id stringlengths 25 25 | question stringlengths 45 1.01k | chain stringlengths 75 4.11k | result stringclasses 5 values | result_float float64 -4,212 100B | question_without_options stringlengths 6 962 | options dict | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | rationale stringlengths 1 2.74k | category stringclasses 6 values |
|---|---|---|---|---|---|---|---|---|---|---|
math_qa__7OnVTmjCayGycgzP | A sum was put a simple interest at a certain rate for 4 years. Had it been put at 3% higher rate, it would have fetched Rs. 120 more. The sum is:
Choose the correct answer:
A) s . 750 B) s . 1000 C) s . 1250 D) s . 1500 E) s . 1750 | <gadget id="calculator">120 / 4</gadget>
<output>30</output>
<gadget id="calculator">30 / 3</gadget>
<output>10</output>
<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<result>B</result> | B | 1,000 | A sum was put a simple interest at a certain rate for 4 years. Had it been put at 3% higher rate, it would have fetched Rs. 120 more. The sum is: | {
"A": "s . 750",
"B": "s . 1000",
"C": "s . 1250",
"D": "s . 1500",
"E": "s . 1750"
} | multiply(divide(divide(120, 4), 3), const_100) | divide(n2,n0)|divide(#0,n1)|multiply(#1,const_100) | explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 3 ) ã — 4 / 100 â ˆ ’ x ã — r ã — 4 / 100 = 120 â ‡ ’ x ã — 3 ã — 4 / 100 = 120 â ‡ ’ x ã — 4 / 100 = 40 â ‡ ’ 4 x = 4000 â ‡ ’ x = 1000 answer : option b | gain |
math_qa__SG8Jp598O0qYf8ZX | √(14)^2 Pick:
A) 7
B) 14
C) 49
D) 21
E) none of these | <gadget id="calculator">14 ** 2</gadget>
<output>196</output>
<gadget id="calculator">196 ** (1/2)</gadget>
<output>14</output>
<result>B</result> | B | 14 | √(14)^2 | {
"A": "7",
"B": "14",
"C": "49",
"D": "21",
"E": "none of these"
} | sqrt(power(14, 2)) | power(n0,n1)|sqrt(#0)| | "explanation √ ( 14 ) ^ 2 = ? or , ? = 14 answer b" | general |
math_qa__OVoDaaRoBdmqu92v | Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? Choose the correct option:
A) 1040 B) 1050 C) 1055 D) 1065 E) 1075 | <gadget id="calculator">8 * 70</gadget>
<output>560</output>
<gadget id="calculator">9 * 55</gadget>
<output>495</output>
<gadget id="calculator">560 + 495</gadget>
<output>1_055</output>
<result>C</result> | C | 1,055 | Bruce purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? | {
"A": "1040",
"B": "1050",
"C": "1055",
"D": "1065",
"E": "1075"
} | add(multiply(8, 70), multiply(9, 55)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 c" | gain |
math_qa__G8Qtx4ilXqZOtCoH | Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many R women are currently in the room? Choose the correct choice from the following options
A) 12
B) 14
C) 15
D) 24
E) 36 | <gadget id="calculator">14 - 2</gadget>
<output>12</output>
<gadget id="calculator">5 * 12</gadget>
<output>60</output>
<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<gadget id="calculator">15 - 3</gadget>
<output>12</output>
<gadget id="calculator">2 * 12</gadget>
<output>24</output>
<result>D</result> | D | 24 | Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many R women are currently in the room? | {
"A": "12",
"B": "14",
"C": "15",
"D": "24",
"E": "36"
} | multiply(2, subtract(divide(multiply(5, subtract(14, 2)), 4), 3)) | subtract(n4,n2)|multiply(n1,#0)|divide(#1,n0)|subtract(#2,n3)|multiply(n2,#3)| | "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d" | other |
math_qa__Nhu2AfTgaQGySuCz | Paul's salary was decreased by 50% and subsequently increased by
50%.How much percent does he lose? Choose the correct choice from the following options:
A) 0
B) 25
C) 50
D) 30
E) 40 | <gadget id="calculator">50 * 50</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 / 100</gadget>
<output>25</output>
<gadget id="calculator">50 + 25</gadget>
<output>75</output>
<gadget id="calculator">100 - 75</gadget>
<output>25</output>
<result>B</result> | B | 25 | Paul's salary was decreased by 50% and subsequently increased by
50%.How much percent does he lose? | {
"A": "0",
"B": "25",
"C": "50",
"D": "30",
"E": "40"
} | subtract(const_100, add(50, divide(multiply(50, 50), const_100))) | multiply(n0,n0)|divide(#0,const_100)|add(n0,#1)|subtract(const_100,#2) | let the original salary = $ 100 new final salary = 150 % of ( 50 % of rs . 100 ) = $ ( ( 150 / 100 ) * ( 50 / 100 ) * 100 ) = $ 75 . decrease = 25 % answer option b ) 25 . | general |
math_qa__dVJerVvO7KPW4FQZ | A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction U of the sum of the 21 numbers in the list?
Options: A) 1 / 20 B) 1 / 6 C) 1 / 5 D) 4 / 21 E) 5 / 21 | <gadget id="calculator">1 * 1</gadget>
<output>1</output>
<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">5 + 21</gadget>
<output>26</output>
<gadget id="calculator">26 / 4</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">(13/2) * 2</gadget>
<output>13</output>
<gadget id="calculator">13 - 4</gadget>
<output>9</output>
<gadget id="calculator">9 - 3</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<result>B</result> | B | 0.166667 | A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction U of the sum of the 21 numbers in the list? | {
"A": "1 / 20",
"B": "1 / 6",
"C": "1 / 5",
"D": "4 / 21",
"E": "5 / 21"
} | divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3)) | divide(n2,n1)|multiply(const_1,const_1)|add(n0,#0)|divide(#2,n1)|multiply(#3,const_2)|subtract(#4,n1)|subtract(#5,const_3)|divide(#1,#6)| | "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction u of n to the total would be 4 a / 24 a or 1 / 6 answer b" | general |
math_qa__hEnYnUjAD1ksNgUN | If an object travels 80 feet in 4 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet) Choose the correct choice from the following answers: A) 7.25 B) 9.47 C) 11.58 D) 13.64 E) 15.92 | <gadget id="calculator">80 / 5_280</gadget>
<output>1/66 = around 0.015152</output>
<gadget id="calculator">1 / 3_600</gadget>
<output>1/3_600 = around 0.000278</output>
<gadget id="calculator">4 * (1/3_600)</gadget>
<output>1/900 = around 0.001111</output>
<gadget id="calculator">(1/66) / (1/900)</gadget>
<output>150/11 = around 13.636364</output>
<result>D</result> | D | 13.64 | If an object travels 80 feet in 4 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet) | {
"A": "7.25",
"B": "9.47",
"C": "11.58",
"D": "13.64",
"E": "15.92"
} | divide(divide(80, 5280), multiply(4, divide(1, const_3600))) | divide(n0,n3)|divide(n2,const_3600)|multiply(n1,#1)|divide(#0,#2)| | "80 feet / 4 seconds = 20 feet / second ( 20 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 13.64 miles / hour ( approximately ) the answer is d ." | physics |
math_qa__pXgL69L3UVhVDqbl | Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer T between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? Select the correct option: A) 12 B) 15 C) 17 D) t = 18 E) 20 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<result>D</result> | D | 18 | Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer T between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? | {
"A": "12",
"B": "15",
"C": "17",
"D": "t = 18",
"E": "20"
} | multiply(multiply(3, const_2), 3) | multiply(const_2,n0)|multiply(n0,#0)| | "since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ." | physics |
math_qa__ETCBXvpaJp6eGyUk | 12 men can complete a piece of work in 30 days. In how many days can 10 men complete that piece of work? Choose the correct option
A) 23 B) 27 C) 36 D) 27 E) 11 | <gadget id="calculator">30 * 12</gadget>
<output>360</output>
<gadget id="calculator">360 / 10</gadget>
<output>36</output>
<result>C</result> | C | 36 | 12 men can complete a piece of work in 30 days. In how many days can 10 men complete that piece of work? | {
"A": "23",
"B": "27",
"C": "36",
"D": "27",
"E": "11"
} | divide(multiply(30, 12), 10) | multiply(n0,n1)|divide(#0,n2)| | "12 * 30 = 10 * x = > x = 36 days answer : c" | physics |
math_qa__rKwEc8DQhMuWpHuj | If a-b= 4 and a^2+b^2=80, find the value of ab
Choose the correct option
A) 10 B) 12 C) 15 D) 18 E) 32 | <gadget id="calculator">80 ** (1/2)</gadget>
<output>4*sqrt(5) = around 8.944272</output>
<gadget id="calculator">(4*sqrt(5)) - 4</gadget>
<output>-4 + 4*sqrt(5) = around 4.944272</output>
<gadget id="calculator">(-4 + 4*sqrt(5)) / 2</gadget>
<output>-2 + 2*sqrt(5) = around 2.472136</output>
<gadget id="calculator">4 + (-2 + 2*sqrt(5))</gadget>
<output>2 + 2*sqrt(5) = around 6.472136</output>
<gadget id="calculator">(2 + 2*sqrt(5)) * (-2 + 2*sqrt(5))</gadget>
<output>(-2 + 2*sqrt(5))*(2 + 2*sqrt(5)) = around 16</output>
<gadget id="calculator">((-2 + 2*sqrt(5))*(2 + 2*sqrt(5))) * 2</gadget>
<output>2*(-2 + 2*sqrt(5))*(2 + 2*sqrt(5)) = around 32</output>
<result>E</result> | E | 32 | If a-b= 4 and a^2+b^2=80, find the value of ab | {
"A": "10",
"B": "12",
"C": "15",
"D": "18",
"E": "32"
} | multiply(multiply(add(4, divide(subtract(sqrt(80), 4), 2)), divide(subtract(sqrt(80), 4), 2)), 2) | sqrt(n3)|subtract(#0,n0)|divide(#1,n1)|add(n0,#2)|multiply(#3,#2)|multiply(n1,#4)| | "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 80 - 16 = 64 = > ab = 32 answer : e" | general |
math_qa__rKt7oX8r2jo6vQTl | In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 3) lies inside the circle and the point (6,-3) lies outside the circle. If the radius r of the circle r is an integer then r= Choose the correct choice from the following answers: A) 6 B) 5 C) 4 D) 7 E) 2 | <gadget id="calculator">-2</gadget>
<output>-2</output>
<gadget id="calculator">6 - (-2)</gadget>
<output>8</output>
<gadget id="calculator">8 + 6</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>D</result> | D | 7 | In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 3) lies inside the circle and the point (6,-3) lies outside the circle. If the radius r of the circle r is an integer then r= | {
"A": "6",
"B": "5",
"C": "4",
"D": "7",
"E": "2"
} | divide(add(subtract(6, negate(2)), 6), 2) | negate(n0)|subtract(n4,#0)|add(n4,#1)|divide(#2,n0) | can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 6 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 6 , - 3 ) - - - > lesser than 8 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,3 ) - - - - > greater than 6 units . thus the radius is > 6 but < 8 and as it is an integer , the only possible value of radius = 7 units . d is the correct answer . | general |
math_qa__CoKLTL0487ylsdbC | The timing of a college is from 11 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. Choose the correct option.
A) 56 minutes B) 52 minutes C) 30 minutes D) 48 minutes E) 44 minutes | <gadget id="calculator">4.2 * 60</gadget>
<output>252</output>
<gadget id="calculator">252 / 5</gadget>
<output>252/5 = around 50.4</output>
<result>B</result> | B | 52 | The timing of a college is from 11 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture. | {
"A": "56 minutes",
"B": "52 minutes",
"C": "30 minutes",
"D": "48 minutes",
"E": "44 minutes"
} | divide(multiply(4.20, const_60), 5) | multiply(n1,const_60)|divide(#0,n2)| | "explanation : total time a student spends in college = 5 hours 20 minutes = 280 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 280 â € “ 20 ) / 5 = 52 minutes answer b" | physics |
math_qa__3uM09JVJ7ZdG6oM0 | A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5km on foot. His total journey is? Choose the correct choice from the following
A) 130
B) 152
C) 225
D) 260
E) 180 | <gadget id="calculator">20 * 6.5</gadget>
<output>130</output>
<result>A</result> | A | 130 | A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5km on foot. His total journey is? | {
"A": "130",
"B": "152",
"C": "225",
"D": "260",
"E": "180"
} | multiply(20, 6.5) | multiply(n3,n4)| | "let the total journey be x km then , ( 3 x / 5 ) + ( 7 x / 20 ) + 6.5 = x 12 x + 7 x + 20 * 6.5 = 20 x x = 130 km answer is a" | general |
math_qa__G7nSvmFwCCm1qM3p | Find the fraction which has the same ratio to 2/3 that 3/5 has to 6/7 Options.
