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__Vr2b0g8Tmdkofx6t | Raman mixed 54 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction? Choose the correct choice from the following answers
A) 129 B) 287 C) 196 D) 188 E) 112 | <gadget id="calculator">54 * 150</gadget>
<output>8_100</output>
<gadget id="calculator">36 * 125</gadget>
<output>4_500</output>
<gadget id="calculator">8_100 + 4_500</gadget>
<output>12_600</output>
<gadget id="calculator">36 + 54</gadget>
<output>90</output>
<gadget id="calculator">12_600 / 90</gadget>
<output>140</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">140 * (2/5)</gadget>
<output>56</output>
<gadget id="calculator">140 + 56</gadget>
<output>196</output>
<result>C</result> | C | 196 | Raman mixed 54 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction? | {
"A": "129",
"B": "287",
"C": "196",
"D": "188",
"E": "112"
} | add(divide(add(multiply(54, 150), multiply(36, 125)), add(36, 54)), multiply(divide(add(multiply(54, 150), multiply(36, 125)), add(36, 54)), divide(40, const_100))) | add(n0,n2)|divide(n4,const_100)|multiply(n0,n1)|multiply(n2,n3)|add(#2,#3)|divide(#4,#0)|multiply(#5,#1)|add(#5,#6)| | "explanation : cp per kg of mixture = [ 54 ( 150 ) + 36 ( 125 ) ] / ( 54 + 36 ) = rs . 140 sp = cp [ ( 100 + profit % ) / 100 ] = 140 * [ ( 100 + 40 ) / 100 ] = rs . 196 . answer : c" | gain |
math_qa__TqCn4KCT0f2VFEb9 | Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 25% the new mean is $850.What was original rent of friend whose rent is increased? Choose the correct answer:
A) 800 B) 900 C) 1000 D) 1100 E) 1200 | <gadget id="calculator">850 - 800</gadget>
<output>50</output>
<gadget id="calculator">50 * 4</gadget>
<output>200</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">200 / (1/4)</gadget>
<output>800</output>
<result>A</result> | A | 800 | Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 25% the new mean is $850.What was original rent of friend whose rent is increased? | {
"A": "800",
"B": "900",
"C": "1000",
"D": "1100",
"E": "1200"
} | divide(multiply(subtract(850, 800), 4), divide(25, const_100)) | divide(n2,const_100)|subtract(n3,n1)|multiply(n0,#1)|divide(#2,#0)| | "0.25 x = 4 ( 850 - 800 ) 0.25 x = 200 x = 800 answer a" | general |
math_qa__Vsu1I3DhAznVrq2v | A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 5% p.a for 2 years. Find his gain in the transaction per year. Choose the correct choice from the following choices.
A) 50 B) 150 C) 225 D) 112.5 E) 212.5 | <gadget id="calculator">5_000 * 5</gadget>
<output>25_000</output>
<gadget id="calculator">25_000 * 2</gadget>
<output>50_000</output>
<gadget id="calculator">50_000 / 100</gadget>
<output>500</output>
<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>
<gadget id="calculator">20_000 * 2</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 / 100</gadget>
<output>400</output>
<gadget id="calculator">500 - 400</gadget>
<output>100</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<result>A</result> | A | 50 | A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 5% p.a for 2 years. Find his gain in the transaction per year. | {
"A": "50",
"B": "150",
"C": "225",
"D": "112.5",
"E": "212.5"
} | divide(subtract(divide(multiply(multiply(5000, 5), 2), const_100), divide(multiply(multiply(5000, 4), 2), const_100)), 2) | multiply(n0,n3)|multiply(n0,n2)|multiply(n1,#0)|multiply(n1,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,#5)|divide(#6,n1)| | "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 5 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 5 × 2 / 100 = 500 his overall gain in 2 years = rs . 500 - rs . 400 = rs . 100 his overall gain in 1 year = 100 / 2 = rs . 50 answer : option a" | gain |
math_qa__t9MZKSHBFPd1U1uH | A chemist mixes one liter of pure water with x liters of a 30% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x?
Pick one.
A) 1 / 4 B) 1 / 3 C) 1 / 2 D) 1 E) 3 | <gadget id="calculator">30 - 15</gadget>
<output>15</output>
<gadget id="calculator">15 / 15</gadget>
<output>1</output>
<result>D</result> | D | 1 | A chemist mixes one liter of pure water with x liters of a 30% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x? | {
"A": "1 / 4",
"B": "1 / 3",
"C": "1 / 2",
"D": "1",
"E": "3"
} | divide(15, subtract(30, 15)) | subtract(n0,n1)|divide(n1,#0)| | "concentration of salt in pure solution = 0 concentration of salt in salt solution = 30 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 30 - 15 ) / ( 15 - 0 ) = 1 / 1 1 / x = 1 / 1 x = 1 answer : d" | gain |
math_qa__zNoCBTYJMZMlOjAr | The surface of a cube is 96sq cm. Find its volume? Choose the correct choice
A) 8 cc B) 9 cc C) 2 cc D) 4 cc E) 64 cc | <gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">96 / 6</gadget>
<output>16</output>
<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<gadget id="calculator">4 ** 3</gadget>
<output>64</output>
<result>E</result> | E | 64 | The surface of a cube is 96sq cm. Find its volume? | {
"A": "8 cc",
"B": "9 cc",
"C": "2 cc",
"D": "4 cc",
"E": "64 cc"
} | volume_cube(sqrt(divide(96, add(const_2, const_4)))) | add(const_2,const_4)|divide(n0,#0)|sqrt(#1)|volume_cube(#2) | 6 a 2 = 96 = 6 * 16 a = 4 = > a 3 = 64 cc answer : e | geometry |
math_qa__IQAQ02hlINibiNiF | Pipe A and pipe B fill water into a tank of capacity 2000 litres, at a rate of 200 l/min and 50 l/min. Pipe C drains at a rate of 25 l/min. Pipe A is open for 1 min and closed, then pipe B is open for 2 min and closed. Further the pipe c is opened and drained for another 2 min. This process is repeated until the tank is filled. How long will it take to fill the tank? Choose the correct option
A) 14 min B) 18 min C) 25 min D) 32 min E) 40 min | <gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">200 + 100</gadget>
<output>300</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<gadget id="calculator">300 - 50</gadget>
<output>250</output>
<gadget id="calculator">2_000 / 250</gadget>
<output>8</output>
<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<result>E</result> | E | 40 | Pipe A and pipe B fill water into a tank of capacity 2000 litres, at a rate of 200 l/min and 50 l/min. Pipe C drains at a rate of 25 l/min. Pipe A is open for 1 min and closed, then pipe B is open for 2 min and closed. Further the pipe c is opened and drained for another 2 min. This process is repeated until the tank is filled. How long will it take to fill the tank? | {
"A": "14 min",
"B": "18 min",
"C": "25 min",
"D": "32 min",
"E": "40 min"
} | multiply(add(add(1, 2), 2), divide(2000, subtract(add(200, multiply(50, 2)), multiply(25, 2)))) | add(n4,n5)|multiply(n2,n5)|multiply(n3,n5)|add(n5,#0)|add(n1,#1)|subtract(#4,#2)|divide(n0,#5)|multiply(#3,#6)| | "tank capacity : 2000 l , 1 st - 200 l / min for 1 min , volume filled : 200 l 2 nd - 100 l / min for 2 min , volume filled : 100 l 3 rd ( water draining ) : 25 l / min * 2 : 50 l total : ( 200 + 100 ) - 50 = 250 l filled for 1 cycle number of 250 in 2000 l tank : 2000 / 250 = 8 time taken to fill : 8 * total time = 8 * 5 = 40 ( option e )" | physics |
math_qa__nnBH4ezmMGb03ieR | How many positive integers less than 25 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?
Answers.
A) 27 B) 25 C) 24 D) 22 E) 20 | <gadget id="calculator">25 - 2</gadget>
<output>23</output>
<gadget id="calculator">23 - 1</gadget>
<output>22</output>
<gadget id="calculator">22 - 1</gadget>
<output>21</output>
<result>E</result> | E | 20 | How many positive integers less than 25 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4? | {
"A": "27",
"B": "25",
"C": "24",
"D": "22",
"E": "20"
} | subtract(subtract(subtract(25, 2), const_1), const_1) | subtract(n0,n2)|subtract(#0,const_1)|subtract(#1,const_1)| | "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 2 odd multiples of 5 : { 5 , 15 } 10 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 2 + 10 - 1 = 20 . answer : e ." | general |
math_qa__De17GWNlpa0vUHAM | In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs? Choose the correct choice from the following answers:
A) 6.25
B) 6.27
C) 6.23
D) 6.29
E) 6.39 | <gadget id="calculator">10 * 3.2</gadget>
<output>32</output>
<gadget id="calculator">282 - 32</gadget>
<output>250</output>
<gadget id="calculator">250 / 40</gadget>
<output>25/4 = around 6.25</output>
<result>A</result> | A | 6.25 | In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs? | {
"A": "6.25",
"B": "6.27",
"C": "6.23",
"D": "6.29",
"E": "6.39"
} | divide(subtract(282, multiply(10, 3.2)), 40) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | "required run rate = [ 282 - ( 3.2 * 10 ) ] / 40 = 250 / 40 = 6.25 ' answer : a" | gain |
math_qa__dzmj9jOEMSbRj610 | Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company M last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos? Choose the correct choice: A) 5 / 22 B) 4 / 22 C) 3 / 22 D) 9 / 22 E) 7 / 22 | <gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<gadget id="calculator">30 / 3</gadget>
<output>10</output>
<gadget id="calculator">10 + 7</gadget>
<output>17</output>
<gadget id="calculator">17 + 5</gadget>
<output>22</output>
<gadget id="calculator">7 / 22</gadget>
<output>7/22 = around 0.318182</output>
<result>E</result> | E | 0.318182 | Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company M last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos? | {
"A": "5 / 22",
"B": "4 / 22",
"C": "3 / 22",
"D": "9 / 22",
"E": "7 / 22"
} | divide(7, add(add(divide(multiply(multiply(3, 5), 2), 3), 7), 5)) | multiply(n1,n3)|multiply(n0,#0)|divide(#1,n1)|add(n2,#2)|add(n3,#3)|divide(n2,#4) | # of basic stereos was 3 / 4 of total and # of deluxe stereos was 1 / 4 of total , let ' s assume total = 16 , then basic = 12 and deluxe = 4 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 12 * 1 = 12 and total time for deluxe would be 4 * 7 / 5 = 28 / 5 - - > total time for both of them would be 12 + 28 / 5 = 88 / 5 - - > deluxe / total = 28 / 5 / 88 / 5 = 28 / 88 = 7 / 22 e | general |
math_qa__i4spqT457cg3W3xS | Rectangular tile each of size 80cm by 40cm must be laid horizontally on a rectangular floor of size 130cm by 230cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: Choose the correct choice:
A) 6 B) 2 C) 8 D) 9 E) 7 | <gadget id="calculator">130 * 230</gadget>
<output>29_900</output>
<gadget id="calculator">80 * 40</gadget>
<output>3_200</output>
<gadget id="calculator">29_900 / 3_200</gadget>
<output>299/32 = around 9.34375</output>
<result>D</result> | D | 9 | Rectangular tile each of size 80cm by 40cm must be laid horizontally on a rectangular floor of size 130cm by 230cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: | {
"A": "6",
"B": "2",
"C": "8",
"D": "9",
"E": "7"
} | divide(multiply(130, 230), multiply(80, 40)) | multiply(n2,n3)|multiply(n0,n1)|divide(#0,#1)| | "area of tile = 80 * 40 = 3200 area of floor = 130 * 230 = 29900 no of tiles = 29900 / 3200 = 9.34 so , the no of tile = 9 answer : d" | geometry |
math_qa__j5NPfyqCfiysy3K8 | Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder Choose the correct choice from the following answers:
A) 1235 B) 1345 C) 1678 D) 1767 E) 1671 | <gadget id="calculator">1_395 - 15</gadget>
<output>1_380</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_380 / 5</gadget>
<output>276</output>
<gadget id="calculator">276 * 6</gadget>
<output>1_656</output>
<result>E</result> | E | 1,671 | Find large number from below question The difference of two numbers is 1395. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder | {
"A": "1235",
"B": "1345",
"C": "1678",
"D": "1767",
"E": "1671"
} | multiply(divide(subtract(1395, 15), subtract(6, const_1)), 6) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | "let the smaller number be x . then larger number = ( x + 1395 ) . x + 1395 = 6 x + 15 5 x = 1380 x = 276 large number = 276 + 1395 = 1671 e" | general |
math_qa__cfXlviTwRHRW0ysB | Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1740?
Choose the correct choice from the following choices
A) rs . 1000 B) rs . 1550 C) rs . 1510 D) rs . 1500 E) none of these | <gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">15 + 3</gadget>
<output>18</output>
<gadget id="calculator">18 / 5</gadget>
<output>18/5 = around 3.6</output>
<gadget id="calculator">(18/5) * 5</gadget>
<output>18</output>
<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">(9/50) + 1</gadget>
<output>59/50 = around 1.18</output>
<gadget id="calculator">1_740 / (59/50)</gadget>
<output>87_000/59 = around 1_474.576271</output>
<result>D</result> | D | 1,500 | Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1740? | {
"A": "rs . 1000",
"B": "rs . 1550",
"C": "rs . 1510",
"D": "rs . 1500",
"E": "none of these"
} | divide(1740, add(divide(multiply(divide(add(multiply(3, 5), 3), 5), 5), const_100), const_1)) | multiply(n1,n3)|add(n1,#0)|divide(#1,n3)|multiply(n0,#2)|divide(#3,const_100)|add(#4,const_1)|divide(n4,#5)| | "explanation : 1740 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1500 answer : option d" | general |
math_qa__c5g0QBdZ0FLPOKtE | The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the possible maximum range of the temperatures?
