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__8xOdFHMMLIGgxeFq | how much percentage 80 is of 480? Choose the correct choice from the following
A) 16.5 B) 14.33 C) 12.5 D) 15.8 E) 16.66 | <gadget id="calculator">80 * 100</gadget>
<output>8_000</output>
<gadget id="calculator">8_000 / 480</gadget>
<output>50/3 = around 16.666667</output>
<result>E</result> | E | 16.66 | how much percentage 80 is of 480? | {
"A": "16.5",
"B": "14.33",
"C": "12.5",
"D": "15.8",
"E": "16.66"
} | divide(multiply(80, const_100), 480) | multiply(n0,const_100)|divide(#0,n1) | 80 * 100 / 480 = 16.66 % answer e | general |
math_qa__fnT2ahOwFFXZOG6k | 3 persons invested rs . 9000 in a joint business . the second person invested rs . 1000 more than the first and the third rs . 1000 more than second . after two years , they gained rs . 1800 . how much third person will get ? Choose the correct choice
A) 400 B) 800 C) 600 D) 1200 E) 1000 | <gadget id="calculator">3 * 1_000</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 + 1_000</gadget>
<output>4_000</output>
<gadget id="calculator">100 * 4_000</gadget>
<output>400_000</output>
<gadget id="calculator">400_000 / 9_000</gadget>
<output>400/9 = around 44.444444</output>
<gadget id="calculator">(400/9) * 1_800</gadget>
<output>80_000</output>
<gadget id="calculator">80_000 / 100</gadget>
<output>800</output>
<result>B</result> | B | 800 | 3 persons invested rs . 9000 in a joint business . the second person invested rs . 1000 more than the first and the third rs . 1000 more than second . after two years , they gained rs . 1800 . how much third person will get ? | {
"A": "400",
"B": "800",
"C": "600",
"D": "1200",
"E": "1000"
} | divide(multiply(divide(multiply(const_100, add(multiply(3, 1000), 1000)), 9000), 1800), const_100) | multiply(n0,n2)|add(n2,#0)|multiply(#1,const_100)|divide(#2,n1)|multiply(n4,#3)|divide(#4,const_100) | first persons investment = x second persons investment = x + 1000 third persons investments = x + 2000 x + x + 1000 + x + 2000 = 9000 3 x = 6000 x = 2000 ratio = 2000 : 3000 : 4000 2 : 3 : 4 4 / 9 * 1800 = 800 answer : b | gain |
math_qa__SD6FMgQEqGRA3vnp | Bombay Express left Delhi for Bombay at 14.30 hrs, travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at 16.30 hrs, travelling at a speed of 80 kmph. How far away from Delhi will the two trains meet?
Choose the correct choice from the following
A) 120 km B) 360 km C) 480 km D) 500 km E) none | <gadget id="calculator">60 * 2</gadget>
<output>120</output>
<gadget id="calculator">80 - 60</gadget>
<output>20</output>
<gadget id="calculator">120 / 20</gadget>
<output>6</output>
<gadget id="calculator">80 * 6</gadget>
<output>480</output>
<result>C</result> | C | 480 | Bombay Express left Delhi for Bombay at 14.30 hrs, travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at 16.30 hrs, travelling at a speed of 80 kmph. How far away from Delhi will the two trains meet? | {
"A": "120 km",
"B": "360 km",
"C": "480 km",
"D": "500 km",
"E": "none"
} | multiply(80, divide(multiply(60, const_2), subtract(80, 60))) | multiply(n1,const_2)|subtract(n3,n1)|divide(#0,#1)|multiply(n3,#2) | sol . suppose they meet x hours after 14.30 hrs . then , 60 x = 80 ( x - 2 ) or x = 8 . ∴ required distance = ( 60 x 8 ) km = 480 km . answer c | physics |
math_qa__xhipake3r13JcuDl | A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.600, what is the reduced price for kg?
Choices: A) 30 B) 60 C) 70 D) 80 E) 20 | <gadget id="calculator">600 * 25</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 / 100</gadget>
<output>150</output>
<gadget id="calculator">150 / 5</gadget>
<output>30</output>
<result>A</result> | A | 30 | A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.600, what is the reduced price for kg? | {
"A": "30",
"B": "60",
"C": "70",
"D": "80",
"E": "20"
} | divide(divide(multiply(600, 25), const_100), 5) | multiply(n0,n2)|divide(#0,const_100)|divide(#1,n1)| | "a 600 * ( 25 / 100 ) = 150 - - - - 5 ? - - - - 1 = > rs . 30" | gain |
math_qa__h5D8FP52TnHB8NzN | the numbers { 1 , 3 , 6 , 7 , 7 , 7 } are used to form 3 2 - digit numbers . if the sum of these 3 numbers is a prime number p , what is the largest possible value of p ?