A) 1 / 5
B) 2 / 22
C) 3 / 4
D) 7 / 15
E) 5 / 6 | <gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">6 / 7</gadget>
<output>6/7 = around 0.857143</output>
<gadget id="calculator">(3/5) / (6/7)</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(7/10) * (2/3)</gadget>
<output>7/15 = around 0.466667</output>
<result>D</result> | D | 0.466667 | Find the fraction which has the same ratio to 2/3 that 3/5 has to 6/7 | {
"A": "1 / 5",
"B": "2 / 22",
"C": "3 / 4",
"D": "7 / 15",
"E": "5 / 6"
} | multiply(divide(divide(3, 5), divide(6, 7)), divide(2, 3)) | divide(n2,n3)|divide(n4,n5)|divide(n0,n1)|divide(#0,#1)|multiply(#3,#2)| | "p : 2 / 3 = 3 / 5 : 6 / 7 as the product of the means is equal to the product of the extremes . p * 6 / 7 = 2 / 3 * 3 / 5 p * 6 / 7 = 6 / 15 p = 7 / 15 = > p = 7 / 15 answer : d" | other |
math_qa__bK5F8m3AARuRTfEA | If the diameter of circle R is 60% of the diameter of circle S, the area of circle R is what percent of the area of circle S? Choose the correct choice from the following answers
A) 50 %
B) 46 %
C) 36 %
D) 26 %
E) 38 % | <gadget id="calculator">pi * (60 ** 2)</gadget>
<output>3600*pi = around 11_309.733553</output>
<gadget id="calculator">(3600*pi) * 100</gadget>
<output>360000*pi = around 1_130_973.355292</output>
<gadget id="calculator">pi * (100 ** 2)</gadget>
<output>10000*pi = around 31_415.926536</output>
<gadget id="calculator">(360000*pi) / (10000*pi)</gadget>
<output>36</output>
<result>C</result> | C | 36 | If the diameter of circle R is 60% of the diameter of circle S, the area of circle R is what percent of the area of circle S? | {
"A": "50 %",
"B": "46 %",
"C": "36 %",
"D": "26 %",
"E": "38 %"
} | divide(multiply(circle_area(60), const_100), circle_area(const_100)) | circle_area(n0)|circle_area(const_100)|multiply(#0,const_100)|divide(#2,#1) | let diameter of circle r , dr = 60 and diameter of circle s , ds = 100 radius of circle r , rr = 30 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 30 / 50 ) ^ 2 = ( 6 / 10 ) ^ 2 = 36 % answer : c | geometry |
math_qa__TLWZyA7lv75gopfq | A small company reduced its faculty by approximately 13 percent to 263 employees. What was the original number of employees?
Pick
A) 182 B) 208 C) 220 D) 224 E) 302 | <gadget id="calculator">100 - 13</gadget>
<output>87</output>
<gadget id="calculator">87 / 100</gadget>
<output>87/100 = around 0.87</output>
<gadget id="calculator">263 / (87/100)</gadget>
<output>26_300/87 = around 302.298851</output>
<result>E</result> | E | 302 | A small company reduced its faculty by approximately 13 percent to 263 employees. What was the original number of employees? | {
"A": "182",
"B": "208",
"C": "220",
"D": "224",
"E": "302"
} | divide(263, divide(subtract(const_100, 13), const_100)) | subtract(const_100,n0)|divide(#0,const_100)|divide(n1,#1) | if x is the original number of employees , then after 13 % reduction in employees number is . 87 x but we are given . 87 x = 263 x = 302 so the original number of employees is 302 correct answer - e | gain |
math_qa__sVSnrwV04QWaBVNp | The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg. What is the weight of the new person? Choose the correct choice from the following answers:
A) 90
B) 65
C) 85
D) 95
E) 80 | <gadget id="calculator">8 * 2.5</gadget>
<output>20</output>
<gadget id="calculator">20 + 70</gadget>
<output>90</output>
<result>A</result> | A | 90 | The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg. What is the weight of the new person? | {
"A": "90",
"B": "65",
"C": "85",
"D": "95",
"E": "80"
} | add(multiply(8, 2.5), 70) | multiply(n0,n1)|add(n2,#0)| | "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 70 = > 20 = x - 70 = > x = 20 + 70 = 90 answer is a ." | general |
math_qa__DktrvC771z26gGi5 | A can contains a mixture of liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter M of liquid A was contained by the can initially?
Choices
A) 10 B) 20 C) 21 D) 25 E) 27 | <gadget id="calculator">7 + 9</gadget>
<output>16</output>
<gadget id="calculator">7 + 5</gadget>
<output>12</output>
<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">(5/12) * 9</gadget>
<output>15/4 = around 3.75</output>
<gadget id="calculator">9 - (15/4)</gadget>
<output>21/4 = around 5.25</output>
<gadget id="calculator">16 * (21/4)</gadget>
<output>84</output>
<gadget id="calculator">9 * 7</gadget>
<output>63</output>
<gadget id="calculator">7 * 5</gadget>
<output>35</output>
<gadget id="calculator">63 - 35</gadget>
<output>28</output>
<gadget id="calculator">84 / 28</gadget>
<output>3</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<result>C</result> | C | 21 | A can contains a mixture of liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter M of liquid A was contained by the can initially? | {
"A": "10",
"B": "20",
"C": "21",
"D": "25",
"E": "27"
} | multiply(7, divide(multiply(add(7, 9), subtract(9, multiply(divide(5, add(7, 5)), 9))), subtract(multiply(9, 7), multiply(7, 5)))) | add(n0,n2)|add(n0,n1)|multiply(n0,n2)|multiply(n0,n1)|divide(n1,#1)|subtract(#2,#3)|multiply(n2,#4)|subtract(n2,#6)|multiply(#0,#7)|divide(#8,#5)|multiply(n0,#9)| | "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) m = 7 * 3 = 21 . c" | physics |
math_qa__U7uthPjB6XN6RX3s | A train running at the speed of 120 km/hr crosses a pole in 12 seconds. What is the length of the train? Choose the correct choice.
A) 200 m
B) 250 m
C) 300 m
D) 350 m
E) 400 m | <gadget id="calculator">120 * 1_000</gadget>
<output>120_000</output>
<gadget id="calculator">120_000 / 3_600</gadget>
<output>100/3 = around 33.333333</output>
<gadget id="calculator">(100/3) * 12</gadget>
<output>400</output>
<result>E</result> | E | 400 | A train running at the speed of 120 km/hr crosses a pole in 12 seconds. What is the length of the train? | {
"A": "200 m",
"B": "250 m",
"C": "300 m",
"D": "350 m",
"E": "400 m"
} | multiply(divide(multiply(120, const_1000), const_3600), 12) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = ( 120 * 5 / 18 ) m / sec = ( 100 / 3 ) m / sec length of the train = ( speed x time ) = ( 100 / 3 * 12 ) m = 400 m . answer : e" | physics |
math_qa__5CISW6OgXL5KExpY | The function f(Y) represents the number of ways that prime numbers can be uniquely summed to form a certain number Y such that Y = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? Choose the correct choice from the following:
A) 4
B) 5
C) 6
D) 7
E) 8 | <gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<result>D</result> | D | 7 | The function f(Y) represents the number of ways that prime numbers can be uniquely summed to form a certain number Y such that Y = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)? | {
"A": "4",
"B": "5",
"C": "6",
"D": "7",
"E": "8"
} | add(add(2, 2), 3) | add(n2,n2)|add(n1,#0) | it is so better to start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d | general |
math_qa__NJ3tw2WswhVrsDHZ | A person can swim in still water at 20 km/h. If the speed of water 12 km/h, how many hours will the man take to swim back against the current for 40km? Choose the correct choice from the following answers.
A) 3 B) 4 C) 5 D) 6 E) 7 | <gadget id="calculator">20 - 12</gadget>
<output>8</output>
<gadget id="calculator">40 / 8</gadget>
<output>5</output>
<result>C</result> | C | 5 | A person can swim in still water at 20 km/h. If the speed of water 12 km/h, how many hours will the man take to swim back against the current for 40km? | {
"A": "3",
"B": "4",
"C": "5",
"D": "6",
"E": "7"
} | divide(40, subtract(20, 12)) | subtract(n0,n1)|divide(n2,#0)| | "m = 20 s = 12 us = 20 - 12 = 8 d = 40 t = 40 / 8 = 5 answer : c" | physics |
math_qa__TDJBUQnxIygSi01T | A person was asked to state his age in years. His reply was , "Take my age 3 years hence, multiply it by 3 and subtract 3 times my age 3 years ago and you will know how old I am." What was the age of the person ? Choose the correct choice from the following choices:
A) 18 B) 92 C) 27 D) 26 E) 19 | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 + 9</gadget>
<output>18</output>
<result>A</result> | A | 18 | A person was asked to state his age in years. His reply was , "Take my age 3 years hence, multiply it by 3 and subtract 3 times my age 3 years ago and you will know how old I am." What was the age of the person ? | {
"A": "18",
"B": "92",
"C": "27",
"D": "26",
"E": "19"
} | add(multiply(3, 3), multiply(3, 3)) | multiply(n0,n1)|add(#0,#0)| | "explanation : let the present age of person be x years . then , 3 ( x + 3 ) - 3 ( x - 3 ) = x < = > ( 3 x + 9 ) - ( 3 x - 9 ) = x < = > x = 18 . . answer : a ) 18" | general |
math_qa__MQHu3FvuKs3pbdFC | If the average of 744, 745, 747, 748, 749, 752, 752, 753, 755 and x is 750, what is the value of x? Choose the correct choice from the following answers.
A) 750
B) 752
C) 754
D) 755
E) 756 | <gadget id="calculator">750 * 10</gadget>
<output>7_500</output>
<gadget id="calculator">744 + 745</gadget>
<output>1_489</output>
<gadget id="calculator">1_489 + 747</gadget>
<output>2_236</output>
<gadget id="calculator">2_236 + 748</gadget>
<output>2_984</output>
<gadget id="calculator">2_984 + 749</gadget>
<output>3_733</output>
<gadget id="calculator">3_733 + 752</gadget>
<output>4_485</output>
<gadget id="calculator">4_485 + 752</gadget>
<output>5_237</output>
<gadget id="calculator">5_237 + 753</gadget>
<output>5_990</output>
<gadget id="calculator">5_990 + 755</gadget>
<output>6_745</output>
<gadget id="calculator">7_500 - 6_745</gadget>
<output>755</output>
<result>D</result> | D | 755 | If the average of 744, 745, 747, 748, 749, 752, 752, 753, 755 and x is 750, what is the value of x? | {
"A": "750",
"B": "752",
"C": "754",
"D": "755",
"E": "756"
} | subtract(multiply(750, const_10), add(add(add(add(add(add(add(add(744, 745), 747), 748), 749), 752), 752), 753), 755)) | add(n0,n1)|multiply(n9,const_10)|add(n2,#0)|add(n3,#2)|add(n4,#3)|add(n5,#4)|add(n5,#5)|add(n7,#6)|add(n8,#7)|subtract(#1,#8)| | "sum of the deviations of the numbers in the set from the mean is always zero 744 , 745 , 747 , 748 , 749 , 752 , 752 , 753 , 755 mean is 750 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 750 + 5 = 755 d" | general |
math_qa__WJr99zJfLZgueBpi | If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is Choose the correct answer
A) 6 B) 12 C) 24 D) 36 E) 48 | <gadget id="calculator">72 / 2</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<result>B</result> | B | 12 | If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is | {
"A": "6",
"B": "12",
"C": "24",
"D": "36",
"E": "48"
} | multiply(sqrt(divide(72, 2)), 2) | divide(n1,n0)|sqrt(#0)|multiply(n0,#1)| | "possible values of n = 12 , 24 , 36 and 48 . but it is 12 that can divide all the possible values of n . if we consider 48 , it will not divide 12 , 24 and 36 . hence , 12 is the value that must divide n . answer : b" | general |
math_qa__T86wNt0ezAZ6ZpBx | Little John had $20.10. He spent $1.05 on sweets and gave to his two friends $1.00 each. How much money was left? Choose the correct choice from the following.
