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math_qa__mOCP13e5a46xvObS | Two good train each 650 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one. Select:
A) 12.4 sec B) 24.3 sec C) 62.4 sec D) 60.1 sec E) none | <gadget id="calculator">45 + 30</gadget>
<output>75</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">75 * (5/18)</gadget>
<output>125/6 = around 20.833333</output>
<gadget id="calculator">1 / (125/6)</gadget>
<output>6/125 = around 0.048</output>
<gadget id="calculator">650 * (6/125)</gadget>
<output>156/5 = around 31.2</output>
<gadget id="calculator">(156/5) * 2</gadget>
<output>312/5 = around 62.4</output>
<result>C</result> | C | 62.4 | Two good train each 650 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one. | {
"A": "12.4 sec",
"B": "24.3 sec",
"C": "62.4 sec",
"D": "60.1 sec",
"E": "none"
} | multiply(multiply(650, inverse(multiply(add(45, 30), const_0_2778))), const_2) | add(n1,n2)|multiply(#0,const_0_2778)|inverse(#1)|multiply(n0,#2)|multiply(#3,const_2)| | "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 650 + 650 ) m = 1300 m . required time = ( 1300 x 6 / 125 ) sec = 62.4 sec . answer c" | physics |
math_qa__UllTZVThSDkWheUb | he total marks obtained by a student in Physics, Chemistry and Mathematics is 130 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics? Choose the correct choice from the following choices
A) 55
B) 65
C) 75
D) 85
E) 95 | <gadget id="calculator">130 / 2</gadget>
<output>65</output>
<result>B</result> | B | 65 | he total marks obtained by a student in Physics, Chemistry and Mathematics is 130 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics? | {
"A": "55",
"B": "65",
"C": "75",
"D": "85",
"E": "95"
} | divide(130, const_2) | divide(n0,const_2)| | "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 130 + p c + m = 130 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 130 / 2 = 65 . answer : b" | general |
math_qa__n3yt7os8RjjKMYSw | a salesman gets commission on total sales at 9 % . if the sale is exceeded rs . 10000 he gets an additional commission as bonus of 3 % on the excess of sales over rs . 10000 . if he gets total commission of rs . 1380 , then the bonus he received is :
Options
A) 22 B) 120 C) 388 D) 377 E) 272 | <gadget id="calculator">9 * 10_000</gadget>
<output>90_000</output>
<gadget id="calculator">90_000 / 100</gadget>
<output>900</output>
<gadget id="calculator">1_380 - 900</gadget>
<output>480</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">480 * (1/4)</gadget>
<output>120</output>
<result>B</result> | B | 120 | a salesman gets commission on total sales at 9 % . if the sale is exceeded rs . 10000 he gets an additional commission as bonus of 3 % on the excess of sales over rs . 10000 . if he gets total commission of rs . 1380 , then the bonus he received is : | {
"A": "22",
"B": "120",
"C": "388",
"D": "377",
"E": "272"
} | multiply(subtract(1380, divide(multiply(9, 10000), const_100)), divide(const_1, const_4)) | divide(const_1,const_4)|multiply(n0,n1)|divide(#1,const_100)|subtract(n4,#2)|multiply(#0,#3) | explanation : commission up to 10000 = \ inline 10000 \ times \ frac { 9 } { 100 } = 900 again after 10000 , commission : bonus 9 : 3 \ inline \ rightarrow 3 x : x \ therefore bonus = \ inline ( 1380 - 900 ) \ times \ frac { 1 } { 4 } = rs . 120 answer : b ) rs . 120 | general |
math_qa__HsbJg0tRapqOqsUG | The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? Pick one: A) 1752 B) 1799 C) 1719 D) 1750 E) 1800 | <gadget id="calculator">216 * 1_000</gadget>
<output>216_000</output>
<gadget id="calculator">60 / 1</gadget>
<output>60</output>
<gadget id="calculator">216_000 / 60</gadget>
<output>3_600</output>
<gadget id="calculator">3_600 / 2</gadget>
<output>1_800</output>
<result>E</result> | E | 1,800 | The length of a train and that of a platform are equal. If with a speed of 216 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? | {
"A": "1752",
"B": "1799",
"C": "1719",
"D": "1750",
"E": "1800"
} | divide(divide(multiply(216, const_1000), divide(const_60, const_1)), const_2) | divide(const_60,const_1)|multiply(n0,const_1000)|divide(#1,#0)|divide(#2,const_2)| | "speed = [ 216 * 5 / 18 ] m / sec = 60 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 60 ã ¨ x = 60 * 60 / 2 = 1800 answer : e" | physics |
math_qa__VGBDfWZsXkOZi7OW | If it takes a machine 4⁄5 minute to produce one item, how many items will it produce in 2 hours? Pick.
A) 1 ⁄ 3 B) 150 C) 80 D) 120 E) 180 | <gadget id="calculator">2 * 60</gadget>
<output>120</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">120 / (4/5)</gadget>
<output>150</output>
<result>B</result> | B | 150 | If it takes a machine 4⁄5 minute to produce one item, how many items will it produce in 2 hours? | {
"A": "1 ⁄ 3",
"B": "150",
"C": "80",
"D": "120",
"E": "180"
} | divide(multiply(2, const_60), divide(4, 5)) | divide(n0,n1)|multiply(n2,const_60)|divide(#1,#0) | 1 item takes 4 / 5 min so it takes 120 min to produce x 4 x / 5 = 120 the x = 150 answer : b | physics |
math_qa__cKU6qTBO52zd70rs | A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 120 sq. feet, how many feet of fencing will be required? Choose the correct choice from the following answers
A) 34
B) 40
C) 68
D) 88
E) 32 | <gadget id="calculator">120 / 20</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">12 + 20</gadget>
<output>32</output>
<result>E</result> | E | 32 | A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 120 sq. feet, how many feet of fencing will be required? | {
"A": "34",
"B": "40",
"C": "68",
"D": "88",
"E": "32"
} | add(multiply(divide(120, 20), const_2), 20) | divide(n1,n0)|multiply(#0,const_2)|add(n0,#1)| | "we have : l = 20 ft and lb = 120 sq . ft . so , b = 6 ft . length of fencing = ( l + 2 b ) = ( 20 + 12 ) ft = 32 ft . answer : e" | geometry |
math_qa__1azMaHrMVlCzgz82 | If equation |x/2| + |y/2| = 2 encloses a certain region on the coordinate plane, what is the area of this region? Choose the correct choice.
A) 20 B) 32 C) 100 D) 200 E) 400 | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 + 16</gadget>
<output>32</output>
<result>B</result> | B | 32 | If equation |x/2| + |y/2| = 2 encloses a certain region on the coordinate plane, what is the area of this region? | {
"A": "20",
"B": "32",
"C": "100",
"D": "200",
"E": "400"
} | add(power(multiply(2, 2), const_2), power(multiply(2, 2), const_2)) | multiply(n0,n0)|power(#0,const_2)|add(#1,#1) | the equation can be reduced to intercept form as | x / 4 | + | y / 4 | = 1 , so these are lines in four quadrants with x and y intercept as 14 , so it is a rhombus with diagonals of 8 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 8 * 8 = 32 . answer b . | general |
math_qa__TEtByIorBpU8Ipjr | Find the area of a rhombus one side of which measures 20 cm and one diagonal is 25 cm. Choose the correct choice from the following answers.
A) 700 cm 2
B) 600 cm 2
C) 500 cm 2
D) 400 cm 2
E) 100 cm 2 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 25</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">400 * 4</gadget>
<output>1_600</output>
<gadget id="calculator">25 * 25</gadget>
<output>625</output>
<gadget id="calculator">1_600 - 625</gadget>
<output>975</output>
<gadget id="calculator">975 ** (1/2)</gadget>
<output>5*sqrt(39) = around 31.22499</output>
<gadget id="calculator">(25/2) * (5*sqrt(39))</gadget>
<output>125*sqrt(39)/2 = around 390.312375</output>
<gadget id="calculator">(125*sqrt(39)/2) + 25</gadget>
<output>25 + 125*sqrt(39)/2 = around 415.312375</output>
<result>D</result> | D | 400 | Find the area of a rhombus one side of which measures 20 cm and one diagonal is 25 cm. | {
"A": "700 cm 2",
"B": "600 cm 2",
"C": "500 cm 2",
"D": "400 cm 2",
"E": "100 cm 2"
} | add(multiply(multiply(divide(const_1, const_2), 25), sqrt(subtract(multiply(multiply(20, 20), const_4), multiply(25, 25)))), 25) | divide(const_1,const_2)|multiply(n0,n0)|multiply(n1,n1)|multiply(n1,#0)|multiply(#1,const_4)|subtract(#4,#2)|sqrt(#5)|multiply(#3,#6)|add(n1,#7)| | "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 25 x 32 ) cm 2 = 400 cm 2 answer : option d" | geometry |
math_qa__l8Qp868DEZetqsnd | What is the smallest integer k for which 64^k > 4^22?
Options:
A) 4 B) 5 C) 6 D) 7 E) 8 | <gadget id="calculator">22 / 3</gadget>
<output>22/3 = around 7.333333</output>
<gadget id="calculator">floor(22/3)</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<result>E</result> | E | 8 | What is the smallest integer k for which 64^k > 4^22? | {
"A": "4",
"B": "5",
"C": "6",
"D": "7",
"E": "8"
} | add(floor(divide(22, const_3)), const_1) | divide(n2,const_3)|floor(#0)|add(#1,const_1)| | "64 ^ k > 4 ^ 22 4 ^ ( 3 k ) > 4 ^ 22 3 k > 22 k = 8 the answer is e ." | general |
math_qa__nGQ8VNNam7OgKMNz | The number 0.8 is how much greater than 1/8 ?
Options
A) ½ B) 27 / 40 C) 1 / 50 D) 1 / 500 E) 2 / 500 | <gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">0.8 - (1/8)</gadget>
<output>0.675</output>
<result>B</result> | B | 0.675 | The number 0.8 is how much greater than 1/8 ? | {
"A": "½",
"B": "27 / 40",
"C": "1 / 50",
"D": "1 / 500",
"E": "2 / 500"
} | subtract(0.8, divide(1, 8)) | divide(n1,n2)|subtract(n0,#0) | let x be the difference then . 8 - 1 / 8 = x 8 / 10 - 1 / 8 = x x = 27 / 40 ans b | general |
math_qa__wZse2wRNUN7f2x6u | If the radius of a circle is decreased by 50%, find the percentage decrease Select the correct option.
A) 22 B) 099 C) 75 D) 26 E) 18 | <gadget id="calculator">100 / 100</gadget>
<output>1</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 2</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>
<result>C</result> | C | 75 | If the radius of a circle is decreased by 50%, find the percentage decrease | {
"A": "22",
"B": "099",
"C": "75",
"D": "26",
"E": "18"
} | multiply(subtract(divide(const_100, const_100), power(subtract(divide(const_100, const_100), divide(50, const_100)), const_2)), const_100) | divide(const_100,const_100)|divide(n0,const_100)|subtract(#0,#1)|power(#2,const_2)|subtract(#0,#3)|multiply(#4,const_100)| | "let original radius = r . new radius = = original area = and new area = decrease in area = = 75 % answer : c" | gain |
math_qa__nIymeXp7TeqmGozW | Guadalupe owns 2 rectangular tracts of land. One is 300 m by 500 m and the other is 250 m by 630 m. The combined area of these 2 tracts is how many square meters? Choose the correct choice from the following answers:
A) 3,360 B) 307,500 C) 621,500 D) 704,000 E) 2 , 816,000 | <gadget id="calculator">300 * 500</gadget>
<output>150_000</output>
<gadget id="calculator">250 * 630</gadget>
<output>157_500</output>
<gadget id="calculator">150_000 + 157_500</gadget>
<output>307_500</output>
<result>B</result> | B | 307,500 | Guadalupe owns 2 rectangular tracts of land. One is 300 m by 500 m and the other is 250 m by 630 m. The combined area of these 2 tracts is how many square meters? | {
"A": "3,360",
"B": "307,500",
"C": "621,500",
"D": "704,000",
"E": "2 , 816,000"
} | add(rectangle_area(300, 500), rectangle_area(250, 630)) | rectangle_area(n1,n2)|rectangle_area(n3,n4)|add(#0,#1) | one is 300 m by 500 m and the other is 250 m by 630 m : ( 300 * 500 ) + ( 250 * 630 ) = 150000 + 157500 307500 answer : b | geometry |
math_qa__orPfgg1xFFQcm02h | A certain hobby shop sold model cars for $5.00 each and model trains for $8.00 each. If a customer purchased both cars and trains from the store for a total of $31.00, what total number of cars and trains did the customer purchase?
Choices:
A) 3
B) 4
C) 5
D) 6
E) 7 | <gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">31 - 15</gadget>
<output>16</output>
<gadget id="calculator">16 / 8</gadget>
<output>2</output>
<gadget id="calculator">15 / 5</gadget>
<output>3</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<result>C</result> | C | 5 | A certain hobby shop sold model cars for $5.00 each and model trains for $8.00 each. If a customer purchased both cars and trains from the store for a total of $31.00, what total number of cars and trains did the customer purchase? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | add(divide(subtract(31, multiply(5, const_3)), 8), divide(multiply(5, const_3), 5)) | multiply(n0,const_3)|divide(#0,n0)|subtract(n2,#0)|divide(#2,n1)|add(#3,#1) | we can take numbers , as price of car 5 , 8 for train and 31 total for ease . now we can determine quickly that total number should range between 31 / 8 < = n < = 31 / 5 , so ans should be between 3 and 7 . now solving the expression 5 a + 8 b = 31 decreasing 31 in multiple of 5 and checking divisibility of that number by 8 . this way we get 3 cars , 2 trains we get $ 31.00 total 3 * 5 + 2 * 8 = 31 hence total number is 3 + 2 = 5 ans c | other |
math_qa__SN1FwsjDB51KcPEn | John and David work at a hospital with 10 other workers. For an internal review, 2 of the 10 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen?
