3)</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(1/2) - (3/7)</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">1 / (1/14)</gadget>
<output>14</output>
<result>D</result> | D | 14 | A pump can fill a tank with water in 2 hours. Because of a leak, it took 2x1/3 hours to fill the tank. The leak can drain all the water of the tank in | {
"A": "5 hours",
"B": "7 hours",
"C": "8 hours",
"D": "14 hours",
"E": "18 hours"
} | inverse(subtract(divide(1, 2), inverse(divide(add(multiply(2, 3), 1), 3)))) | divide(n2,n0)|multiply(n0,n3)|add(n2,#1)|divide(#2,n3)|inverse(#3)|subtract(#0,#4)|inverse(#5)| | "work done by the leak in 1 hour = 1 / 2 - 3 / 7 = 1 / 14 . leak will empty the tank in 14 hrs . answer : d" | physics |
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