A) $ 17.05 B) $ 17.55 C) $ 17.15 D) $ 17.35 E) $ 17.25 | <gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">1.05 + 2</gadget>
<output>3.05</output>
<gadget id="calculator">20.1 - 3.05</gadget>
<output>17.05</output>
<result>A</result> | A | 17.05 | Little John had $20.10. He spent $1.05 on sweets and gave to his two friends $1.00 each. How much money was left? | {
"A": "$ 17.05",
"B": "$ 17.55",
"C": "$ 17.15",
"D": "$ 17.35",
"E": "$ 17.25"
} | subtract(20.10, add(1.05, add(1.00, 1.00))) | add(n2,n2)|add(n1,#0)|subtract(n0,#1)| | "john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 20.10 - 3.05 = $ 17.05 answer : a" | general |
math_qa__Pf5Cf0jTPYux0qd5 | A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons? Choose the correct answer
A) 1000 B) 1250 C) 1300 D) 1600 E) 1625 | <gadget id="calculator">300 * 100</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 30</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 + 300</gadget>
<output>1_300</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1_300 / (4/5)</gadget>
<output>1_625</output>
<result>E</result> | E | 1,625 | A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons? | {
"A": "1000",
"B": "1250",
"C": "1300",
"D": "1600",
"E": "1625"
} | divide(add(divide(multiply(300, const_100), 30), 300), divide(80, const_100)) | divide(n1,const_100)|multiply(n0,const_100)|divide(#1,n3)|add(n0,#2)|divide(#3,#0)| | "since pumping in additional 300 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 300 = 0.8 * { total } - - > { total } = 1,625 . answer : e ." | general |
math_qa__qS4nTsVfSbD6Lnh1 | the area of sector of a circle whose radius is 12 metro and whose angle at the center is 30 еў is ? Choose the correct answer: A) 35 m 2 B) 36 m 2 C) 37 m 2 D) 38 m 2 E) 40 m 2 | <gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 2</gadget>
<output>22</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">144 * (22/7)</gadget>
<output>3_168/7 = around 452.571429</output>
<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">30 / 360</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(3_168/7) * (1/12)</gadget>
<output>264/7 = around 37.714286</output>
<result>C</result> | C | 37 | the area of sector of a circle whose radius is 12 metro and whose angle at the center is 30 еў is ? | {
"A": "35 m 2",
"B": "36 m 2",
"C": "37 m 2",
"D": "38 m 2",
"E": "40 m 2"
} | multiply(multiply(power(12, const_2), divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), divide(30, divide(const_3600, const_10))) | add(const_3,const_4)|divide(const_3600,const_10)|multiply(const_10,const_2)|power(n0,const_2)|add(#2,const_2)|divide(n1,#1)|divide(#4,#0)|multiply(#6,#3)|multiply(#5,#7)| | "30 / 360 * 22 / 7 * 12 * 12 = 37 m 2 answer : c" | geometry |
math_qa__qbTR4n5SybZUOQLj | If the volume and surface area of a sphere are numerically the same, then its radius is:? Choose the correct choice from the following answers
A) 2 B) 4 C) 1 D) 5 E) 3 | <gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) * pi</gadget>
<output>4*pi/3 = around 4.18879</output>
<gadget id="calculator">4 * pi</gadget>
<output>4*pi = around 12.566371</output>
<gadget id="calculator">(4*pi/3) / (4*pi)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / (1/3)</gadget>
<output>3</output>
<result>E</result> | E | 3 | If the volume and surface area of a sphere are numerically the same, then its radius is:? | {
"A": "2",
"B": "4",
"C": "1",
"D": "5",
"E": "3"
} | divide(const_1, divide(multiply(divide(const_4, const_3), const_pi), multiply(const_4, const_pi))) | divide(const_4,const_3)|multiply(const_4,const_pi)|multiply(#0,const_pi)|divide(#2,#1)|divide(const_1,#3) | 4 / 3 π r ( power 3 ) = 4 π r ( power 2 ) r = 3 answer is e . | geometry |
math_qa__JwaFCNKha4hrSdWG | There are 200 female managers in a certain company. Find the total number T of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers. Choose the correct choice from the following answers:
A) 300 B) t = 400 C) t = 500 D) 600 E) none of these | <gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">200 / (2/5)</gadget>
<output>500</output>
<result>C</result> | C | 500 | There are 200 female managers in a certain company. Find the total number T of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers. | {
"A": "300",
"B": "t = 400",
"C": "t = 500",
"D": "600",
"E": "none of these"
} | divide(200, divide(2, 5)) | divide(n1,n2)|divide(n0,#0)| | "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ." | general |
math_qa__CXBKPsQnuzyYTSng | 60 + 5 * 12 / (180/3) = ? Choose the correct choice from the following choices.
A) 23 B) 78 C) 27 D) 61 E) 81 | <gadget id="calculator">5 * 12</gadget>
<output>60</output>
<gadget id="calculator">180 / 3</gadget>
<output>60</output>
<gadget id="calculator">60 / 60</gadget>
<output>1</output>
<gadget id="calculator">60 + 1</gadget>
<output>61</output>
<result>D</result> | D | 61 | 60 + 5 * 12 / (180/3) = ? | {
"A": "23",
"B": "78",
"C": "27",
"D": "61",
"E": "81"
} | add(60, divide(multiply(5, 12), divide(180, 3))) | divide(n3,n4)|multiply(n1,n2)|divide(#1,#0)|add(n0,#2)| | "explanation : 60 + 5 * 12 / ( 180 / 3 ) = 60 + 5 * 12 / ( 60 ) = 60 + ( 5 * 12 ) / 60 = 60 + 1 = 61 . answer : d" | general |
math_qa__ERvr1VXhnUyxH0tt | To a sugar solution of 3 liters containing 40% sugar, one liter of water is added. The percentage of sugar in the new solution is? Choose the correct choice from the following
A) 20 %
B) 30 %
C) 25 %
D) 15 %
E) 50 % | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 3</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">(6/5) / 4</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>B</result> | B | 30 | To a sugar solution of 3 liters containing 40% sugar, one liter of water is added. The percentage of sugar in the new solution is? | {
"A": "20 %",
"B": "30 %",
"C": "25 %",
"D": "15 %",
"E": "50 %"
} | multiply(divide(multiply(divide(40, const_100), 3), add(3, const_1)), const_100) | add(n0,const_1)|divide(n1,const_100)|multiply(n0,#1)|divide(#2,#0)|multiply(#3,const_100) | quantity of sugar = 40 * 3 / 100 = 1.2 kg new percentage = 1.2 / 4 * 100 = 30 % answer is b | gain |
math_qa__bMzMW7HWdDn19m4n | If 2^98=256L+N , where Land N are integers and 0≤N≤4 , what is the value of N ? Select the correct option: A) 0 B) 1 C) 2 D) 3 E) 4 | <gadget id="calculator">2 ** 98</gadget>
<output>316_912_650_057_057_350_374_175_801_344</output>
<gadget id="calculator">316_912_650_057_057_350_374_175_801_344 % 256</gadget>
<output>0</output>
<result>A</result> | A | 0 | If 2^98=256L+N , where Land N are integers and 0≤N≤4 , what is the value of N ? | {
"A": "0",
"B": "1",
"C": "2",
"D": "3",
"E": "4"
} | reminder(power(2, 98), 256) | power(n0,n1)|reminder(#0,n2) | if 2 ^ 98 = 256 l + n and 0 < = n < = 4 , what is the value of n ? to solve this , note that 2 ^ 8 = 256 , so 2 ^ 98 = 2 ^ [ ( 8 * 12 ) + 2 ] = 4 * [ 256 * 256 * . . . . . . 12 times ] as this is a multiple of 256 , n can only be 0 . answer : a | general |
math_qa__hSoVyFHStywFTkOk | The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle? Choose the correct choice from the following options.
A) 300 square meters B) 400 square meters C) 500 square meters D) 600 square meters E) 700 square meters | <gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">1_800 / 6</gadget>
<output>300</output>
<result>A</result> | A | 300 | The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle? | {
"A": "300 square meters",
"B": "400 square meters",
"C": "500 square meters",
"D": "600 square meters",
"E": "700 square meters"
} | divide(1800, multiply(const_2, const_3)) | multiply(const_2,const_3)|divide(n2,#0) | if l and w be the original length and width of the rectangle and its area is given by l ? w after increase the length becomes 2 l and the width becomes 3 w . the area is then given by ( 2 l ) ? ( 3 w ) and is known . hence ( 2 l ) ? ( 3 w ) = 1800 solve the above equation to find l ? w 6 l ? w = 1800 l ? w = 1800 / 6 = 300 square meters , area of original rectangle correct answer a | geometry |
math_qa__jz0XeIU09xnaLDPF | There are 200 female managers in a certain company. Find the total number Y of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
Choose the correct answer
A) 300
B) y = 400
C) y = 500
D) y = 600
E) none of these | <gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">200 / (2/5)</gadget>
<output>500</output>
<result>C</result> | C | 500 | There are 200 female managers in a certain company. Find the total number Y of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers. | {
"A": "300",
"B": "y = 400",
"C": "y = 500",
"D": "y = 600",
"E": "none of these"
} | divide(200, divide(2, 5)) | divide(n1,n2)|divide(n0,#0)| | "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ." | general |
math_qa__eCqpw5ZatcPRrZ3A | A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000 Choose the correct choice from the following answers
A) 33361667 B) 33391667 C) 33331666 D) 33331668 E) 33331669 | <gadget id="calculator">1_000 + 2_000</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 + 5_000</gadget>
<output>8_000</output>
<gadget id="calculator">8_000 * 2</gadget>
<output>16_000</output>
<gadget id="calculator">16_000 * 4</gadget>
<output>64_000</output>
<gadget id="calculator">64_000 * 2_000</gadget>
<output>128_000_000</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">128_000_000 / 3</gadget>
<output>128_000_000/3 = around 42_666_666.666667</output>
<gadget id="calculator">2_000 * 5_000</gadget>
<output>10_000_000</output>
<gadget id="calculator">(128_000_000/3) - 10_000_000</gadget>
<output>98_000_000/3 = around 32_666_666.666667</output>
<result>C</result> | C | 33,331,666 | A and B r 2 men who enter into business and they invest Rs 1000, Rs 2000respectively. How will they divide the income of Rs 5000 | {
"A": "33361667",
"B": "33391667",
"C": "33331666",
"D": "33331668",
"E": "33331669"
} | subtract(divide(multiply(multiply(multiply(add(add(1000, 2000), 5000), 2), const_4), 2000), add(const_2, const_1)), multiply(2000, 5000)) | add(n1,n2)|add(const_1,const_2)|multiply(n2,n3)|add(n3,#0)|multiply(n0,#3)|multiply(#4,const_4)|multiply(n2,#5)|divide(#6,#1)|subtract(#7,#2) | they invested in the ratio 1 : 2 a ' s share = 1 / 3 * 5000 = 1666 b ' s share = 2 / 3 * 5000 = 3333 answer : c | gain |
math_qa__m2YqapRQrUxEK9VP | If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (4 Ø 2) Ø 3 = ? Choose the correct choice from the following answers:
A) 2 B) 4 C) 8 D) 16 E) 32 | <gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">16 / 8</gadget>
<output>2</output>
<result>A</result> | A | 2 | If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (4 Ø 2) Ø 3 = ? | {
"A": "2",
"B": "4",
"C": "8",
"D": "16",
"E": "32"
} | divide(power(2, divide(power(2, 4), power(2, 2))), power(2, 3)) | power(n0,n2)|power(n0,n0)|power(n0,n4)|divide(#0,#1)|power(n0,#3)|divide(#4,#2) | 4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 4 ø 3 = 2 ^ 4 / 2 ^ 3 = 2 the answer is a . | general |
math_qa__uAylBteKukoiYsuz | A survey was taken among 100 brainiacs. Of those surveyed, twice as many brainiacs likerebus teasers as math teasers. If 18 brainiacs like both rebus teasers and math teasers and 4like neither kind of teaser, how many brainiacs like math teasers but not rebus teasers? Choose the correct option
A) 17 B) 18 C) 19 D) 20 E) 21 | <gadget id="calculator">100 - 4</gadget>
<output>96</output>
<gadget id="calculator">96 + 18</gadget>
<output>114</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">114 / 3</gadget>
<output>38</output>
<gadget id="calculator">38 - 18</gadget>
<output>20</output>
<result>D</result> | D | 20 | A survey was taken among 100 brainiacs. Of those surveyed, twice as many brainiacs likerebus teasers as math teasers. If 18 brainiacs like both rebus teasers and math teasers and 4like neither kind of teaser, how many brainiacs like math teasers but not rebus teasers? | {
"A": "17",
"B": "18",
"C": "19",
"D": "20",
"E": "21"
} | subtract(divide(add(subtract(100, 4), 18), add(const_1, const_2)), 18) | add(const_1,const_2)|subtract(n0,n2)|add(n1,#1)|divide(#2,#0)|subtract(#3,n1) | let x brainiacs like only rebus teasers and y brainiacs like only math teasers . now , x + y = 100 - 18 - 4 = 78 . also given that , x + 18 = 2 ( y + 18 ) x = 2 y + 18 . 78 - y = 2 y + 18 3 y = 60 y = 20 so 20 brainiacs like math teasers but not rebus teasers answer : d | other |
math_qa__Fu1Ek048gPMEj4VN | In a certain pond, 80 fish were caught, tagged, and returned to the pond. A few days later, 80 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? Answers: A) 400 B) 625 C) 3,200 D) 4,500 E) 10,000 | <gadget id="calculator">2 / 80</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">80 / (1/40)</gadget>
<output>3_200</output>
<result>C</result> | C | 3,200 | In a certain pond, 80 fish were caught, tagged, and returned to the pond. A few days later, 80 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? | {
"A": "400",
"B": "625",
"C": "3,200",