Choose the correct choice from the following options.
A) 1 / 45 B) 1 / 35 C) 1 / 25 D) 1 / 15 E) 1 / 10 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/9) * (1/10)</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">2 * (1/90)</gadget>
<output>1/45 = around 0.022222</output>
<result>A</result> | A | 0.022222 | John and David work at a hospital with 10 other workers. For an internal review, 2 of the 10 workers will be randomly chosen to be interviewed. What is the probability that John and David will both be chosen? | {
"A": "1 / 45",
"B": "1 / 35",
"C": "1 / 25",
"D": "1 / 15",
"E": "1 / 10"
} | multiply(2, multiply(divide(const_1, subtract(10, const_1)), divide(const_1, 10))) | divide(const_1,n0)|subtract(n0,const_1)|divide(const_1,#1)|multiply(#2,#0)|multiply(n1,#3)| | "probability that john and david will both be chosen out of 8 workers = ( 2 / 10 ) * ( 1 / 9 ) = 1 / 45 answer a" | physics |
math_qa__IuuHosdcHlPWpH5V | in a two - digit , if it is known that its unit ' s digit exceeds its 10 ' s digit by 2 and that the product of the given number and the sum of its digits is equal to 144 , then the number is ?
Choices:
A) 24
B) 26
C) 28
D) 30
E) none | <gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">20 + 4</gadget>
<output>24</output>
<result>A</result> | A | 24 | in a two - digit , if it is known that its unit ' s digit exceeds its 10 ' s digit by 2 and that the product of the given number and the sum of its digits is equal to 144 , then the number is ? | {
"A": "24",
"B": "26",
"C": "28",
"D": "30",
"E": "none"
} | add(multiply(10, 2), const_4) | multiply(n0,n1)|add(#0,const_4) | let the ten ' s digit be x . then , unit ' s digit = x + 2 . number = 10 x + ( x + 2 ) = 11 x + 2 . sum of digits = x + ( x + 2 ) = 2 x + 2 . ( 11 x + 2 ) ( 2 x + 2 ) = 144 22 x 2 + 26 x - 140 = 0 11 x 2 + 13 x - 70 = 0 ( x - 2 ) ( 11 x + 35 ) = 0 x = 2 . hence , required number = 11 x + 2 = 24 . option a | general |
math_qa__RpxoiLObSa0AeGmL | Mrs. Evans gave a test to her freshmen economics class, which has 30 students enrolled and 25 of them answered question 1 correctly. If 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly? Choose the correct choice from the following:
A) 30
B) 28
C) 26
D) 22
E) 19 | <gadget id="calculator">25 + 22</gadget>
<output>47</output>
<gadget id="calculator">47 + 5</gadget>
<output>52</output>
<gadget id="calculator">52 - 30</gadget>
<output>22</output>
<result>D</result> | D | 22 | Mrs. Evans gave a test to her freshmen economics class, which has 30 students enrolled and 25 of them answered question 1 correctly. If 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly? | {
"A": "30",
"B": "28",
"C": "26",
"D": "22",
"E": "19"
} | subtract(add(add(25, 22), 5), 30) | add(n1,n3)|add(n5,#0)|subtract(#1,n0) | total number of enrolled students = 30 number of students who did not take test = 5 hence , number of students who took test = 30 - 5 = 25 number of students who answered q 2 correctly = 22 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 22 . number of students who answered both q 1 & q 2 correctly = 22 . answer : d | other |
math_qa__dM1kNN4HSud1H2sO | What is the smallest number which when diminished by 12, is divisible 8, 12, 22 and 24? Choose the correct choice from the following options:
A) 276 B) 295 C) 230 D) 225 E) 245 | <gadget id="calculator">lcm(8, 12)</gadget>
<output>24</output>
<gadget id="calculator">lcm(22, 24)</gadget>
<output>264</output>
<gadget id="calculator">lcm(24, 264)</gadget>
<output>264</output>
<gadget id="calculator">264 + 12</gadget>
<output>276</output>
<result>A</result> | A | 276 | What is the smallest number which when diminished by 12, is divisible 8, 12, 22 and 24? | {
"A": "276",
"B": "295",
"C": "230",
"D": "225",
"E": "245"
} | add(lcm(lcm(8, 12), lcm(22, 24)), 12) | lcm(n1,n2)|lcm(n3,n4)|lcm(#0,#1)|add(n0,#2)| | "required number = ( lcm of 8 , 12 , 22 and 24 ) + 12 = 264 + 12 = 276 answer : option a" | general |
math_qa__BZmml8AhvgzPg65W | K is a 3 digit number such that the the ratio of the number to the sum of its digits is least.What is the difference between the hundreds and tens digit?
Choose the correct choice from the following answers:
A) 9 B) 8 C) 7 D) 6 E) 5 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<result>B</result> | B | 8 | K is a 3 digit number such that the the ratio of the number to the sum of its digits is least.What is the difference between the hundreds and tens digit? | {
"A": "9",
"B": "8",
"C": "7",
"D": "6",
"E": "5"
} | add(add(3, const_4), const_1) | add(n0,const_4)|add(#0,const_1) | explanation : this is only possible only when the hundreds digit has the least value and tens and units has the highest value . so we could get the highest possible sum but possible lowest number . so by this logic this number could only be 199 . so the difference is 8 . note : remember a number given as abc i . e abc = ax 100 + bx 10 + c . so 123 = 1 x 100 + 2 x 10 + 3 . answer : b | general |
math_qa__N9t9M88lqZkLXnWP | One hour after Yolanda started walking from X to Y, a distance of 65 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 5 miles per hour and Bobâs was 7 miles per hour, how many miles had Bob walked when they met? Options:
A) 31
B) 32
C) 33
D) 34
E) 35 | <gadget id="calculator">65 - 5</gadget>
<output>60</output>
<gadget id="calculator">5 + 7</gadget>
<output>12</output>
<gadget id="calculator">60 / 12</gadget>
<output>5</output>
<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<result>E</result> | E | 35 | One hour after Yolanda started walking from X to Y, a distance of 65 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 5 miles per hour and Bobâs was 7 miles per hour, how many miles had Bob walked when they met? | {
"A": "31",
"B": "32",
"C": "33",
"D": "34",
"E": "35"
} | multiply(divide(subtract(65, 5), add(5, 7)), 7) | add(n1,n2)|subtract(n0,n1)|divide(#1,#0)|multiply(n2,#2)| | "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 5 ( t + 1 ) miles . these distances must sum to 65 miles , so 7 t + 5 ( t + 1 ) = 65 , which may be solved for t as follows 7 t + 5 ( t + 1 ) = 65 7 t + 5 t + 5 = 65 12 t = 60 t = 5 ( hours ) therefore , bob had walked 7 t = 7 ( 5 ) = 35 miles when they met . the best answer is e ." | physics |
math_qa__G3iKGyPdnyxmHP46 | If 30% of 100 is greater than 50% of a number by 10, then the number is? Select: A) 40 B) 30 C) 60 D) 80 E) 50 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<gadget id="calculator">30 - 10</gadget>
<output>20</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">20 / (1/2)</gadget>
<output>40</output>
<result>A</result> | A | 40 | If 30% of 100 is greater than 50% of a number by 10, then the number is? | {
"A": "40",
"B": "30",
"C": "60",
"D": "80",
"E": "50"
} | divide(subtract(multiply(divide(30, const_100), 100), 10), divide(50, const_100)) | divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|subtract(#2,n3)|divide(#3,#1)| | "let the number be x 30 % of 100 - 50 % of x = 10 50 / 100 x = ( 30 / 100 * 100 ) - 10 x / 2 = 20 x = 40 answer is a" | gain |
math_qa__uKNscfEztFrTIjPn | There were 35 students in a hostel. Due to the admission of 7 new students, he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. What was the original expenditure of the mess? Choose the correct choice.
A) 125
B) 321
C) 561
D) 852
E) 420 | <gadget id="calculator">42 + 42</gadget>
<output>84</output>
<gadget id="calculator">42 - 35</gadget>
<output>7</output>
<gadget id="calculator">84 / 7</gadget>
<output>12</output>
<gadget id="calculator">12 * 35</gadget>
<output>420</output>
<gadget id="calculator">42 - 12</gadget>
<output>30</output>
<gadget id="calculator">30 - 12</gadget>
<output>18</output>
<gadget id="calculator">18 + 2</gadget>
<output>20</output>
<gadget id="calculator">420 - 20</gadget>
<output>400</output>
<result>E</result> | E | 420 | There were 35 students in a hostel. Due to the admission of 7 new students, he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. What was the original expenditure of the mess? | {
"A": "125",
"B": "321",
"C": "561",
"D": "852",
"E": "420"
} | subtract(multiply(divide(add(42, 42), subtract(42, 35)), 35), add(subtract(subtract(42, divide(add(42, 42), subtract(42, 35))), divide(add(42, 42), subtract(42, 35))), const_2)) | add(n2,n2)|subtract(n2,n0)|divide(#0,#1)|multiply(n0,#2)|subtract(n2,#2)|subtract(#4,#2)|add(#5,const_2)|subtract(#3,#6)| | "let the original average expenditure be rs . x . then , 42 ( x - 1 ) - 35 x = 42 ; 7 x = 84 ; x = 12 . original expenditure = rs . ( 35 x 12 ) = rs . 420 . . ans : e" | general |
math_qa__knufKdMqJz4tYbze | At a speed of 40 miles per hour, a certain car uses 1 gallon of gasoline every 40 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 40 miles per hour, the amount of gasoline used would be what fraction of a full tank?
Choose the correct answer.
A) 3 / 25 B) 5 / 12 C) 7 / 12 D) 2 / 3 E) 25 / 36 | <gadget id="calculator">40 * 5</gadget>
<output>200</output>
<gadget id="calculator">200 / 40</gadget>
<output>5</output>
<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>
<result>B</result> | B | 0.416667 | At a speed of 40 miles per hour, a certain car uses 1 gallon of gasoline every 40 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 40 miles per hour, the amount of gasoline used would be what fraction of a full tank? | {
"A": "3 / 25",
"B": "5 / 12",
"C": "7 / 12",
"D": "2 / 3",
"E": "25 / 36"
} | divide(divide(multiply(40, 5), 40), 12) | multiply(n0,n4)|divide(#0,n2)|divide(#1,n3)| | "gas used = ( 5 hours ) * ( 40 miles / hour ) * ( 1 gallon / 40 miles ) = 5 gallons portion used = ( 5 ) / 12 = 5 / 12 ans b" | physics |
math_qa__UTUB4YUHGaepSIJc | Niharika covers a distance in 30 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 30%. Pick: A) 84.71 kmph . B) 85.74 kmph . C) 83.71 kmph . D) 85.71 kmph . E) 84.71 kmph . | <gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 - 4</gadget>
<output>86</output>
<result>D</result> | D | 85.71 | Niharika covers a distance in 30 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 30%. | {
"A": "84.71 kmph .",
"B": "85.74 kmph .",
"C": "83.71 kmph .",
"D": "85.71 kmph .",
"E": "84.71 kmph ."
} | subtract(subtract(const_100, const_10), const_4) | subtract(const_100,const_10)|subtract(#0,const_4) | given speed = 60 kmph . it means niharika covered 60 km in 60 min ( 1 hour ) . so , in 30 min he will cover 30 km . 30 % time reduced = 30 - 30 % of 30 = 21 min . thus , niharika needs to cover 30 km in 21 min ( 0.35 hour ) . speed * time = distance . speed * 0.35 = 30 speed = 85.71 kmph . answer : option d | general |
math_qa__I46KxsauuZGSCGp3 | Rahul's housing colony have One tap, working alone at its maximum constant rate, can fill a certain tank in 230 seconds. A second tap, working alone at its maximum constant rate, can fill the same tank in 234 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the tank is closest to
Choose the most appropriate option.
A) 116 seconds
B) 150 seconds
C) 177 seconds
D) 200 seconds
E) 270 seconds | <gadget id="calculator">230 + 234</gadget>
<output>464</output>
<gadget id="calculator">230 / 464</gadget>
<output>115/232 = around 0.49569</output>
<gadget id="calculator">(115/232) * 230</gadget>
<output>13_225/116 = around 114.008621</output>
<result>A</result> | A | 116 | Rahul's housing colony have One tap, working alone at its maximum constant rate, can fill a certain tank in 230 seconds. A second tap, working alone at its maximum constant rate, can fill the same tank in 234 seconds. If both taps work together at their respective maximum constant rates, the time it will take to fill the tank is closest to | {
"A": "116 seconds",
"B": "150 seconds",
"C": "177 seconds",
"D": "200 seconds",
"E": "270 seconds"
} | multiply(divide(230, add(230, 234)), 230) | add(n0,n1)|divide(n0,#0)|multiply(n0,#1) | tap 1 : 230 secs tap 2 : 234 secs considering the average of these 2 taps : 232 secs . so 1 tap can fill the tank in 232 secs , so 2 taps can fill the tank in 232 / 2 = 116 secs . closest answer is a . | physics |
math_qa__H7zmbS3OHrNI5egZ | A can do a work in 20days, B in 30days. A alone start the work after 10days he left work. In how many days B can finish the work? Choose the correct option
A) 30 days B) 25 days C) 20 days D) 10 days E) 15 days | <gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">10 * (1/20)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/2) / (1/30)</gadget>
<output>15</output>
<result>E</result> | E | 15 | A can do a work in 20days, B in 30days. A alone start the work after 10days he left work. In how many days B can finish the work? | {
"A": "30 days",
"B": "25 days",
"C": "20 days",
"D": "10 days",
"E": "15 days"
} | divide(subtract(const_1, multiply(10, divide(const_1, 20))), divide(const_1, 30)) | divide(const_1,n0)|divide(const_1,n1)|multiply(n2,#0)|subtract(const_1,#2)|divide(#3,#1)| | "10 days work of a = 10 / 20 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 b can finish 1 / 2 work = 30 * 1 / 2 = 15 days answer is e" | physics |
math_qa__cUEQ9WGYa17pidZZ | A shopkeeper sells 450 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth? Choose the correct option.