Select:
A) 20
B) 25
C) 40
D) 45
E) 75 | <gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">50 * 5</gadget>
<output>250</output>
<gadget id="calculator">45 * 4</gadget>
<output>180</output>
<gadget id="calculator">250 - 180</gadget>
<output>70</output>
<gadget id="calculator">70 - 45</gadget>
<output>25</output>
<result>B</result> | B | 25 | The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the possible maximum range of the temperatures? | {
"A": "20",
"B": "25",
"C": "40",
"D": "45",
"E": "75"
} | subtract(subtract(multiply(50, add(const_2, const_3)), multiply(45, const_4)), 45) | add(const_2,const_3)|multiply(n1,const_4)|multiply(n0,#0)|subtract(#2,#1)|subtract(#3,n1)| | "average = 50 , sum of temperatures = 50 * 5 = 250 as the min temperature is 45 , max would be 250 - 4 * 45 = 70 - - > the range = 70 ( max ) - 45 ( min ) = 25 answer : b ." | general |
math_qa__Zc99yc9DWUngex5K | A grocer has a sale of Rs. 800, Rs. 900, Rs. 1000, Rs. 700 and Rs. 800 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 850? Pick one:
A) s . 440 B) s . 850 C) s . 450 D) s . 900 E) s . 950 | <gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 850</gadget>
<output>5_100</output>
<gadget id="calculator">800 + 900</gadget>
<output>1_700</output>
<gadget id="calculator">1_700 + 1_000</gadget>
<output>2_700</output>
<gadget id="calculator">2_700 + 700</gadget>
<output>3_400</output>
<gadget id="calculator">3_400 + 800</gadget>
<output>4_200</output>
<gadget id="calculator">5_100 - 4_200</gadget>
<output>900</output>
<result>D</result> | D | 900 | A grocer has a sale of Rs. 800, Rs. 900, Rs. 1000, Rs. 700 and Rs. 800 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 850? | {
"A": "s . 440",
"B": "s . 850",
"C": "s . 450",
"D": "s . 900",
"E": "s . 950"
} | subtract(multiply(add(5, const_1), 850), add(add(add(add(800, 900), 1000), 700), 800)) | add(n5,const_1)|add(n0,n1)|add(n2,#1)|multiply(n6,#0)|add(n3,#2)|add(n4,#4)|subtract(#3,#5)| | "total sale for 5 months = rs . ( 800 + 900 + 1000 + 700 + 800 ) = rs . 4200 required sale = rs . [ ( 850 x 6 ) - 4200 ] = rs . ( 5100 - 4200 ) = rs . 900 . option d" | general |
math_qa__NWxHETtZqYTf0kdq | A can finish a piece of work in 5 days. B can do it in 16 days. They work together for two days and then A goes away. In how many days will B finish the work?
Select the correct option.
A) 4 B) 5 C) 6 D) 7 E) 8 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">(1/16) * 2</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/2) + (1/8)</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/8) / (1/16)</gadget>
<output>6</output>
<result>C</result> | C | 6 | A can finish a piece of work in 5 days. B can do it in 16 days. They work together for two days and then A goes away. In how many days will B finish the work? | {
"A": "4",
"B": "5",
"C": "6",
"D": "7",
"E": "8"
} | divide(subtract(const_1, add(multiply(divide(const_1, const_4.0), const_2), multiply(divide(const_1, 16), const_2))), divide(const_1, 16)) | divide(const_1,const_4.0)|divide(const_1,n1)|multiply(#0,const_2)|multiply(#1,const_2)|add(#2,#3)|subtract(const_1,#4)|divide(#5,#1)| | "2 / 4 + ( 2 + x ) / 16 = 1 = > x = 6 days answer : c" | physics |
math_qa__8JaqMBJb09hm2FEm | In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? Select the correct option:
A) 45 B) 56 C) 47 D) 57 E) 49 | <gadget id="calculator">48 - 1</gadget>
<output>47</output>
<result>C</result> | C | 47 | In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? | {
"A": "45",
"B": "56",
"C": "47",
"D": "57",
"E": "49"
} | subtract(48, const_1) | subtract(n0,const_1)| | "explanation : with all the talk of doubling and halves , your brain jumps to the conclusion that to solve the problem of when the lily patch covers half the lake , all you have to do is divide the number of days it took to fill the lake ( 48 ) in half . it ' s understandable but wrong . the problem says that the patch doubles in size every day , which means that on any day , the lily patch was half the size the day before . so if the patch reaches the entire size of the lake on the 48 th day , it means the lily pad was half the size of the lake on day 47 . correct answer is c ) 47" | physics |
math_qa__grkwKlp8r3SK3a1d | The least common multiple of positive integer d and 3-digit integer n is 690. If n is not divisible by 3 and d is not divisible by 2, what is the value of n? Choose the correct answer: A) 115 B) 230 C) 460 D) 575 E) 690 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">690 / 2</gadget>
<output>345</output>
<gadget id="calculator">345 / 3</gadget>
<output>115</output>
<gadget id="calculator">115 / 5</gadget>
<output>23</output>
<gadget id="calculator">10 * 23</gadget>
<output>230</output>
<result>B</result> | B | 230 | The least common multiple of positive integer d and 3-digit integer n is 690. If n is not divisible by 3 and d is not divisible by 2, what is the value of n? | {
"A": "115",
"B": "230",
"C": "460",
"D": "575",
"E": "690"
} | multiply(multiply(2, add(const_3, const_2)), divide(divide(divide(690, const_2), const_3), add(const_3, const_2))) | add(const_2,const_3)|divide(n1,const_2)|divide(#1,const_3)|multiply(n3,#0)|divide(#2,#0)|multiply(#4,#3) | the lcm of n and d is 690 = 2 * 3 * 5 * 23 . d is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to d . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b . | general |
math_qa__hK9XasNxaw0WfqT9 | In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day. Choose the correct choice from the following options
A) 172,700 B) 172,800 C) 172,900 D) 173,000 E) 173,100 | <gadget id="calculator">7 - 3</gadget>
<output>4</output>
<gadget id="calculator">4 * 3_600</gadget>
<output>14_400</output>
<gadget id="calculator">14_400 * 12</gadget>
<output>172_800</output>
<result>B</result> | B | 172,800 | In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day. | {
"A": "172,700",
"B": "172,800",
"C": "172,900",
"D": "173,000",
"E": "173,100"
} | multiply(multiply(subtract(7, 3), const_3600), const_12) | subtract(n0,n1)|multiply(#0,const_3600)|multiply(#1,const_12)| | "this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 7 - 3 = 4 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 4 = 172,800 . hence b ." | general |
math_qa__Cw0q1PPePPc7WJRZ | Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 54 sec. The length of each train is? Choose the correct choice from the following answers:
A) 50
B) 26
C) 75
D) 28
E) 21 | <gadget id="calculator">46 - 36</gadget>
<output>10</output>
<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 3_600</gadget>
<output>25/9 = around 2.777778</output>
<gadget id="calculator">54 * (25/9)</gadget>
<output>150</output>
<gadget id="calculator">150 / 2</gadget>
<output>75</output>
<result>C</result> | C | 75 | Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 54 sec. The length of each train is? | {
"A": "50",
"B": "26",
"C": "75",
"D": "28",
"E": "21"
} | divide(multiply(54, divide(multiply(subtract(46, 36), const_1000), const_3600)), const_2) | subtract(n0,n1)|multiply(#0,const_1000)|divide(#1,const_3600)|multiply(n2,#2)|divide(#3,const_2)| | "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 54 = 25 / 9 = > x = 75 . answer : c" | general |
math_qa__ESYrznBlZFPXY751 | A number is doubled and 8 is added. If the resultant is trebled, it becomes 84. What is that number? Options:
A) 10
B) 6
C) 8
D) none of these
E) can not be determined | <gadget id="calculator">3 * 8</gadget>
<output>24</output>
<gadget id="calculator">84 - 24</gadget>
<output>60</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">60 / 6</gadget>
<output>10</output>
<result>A</result> | A | 10 | A number is doubled and 8 is added. If the resultant is trebled, it becomes 84. What is that number? | {
"A": "10",
"B": "6",
"C": "8",
"D": "none of these",
"E": "can not be determined"
} | divide(subtract(84, multiply(const_3, 8)), multiply(const_3, const_2)) | multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)| | "solution let the number be x . then , 3 ( 2 x + 8 ) ‹ = › 84 ‹ = › 2 x + 8 = 28 ‹ = › 2 x = 20 x = 10 . answer a" | general |
math_qa__07pEs7iJS05UA1li | The average of 10 numbers is calculated as 5. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? Choose the most appropriate option.
A) 2 B) 3 C) 4 D) 5 E) 6 | <gadget id="calculator">36 - 26</gadget>
<output>10</output>
<gadget id="calculator">10 / 10</gadget>
<output>1</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<result>E</result> | E | 6 | The average of 10 numbers is calculated as 5. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? | {
"A": "2",
"B": "3",
"C": "4",
"D": "5",
"E": "6"
} | add(5, divide(subtract(36, 26), 10)) | subtract(n2,n3)|divide(#0,n0)|add(n1,#1)| | "10 * 5 + 36 – 26 = 60 / 10 = 6 answer : e" | general |
math_qa__Jt3FRUhdQEU1EnU6 | If (10^4 * 3.456789)^14 is written as a single term, how many digits would be to the right of the decimal place?
Pick one
A) 9
B) 14
C) 21
D) 28
E) 42 | <gadget id="calculator">14 * 2</gadget>
<output>28</output>
<result>D</result> | D | 28 | If (10^4 * 3.456789)^14 is written as a single term, how many digits would be to the right of the decimal place? | {
"A": "9",
"B": "14",
"C": "21",
"D": "28",
"E": "42"
} | multiply(14, const_2) | multiply(n3,const_2) | 3.456789 ^ 14 has 6 * 14 = 84 decimal places . 10 ^ 56 moves the decimal place to the right 56 places . ( 10 ^ 4 * 3.456789 ) ^ 14 has 84 - 56 = 28 digits after the decimal point . the answer is d . | general |
math_qa__oG7EebxGXSCyeNMD | A,B,C can complete a piece of work in 16,6,12 days. Working together, they complete the same work in how many days? Options: A) 2 B) 48 / 15 C) 7 / 9 D) 10 E) 24 / 7 | <gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/16) + (1/6)</gadget>
<output>11/48 = around 0.229167</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(11/48) + (1/12)</gadget>
<output>5/16 = around 0.3125</output>
<gadget id="calculator">1 / (5/16)</gadget>
<output>16/5 = around 3.2</output>
<result>B</result> | B | 3.2 | A,B,C can complete a piece of work in 16,6,12 days. Working together, they complete the same work in how many days? | {
"A": "2",
"B": "48 / 15",
"C": "7 / 9",
"D": "10",
"E": "24 / 7"
} | divide(const_1, add(add(divide(const_1, 16), divide(const_1, add(const_4, const_2))), divide(const_1, multiply(const_2, add(const_4, const_2))))) | add(const_2,const_4)|divide(const_1,n0)|divide(const_1,#0)|multiply(#0,const_2)|add(#1,#2)|divide(const_1,#3)|add(#4,#5)|divide(const_1,#6) | a + b + c 1 day work = 1 / 16 + 1 / 6 + 1 / 12 = 15 / 48 a , b , c together will complete the job in 48 / 15 days answer is b | physics |
math_qa__uWdJQwUUmxfqGEEm | Certain stocks in January were 10% less than they were in February and 20% greater than they were in March. What was the percentage decrease in the stocks from February to March? Choose the correct option
A) 5 % B) 10 % C) 20 % D) 25 % E) 50 % | <gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">100 / (9/10)</gadget>
<output>1_000/9 = around 111.111111</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">100 / (6/5)</gadget>
<output>250/3 = around 83.333333</output>
<gadget id="calculator">(1_000/9) - (250/3)</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">(250/9) / (1_000/9)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>D</result> | D | 25 | Certain stocks in January were 10% less than they were in February and 20% greater than they were in March. What was the percentage decrease in the stocks from February to March? | {
"A": "5 %",
"B": "10 %",
"C": "20 %",
"D": "25 %",
"E": "50 %"
} | multiply(divide(subtract(divide(const_100, divide(subtract(const_100, 10), const_100)), divide(const_100, divide(add(const_100, 20), const_100))), divide(const_100, divide(subtract(const_100, 10), const_100))), const_100) | add(n1,const_100)|subtract(const_100,n0)|divide(#1,const_100)|divide(#0,const_100)|divide(const_100,#2)|divide(const_100,#3)|subtract(#4,#5)|divide(#6,#4)|multiply(#7,const_100) | let j , f , m be the values of the stock in jan , feb and march . thus , per the question , j = 0.9 f = 1.2 m - - - - > m = 0.75 f thus the % decrease from f to m = ( f - m ) / ( f ) * 100 = ( f - 0.75 f ) / f * 100 = 0.25 * 100 = 25 % , d is the correct answer . | general |
math_qa__dzaBTh0EJbKyJyre | To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 15 hours a day?