Choose the correct choice from the following choices: A) 97 B) 151 C) 209 D) 211 E) 219 | <gadget id="calculator">7 * 10</gadget>
<output>70</output>
<gadget id="calculator">7 + 70</gadget>
<output>77</output>
<gadget id="calculator">70 + 3</gadget>
<output>73</output>
<gadget id="calculator">77 + 73</gadget>
<output>150</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">60 + 1</gadget>
<output>61</output>
<gadget id="calculator">150 + 61</gadget>
<output>211</output>
<result>D</result> | D | 211 | the numbers { 1 , 3 , 6 , 7 , 7 , 7 } are used to form 3 2 - digit numbers . if the sum of these 3 numbers is a prime number p , what is the largest possible value of p ? | {
"A": "97",
"B": "151",
"C": "209",
"D": "211",
"E": "219"
} | add(add(add(7, multiply(7, const_10)), add(multiply(7, const_10), 3)), add(multiply(6, const_10), 1)) | multiply(n3,const_10)|multiply(n2,const_10)|add(n3,#0)|add(n1,#0)|add(n0,#1)|add(#2,#3)|add(#5,#4) | what is the largest possible sum of these three numbers that we can form ? maximize the first digit : 76 + 73 + 71 = 220 = even , so not a prime . let ' s try next largest sum , switch digits in 76 and we ' ll get : 67 + 73 + 71 = 211 = prime . answer : d . | general |
math_qa__QyLBMOzQl75wP1LV | What is the sum of the digits of integer k, if k = (10^40- 46)
Choose the correct option:
A) 351 B) 360 C) 363 D) 369 E) 378 | <gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">40 - 2</gadget>
<output>38</output>
<gadget id="calculator">9 * 38</gadget>
<output>342</output>
<gadget id="calculator">342 + 10</gadget>
<output>352</output>
<result>A</result> | A | 351 | What is the sum of the digits of integer k, if k = (10^40- 46) | {
"A": "351",
"B": "360",
"C": "363",
"D": "369",
"E": "378"
} | add(multiply(subtract(10, const_1), subtract(40, const_2)), 10) | subtract(n0,const_1)|subtract(n1,const_2)|multiply(#0,#1)|add(#2,n0)| | "there are 41 digits in 10 ^ 4 when we subtract 46 from it , there will be 40 digits left . 10 ^ 4 can be written as 9999999 . . . . ( 40 times ) + 1 so , 10 ^ 40 - 46 = 9999999 . . . . ( 40 times ) + 1 - 46 = 9999999 . . . . ( 40 times ) - 45 consider the last 2 digits , 99 - 45 = 54 the last 2 digits will be 54 . and our number would be 99999 . . . . . . 99954 with 2 less 9 s after subtraction . number of 9 s left are 38 and the last two digits are 54 the sum of the digits will be ( 38 * 9 ) + 5 + 4 = 351 answer : - a" | general |
math_qa__xKTFZtVQci6oHiDv | Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 81th number in this set? Choose one:
A) 605 B) 608 C) 613 D) 616 E) 645 | <gadget id="calculator">81 - 1</gadget>
<output>80</output>
<gadget id="calculator">80 * 8</gadget>
<output>640</output>
<gadget id="calculator">640 + 5</gadget>
<output>645</output>
<result>E</result> | E | 645 | Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 81th number in this set? | {
"A": "605",
"B": "608",
"C": "613",
"D": "616",
"E": "645"
} | add(multiply(subtract(81, const_1), 8), 5) | subtract(n2,const_1)|multiply(n0,#0)|add(n1,#1)| | "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 81 th number = 8 * ( 81 - 1 ) + 5 = 645 answer = e" | general |
math_qa__kG79YwNsNFkZtzr1 | How many multiples of 5 are there between 0 and 358? Choose the correct option: A) 54 B) 75 C) 76 D) 71 E) 58 | <gadget id="calculator">358 - 0</gadget>
<output>358</output>
<gadget id="calculator">358 / 5</gadget>
<output>358/5 = around 71.6</output>
<gadget id="calculator">(358/5) + 1</gadget>
<output>363/5 = around 72.6</output>
<result>D</result> | D | 71 | How many multiples of 5 are there between 0 and 358? | {
"A": "54",
"B": "75",
"C": "76",
"D": "71",
"E": "58"
} | add(divide(subtract(358, 0), 5), const_1) | subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)| | "5 * 1 = 5 5 * 71 = 355 total number of multiples = ( 71 + 1 ) = 72 answer d" | general |
math_qa__cYC0BtNSLgiEzvtR | A bowl was filled with 10 ounces of water, and 0.012 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period? Select the correct option:
A) 0.004 %
B) 0.04 %
C) 0.40 %
D) 6 %
E) 40 % | <gadget id="calculator">50 * 0.012</gadget>
<output>0.6</output>
<gadget id="calculator">0.6 / 10</gadget>
<output>0.06</output>
<gadget id="calculator">0.06 * 100</gadget>
<output>6</output>
<result>D</result> | D | 6 | A bowl was filled with 10 ounces of water, and 0.012 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period? | {
"A": "0.004 %",
"B": "0.04 %",
"C": "0.40 %",
"D": "6 %",
"E": "40 %"
} | multiply(divide(multiply(50, 0.012), 10), const_100) | multiply(n1,n2)|divide(#0,n0)|multiply(#1,const_100)| | "total amount of water evaporated each day during a 50 - day period = . 012 * 50 = . 012 * 100 / 2 = 1.2 / 2 = . 6 percent of the original amount of water evaporated during this period = ( . 6 / 10 ) * 100 % = 6 % answer d" | gain |
math_qa__zmVncxgg1pxosYsy | Company Z has 61 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday. Choose the most appropriate option: A) 6 B) 7 C) 13 D) 9 E) 12 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">61 / 7</gadget>
<output>61/7 = around 8.714286</output>
<gadget id="calculator">floor(61/7)</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">4 + 9</gadget>
<output>13</output>
<result>C</result> | C | 13 | Company Z has 61 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday. | {
"A": "6",
"B": "7",
"C": "13",
"D": "9",
"E": "12"
} | add(const_4, add(floor(divide(61, add(const_4, const_3))), const_1)) | add(const_3,const_4)|divide(n0,#0)|floor(#1)|add(#2,const_1)|add(#3,const_4) | say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 61 . now , plug options for x . only c and e give an integer value for y . but only for c x > y as needed . answer : c . | general |
math_qa__k7IJlOFX93gR38QP | A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.155. Find the unknown rate of two towels? Choose the correct choice from the following options:
A) 400 B) 450 C) 500 D) 550 E) 600 | <gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 155</gadget>
<output>1_550</output>
<gadget id="calculator">5 * 150</gadget>
<output>750</output>
<gadget id="calculator">1_550 - 750</gadget>
<output>800</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">800 - 300</gadget>
<output>500</output>
<result>C</result> | C | 500 | A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.155. Find the unknown rate of two towels? | {
"A": "400",
"B": "450",
"C": "500",
"D": "550",
"E": "600"
} | subtract(subtract(multiply(add(add(3, 5), const_2), 155), multiply(5, 150)), multiply(3, 100)) | add(n0,n2)|multiply(n2,n3)|multiply(n0,n1)|add(#0,const_2)|multiply(n4,#3)|subtract(#4,#1)|subtract(#5,#2) | 10 * 155 = 1550 3 * 100 + 5 * 150 = 1050 1550 – 1050 = 500 c | general |
math_qa__Rg4jXXrMyOqGUjg5 | If there are 4 peanuts in a box and Mary puts 4 more peanuts inside, how many peanuts are in the box? Choose the correct choice from the following options
A) 8 B) 9 C) 10 D) 11 E) 12 | <gadget id="calculator">4 + 4</gadget>
<output>8</output>
<result>A</result> | A | 8 | If there are 4 peanuts in a box and Mary puts 4 more peanuts inside, how many peanuts are in the box? | {
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "12"
} | add(4, 4) | add(n0,n1)| | "4 + 4 = 8 correct answer is a ) 8" | general |
math_qa__YvUFOwGTrUzIElxB | The average marks of 30 students in a class is 60. But a student mark is wrongly noted as 90 instead of 15 then find the correct average marks? Choose the correct choice from the following choices:
A) 55.65 B) 57.5 C) 62.5 D) 45.25 E) 50 | <gadget id="calculator">60 * 30</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 - 90</gadget>
<output>1_710</output>
<gadget id="calculator">1_710 + 15</gadget>
<output>1_725</output>
<gadget id="calculator">1_725 / 30</gadget>
<output>115/2 = around 57.5</output>
<result>B</result> | B | 57.5 | The average marks of 30 students in a class is 60. But a student mark is wrongly noted as 90 instead of 15 then find the correct average marks? | {
"A": "55.65",
"B": "57.5",
"C": "62.5",
"D": "45.25",
"E": "50"
} | divide(add(subtract(multiply(60, 30), 90), 15), 30) | multiply(n0,n1)|subtract(#0,n2)|add(n3,#1)|divide(#2,n0) | correct avg marks = 60 + ( 15 - 90 ) / 30 avg = 60 - 2.5 = 57.5 answer is b | general |
math_qa__Ub9B6nRoyv896jM6 | There are two inlets and one outlet to a cistern. One of the inlets takes 2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:00AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full? Choices
A) 2 hours B) 2.5 hours C) 3 hours D) 3.5 hours E) 4 hours | <gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">10 - 8</gadget>
<output>2</output>
<result>A</result> | A | 2 | There are two inlets and one outlet to a cistern. One of the inlets takes 2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:00AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full? | {
"A": "2 hours",
"B": "2.5 hours",
"C": "3 hours",
"D": "3.5 hours",
"E": "4 hours"
} | subtract(10, subtract(9, subtract(2, 1))) | subtract(n0,n5)|subtract(n1,#0)|subtract(n3,#1) | the combined inflow rate of the two inlets is 1 / 2 + 1 / 4 = 3 / 4 cistern / hour . thus , working together , it takes 4 / 3 hours ( time is reciprocal of rate ) to fill the cistern . from 9 : 00 am to 10 : 00 am , so in 1 hours , the inlet pipes will fill ( time ) * ( rate ) = 1 * 3 / 4 = 3 / 4 th of the cistern . then the outlet is turned on and the remaining 1 / 4 th of the cistern is filled in 1 hour . letting x to be the rate of the outlet , we would have : 3 / 4 - x = 1 / 4 - - > x = 1 / 2 cistern / hour , which means that it takes 2 hours the outlet working alone to empty the cistern . answer : a | physics |
math_qa__UnQAXsBpikhBg8xX | If log 0.318=0.3364 and log 0.317=0.33320 then log 0.319 =? Choose the correct option
A) 0.33365 B) 0.3368 C) 0.3396 D) 0.3369 E) 0.3469 | <gadget id="calculator">0.3364 / 0.3332</gadget>
<output>1.009604</output>
<gadget id="calculator">0.3364 * 1.009604</gadget>
<output>0.339631</output>
<result>C</result> | C | 0.3396 | If log 0.318=0.3364 and log 0.317=0.33320 then log 0.319 =? | {
"A": "0.33365",
"B": "0.3368",
"C": "0.3396",
"D": "0.3369",
"E": "0.3469"
} | multiply(0.3364, divide(0.3364, 0.3332)) | divide(n1,n3)|multiply(n1,#0) | log 0.318 / log 0.317 = log ( 0.318 - 0.317 ) = log 0.001 = 0.3364 / 0.33320 = 1.0096 now , log 0.318 * log 0.001 = log ( 0.318 + 0.001 ) = log 0.319 = 0.3364 * 1.0096 = 0.3396 so option c answer : c | other |
math_qa__f91EGl7ob10QdMi7 | The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria Choices: A) 10 B) 12 C) 14 D) 16 E) 18 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 * 100</gadget>
<output>500_000</output>
<gadget id="calculator">500_000 / 1_000</gadget>
<output>500</output>
<gadget id="calculator">log(500)</gadget>
<output>log(500) = around 6.214608</output>
<gadget id="calculator">log(500) * 2</gadget>
<output>2*log(500) = around 12.429216</output>
<result>B</result> | B | 12 | The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria | {
"A": "10",
"B": "12",
"C": "14",
"D": "16",
"E": "18"
} | multiply(log(divide(multiply(multiply(add(const_4, const_1), 1,000), const_100), 1,000)), 2) | add(const_1,const_4)|multiply(#0,n1)|multiply(#1,const_100)|divide(#2,n1)|log(#3)|multiply(n0,#4)| | "the question basically asks how many minutes it takes for a population to increase by factor 50 ( 50,000 / 1,000 = 50 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 50 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 6 = 64 , i . e . the population has to double 6 times . since it takes the population 2 minutes to double once it takes 6 * 2 minutes = 12 minutes to double nine times . thus , solution b = 12 is correct ." | general |
math_qa__cKqsX327NayWIACm | A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 900 m long? Choose the most appropriate option.