A) 12
B) 27
C) 29
D) 45
E) 21 | <gadget id="calculator">18_000 / 450</gadget>
<output>40</output>
<gadget id="calculator">40 + 5</gadget>
<output>45</output>
<result>D</result> | D | 45 | A shopkeeper sells 450 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth? | {
"A": "12",
"B": "27",
"C": "29",
"D": "45",
"E": "21"
} | add(divide(18000, 450), 5) | divide(n1,n0)|add(n2,#0) | sp per metre = 18000 / 450 = rs . 40 loss per metre = rs . 5 cp per metre = 40 + 5 = rs . 45 . answer : d | gain |
math_qa__NOLVOcK1Enr3zuZj | A vessel of capacity 2 litre has 20% of alcohol and another vessel of capacity 6 litre had 55% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture? Choose the most appropriate option: A) 37 % . B) 71 % . C) 49 % . D) 29 % . E) 51 % . | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 2</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">(11/20) * 6</gadget>
<output>33/10 = around 3.3</output>
<gadget id="calculator">(2/5) + (33/10)</gadget>
<output>37/10 = around 3.7</output>
<gadget id="calculator">(37/10) / 10</gadget>
<output>37/100 = around 0.37</output>
<gadget id="calculator">(37/100) * 100</gadget>
<output>37</output>
<result>A</result> | A | 37 | A vessel of capacity 2 litre has 20% of alcohol and another vessel of capacity 6 litre had 55% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture? | {
"A": "37 % .",
"B": "71 % .",
"C": "49 % .",
"D": "29 % .",
"E": "51 % ."
} | multiply(divide(add(multiply(divide(20, const_100), 2), multiply(divide(55, const_100), 6)), 10), const_100) | divide(n1,const_100)|divide(n3,const_100)|multiply(n0,#0)|multiply(n2,#1)|add(#2,#3)|divide(#4,n5)|multiply(#5,const_100)| | "20 % of 2 litres = 0.4 litres 55 % of 6 litres = 3.3 litres therefore , total quantity of alcohol is 3.7 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 37 % a" | general |
math_qa__Wl5vKp0Oe4EA8JLr | The parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 20 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. Pick one.
A) 23.56 B) 33.0 C) 23.55 D) 23.53 E) 23.57 | <gadget id="calculator">2 * (22 + 20)</gadget>
<output>84</output>
<gadget id="calculator">84 / 4</gadget>
<output>21</output>
<gadget id="calculator">21 / 2</gadget>
<output>21/2 = around 10.5</output>
<gadget id="calculator">2 * pi * (21/2)</gadget>
<output>21*pi = around 65.973446</output>
<gadget id="calculator">(21*pi) / 2</gadget>
<output>21*pi/2 = around 32.986723</output>
<result>B</result> | B | 33 | The parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 20 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. | {
"A": "23.56",
"B": "33.0",
"C": "23.55",
"D": "23.53",
"E": "23.57"
} | divide(circumface(divide(square_edge_by_perimeter(rectangle_perimeter(22, 20)), const_2)), const_2) | rectangle_perimeter(n0,n1)|square_edge_by_perimeter(#0)|divide(#1,const_2)|circumface(#2)|divide(#3,const_2)| | "let the side of the square be a cm . parameter of the rectangle = 2 ( 22 + 20 ) = 84 cm parameter of the square = 84 cm i . e . 4 a = 84 a = 21 diameter of the semicircle = 21 cm circimference of the semicircle = 1 / 2 ( â ˆ ) 21 = 1 / 2 ( 22 / 7 ) ( 21 ) = 66 / 2 = 33 cm answer : b" | geometry |
math_qa__IRCgWOGLBfrMI0rm | The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle. Choices:
A) w = 15 and l = 20 B) w = 25 and l = 30 C) w = 35 and l = 40 D) w = 45 and l = 50 E) w = 55 and l = 60 | <gadget id="calculator">70 / 2</gadget>
<output>35</output>
<gadget id="calculator">35 ** 2</gadget>
<output>1_225</output>
<gadget id="calculator">4 * 300</gadget>
<output>1_200</output>
<gadget id="calculator">1_225 - 1_200</gadget>
<output>25</output>
<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">35 - 5</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<result>A</result> | A | 15 | The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle. | {
"A": "w = 15 and l = 20",
"B": "w = 25 and l = 30",
"C": "w = 35 and l = 40",
"D": "w = 45 and l = 50",
"E": "w = 55 and l = 60"
} | divide(subtract(divide(70, const_2), sqrt(subtract(power(divide(70, const_2), const_2), multiply(const_4, 300)))), const_2) | divide(n1,const_2)|multiply(n0,const_4)|power(#0,const_2)|subtract(#2,#1)|sqrt(#3)|subtract(#0,#4)|divide(#5,const_2) | l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer a | geometry |
math_qa__I42YL9HWUYk9qKUa | The total number of digits used in numbering the pages of a book having 346 pages is
Pick one: A) 732 B) 990 C) 1098 D) 930 E) 1405 | <gadget id="calculator">346 * 3</gadget>
<output>1_038</output>
<gadget id="calculator">100 - 1</gadget>
<output>99</output>
<gadget id="calculator">1_038 - 99</gadget>
<output>939</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">939 - 9</gadget>
<output>930</output>
<result>D</result> | D | 930 | The total number of digits used in numbering the pages of a book having 346 pages is | {
"A": "732",
"B": "990",
"C": "1098",
"D": "930",
"E": "1405"
} | subtract(subtract(multiply(346, const_3), subtract(const_100, const_1)), subtract(const_10, const_1)) | multiply(n0,const_3)|subtract(const_100,const_1)|subtract(const_10,const_1)|subtract(#0,#1)|subtract(#3,#2)| | "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 247 ) = ( 9 + 180 + 741 ) = 930 . answer : d" | general |
math_qa__66aARPEfP2aU1WP7 | A light has a rating of 110 watts, it is replaced with a new light that has 30% higher wattage. How many watts does the new light have?
Choose one: A) 143 B) 145 C) 156 D) 134 E) 100 | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">110 * (13/10)</gadget>
<output>143</output>
<result>A</result> | A | 143 | A light has a rating of 110 watts, it is replaced with a new light that has 30% higher wattage. How many watts does the new light have? | {
"A": "143",
"B": "145",
"C": "156",
"D": "134",
"E": "100"
} | multiply(110, add(const_1, divide(30, const_100))) | divide(n1,const_100)|add(#0,const_1)|multiply(n0,#1)| | "final number = initial number + 30 % ( original number ) = 110 + 30 % ( 110 ) = 110 + 33 = 143 . answer a" | gain |
math_qa__KEqOjO5z7bZgkSue | There are 200 doctors and nurses at a hospital. If the ratio of doctors to nurses is 4 to 6, how many nurses are at the hospital? Pick one
A) 110 B) 120 C) 130 D) 140 E) 150 | <gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">200 / 10</gadget>
<output>20</output>
<gadget id="calculator">20 * 6</gadget>
<output>120</output>
<result>B</result> | B | 120 | There are 200 doctors and nurses at a hospital. If the ratio of doctors to nurses is 4 to 6, how many nurses are at the hospital? | {
"A": "110",
"B": "120",
"C": "130",
"D": "140",
"E": "150"
} | multiply(divide(200, add(4, 6)), 6) | add(n1,n2)|divide(n0,#0)|multiply(n2,#1)| | "the number of nurses at the hospital is ( 6 / 10 ) * 200 = 120 . the answer is b ." | other |
math_qa__XaJV5pKGzBcXrFyg | Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%? Select the correct option: A) 10 liters B) 15 liters C) 20 liters D) 18 liters E) 22 liters | <gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 10</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/2) / (1/50)</gadget>
<output>25</output>
<gadget id="calculator">25 - 10</gadget>
<output>15</output>
<result>B</result> | B | 15 | Milk contains 5% water. What content of pure milk should be added to 10 liters of milk to reduce this to 2%? | {
"A": "10 liters",
"B": "15 liters",
"C": "20 liters",
"D": "18 liters",
"E": "22 liters"
} | subtract(divide(multiply(divide(5, const_100), 10), divide(2, const_100)), 10) | divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|divide(#2,#1)|subtract(#3,n1)| | "quantity of water in 10 liters = 5 % of 10 liters = 0.5 liters let x liters of pure milk be added . then , 0.5 / ( 10 + x ) = 2 / 100 2 x = 30 x = 15 liters answer is b" | gain |
math_qa__zX4IFnFYDO2sk1Ji | The current in a river is 4 mph. A boat can travel 18 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?
Options: A) 69 miles B) 85.5 miles C) 96 miles D) 100 miles E) 112 miles | <gadget id="calculator">18 - 4</gadget>
<output>14</output>
<gadget id="calculator">18 + 4</gadget>
<output>22</output>
<gadget id="calculator">14 * 22</gadget>
<output>308</output>
<gadget id="calculator">308 * 10</gadget>
<output>3_080</output>
<gadget id="calculator">22 + 14</gadget>
<output>36</output>
<gadget id="calculator">3_080 / 36</gadget>
<output>770/9 = around 85.555556</output>
<result>B</result> | B | 85.5 | The current in a river is 4 mph. A boat can travel 18 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours? | {
"A": "69 miles",
"B": "85.5 miles",
"C": "96 miles",
"D": "100 miles",
"E": "112 miles"
} | divide(multiply(multiply(subtract(18, 4), add(18, 4)), 10), add(add(18, 4), subtract(18, 4))) | add(n0,n1)|subtract(n1,n0)|add(#0,#1)|multiply(#0,#1)|multiply(n2,#3)|divide(#4,#2)| | "upstream speed = 18 - 4 = 14 mph downstream speed = 18 + 4 = 22 mph d / 14 + d / 22 = 10 hours solving for d we get d = 85.5 answer : b" | physics |
math_qa__J9UUPAJJFw96f6zC | The ratio of three numbers is 1:2:4 and the sum of their squares is 1701. The sum of the numbers is? Answers
A) 10 B) 12 C) 15 D) 14 E) 9 | <gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">1 ** 2</gadget>
<output>1</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">16 + 5</gadget>
<output>21</output>
<gadget id="calculator">1_701 / 21</gadget>
<output>81</output>
<gadget id="calculator">81 ** (1/2)</gadget>
<output>9</output>
<result>E</result> | E | 9 | The ratio of three numbers is 1:2:4 and the sum of their squares is 1701. The sum of the numbers is? | {
"A": "10",
"B": "12",
"C": "15",
"D": "14",
"E": "9"
} | sqrt(divide(1701, add(power(4, 2), add(power(1, 2), power(2, 2))))) | power(n0,n1)|power(n1,n1)|power(n2,n1)|add(#0,#1)|add(#3,#2)|divide(n3,#4)|sqrt(#5)| | "let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e" | other |
math_qa__egpJbvq7fayqtDbF | At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $8.50 per hour, how much less than a manager does a chef earn each hour? Choose the correct choice from the following:
A) $ 1.40
B) $ 2.40
C) $ 3.40
D) $ 4.40
E) $ 5.40 | <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">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(6/5) * (1/2)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 8.5</gadget>
<output>3.4</output>
<result>C</result> | C | 3.4 | At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $8.50 per hour, how much less than a manager does a chef earn each hour? | {
"A": "$ 1.40",
"B": "$ 2.40",
"C": "$ 3.40",
"D": "$ 4.40",
"E": "$ 5.40"
} | multiply(subtract(const_1, multiply(divide(add(const_100, 20), const_100), divide(const_1, const_2))), 8.50) | add(n0,const_100)|divide(const_1,const_2)|divide(#0,const_100)|multiply(#2,#1)|subtract(const_1,#3)|multiply(n1,#4)| | "manager wages per hour = $ 8.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 8.50 ) = = > $ 4.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 4.25 = ( 20 * ( $ 4.25 ) ) / 100 - - > ( $ 85 ) / 100 - - > $ 0.85 therefore , chef wages per hour = $ 4.25 + $ 0.85 = = > $ 5.10 difference of wages between manager and chef = $ 8.50 - $ 5.10 = = > $ 3.40 answer : c" | general |
math_qa__hWGSNN7CQjmqnTVy | 101 × 101 + 99 × 99 = ? Select the correct option
A) 10002
B) 20004
C) 20002
D) 20102
E) 20202 | <gadget id="calculator">101 ** 2</gadget>
<output>10_201</output>
<gadget id="calculator">10_201 - 101</gadget>
<output>10_100</output>
<gadget id="calculator">99 ** 2</gadget>
<output>9_801</output>
<gadget id="calculator">9_801 - 99</gadget>
<output>9_702</output>
<gadget id="calculator">10_100 + 9_702</gadget>
<output>19_802</output>
<result>C</result> | C | 20,002 | 101 × 101 + 99 × 99 = ? | {
"A": "10002",
"B": "20004",
"C": "20002",
"D": "20102",
"E": "20202"
} | add(subtract(power(101, const_2), 101), subtract(power(99, const_2), 99)) | power(n0,const_2)|power(n2,const_2)|subtract(#0,n0)|subtract(#1,n2)|add(#2,#3)| | "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1012 + 992 = ( 100 + 1 ) 2 + ( 100 â ˆ ’ 1 ) 2 = 2 ( 1002 + 12 ) = 2 ( 10000 + 1 ) = 20002 . answer : option c" | general |
math_qa__xVD1RV2LQUWbUiLG | 60 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor? Choose the most appropriate option.