Choose the correct option
A) 23 B) 22 C) 21 D) 20 E) 19.2 | <gadget id="calculator">30 * 12</gadget>
<output>360</output>
<gadget id="calculator">360 * 8</gadget>
<output>2_880</output>
<gadget id="calculator">2_880 * 2</gadget>
<output>5_760</output>
<gadget id="calculator">20 * 15</gadget>
<output>300</output>
<gadget id="calculator">5_760 / 300</gadget>
<output>96/5 = around 19.2</output>
<result>E</result> | E | 19.2 | To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 15 hours a day? | {
"A": "23",
"B": "22",
"C": "21",
"D": "20",
"E": "19.2"
} | divide(multiply(multiply(multiply(30, 12), 8), 2), multiply(20, 15)) | multiply(n1,n2)|multiply(n4,n6)|multiply(n3,#0)|multiply(n5,#2)|divide(#3,#1)| | "man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 15 = 300 therefore number of days = 5760 / 300 = 19.2 days ans = e" | physics |
math_qa__9qgcHMl4bu3OtUNC | A scuba diver descends at a rate of 80 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 4000feet below the sea level..how long will he take to reach the ship?
Select the correct option.
A) 70 minutes
B) 72 minutes
C) 50 minutes
D) 66 minutes
E) 67 minutes | <gadget id="calculator">4_000 / 80</gadget>
<output>50</output>
<result>C</result> | C | 50 | A scuba diver descends at a rate of 80 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 4000feet below the sea level..how long will he take to reach the ship? | {
"A": "70 minutes",
"B": "72 minutes",
"C": "50 minutes",
"D": "66 minutes",
"E": "67 minutes"
} | divide(4000, 80) | divide(n1,n0)| | "time taken to reach = 4000 / 80 = 50 minutes answer : c" | gain |
math_qa__hDtoYJE0cZyybpOE | The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 784 feet squared, what is the difference between the length and the width of the roof? Choices.
A) 38 . B) 40 . C) 42 . D) 44 . E) 46 . | <gadget id="calculator">784 / 4</gadget>
<output>196</output>
<gadget id="calculator">196 ** (1/2)</gadget>
<output>14</output>
<gadget id="calculator">14 * 4</gadget>
<output>56</output>
<gadget id="calculator">56 - 14</gadget>
<output>42</output>
<result>C</result> | C | 42 | The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 784 feet squared, what is the difference between the length and the width of the roof? | {
"A": "38 .",
"B": "40 .",
"C": "42 .",
"D": "44 .",
"E": "46 ."
} | subtract(multiply(sqrt(divide(784, 4)), 4), sqrt(divide(784, 4))) | divide(n1,n0)|sqrt(#0)|multiply(#1,n0)|subtract(#2,#1)| | "let the width = x x * 4 x = 784 x ^ 2 = 196 x = 14 length = 4 * 14 = 56 difference = 56 - 14 = 42 c is the answer" | geometry |
math_qa__5hx7zPNP82bW65Eg | two water pumps , working simultaneously at their respective constant rates , took exactly 5 hours to fill a certain swimming pool . if the constant rate of one pump was 1.5 times the constant rate of the other , how many hours would it have taken the slower pump to fill the pool if it had worked alone at its constant rate ? Answers.
A) 8.5
B) 10.5
C) 12.5
D) 14.5
E) 16.5 | <gadget id="calculator">1.5 + 1</gadget>
<output>2.5</output>
<gadget id="calculator">2.5 * 5</gadget>
<output>12.5</output>
<result>C</result> | C | 12.5 | two water pumps , working simultaneously at their respective constant rates , took exactly 5 hours to fill a certain swimming pool . if the constant rate of one pump was 1.5 times the constant rate of the other , how many hours would it have taken the slower pump to fill the pool if it had worked alone at its constant rate ? | {
"A": "8.5",
"B": "10.5",
"C": "12.5",
"D": "14.5",
"E": "16.5"
} | multiply(add(1.5, const_1), 5) | add(n1,const_1)|multiply(n0,#0) | let x be the rate of the slower pump . then 1.5 x is the rate of the faster pump . both pumps together can fill 1 / 5 of the pool each hour . 2.5 x = 1 / 5 x = 1 / 12.5 = 2 / 25 the slower pump could fill the pool in 25 / 2 = 12.5 hours . the answer is c . | physics |
math_qa__JfPJ8qX23ot9xL2u | A positive number x is multiplied by 4, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ? Choose the correct choice from the following answers: A) 9 / 4 B) 3 / 2 C) 4 / 3 D) 2 / 3 E) 1 / 2 | <gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<result>C</result> | C | 1.333333 | A positive number x is multiplied by 4, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ? | {
"A": "9 / 4",
"B": "3 / 2",
"C": "4 / 3",
"D": "2 / 3",
"E": "1 / 2"
} | divide(4, 3) | divide(n0,n1) | sq rt ( 4 x / 3 ) = x = > 4 x / 3 = x ^ 2 = > x = 4 / 3 ans - c | general |
math_qa__Qr6yAFaV9ly7MVfE | A 270 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train. Choose the correct choice from the following answers.
A) 210 m
B) 220 m
C) 230 m
D) 240 m
E) 250 m | <gadget id="calculator">120 + 80</gadget>
<output>200</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">200 * (5/18)</gadget>
<output>500/9 = around 55.555556</output>
<gadget id="calculator">9 * (500/9)</gadget>
<output>500</output>
<gadget id="calculator">500 - 270</gadget>
<output>230</output>
<result>C</result> | C | 230 | A 270 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train. | {
"A": "210 m",
"B": "220 m",
"C": "230 m",
"D": "240 m",
"E": "250 m"
} | subtract(multiply(9, multiply(add(120, 80), const_0_2778)), 270) | add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)| | "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 270 / 9 = 500 / 9 x = 230 ans is 230 m answer : c" | physics |
math_qa__TIh6kmiBZFykTu9y | Car Z travels 51 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour? Choose the correct answer
A) 320 B) 375.2 C) 400 D) 408 E) 440 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 51</gadget>
<output>204/5 = around 40.8</output>
<gadget id="calculator">(204/5) * 10</gadget>
<output>408</output>
<result>D</result> | D | 408 | Car Z travels 51 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour? | {
"A": "320",
"B": "375.2",
"C": "400",
"D": "408",
"E": "440"
} | multiply(multiply(subtract(const_1, divide(20, const_100)), 51), 10) | divide(n2,const_100)|subtract(const_1,#0)|multiply(n0,#1)|multiply(n4,#2)| | "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 51 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 40.8 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 40.8 miles / gallon * 10 gallons = 408 miles . answer d ." | gain |
math_qa__MriDUqGUemW64wdp | What is 0.02 percent of 12,356? Choose the correct choice from the following.
A) 0.247 B) 2.47 C) 24.7 D) 0.0247 E) 0.00247 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 * 100</gadget>
<output>1_200</output>
<gadget id="calculator">10 * 1_200</gadget>
<output>12_000</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 5</gadget>
<output>35</output>
<gadget id="calculator">35 * 10</gadget>
<output>350</output>
<gadget id="calculator">12_000 + 350</gadget>
<output>12_350</output>
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">12_350 + 6</gadget>
<output>12_356</output>
<gadget id="calculator">0.02 * 12_356</gadget>
<output>247.12</output>
<gadget id="calculator">247.12 / 100</gadget>
<output>2.4712</output>
<result>B</result> | B | 2.47 | What is 0.02 percent of 12,356? | {
"A": "0.247",
"B": "2.47",
"C": "24.7",
"D": "0.0247",
"E": "0.00247"
} | divide(multiply(0.02, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100) | add(const_2,const_3)|add(const_3,const_4)|add(const_3,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#3,const_100)|multiply(#1,#0)|multiply(#4,#5)|multiply(#6,#4)|add(#7,#8)|add(#9,#2)|multiply(n0,#10)|divide(#11,const_100)| | since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.02 ( 1 / 100 ) 12,356 . the answer is 2.47 . hence , the correct answer is b . | gain |
math_qa__zhOCfPAfOCEY1MDT | Because he’s taxed by his home planet, Mork pays a tax rate of 45% on his income, while Mindy pays a rate of only 25% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate? Pick: A) 29 % B) 31 % C) 33 % D) 35 % E) 37 % | <gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">4 * (1/4)</gadget>
<output>1</output>
<gadget id="calculator">(9/20) + 1</gadget>
<output>29/20 = around 1.45</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">(29/20) / 5</gadget>
<output>29/100 = around 0.29</output>
<gadget id="calculator">100 * (29/100)</gadget>
<output>29</output>
<result>A</result> | A | 29 | Because he’s taxed by his home planet, Mork pays a tax rate of 45% on his income, while Mindy pays a rate of only 25% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate? | {
"A": "29 %",
"B": "31 %",
"C": "33 %",
"D": "35 %",
"E": "37 %"
} | multiply(const_100, divide(add(divide(45, const_100), multiply(4, divide(25, const_100))), add(const_1, 4))) | 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)| | "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.45 x + 1.0 x = 1.45 x 1.45 x / 5 x = 0.29 the answer is a ." | gain |
math_qa__LSg59cN87ZUTqf0h | Reema took a loan of Rs 1100 with simple interest for as many years as the rate of interest. If she paid Rs. 704 as interest at the end of the loan period, what was the rate of interest. Choose the correct choice from the following choices: A) 5 % B) 6 % C) 7 % D) 8 % E) 9 % | <gadget id="calculator">1_100 / 100</gadget>
<output>11</output>
<gadget id="calculator">704 / 11</gadget>
<output>64</output>
<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>
<result>D</result> | D | 8 | Reema took a loan of Rs 1100 with simple interest for as many years as the rate of interest. If she paid Rs. 704 as interest at the end of the loan period, what was the rate of interest. | {
"A": "5 %",
"B": "6 %",
"C": "7 %",
"D": "8 %",
"E": "9 %"
} | sqrt(divide(704, divide(1100, const_100))) | divide(n0,const_100)|divide(n1,#0)|sqrt(#1)| | "explanation : let rate = r % then time = r years . = > 1100 ∗ r ∗ r / 100 = 704 = > r 2 = 64 = > r = 8 % option d" | gain |
math_qa__H06MxJF4SF5OOxNk | In a company, 52 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women? Pick one: A) 65 % B) 70 % C) 75 % D) 80 % E) 85 % | <gadget id="calculator">100 - 52</gadget>
<output>48</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">60 * (7/10)</gadget>
<output>42</output>
<gadget id="calculator">60 - 42</gadget>
<output>18</output>
<gadget id="calculator">48 - 18</gadget>
<output>30</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">30 / 40</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">100 * (3/4)</gadget>
<output>75</output>
<result>C</result> | C | 75 | In a company, 52 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women? | {
"A": "65 %",
"B": "70 %",
"C": "75 %",
"D": "80 %",
"E": "85 %"
} | multiply(const_100, divide(subtract(subtract(const_100, 52), subtract(60, multiply(60, divide(70, const_100)))), subtract(const_100, 60))) | divide(n2,const_100)|subtract(const_100,n0)|subtract(const_100,n1)|multiply(n1,#0)|subtract(n1,#3)|subtract(#1,#4)|divide(#5,#2)|multiply(#6,const_100)| | "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 48 % of all employees are women , so non - union women are 48 % - 18 % = 30 % 40 % of all employees are non - union . the percent of non - union employees who are women is 30 % / 40 % = 75 % the answer is c ." | gain |
math_qa__E6g3scMszAXDKbRh | How long does a lorry 200 m long traveling at 80 kmph takes to cross a bridge of 200 m in length? Options:
A) 15
B) 17
C) 15
D) 16
E) 18 | <gadget id="calculator">200 + 200</gadget>
<output>400</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">80 * (5/18)</gadget>
<output>200/9 = around 22.222222</output>
<gadget id="calculator">400 / (200/9)</gadget>
<output>18</output>
<result>E</result> | E | 18 | How long does a lorry 200 m long traveling at 80 kmph takes to cross a bridge of 200 m in length? | {
"A": "15",
"B": "17",
"C": "15",
"D": "16",
"E": "18"
} | divide(add(200, 200), multiply(80, const_0_2778)) | add(n0,n0)|multiply(n1,const_0_2778)|divide(#0,#1) | d = 200 + 200 = 400 m s = 80 * 5 / 18 = 200 / 9 t = 400 * 9 / 200 = 18 sec answer : e | physics |
math_qa__6AnmrHmxAc4nYxQ6 | Pradeep has to obtain 20% of the total marks to pass. He got 160 marks and failed by 25 marks. The maximum marks are Select the correct option:
A) 1925 B) 600 C) 925 D) 1325 E) 900 | <gadget id="calculator">160 + 25</gadget>
<output>185</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">185 / (1/5)</gadget>
<output>925</output>
<result>C</result> | C | 925 | Pradeep has to obtain 20% of the total marks to pass. He got 160 marks and failed by 25 marks. The maximum marks are | {
"A": "1925",
"B": "600",
"C": "925",
"D": "1325",
"E": "900"
} | divide(add(160, 25), divide(20, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1)| | "explanation : let their maximum marks be x . then , 20 % of x = 160 + 25 = > 20 / 100 x = 185 x = ( 18500 / 20 ) x = 925 . answer : c" | general |
math_qa__OMfXAZg62brIw2bQ | What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? Pick
A) rs . 2.04 B) rs . 2.09 C) rs . 2.06 D) rs . 2.22 E) rs . 2.08 | <gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">1 + (1/50)</gadget>
<output>51/50 = around 1.02</output>
<gadget id="calculator">(51/50) * (51/50)</gadget>
<output>2_601/2_500 = around 1.0404</output>
<gadget id="calculator">(2_601/2_500) * (51/50)</gadget>
<output>132_651/125_000 = around 1.061208</output>
<gadget id="calculator">5_000 * (132_651/125_000)</gadget>
<output>132_651/25 = around 5_306.04</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">(51/50) * (26/25)</gadget>
<output>663/625 = around 1.0608</output>
<gadget id="calculator">5_000 * (663/625)</gadget>
<output>5_304</output>
<gadget id="calculator">(132_651/25) - 5_304</gadget>
<output>51/25 = around 2.04</output>
<result>A</result> | A | 2.04 | What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly? | {
"A": "rs . 2.04",
"B": "rs . 2.09",
"C": "rs . 2.06",
"D": "rs . 2.22",
"E": "rs . 2.08"
} | subtract(multiply(5000, multiply(multiply(add(1, divide(2, const_100)), add(1, divide(2, const_100))), add(1, divide(2, const_100)))), multiply(5000, multiply(add(1, divide(2, const_100)), add(1, divide(4, const_100))))) | divide(n3,const_100)|divide(n4,const_100)|add(#0,n1)|add(#1,n1)|multiply(#2,#2)|multiply(#2,#3)|multiply(#2,#4)|multiply(n0,#5)|multiply(n0,#6)|subtract(#8,#7)| | "c . i . when interest is compounded yearly = [ 5000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 5000 * 26 / 25 * 51 / 50 = rs . 5304 c . i . when interest is compounded half - yearly = [ 5000 * ( 1 + 2 / 100 ) 2 ] = ( 5000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 5306.04 difference = ( 5306.04 - 5304 ) = rs . 2.04 . answer : a" | general |
math_qa__erE9xlQAnffNW22E | A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 30 hour to row to a place and come back, how far is the place? Choose the correct choice from the following: A) 144 km B) 30 km C) 48 km D) 12 km E) 15 km | <gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">96 * 30</gadget>
<output>2_880</output>
<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<gadget id="calculator">2_880 / 20</gadget>
<output>144</output>
<result>A</result> | A | 144 | A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 30 hour to row to a place and come back, how far is the place? | {
"A": "144 km",
"B": "30 km",
"C": "48 km",
"D": "12 km",
"E": "15 km"
} | divide(multiply(multiply(subtract(10, 2), add(10, 2)), 30), add(subtract(10, 2), add(10, 2))) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|multiply(#0,#1)|multiply(n2,#3)|divide(#4,#2)| | "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 30 2 x + 3 x = 720 x = 144 km answer is a" | physics |
math_qa__gdvJaE75ocMhteoO | Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate Q in miles per hour for the entire trip? Choose the correct choice from the following answers: A) q = 26.7 B) q = 30.0 C) q = 40.0 D) q = 53.3 E) q = 60.0 | <gadget id="calculator">640 / 2</gadget>
<output>320</output>
<gadget id="calculator">320 / 80</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">640 / 16</gadget>
<output>40</output>
<result>C</result> | C | 40 | Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate Q in miles per hour for the entire trip? | {
"A": "q = 26.7",
"B": "q = 30.0",
"C": "q = 40.0",
"D": "q = 53.3",
"E": "q = 60.0"
} | divide(640, add(add(multiply(divide(divide(640, const_2), 80), const_2), divide(divide(640, const_2), 80)), divide(divide(640, const_2), 80))) | divide(n0,const_2)|divide(#0,n1)|multiply(#1,const_2)|add(#1,#2)|add(#3,#1)|divide(n0,#4)| | "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ." | physics |
math_qa__QQfNgEVD0ofHVF0D | 6 friends went to a hotel and decided to pay the bill amount equally. But 5 of them could pay Rs. 100 each as a result 6th has to pay Rs. 100 extra than his share. Find the amount paid by him.