A) 200 sec B) 210 sec C) 167 sec D) 197 sec E) 179 sec | <gadget id="calculator">1_200 + 900</gadget>
<output>2_100</output>
<gadget id="calculator">1_200 / 120</gadget>
<output>10</output>
<gadget id="calculator">2_100 / 10</gadget>
<output>210</output>
<result>B</result> | B | 210 | A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 900 m long? | {
"A": "200 sec",
"B": "210 sec",
"C": "167 sec",
"D": "197 sec",
"E": "179 sec"
} | divide(add(1200, 900), divide(1200, 120)) | add(n0,n2)|divide(n0,n1)|divide(#0,#1)| | "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2100 m t = d / s t = 2100 / 10 t = 210 sec answer : b" | physics |
math_qa__pQhEvorY8mIDDjXM | We bought a total of 80 books at the store. Math books cost $4 and history books cost $5. The total price was $368. How many math books did we buy? Choose one: A) 28 B) 32 C) 36 D) 40 E) 44 | <gadget id="calculator">80 * 4</gadget>
<output>320</output>
<gadget id="calculator">368 - 320</gadget>
<output>48</output>
<gadget id="calculator">80 - 48</gadget>
<output>32</output>
<result>B</result> | B | 32 | We bought a total of 80 books at the store. Math books cost $4 and history books cost $5. The total price was $368. How many math books did we buy? | {
"A": "28",
"B": "32",
"C": "36",
"D": "40",
"E": "44"
} | subtract(80, subtract(368, multiply(80, 4))) | multiply(n0,n1)|subtract(n3,#0)|subtract(n0,#1) | m + h = 80 h = 80 - m 4 m + 5 h = 368 4 m + 5 * ( 80 - m ) = 368 m = 32 the answer is b . | general |
math_qa__ppgeh7JkHSEzmckq | How many seconds will a 420 metre long train take to cross a man running with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 30 km/hr? Options.
A) 25 B) 63 C) 40 D) 45 E) 60 | <gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">30 - 6</gadget>
<output>24</output>
<gadget id="calculator">(5/18) * 24</gadget>
<output>20/3 = around 6.666667</output>
<gadget id="calculator">420 / (20/3)</gadget>
<output>63</output>
<result>B</result> | B | 63 | How many seconds will a 420 metre long train take to cross a man running with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 30 km/hr? | {
"A": "25",
"B": "63",
"C": "40",
"D": "45",
"E": "60"
} | divide(420, multiply(const_0_2778, subtract(30, 6))) | subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)| | "explanation : speed of train relatively to man = ( 30 - 6 ) km / hr = 24 km / hr = ( 24 x 5 / 18 ) m / sec = 6.66 m / sec time taken to pass the man = ( 420 / 6.66 ) sec = 63 sec . answer : b" | physics |
math_qa__AoFzb6i73nfVJNr0 | If x+y=25 and x2y3 + y2x3=25, what is the value of xy?
Choose the correct choice from the following choices.
A) 1 B) 2 C) 3 D) 4 E) 5 | <gadget id="calculator">25 / 25</gadget>
<output>1</output>
<gadget id="calculator">1 ** (1/2)</gadget>
<output>1</output>
<result>A</result> | A | 1 | If x+y=25 and x2y3 + y2x3=25, what is the value of xy? | {
"A": "1",
"B": "2",
"C": "3",
"D": "4",
"E": "5"
} | sqrt(divide(25, 25)) | divide(n0,n0)|sqrt(#0) | xy = 1 as x + y = 25 x 2 y 3 + y 2 x 3 = 25 x 2 y 2 ( y + x ) = 25 substituting x + y x 2 y 2 = 1 xy = 1 answer : a | general |
math_qa__268Z4LHrAy7ByX3L | There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs. 2288, then what was the price of the article initially?
Choose the correct choice:
A) rs . 2008
B) rs . 2022
C) rs . 2000
D) rs . 2029
E) rs . 2021 | <gadget id="calculator">30 - 20</gadget>
<output>10</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">2_288 / (6/5)</gadget>
<output>5_720/3 = around 1_906.666667</output>
<result>C</result> | C | 2,000 | There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs. 2288, then what was the price of the article initially? | {
"A": "rs . 2008",
"B": "rs . 2022",
"C": "rs . 2000",
"D": "rs . 2029",
"E": "rs . 2021"
} | divide(2288, add(const_1, divide(add(subtract(30, 20), 10), const_100))) | subtract(n0,n1)|add(n2,#0)|divide(#1,const_100)|add(#2,const_1)|divide(n3,#3) | let the price of the article , four years age be rs . 100 in the 1 st year , price of the article = 100 + 30 = rs . 130 . in the 2 nd year , price = 130 - 20 % of 130 = 130 - 26 = rs . 104 . in the 3 rd year , price = 104 + 10 % of 104 = 104 + 10.4 = rs . 114.40 . but present price of the article is rs . 2288 for 114.4 - - - > 100 ; 2288 - - - > ? required price = ( 2288 * 100 ) / 114.4 = 20 * 100 = rs . 2000 . answer : c | general |
math_qa__3vx1vBa5lsFqFzJv | If P(A) = 2/5 and P (B) = 2/5, find P (A n B) if A and B are independent events. Choose the correct choice from the following choices:
A) 7 / 25
B) 4 / 25
C) 8 / 25
D) 2 / 13
E) 3 / 17 | <gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * (2/5)</gadget>
<output>4/25 = around 0.16</output>
<result>B</result> | B | 0.16 | If P(A) = 2/5 and P (B) = 2/5, find P (A n B) if A and B are independent events. | {
"A": "7 / 25",
"B": "4 / 25",
"C": "8 / 25",
"D": "2 / 13",
"E": "3 / 17"
} | multiply(divide(2, 5), divide(2, 5)) | divide(n0,n1)|divide(n2,n3)|multiply(#0,#1)| | "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 2 / 5 . 2 / 5 p ( a n b ) = 4 / 25 . b" | general |
math_qa__zW1K2aOmEBIuzLGl | If the difference between compound interest (interest compounded yearly)and simple interest on a sum for 2 years at 10% p.a. is Rs.150 then sum is
Select the correct option:
A) rs . 12000 B) rs . 15000 C) rs . 13000 D) rs . 10000 E) rs . 14000 | <gadget id="calculator">150 * 10</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 * 10</gadget>
<output>15_000</output>
<result>B</result> | B | 15,000 | If the difference between compound interest (interest compounded yearly)and simple interest on a sum for 2 years at 10% p.a. is Rs.150 then sum is | {
"A": "rs . 12000",
"B": "rs . 15000",
"C": "rs . 13000",
"D": "rs . 10000",
"E": "rs . 14000"
} | multiply(multiply(150, 10), 10) | multiply(n1,n2)|multiply(n1,#0) | compund interest = p [ 1 + r / 100 ] ^ t - p ci = p [ 21 / 100 ] simple interest = ptr / 100 si = p [ 20 / 100 ] difference p [ 21 / 100 ] - p [ 20 / 100 ] = 150 p = 15000 answer : b | gain |
math_qa__6dpu9O2nmussRamm | A leak in the bottom of a tank can empty the full tank in 7 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold? Choose the correct choice from the following:
A) 7580 B) 7960 C) 8290 D) 6048 E) none | <gadget id="calculator">12 * 60</gadget>
<output>720</output>
<gadget id="calculator">6 * 720</gadget>
<output>4_320</output>
<gadget id="calculator">7 * 60</gadget>
<output>420</output>
<gadget id="calculator">720 / 420</gadget>
<output>12/7 = around 1.714286</output>
<gadget id="calculator">(12/7) - 1</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">4_320 / (5/7)</gadget>
<output>6_048</output>
<result>D</result> | D | 6,048 | A leak in the bottom of a tank can empty the full tank in 7 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold? | {
"A": "7580",
"B": "7960",
"C": "8290",
"D": "6048",
"E": "none"
} | divide(multiply(6, multiply(12, const_60)), subtract(divide(multiply(12, const_60), multiply(7, const_60)), const_1)) | multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4)| | "solution work done by the inlet in 1 hour = ( 1 / 7 - 1 / 12 ) = 5 / 84 work done by the inlet in 1 min . = ( 5 / 84 × 1 / 60 ) = 0.000992 volume of 0.000992 part = 6 litres . therefore , volume of whole = ( ( 1 / 0.000992 ) × 6 ) ‹ = › 6048 litres . answer d" | physics |
math_qa__r4rvllxy0dU6w7U9 | In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 500 newborn members of the population, approximately how many would be expected to survive the first 3 months of life? Choose the most appropriate option
A) 340 B) 346 C) 352 D) 365 E) 370 | <gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">500 * (9/10)</gadget>
<output>450</output>
<gadget id="calculator">450 * (9/10)</gadget>
<output>405</output>
<gadget id="calculator">405 * (9/10)</gadget>
<output>729/2 = around 364.5</output>
<result>D</result> | D | 365 | In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 500 newborn members of the population, approximately how many would be expected to survive the first 3 months of life? | {
"A": "340",
"B": "346",
"C": "352",
"D": "365",
"E": "370"
} | multiply(multiply(multiply(500, subtract(1, divide(const_1, 10))), subtract(1, divide(const_1, 10))), subtract(1, divide(const_1, 10))) | divide(const_1,n2)|subtract(n1,#0)|multiply(n3,#1)|multiply(#2,#1)|multiply(#3,#1) | number of newborns that can die in first month = 1 / 10 * 500 = 50 survived = 450 number of newborns that can die in second month = 1 / 10 * 450 = 45 survived = 405 number of newborns that can die in third month = 1 / 10 * 405 = 40 survived = 365 answer : d | probability |
math_qa__Lu3Psw6fcPMFIPZo | Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color?
Choose the most appropriate option
A) 2 / 5 B) 1 / 5 C) 1 / 9 D) 1 / 10 E) 1 / 25 | <gadget id="calculator">binomial(10, 2)</gadget>
<output>45</output>
<gadget id="calculator">5 / 45</gadget>
<output>1/9 = around 0.111111</output>
<result>C</result> | C | 0.111111 | Kim has 5 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 10 shoes, what is the probability that she will select 2 shoes of the same color? | {
"A": "2 / 5",
"B": "1 / 5",
"C": "1 / 9",
"D": "1 / 10",
"E": "1 / 25"
} | divide(5, choose(10, 2)) | choose(n2,n1)|divide(n0,#0)| | "total pairs = 10 c 2 = 45 ; same color pairs = 5 c 1 * 1 c 1 = 5 ; prob = 1 / 9 or 2 / 10 * 1 / 9 * 5 = 1 / 9 ans c" | probability |
math_qa__jNzkTvlSAM0PYRdD | The mean of 50 observations was 36. It was found later that an observation 45 was wrongly taken as 23. The corrected new mean is Choose the correct answer
A) 35.24 B) 36.14 C) 36.24 D) 36.44 E) none | <gadget id="calculator">36 * 50</gadget>
<output>1_800</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 - 23</gadget>
<output>25</output>
<gadget id="calculator">1_800 + 25</gadget>
<output>1_825</output>
<gadget id="calculator">1_825 / 50</gadget>
<output>73/2 = around 36.5</output>
<result>D</result> | D | 36.44 | The mean of 50 observations was 36. It was found later that an observation 45 was wrongly taken as 23. The corrected new mean is | {
"A": "35.24",
"B": "36.14",
"C": "36.24",
"D": "36.44",
"E": "none"
} | divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50) | multiply(n0,n1)|subtract(n0,const_2)|subtract(#1,n3)|add(#0,#2)|divide(#3,n0)| | "solution correct sum = ( 36 x 50 + 45 - 23 ) = 1822 . â ˆ ´ correct mean = 1822 / 50 = 36.44 . answer d" | general |
math_qa__CyazzVxLUn901Opd | A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and one-legged captain) to a nearby port. Altogether, these passengers have 15 heads and 43 legs. How many cats does the ship host? Choose the correct choice from the following choices.