A) 14.4 B) 180 / 7 C) 50.4 D) 60 E) 90 | <gadget id="calculator">4 * 9</gadget>
<output>36</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">36 / (3/5)</gadget>
<output>60</output>
<result>D</result> | D | 60 | 60 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor? | {
"A": "14.4",
"B": "180 / 7",
"C": "50.4",
"D": "60",
"E": "90"
} | divide(multiply(4, 9), divide(60, const_100)) | divide(n0,const_100)|multiply(n1,n2)|divide(#1,#0)| | "60 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 60 ) * 100 = 60 square feet answer : option d" | gain |
math_qa__o3XJR5IJQEhTU8wk | A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? Choose the most appropriate option.
A) 500 bc B) 500 b / c C) 1000 bc D) 1000 b / c E) 1000 / bc | <gadget id="calculator">2 * 500</gadget>
<output>1_000</output>
<result>C</result> | C | 1,000 | A case contains c cartons. Each carton contains b boxes, and each box contains 500 paper clips. How many paper clips are contained in 2 cases? | {
"A": "500 bc",
"B": "500 b / c",
"C": "1000 bc",
"D": "1000 b / c",
"E": "1000 / bc"
} | multiply(2, 500) | multiply(n0,n1)| | "2 cases * c cartons / case * b boxes / carton * 500 clips / box = 1000 bc paper clips the answer is c ." | general |
math_qa__NAzOyrT5UDJTrqs2 | a , b and c start a business with each investing rs 20000 . after 5 months a withdraws rs 5000 , b withdraws rs 4000 and c invests rs 6000 more . at the end of the year , a total profit of rs 69900 was recorded . find the share of a . Choose the correct choice from the following:
A) 20000 B) 21500 C) 20500 D) 22000 E) 21000 | <gadget id="calculator">5_000 / 10</gadget>
<output>500</output>
<gadget id="calculator">20_000 + 500</gadget>
<output>20_500</output>
<result>C</result> | C | 20,500 | a , b and c start a business with each investing rs 20000 . after 5 months a withdraws rs 5000 , b withdraws rs 4000 and c invests rs 6000 more . at the end of the year , a total profit of rs 69900 was recorded . find the share of a . | {
"A": "20000",
"B": "21500",
"C": "20500",
"D": "22000",
"E": "21000"
} | add(20000, divide(5000, const_10)) | divide(n2,const_10)|add(n0,#0) | a : b : c = ( 20000 × 5 + 15000 × 7 ) : ( 20000 × 5 + 16000 × 7 ) : ( 20000 × 5 + 26000 × 7 ) = ( 20 × 5 + 15 × 7 ) : ( 20 × 5 + 16 × 7 ) : ( 20 × 5 + 26 × 7 ) = 205 : 212 : 282 a ' s share = 69900 × 205 / ( 205 + 212 + 282 ) = 69900 × 205 / 699 = 20500 answer is c . | gain |
math_qa__38bUzRURBV3fTtrB | The C.P of 15 books is equal to the S.P of 20 books. Find his gain% or loss%? Select: A) 25 % loss B) 16 2 / 8 % loss C) 16 3 / 3 % loss D) 36 2 / 3 % loss E) 56 2 / 3 % loss | <gadget id="calculator">15 / 20</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>A</result> | A | 25 | The C.P of 15 books is equal to the S.P of 20 books. Find his gain% or loss%? | {
"A": "25 % loss",
"B": "16 2 / 8 % loss",
"C": "16 3 / 3 % loss",
"D": "36 2 / 3 % loss",
"E": "56 2 / 3 % loss"
} | multiply(subtract(const_1, divide(15, 20)), const_100) | divide(n0,n1)|subtract(const_1,#0)|multiply(#1,const_100)| | "15 cp = 20 sp 20 - - - 5 cp loss 100 - - - ? = > 25 % loss answer : a" | gain |
math_qa__SVTyknWPesQMQhzU | Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6647, how much amount did Raghu invest ? Choices: A) 2300 B) 2887 C) 2000 D) 1129 E) 1192 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(9/10) * (11/10)</gadget>
<output>99/100 = around 0.99</output>
<gadget id="calculator">(99/100) + (9/10)</gadget>
<output>189/100 = around 1.89</output>
<gadget id="calculator">(189/100) + 1</gadget>
<output>289/100 = around 2.89</output>
<gadget id="calculator">6_647 / (289/100)</gadget>
<output>2_300</output>
<result>A</result> | A | 2,300 | Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 6647, how much amount did Raghu invest ? | {
"A": "2300",
"B": "2887",
"C": "2000",
"D": "1129",
"E": "1192"
} | divide(6647, add(add(multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(10, const_100))), subtract(const_1, divide(10, const_100))), const_1)) | divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#0)|multiply(#1,#2)|add(#3,#2)|add(#4,const_1)|divide(n2,#5)| | "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6647 = x = 6647 / 2.89 = 2300 therefore , amount invested by raghu is rs . 2300 . answer : a" | general |
math_qa__fq8CmgSZVO6IgTuY | In a weight-lifting competition, the total weight of Joe's two lifts was 600 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift? Choose one: A) 225 B) 275 C) 300 D) 350 E) 400 | <gadget id="calculator">600 + 300</gadget>
<output>900</output>
<gadget id="calculator">900 / 3</gadget>
<output>300</output>
<result>C</result> | C | 300 | In a weight-lifting competition, the total weight of Joe's two lifts was 600 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift? | {
"A": "225",
"B": "275",
"C": "300",
"D": "350",
"E": "400"
} | divide(add(600, 300), const_3) | add(n0,n1)|divide(#0,const_3)| | "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 600 pounds . we sum the two variables to obtain : f + s = 600 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 600 3 f = 900 f = 300 answer is c" | general |
math_qa__K2lkuebha5KJqCj6 | In measuring the sides of a rectangle, one side is taken 8% in excess, and the other 7% in deficit. Find the error percent in the area calculated from these measurements. Choose the most appropriate option.
A) 0.11 % B) 0.7 % C) 0.44 % D) 0.6 % E) 0.8 % | <gadget id="calculator">8 - 7</gadget>
<output>1</output>
<gadget id="calculator">8 * 7</gadget>
<output>56</output>
<gadget id="calculator">56 / 100</gadget>
<output>14/25 = around 0.56</output>
<gadget id="calculator">1 - (14/25)</gadget>
<output>11/25 = around 0.44</output>
<result>C</result> | C | 0.44 | In measuring the sides of a rectangle, one side is taken 8% in excess, and the other 7% in deficit. Find the error percent in the area calculated from these measurements. | {
"A": "0.11 %",
"B": "0.7 %",
"C": "0.44 %",
"D": "0.6 %",
"E": "0.8 %"
} | subtract(subtract(8, 7), divide(multiply(8, 7), const_100)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,const_100)|subtract(#1,#2)| | "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 27 / 25 ) x ( 40 / 43 ) y = ( 913 / 909 ) ( xy ) error in measurement = ( 913 / 909 ) xy - xy = ( 4 / 909 ) xy error percentage = [ ( 4 / 909 ) xy ( 1 / xy ) 100 ] % = ( 11 / 25 ) % = 0.44 % . answer is c ." | geometry |
math_qa__uDpQYcNgMupNP7WZ | A is two years older than B who is twice as old as C. The total of the ages of A, B and C is 27. How old is B? Pick one
A) 25 B) 20 C) 15 D) 10 E) 5 | <gadget id="calculator">27 - 2</gadget>
<output>25</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<result>D</result> | D | 10 | A is two years older than B who is twice as old as C. The total of the ages of A, B and C is 27. How old is B? | {
"A": "25",
"B": "20",
"C": "15",
"D": "10",
"E": "5"
} | divide(multiply(subtract(27, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)| | "let age of c = x . then , age of b = 2 x age of a = 2 + 2 x total age of a , b and c = 27 ⇒ ( 2 + 2 x ) + 2 x + x = 27 ⇒ 5 x = 25 ⇒ x = 255 = 5 b ' s age = 2 x = 2 × 5 = 10 answer is d ." | general |
math_qa__A7Kl1slQph1dXgwG | Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/6 of all the paint. During the second week, he uses 1/5 of the remaining paint. How many gallons of paint has Joe used? Choose the correct answer
A) 18 B) 120 C) 175 D) 216 E) 250 | <gadget id="calculator">360 / 6</gadget>
<output>60</output>
<gadget id="calculator">60 * 1</gadget>
<output>60</output>
<gadget id="calculator">360 - 60</gadget>
<output>300</output>
<gadget id="calculator">300 / 5</gadget>
<output>60</output>
<gadget id="calculator">60 + 60</gadget>
<output>120</output>
<result>B</result> | B | 120 | Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/6 of all the paint. During the second week, he uses 1/5 of the remaining paint. How many gallons of paint has Joe used? | {
"A": "18",
"B": "120",
"C": "175",
"D": "216",
"E": "250"
} | add(multiply(divide(360, 6), 1), divide(subtract(360, multiply(divide(360, 6), 1)), 5)) | divide(n0,n2)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n4)|add(#3,#1)| | "total paint initially = 360 gallons paint used in the first week = ( 1 / 6 ) * 360 = 60 gallons . remaning paint = 300 gallons paint used in the second week = ( 1 / 5 ) * 300 = 60 gallons total paint used = 120 gallons . option b" | physics |
math_qa__eG3LwVfWjBS3SJtL | The E train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the E train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m? Select the correct option:
A) 1.8 m
B) 6 m
C) 7 m
D) 9 m
E) 12 m | <gadget id="calculator">7 + 5</gadget>
<output>12</output>
<gadget id="calculator">7 - 5</gadget>
<output>2</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<result>B</result> | B | 6 | The E train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the E train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m? | {
"A": "1.8 m",
"B": "6 m",
"C": "7 m",
"D": "9 m",
"E": "12 m"
} | divide(add(7, 5), subtract(7, 5)) | add(n0,n1)|subtract(n0,n1)|divide(#0,#1) | the reason it is failing for you is that you chose incorrect numbers . if the question says e it took 7 hrs to reach from a to b and 5 hrs to reach from b to c at a constant speed . it shows that distance ab and bc should be in ratio of 7 / 5 . if you take such numbers you can solve problem . ab = 7 , bc = 5 therefore ab - bc = 2 but from question , ab - bc = m = > m = 2 now total distance = ab + bc = 12 substitute 12 to get answer in terms of m total distance = 12 = 6 m ans b | physics |
math_qa__z0cBLPRhMpePcZhB | dana borrows 5000 pounds annually for her college education . if dana gives her parents 4 % of that amount back each month , how much will she still owe her parents after 4 years of college ? Choose the correct choice from the following options:
A) 9800 B) 10000 C) 10200 D) 10400 E) 10600 | <gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">20_000 / 100</gadget>
<output>200</output>
<gadget id="calculator">12 * 200</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 * 4</gadget>
<output>9_600</output>
<gadget id="calculator">20_000 - 9_600</gadget>
<output>10_400</output>
<result>C</result> | C | 10,200 | dana borrows 5000 pounds annually for her college education . if dana gives her parents 4 % of that amount back each month , how much will she still owe her parents after 4 years of college ? | {
"A": "9800",
"B": "10000",
"C": "10200",
"D": "10400",
"E": "10600"
} | subtract(multiply(5000, 4), multiply(multiply(multiply(const_3, const_4), divide(multiply(5000, 4), const_100)), 4)) | multiply(n0,n1)|multiply(const_3,const_4)|divide(#0,const_100)|multiply(#2,#1)|multiply(n1,#3)|subtract(#0,#4) | dana borrows 5000 and returns 4 % per month . so returns 200 per month . and 2400 per year . so dana owes 5000 - 2400 = 2600 per year . after 4 years she will owe 10400 . ans ( c ) | gain |
math_qa__vFF7r7Mg34OjaUlM | A student scored an average of 75 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics? Pick: A) 86 B) 16 C) 76 D) 95 E) 26 | <gadget id="calculator">90 * 2</gadget>
<output>180</output>
<gadget id="calculator">70 * 2</gadget>
<output>140</output>
<gadget id="calculator">180 + 140</gadget>
<output>320</output>
<gadget id="calculator">75 * 3</gadget>
<output>225</output>
<gadget id="calculator">320 - 225</gadget>
<output>95</output>
<result>D</result> | D | 95 | A student scored an average of 75 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics? | {
"A": "86",
"B": "16",
"C": "76",
"D": "95",
"E": "26"
} | subtract(add(multiply(90, const_2), multiply(70, const_2)), multiply(75, 3)) | multiply(n2,const_2)|multiply(n3,const_2)|multiply(n0,n1)|add(#0,#1)|subtract(#3,#2)| | "given m + p + c = 75 * 3 = 225 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 225 = 95 answer : d" | general |
math_qa__UNjOkG5tQDbLx2tr | A positive number x is multiplied by 8, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ? Choose the correct choice: A) 9 / 4 B) 3 / 2 C) 8 / 3 D) 2 / 3 E) 1 / 2 | <gadget id="calculator">8 / 3</gadget>
<output>8/3 = around 2.666667</output>
<result>C</result> | C | 2.666667 | A positive number x is multiplied by 8, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ? | {
"A": "9 / 4",
"B": "3 / 2",
"C": "8 / 3",
"D": "2 / 3",
"E": "1 / 2"
} | divide(8, 3) | divide(n0,n1)| | "sq rt ( 8 x / 3 ) = x = > 8 x / 3 = x ^ 2 = > x = 8 / 3 ans - c" | general |
math_qa__CIYwx0FABwT0h5YP | A and B working together could mow a field in 28days and with the help of C they could have mowed it in 21 days. How long would C take by himself?