Options:
A) 156
B) 220
C) 130
D) 240
E) none | <gadget id="calculator">100 * 5</gadget>
<output>500</output>
<gadget id="calculator">500 + 100</gadget>
<output>600</output>
<gadget id="calculator">600 / 5</gadget>
<output>120</output>
<gadget id="calculator">100 + 120</gadget>
<output>220</output>
<result>B</result> | B | 220 | 6 friends went to a hotel and decided to pay the bill amount equally. But 5 of them could pay Rs. 100 each as a result 6th has to pay Rs. 100 extra than his share. Find the amount paid by him. | {
"A": "156",
"B": "220",
"C": "130",
"D": "240",
"E": "none"
} | add(100, divide(add(multiply(100, 5), 100), 5)) | multiply(n1,n2)|add(n4,#0)|divide(#1,n1)|add(n4,#2)| | "explanation : average amount paid by 5 persons = rs . 100 increase in average due to rs . 120 paid extra by the 6 th men = rs . 100 / 5 = rs . 20 therefore , average expenditure of 6 friends = rs . 100 + rs . 20 = rs . 120 therefore , amount paid by the 6 th men = rs . 120 + rs . 100 = rs . 220 correct option : b" | general |
math_qa__BrSBUCjsO9ur3CLr | The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is: Choose the correct choice from the following options.
A) 12
B) 24
C) 84
D) 48
E) 42 | <gadget id="calculator">84 * 21</gadget>
<output>1_764</output>
<gadget id="calculator">1_764 / 4</gadget>
<output>441</output>
<gadget id="calculator">441 ** (1/2)</gadget>
<output>21</output>
<gadget id="calculator">21 * 4</gadget>
<output>84</output>
<result>C</result> | C | 84 | The H.C.F and L.C.M of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is: | {
"A": "12",
"B": "24",
"C": "84",
"D": "48",
"E": "42"
} | multiply(sqrt(divide(multiply(84, 21), 4)), 4) | multiply(n0,n1)|divide(#0,n3)|sqrt(#1)|multiply(n3,#2)| | "let the numbers be x and 4 x . then , x * 4 x = 84 * 21 x 2 = ( 84 * 21 ) / 4 = x = 21 . hence , larger number = 4 x = 84 . answer : c" | other |
math_qa__1ehxRnzOBM4AynoM | If 50% of 3/5 of a number is 36, then the number is?
Choose the correct choice from the following options.
A) 120 B) 100 C) 75 D) 90 E) none of these | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(1/2) * (3/5)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">36 / (3/10)</gadget>
<output>120</output>
<result>A</result> | A | 120 | If 50% of 3/5 of a number is 36, then the number is? | {
"A": "120",
"B": "100",
"C": "75",
"D": "90",
"E": "none of these"
} | divide(36, multiply(divide(50, const_100), divide(3, 5))) | divide(n0,const_100)|divide(n1,n2)|multiply(#0,#1)|divide(n3,#2) | let the number be x . then 50 % of 3 / 5 of x = 36 50 / 100 * 3 / 5 * x = 36 x = ( 36 * 10 / 3 ) = 120 required number = 120 . correct option : a | gain |
math_qa__JQmKBdFuLMeONfx5 | A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability T that both selected dogs are NOT littermates? Pick:
A) 1 / 6
B) 2 / 9
C) 5 / 6
D) 7 / 9
E) 8 / 9 | <gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>
<result>C</result> | C | 0.833333 | A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability T that both selected dogs are NOT littermates? | {
"A": "1 / 6",
"B": "2 / 9",
"C": "5 / 6",
"D": "7 / 9",
"E": "8 / 9"
} | divide(const_5, 6) | divide(const_5,n1)| | "we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) t = 5 / 6 . answer : c" | other |
math_qa__42cZoVMHIv7AG2Te | The manufacturing cost of a shoe is Rs.180 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains Choose one:
A) rs 222 B) rs 216 C) rs 220 D) rs 210 E) rs 217 | <gadget id="calculator">500 / 100</gadget>
<output>5</output>
<gadget id="calculator">180 + 5</gadget>
<output>185</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 185</gadget>
<output>37</output>
<gadget id="calculator">185 + 37</gadget>
<output>222</output>
<result>A</result> | A | 222 | The manufacturing cost of a shoe is Rs.180 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains | {
"A": "rs 222",
"B": "rs 216",
"C": "rs 220",
"D": "rs 210",
"E": "rs 217"
} | add(add(180, divide(500, 100)), multiply(divide(20, const_100), add(180, divide(500, 100)))) | divide(n1,n2)|divide(n3,const_100)|add(n0,#0)|multiply(#2,#1)|add(#2,#3) | explanation : total cost of a watch = 180 + ( 500 / 100 ) = 185 . gain = 20 % = > sp = 1.2 cp = 1.2 x 185 = 222 answer : a | gain |
math_qa__uvhl7HICBo6p7ipF | A shirt goes on sale for 80% of its original price. One week later, the sale price is marked down 20%. The final price is what percent of the original price? Options.
A) 72 %
B) 70 %
C) 52 %
D) 64 %
E) 28 % | <gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 20</gadget>
<output>16</output>
<gadget id="calculator">80 - 16</gadget>
<output>64</output>
<result>D</result> | D | 64 | A shirt goes on sale for 80% of its original price. One week later, the sale price is marked down 20%. The final price is what percent of the original price? | {
"A": "72 %",
"B": "70 %",
"C": "52 %",
"D": "64 %",
"E": "28 %"
} | subtract(80, multiply(divide(80, const_100), 20)) | divide(n0,const_100)|multiply(n1,#0)|subtract(n0,#1)| | "just assume original price is 100 . sale price = 80 then it is marked down by 20 % = 80 - 16 = 64 . hence it is 64 % od the original price . hence answer is d ." | gain |
math_qa__zJcHnTUrqlQUspXc | To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 14 hours a day? Choose the correct option.
A) 24 B) 23 C) 24 D) 20.57 E) 22 | <gadget id="calculator">30 * 12</gadget>
<output>360</output>
<gadget id="calculator">360 * 8</gadget>
<output>2_880</output>
<gadget id="calculator">2_880 * 2</gadget>
<output>5_760</output>
<gadget id="calculator">20 * 14</gadget>
<output>280</output>
<gadget id="calculator">5_760 / 280</gadget>
<output>144/7 = around 20.571429</output>
<result>D</result> | D | 20.57 | To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 14 hours a day? | {
"A": "24",
"B": "23",
"C": "24",
"D": "20.57",
"E": "22"
} | divide(multiply(multiply(multiply(30, 12), 8), 2), multiply(20, 14)) | multiply(n1,n2)|multiply(n4,n6)|multiply(n3,#0)|multiply(n5,#2)|divide(#3,#1) | man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 14 = 280 therefore number of days = 5760 / 280 = 20.57 days ans = d | physics |
math_qa__GUHg4gozDND2ZX7o | Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is? Choose the correct choice.
A) 36.7 ° c B) 38.6 ° c C) 39.8 ° c D) 41.9 ° c E) 51.9 ° c | <gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">40.3 * 4</gadget>
<output>161.2</output>
<gadget id="calculator">39.1 * 4</gadget>
<output>156.4</output>
<gadget id="calculator">161.2 - 156.4</gadget>
<output>4.8</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) / 3</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">4.8 + (1/9)</gadget>
<output>4.911111</output>
<gadget id="calculator">36 + 4.911111</gadget>
<output>40.911111</output>
<result>D</result> | D | 41.9 | Average temperature of first 4 days of a week is 6°C and that of the last 4 days is 40.3°C. If the average temperature of the week be 39.1°C, the temperature on 4th day is? | {
"A": "36.7 ° c",
"B": "38.6 ° c",
"C": "39.8 ° c",
"D": "41.9 ° c",
"E": "51.9 ° c"
} | add(multiply(6, 6), add(subtract(multiply(40.3, 4), multiply(39.1, 4)), divide(const_0_33, const_3))) | divide(const_0_33,const_3)|multiply(n0,n3)|multiply(n0,n4)|multiply(n1,n1)|subtract(#1,#2)|add(#0,#4)|add(#5,#3) | let temperature on 4 th day be x ° c therefore , 4 x 38.6 + 4 x 40.3 - x = 7 x 39.1 = > x = 41.9 therefore , temperature on 4 th day = 41.9 ° c . answer : d | physics |
math_qa__viKH6ZZVuiPIPZlS | There are 18 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season? Choose the correct choice from the following choices:
A) 1370
B) 1530
C) 1790
D) 1950
E) 2110 | <gadget id="calculator">18 - 1</gadget>
<output>17</output>
<gadget id="calculator">18 * 17</gadget>
<output>306</output>
<gadget id="calculator">306 * 10</gadget>
<output>3_060</output>
<gadget id="calculator">3_060 / 2</gadget>
<output>1_530</output>
<result>B</result> | B | 1,530 | There are 18 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season? | {
"A": "1370",
"B": "1530",
"C": "1790",
"D": "1950",
"E": "2110"
} | divide(multiply(multiply(18, subtract(18, const_1)), 10), const_2) | subtract(n0,const_1)|multiply(n0,#0)|multiply(n1,#1)|divide(#2,const_2)| | "the number of ways to choose two teams is 18 c 2 = 18 * 17 / 2 = 153 the total number of games in the season is 10 * 153 = 1530 . the answer is b ." | general |
math_qa__Pt1jHVwoYBGMs0rg | A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 7% dividend at the end of the year,then how much does he get ? Choose one:
A) rs . 500 B) rs . 840 C) rs . 650 D) rs . 720 E) none | <gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">4 * 1_000</gadget>
<output>4_000</output>
<gadget id="calculator">10_000 + 4_000</gadget>
<output>14_000</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">14_000 + 400</gadget>
<output>14_400</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">100 * (1/5)</gadget>
<output>20</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">14_400 / 120</gadget>
<output>120</output>
<gadget id="calculator">100 * 120</gadget>
<output>12_000</output>
<gadget id="calculator">7 / 100</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">12_000 * (7/100)</gadget>
<output>840</output>
<result>B</result> | B | 840 | A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 7% dividend at the end of the year,then how much does he get ? | {
"A": "rs . 500",
"B": "rs . 840",
"C": "rs . 650",
"D": "rs . 720",
"E": "none"
} | multiply(multiply(100, divide(add(add(multiply(const_10, const_1000), multiply(const_4, const_1000)), multiply(const_4, const_100)), add(100, multiply(100, divide(20, const_100))))), divide(7, const_100)) | divide(n3,const_100)|divide(n2,const_100)|multiply(const_10,const_1000)|multiply(const_1000,const_4)|multiply(const_100,const_4)|add(#2,#3)|multiply(n1,#1)|add(#5,#4)|add(n1,#6)|divide(#7,#8)|multiply(n1,#9)|multiply(#0,#10) | solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 7 / 100 x 12000 ) = rs . 840 . answer b | gain |
math_qa__X106jTFzGcoYRb0h | The distance between Delhi and Mathura is 130 kms. A starts from Delhi with a speed of 25 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 30 kmph at 9 p.m. from Delhi. When will they meet? Choose the most appropriate option.