A) 4 B) 5 C) 6 D) 7 E) 8 | <gadget id="calculator">43 - 1</gadget>
<output>42</output>
<gadget id="calculator">15 - 1</gadget>
<output>14</output>
<gadget id="calculator">14 * 2</gadget>
<output>28</output>
<gadget id="calculator">42 - 28</gadget>
<output>14</output>
<gadget id="calculator">14 * 4</gadget>
<output>56</output>
<gadget id="calculator">56 - 28</gadget>
<output>28</output>
<gadget id="calculator">14 / 28</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 14</gadget>
<output>7</output>
<result>D</result> | D | 7 | A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and one-legged captain) to a nearby port. Altogether, these passengers have 15 heads and 43 legs. How many cats does the ship host? | {
"A": "4",
"B": "5",
"C": "6",
"D": "7",
"E": "8"
} | multiply(divide(subtract(subtract(43, const_1), multiply(subtract(15, const_1), const_2)), subtract(multiply(subtract(15, const_1), const_4), multiply(subtract(15, const_1), const_2))), subtract(15, const_1)) | subtract(n1,const_1)|subtract(n0,const_1)|multiply(#1,const_2)|multiply(#1,const_4)|subtract(#0,#2)|subtract(#3,#2)|divide(#4,#5)|multiply(#6,#1)| | "sa ' s + co + ca + cats = 15 . sa ' s + 1 + 1 + cats = 15 or sa ' s + cats = 13 . sa ' s ( 2 ) + 2 + 1 + cats * 4 = 43 sa ' s * 2 + cats * 4 = 40 or sa ' s + cats * 2 = 20 or 13 - cats + cat * 2 = 20 then cats = 7 d" | general |
math_qa__9jVEzCHrpTQyYSYb | Find the amount on Rs.5000 in 2 years, the rate of interest being 20% per first year and 25% for the second year?
Choose the correct answer
A) 3377 B) 2678 C) 5460 D) 7500 E) 1671 | <gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">5_000 * 120</gadget>
<output>600_000</output>
<gadget id="calculator">600_000 / 100</gadget>
<output>6_000</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">6_000 * 125</gadget>
<output>750_000</output>
<gadget id="calculator">750_000 / 100</gadget>
<output>7_500</output>
<result>D</result> | D | 7,500 | Find the amount on Rs.5000 in 2 years, the rate of interest being 20% per first year and 25% for the second year? | {
"A": "3377",
"B": "2678",
"C": "5460",
"D": "7500",
"E": "1671"
} | divide(multiply(divide(multiply(5000, add(const_100, 20)), const_100), add(const_100, 25)), const_100) | add(n3,const_100)|add(n2,const_100)|multiply(n0,#1)|divide(#2,const_100)|multiply(#0,#3)|divide(#4,const_100)| | "5000 * 120 / 100 * 125 / 100 = > 7500 answer : d" | gain |
math_qa__vk9pOki9jXvzolfc | The average age of a group of n people is 15 years old. One more person aged 35 joins the group and the new average is 17 years old. What is the value of n? Choose the correct choice from the following options:
A) 8
B) 9
C) 10
D) 11
E) 12 | <gadget id="calculator">35 - 17</gadget>
<output>18</output>
<gadget id="calculator">17 - 15</gadget>
<output>2</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<result>B</result> | B | 9 | The average age of a group of n people is 15 years old. One more person aged 35 joins the group and the new average is 17 years old. What is the value of n? | {
"A": "8",
"B": "9",
"C": "10",
"D": "11",
"E": "12"
} | divide(subtract(35, 17), subtract(17, 15)) | subtract(n1,n2)|subtract(n2,n0)|divide(#0,#1) | 15 n + 35 = 17 ( n + 1 ) 2 n = 18 n = 9 the answer is b . | general |
math_qa__yp1Zn8DBeKv6OYjz | What is the measure of the radius of the circle inscribed in a triangle whose sides measure 4, 11 and 12 units?
Choose the correct choice from the following options.
A) 1.6 units B) 6 units C) 3 units D) 5 units E) 12 units | <gadget id="calculator">(((4 + 11 + 12) / 2) * ((4 + 11 + 12) / 2 - 4) * ((4 + 11 + 12) / 2 - 11) * ((4 + 11 + 12) / 2 - 12)) ** (1/2)</gadget>
<output>9*sqrt(95)/4 = around 21.930287</output>
<gadget id="calculator">4 + 11 + 12</gadget>
<output>27</output>
<gadget id="calculator">27 / 2</gadget>
<output>27/2 = around 13.5</output>
<gadget id="calculator">(9*sqrt(95)/4) / (27/2)</gadget>
<output>sqrt(95)/6 = around 1.624466</output>
<result>A</result> | A | 1.6 | What is the measure of the radius of the circle inscribed in a triangle whose sides measure 4, 11 and 12 units? | {
"A": "1.6 units",
"B": "6 units",
"C": "3 units",
"D": "5 units",
"E": "12 units"
} | divide(triangle_area_three_edges(4, 11, 12), divide(triangle_perimeter(4, 11, 12), const_2)) | triangle_area_three_edges(n0,n1,n2)|triangle_perimeter(n0,n1,n2)|divide(#1,const_2)|divide(#0,#2) | sides are 4 , 11 and 12 . . . thus it is right angle triangle since 12 ^ 2 = 4 ^ 2 + 11 ^ 2 therefore , area = 1 / 2 * 11 * 4 = 22 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 12 + 11 + 4 / 2 = 13,5 thus , 22 = 13,5 * r and hence r = in - radius = 1.6 option a | geometry |
math_qa__43iFaY9OpEQj9R27 | What is x if x + 2y = 10 and y = 4?