Choose the correct choice from the following answers
A) 68 days B) 84 days C) 90 days D) 72 days E) 50 days | <gadget id="calculator">1 / 21</gadget>
<output>1/21 = around 0.047619</output>
<gadget id="calculator">1 / 28</gadget>
<output>1/28 = around 0.035714</output>
<gadget id="calculator">(1/21) - (1/28)</gadget>
<output>1/84 = around 0.011905</output>
<gadget id="calculator">1 / (1/84)</gadget>
<output>84</output>
<result>B</result> | B | 84 | A and B working together could mow a field in 28days and with the help of C they could have mowed it in 21 days. How long would C take by himself? | {
"A": "68 days",
"B": "84 days",
"C": "90 days",
"D": "72 days",
"E": "50 days"
} | inverse(subtract(divide(const_1, 21), divide(const_1, 28))) | divide(const_1,n1)|divide(const_1,n0)|subtract(#0,#1)|inverse(#2) | required answer = 28 * 21 / 28 - 21 = 84 days answer is b | physics |
math_qa__fKmeOo781hUl9rxt | Two employees X and Y are paid a total of Rs. 590 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Choose the most appropriate option
A) s . 268 B) s . 288 C) s . 298 D) s . 300 E) s . 388 | <gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">590 * 10</gadget>
<output>5_900</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">5_900 / 22</gadget>
<output>2_950/11 = around 268.181818</output>
<result>A</result> | A | 268 | Two employees X and Y are paid a total of Rs. 590 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? | {
"A": "s . 268",
"B": "s . 288",
"C": "s . 298",
"D": "s . 300",
"E": "s . 388"
} | divide(multiply(590, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2)) | add(const_1,const_4)|multiply(#0,const_2)|add(#1,const_1)|multiply(n0,#1)|multiply(#2,const_2)|divide(#3,#4)| | "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 590 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 590 ⇒ y [ 12 / 10 + 1 ] = 590 ⇒ 22 y / 10 = 590 ⇒ 22 y = 5900 ⇒ y = 5900 / 22 = 500 / 2 = rs . 268 a )" | general |
math_qa__AN3Xk3nFsYWpDmyC | Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.36000 after completion of one year. What will be Jose's share of profit? Select.
A) 20000 B) 10000 C) 25000 D) 34000 E) 30000 | <gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">30_000 * 12</gadget>
<output>360_000</output>
<gadget id="calculator">12 - 2</gadget>
<output>10</output>
<gadget id="calculator">45_000 * 10</gadget>
<output>450_000</output>
<gadget id="calculator">450_000 + 360_000</gadget>
<output>810_000</output>
<gadget id="calculator">360_000 / 810_000</gadget>
<output>4/9 = around 0.444444</output>
<gadget id="calculator">1 - (4/9)</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">36_000 * (5/9)</gadget>
<output>20_000</output>
<result>A</result> | A | 20,000 | Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.36000 after completion of one year. What will be Jose's share of profit? | {
"A": "20000",
"B": "10000",
"C": "25000",
"D": "34000",
"E": "30000"
} | multiply(36000, subtract(const_1, divide(multiply(30000, multiply(2, multiply(2, const_3))), add(multiply(45000, subtract(multiply(2, multiply(2, const_3)), 2)), multiply(30000, multiply(2, multiply(2, const_3))))))) | multiply(n1,const_3)|multiply(#0,n1)|multiply(n0,#1)|subtract(#1,n1)|multiply(n2,#3)|add(#4,#2)|divide(#2,#5)|subtract(const_1,#6)|multiply(n3,#7)| | "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 36000 = 20000 a" | gain |
math_qa__ggHVLvbiC1jsJb28 | If 10% of x = 20% of y, then x:y is equal to?
Choose the correct choice from the following choices: A) 2 : 6 B) 2 : 1 C) 7 : 1 D) 2 : 8 E) 2 : 2 | <gadget id="calculator">20 / 10</gadget>
<output>2</output>
<result>B</result> | B | 2 | If 10% of x = 20% of y, then x:y is equal to? | {
"A": "2 : 6",
"B": "2 : 1",
"C": "7 : 1",
"D": "2 : 8",
"E": "2 : 2"
} | divide(20, 10) | divide(n1,n0) | 10 % of x = 20 % of y 10 x / 100 = 20 y / 100 = > x / 10 = y / 5 x / y = 10 / 5 = 2 / 1 x : y = 2 : 1 . answer : b | general |
math_qa__D8AFqnTgnqi5BTqB | In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 70% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that a beginner Trigonometry student is selected?
Pick one:
A) 40 %
B) 44 %
C) 48 %
D) 52 %
E) 56 % | <gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">150 + 100</gadget>
<output>250</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">250 * (4/5)</gadget>
<output>200</output>
<gadget id="calculator">200 - 70</gadget>
<output>130</output>
<gadget id="calculator">130 / 250</gadget>
<output>13/25 = around 0.52</output>
<gadget id="calculator">(13/25) * 100</gadget>
<output>52</output>
<result>D</result> | D | 52 | In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 70% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that a beginner Trigonometry student is selected? | {
"A": "40 %",
"B": "44 %",
"C": "48 %",
"D": "52 %",
"E": "56 %"
} | multiply(divide(subtract(multiply(add(add(multiply(50, const_2), 50), multiply(50, const_2)), divide(4, 5)), 70), add(add(multiply(50, const_2), 50), multiply(50, const_2))), multiply(50, const_2)) | divide(n2,n3)|multiply(n0,const_2)|add(n0,#1)|add(#2,#1)|multiply(#3,#0)|subtract(#4,n1)|divide(#5,#3)|multiply(#6,#1)| | "let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.7 x the number of students in beginner trigonometry is 4 / 5 * ( 2.5 x ) - 0.7 x = 1.3 x the percentage in beginner trigonometry is 1.3 x / 2.5 x = 52 % the answer is d ." | gain |
math_qa__Nq1Tj2umKXqjG63e | A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together? Choose the most appropriate option
A) 180 / 15 B) 180 / 10 C) 180 / 13 D) 180 / 15 E) 180 / 11 | <gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/12) + (1/30)</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">(7/60) + (1/36)</gadget>
<output>13/90 = around 0.144444</output>
<gadget id="calculator">(13/90) / 2</gadget>
<output>13/180 = around 0.072222</output>
<gadget id="calculator">1 / (13/180)</gadget>
<output>180/13 = around 13.846154</output>
<result>C</result> | C | 13.846154 | A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together? | {
"A": "180 / 15",
"B": "180 / 10",
"C": "180 / 13",
"D": "180 / 15",
"E": "180 / 11"
} | divide(const_1, divide(add(add(inverse(12), inverse(30)), inverse(36)), const_2)) | inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|divide(#4,const_2)|divide(const_1,#5)| | "one day work of a and b = 1 / 12 one day work of b and c = 1 / 30 one day work of c and a = 1 / 36 2 ( a + b + c ) = 1 / 12 + 1 / 30 + 1 / 36 2 ( a + b + c ) = 13 / 90 ( a + b + c ) = 13 / 180 number of days required = 180 / 13 days . answer : c" | physics |
math_qa__ldErqyhWRXjnljXj | A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together? Choose the correct choice from the following answers
A) 15 days
B) 12 days
C) 8 days
D) 16 days
E) 9 days | <gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/18) + (1/24)</gadget>
<output>7/72 = around 0.097222</output>
<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">(7/72) + (1/36)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) / 2</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">1 / (1/16)</gadget>
<output>16</output>
<result>D</result> | D | 16 | A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together? | {
"A": "15 days",
"B": "12 days",
"C": "8 days",
"D": "16 days",
"E": "9 days"
} | divide(const_1, divide(add(add(inverse(18), inverse(24)), inverse(36)), const_2)) | inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|divide(#4,const_2)|divide(const_1,#5) | sol . ( a + b ) ' s 1 day ' s work = ( 1 / 18 ) ( b + c ) ' s 1 day ' s work = ( 1 / 24 ) and ( a + c ) ' s 1 day ' s work = ( 1 / 36 ) adding , we get : 2 ( a + b + c ) ' s 1 day ' s work = ¬ ( 1 / 18 + 1 / 24 + 1 / 36 ) = 9 / 72 = 1 / 8 ( a + b + c ) ' s 1 day ' s work = 1 / 16 thus , a , band c together can finish the work in 16 days . ans : d | physics |
math_qa__u7928S1BRIdp2XrC | Let the number which when multiplied by 12 is increased by 198. Choose the correct option
A) 18 B) 20 C) 26 D) 28 E) 30 | <gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">198 / 11</gadget>
<output>18</output>
<result>A</result> | A | 18 | Let the number which when multiplied by 12 is increased by 198. | {
"A": "18",
"B": "20",
"C": "26",
"D": "28",
"E": "30"
} | divide(198, subtract(12, const_1)) | subtract(n0,const_1)|divide(n1,#0)| | "solution let the number be x . then , 12 x - x = 198 ‹ = › 11 x = 198 x ‹ = › 18 . answer a" | general |
math_qa__oIobwk7ir7vytpiL | What is the smallest no. that should be added to 27452 to make it exactly divisible by 9? Choose the most appropriate option
A) 1
B) 3
C) 5
D) 6
E) 9 | <gadget id="calculator">27_452 % 9</gadget>
<output>2</output>
<gadget id="calculator">9 - 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<result>E</result> | E | 9 | What is the smallest no. that should be added to 27452 to make it exactly divisible by 9? | {
"A": "1",
"B": "3",
"C": "5",
"D": "6",
"E": "9"
} | add(subtract(9, reminder(27452, 9)), const_2) | reminder(n0,n1)|subtract(n1,#0)|add(#1,const_2) | if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 2 + 7 + 4 + 5 + 2 = 20 , the next multiple of 9 is 27 . 7 must be added to 27452 to make it divisible by 9 e | general |
math_qa__Deh9GPOVwIRr0N95 | A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 25% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research? Select: A) 8 ° B) 10 ° C) 18 ° D) 33 ° E) 52 ° | <gadget id="calculator">14 + 25</gadget>
<output>39</output>
<gadget id="calculator">39 + 15</gadget>
<output>54</output>
<gadget id="calculator">54 + 29</gadget>
<output>83</output>
<gadget id="calculator">83 + 8</gadget>
<output>91</output>
<gadget id="calculator">100 - 91</gadget>
<output>9</output>
<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">9 * 360</gadget>
<output>3_240</output>
<gadget id="calculator">3_240 / 100</gadget>
<output>162/5 = around 32.4</output>
<result>D</result> | D | 33 | A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 25% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research? | {
"A": "8 °",
"B": "10 °",
"C": "18 °",
"D": "33 °",
"E": "52 °"
} | divide(multiply(subtract(const_100, add(add(add(add(14, 25), 15), 29), 8)), divide(const_3600, const_10)), const_100) | add(n0,n1)|divide(const_3600,const_10)|add(n2,#0)|add(n3,#2)|add(n4,#3)|subtract(const_100,#4)|multiply(#1,#5)|divide(#6,const_100)| | "here all percentage when summed we need to get 100 % . as per data 14 + 25 + 15 + 29 + 8 = 91 % . so remaining 9 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 9 % will be 33 degrees . . imo option d ." | gain |
math_qa__Y9OAetZns9dnZ3I9 | Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is: Select the correct option: A) 9 B) 9.6 C) 10 D) 10.8 E) 7 | <gadget id="calculator">140 + 160</gadget>
<output>300</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">300 / (250/9)</gadget>
<output>54/5 = around 10.8</output>
<result>D</result> | D | 10.8 | Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is: | {
"A": "9",
"B": "9.6",
"C": "10",
"D": "10.8",
"E": "7"
} | divide(add(140, 160), multiply(add(60, 40), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | "explanation : relative speed = ( 60 + 40 ) km / hr = [ 100 x ( 5 / 18 ) ] m / sec = ( 250 / 9 ) m / sec . distance covered in crossing each other = ( 140 + 160 ) m = 300 m . required time = [ 300 x ( 9 / 250 ) ] sec = ( 54 / 5 ) sec = 10.8 sec . answer : d" | physics |
math_qa__Eac4UrdmxqqjJ7IZ | A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio T of revenue from car sales in 1996 to revenue from truck sales in 1996? Choose the correct choice from the following: A) 1 : 2 B) 4 : 5 C) 1 : 1 D) 3 : 2 E) 5 : 3 | <gadget id="calculator">100 + 7</gadget>
<output>107</output>
<gadget id="calculator">100 + 1</gadget>
<output>101</output>
<gadget id="calculator">107 - 101</gadget>
<output>6</output>
<gadget id="calculator">100 - 11</gadget>
<output>89</output>
<gadget id="calculator">101 - 89</gadget>
<output>12</output>
<gadget id="calculator">6 / 12</gadget>
<output>1/2 = around 0.5</output>
<result>A</result> | A | 0.5 | A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio T of revenue from car sales in 1996 to revenue from truck sales in 1996? | {
"A": "1 : 2",
"B": "4 : 5",
"C": "1 : 1",
"D": "3 : 2",
"E": "5 : 3"
} | divide(subtract(add(const_100, 7), add(const_100, 1)), subtract(add(const_100, 1), subtract(const_100, 11))) | add(n3,const_100)|add(n6,const_100)|subtract(const_100,n1)|subtract(#0,#1)|subtract(#1,#2)|divide(#3,#4)| | a . . i have probably solved this question 3 - 4 times by now . . remember the answer . . 1 : 2 | other |
math_qa__z7y7ndeIxFntqyPh | In a recent election, Geoff received 0.5 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3,000 more votes to win the election, what is the value of x ?