A) 11
B) 77
C) 16
D) 10
E) 98 | <gadget id="calculator">25 + 30</gadget>
<output>55</output>
<gadget id="calculator">130 / 55</gadget>
<output>26/11 = around 2.363636</output>
<gadget id="calculator">9 + (26/11)</gadget>
<output>125/11 = around 11.363636</output>
<result>A</result> | A | 11 | The distance between Delhi and Mathura is 130 kms. A starts from Delhi with a speed of 25 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 30 kmph at 9 p.m. from Delhi. When will they meet? | {
"A": "11",
"B": "77",
"C": "16",
"D": "10",
"E": "98"
} | add(9, divide(130, add(25, 30))) | add(n1,n3)|divide(n0,#0)|add(n4,#1)| | "d = 130 – 25 = 105 rs = 30 + 25 = 55 t = 105 / 55 = 2 hours 8 a . m . + 2 = 11 a . m . . answer : a" | physics |
math_qa__vGcm2k5Q3PbR8Ron | How is 1/2 % expressed as a decimal fraction? Choose the correct choice from the following:
A) 0.5 B) 0.05 C) 0.005 D) 0.0005 E) 5 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) / 100</gadget>
<output>1/200 = around 0.005</output>
<result>C</result> | C | 0.005 | How is 1/2 % expressed as a decimal fraction? | {
"A": "0.5",
"B": "0.05",
"C": "0.005",
"D": "0.0005",
"E": "5"
} | divide(divide(1, 2), const_100) | divide(n0,n1)|divide(#0,const_100) | as 1 / 2 = 0.5 and its percent value will be 0.5 / 100 = 0.005 answer : c | general |
math_qa__Qr34ow3GRmwnNCJ4 | A hostel had provisions for 250 men for 28 days. If 50 men left the hostel, how long will the food last at the same rate?
Pick: A) 35 B) 40 C) 50 D) 60 E) 65 | <gadget id="calculator">250 * 28</gadget>
<output>7_000</output>
<gadget id="calculator">250 - 50</gadget>
<output>200</output>
<gadget id="calculator">7_000 / 200</gadget>
<output>35</output>
<result>A</result> | A | 35 | A hostel had provisions for 250 men for 28 days. If 50 men left the hostel, how long will the food last at the same rate? | {
"A": "35",
"B": "40",
"C": "50",
"D": "60",
"E": "65"
} | divide(multiply(250, 28), subtract(250, 50)) | multiply(n0,n1)|subtract(n0,n2)|divide(#0,#1) | a hostel had provisions for 250 men for 28 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 28 250 × 28 = 200 x 5 × 28 = 4 x x = 5 × 7 = 35 answer a | gain |
math_qa__bjq0d4RMlUxNgrc4 | The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 25 percent of a, and m equals b decreased by 20 percent of b, what is the value of m/x? Choose the most appropriate option
A) 2 / 5
B) 3 / 4
C) 4 / 5
D) 5 / 4
E) 3 / 2 | <gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">80 / 125</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(16/25) * (5/4)</gadget>
<output>4/5 = around 0.8</output>
<result>C</result> | C | 0.8 | The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 25 percent of a, and m equals b decreased by 20 percent of b, what is the value of m/x? | {
"A": "2 / 5",
"B": "3 / 4",
"C": "4 / 5",
"D": "5 / 4",
"E": "3 / 2"
} | multiply(divide(subtract(const_100, 20), add(const_100, 25)), divide(5, 4)) | add(n2,const_100)|divide(n1,n0)|subtract(const_100,n3)|divide(#2,#0)|multiply(#3,#1)| | "x equals a increased by 25 percent of a = > x = a + 25 % a = 1.25 a m equals b decreased by 20 percent of b = > m = b - 20 % b = 0.8 b m / x = 0.8 b / 1.25 a putting the value of b / a = 5 / 4 we get m / x = 4 / 5 answer : c" | general |
math_qa__bSvF10mrYkUAHXXn | The perimeter of a square is 48 m. Find the area of the square.
Choose the correct choice from the following answers:
A) 161 m â ² . B) 144 m â ² . C) 166 m â ² . D) 169 m â ² . E) 273 m â ² . | <gadget id="calculator">48 / 4</gadget>
<output>12</output>
<gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<result>B</result> | B | 144 | The perimeter of a square is 48 m. Find the area of the square. | {
"A": "161 m â ² .",
"B": "144 m â ² .",
"C": "166 m â ² .",
"D": "169 m â ² .",
"E": "273 m â ² ."
} | square_area(divide(48, const_4)) | divide(n0,const_4)|square_area(#0) | perimeter of square = 48 m but perimeter of square = 4 ã — side therefore , 4 ã — side = 48 m therefore , side = 48 / 4 m = 12 m now , the area of the square = ( side ã — side ) therefore , area of the square = 12 ã — 12 m â ² = 144 m â ² . answer : option b | geometry |
math_qa__Z4btt0Umyppmt2GB | Rectangular tile each of size 25cm by 16cm must be laid horizontally on a rectangular floor of size 180cm by 120cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: Pick.
A) 52 B) 54 C) 55 D) 65 E) 48 | <gadget id="calculator">180 * 120</gadget>
<output>21_600</output>
<gadget id="calculator">25 * 16</gadget>
<output>400</output>
<gadget id="calculator">21_600 / 400</gadget>
<output>54</output>
<result>B</result> | B | 54 | Rectangular tile each of size 25cm by 16cm must be laid horizontally on a rectangular floor of size 180cm by 120cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is: | {
"A": "52",
"B": "54",
"C": "55",
"D": "65",
"E": "48"
} | divide(multiply(180, 120), multiply(25, 16)) | multiply(n2,n3)|multiply(n0,n1)|divide(#0,#1)| | "area of tile = 25 * 16 = 400 area of floor = 180 * 120 = 21600 no of tiles = 21600 / 400 = 54 so , the no of tile = 54 answer : b" | geometry |
math_qa__wQx7XgYYnp6Od9I2 | A house wife saved $2.75 in buying an item on sale. If she spent $20 for the item, approximately how much percent she saved in the transaction?
Choose the correct choice from the following
A) 8 %
B) 9 %
C) 10 %
D) 11 %
E) 12 % | <gadget id="calculator">20 + 2.75</gadget>
<output>22.75</output>
<gadget id="calculator">2.75 / 22.75</gadget>
<output>0.120879</output>
<gadget id="calculator">0.120879 * 100</gadget>
<output>12.0879</output>
<result>E</result> | E | 12 | A house wife saved $2.75 in buying an item on sale. If she spent $20 for the item, approximately how much percent she saved in the transaction? | {
"A": "8 %",
"B": "9 %",
"C": "10 %",
"D": "11 %",
"E": "12 %"
} | multiply(divide(2.75, add(20, 2.75)), const_100) | add(n0,n1)|divide(n0,#0)|multiply(#1,const_100)| | "actual price = 20 + 2.75 = $ 22.75 saving = 2.75 / 22.75 * 100 = 12 % approximately answer is e" | general |
math_qa__4bjirpCzy7RyBPm2 | The ratio of buses to cars on River Road is 1 to 3. If there are 40 fewer buses than cars on River Road, how many cars are on River Road? Choose the correct choice from the following answers
A) 60 B) 75 C) 85 D) 95 E) 105 | <gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<result>A</result> | A | 60 | The ratio of buses to cars on River Road is 1 to 3. If there are 40 fewer buses than cars on River Road, how many cars are on River Road? | {
"A": "60",
"B": "75",
"C": "85",
"D": "95",
"E": "105"
} | multiply(divide(40, subtract(3, 1)), 3) | subtract(n1,n0)|divide(n2,#0)|multiply(n1,#1)| | "b / c = 1 / 3 c - b = 40 . . . . . . . . . > b = c - 40 ( c - 40 ) / c = 1 / 3 testing answers . clearly eliminate bcde put c = 60 . . . . . . . . . > ( 60 - 40 ) / 60 = 20 / 60 = 1 / 3 answer : a" | other |
math_qa__xYB2BtMMka9lxMEQ | In a garden, 26 trees are planted at equal distances along a yard 600 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees? Choose the most appropriate option.
A) 10 B) 8 C) 12 D) 24 E) 16 | <gadget id="calculator">26 - 1</gadget>
<output>25</output>
<gadget id="calculator">600 / 25</gadget>
<output>24</output>
<result>D</result> | D | 24 | In a garden, 26 trees are planted at equal distances along a yard 600 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees? | {
"A": "10",
"B": "8",
"C": "12",
"D": "24",
"E": "16"
} | divide(600, subtract(26, const_1)) | subtract(n0,const_1)|divide(n1,#0)| | "26 trees have 25 gaps between them . length of each gap = 600 / 25 = 24 i . e . , distance between two consecutive trees = 24 answer is d ." | physics |
math_qa__1Pa3ck1dp7qcx09p | On a wedding catering service, An experienced chef can prepare a service for a wedding in 6 hours while an novice chef would finish the preparations in 7 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes? Select the correct option.
A) 2 B) 3 C) 4 D) 6 E) 8 | <gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/6) + (1/7)</gadget>
<output>13/42 = around 0.309524</output>
<gadget id="calculator">36 / 60</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(13/42) * (8/5)</gadget>
<output>52/105 = around 0.495238</output>
<gadget id="calculator">2 / (52/105)</gadget>
<output>105/26 = around 4.038462</output>
<gadget id="calculator">floor(105/26)</gadget>
<output>4</output>
<result>C</result> | C | 4 | On a wedding catering service, An experienced chef can prepare a service for a wedding in 6 hours while an novice chef would finish the preparations in 7 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes? | {
"A": "2",
"B": "3",
"C": "4",
"D": "6",
"E": "8"
} | floor(divide(const_2, multiply(add(divide(const_1, 6), divide(const_1, 7)), add(1, divide(36, const_60))))) | divide(const_1,n0)|divide(const_1,n1)|divide(n3,const_60)|add(#0,#1)|add(n2,#2)|multiply(#3,#4)|divide(const_2,#5)|floor(#6) | experienced chefs work = 1 wedding / 6 hours novice chefs work = 1 wedding / 7 hours since we do n ' t know the number of experienced or novice chefs but know that there is an equal number each , let the number of chefs for each group equalx 1 hr and 36 mins = 8 / 5 an hour x / 6 + x / 7 = 1 wedding / ( 8 / 5 ) x / 6 + x / 7 = 5 / 8 x = 2 so there are 2 novice chefs and 2 experienced chefs . in total there are 4 . the answer is c . | physics |
math_qa__V0uXXbpJL2pu3PTc | A 150 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? Choose the correct choice from the following choices
A) 220 meter B) 225 meter C) 230 meter D) 350 meter E) none of these | <gadget id="calculator">120 + 80</gadget>
<output>200</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">200 * (5/18)</gadget>
<output>500/9 = around 55.555556</output>
<gadget id="calculator">(500/9) * 9</gadget>
<output>500</output>
<gadget id="calculator">500 - 150</gadget>
<output>350</output>
<result>D</result> | D | 350 | A 150 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? | {
"A": "220 meter",
"B": "225 meter",
"C": "230 meter",
"D": "350 meter",
"E": "none of these"
} | subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 150) | add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)| | "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 150 / 9 = 500 / 9 = > x + 150 = 500 = > x = 350 so the length of the train is 350 meters option d" | physics |
math_qa__Olu99RaXaiLNHIrR | The average age of 7 men increases by 3 years when two women are included in place of two men of ages 18 and 22 years. Find the average age of the women? Choose the correct choice from the following options.