Select the correct option
A) 10 B) 8 C) 6 D) 4 E) 2 | <gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">10 - 8</gadget>
<output>2</output>
<result>E</result> | E | 2 | What is x if x + 2y = 10 and y = 4? | {
"A": "10",
"B": "8",
"C": "6",
"D": "4",
"E": "2"
} | subtract(10, multiply(2, 4)) | multiply(n0,n2)|subtract(n1,#0)| | "x = 10 - 2 y x = 10 - 8 . x = 2 answer : e" | general |
math_qa__Pj9pT73jGBcIjHQo | We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $396. How many math books did we buy? Pick one
A) 47 B) 54 C) 56 D) 61 E) 64 | <gadget id="calculator">90 * 4</gadget>
<output>360</output>
<gadget id="calculator">396 - 360</gadget>
<output>36</output>
<gadget id="calculator">90 - 36</gadget>
<output>54</output>
<result>B</result> | B | 54 | We bought a total of 90 books at the store. Math books cost $4 and history books cost $5. The total price was $396. How many math books did we buy? | {
"A": "47",
"B": "54",
"C": "56",
"D": "61",
"E": "64"
} | subtract(90, subtract(396, multiply(90, 4))) | multiply(n0,n1)|subtract(n3,#0)|subtract(n0,#1)| | "m + h = 90 h = 90 - m 4 m + 5 h = 396 4 m + 5 * ( 90 - m ) = 396 m = 54 the answer is b ." | general |
math_qa__XRsRDIcZtE8JTbqv | Find the probability that a leap year selected at random will have 53 Mondays Choose the most appropriate option:
A) 6 / 7 B) 5 / 7 C) 4 / 7 D) 3 / 7 E) 2 / 7 | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>
<result>E</result> | E | 0.285714 | Find the probability that a leap year selected at random will have 53 Mondays | {
"A": "6 / 7",
"B": "5 / 7",
"C": "4 / 7",
"D": "3 / 7",
"E": "2 / 7"
} | divide(const_2, add(const_3, const_4)) | add(const_3,const_4)|divide(const_2,#0) | there are 366 days in a leap year : 52 weeks and 2 more days . so , 52 mondays and 2 days . these 2 days can be : { mon , tue } , { tue , wed } , { wed , thu } , { thu , fri } , { fri , sat } , { sat , sun } and { sun , mon } ( 7 cases ) . in order to have 53 mondays we should have either { mon , tuesday } or { sun , mon } case . the probability of that is 2 / 7 . answer : e . | probability |
math_qa__fSFk8H6vHTumBoy2 | Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 32% chemical A, what percent of the mixture is Solution X? Choose the correct choice from the following options: A) 85 % B) 80 % C) 75 % D) 70 % E) 65 % | <gadget id="calculator">40 - 32</gadget>
<output>8</output>
<gadget id="calculator">32 - 30</gadget>
<output>2</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>B</result> | B | 80 | Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 32% chemical A, what percent of the mixture is Solution X? | {
"A": "85 %",
"B": "80 %",
"C": "75 %",
"D": "70 %",
"E": "65 %"
} | multiply(divide(divide(subtract(40, 32), subtract(32, 30)), add(divide(subtract(40, 32), subtract(32, 30)), const_1)), const_100) | subtract(n2,n4)|subtract(n4,n0)|divide(#0,#1)|add(#2,const_1)|divide(#2,#3)|multiply(#4,const_100) | the volume of the mixture be x + y . 0.3 x + 0.4 y = 0.32 ( x + y ) x = 4 y x / ( x + y ) = 4 / 5 = 80 % . the answer is b . | gain |
math_qa__pVtiqDUIRM3OBRhy | The wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 50% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin? Choose the correct option
A) 18.75 %
B) 23 %
C) 15 %
D) 50 %
E) 100 % | <gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">150 - 130</gadget>
<output>20</output>
<gadget id="calculator">20 / 130</gadget>
<output>2/13 = around 0.153846</output>
<gadget id="calculator">(2/13) * 100</gadget>
<output>200/13 = around 15.384615</output>
<result>C</result> | C | 15 | The wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 50% more than that earned by Erica. How much percent is the wages earned by Charles more than that earned by Robin? | {
"A": "18.75 %",
"B": "23 %",
"C": "15 %",
"D": "50 %",
"E": "100 %"
} | multiply(divide(subtract(add(const_100, 50), add(const_100, 30)), add(const_100, 30)), const_100) | add(n1,const_100)|add(n0,const_100)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100)| | "let wage of erica = 10 wage of robin = 1.3 * 10 = 13 wage of charles = 1.5 * 10 = 15 percentage by which wage earned by charles is more than that earned by robin = ( 15 - 13 ) / 13 * 100 % = 2 / 13 * 100 % = 15 % answer c" | general |
math_qa__vzBUlrrYJgYSCc68 | 8 x 5.4 - 0.6 x 10/1.2 = ? Pick one
A) 30 B) 45 C) 50 D) 31 E) 21 | <gadget id="calculator">8 * 5.4</gadget>
<output>43.2</output>
<gadget id="calculator">0.6 * 10</gadget>
<output>6</output>
<gadget id="calculator">43.2 - 6</gadget>
<output>37.2</output>
<gadget id="calculator">37.2 / 1.2</gadget>
<output>31</output>
<result>D</result> | D | 31 | 8 x 5.4 - 0.6 x 10/1.2 = ? | {
"A": "30",
"B": "45",
"C": "50",
"D": "31",
"E": "21"
} | divide(subtract(multiply(8, 5.4), multiply(0.6, 10)), 1.2) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4)| | "given expression = ( 43.2 - 6 ) / 1.2 = 37.2 / 1.2 = 31 answer is d ." | general |
math_qa__ABOMRvY92228w6V7 | Veena ranks 65rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination? Choose the correct choice from the following options.