Choose the most appropriate option:
A) 50 B) 50.5 C) 56 D) 60 E) 63 | <gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">50 + 0.5</gadget>
<output>50.5</output>
<result>B</result> | B | 50.5 | In a recent election, Geoff received 0.5 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3,000 more votes to win the election, what is the value of x ? | {
"A": "50",
"B": "50.5",
"C": "56",
"D": "60",
"E": "63"
} | add(divide(const_100, const_2), 0.5) | divide(const_100,const_2)|add(n0,#0) | word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 30 votes he needs 3571 more votes so : 30 + 3000 = 3030 now what ' s the problem wants ? ? a x % . . . . . . . . 3030 is what % of total votes 6000 . . . . . . . . translating : 3030 = x / 100 * 6000 - - - x = 50.5 % . . . . . . . . . . b | gain |
math_qa__hdQd1gRMDd6WvzgV | If a^3 is divisible by 240 what is the least possible value of integer a?
Choose the most appropriate option
A) 12 B) 30 C) 60 D) 90 E) 120 | <gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">240 / 8</gadget>
<output>30</output>
<gadget id="calculator">30 * 2</gadget>
<output>60</output>
<result>C</result> | C | 60 | If a^3 is divisible by 240 what is the least possible value of integer a? | {
"A": "12",
"B": "30",
"C": "60",
"D": "90",
"E": "120"
} | multiply(divide(240, power(const_2, const_3)), const_2) | power(const_2,const_3)|divide(n1,#0)|multiply(#1,const_2) | 240 can be written as ( 2 ^ 4 ) * 3 * 5 . for a ^ 3 to be divisible by 240 it should contain atleast 2 ^ 4 and 3 and 5 in its factors . we can leave out option a because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 3 will have 3 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 3 = ( 2 ^ 6 ) * ( 3 ^ 3 ) * ( 5 ^ 3 ) . so it shows that 60 ^ 3 is divisible by 240 and hence the answer . answer : c | general |
math_qa__2oDZiqTd5Ps3eQlf | A goods train runs at a speed of 72 kmph and crosses a 250 m long platform in 26 seconds.What is the length of the goods train? Choose one:
A) 230 m
B) 240 m
C) 260 m
D) 270 m
E) 250 m | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">20 * 26</gadget>
<output>520</output>
<gadget id="calculator">520 - 250</gadget>
<output>270</output>
<result>D</result> | D | 270 | A goods train runs at a speed of 72 kmph and crosses a 250 m long platform in 26 seconds.What is the length of the goods train? | {
"A": "230 m",
"B": "240 m",
"C": "260 m",
"D": "270 m",
"E": "250 m"
} | subtract(multiply(multiply(72, const_0_2778), 26), 250) | multiply(n0,const_0_2778)|multiply(n2,#0)|subtract(#1,n1)| | "s = 250 + x / t 72 * 5 / 18 = 250 + x / 26 x = 270 answer : d" | physics |
math_qa__384eVXg2rbSpR1UA | A metallic sheet is of rectangular shape with dimensions 40m x 30 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is: Choose the most appropriate option: A) 3220 m cube B) 4140 m cube C) 2688 m cube D) 4000 m cube E) none of these | <gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">40 - 16</gadget>
<output>24</output>
<gadget id="calculator">30 - 16</gadget>
<output>14</output>
<gadget id="calculator">24 * 14 * 8</gadget>
<output>2_688</output>
<result>C</result> | C | 2,688 | A metallic sheet is of rectangular shape with dimensions 40m x 30 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is: | {
"A": "3220 m cube",
"B": "4140 m cube",
"C": "2688 m cube",
"D": "4000 m cube",
"E": "none of these"
} | volume_rectangular_prism(subtract(40, multiply(8, const_2)), subtract(30, multiply(8, const_2)), 8) | multiply(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|volume_rectangular_prism(n2,#1,#2) | explanation : l = ( 40 - 16 ) m = 24 m , [ because 8 + 8 = 16 ] b = ( 30 - 16 ) m = 14 m , h = 8 m . volume of the box = ( 24 x 14 x 8 ) m cube = 2688 m cube . option c | geometry |
math_qa__CZheqyQs9Ax0f1Ja | The average of temperatures at noontime from Monday to Friday is 60; the lowest one is 50, what is the possible maximum range of the temperatures? Choose the correct choice from the following choices: A) 50 B) 25 C) 40 D) 45 E) 75 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">60 * 5</gadget>
<output>300</output>
<gadget id="calculator">50 * 4</gadget>
<output>200</output>
<gadget id="calculator">300 - 200</gadget>
<output>100</output>
<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<result>A</result> | A | 50 | The average of temperatures at noontime from Monday to Friday is 60; the lowest one is 50, what is the possible maximum range of the temperatures? | {
"A": "50",
"B": "25",
"C": "40",
"D": "45",
"E": "75"
} | subtract(subtract(multiply(60, add(const_2, const_3)), multiply(50, const_4)), 50) | add(const_2,const_3)|multiply(n1,const_4)|multiply(n0,#0)|subtract(#2,#1)|subtract(#3,n1)| | "average = 60 , sum of temperatures = 60 * 5 = 300 as the min temperature is 50 , max would be 300 - 4 * 50 = 100 - - > the range = 100 ( max ) - 50 ( min ) = 50 answer : a" | general |
math_qa__4dmXdZ3VspQk7Gjg | Find the area of a rhombus one side of which measures 20 cm and one diagonal is 26 cm. Choose the correct answer:
A) 600 cm 2 B) 500 cm 2 C) 516 cm 2 D) 416 cm 2 E) 100 cm 2 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 26</gadget>
<output>13</output>
<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">400 * 4</gadget>
<output>1_600</output>
<gadget id="calculator">26 * 26</gadget>
<output>676</output>
<gadget id="calculator">1_600 - 676</gadget>
<output>924</output>
<gadget id="calculator">924 ** (1/2)</gadget>
<output>2*sqrt(231) = around 30.397368</output>
<gadget id="calculator">13 * (2*sqrt(231))</gadget>
<output>26*sqrt(231) = around 395.165788</output>
<gadget id="calculator">(26*sqrt(231)) + 26</gadget>
<output>26 + 26*sqrt(231) = around 421.165788</output>
<result>D</result> | D | 416 | Find the area of a rhombus one side of which measures 20 cm and one diagonal is 26 cm. | {
"A": "600 cm 2",
"B": "500 cm 2",
"C": "516 cm 2",
"D": "416 cm 2",
"E": "100 cm 2"
} | add(multiply(multiply(divide(const_1, const_2), 26), sqrt(subtract(multiply(multiply(20, 20), const_4), multiply(26, 26)))), 26) | divide(const_1,const_2)|multiply(n0,n0)|multiply(n1,n1)|multiply(n1,#0)|multiply(#1,const_4)|subtract(#4,#2)|sqrt(#5)|multiply(#3,#6)|add(n1,#7)| | "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 26 x 32 ) cm 2 = 416 cm 2 answer : option d" | geometry |
math_qa__QS0oVahUcafD3I4W | What are the last two digits of (301*402*503*604*646*547*448*349)^2 Choose the correct choice from the following answers: A) 96 B) 76 C) 56 D) 36 E) 16 | <gadget id="calculator">100 / 4</gadget>
<output>25</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">1 - 2</gadget>
<output>-1</output>
<gadget id="calculator">6 * (-1)</gadget>
<output>-6</output>
<gadget id="calculator">(-6) * (-1)</gadget>
<output>6</output>
<gadget id="calculator">25 + (-6)</gadget>
<output>19</output>
<gadget id="calculator">19 * 4</gadget>
<output>76</output>
<result>B</result> | B | 76 | What are the last two digits of (301*402*503*604*646*547*448*349)^2 | {
"A": "96",
"B": "76",
"C": "56",
"D": "36",
"E": "16"
} | multiply(add(divide(const_100, const_4), multiply(multiply(multiply(multiply(2, const_3), subtract(const_1, 2)), subtract(const_1, 2)), subtract(const_1, 2))), const_4) | divide(const_100,const_4)|multiply(n8,const_3)|subtract(const_1,n8)|multiply(#1,#2)|multiply(#3,#2)|multiply(#4,#2)|add(#0,#5)|multiply(#6,const_4)| | "( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 448 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 8,9 ; 5 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 48 * 49 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 46 ) ( 56 * 49 ) ) ^ 2 = ( 44 * 44 ) ^ 2 = 36 ^ 2 = 76 hence answer is b" | general |
math_qa__aEDIPe6r5aHf4xVH | if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability t that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ? Choose the correct option:
A) 1 / 2
B) 1 / 3
C) 1 / 4
D) 1 / 5
E) t = 1 / 6 | <gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">24 / 4</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<result>E</result> | E | 0.166667 | if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability t that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ? | {
"A": "1 / 2",
"B": "1 / 3",
"C": "1 / 4",
"D": "1 / 5",
"E": "t = 1 / 6"
} | divide(const_1, divide(factorial(4), multiply(factorial(2), factorial(2)))) | factorial(n0)|factorial(n3)|multiply(#1,#1)|divide(#0,#2)|divide(const_1,#3) | only ( x + y ) ( x - y ) pair will give the form x ^ 2 - ( by ) ^ 2 the probability of selecting these two pairs are 1 / 4 * 1 / 3 = 1 / 12 , assuming x + y is picked first , then x - y , but x - y can be picked first followed by x + y . so the probability t = 1 / 12 * 2 = 1 / 6 ans e | general |
math_qa__R74UcY2XuaINrcVZ | List F consists of 12 consecutive integers. If -4 is the least integer in list F, what is the range of positive integers in list F? Pick:
A) 5 B) 6 C) 7 D) 11 E) 12 | <gadget id="calculator">12 / 2</gadget>
<output>6</output>
<result>B</result> | B | 6 | List F consists of 12 consecutive integers. If -4 is the least integer in list F, what is the range of positive integers in list F? | {
"A": "5",
"B": "6",
"C": "7",
"D": "11",
"E": "12"
} | divide(12, const_2) | divide(n0,const_2) | since - 4 is the least integer in list f , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b . | general |
math_qa__Zk51ke6897ptcGuT | A man is 32 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is? Choose the correct choice from the following: A) 16 B) 19 C) 15 D) 22 E) 30 | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">32 - 2</gadget>
<output>30</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">30 / 1</gadget>
<output>30</output>
<result>E</result> | E | 30 | A man is 32 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is? | {
"A": "16",
"B": "19",
"C": "15",
"D": "22",
"E": "30"
} | divide(subtract(32, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 32 ) + 2 = 2 ( x + 2 ) x + 34 = 2 x + 4 = > x = 30 . answer : e" | general |
math_qa__EmokbcvAlyDlxd2y | A vessel of capacity 30 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution? Choose the correct answer:
A) 14.7
B) 2.9
C) 38.3
D) 78.3
E) 79.3 | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">30 - 9</gadget>
<output>21</output>
<gadget id="calculator">21 / 30</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">(7/10) * 9</gadget>
<output>63/10 = around 6.3</output>
<gadget id="calculator">21 - (63/10)</gadget>
<output>147/10 = around 14.7</output>
<result>A</result> | A | 14.7 | A vessel of capacity 30 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution? | {
"A": "14.7",
"B": "2.9",
"C": "38.3",
"D": "78.3",
"E": "79.3"
} | subtract(subtract(30, multiply(const_3, const_3)), multiply(divide(subtract(30, multiply(const_3, const_3)), 30), multiply(const_3, const_3))) | multiply(const_3,const_3)|subtract(n0,#0)|divide(#1,n0)|multiply(#2,#0)|subtract(#1,#3)| | "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 30 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 30 - 9 ) / 30 ] ^ 2 ( 30 ) = 14.7 litres . answer : option a" | physics |
math_qa__1rybcVDz4AE5LCSq | The tax on a commodity is diminished by 20% but its consumption is increased by 5%. Find the decrease percent in the revenue derived from it? Choose the correct choice from the following answers:
A) 12 % B) 14 % C) 16 % D) 20 % E) 22 % | <gadget id="calculator">100 + 5</gadget>
<output>105</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">105 * 80</gadget>
<output>8_400</output>
<gadget id="calculator">8_400 / 100</gadget>
<output>84</output>
<gadget id="calculator">100 - 84</gadget>
<output>16</output>
<result>C</result> | C | 16 | The tax on a commodity is diminished by 20% but its consumption is increased by 5%. Find the decrease percent in the revenue derived from it? | {
"A": "12 %",
"B": "14 %",
"C": "16 %",
"D": "20 %",
"E": "22 %"
} | subtract(const_100, divide(multiply(add(const_100, 5), subtract(const_100, 20)), const_100)) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)| | "explanation : 100 * 100 = 10000 80 * 105 = 8400 10000 - - - - - - - 1600 100 - - - - - - - ? = 16 % c )" | general |
math_qa__9f9myvHfZmkzHYuQ | How many cubes of 50 cm edge can be put in a cubical box of 1 m edge. Answers.