A) 30.5
B) 26
C) 30
D) 18
E) 11 | <gadget id="calculator">18 + 22</gadget>
<output>40</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">40 + 21</gadget>
<output>61</output>
<gadget id="calculator">61 / 2</gadget>
<output>61/2 = around 30.5</output>
<result>A</result> | A | 30.5 | The average age of 7 men increases by 3 years when two women are included in place of two men of ages 18 and 22 years. Find the average age of the women? | {
"A": "30.5",
"B": "26",
"C": "30",
"D": "18",
"E": "11"
} | divide(add(add(18, 22), multiply(7, 3)), const_2) | add(n2,n3)|multiply(n0,n1)|add(#0,#1)|divide(#2,const_2)| | "explanation : 18 + 22 + 7 * 3 = 61 / 2 = 30.5 answer : a" | general |
math_qa__z5GgTiRDNGc0SBXg | Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $100 and $105 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings? Choose the correct choice from the following choices
A) 600 B) 720 C) 1000 D) 1200 E) 1440 | <gadget id="calculator">105 - 100</gadget>
<output>5</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">100 / (1/10)</gadget>
<output>1_000</output>
<result>C</result> | C | 1,000 | Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $100 and $105 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings? | {
"A": "600",
"B": "720",
"C": "1000",
"D": "1200",
"E": "1440"
} | divide(100, divide(multiply(const_2, subtract(105, 100)), 100)) | subtract(n1,n0)|multiply(#0,const_2)|divide(#1,n0)|divide(n0,#2)| | "$ 100 for 2 years = $ 50 per year . extra $ 5 yearned with the compound interest is the percent yearned on percent . so , $ 5 is yearned on $ 50 , which means that the interest = 10 % . this on the other hand means that half of the savings = 50 * 10 = $ 500 . twice of that = $ 1,000 . answer : c ." | gain |
math_qa__OG46oZpFNNnuFsjM | Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 10% so that the total annual income will be equal to 6% of her entire investment? Pick one
A) 120 B) 600 C) 1000 D) 360 E) 240 | <gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(3/50) * 2_400</gadget>
<output>144</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">2_400 * (1/20)</gadget>
<output>120</output>
<gadget id="calculator">144 - 120</gadget>
<output>24</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) - (3/50)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">24 / (1/25)</gadget>
<output>600</output>
<result>B</result> | B | 600 | Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 10% so that the total annual income will be equal to 6% of her entire investment? | {
"A": "120",
"B": "600",
"C": "1000",
"D": "360",
"E": "240"
} | divide(subtract(multiply(divide(6, const_100), 2400), multiply(2400, divide(5, const_100))), subtract(divide(10, const_100), divide(6, const_100))) | divide(n3,const_100)|divide(n1,const_100)|divide(n2,const_100)|multiply(n0,#0)|multiply(n0,#1)|subtract(#2,#0)|subtract(#3,#4)|divide(#6,#5)| | "let the additional invested amount for 10 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.10 x = 2400 + x + 0.06 ( 2400 + x ) 0.05 * 2400 + 0.10 x = 0.06 x + 0.06 * 2400 0.04 x = 2400 ( 0.06 - 0.05 ) x = 2400 * 0.01 / 0.04 = 600 ans : b" | general |
math_qa__Sde1hNwAaGXaYNDh | 100 is increased by 50%. Find the final number.
Choose the correct choice from the following answers: A) 100 B) 110 C) 150 D) 155 E) 160 | <gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">100 * (1/2)</gadget>
<output>50</output>
<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<result>C</result> | C | 150 | 100 is increased by 50%. Find the final number. | {
"A": "100",
"B": "110",
"C": "150",
"D": "155",
"E": "160"
} | add(100, multiply(100, divide(50, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | "final number = initial number + 50 % ( original number ) = 100 + 50 % ( 100 ) = 100 + 50 = 150 . answer c" | gain |
math_qa__YQNLdk20IxjeSbzp | Two cyclist start from the same places in opposite directions. One is going towards north at 5kmph and the other is going towards south 5kmph. What time will they take to be 50km apart? Select.
A) 1 hr B) 2 hrs C) 3 hrs D) 5 hrs E) 6 hrs | <gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">50 / 10</gadget>
<output>5</output>
<result>D</result> | D | 5 | Two cyclist start from the same places in opposite directions. One is going towards north at 5kmph and the other is going towards south 5kmph. What time will they take to be 50km apart? | {
"A": "1 hr",
"B": "2 hrs",
"C": "3 hrs",
"D": "5 hrs",
"E": "6 hrs"
} | divide(50, add(5, 5)) | add(n0,n1)|divide(n2,#0)| | "to be ( 5 + 5 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 10 * 50 = 5 hrs answer is d" | physics |
math_qa__V6j80OQqKt7Z1VyI | A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun two times, approximately what is the probability that the product of the two winning sectors’ integers will be even?
Choices.
A) 88 %
B) 75 %
C) 67 %
D) 63 %
E) 50 % | <gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 2</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>
<result>B</result> | B | 75 | A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun two times, approximately what is the probability that the product of the two winning sectors’ integers will be even? | {
"A": "88 %",
"B": "75 %",
"C": "67 %",
"D": "63 %",
"E": "50 %"
} | multiply(subtract(1, power(divide(divide(10, const_2), 10), const_2)), const_100) | divide(n0,const_2)|divide(#0,n0)|power(#1,const_2)|subtract(n1,#2)|multiply(#3,const_100) | the only way to have an odd product is if both integers are odd . p ( odd product ) = 1 / 2 * 1 / 2 = 1 / 4 p ( even product ) = 1 - 1 / 4 = 3 / 4 = 75 % the answer is b . | general |
math_qa__DGyppTRUUq0DByWJ | A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 17. What could be the ratio of Cats to dogs in the pet store?
Pick:
A) 1 : 3
B) 1 : 4
C) 1 : 5
D) 2 : 5
E) 68 : 85 | <gadget id="calculator">17 * 4</gadget>
<output>68</output>
<gadget id="calculator">68 + 17</gadget>
<output>85</output>
<gadget id="calculator">68 / 85</gadget>
<output>4/5 = around 0.8</output>
<result>E</result> | E | 0.8 | A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 17. What could be the ratio of Cats to dogs in the pet store? | {
"A": "1 : 3",
"B": "1 : 4",
"C": "1 : 5",
"D": "2 : 5",
"E": "68 : 85"
} | divide(multiply(17, const_4), add(multiply(17, const_4), 17)) | multiply(n0,const_4)|add(n0,#0)|divide(#0,#1)| | "say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 17 - - > x ( a - b ) = 17 . since 17 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 17 . the above implies that either x = 1 and ( a - b ) = 17 or x = 17 anda - b = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 17 . for the original question only option which fits is e , 4 : 5 . cats = 17 * 4 = 68 and dogs = 17 * 5 = 85 . answer : e ." | other |
math_qa__Dr5SREcWFHxkTcRE | In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008? Choose the correct choice:
A) 80 % B) 105 % C) 120 % D) 124.2 % E) 138 % | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">15 * (4/5)</gadget>
<output>12</output>
<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * 100</gadget>
<output>120</output>
<result>C</result> | C | 120 | In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008? | {
"A": "80 %",
"B": "105 %",
"C": "120 %",
"D": "124.2 %",
"E": "138 %"
} | multiply(divide(multiply(15, subtract(const_1, divide(20, const_100))), 10), const_100) | divide(n3,const_100)|subtract(const_1,#0)|multiply(n4,#1)|divide(#2,n1)|multiply(#3,const_100)| | "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,15 = 15 / 100 x = 80 * 15 / 100 x = 12 12 / 10 = 1,2 = 120 % , answer c" | gain |
math_qa__zufBf3L9uZPt6DHu | A hall 36m long and 15m broad is to be paved with stones, each measuring 3dm by 5 dm. The number of stones required is: Choose the correct answer:
A) 3600
B) 1800
C) 18
D) 18000
E) 1.8 | <gadget id="calculator">36 * 15</gadget>
<output>540</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">540 / (3/20)</gadget>
<output>3_600</output>
<result>A</result> | A | 3,600 | A hall 36m long and 15m broad is to be paved with stones, each measuring 3dm by 5 dm. The number of stones required is: | {
"A": "3600",
"B": "1800",
"C": "18",
"D": "18000",
"E": "1.8"
} | divide(multiply(36, 15), divide(multiply(3, 5), const_100)) | multiply(n0,n1)|multiply(n2,n3)|divide(#1,const_100)|divide(#0,#2)| | "area of the hall = 3600 * 1500 area of each stone = ( 30 * 50 ) therefore , number of stones = ( 3600 * 1500 / 30 * 50 ) = 3600 answer : a" | physics |
math_qa__aLYl3pBcG7D7NVM2 | Jill has 28 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?
Answers: A) 3 B) 6 C) 48 D) 12 E) 14 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 + (3/4)</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">28 / (7/4)</gadget>
<output>16</output>
<gadget id="calculator">16 * 3</gadget>
<output>48</output>
<result>C</result> | C | 48 | Jill has 28 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars? | {
"A": "3",
"B": "6",
"C": "48",
"D": "12",
"E": "14"
} | multiply(divide(28, add(const_1, add(const_0_25, divide(const_1, const_2)))), const_3) | divide(const_1,const_2)|add(#0,const_0_25)|add(#1,const_1)|divide(n0,#2)|multiply(#3,const_3)| | let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 28 1 3 / 4 w = 28 w = 16 the total number of jars = 3 w = 48 answer : c | general |
math_qa__AobrQInSWqmEw13v | The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 330 the Other is Choose the correct choice from the following choices:
A) 330 B) 300 C) 210 D) 250 E) 350 | <gadget id="calculator">30 * 2_310</gadget>
<output>69_300</output>
<gadget id="calculator">69_300 / 330</gadget>
<output>210</output>
<result>C</result> | C | 210 | The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 330 the Other is | {
"A": "330",
"B": "300",
"C": "210",
"D": "250",
"E": "350"
} | divide(multiply(30, 2310), 330) | multiply(n0,n1)|divide(#0,n2)| | "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 330 = 210 answer is c ." | physics |
math_qa__2UwHHyh5qyURhdct | 11 friends went to a hotel and decided to pay the bill amount equally. But 10 of them could pay Rs. 60 each as a result 11th has to pay Rs. 50 extra than his share. Find the amount paid by him. Choose the correct choice from the following: A) 110 B) 111 C) 115 D) 123 E) none | <gadget id="calculator">60 * 10</gadget>
<output>600</output>
<gadget id="calculator">600 + 50</gadget>
<output>650</output>
<gadget id="calculator">650 / 10</gadget>
<output>65</output>
<gadget id="calculator">50 + 65</gadget>
<output>115</output>
<result>C</result> | C | 115 | 11 friends went to a hotel and decided to pay the bill amount equally. But 10 of them could pay Rs. 60 each as a result 11th has to pay Rs. 50 extra than his share. Find the amount paid by him. | {
"A": "110",
"B": "111",
"C": "115",
"D": "123",
"E": "none"
} | add(50, divide(add(multiply(60, 10), 50), 10)) | multiply(n1,n2)|add(n4,#0)|divide(#1,n1)|add(n4,#2) | explanation : average amount paid by 10 persons = rs . 60 increase in average due to rs . 50 paid extra by the 11 th men = rs . 50 / 10 = rs . 5 therefore , average expenditure of 11 friends = rs . 60 + rs . 5 = rs . 65 therefore , amount paid by the 11 th men = rs . 65 + rs . 50 = rs . 115 correct option : c | general |
math_qa__afSuQ60eEDjIqMWz | At a certain zoo, the ratio of sea horse to penguins is 5 to 11. If there are 85 more penguins than sea horses at the zoo, how many sea horses are there? Choose the correct choice from the following answers:
A) 24 B) 36 C) 48 D) 70 E) 132 | <gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">85 / 6</gadget>
<output>85/6 = around 14.166667</output>
<gadget id="calculator">(85/6) * 5</gadget>
<output>425/6 = around 70.833333</output>
<gadget id="calculator">floor(425/6)</gadget>
<output>70</output>
<result>D</result> | D | 70 | At a certain zoo, the ratio of sea horse to penguins is 5 to 11. If there are 85 more penguins than sea horses at the zoo, how many sea horses are there? | {
"A": "24",
"B": "36",
"C": "48",
"D": "70",
"E": "132"
} | floor(multiply(divide(85, add(5, const_1)), 5)) | add(n0,const_1)|divide(n2,#0)|multiply(n0,#1)|floor(#2) | 5 / 11 = x / x + 85 5 * 85 = 6 x x = 70 d . 70 | other |
math_qa__ajWWY0RgoQoD4pYq | Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
Choose one:
A) 12 hours B) 24 hours C) 36 hours D) 48 hours E) none | <gadget id="calculator">9 + 1.5</gadget>
<output>10.5</output>
<gadget id="calculator">105 / 10.5</gadget>
<output>10</output>
<gadget id="calculator">9 - 1.5</gadget>
<output>7.5</output>
<gadget id="calculator">105 / 7.5</gadget>
<output>14</output>
<gadget id="calculator">10 + 14</gadget>
<output>24</output>
<result>B</result> | B | 24 | Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to place at a distance of 105 km and comes back to the starting point. The total time taken by him is: | {
"A": "12 hours",
"B": "24 hours",
"C": "36 hours",
"D": "48 hours",
"E": "none"
} | add(divide(105, add(9, 1.5)), divide(105, subtract(9, 1.5))) | add(n0,n1)|subtract(n0,n1)|divide(n2,#0)|divide(n2,#1)|add(#2,#3)| | "sol . speed upstream = 7.5 kmph ; speed downstream = 10.5 kmph . ∴ total time taken = [ 105 / 7.5 + 105 / 10.5 ] hours = 24 hours . answer b" | physics |
math_qa__sMHOi38X6Mv3ROKd | what is the remainder when 7^700 is divided by 100? Choose the correct choice from the following options: A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">7 * 7</gadget>
<output>49</output>
<gadget id="calculator">50 - 49</gadget>
<output>1</output>
<result>A</result> | A | 1 | what is the remainder when 7^700 is divided by 100? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | subtract(divide(100, const_2), multiply(7, 7)) | divide(n2,const_2)|multiply(n0,n0)|subtract(#0,#1)| | "( 7 ^ 700 ) mod 100 = [ 7 ^ ( 2 * 350 ) ] mod 100 = [ 49 ^ 350 ] mod 100 = [ ( 50 - 1 ) ^ 350 ] mod 100 = [ { 350 c 349 } * 50 * ( - 1 ) ^ 349 + 350 c 350 * ( - 1 ) ^ 350 ] mod 100 = [ - 350 * 50 + 1 ] mod 100 = 1 mod 100 so , evidently , the remainder will be 1 . answer : a" | general |
math_qa__9vpiyB3KVjWt0Vct | A person bought 110 glass bowls at a rate of Rs. 10 per bowl. He sold 100 of them at Rs. 14 and the remaining broke. What is the percentage gain for A? Pick:
A) 40
B) 300 / 11
C) 243 / 7
D) 279 / 11
E) 279 / 8 | <gadget id="calculator">100 * 14</gadget>
<output>1_400</output>
<gadget id="calculator">110 * 10</gadget>
<output>1_100</output>
<gadget id="calculator">1_400 - 1_100</gadget>
<output>300</output>
<gadget id="calculator">300 / 1_100</gadget>
<output>3/11 = around 0.272727</output>
<gadget id="calculator">(3/11) * 100</gadget>
<output>300/11 = around 27.272727</output>
<result>B</result> | B | 27.272727 | A person bought 110 glass bowls at a rate of Rs. 10 per bowl. He sold 100 of them at Rs. 14 and the remaining broke. What is the percentage gain for A? | {
"A": "40",
"B": "300 / 11",
"C": "243 / 7",
"D": "279 / 11",
"E": "279 / 8"
} | multiply(divide(subtract(multiply(100, 14), multiply(110, 10)), multiply(110, 10)), const_100) | multiply(n2,n3)|multiply(n0,n1)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100)| | "cp = 110 * 10 = 1100 and sp = 100 * 14 = 1400 gain % = 100 * ( 1400 - 1100 ) / 1100 = 300 / 11 answer : b" | gain |
math_qa__cM238bt4azR3qPB6 | The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is: Pick
A) 12 B) 16 C) 24 D) 48 E) 98 | <gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">lcm(12, 16)</gadget>
<output>48</output>
<result>D</result> | D | 48 | The ratio of numbers is 3:4 and their H.C.F is 4. Their L.C.M is: | {
"A": "12",
"B": "16",
"C": "24",
"D": "48",
"E": "98"
} | lcm(multiply(3, 4), multiply(4, 4)) | multiply(n0,n2)|multiply(n1,n2)|lcm(#0,#1)| | "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 4 . so , the numbers are 12 and 16 . l . c . m of 12 and 16 = 48 . answer : d" | other |
math_qa__fGs2RTnfv3OwRK1W | In the first M games of a team's season, the ratio of the team's wins to its losses was 3:1. In the subsequent N games, the ratio of the team´s wins to losses was 2:3. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games? Choose the correct choice from the following answers
A) 7 : 8 B) 9 : 2 C) 1 : 2 D) 5 : 4 E) 3 : 2 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>
<result>D</result> | D | 1.25 | In the first M games of a team's season, the ratio of the team's wins to its losses was 3:1. In the subsequent N games, the ratio of the team´s wins to losses was 2:3. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games? | {
"A": "7 : 8",
"B": "9 : 2",
"C": "1 : 2",
"D": "5 : 4",
"E": "3 : 2"
} | divide(add(3, 2), add(const_3.0, 1)) | add(n0,n2)|add(n3,n1)|divide(#0,#1)| | "m = 4 / 9 of total games n = 5 / 9 of total games wins = 3 / 4 * 4 / 9 + 2 / 5 * 5 / 9 = 3 / 9 + 2 / 9 = 5 / 9 losses = 1 - 5 / 9 = 4 / 9 the ratio of wins to losses is 5 : 4 . the answer is d ." | general |
math_qa__ruJARjH4qVFPEtT6 | A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
Choose the most appropriate option.