"D": "4,500",
"E": "10,000"
} | divide(80, divide(2, 80)) | divide(n2,n1)|divide(n0,#0)| | "total fish = x percentage of second catch = ( 2 / 80 ) * 100 = 2.5 % so , x * 2.5 % = 80 x = 3200 ans c ." | gain |
math_qa__hfiEVaGzyF2UF3rp | x is a positive integer of T less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there? Choose the correct choice from the following answers:
A) 21 B) 22 C) 23 D) 24 E) 25 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">500 - 5</gadget>
<output>495</output>
<gadget id="calculator">495 / 3</gadget>
<output>165</output>
<gadget id="calculator">165 / 7</gadget>
<output>165/7 = around 23.571429</output>
<result>D</result> | D | 24 | x is a positive integer of T less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there? | {
"A": "21",
"B": "22",
"C": "23",
"D": "24",
"E": "25"
} | divide(divide(subtract(500, add(2, 3)), 3), 7) | add(n3,n4)|subtract(n0,#0)|divide(#1,n3)|divide(#2,n1) | took me more than 2 mins to solve . that ' s how i did it . x is between 1 - 499 included . smallest number that can be written as 7 n + 1 ( 7 * 0 + 1 ) is 1 largest number that can be written as 7 n + 1 is ( 7 * 71 + 1 ) is 498 so there are total 72 numbers that can be written as 7 n + 1 because x can also be written as 3 m + 2 , we have to see how many numbers that can be written as 7 n + 1 also can be written as 3 m + 2 7 * 0 + 1 can not be written in the form 3 m + 2 7 * 1 + 1 can be written in the form 3 m + 2 7 * 2 + 1 can not be written in the form 3 m + 2 7 * 3 + 1 can not be written in the form 3 m + 2 7 * 4 + 1 can be written in the form 3 m + 2 here we see a sequence that one out of every 4 numbers can be written as 3 m + 1 72 / 4 = 24 numbers can be written as 3 m + 1 d is the answer | general |
math_qa__SAebWnywbXm5vSv4 | The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1400 per sq. metre. Choose one
A) rs . 15000 B) rs . 15550 C) rs . 15600 D) rs . 28875 E) none of these | <gadget id="calculator">5.5 * 3.75</gadget>
<output>20.625</output>
<gadget id="calculator">1_400 * 20.625</gadget>
<output>28_875</output>
<result>D</result> | D | 28,875 | The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1400 per sq. metre. | {
"A": "rs . 15000",
"B": "rs . 15550",
"C": "rs . 15600",
"D": "rs . 28875",
"E": "none of these"
} | multiply(1400, multiply(5.5, 3.75)) | multiply(n0,n1)|multiply(n2,#0)| | "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 1400 × 20.625 ) = 28875 . answer d" | physics |
math_qa__6yHR7P3Q4XFxSvz5 | In a rectangular box measuring 12 inches by 14 inches by 16 inches if small rectangular boxes measuring 3 inches by 7 inches by 2 inches are arranged in it, what is the max number of boxes that fit into it? Choose one:
A) 23 B) 32 C) 44 D) 15 E) 64 | <gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">14 / 7</gadget>
<output>2</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 8</gadget>
<output>64</output>
<result>E</result> | E | 64 | In a rectangular box measuring 12 inches by 14 inches by 16 inches if small rectangular boxes measuring 3 inches by 7 inches by 2 inches are arranged in it, what is the max number of boxes that fit into it? | {
"A": "23",
"B": "32",
"C": "44",
"D": "15",
"E": "64"
} | multiply(multiply(divide(12, 3), divide(14, 7)), divide(16, 2)) | divide(n2,n5)|divide(n0,n3)|divide(n1,n4)|multiply(#1,#2)|multiply(#0,#3) | the 3 inch side should be aligned to the 12 inch side ( 4 layer ) 7 inch side should be aligned to the 14 inch side . ( 2 layer ) and 2 inch side should be aligned to the 16 inch side . ( 8 layer ) maximum number of rectangles = 4 * 2 * 8 = 64 answer is e | general |
math_qa__R65tw05SzslHuEuO | Ashis's height is 25% more than Babji, by how much percent Babji's height is less than Ashis. Choose the correct choice from the following choices:
A) 30 % B) 25 % C) 75 % D) 20 % E) none of these | <gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">25 / 125</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>D</result> | D | 20 | Ashis's height is 25% more than Babji, by how much percent Babji's height is less than Ashis. | {
"A": "30 %",
"B": "25 %",
"C": "75 %",
"D": "20 %",
"E": "none of these"
} | multiply(divide(25, add(const_100, 25)), const_100) | add(n0,const_100)|divide(n0,#0)|multiply(#1,const_100) | explanation : solution : babji is less than ashis by ( 25 / ( 100 + 25 ) * 100 ) % = 20 % answer : d | general |
math_qa__vJoOgR5hoOqFPSka | What is the difference between the place value and the face value of 7 in the numeral 297832?
Choices.
A) none of these B) 5993 C) 994 D) 5994 E) 995 | <gadget id="calculator">297_832 / 7</gadget>
<output>297_832/7 = around 42_547.428571</output>
<gadget id="calculator">(297_832/7) / 7</gadget>
<output>297_832/49 = around 6_078.204082</output>
<result>B</result> | B | 5,993 | What is the difference between the place value and the face value of 7 in the numeral 297832? | {
"A": "none of these",
"B": "5993",
"C": "994",
"D": "5994",
"E": "995"
} | divide(divide(297832, 7), 7) | divide(n1,n0)|divide(#0,n0) | explanation : place value of 6 = 7000 face value of 6 = 7 difference = 6000 - 7 = 5993 answer : b | general |
math_qa__kTjtGiVDy4uQtJVP | In a graduating class, 40 percent of the students are male. In this class, 40 percent of the male students and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old? Answers: A) 0.9 B) 0.72 C) 0.45 D) 0.35 E) 0.28 | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * (2/5)</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(1/5) * (3/5)</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(4/25) + (3/25)</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">1 - (7/25)</gadget>
<output>18/25 = around 0.72</output>
<result>B</result> | B | 0.72 | In a graduating class, 40 percent of the students are male. In this class, 40 percent of the male students and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old? | {
"A": "0.9",
"B": "0.72",
"C": "0.45",
"D": "0.35",
"E": "0.28"
} | subtract(const_1, add(multiply(divide(40, const_100), divide(40, const_100)), multiply(divide(20, const_100), subtract(const_1, divide(40, const_100))))) | divide(n0,const_100)|divide(n1,const_100)|divide(n2,const_100)|multiply(#0,#1)|subtract(const_1,#0)|multiply(#2,#4)|add(#3,#5)|subtract(const_1,#6)| | "let x be the total number of students . the number students who are younger than 25 is 0.6 * 0.4 x + 0.8 * 0.6 x = 0.72 x the answer is b ." | general |
math_qa__ggHUqAHnyGmAFh4x | If the remainder is 12 when the integer n is divided by 22, what is the remainder when 2n is divided by 11? Select the correct option: A) 0 B) 2 C) 3 D) 6 E) 7 | <gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">24 - 22</gadget>
<output>2</output>
<result>B</result> | B | 2 | If the remainder is 12 when the integer n is divided by 22, what is the remainder when 2n is divided by 11? | {
"A": "0",
"B": "2",
"C": "3",
"D": "6",
"E": "7"
} | subtract(multiply(12, 2), 22) | multiply(n0,n2)|subtract(#0,n1)| | "n = 22 k + 12 2 n = 2 ( 22 k + 12 ) = 4 * 11 k + 24 = 4 * 11 k + 2 * 11 + 2 = 11 j + 2 . the answer is b ." | general |
math_qa__6Nf1Bom2EpiQS9hc | The average marks of a class of 30 students is 40 and that of another class of 50 students is 80. Find the average marks of all the students? Choose the correct choice from the following choices.
A) 52.5 B) 52.9 C) 52.1 D) 52.3 E) 65 | <gadget id="calculator">30 * 40</gadget>
<output>1_200</output>
<gadget id="calculator">50 * 80</gadget>
<output>4_000</output>
<gadget id="calculator">1_200 + 4_000</gadget>
<output>5_200</output>
<gadget id="calculator">30 + 50</gadget>
<output>80</output>
<gadget id="calculator">5_200 / 80</gadget>
<output>65</output>
<result>E</result> | E | 65 | The average marks of a class of 30 students is 40 and that of another class of 50 students is 80. Find the average marks of all the students? | {
"A": "52.5",
"B": "52.9",
"C": "52.1",
"D": "52.3",
"E": "65"
} | divide(add(multiply(30, 40), multiply(50, 80)), add(30, 50)) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)| | "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 80 = 4000 sum of the marks for the class of 80 students = 1200 + 4000 = 5200 average marks of all the students = 5200 / 80 = 65 answer : e" | general |
math_qa__VXO22sbktaHQBCFz | A Jar contains a mixture of A & B in the ratio 4:1. When 10 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially. Choose the correct option: A) 12 B) 15 C) 16 D) 20 E) 25 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">10 * (4/5)</gadget>
<output>8</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(4/5) - (2/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">8 / (2/5)</gadget>
<output>20</output>
<gadget id="calculator">(4/5) * 20</gadget>
<output>16</output>
<result>C</result> | C | 16 | A Jar contains a mixture of A & B in the ratio 4:1. When 10 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially. | {
"A": "12",
"B": "15",
"C": "16",
"D": "20",
"E": "25"
} | multiply(divide(4, add(4, 1)), divide(multiply(10, divide(4, add(4, 1))), subtract(divide(4, add(4, 1)), divide(2, add(2, 3))))) | add(n0,n1)|add(n3,n4)|divide(n0,#0)|divide(n3,#1)|multiply(n2,#2)|subtract(#2,#3)|divide(#4,#5)|multiply(#2,#6) | 10 litres of mixture that is replaced will contain 8 litres of a and 2 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 8 ] / [ k - 2 + 10 ] = 2 / 3 solve for k which is k = 4 so initial volume of liquid a = 4 k = 16 litres answer : c | other |
math_qa__8TLTbO0YgzWA2lIa | at an m & m factory , two types of m & ms are produced , red and blue . the m & ms are transported individually on a conveyor belt . anna is watching the conveyor belt , and has determined that 4 out of every 5 red m & ms are followed by a blue one , while one out of every 6 blue m & ms is followed by a red one . what proportion of the m & ms are red ? Choose the correct choice from the following options: A) 1 / 29 B) 2 / 29 C) 3 / 29 D) 4 / 29 E) 5 / 29 | <gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">4 + 5</gadget>
<output>9</output>
<gadget id="calculator">20 + 9</gadget>
<output>29</output>
<gadget id="calculator">5 / 29</gadget>
<output>5/29 = around 0.172414</output>
<result>E</result> | E | 0.172414 | at an m & m factory , two types of m & ms are produced , red and blue . the m & ms are transported individually on a conveyor belt . anna is watching the conveyor belt , and has determined that 4 out of every 5 red m & ms are followed by a blue one , while one out of every 6 blue m & ms is followed by a red one . what proportion of the m & ms are red ? | {
"A": "1 / 29",
"B": "2 / 29",
"C": "3 / 29",
"D": "4 / 29",
"E": "5 / 29"
} | divide(5, add(multiply(4, 5), add(4, 5))) | add(n0,n1)|multiply(n0,n1)|add(#0,#1)|divide(n1,#2) | suppose that the fraction of red m & ms is fr and the fraction of blue m & ms is fb . then the probability that anna sees a red one emerge next is fr . this probabil - ity can also be expressed using conditional probabilities as fr = p ( blue ) p ( red after blue ) + p ( red ) p ( red after red ) , or fr = fb ( 1 = 6 ) + fr ( 1 = 5 ) . likewise , we find fb = fr ( 4 = 5 ) + fb ( 5 = 6 ) . solving the system of equations gives fb = 24 29 and fr = 5 / 29 correct answer e | other |
math_qa__63MqDRSjarfW7ZAl | Ravi and Kavi start a business by investing ₹ 5000 and ₹ 72000, respectively. Find the ratio of their profits at the end of year. Choose the correct choice from the following:
A) 2 : 72 B) 5 : 72 C) 7 : 72 D) 1 : 72 E) 3 : 72 | <gadget id="calculator">5_000 / 72_000</gadget>
<output>5/72 = around 0.069444</output>
<result>B</result> | B | 0.069444 | Ravi and Kavi start a business by investing ₹ 5000 and ₹ 72000, respectively. Find the ratio of their profits at the end of year. | {
"A": "2 : 72",
"B": "5 : 72",
"C": "7 : 72",
"D": "1 : 72",
"E": "3 : 72"
} | divide(5000, 72000) | divide(n0,n1)| | "ratio of profit = ratio of investments = 5000 : 72000 = 5 : 72 answer : b" | gain |
math_qa__9IxLgYoNnOWQ3wHc | By selling 18 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Choose the correct choice from the following options: A) 8 B) 12 C) 6 D) 4 E) 9 | <gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">120 * (1/80)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">1 / (3/2)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 18</gadget>
<output>12</output>
<result>B</result> | B | 12 | By selling 18 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%? | {
"A": "8",
"B": "12",
"C": "6",
"D": "4",
"E": "9"
} | multiply(divide(const_1, multiply(add(const_100, 20), divide(const_1, subtract(const_100, 20)))), 18) | add(n2,const_100)|subtract(const_100,n1)|divide(const_1,#1)|multiply(#0,#2)|divide(const_1,#3)|multiply(n0,#4)| | "80 % - - - 18 120 % - - - ? 80 / 120 * 18 = 12 answer : b" | gain |
math_qa__jT2lyua8Rdf7QsNP | If x is a sum of all even integers on the interval 13...63 and y is their number, what is the GCD (x, y)? Choose the correct choice from the following.