A) 17 cm B) 10 cm C) 8 cm D) 6 cm E) 7 cm | <gadget id="calculator">1 ** 3</gadget>
<output>1</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 3</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / (1/8)</gadget>
<output>8</output>
<result>C</result> | C | 8 | How many cubes of 50 cm edge can be put in a cubical box of 1 m edge. | {
"A": "17 cm",
"B": "10 cm",
"C": "8 cm",
"D": "6 cm",
"E": "7 cm"
} | divide(volume_cube(1), volume_cube(divide(50, const_100))) | divide(n0,const_100)|volume_cube(n1)|volume_cube(#0)|divide(#1,#2)| | "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 50 * 50 * 50 = 8 number of cubes = 100 â ˆ — 100 â ˆ — 10010 â ˆ — 10 â ˆ — 10 = 1000 note : 1 m = 100 cm answer : c" | physics |
math_qa__BfZwCbbF6D8PxHS7 | We have boxes colored either red or blue. In each blue box there is a fixed number of blueberries. In each red box there is a fixed number of strawberries. If we dispose of one blue box for one additional red box, the total number of berries would increase by 20, and the difference between the total number of strawberries and the total number of blueberries would increase by 80. Each blue box contains how many blueberries? Pick one: A) 25 B) 30 C) 35 D) 40 E) 45 | <gadget id="calculator">80 - 20</gadget>
<output>60</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<result>B</result> | B | 30 | We have boxes colored either red or blue. In each blue box there is a fixed number of blueberries. In each red box there is a fixed number of strawberries. If we dispose of one blue box for one additional red box, the total number of berries would increase by 20, and the difference between the total number of strawberries and the total number of blueberries would increase by 80. Each blue box contains how many blueberries? | {
"A": "25",
"B": "30",
"C": "35",
"D": "40",
"E": "45"
} | divide(subtract(80, 20), const_2) | subtract(n1,n0)|divide(#0,const_2) | let x be the number of blueberries in each blue box . then there are x + 20 strawberries in each red box . x + ( x + 20 ) = 80 x = 30 the answer is b . | general |
math_qa__tSwINIyGhUFBmbCm | A portion of the 90% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 40% solution of chemicals resulted. What part of the original solution was replaced? Choices
A) 5 / 7 B) 6 / 7 C) 9 / 5 D) 13 / 9 E) 13 / 6 | <gadget id="calculator">90 - 40</gadget>
<output>50</output>
<gadget id="calculator">90 - 20</gadget>
<output>70</output>
<gadget id="calculator">50 / 70</gadget>
<output>5/7 = around 0.714286</output>
<result>A</result> | A | 0.714286 | A portion of the 90% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 40% solution of chemicals resulted. What part of the original solution was replaced? | {
"A": "5 / 7",
"B": "6 / 7",
"C": "9 / 5",
"D": "13 / 9",
"E": "13 / 6"
} | divide(subtract(90, 40), subtract(90, 20)) | subtract(n0,n2)|subtract(n0,n1)|divide(#0,#1) | this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.90 ( 1 - x ) + 0.2 * x = 0.4 - - > x = 5 / 7 . answer : a . | gain |
math_qa__I4JmeDuwOU4ggyMu | In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what S percent of all the people in Smithtown are left-handed women? Choose one
A) 50 % B) 40 % C) 25 % D) 20 % E) 10 % | <gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">2 * (4/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">3 * (4/5)</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">3 - (12/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(8/5) - (3/5)</gadget>
<output>1</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>C</result> | C | 25 | In Smithtown, the ratio of right-handed people to left-handed people is 3 to 1 and the ratio of men to women is 3 to 2. If the number of right-handed men is maximized, then what S percent of all the people in Smithtown are left-handed women? | {
"A": "50 %",
"B": "40 %",
"C": "25 %",
"D": "20 %",
"E": "10 %"
} | multiply(divide(subtract(multiply(2, divide(add(3, 1), add(3, 2))), subtract(3, multiply(3, divide(add(3, 1), add(3, 2))))), add(3, 1)), const_100) | add(n0,n1)|add(n0,n3)|divide(#0,#1)|multiply(n3,#2)|multiply(n0,#2)|subtract(n0,#4)|subtract(#3,#5)|divide(#6,#0)|multiply(#7,const_100)| | "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c" | general |
math_qa__QinF1JO40blN9jSl | A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is Answers:
A) 21 years
B) 22 years
C) 23 years
D) 24 years
E) 26 years | <gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">24 - 2</gadget>
<output>22</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">22 / 1</gadget>
<output>22</output>
<result>B</result> | B | 22 | A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is | {
"A": "21 years",
"B": "22 years",
"C": "23 years",
"D": "24 years",
"E": "26 years"
} | divide(subtract(24, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | "explanation : let ' s son age is x , then father age is x + 24 . = > 2 ( x + 2 ) = ( x + 24 + 2 ) = > 2 x + 4 = x + 26 = > x = 22 years option b" | general |
math_qa__eEpGzWCQoc5EtOvN | How many cubes of 10cm edge can be put in a cubical box of 1m edge Pick one:
A) 10 B) 100 C) 1000 D) 10000 E) none of these | <gadget id="calculator">1 ** 3</gadget>
<output>1</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) ** 3</gadget>
<output>1/1_000 = around 0.001</output>
<gadget id="calculator">1 / (1/1_000)</gadget>
<output>1_000</output>
<result>C</result> | C | 1,000 | How many cubes of 10cm edge can be put in a cubical box of 1m edge | {
"A": "10",
"B": "100",
"C": "1000",
"D": "10000",
"E": "none of these"
} | divide(volume_cube(1), volume_cube(divide(10, const_100))) | divide(n0,const_100)|volume_cube(n1)|volume_cube(#0)|divide(#1,#2)| | "explanation : number of cubes = ( 100 x 100 x 100 ) / ( 10 x 10 x 10 ) = 1000 answer : c" | physics |
math_qa__nxJwKJRGTeoqjqM5 | Each of the integers from 1 to 14 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even? Choose the correct choice from the following options:
A) 19 B) 12 C) 11 D) 10 E) 8 | <gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<result>E</result> | E | 8 | Each of the integers from 1 to 14 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even? | {
"A": "19",
"B": "12",
"C": "11",
"D": "10",
"E": "8"
} | add(divide(14, const_2), 1) | divide(n1,const_2)|add(n0,#0)| | "out of the 14 integers : 7 are odd and 7 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 7 odd numbers first 2 . 8 th number will be the first even number so we need to withdraw at least 8 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 8 . ( e )" | general |
math_qa__9D5qiwpw73X8IwPS | I chose a number and divide it by 6. Then I subtracted 15 from the result and got 5. What was the number I chose? Pick:
A) 600 B) 700 C) 120 D) 900 E) none | <gadget id="calculator">15 + 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 6</gadget>
<output>120</output>
<result>C</result> | C | 120 | I chose a number and divide it by 6. Then I subtracted 15 from the result and got 5. What was the number I chose? | {
"A": "600",
"B": "700",
"C": "120",
"D": "900",
"E": "none"
} | multiply(add(15, 5), 6) | add(n1,n2)|multiply(n0,#0)| | "solution : let xx be the number i chose , then x / 6 â ˆ ’ 15 = 5 x / 6 = 20 x = 120 answer c" | general |
math_qa__xAQXyrXvpTOIDeVP | Veena ranks 44rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination? Pick one:
A) 88 B) 108 C) 110 D) 90 E) 117 | <gadget id="calculator">182 - 22</gadget>
<output>160</output>
<gadget id="calculator">44 - 1</gadget>
<output>43</output>
<gadget id="calculator">160 - 43</gadget>
<output>117</output>
<gadget id="calculator">117 - 4</gadget>
<output>113</output>
<result>E</result> | E | 117 | Veena ranks 44rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination? | {
"A": "88",
"B": "108",
"C": "110",
"D": "90",
"E": "117"
} | subtract(subtract(subtract(182, 22), subtract(44, const_1)), const_4) | subtract(n1,n2)|subtract(n0,const_1)|subtract(#0,#1)|subtract(#2,const_4)| | "total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 44 + 1 = 117 answer : e" | other |
math_qa__RG5nWnZB6vJRBquA | An alloy of copper and zinc contains copper and zinc in the ratio 5 : 4. Another alloy of copper and zinc contains copper and zinc in the ratio 3 : 6. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc? Choices:
A) 4 : 1 B) 6 : 1 C) 1 : 3 D) 2 : 1 E) 4 : 1 | <gadget id="calculator">3 + 6</gadget>
<output>9</output>
<gadget id="calculator">5 / 9</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">3 / 6</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(5/9) - (1/2)</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">3 / 9</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/2) - (1/3)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/18) / (1/6)</gadget>
<output>1/3 = around 0.333333</output>
<result>C</result> | C | 0.333333 | An alloy of copper and zinc contains copper and zinc in the ratio 5 : 4. Another alloy of copper and zinc contains copper and zinc in the ratio 3 : 6. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc? | {
"A": "4 : 1",
"B": "6 : 1",
"C": "1 : 3",
"D": "2 : 1",
"E": "4 : 1"
} | divide(subtract(divide(5, add(3, 6)), divide(3, 6)), subtract(divide(3, 6), divide(3, add(3, 6)))) | add(n2,n3)|divide(n2,n3)|divide(n0,#0)|divide(n2,#0)|subtract(#2,#1)|subtract(#1,#3)|divide(#4,#5) | let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 5 x / 9 , and fraction of zinc in alloy _ 1 = 4 x / 9 . similarly , fraction of copper in alloy _ 2 = 3 y / 9 , and fraction of zinc in alloy _ 2 = 6 y / 9 . mixing them , we get copper = 5 x / 9 + 3 y / 9 ; zinc = 4 x / 9 + 6 y / 9 so , 5 x + 3 y = 4 x + 6 y - > x = 3 y - > x / y = 1 / 3 so , they must be mixed in the ratio 1 : 3 answer : c | general |
math_qa__xBDCgdDOQ7brIBHS | Find the area of a parallelogram with base 26 cm and height 14 cm? Options: A) 287 cm 2 B) 887 cm 2 C) 364 cm 2 D) 368 cm 2 E) 668 cm 2 | <gadget id="calculator">26 * 14</gadget>
<output>364</output>
<result>C</result> | C | 364 | Find the area of a parallelogram with base 26 cm and height 14 cm? | {
"A": "287 cm 2",
"B": "887 cm 2",
"C": "364 cm 2",
"D": "368 cm 2",
"E": "668 cm 2"
} | multiply(26, 14) | multiply(n0,n1)| | "area of a parallelogram = base * height = 26 * 14 = 364 cm 2 answer : c" | geometry |
math_qa__By7wRAOAVY1PWd0V | After decreasing 24% in the price of an article costs Rs.532. Find the actual cost of an article? Choose the correct answer.