A) 22
B) 88
C) 12
D) 73
E) 29 | <gadget id="calculator">12_005 - 9_800</gadget>
<output>2_205</output>
<gadget id="calculator">9_800 * 8</gadget>
<output>78_400</output>
<gadget id="calculator">5 * 12_005</gadget>
<output>60_025</output>
<gadget id="calculator">78_400 - 60_025</gadget>
<output>18_375</output>
<gadget id="calculator">2_205 / 18_375</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) * 100</gadget>
<output>12</output>
<result>C</result> | C | 12 | A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is: | {
"A": "22",
"B": "88",
"C": "12",
"D": "73",
"E": "29"
} | multiply(divide(subtract(12005, 9800), subtract(multiply(9800, 8), multiply(5, 12005))), const_100) | multiply(n0,n3)|multiply(n1,n2)|subtract(n2,n0)|subtract(#0,#1)|divide(#2,#3)|multiply(#4,const_100)| | "explanation : s . i . for 3 years = rs . ( 12005 - 9800 ) = rs . 2205 . s . i . for 5 years = rs . = rs . 3675 principle = rs . ( 9800 - 3675 ) = rs . 6125 hence , rate = = 12 % answer : c ) 12 %" | gain |
math_qa__UOuoBocxKK9UUgZa | How many seconds will a train 110 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph? Choices:
A) 28 sec B) 23 sec C) 24 sec D) 25 sec E) 26 sec | <gadget id="calculator">150 + 110</gadget>
<output>260</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">260 / 10</gadget>
<output>26</output>
<result>E</result> | E | 26 | How many seconds will a train 110 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph? | {
"A": "28 sec",
"B": "23 sec",
"C": "24 sec",
"D": "25 sec",
"E": "26 sec"
} | divide(add(150, 110), multiply(36, const_0_2778)) | add(n0,n1)|multiply(n2,const_0_2778)|divide(#0,#1)| | "d = 110 + 150 = 260 s = 36 * 5 / 18 = 10 mps t = 260 / 10 = 26 sec e" | physics |
math_qa__JqH57x5mLaSmPdu7 | a teacher gave the same test to 3 history classes : a , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 90 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ?
Choose the correct choice from the following choices:
A) 74 B) 75 C) 76 D) 77 E) 79 | <gadget id="calculator">65 * 4</gadget>
<output>260</output>
<gadget id="calculator">90 * 6</gadget>
<output>540</output>
<gadget id="calculator">260 + 540</gadget>
<output>800</output>
<gadget id="calculator">77 * 5</gadget>
<output>385</output>
<gadget id="calculator">800 + 385</gadget>
<output>1_185</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">1_185 / 15</gadget>
<output>79</output>
<result>E</result> | E | 79 | a teacher gave the same test to 3 history classes : a , b , and c . the average ( arithmetic mean ) scores for the 3 classes were 65 , 90 , and 77 , respectively . the ratio of the numbers of students in each class who took the test was 4 to 6 to 5 , respectively . what was the average score for the 3 classes combined ? | {
"A": "74",
"B": "75",
"C": "76",
"D": "77",
"E": "79"
} | divide(add(add(multiply(65, 4), multiply(90, 6)), multiply(77, 5)), add(add(4, 6), 5)) | add(n5,n6)|multiply(n2,n5)|multiply(n3,n6)|multiply(n4,n7)|add(#1,#2)|add(n7,#0)|add(#4,#3)|divide(#6,#5) | ratio is 4 : 6 : 5 , numbers are 4 x , 6 x , 5 x total scores of each class is ( 65 * 4 x + 6 x * 90 + 77 * 5 x ) = 260 x + 540 x + 385 x = 1185 x total number of students = 15 x average = 1185 x / 15 x = 79 e is the answer | general |
math_qa__fY4jDgNnVLCHMONW | A merchant purchased a jacket for $54 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale? Pick one.
A) $ 0 B) $ 3 C) $ 4 D) $ 12 E) $ 18 | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">54 / (3/5)</gadget>
<output>90</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">90 * (4/5)</gadget>
<output>72</output>
<gadget id="calculator">72 - 54</gadget>
<output>18</output>
<result>E</result> | E | 18 | A merchant purchased a jacket for $54 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale? | {
"A": "$ 0",
"B": "$ 3",
"C": "$ 4",
"D": "$ 12",
"E": "$ 18"
} | subtract(multiply(divide(54, subtract(const_1, divide(40, const_100))), subtract(const_1, divide(20, const_100))), 54) | divide(n1,const_100)|divide(n2,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|divide(n0,#2)|multiply(#4,#3)|subtract(#5,n0)| | "actual cost = $ 54 sp = actual cost + mark up = actual cost + 40 % sp = 54 * 100 / 60 on sale sp = 80 / 100 ( 54 * 100 / 60 ) = 72 gross profit = $ 18 answer is e" | gain |
math_qa__fReiMCMDy0WBbiRW | A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $19 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item? Pick
A) $ 27.50 B) $ 28.50 C) $ 29.50 D) $ 30.50 E) $ 31.50 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 19</gadget>
<output>19/5 = around 3.8</output>
<gadget id="calculator">(19/5) + 19</gadget>
<output>114/5 = around 22.8</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(114/5) / (4/5)</gadget>
<output>57/2 = around 28.5</output>
<result>B</result> | B | 28.5 | A distributor sells a product through an online store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $19 per item. What is the price that the buyer observers online if the distributor wants to maintain a 20% profit on the cost of the item? | {
"A": "$ 27.50",
"B": "$ 28.50",
"C": "$ 29.50",
"D": "$ 30.50",
"E": "$ 31.50"
} | divide(add(multiply(divide(20, const_100), 19), 19), divide(subtract(const_100, 20), const_100)) | divide(n0,const_100)|subtract(const_100,n0)|divide(#1,const_100)|multiply(n1,#0)|add(n1,#3)|divide(#4,#2)| | "let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 19 ) = 0.8 x x = 1.2 ( 19 ) / 0.8 = 1.5 ( 19 ) = $ 28.50 the answer is b ." | gain |
math_qa__0F8jQuZW9y0Ey4cL | Three pipes of same capacity can fill a tank in 12 hours. If there are only two pipes of same capacity, the tank can be filled in? Options: A) 18 B) 8 C) 12 D) 6 E) 4 | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(2/3) * (1/12)</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">1 / (1/18)</gadget>
<output>18</output>
<result>A</result> | A | 18 | Three pipes of same capacity can fill a tank in 12 hours. If there are only two pipes of same capacity, the tank can be filled in? | {
"A": "18",
"B": "8",
"C": "12",
"D": "6",
"E": "4"
} | inverse(multiply(divide(const_2, const_3), divide(const_1, 12))) | divide(const_2,const_3)|divide(const_1,n0)|multiply(#0,#1)|inverse(#2)| | "the part of the tank filled by three pipes in one hour = 1 / 12 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 12 = 1 / 18 . the tank can be filled in 18 hours . answer : a" | physics |
math_qa__S9uHS2o0dCN0zyjk | A train crosses a platform of 110 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? Choose the correct choice from the following answers
A) 150 B) 88 C) 77 D) 310 E) 52 | <gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">15 / 5</gadget>
<output>3</output>
<gadget id="calculator">250 * 3</gadget>
<output>750</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">110 * 4</gadget>
<output>440</output>
<gadget id="calculator">750 - 440</gadget>
<output>310</output>
<result>D</result> | D | 310 | A train crosses a platform of 110 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? | {
"A": "150",
"B": "88",
"C": "77",
"D": "310",
"E": "52"
} | subtract(multiply(250, divide(15, divide(15, const_3))), multiply(110, divide(20, divide(15, const_3)))) | divide(n1,const_3)|divide(n1,#0)|divide(n3,#0)|multiply(n2,#1)|multiply(n0,#2)|subtract(#3,#4)| | "length of the train be â € ˜ x â € ™ x + 110 / 15 = x + 250 / 20 4 x + 440 = 3 x + 750 x = 310 m answer : d" | physics |
math_qa__z5a0by02D7QFcoUW | Bucket P has thrice the capacity as bucket Q. It takes 80 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q, having each turn together to fill the empty drum? Pick one:
A) 30 B) 45 C) 60 D) 80 E) 100 | <gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">80 * 3</gadget>
<output>240</output>
<gadget id="calculator">1 / 240</gadget>
<output>1/240 = around 0.004167</output>
<gadget id="calculator">(1/80) + (1/240)</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">1 / (1/60)</gadget>
<output>60</output>
<result>C</result> | C | 60 | Bucket P has thrice the capacity as bucket Q. It takes 80 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q, having each turn together to fill the empty drum? | {
"A": "30",
"B": "45",
"C": "60",
"D": "80",
"E": "100"
} | divide(const_1, add(divide(const_1, 80), divide(const_1, multiply(80, const_3)))) | divide(const_1,n0)|multiply(n0,const_3)|divide(const_1,#1)|add(#0,#2)|divide(const_1,#3)| | "explanation : let capacity of q = 1 litre . then , capacity of p = 3 litre . given that it takes 80 turns for bucket p to fill the empty drum . = > capacity of the drum = 80 × 3 = 240 litre . number of turns required if both p and q are used having each turn together 240 / 3 + 1 = 60 litre . answer : option c" | other |
math_qa__Y8bGVXjkZhZUkaLZ | Weights of two friends Ram and Shyam are in the ratio 7:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased? Choose the correct answer
A) 19 % B) 10 % C) 22 % D) 16 % E) none | <gadget id="calculator">15 - 10</gadget>
<output>5</output>
<gadget id="calculator">7 / 5</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">5 * (7/5)</gadget>
<output>7</output>
<gadget id="calculator">15 + 7</gadget>
<output>22</output>
<result>C</result> | C | 22 | Weights of two friends Ram and Shyam are in the ratio 7:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased? | {
"A": "19 %",
"B": "10 %",
"C": "22 %",
"D": "16 %",
"E": "none"
} | add(15, multiply(subtract(15, 10), divide(7, 5))) | divide(n0,n1)|subtract(n4,n2)|multiply(#0,#1)|add(n4,#2)| | "solution : given ratio of ram and shayam ' s weight = 7 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 7 / 5 or , x = 22 % . answer : option c" | gain |
math_qa__yrCpUqy5upOZjrXM | In Town X, 90 percent of the population are employed, and 20 percent of the population are employed males. What percent of the employed people in Town X are females? Pick.