A) 1 B) 13 C) 26 D) 25 E) 1014 | <gadget id="calculator">13 - 10</gadget>
<output>3</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<result>D</result> | D | 25 | If x is a sum of all even integers on the interval 13...63 and y is their number, what is the GCD (x, y)? | {
"A": "1",
"B": "13",
"C": "26",
"D": "25",
"E": "1014"
} | multiply(add(subtract(13, const_10), const_2), add(subtract(13, const_10), const_2)) | subtract(n0,const_10)|add(#0,const_2)|multiply(#1,#1) | x = 14 + 16 + . . . + 62 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 62 ) / 2 * 25 = 38 * 25 . gcd of 25 and 39 * 25 is 25 . answer : d . | general |
math_qa__hhJMwSTuyUVE29xR | Joe invested a certain sum of money in a simple interest bond whose value grew to $260 at the end of 3 years and to $360 at the end of another 5 years. What was the rate of interest in which he invested his sum? Select:
A) 6 % B) 8 % C) 10 % D) 12 % E) 15 % | <gadget id="calculator">360 - 260</gadget>
<output>100</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">260 - 60</gadget>
<output>200</output>
<gadget id="calculator">20 / 200</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>C</result> | C | 10 | Joe invested a certain sum of money in a simple interest bond whose value grew to $260 at the end of 3 years and to $360 at the end of another 5 years. What was the rate of interest in which he invested his sum? | {
"A": "6 %",
"B": "8 %",
"C": "10 %",
"D": "12 %",
"E": "15 %"
} | multiply(divide(divide(subtract(360, 260), 5), subtract(260, multiply(divide(subtract(360, 260), 5), 3))), const_100) | subtract(n2,n0)|divide(#0,n3)|multiply(n1,#1)|subtract(n0,#2)|divide(#1,#3)|multiply(#4,const_100)| | "in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 260 - $ 60 = 200 . the interest rate is $ 20 / $ 200 = 10 % the answer is c ." | gain |
math_qa__0LNqFLcFHgJp6fyT | a cuban cigar would cost 3 dollar less than 1.5 times a french cigar , had the french cigar cost 0.7 dollar less than it does now . an arabian cigar costs 50 cents more than 1.5 times the cuban cigar . the 3 cigars together cost 74.7 dollars . what is the price of the french cigar ? Choose the correct option: A) 19.7 $ . B) 23 $ . C) 14.7 $ . D) 35 $ . E) 37.4 $ . | <gadget id="calculator">1.5 * 0.7</gadget>
<output>1.05</output>
<gadget id="calculator">1.05 + 3</gadget>
<output>4.05</output>
<gadget id="calculator">1.5 * 4.05</gadget>
<output>6.075</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">6.075 - (1/2)</gadget>
<output>5.575</output>
<gadget id="calculator">4.05 + 5.575</gadget>
<output>9.625</output>
<gadget id="calculator">74.7 - 9.625</gadget>
<output>65.075</output>
<gadget id="calculator">1.5 * 1.5</gadget>
<output>2.25</output>
<gadget id="calculator">1.5 + 2.25</gadget>
<output>3.75</output>
<gadget id="calculator">3.75 + 1</gadget>
<output>4.75</output>
<gadget id="calculator">65.075 / 4.75</gadget>
<output>13.7</output>
<gadget id="calculator">13.7 + 0.7</gadget>
<output>14.4</output>
<result>C</result> | C | 14.7 | a cuban cigar would cost 3 dollar less than 1.5 times a french cigar , had the french cigar cost 0.7 dollar less than it does now . an arabian cigar costs 50 cents more than 1.5 times the cuban cigar . the 3 cigars together cost 74.7 dollars . what is the price of the french cigar ? | {
"A": "19.7 $ .",
"B": "23 $ .",
"C": "14.7 $ .",
"D": "35 $ .",
"E": "37.4 $ ."
} | add(divide(subtract(74.7, add(add(multiply(1.5, 0.7), 3), subtract(multiply(1.5, add(multiply(1.5, 0.7), 3)), divide(50, const_100)))), add(add(1.5, multiply(1.5, 1.5)), const_1)), 0.7) | divide(n3,const_100)|multiply(n1,n2)|multiply(n1,n1)|add(n0,#1)|add(n1,#2)|add(#4,const_1)|multiply(n1,#3)|subtract(#6,#0)|add(#3,#7)|subtract(n6,#8)|divide(#9,#5)|add(n2,#10) | the three cigars together cost 74.7 dollars . if each cost the same , they would have cost a little less than 25 dollars each . from the given data we know french cigar < cuban cigar < arabic cigar and each is more expensive 1.5 times . therefore eliminate options a , d , e straightaway . since french cigar is at least 1.5 times cheaper we know b can not be the answer . therefore c is the answer . | general |
math_qa__rP6xV1c1cTfmFXsJ | The salary of a worker is first increased by 15% and afterwards reduced by 15%. What is the net change in the worker's salary? Choose the correct answer:
A) 5.25 % increase B) 5.25 % decrease C) 2.25 % increase D) 2.25 % decrease E) no change | <gadget id="calculator">15 + 100</gadget>
<output>115</output>
<gadget id="calculator">115 * 15</gadget>
<output>1_725</output>
<gadget id="calculator">1_725 / 100</gadget>
<output>69/4 = around 17.25</output>
<gadget id="calculator">115 - (69/4)</gadget>
<output>391/4 = around 97.75</output>
<gadget id="calculator">100 - (391/4)</gadget>
<output>9/4 = around 2.25</output>
<result>D</result> | D | 2.25 | The salary of a worker is first increased by 15% and afterwards reduced by 15%. What is the net change in the worker's salary? | {
"A": "5.25 % increase",
"B": "5.25 % decrease",
"C": "2.25 % increase",
"D": "2.25 % decrease",
"E": "no change"
} | subtract(const_100, subtract(add(15, const_100), divide(multiply(add(15, const_100), 15), const_100))) | add(n0,const_100)|multiply(n0,#0)|divide(#1,const_100)|subtract(#0,#2)|subtract(const_100,#3)| | "let x be the original salary . the final salary is 0.85 ( 1.15 x ) = 0.9775 x the answer is d ." | gain |
math_qa__YPw1jp281RpKVdBY | A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? Options: A) 2.0 B) 4.0 C) 5.0 D) 6.0 E) 8.0 | <gadget id="calculator">100 / 25</gadget>
<output>4</output>
<result>B</result> | B | 4 | A company decreased the price of its main product by 25%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? | {
"A": "2.0",
"B": "4.0",
"C": "5.0",
"D": "6.0",
"E": "8.0"
} | divide(const_100, 25) | divide(const_100,n0)| | "for the total revenue to remain the same when the price is one fourth , the number of products sold must four times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 25 % = 4.0 answer : b" | general |
math_qa__F4rQKpjLtXxbsyFn | A firm is comprised of partners and associates in a ratio of 2:63. If 35 more associates were hired, the ratio of partners to associates would be 1:34. How many partners are currently in the firm? Choices:
A) 12 B) 14 C) 16 D) 18 E) 20 | <gadget id="calculator">34 * 2</gadget>
<output>68</output>
<gadget id="calculator">68 - 63</gadget>
<output>5</output>
<gadget id="calculator">35 / 5</gadget>
<output>7</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<result>B</result> | B | 14 | A firm is comprised of partners and associates in a ratio of 2:63. If 35 more associates were hired, the ratio of partners to associates would be 1:34. How many partners are currently in the firm? | {
"A": "12",
"B": "14",
"C": "16",
"D": "18",
"E": "20"
} | multiply(divide(35, subtract(multiply(34, 2), 63)), 2) | multiply(n0,n4)|subtract(#0,n1)|divide(n2,#1)|multiply(n0,#2)| | "the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 7 of the increase in 35 associates . the ratio changed from 14 : 441 to 14 : 476 . thus the number of partners is 14 . the answer is b ." | other |
math_qa__HMI33Le3bMhOnnut | Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 9 inches long, how wide is Jordan's rectangle, in inches? Choose the correct choice from the following answers:
A) 17 B) 18 C) 19 D) 20 E) 21 | <gadget id="calculator">12 * 15</gadget>
<output>180</output>
<gadget id="calculator">180 / 9</gadget>
<output>20</output>
<result>D</result> | D | 20 | Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 12 inches by 15 inches and Jordan's rectangle is 9 inches long, how wide is Jordan's rectangle, in inches? | {
"A": "17",
"B": "18",
"C": "19",
"D": "20",
"E": "21"
} | divide(rectangle_area(12, 15), 9) | rectangle_area(n0,n1)|divide(#0,n2)| | "area of first rectangle is 12 * 15 = 180 hence area of second would be 9 x = 180 x x = 20 answer is d" | geometry |
math_qa__YlIpxkKUV9ajkBj2 | The average of runs of a cricket player of 10 innings was 30. How many runs must he make in his next innings so as to increase his average of runs by 4? Choose one
A) 87 B) 74 C) 10 D) 76 E) 17 | <gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">4 + 30</gadget>
<output>34</output>
<gadget id="calculator">11 * 34</gadget>
<output>374</output>
<gadget id="calculator">10 * 30</gadget>
<output>300</output>
<gadget id="calculator">374 - 300</gadget>
<output>74</output>
<result>B</result> | B | 74 | The average of runs of a cricket player of 10 innings was 30. How many runs must he make in his next innings so as to increase his average of runs by 4? | {
"A": "87",
"B": "74",
"C": "10",
"D": "76",
"E": "17"
} | subtract(multiply(add(10, const_1), add(4, 30)), multiply(10, 30)) | add(n0,const_1)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | "average after 11 innings = 34 required number of runs = ( 34 * 11 ) - ( 30 * 10 ) = 374 - 300 = 74 . answer : b" | general |
math_qa__Fe5v8Ezy2zYxpOsf | If 30% of a number is equal to one-fourth of another number, what is the ratio of first number to the second number? Answers:
A) 4 : 7
B) 6 : 5
C) 1 : 2
D) 2 : 3
E) 5 : 6 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/4) / (3/10)</gadget>
<output>5/6 = around 0.833333</output>
<result>E</result> | E | 0.833333 | If 30% of a number is equal to one-fourth of another number, what is the ratio of first number to the second number? | {
"A": "4 : 7",
"B": "6 : 5",
"C": "1 : 2",
"D": "2 : 3",
"E": "5 : 6"
} | divide(divide(const_1, const_4), divide(30, const_100)) | divide(const_1,const_4)|divide(n0,const_100)|divide(#0,#1) | let 30 % of a = 1 / 4 b . then , 30 a / 100 = 1 b / 4 = > 3 a / 10 = 1 b / 4 a / b = ( 1 / 4 * 10 / 3 ) = 5 / 6 a : b = 5 : 6 . answer : e | general |
math_qa__6RGEysKd7VJU341l | A cistern is two-third full of water. Pipe A can fill the remaining part in 12 minutes and pipe B in 8 minutes. Once the cistern is emptied, how much time will they take to fill it together completely? Choose the correct choice from the following choices: A) 12 minutes B) 12.5 min C) 14.4 min D) 10.2 min E) 14.66 min | <gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">36 * 24</gadget>
<output>864</output>
<gadget id="calculator">36 + 24</gadget>
<output>60</output>
<gadget id="calculator">864 / 60</gadget>
<output>72/5 = around 14.4</output>
<result>C</result> | C | 14.4 | A cistern is two-third full of water. Pipe A can fill the remaining part in 12 minutes and pipe B in 8 minutes. Once the cistern is emptied, how much time will they take to fill it together completely? | {
"A": "12 minutes",
"B": "12.5 min",
"C": "14.4 min",
"D": "10.2 min",
"E": "14.66 min"
} | divide(multiply(multiply(12, const_3), multiply(8, const_3)), add(multiply(12, const_3), multiply(8, const_3))) | multiply(n0,const_3)|multiply(n1,const_3)|add(#0,#1)|multiply(#0,#1)|divide(#3,#2) | as pipe a takes 12 min . to fill remaining one - third it takes 36 min . to fill completely . similarly pipe b takes 24 min . to fill completely so , total time taken by both together is reciprocal of : ( 1 / 36 ) + ( 1 / 24 ) = 5 / 72 ans : 14.4 min . answer : c | physics |
math_qa__YjjwIAG6TiusRkVZ | When a student Joe, weighing 44 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?
Choices: A) 5.5 kg B) 11 kg C) 30 kg D) 36.5 kg E) 7 kg | <gadget id="calculator">30 + 1</gadget>
<output>31</output>
<gadget id="calculator">44 - 31</gadget>
<output>13</output>
<gadget id="calculator">30 * 13</gadget>
<output>390</output>
<gadget id="calculator">390 + 44</gadget>
<output>434</output>
<gadget id="calculator">13 - 1</gadget>
<output>12</output>
<gadget id="calculator">12 * 30</gadget>
<output>360</output>
<gadget id="calculator">434 - 360</gadget>
<output>74</output>
<gadget id="calculator">74 / 2</gadget>
<output>37</output>
<gadget id="calculator">44 - 37</gadget>
<output>7</output>
<result>E</result> | E | 7 | When a student Joe, weighing 44 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe? | {
"A": "5.5 kg",
"B": "11 kg",
"C": "30 kg",
"D": "36.5 kg",
"E": "7 kg"
} | subtract(44, divide(subtract(add(multiply(30, subtract(44, add(30, 1))), 44), multiply(subtract(subtract(44, add(30, 1)), 1), 30)), const_2)) | add(n1,n2)|subtract(n0,#0)|multiply(n1,#1)|subtract(#1,n2)|add(n0,#2)|multiply(n1,#3)|subtract(#4,#5)|divide(#6,const_2)|subtract(n0,#7)| | "after two persons leave the group the average remains the same . that means the weight of the two persons = 44 + 30 = 74 so , the average the two persons = 37 that gives the answer 44 - 37 = 7 answer e" | general |
math_qa__SZsHjZN5kBRcikSq | 70 is what percent of 125?