A) 118 B) 677 C) 700 D) 2688 E) 1991 | <gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>
<gadget id="calculator">532 / (19/25)</gadget>
<output>700</output>
<result>C</result> | C | 700 | After decreasing 24% in the price of an article costs Rs.532. Find the actual cost of an article? | {
"A": "118",
"B": "677",
"C": "700",
"D": "2688",
"E": "1991"
} | divide(532, subtract(const_1, divide(24, const_100))) | divide(n0,const_100)|subtract(const_1,#0)|divide(n1,#1)| | "cp * ( 76 / 100 ) = 532 cp = 7 * 100 = > cp = 700 answer : c" | gain |
math_qa__XV7lC0bt1WmLx1fY | A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 25 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C? Choose the most appropriate option
A) 40
B) 45
C) 108
D) 55
E) 60 | <gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">60 + 120</gadget>
<output>180</output>
<gadget id="calculator">180 / 25</gadget>
<output>36/5 = around 7.2</output>
<gadget id="calculator">(36/5) / 4</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">(9/5) * 60</gadget>
<output>108</output>
<result>C</result> | C | 108 | A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 25 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C? | {
"A": "40",
"B": "45",
"C": "108",
"D": "55",
"E": "60"
} | multiply(divide(divide(add(divide(120, const_2), 120), 25), const_4), divide(120, const_2)) | divide(n0,const_2)|add(n0,#0)|divide(#1,n1)|divide(#2,const_4)|multiply(#3,#0)| | "a - b = 120 miles b - c = 60 miles avg speed = 25 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 25 = 180 / 4 t t = 108 b - c = 108 mph answer c" | physics |
math_qa__1PPnuGrmgLCrCBFq | An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 44.5 meters. How many times did the ball bounce? Choose the correct choice: A) 4 B) 6 C) 7 D) 8 E) 9 | <gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<result>A</result> | A | 4 | An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 44.5 meters. How many times did the ball bounce? | {
"A": "4",
"B": "6",
"C": "7",
"D": "8",
"E": "9"
} | divide(divide(16, const_2), const_2) | divide(n0,const_2)|divide(#0,const_2)| | "division of total diatance travelled will be 16 + 16 + 8 + 4 + 0.5 ans : 4" | general |
math_qa__5FkU5Bq7pDCU9eth | Of 70 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? Pick one:
A) 54 B) 55 C) 59 D) 71 E) 92 | <gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">70 - 37</gadget>
<output>33</output>
<gadget id="calculator">(2/3) * 33</gadget>
<output>22</output>
<gadget id="calculator">37 + 22</gadget>
<output>59</output>
<result>C</result> | C | 59 | Of 70 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? | {
"A": "54",
"B": "55",
"C": "59",
"D": "71",
"E": "92"
} | add(37, multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 37))) | divide(const_1,const_3)|subtract(n0,n1)|subtract(const_1,#0)|multiply(#2,#1)|add(n1,#3)| | "total = 90 thrower = 37 rest = 90 - 37 = 33 left handed = 33 / 3 = 11 right handed = 22 if all thrower are right handed then total right handed is 37 + 22 = 59 so c . 59 is the right answer" | general |
math_qa__RzwcZXDLdrKHMjTj | An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 4 ? Select: A) 1 / 9 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 5 / 6 | <gadget id="calculator">100 / 4</gadget>
<output>25</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 2</gadget>
<output>1/2 = around 0.5</output>
<result>C</result> | C | 0.5 | An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 4 ? | {
"A": "1 / 9",
"B": "1 / 3",
"C": "1 / 2",
"D": "2 / 3",
"E": "5 / 6"
} | multiply(divide(divide(100, 4), 100), const_2.0) | divide(n1,n3)|divide(#0,n1)|multiply(const_2.0,#1)| | "n ( n + 1 ) to be divisible by 4 either n or n + 1 must be a multiples of 4 . in each following group of numbers : { 1 , 2 , 3 , 4 } , { 5 , 6 , 7 , 8 } , . . . , { 97 , 98 , 99 , 100 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 , 4 } n can be : 3 , or 4 . thus , the overall probability is 2 / 4 = 1 / 2 . answer : c ." | general |
math_qa__IAoYomONgAxm4yln | The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is? Select: A) 23 B) 25 C) 27 D) 31 E) 35 | <gadget id="calculator">2 * 120</gadget>
<output>240</output>
<gadget id="calculator">289 - 240</gadget>
<output>49</output>
<gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>
<gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">4 * 120</gadget>
<output>480</output>
<gadget id="calculator">49 + 480</gadget>
<output>529</output>
<gadget id="calculator">529 ** (1/2)</gadget>
<output>23</output>
<result>A</result> | A | 23 | The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is? | {
"A": "23",
"B": "25",
"C": "27",
"D": "31",
"E": "35"
} | sqrt(add(power(sqrt(subtract(289, multiply(const_2, 120))), const_2), multiply(const_4, 120))) | multiply(n0,const_4)|multiply(n0,const_2)|subtract(n1,#1)|sqrt(#2)|power(#3,const_2)|add(#0,#4)|sqrt(#5) | let the numbers be x and y . then , xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . option a | general |
math_qa__XXWzZNxN1MnQ6rIY | out of 9 persons , 8 persons spent rs . 30 each for their meals . the ninth one spent rs . 20 more than the average expenditure of all the 9 . the total money spent by all of them was
Select the correct option
A) rs . 292.50 B) rs . 297.50 C) rs . 298 D) rs . 298.50 E) none of these | <gadget id="calculator">8 * 30</gadget>
<output>240</output>
<gadget id="calculator">9 * 20</gadget>
<output>180</output>
<gadget id="calculator">240 + 180</gadget>
<output>420</output>
<gadget id="calculator">420 / 8</gadget>
<output>105/2 = around 52.5</output>
<gadget id="calculator">240 + (105/2)</gadget>
<output>585/2 = around 292.5</output>
<result>A</result> | A | 292.5 | out of 9 persons , 8 persons spent rs . 30 each for their meals . the ninth one spent rs . 20 more than the average expenditure of all the 9 . the total money spent by all of them was | {
"A": "rs . 292.50",
"B": "rs . 297.50",
"C": "rs . 298",
"D": "rs . 298.50",
"E": "none of these"
} | add(multiply(8, 30), divide(add(multiply(8, 30), multiply(9, 20)), 8)) | multiply(n1,n2)|multiply(n0,n3)|add(#0,#1)|divide(#2,n1)|add(#3,#0) | explanation : let the average expenditure be rs . x then , 9 x = [ 8 × 30 + ( x + 20 ) ] ⇔ 9 x = x + 260 ⇔ x = 32.50 total money spent = 9 x = rs . ( 9 x 32.5 o ) = rs 292 . 50 answer : a | general |
math_qa__bzpUK4Ria8LCIRDn | A driver just filled the car's gas tank with 36 liters of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If the car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance? Choose the correct choice from the following answers: A) 1 B) 1.5 C) 2 D) 2.5 E) 3 | <gadget id="calculator">36 * 5</gadget>
<output>180</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">180 / 90</gadget>
<output>2</output>
<result>C</result> | C | 2 | A driver just filled the car's gas tank with 36 liters of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If the car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance? | {
"A": "1",
"B": "1.5",
"C": "2",
"D": "2.5",
"E": "3"
} | divide(multiply(36, 5), subtract(const_100, 10)) | multiply(n0,n1)|subtract(const_100,n3)|divide(#0,#1)| | "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 36 ) + x = 0.1 ( 36 + x ) 0.9 x = 3.6 - 1.8 = 1.8 x = 2 liters the answer is c ." | general |
math_qa__vO7HJmmrTsl3Y4yH | A cylinder and a cone have the same height and same radius of base. The ratio between the volumes of the cylinder and the cone is: Pick one:
A) 4 : 1
B) 2 : 1
C) 7 : 1
D) 5 : 1
E) 3 : 1 | <gadget id="calculator">pi * (1 ** 2) * 1</gadget>
<output>pi = around 3.141593</output>
<gadget id="calculator">pi * (1 ** 2) * 1 / 3</gadget>
<output>pi/3 = around 1.047198</output>
<gadget id="calculator">pi / (pi/3)</gadget>
<output>3</output>
<result>E</result> | E | 3 | A cylinder and a cone have the same height and same radius of base. The ratio between the volumes of the cylinder and the cone is: | {
"A": "4 : 1",
"B": "2 : 1",
"C": "7 : 1",
"D": "5 : 1",
"E": "3 : 1"
} | divide(volume_cylinder(const_1, const_1), volume_cone(const_1, const_1)) | volume_cone(const_1,const_1)|volume_cylinder(const_1,const_1)|divide(#1,#0) | volume of the cylinder = π r ( power 2 ) h volume of the cone = 1 / 3 π r ( power 2 ) h ( π r ( power 2 ) h ) / ( 1 / 3 π r ( power 2 ) h ) = 3 / 1 = 3 : 1 answer is e . | geometry |
math_qa__0RQ37oOwjCcnVjKw | A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,054. How much did she invest at 5%? Choose the correct choice from the following options.
A) $ 500 B) $ 600 C) $ 700 D) $ 900 E) $ 950 | <gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">50 + 4</gadget>
<output>54</output>
<gadget id="calculator">1_000 + 54</gadget>
<output>1_054</output>
<gadget id="calculator">1_054 - 1_000</gadget>
<output>54</output>
<gadget id="calculator">54 * 100</gadget>
<output>5_400</output>
<gadget id="calculator">5 * 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_400 - 5_000</gadget>
<output>400</output>
<gadget id="calculator">1_000 - 400</gadget>
<output>600</output>
<result>B</result> | B | 600 | A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,054. How much did she invest at 5%? | {
"A": "$ 500",
"B": "$ 600",
"C": "$ 700",
"D": "$ 900",
"E": "$ 950"
} | subtract(multiply(multiply(5, const_2), const_100), subtract(multiply(subtract(add(multiply(multiply(5, const_2), const_100), add(multiply(multiply(5, const_2), 5), const_4)), multiply(multiply(5, const_2), const_100)), const_100), multiply(5, multiply(multiply(5, const_2), const_100)))) | multiply(n1,const_2)|multiply(#0,const_100)|multiply(n1,#0)|add(#2,const_4)|multiply(n1,#1)|add(#3,#1)|subtract(#5,#1)|multiply(#6,const_100)|subtract(#7,#4)|subtract(#1,#8) | et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1054 / 1000 ) - 1 = 0.054 = 5.4 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.054 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.054 - 0.01 x = - 0.006 x = - 0.006 / - 0.01 = 6 / 10 = 60 % so x = 60 % of the 1000 which is 600 answer : b | gain |
math_qa__GsBDlDbMwBlPxls3 | What is the rate percent when the simple interest on Rs.800 amount to Rs.192 in 4 Years? Choose the correct choice from the following answers.
A) 5 % B) 6 % C) 3 % D) 9 % E) 1 % | <gadget id="calculator">100 * 192</gadget>
<output>19_200</output>
<gadget id="calculator">800 * 4</gadget>
<output>3_200</output>
<gadget id="calculator">19_200 / 3_200</gadget>
<output>6</output>
<result>B</result> | B | 6 | What is the rate percent when the simple interest on Rs.800 amount to Rs.192 in 4 Years? | {
"A": "5 %",
"B": "6 %",
"C": "3 %",
"D": "9 %",
"E": "1 %"
} | divide(multiply(const_100, 192), multiply(800, 4)) | multiply(n1,const_100)|multiply(n0,n2)|divide(#0,#1)| | "192 = ( 800 * 4 * r ) / 100 r = 6 % answer : b" | gain |
math_qa__ubkJbzOSepHWNbEf | The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 45 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average? Choose the correct choice: A) 17 B) 18 C) 22 D) 26 E) 36 | <gadget id="calculator">16 * 10</gadget>
<output>160</output>
<gadget id="calculator">160 - 25</gadget>
<output>135</output>
<gadget id="calculator">135 + 45</gadget>
<output>180</output>
<gadget id="calculator">180 / 10</gadget>
<output>18</output>
<result>B</result> | B | 18 | The average of 10 numbers is calculated as 16. It is discovered later on that while calculating the average, the number 45 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average? | {
"A": "17",
"B": "18",
"C": "22",
"D": "26",
"E": "36"
} | divide(add(subtract(multiply(16, 10), 25), 45), 10) | multiply(n0,n1)|subtract(#0,n3)|add(n2,#1)|divide(#2,n0)| | "the total sum of the numbers should be increased by 20 . then the average will increase by 20 / 10 = 2 . the correct average is 18 . the answer is b ." | general |
math_qa__gtbWYkmAevK3uvp9 | Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 70kmph, find the rate at which the train B runs. Pick one: A) 40 B) 60 C) 120 D) 80 E) 105 | <gadget id="calculator">9 / 4</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">(9/4) ** (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">70 * (3/2)</gadget>
<output>105</output>
<result>E</result> | E | 105 | Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 70kmph, find the rate at which the train B runs. | {
"A": "40",
"B": "60",
"C": "120",
"D": "80",
"E": "105"
} | multiply(70, sqrt(divide(9, 4))) | divide(n0,n1)|sqrt(#0)|multiply(n2,#1)| | "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 9 ) = 2 / 3 this gives us that the ratio of the speed of a : speed of b as 2 : 3 . since speed of a is 80 kmph , speed of b must be 70 * ( 3 / 2 ) = 105 kmph e" | physics |
math_qa__KsQa7upODzjdYrle | In a urban village of india named "owlna" , 70% people have refrigerator , 75% people have television , 90% people got computers and 85% got Air-conditionor. how many people(minimum) got all these luxury. Choose one
A) 23 % B) 17 % C) 11 % D) 10 % E) 20 % | <gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">100 - 75</gadget>
<output>25</output>
<gadget id="calculator">30 + 25</gadget>
<output>55</output>
<gadget id="calculator">100 - 90</gadget>
<output>10</output>
<gadget id="calculator">55 + 10</gadget>
<output>65</output>
<gadget id="calculator">100 - 85</gadget>
<output>15</output>
<gadget id="calculator">65 + 15</gadget>
<output>80</output>
<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<result>E</result> | E | 20 | In a urban village of india named "owlna" , 70% people have refrigerator , 75% people have television , 90% people got computers and 85% got Air-conditionor. how many people(minimum) got all these luxury. | {
"A": "23 %",
"B": "17 %",
"C": "11 %",
"D": "10 %",
"E": "20 %"
} | subtract(const_100, add(add(add(subtract(const_100, 70), subtract(const_100, 75)), subtract(const_100, 90)), subtract(const_100, 85))) | subtract(const_100,n0)|subtract(const_100,n1)|subtract(const_100,n2)|subtract(const_100,n3)|add(#0,#1)|add(#4,#2)|add(#5,#3)|subtract(const_100,#6)| | "e 10 % 100 - [ ( 100 - 85 ) + ( 100 - 90 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 30 + 25 + 10 + 15 ) = 100 - 80" | general |
math_qa__hbJKjhtMbDmwZ8Wk | A merchant has selected two items to be placed on sale, one of which currently sells for 20 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item? Choose the correct choice from the following options:
A) 23 %
B) 24 %
C) 25 %
D) 26 %
E) 27 % | <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">(1/5) / (4/5)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>C</result> | C | 25 | A merchant has selected two items to be placed on sale, one of which currently sells for 20 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item? | {
"A": "23 %",
"B": "24 %",
"C": "25 %",
"D": "26 %",
"E": "27 %"
} | multiply(divide(divide(20, const_100), subtract(const_1, divide(20, const_100))), const_100) | divide(n0,const_100)|subtract(const_1,#0)|divide(#0,#1)|multiply(#2,const_100) | expensive item = $ 100 ; cheap item = $ 80 ; we must increase $ 80 to $ 100 , so by $ 20 , which is 25 % increase : ( 100 - 80 ) / 80 = 1 / 4 = 0.25 answer : c . | general |
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