A) 16 % B) 66 % C) 77 % D) 88 % E) 52 % | <gadget id="calculator">90 - 20</gadget>
<output>70</output>
<gadget id="calculator">70 / 90</gadget>
<output>7/9 = around 0.777778</output>
<gadget id="calculator">(7/9) * 100</gadget>
<output>700/9 = around 77.777778</output>
<result>C</result> | C | 77 | In Town X, 90 percent of the population are employed, and 20 percent of the population are employed males. What percent of the employed people in Town X are females? | {
"A": "16 %",
"B": "66 %",
"C": "77 %",
"D": "88 %",
"E": "52 %"
} | multiply(divide(subtract(90, 20), 90), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | "total employed people 90 % , out of which 20 are employed males , hence 70 % are employed females . ( employed females ) / ( total employed people ) = 70 / 90 = 7 / 9 = 77 % answer : c ." | gain |
math_qa__BdiIErWReCVxCWNr | The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person? Choose the correct choice from the following answers: A) 10 B) 20 C) 30 D) 40 E) 50 | <gadget id="calculator">3 * 6</gadget>
<output>18</output>
<gadget id="calculator">16 - 6</gadget>
<output>10</output>
<gadget id="calculator">18 + 10</gadget>
<output>28</output>
<gadget id="calculator">28 / 2</gadget>
<output>14</output>
<gadget id="calculator">14 + 16</gadget>
<output>30</output>
<result>C</result> | C | 30 | The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person? | {
"A": "10",
"B": "20",
"C": "30",
"D": "40",
"E": "50"
} | add(divide(add(multiply(3, 6), subtract(16, 6)), const_2), 16) | multiply(n1,n2)|subtract(n0,n1)|add(#0,#1)|divide(#2,const_2)|add(n0,#3) | let present age of the elder person = x and present age of the younger person = x − 16 ( x − 6 ) = 3 ( x − 16 − 6 ) x − 6 = 3 x − 66 2 x = 60 x = 60 / 2 = 30 answer : option c | general |
math_qa__6rJDlf2DvMcfIMlR | A cistern 7 m long and 5 m wide contains water up to a breadth of 1 m 40 cm. Find the total area of the wet surface. Choices:
A) 69 m sqaure B) 49 m sqaure C) 52 m sqaure D) 64 m sqaure E) none of these | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) + 1</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(7/5) * 5</gadget>
<output>7</output>
<gadget id="calculator">(7/5) * 7</gadget>
<output>49/5 = around 9.8</output>
<gadget id="calculator">7 + (49/5)</gadget>
<output>84/5 = around 16.8</output>
<gadget id="calculator">2 * (84/5)</gadget>
<output>168/5 = around 33.6</output>
<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<gadget id="calculator">(168/5) + 35</gadget>
<output>343/5 = around 68.6</output>
<result>A</result> | A | 69 | A cistern 7 m long and 5 m wide contains water up to a breadth of 1 m 40 cm. Find the total area of the wet surface. | {
"A": "69 m sqaure",
"B": "49 m sqaure",
"C": "52 m sqaure",
"D": "64 m sqaure",
"E": "none of these"
} | add(multiply(const_2, add(multiply(add(divide(40, const_100), 1), 5), multiply(add(divide(40, const_100), 1), 7))), multiply(5, 7)) | divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|add(#3,#4)|multiply(#5,const_2)|add(#6,#1)| | "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 5 * 1.40 + 7 * 1.40 ) ] + 7 * 5 = 69 m square option a" | physics |
math_qa__yKoTNXpNvuZZ50SM | In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 9 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
Pick:
A) 2 / 1 B) 4 / 1 C) 2 / 3 D) 3 / 4 E) 3 / 2 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">45 / 5</gadget>
<output>9</output>
<gadget id="calculator">45 - 9</gadget>
<output>36</output>
<gadget id="calculator">9 + 9</gadget>
<output>18</output>
<gadget id="calculator">36 / 18</gadget>
<output>2</output>
<result>A</result> | A | 2 | In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 9 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture. | {
"A": "2 / 1",
"B": "4 / 1",
"C": "2 / 3",
"D": "3 / 4",
"E": "3 / 2"
} | divide(subtract(45, divide(45, add(4, 1))), add(divide(45, add(4, 1)), 9)) | add(n1,n2)|divide(n0,#0)|add(n3,#1)|subtract(n0,#1)|divide(#3,#2)| | "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 9 ) = 36 / 18 = 2 / 1 . answer : a ." | general |
math_qa__YRD8lq9SJrkYH1uO | Find the area of a rhombus one side of which measures 20 cm and one diagonal is 27 cm. Pick:
A) 600 cm 2 B) 500 cm 2 C) 400 cm 2 D) 432 cm 2 E) 100 cm 2 | <gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 27</gadget>
<output>27/2 = around 13.5</output>
<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">400 * 4</gadget>
<output>1_600</output>
<gadget id="calculator">27 * 27</gadget>
<output>729</output>
<gadget id="calculator">1_600 - 729</gadget>
<output>871</output>
<gadget id="calculator">871 ** (1/2)</gadget>
<output>sqrt(871) = around 29.512709</output>
<gadget id="calculator">(27/2) * (sqrt(871))</gadget>
<output>27*sqrt(871)/2 = around 398.421573</output>
<gadget id="calculator">(27*sqrt(871)/2) + 27</gadget>
<output>27 + 27*sqrt(871)/2 = around 425.421573</output>
<result>D</result> | D | 432 | Find the area of a rhombus one side of which measures 20 cm and one diagonal is 27 cm. | {
"A": "600 cm 2",
"B": "500 cm 2",
"C": "400 cm 2",
"D": "432 cm 2",
"E": "100 cm 2"
} | add(multiply(multiply(divide(const_1, const_2), 27), sqrt(subtract(multiply(multiply(20, 20), const_4), multiply(27, 27)))), 27) | divide(const_1,const_2)|multiply(n0,n0)|multiply(n1,n1)|multiply(n1,#0)|multiply(#1,const_4)|subtract(#4,#2)|sqrt(#5)|multiply(#3,#6)|add(n1,#7)| | "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 27 x 32 ) cm 2 = 432 cm 2 answer : option d" | geometry |
math_qa__XGujcvnAVedoMf41 | A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.10.50 less, he would have gained 30%. Find the cost of the article. Choose the correct choice from the following answers.
A) 30 B) 40 C) 50 D) 60 E) 70 | <gadget id="calculator">10.5 * 100</gadget>
<output>1_050</output>
<gadget id="calculator">25 + 100</gadget>
<output>125</output>
<gadget id="calculator">30 + 100</gadget>
<output>130</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">130 * 80</gadget>
<output>10_400</output>
<gadget id="calculator">10_400 / 100</gadget>
<output>104</output>
<gadget id="calculator">125 - 104</gadget>
<output>21</output>
<gadget id="calculator">1_050 / 21</gadget>
<output>50</output>
<result>C</result> | C | 50 | A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.10.50 less, he would have gained 30%. Find the cost of the article. | {
"A": "30",
"B": "40",
"C": "50",
"D": "60",
"E": "70"
} | divide(multiply(10.5, const_100), subtract(add(25, const_100), divide(multiply(add(30, const_100), subtract(const_100, 20)), const_100))) | add(n0,const_100)|add(n3,const_100)|multiply(n2,const_100)|subtract(const_100,n1)|multiply(#1,#3)|divide(#4,const_100)|subtract(#0,#5)|divide(#2,#6) | let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 10.50 when c . p = ( 100 * 10.50 ) / 21 = 50 answer : c | gain |
math_qa__mQmDUdjtNwIIzE6z | If A lends Rs.1500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? Pick one.
A) 112.5 B) 122.5 C) 132.5 D) 67.5 E) 212.5 | <gadget id="calculator">1_500 * 11.5</gadget>
<output>17_250</output>
<gadget id="calculator">17_250 * 3</gadget>
<output>51_750</output>
<gadget id="calculator">51_750 / 100</gadget>
<output>1_035/2 = around 517.5</output>
<gadget id="calculator">1_500 * 10</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 * 3</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 100</gadget>
<output>450</output>
<gadget id="calculator">(1_035/2) - 450</gadget>
<output>135/2 = around 67.5</output>
<result>D</result> | D | 67.5 | If A lends Rs.1500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? | {
"A": "112.5",
"B": "122.5",
"C": "132.5",
"D": "67.5",
"E": "212.5"
} | subtract(divide(multiply(multiply(1500, 11.5), 3), const_100), divide(multiply(multiply(1500, 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)| | "( 1500 * 1.5 * 3 ) / 100 = > 67.5 answer : d" | gain |
math_qa__TVliM7DwFQHsmhBH | If x and y are both odd prime numbers and x < y, how many distinct positive integer Q factors does 2xy have? Choose the correct choice:
A) 3 B) 4 C) 6 D) 8 E) 12 | <gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<result>D</result> | D | 8 | If x and y are both odd prime numbers and x < y, how many distinct positive integer Q factors does 2xy have? | {
"A": "3",
"B": "4",
"C": "6",
"D": "8",
"E": "12"
} | multiply(multiply(2, add(const_1, const_1)), add(const_1, const_1)) | add(const_1,const_1)|multiply(n0,#0)|multiply(#0,#1)| | since 2 xy prime q factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer . | other |
math_qa__pHnLX563Od3Jkzmn | What is the sum of all possible solutions to |x - 5|^2 + |x - 5| = 20 ? Choose the correct choice from the following
A) - 1
B) 6
C) 7
D) 10
E) 14 | <gadget id="calculator">4 + 5</gadget>
<output>9</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<result>D</result> | D | 10 | What is the sum of all possible solutions to |x - 5|^2 + |x - 5| = 20 ? | {
"A": "- 1",
"B": "6",
"C": "7",
"D": "10",
"E": "14"
} | add(add(const_4, 5), subtract(5, const_4)) | add(n0,const_4)|subtract(n0,const_4)|add(#0,#1)| | "denote | x - 5 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 5 | , so it ' s an absolute value and thus can not be negative . y = | x - 5 | = 4 - - > x = 9 or x = - 1 . the sum = 10 answer : d ." | general |
math_qa__6CoS42fCPzABdxdt | Anil had to do a multiplication. Instead of taking 35 as one of the multipliers, he took 53. As a result, the product went up by 540. What is the new product? Choices: A) 1590 B) 1600 C) 1950 D) 1630 E) 1760 | <gadget id="calculator">35 * 53</gadget>
<output>1_855</output>
<gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">1_855 + 30</gadget>
<output>1_885</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">1_885 - 400</gadget>
<output>1_485</output>
<gadget id="calculator">1_485 + 100</gadget>
<output>1_585</output>
<result>A</result> | A | 1,590 | Anil had to do a multiplication. Instead of taking 35 as one of the multipliers, he took 53. As a result, the product went up by 540. What is the new product? | {
"A": "1590",
"B": "1600",
"C": "1950",
"D": "1630",
"E": "1760"
} | add(subtract(add(multiply(35, 53), multiply(const_3, const_10)), multiply(const_4, const_100)), const_100) | multiply(n0,n1)|multiply(const_10,const_3)|multiply(const_100,const_4)|add(#0,#1)|subtract(#3,#2)|add(#4,const_100) | explanation : let the number that anil wanted to multiply be ' y ' . he was expected to find the value of 35 y . instead , he found the value of 53 y . the difference between the value that he got ( 53 y ) and what he was expected to get ( 35 y ) is 540 . = > 53 y - 35 y = 540 = > ( 53 - 35 ) * y = 540 = > y = 30 therefore , the correct product = 53 * 30 = 1590 answer : a | general |
math_qa__Yy8wk28eWDh7ZjCM | At what rate percent of simple interest will a sum of money double itself in 33 years?
Choose the correct option.
A) 6.54 % B) 4.54 % C) 8 . 2 % D) 3.03 % E) 5.54 % | <gadget id="calculator">100 / 33</gadget>
<output>100/33 = around 3.030303</output>
<result>D</result> | D | 3.03 | At what rate percent of simple interest will a sum of money double itself in 33 years? | {
"A": "6.54 %",
"B": "4.54 %",
"C": "8 . 2 %",
"D": "3.03 %",
"E": "5.54 %"
} | divide(const_100, 33) | divide(const_100,n0)| | "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 33 ) = 100 / 33 = 3.03 % answer : d" | gain |
math_qa__RcZyMOi4pHBEZy22 | One-tenth of the students at a nursery school are 4 years old or older. If 20 students have not yet reached their third birthday, and a total of 25 students are not between 3 years old and 4 years old, how many children are in the nursery school? Choose the correct choice:
A) 51
B) 20
C) 40
D) 50
E) 55 | <gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">5 * 10</gadget>
<output>50</output>
<result>D</result> | D | 50 | One-tenth of the students at a nursery school are 4 years old or older. If 20 students have not yet reached their third birthday, and a total of 25 students are not between 3 years old and 4 years old, how many children are in the nursery school? | {
"A": "51",
"B": "20",
"C": "40",
"D": "50",
"E": "55"
} | multiply(subtract(25, 20), const_10) | subtract(n2,n1)|multiply(#0,const_10)| | "x / 10 students are > 4 yrs 20 students are < 3 yrs x / 10 + 20 = 25 x / 10 = 5 x = 50 answer : d" | general |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.