Choose the most appropriate option:
A) 35 % B) 40 % C) 45 % D) 50 % E) 56 % | <gadget id="calculator">70 / 125</gadget>
<output>14/25 = around 0.56</output>
<gadget id="calculator">(14/25) * 100</gadget>
<output>56</output>
<result>E</result> | E | 56 | 70 is what percent of 125? | {
"A": "35 %",
"B": "40 %",
"C": "45 %",
"D": "50 %",
"E": "56 %"
} | multiply(divide(70, 125), const_100) | divide(n0,n1)|multiply(#0,const_100)| | 70 / 125 × 100 = 56 % answer : e | gain |
math_qa__0n7WBeA0lDyb3lvj | If a2 - b2 = 8 and a*b = 2, find a4 + b4. Choose the correct choice from the following:
A) 62
B) 72
C) 82
D) 92
E) 62 | <gadget id="calculator">8 ** 2</gadget>
<output>64</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">64 + 8</gadget>
<output>72</output>
<result>B</result> | B | 72 | If a2 - b2 = 8 and a*b = 2, find a4 + b4. | {
"A": "62",
"B": "72",
"C": "82",
"D": "92",
"E": "62"
} | add(power(8, 2), multiply(power(2, 2), 2)) | power(n3,n0)|power(n2,n0)|multiply(#0,n0)|add(#2,#1)| | "a 2 - b 2 = 8 : given a 4 + b 4 - 2 a 2 b 2 = 82 : square both sides and expand . a * b = 2 : given a 2 b 2 = 22 : square both sides . a 4 + b 4 - 2 ( 4 ) = 82 : substitute a 4 + b 4 = 72 correct answer b" | general |
math_qa__EMjG45GXojDJMMh8 | When positive integer X is divided by positive integer Y, the remainder is 5.76. If X/Y = 96.12, what is the value of Y? Options: A) 96 B) 75 C) 48 D) 25 E) 12 | <gadget id="calculator">floor(96.12)</gadget>
<output>96</output>
<gadget id="calculator">96.12 - 96</gadget>
<output>0.12</output>
<gadget id="calculator">5.76 / 0.12</gadget>
<output>48</output>
<result>C</result> | C | 48 | When positive integer X is divided by positive integer Y, the remainder is 5.76. If X/Y = 96.12, what is the value of Y? | {
"A": "96",
"B": "75",
"C": "48",
"D": "25",
"E": "12"
} | divide(5.76, subtract(96.12, floor(96.12))) | floor(n1)|subtract(n1,#0)|divide(n0,#1)| | "when positive integer x is divided by positive integer y , the remainder is 5.76 - - > x = qy + 5.76 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 5.76 - - > y = 48 . answer : c ." | general |
math_qa__1zLBJxoTsWc2zFDP | Timothy leaves home for school, riding his bicycle at a rate of 6 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 36 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks
Choose the correct answer: A) 1 / 3 B) 9 / 5 C) 4 D) 9 E) 12 | <gadget id="calculator">36 - 6</gadget>
<output>30</output>
<gadget id="calculator">4 * 30</gadget>
<output>120</output>
<gadget id="calculator">6 / 120</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 36</gadget>
<output>9/5 = around 1.8</output>
<result>B</result> | B | 1.8 | Timothy leaves home for school, riding his bicycle at a rate of 6 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 36 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks | {
"A": "1 / 3",
"B": "9 / 5",
"C": "4",
"D": "9",
"E": "12"
} | multiply(divide(6, multiply(const_4, subtract(36, 6))), 36) | subtract(n1,n0)|multiply(#0,const_4)|divide(n0,#1)|multiply(n1,#2) | in 15 mins , timothy travels = 6 / 4 miles . now , let his mother takes x hours to reach him , traveling at 36 mph . so , 36 x = 6 x + 6 / 4 x = 1 / 20 hrs . thus , the distance traveled by his mother to reach = 36 * 1 / 20 = 9 / 5 miles . ans b | physics |
math_qa__RV3jifEBRhxHzZfN | Two trains of equal length, running with the speeds of 60 and 40 kmph, take 55 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Choose the correct choice from the following answers:
A) 10 sec B) 16 sec C) 13 sec D) 67 sec E) 11 sec | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">(5/18) * 20</gadget>
<output>50/9 = around 5.555556</output>
<gadget id="calculator">(50/9) * 55</gadget>
<output>2_750/9 = around 305.555556</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">(5/18) * 100</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">1 / (250/9)</gadget>
<output>9/250 = around 0.036</output>
<gadget id="calculator">(2_750/9) * (9/250)</gadget>
<output>11</output>
<result>E</result> | E | 11 | Two trains of equal length, running with the speeds of 60 and 40 kmph, take 55 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? | {
"A": "10 sec",
"B": "16 sec",
"C": "13 sec",
"D": "67 sec",
"E": "11 sec"
} | multiply(multiply(multiply(const_0_2778, subtract(60, 40)), 55), inverse(multiply(const_0_2778, add(60, 40)))) | add(n0,n1)|subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(#1,const_0_2778)|inverse(#2)|multiply(n2,#3)|multiply(#4,#5)| | "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 55 d = 55 * 100 / 18 = 2750 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2750 / 9 * 18 / 500 = 11 sec answer : e" | physics |
math_qa__WXKoWzUvSVpTjdfL | The instructions state that Cheryl needs 5/9 square yards of one type of material and 1/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 8/24 square yards left that she did not use. What is the total amount of square yards of material Cheryl used? Select
A) 1 / 12 B) 1 / 9 C) 2 / 3 D) 5 / 9 E) 2 1 / 9 | <gadget id="calculator">5 / 9</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(5/9) + (1/3)</gadget>
<output>8/9 = around 0.888889</output>
<gadget id="calculator">8 / 24</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(8/9) - (1/3)</gadget>
<output>5/9 = around 0.555556</output>
<result>D</result> | D | 0.555556 | The instructions state that Cheryl needs 5/9 square yards of one type of material and 1/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 8/24 square yards left that she did not use. What is the total amount of square yards of material Cheryl used? | {
"A": "1 / 12",
"B": "1 / 9",
"C": "2 / 3",
"D": "5 / 9",
"E": "2 1 / 9"
} | subtract(add(divide(5, 9), divide(1, 3)), divide(8, 24)) | divide(n0,n1)|divide(n2,n3)|divide(n4,n5)|add(#0,#1)|subtract(#3,#2)| | "total bought = 5 / 9 + 1 / 3 left part 8 / 24 - - - > 1 / 3 so used part 5 / 9 + 1 / 3 - 1 / 3 = 5 / 9 answer : d" | general |
math_qa__7qCkWfAmLUqdKTqC | What is the value of n if the sum of the consecutive odd intergers Q from 1 to n equals 169? Choose one:
A) 47 B) 25 C) 37 D) 33 E) 29 | <gadget id="calculator">169 ** (1/2)</gadget>
<output>13</output>
<gadget id="calculator">13 * 2</gadget>
<output>26</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">26 - 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<result>B</result> | B | 25 | What is the value of n if the sum of the consecutive odd intergers Q from 1 to n equals 169? | {
"A": "47",
"B": "25",
"C": "37",
"D": "33",
"E": "29"
} | add(subtract(multiply(sqrt(169), const_2), multiply(const_2, 1)), 1) | multiply(n0,const_2)|sqrt(n1)|multiply(#1,const_2)|subtract(#2,#0)|add(n0,#3)| | "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ." | general |
math_qa__6RYDsmS229ramIFe | How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 30% solution?
Choose the correct choice from the following answers:
A) 6.7 B) 1.3 C) 9.6 D) 12.5 E) 28.6 | <gadget id="calculator">30 - 10</gadget>
<output>20</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 - (3/10)</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">20 / (7/10)</gadget>
<output>200/7 = around 28.571429</output>
<result>E</result> | E | 28.6 | How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 30% solution? | {
"A": "6.7",
"B": "1.3",
"C": "9.6",
"D": "12.5",
"E": "28.6"
} | divide(subtract(30, 10), subtract(const_1, divide(30, 100))) | divide(n2,n0)|subtract(n2,n1)|subtract(const_1,#0)|divide(#1,#2)| | "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 30 / 100 100 + 10 x = 300 + 3 x 7 x = 200 x = 28.6 answer is e" | general |
math_qa__l2ENZ56Q1ai6i1YJ | The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 3600 for a computer table, then what was the cost price of the computer table? Choose the correct choice from the following: A) 2299 B) 2699 C) 3000 D) 6725 E) 2601 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">3_600 / (6/5)</gadget>
<output>3_000</output>
<result>C</result> | C | 3,000 | The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 3600 for a computer table, then what was the cost price of the computer table? | {
"A": "2299",
"B": "2699",
"C": "3000",
"D": "6725",
"E": "2601"
} | divide(3600, add(const_1, divide(20, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | "cp = sp * ( 100 / ( 100 + profit % ) ) = 3600 ( 100 / 120 ) = rs . 3000 answer : c" | gain |
math_qa__tGzLBmXPsXw8itIT | Because he’s taxed by his home planet, Mork pays a tax rate of 30% on his income, while Mindy pays a rate of only 20% on hers. If Mindy earned 3 times as much as Mork did, what was their combined tax rate? Pick one:
A) 32.5 %
B) 34 %
C) 35 %
D) 36 %
E) 22.5 % | <gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">3 * (1/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/10) + (3/5)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">(9/10) / 4</gadget>
<output>9/40 = around 0.225</output>
<gadget id="calculator">100 * (9/40)</gadget>
<output>45/2 = around 22.5</output>
<result>E</result> | E | 22.5 | Because he’s taxed by his home planet, Mork pays a tax rate of 30% on his income, while Mindy pays a rate of only 20% on hers. If Mindy earned 3 times as much as Mork did, what was their combined tax rate? | {
"A": "32.5 %",
"B": "34 %",
"C": "35 %",
"D": "36 %",
"E": "22.5 %"
} | multiply(const_100, divide(add(divide(30, const_100), multiply(3, divide(20, const_100))), add(const_1, 3))) | add(n2,const_1)|divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#2)|add(#1,#3)|divide(#4,#0)|multiply(#5,const_100) | say morks income is - 100 so tax paid will be 30 say mindys income is 3 * 100 = 300 so tax paid is 20 % * 300 = 60 total tax paid = 30 + 60 = 90 . combined tax % will be 90 / 100 + 300 = 22.5 % | gain |
math_qa__P5LxIsOdE5F7GXZq | Sahil purchased a machine at Rs 9000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it. Pick one.
A) rs . 22500 B) rs . 24500 C) rs . 26500 D) rs . 28500 E) none of these | <gadget id="calculator">9_000 + 5_000</gadget>
<output>14_000</output>
<gadget id="calculator">14_000 + 1_000</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 / 100</gadget>
<output>150</output>
<gadget id="calculator">150 * 50</gadget>
<output>7_500</output>
<gadget id="calculator">15_000 + 7_500</gadget>
<output>22_500</output>
<result>A</result> | A | 22,500 | Sahil purchased a machine at Rs 9000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it. | {
"A": "rs . 22500",
"B": "rs . 24500",
"C": "rs . 26500",
"D": "rs . 28500",
"E": "none of these"
} | add(add(add(9000, 5000), 1000), multiply(divide(add(add(9000, 5000), 1000), const_100), 50)) | add(n0,n1)|add(n2,#0)|divide(#1,const_100)|multiply(n3,#2)|add(#1,#3)| | "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 9000 + 5000 + 1000 = 15000 150 % of 15000 = 150 / 100 * 15000 = 22500 option a" | gain |
math_qa__bQFIyq480noDRcNQ | Find the surface area of a 10cm*4cm*3cm brick. Pick one:
A) 154 cm square B) 156 cm square C) 160 cm square D) 164 cm square E) none of these | <gadget id="calculator">2 * (3 * 4 + 4 * 10 + 3 * 10)</gadget>
<output>164</output>
<result>D</result> | D | 164 | Find the surface area of a 10cm*4cm*3cm brick. | {
"A": "154 cm square",
"B": "156 cm square",
"C": "160 cm square",
"D": "164 cm square",
"E": "none of these"
} | surface_rectangular_prism(3, 4, 10) | surface_rectangular_prism(n0,n1,n2) | explanation : surface area of a cuboid = 2 ( lb + bh + hl ) cm square so , surface area of a brick = 2 ( 10 * 4 + 4 * 3 + 3 * 10 ) cm square = 2 ( 82 ) cm square = 164 cm square option d | geometry |
math_qa__DUMtbQ7TXnPHIiL7 | If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 15% per annum then the gain of B in a period of 3 years is? Choose the correct choice from the following choices
A) 525 B) 500 C) 510 D) 530 E) 550 | <gadget id="calculator">3_500 * 15</gadget>
<output>52_500</output>
<gadget id="calculator">52_500 * 3</gadget>
<output>157_500</output>
<gadget id="calculator">157_500 / 100</gadget>
<output>1_575</output>
<gadget id="calculator">3_500 * 10</gadget>
<output>35_000</output>
<gadget id="calculator">35_000 * 3</gadget>
<output>105_000</output>
<gadget id="calculator">105_000 / 100</gadget>
<output>1_050</output>
<gadget id="calculator">1_575 - 1_050</gadget>
<output>525</output>
<result>A</result> | A | 525 | If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 15% per annum then the gain of B in a period of 3 years is? | {
"A": "525",
"B": "500",
"C": "510",
"D": "530",
"E": "550"
} | subtract(divide(multiply(multiply(3500, 15), 3), const_100), divide(multiply(multiply(3500, 10), 3), const_100)) | multiply(n0,n2)|multiply(n0,n1)|multiply(#0,n3)|multiply(n3,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,#5)| | "( 3500 * 5 * 3 ) / 100 = > 525 answer : a" | gain |
math_qa__PkoCcZhBQeaMlMHE | Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 10 km each. Then they turned left and ran for another 7.5 km.
What is the distance (in kilometers) between the the two twins when they stop? Pick
A) 21 B) 23 C) 25 D) 27 E) 30 | <gadget id="calculator">7.5 * 2</gadget>
<output>15</output>
<gadget id="calculator">15 ** 2</gadget>
<output>225</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">20 ** 2</gadget>
<output>400</output>
<gadget id="calculator">225 + 400</gadget>
<output>625</output>
<gadget id="calculator">625 ** (1/2)</gadget>
<output>25</output>
<result>C</result> | C | 25 | Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 10 km each. Then they turned left and ran for another 7.5 km.
What is the distance (in kilometers) between the the two twins when they stop? | {
"A": "21",
"B": "23",
"C": "25",
"D": "27",
"E": "30"
} | sqrt(add(power(multiply(7.5, const_2), const_2), power(multiply(10, const_2), const_2))) | multiply(n1,const_2)|multiply(n0,const_2)|power(#0,const_2)|power(#1,const_2)|add(#2,#3)|sqrt(#4) | the distance between them is the hypotenuse of a right angle triangle with sides 15 km and 20 km . the hypotenuse = sqrt ( 15 ^ 2 + 20 ^ 2 ) = 25 the answer is c . | physics |
math_qa__uYCgPzuJZ2rF0iTF | A train running at the speed of 30 km/hr crosses a pole in 6 sec. What is the length of the train?
Pick:
A) 20 m
B) 70 m
C) 50 m
D) can not be determined
E) none of these | <gadget id="calculator">30 * 1_000</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 3_600</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">(25/3) * 6</gadget>
<output>50</output>
<result>C</result> | C | 50 | A train running at the speed of 30 km/hr crosses a pole in 6 sec. What is the length of the train? | {
"A": "20 m",
"B": "70 m",
"C": "50 m",
"D": "can not be determined",
"E": "none of these"
} | multiply(divide(multiply(30, const_1000), const_3600), 6) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | "speed = 30 * 5 / 18 = 25 / 3 m / sec length of the train = speed * time = 25 / 3 * 6 = 50 m answer : c" | physics |
math_qa__FNXSaPND5cZ6nvco | In how many ways can the integer 15 be expressed as a product of two different positive integers? Select the correct option
A) 10
B) 8
C) 5
D) 4
E) 2 | <gadget id="calculator">15 / 1</gadget>
<output>15</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<result>E</result> | E | 2 | In how many ways can the integer 15 be expressed as a product of two different positive integers? | {
"A": "10",
"B": "8",
"C": "5",
"D": "4",
"E": "2"
} | subtract(divide(divide(15, const_1), const_3), const_3) | divide(n0,const_1)|divide(#0,const_3)|subtract(#1,const_3) | 15 = 3 * 5 since 15 is not a perfect square , no of ways = 2 answer e | general |
math_qa__XwwTaVeZuU2yfXZ9 | If 5x + 3 = 10x – 17, what is the value of x? Choose the correct answer:
A) 1
B) 2
C) 3
D) 4
E) 5 | <gadget id="calculator">3 + 17</gadget>
<output>20</output>
<gadget id="calculator">10 - 5</gadget>
<output>5</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<result>D</result> | D | 4 | If 5x + 3 = 10x – 17, what is the value of x? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | divide(add(3, 17), subtract(10, 5)) | add(n1,n3)|subtract(n2,n0)|divide(#0,#1)| | "solve for x : 5 x + 3 = 10 x - 17 20 = 5 x 4 = x correct answer d ) 4" | general |
math_qa__wwyhpN4naZUDba8e | A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1.8 cm when a man gets on it. The mass of man is
Choose the correct answer: A) 12 kg B) 60 kg C) 108 kg D) 96 kg E) none | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">1.8 / 100</gadget>
<output>0.018</output>
<gadget id="calculator">6 * 0.018</gadget>
<output>0.108</output>
<gadget id="calculator">0.108 * 1_000</gadget>
<output>108</output>
<result>C</result> | C | 108 | A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1.8 cm when a man gets on it. The mass of man is | {
"A": "12 kg",
"B": "60 kg",
"C": "108 kg",
"D": "96 kg",
"E": "none"
} | multiply(multiply(multiply(3, 2), divide(1.8, const_100)), const_1000) | divide(n2,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(#2,const_1000)| | "solution volume of water displaced = ( 3 x 2 x 0.018 ) m 3 = 0.108 m 3 . mass of man = volume of water displaced × density of water = ( 0.108 × 1000 ) kg = 108 kg . answer c" | physics |
math_qa__XbCJDEUgG2eK0TmT | A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 50% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
Select the correct option:
A) 60 % B) 70 % C) 100 % D) 90 % E) 80 % | <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">150 / (1/2)</gadget>
<output>300</output>
<gadget id="calculator">300 - 150</gadget>
<output>150</output>
<gadget id="calculator">150 * 100</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 / 150</gadget>
<output>100</output>
<result>C</result> | C | 100 | A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 50% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk? | {
"A": "60 %",
"B": "70 %",
"C": "100 %",
"D": "90 %",
"E": "80 %"
} | divide(multiply(subtract(divide(150, subtract(const_1, divide(50, const_100))), 150), const_100), 150) | divide(n1,const_100)|subtract(const_1,#0)|divide(n0,#1)|subtract(#2,n0)|multiply(#3,const_100)|divide(#4,n0)| | "anyway , in this question , there is no discount but the mark up is given as 50 % of the selling price . so it is not 50 % of $ 150 but instead , 50 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 50 % of s = s s = 300 profit = 150 which is calculated on cost price in % terms . so 150 / 150 * 100 = 100 % is profit . c" | gain |
math_qa__F6rqZeGglIKSCiuk | 1 / 216 , 415 , 356 , _ ? Choose the correct choice
A) 28 / 3 B) 27 / 3 C) 26 / 3 D) 25 / 3 E) 24 / 3 | <gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">8 + 20</gadget>
<output>28</output>
<gadget id="calculator">28 / 3</gadget>
<output>28/3 = around 9.333333</output>
<result>A</result> | A | 9.333333 | 1 / 216 , 415 , 356 , _ ? | {
"A": "28 / 3",
"B": "27 / 3",
"C": "26 / 3",
"D": "25 / 3",
"E": "24 / 3"
} | divide(add(multiply(const_2, const_4), multiply(const_10, const_2)), const_3) | multiply(const_2,const_4)|multiply(const_10,const_2)|add(#0,#1)|divide(#2,const_3) | take alternative no . 1 / 2 , 43 16 / 4 = 4 15 / 5 = 3 56 / 6 = 28 / 3 hence ans is 28 / 3 answer : a | general |
math_qa__95HDsOAepkxqsTTv | The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 16. The larger of the two numbers is: Choices:
A) 276 B) 299 C) 322 D) 345 E) 368 | <gadget id="calculator">23 * 16</gadget>
<output>368</output>
<result>E</result> | E | 368 | The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 16. The larger of the two numbers is: | {
"A": "276",
"B": "299",
"C": "322",
"D": "345",
"E": "368"
} | multiply(23, 16) | multiply(n0,n2)| | "clearly , the numbers are ( 23 x 13 ) and ( 23 x 16 ) . larger number = ( 23 x 16 ) = 368 . answer : option e" | other |
math_qa__B91Uk4yz7q3u8fla | Two good train each 100 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) 1.2 sec B) 2.4 sec C) 4.8 sec D) 9.6 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">100 * (6/125)</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">(24/5) * 2</gadget>
<output>48/5 = around 9.6</output>
<result>D</result> | D | 9.6 | Two good train each 100 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": "1.2 sec",
"B": "2.4 sec",
"C": "4.8 sec",
"D": "9.6 sec",
"E": "none"
} | multiply(multiply(100, 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 = ( 100 + 100 ) m = 1000 m . required time = ( 200 x 6 / 125 ) sec = 9.6 sec . answer d" | physics |
math_qa__ba66ExysigUMjO9D | The amount of time that three people worked on a special project was in the ratio of 1 to 2 to 3. If the project took 120 hours, how many more hours did the hardest working person work than the person who worked the least? Choose the correct choice
A) 35 hours
B) 40 hours
C) 36 hours
D) 38 hours
E) 42 hours | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">120 / 6</gadget>
<output>20</output>
<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">20 * 1</gadget>
<output>20</output>
<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<result>B</result> | B | 40 | The amount of time that three people worked on a special project was in the ratio of 1 to 2 to 3. If the project took 120 hours, how many more hours did the hardest working person work than the person who worked the least? | {
"A": "35 hours",
"B": "40 hours",
"C": "36 hours",
"D": "38 hours",
"E": "42 hours"
} | subtract(multiply(divide(120, add(add(1, 2), 3)), 3), multiply(divide(120, add(add(1, 2), 3)), 1)) | add(n0,n1)|add(n2,#0)|divide(n3,#1)|multiply(n2,#2)|multiply(n0,#2)|subtract(#3,#4)| | "let the persons be a , b , c . hours worked : a = 1 * 120 / 6 = 20 hours b = 2 * 120 / 6 = 40 hours c = 3 * 120 / 6 = 60 hours c is the hardest worker and a worked for the least number of hours . so the difference is 60 - 20 = 40 hours . answer : b" | physics |
math_qa__O9dulaYLNFzfcDMi | Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 50 km more than the other. What is the distance between the two stations? Options
A) 540 km B) 767 km C) 276 km D) 450 km E) 176 km | <gadget id="calculator">20 + 25</gadget>
<output>45</output>
<gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<gadget id="calculator">45 * 10</gadget>
<output>450</output>
<result>D</result> | D | 450 | Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 50 km more than the other. What is the distance between the two stations? | {
"A": "540 km",
"B": "767 km",
"C": "276 km",
"D": "450 km",
"E": "176 km"
} | multiply(add(20, 25), divide(50, subtract(25, 20))) | add(n0,n1)|subtract(n1,n0)|divide(n2,#1)|multiply(#0,#2) | explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 50 km more than the other , 25 x â € “ 20 x = 50 5 x = 50 x = 10 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 10 = 450 km . answer : d | general |
math_qa__pFKkygeVNcNiCPpD | Sides of a triangle are 13 cm.14cm.and 15cm.respectively.calculate the area of triangle. Pick one
A) 80
B) 82
C) 84
D) 86
E) 88 | <gadget id="calculator">(((13 + 14 + 15) / 2) * ((13 + 14 + 15) / 2 - 13) * ((13 + 14 + 15) / 2 - 14) * ((13 + 14 + 15) / 2 - 15)) ** (1/2)</gadget>
<output>84</output>
<result>C</result> | C | 84 | Sides of a triangle are 13 cm.14cm.and 15cm.respectively.calculate the area of triangle. | {
"A": "80",
"B": "82",
"C": "84",
"D": "86",
"E": "88"
} | triangle_area_three_edges(13, 14, 15) | triangle_area_three_edges(n0,n1,n2) | let a = 13 cm , b = 14 cm . and c = 15 cm . s = 1 / 2 ( 13 + 14 + 15 ) = 21 , ( s - a ) = 8 , ( s - b ) = 7 and ( s - c ) = 6 area = √ 21 * 8 * 7 * 6 = 84 sq . cm answer c | geometry |
math_qa__RySz6DRGS4HOEbSD | A test has 150 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers? Choose the correct answer:
A) 19 B) 21 C) 23 D) 25 E) 27 | <gadget id="calculator">150 - 40</gadget>
<output>110</output>
<gadget id="calculator">110 / 5</gadget>
<output>22</output>
<gadget id="calculator">22 + 1</gadget>
<output>23</output>
<gadget id="calculator">23 + 1</gadget>
<output>24</output>
<result>C</result> | C | 23 | A test has 150 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers? | {
"A": "19",
"B": "21",
"C": "23",
"D": "25",
"E": "27"
} | add(add(divide(subtract(150, 40), 5), 1), 1) | subtract(n0,n5)|divide(#0,n1)|add(#1,n2)|add(#2,n2)| | "a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 150 . thus 5 c < = 310 and so c < = 62 . then 40 < = c < = 62 and c can have 23 possible values . the answer is c ." | general |
math_qa__mVfqSvWhmS55zwu8 | The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $24. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour?
Choose one.
A) 347.4 B) 987.4 C) 877.2 D) 1027.2 E) 1667.2 | <gadget id="calculator">24 / 10</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">24 * 6</gadget>
<output>144</output>
<gadget id="calculator">144 / 2</gadget>
<output>72</output>
<gadget id="calculator">(12/5) * 72</gadget>
<output>864/5 = around 172.8</output>
<gadget id="calculator">4 * (864/5)</gadget>
<output>3_456/5 = around 691.2</output>
<gadget id="calculator">3 * 72</gadget>
<output>216</output>
<gadget id="calculator">(3_456/5) + 216</gadget>
<output>4_536/5 = around 907.2</output>
<gadget id="calculator">5 * 24</gadget>
<output>120</output>
<gadget id="calculator">(4_536/5) + 120</gadget>
<output>5_136/5 = around 1_027.2</output>
<result>D</result> | D | 1,027.2 | The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $24. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour? | {
"A": "347.4",
"B": "987.4",
"C": "877.2",
"D": "1027.2",
"E": "1667.2"
} | add(add(multiply(4, multiply(divide(24, 10), divide(multiply(24, 6), 2))), multiply(3, divide(multiply(24, 6), 2))), multiply(5, 24)) | divide(n1,n0)|multiply(n2,n4)|multiply(n4,n7)|divide(#1,n3)|multiply(#0,#3)|multiply(n6,#3)|multiply(n5,#4)|add(#6,#5)|add(#7,#2)| | "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 24 = 2 r a = 12 / 5 r and r = 72 a = 144 required total cost = 4 * 144 + 3 * 72 + 5 * 24 = 691.2 + 216 + 120 = $ 1027.20 d" | general |
math_qa__NVX8R8FeTnTadQH6 | In one hour, a boat goes 11 km along the steram and 5 km against the stream. The speed of the boat in still waer (in km/hr) is:
Choose the correct answer:
A) 2 B) 4 C) 8 D) 12 E) 15 | <gadget id="calculator">11 + 5</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>C</result> | C | 8 | In one hour, a boat goes 11 km along the steram and 5 km against the stream. The speed of the boat in still waer (in km/hr) is: | {
"A": "2",
"B": "4",
"C": "8",
"D": "12",
"E": "15"
} | divide(add(11, 5), const_2) | add(n0,n1)|divide(#0,const_2) | sol . speed in still water = 1 / 2 ( 11 + 5 ) kmph = 8 kmph . answer c | physics |
math_qa__XVcbs51Aj7HaP62U | If n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2^k is a factor of n? Choices
A) 10 B) 12 C) 15 D) 18 E) 20 | <gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">20 / 16</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">floor(5/4)</gadget>
<output>1</output>
<gadget id="calculator">15 + 1</gadget>
<output>16</output>
<gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">20 / 8</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">floor(5/2)</gadget>
<output>2</output>
<gadget id="calculator">16 + 2</gadget>
<output>18</output>
<result>D</result> | D | 18 | If n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2^k is a factor of n? | {
"A": "10",
"B": "12",
"C": "15",
"D": "18",
"E": "20"
} | add(add(add(divide(20, 2), divide(20, power(2, 2))), floor(divide(20, power(power(2, 2), 2)))), floor(divide(20, power(2, const_3)))) | divide(n1,n2)|power(n2,n2)|power(n2,const_3)|divide(n1,#1)|divide(n1,#2)|power(#1,n2)|add(#0,#3)|divide(n1,#5)|floor(#4)|floor(#7)|add(#6,#9)|add(#10,#8)| | "given : n = 20 ! n = 20 ! . the highest power k for which 2 ^ k is a factor of n can be found with the above formula : k = 20 / 2 + 20 / 4 + 20 / 8 + 20 / 16 = 10 + 5 + 2 + 1 = 18 answer : d ." | general |
math_qa__RTfgz7KzbaPbHjrs | A dog travelled for 2 hours. He covered the first half of the distance at 10 kmph and remaining half of the distance at 5 kmph. Find the distance travelled by the dog?
Options
A) 20 km B) 16 km C) 6 km D) 3 km E) 61 km | <gadget id="calculator">2 * 10</gadget>
<output>20</output>
<result>A</result> | A | 20 | A dog travelled for 2 hours. He covered the first half of the distance at 10 kmph and remaining half of the distance at 5 kmph. Find the distance travelled by the dog? | {
"A": "20 km",
"B": "16 km",
"C": "6 km",
"D": "3 km",
"E": "61 km"
} | multiply(2, 10) | multiply(n0,n1) | let the distance travelled be x km . total time = ( x / 2 ) / 10 + ( x / 2 ) / 5 = 2 = > x / 20 + x / 10 = 2 = > ( 1 x + 2 x ) / 20 = 2 = > x = 20 km answer : a | physics |
math_qa__MjpzDoq0JFrBBm6A | Find the value of 72519 x 9999 = m? Choose the correct choice from the following answers.
A) 455465473 B) 654676854 C) 667676753 D) 725117481 E) 764534522 | <gadget id="calculator">9_999 - 4</gadget>
<output>9_995</output>
<gadget id="calculator">9_995 * 72_519</gadget>
<output>724_827_405</output>
<result>D</result> | D | 725,117,481 | Find the value of 72519 x 9999 = m? | {
"A": "455465473",
"B": "654676854",
"C": "667676753",
"D": "725117481",
"E": "764534522"
} | multiply(subtract(9999, const_4), 72519) | subtract(n1,const_4)|multiply(#0,n0)| | "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d" | general |
math_qa__TlJgAGZGJ32LoKqZ | 3 , 15 , x , 51 , 53 , 159161 value of x ? Choose the correct choice from the following options.
A) 17
B) 34
C) 54
D) 64
E) 112 | <gadget id="calculator">15 + 2</gadget>
<output>17</output>
<result>A</result> | A | 17 | 3 , 15 , x , 51 , 53 , 159161 value of x ? | {
"A": "17",
"B": "34",
"C": "54",
"D": "64",
"E": "112"
} | add(15, const_2) | add(n1,const_2) | 3 * 5 = 15 15 + 2 = 17 17 * 3 = 51 51 + 2 = 53 answer : a | general |
math_qa__1vdrOlHgnayuQEtc | A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.300 when the rate to profit rises from 5 to 7 percent. Find the Capital of A? Pick.
A) 5000 B) 10000 C) 15000 D) 2778 E) 1991 | <gadget id="calculator">300 * 100</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 2</gadget>
<output>15_000</output>
<result>C</result> | C | 15,000 | A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.300 when the rate to profit rises from 5 to 7 percent. Find the Capital of A? | {
"A": "5000",
"B": "10000",
"C": "15000",
"D": "2778",
"E": "1991"
} | divide(multiply(300, const_100), 2) | multiply(n2,const_100)|divide(#0,n0) | a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 300 a ' s capital = 22500 * 2 / 3 = 15000 answer : c | general |
math_qa__cMWRCdtnnHgKCfmW | How many zeros does 100! end with? Answers
A) 20 B) 24 C) 25 D) 30 E) 32 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">95 / 25</gadget>
<output>19/5 = around 3.8</output>
<gadget id="calculator">20 + (19/5)</gadget>
<output>119/5 = around 23.8</output>
<gadget id="calculator">5 ** 3</gadget>
<output>125</output>
<gadget id="calculator">95 / 125</gadget>
<output>19/25 = around 0.76</output>
<gadget id="calculator">(119/5) + (19/25)</gadget>
<output>614/25 = around 24.56</output>
<result>B</result> | B | 24 | How many zeros does 100! end with? | {
"A": "20",
"B": "24",
"C": "25",
"D": "30",
"E": "32"
} | add(add(divide(100, add(const_4, const_1)), divide(subtract(100, add(const_4, const_1)), power(add(const_4, const_1), const_2))), divide(subtract(100, add(const_4, const_1)), power(add(const_4, const_1), const_3))) | add(const_1,const_4)|divide(n0,#0)|power(#0,const_2)|power(#0,const_3)|subtract(n0,#0)|divide(#4,#2)|divide(#4,#3)|add(#1,#5)|add(#7,#6)| | "according to above 100 ! has 100 / 5 + 100 / 25 = 20 + 4 = 24 trailing zeros . answer : b ." | other |
math_qa__yZiBninvxWsq2Tq6 | How many two-digit numbers yield a remainder of 3 when divided by both 4 and 14? Answers.
A) 0 B) 1 C) 2 D) 3 E) 4 | <gadget id="calculator">14 * 4</gadget>
<output>56</output>
<gadget id="calculator">3 + 56</gadget>
<output>59</output>
<gadget id="calculator">59 - 56</gadget>
<output>3</output>
<result>D</result> | D | 3 | How many two-digit numbers yield a remainder of 3 when divided by both 4 and 14? | {
"A": "0",
"B": "1",
"C": "2",
"D": "3",
"E": "4"
} | subtract(add(3, multiply(14, 4)), multiply(14, 4)) | multiply(n1,n2)|add(n0,#0)|subtract(#1,#0)| | "easier to start with numbers that are of the form 14 p + 3 - - - > 17,31 , 45,59 , 73,87 . out of these 3 ( 31 , 59,87 ) are also of the form 4 q + 3 . thus 3 is the answer . d is the correct answer ." | general |
math_qa__J2OAXcmXolxHf5Jz | A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? Choose the correct choice from the following answers: A) 15 minutes B) 18 minutes C) 12 minutes D) 58 minutes E) 10 minutes | <gadget id="calculator">26 / 2</gadget>
<output>13</output>
<gadget id="calculator">13 + 2</gadget>
<output>15</output>
<result>A</result> | A | 15 | A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres? | {
"A": "15 minutes",
"B": "18 minutes",
"C": "12 minutes",
"D": "58 minutes",
"E": "10 minutes"
} | add(divide(26, 2), 2) | divide(n2,n1)|add(n1,#0) | explanation : as the squirrel climbs 5 m in one minute and slips 2 metres in the next minute , it climbs 3 metres in 2 minute to climb 26 metres , the time required is : the squirrel will climb ( 26 – 5 ) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes also , the last 5 metres it climbs in another 1 minute hence , total time required = 14 + 1 = 15 minutes answer : a | physics |
math_qa__iZmzUrpW1BltMqYJ | A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:2. The ratio of economy cars to sport utility vehicles is 4:2. What is the ratio of luxury cars to sport utility vehicles? Pick one: A) 9 : 8 B) 8 : 9 C) 3 : 2 D) 8 : 6 E) 1 : 2 | <gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">8 / 6</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 / 8</gadget>
<output>1</output>
<gadget id="calculator">(4/3) / 1</gadget>
<output>4/3 = around 1.333333</output>
<result>D</result> | D | 1.333333 | A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:2. The ratio of economy cars to sport utility vehicles is 4:2. What is the ratio of luxury cars to sport utility vehicles? | {
"A": "9 : 8",
"B": "8 : 9",
"C": "3 : 2",
"D": "8 : 6",
"E": "1 : 2"
} | divide(divide(multiply(const_4, 2), multiply(const_3.0, 2)), divide(multiply(2, const_4), multiply(2, const_4))) | multiply(n3,const_4)|multiply(const_3.0,n3)|multiply(n1,const_4)|divide(#0,#1)|divide(#0,#2)|divide(#3,#4)| | "the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 12 : 8 . the ratio of economy cars to sport utility vehicles is 4 : 2 - - > e : s = 4 : 2 = 12 : 6 . thus , l : s = 8 : 6 . answer : d ." | other |
math_qa__sjtUX2c96tzTRH6X | A cycle is bought for Rs.900 and sold for Rs.1100, find the gain percent? Pick one:
A) 11 B) 22 C) 99 D) 77 E) 18 | <gadget id="calculator">1_100 - 900</gadget>
<output>200</output>
<gadget id="calculator">200 / 900</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">(2/9) * 100</gadget>
<output>200/9 = around 22.222222</output>
<result>B</result> | B | 22 | A cycle is bought for Rs.900 and sold for Rs.1100, find the gain percent? | {
"A": "11",
"B": "22",
"C": "99",
"D": "77",
"E": "18"
} | multiply(divide(subtract(1100, 900), 900), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | "900 - - - - 200 100 - - - - ? = > 22 % answer : b" | gain |
math_qa__sHanXUlF90TVEeS1 | Two trains of length 120 m and 320 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? Choose the correct choice from the following options.
A) 10 sec
B) 22 sec
C) 82 sec
D) 20 sec
E) 89 sec | <gadget id="calculator">120 + 320</gadget>
<output>440</output>
<gadget id="calculator">42 + 30</gadget>
<output>72</output>
<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">440 / 20</gadget>
<output>22</output>
<result>B</result> | B | 22 | Two trains of length 120 m and 320 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? | {
"A": "10 sec",
"B": "22 sec",
"C": "82 sec",
"D": "20 sec",
"E": "89 sec"
} | divide(add(120, 320), multiply(add(42, 30), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 320 = 440 m . the time required = d / s = 440 / 20 = 22 sec . answer : b" | physics |
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