A) 96 B) 108 C) 110 D) 90 E) 93 | <gadget id="calculator">182 - 22</gadget>
<output>160</output>
<gadget id="calculator">65 - 1</gadget>
<output>64</output>
<gadget id="calculator">160 - 64</gadget>
<output>96</output>
<gadget id="calculator">96 - 4</gadget>
<output>92</output>
<result>A</result> | A | 96 | Veena ranks 65rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination? | {
"A": "96",
"B": "108",
"C": "110",
"D": "90",
"E": "93"
} | subtract(subtract(subtract(182, 22), subtract(65, const_1)), const_4) | subtract(n1,n2)|subtract(n0,const_1)|subtract(#0,#1)|subtract(#2,const_4)| | "total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 65 + 1 = 96 answer : a" | other |
math_qa__pm8sb09ejac8HMJC | there were 36000 hardback copies of a certain novel sold before the paperback version was issued . from the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold . if a total of 440000 copies of the novel were sold in all , how many paperback copies were sold ? Options
A) 45,000 B) 360,000 C) 364,500 D) 363,600 E) 396,900 | <gadget id="calculator">440_000 - 36_000</gadget>
<output>404_000</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">404_000 / 10</gadget>
<output>40_400</output>
<gadget id="calculator">9 * 40_400</gadget>
<output>363_600</output>
<result>D</result> | D | 363,600 | there were 36000 hardback copies of a certain novel sold before the paperback version was issued . from the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold . if a total of 440000 copies of the novel were sold in all , how many paperback copies were sold ? | {
"A": "45,000",
"B": "360,000",
"C": "364,500",
"D": "363,600",
"E": "396,900"
} | multiply(9, divide(subtract(440000, 36000), add(9, const_1))) | add(n1,const_1)|subtract(n2,n0)|divide(#1,#0)|multiply(n1,#2) | say x was the # of hardback copies sold from the time the first paperback copy was sold . then the total # of paperback copies sold was 9 x ; hence the total # of copies sold was ( hardback ) + ( paperback ) = ( 36 + x ) + ( 9 x ) = 440 - - > x = 40.4 . so , the total # of paperback copies sold was 9 x = 9 * 40.4 = 363.6 or 363,600 . answer : d . | general |
math_qa__tDTXH1Wfo7dgouuT | In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
Choices: A) 8 hrs B) 9 hrs C) 2 hrs D) 2 hrs E) 9 hrs | <gadget id="calculator">30 / 60</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">4 * (1/2)</gadget>
<output>2</output>
<result>C</result> | C | 2 | In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is? | {
"A": "8 hrs",
"B": "9 hrs",
"C": "2 hrs",
"D": "2 hrs",
"E": "9 hrs"
} | multiply(4, divide(30, const_60)) | divide(n2,const_60)|multiply(n1,#0) | ratio of speeds = 3 : 4 ratio of times taken = 4 : 3 suppose a takes 4 x hrs and b takes 3 x hrs to reach the destination . then , 4 x - 3 x = 30 / 60 = > x = 1 / 2 time taken by a = 4 x hrs = 4 * 1 / 2 = 2 hrs . answer : c | physics |
math_qa__9Vp0OVc9ZSGHfIq8 | In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes. Pick: A) 10 B) 12 C) 14 D) 16 E) 19 | <gadget id="calculator">24 / 2</gadget>
<output>12</output>
<result>B</result> | B | 12 | In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes. | {
"A": "10",
"B": "12",
"C": "14",
"D": "16",
"E": "19"
} | divide(24, const_2) | divide(n0,const_2)| | "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 24 = > 2 x = 24 = > x = 12 b" | general |
math_qa__pEC5s6qFPzXHxviG | Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 2500. then his monthly salary is Select the correct option:
A) rs . 12500 B) rs . 1000 C) rs . 8000 D) rs . 6000 E) rs . 15000 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">2_500 * 5</gadget>
<output>12_500</output>
<result>A</result> | A | 12,500 | Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 2500. then his monthly salary is | {
"A": "rs . 12500",
"B": "rs . 1000",
"C": "rs . 8000",
"D": "rs . 6000",
"E": "rs . 15000"
} | multiply(2500, add(const_4, const_1)) | add(const_1,const_4)|multiply(n4,#0)| | "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 2500 â ‡ ” 20 / 100 x = 2500 â ‡ ” x = 2500 ã — 5 = 12500 . answer a" | gain |
math_qa__bKHBney9HZpmhB4e | A man complete a journey in 10 hours. He travels first half of the journey at the rate of 20 km/hr and second half at the rate of 20 km/hr. Find the total journey in km.
Choices:
A) 220 km B) 224 km C) 230 km D) 232 km E) 200 km | <gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">400 * 10</gadget>
<output>4_000</output>
<gadget id="calculator">20 + 20</gadget>
<output>40</output>
<gadget id="calculator">4_000 / 40</gadget>
<output>100</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<result>E</result> | E | 200 | A man complete a journey in 10 hours. He travels first half of the journey at the rate of 20 km/hr and second half at the rate of 20 km/hr. Find the total journey in km. | {
"A": "220 km",
"B": "224 km",
"C": "230 km",
"D": "232 km",
"E": "200 km"
} | multiply(const_2, divide(multiply(multiply(20, 20), 10), add(20, 20))) | add(n1,n2)|multiply(n1,n2)|multiply(n0,#1)|divide(#2,#0)|multiply(#3,const_2)| | "0.5 x / 20 + 0.5 x / 20 = 10 - - > x / 20 + x / 20 = 20 - - > 2 x = 20 x 20 - - > x = ( 20 x 20 ) / 2 = 200 km . answer : e ." | physics |
math_qa__nOj3M3V3F60As3wj | the probability of a student possessing a ball point pen in exam is 3/5 & possessing an ink pen is 2/3. find his probability of possessing at least one of them
Select:
A) 10 / 15 B) 11 / 15 C) 12 / 15 D) 13 / 15 E) 14 / 15 | <gadget id="calculator">12 + 1</gadget>
<output>13</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">13 / 15</gadget>
<output>13/15 = around 0.866667</output>
<result>D</result> | D | 0.866667 | the probability of a student possessing a ball point pen in exam is 3/5 & possessing an ink pen is 2/3. find his probability of possessing at least one of them | {
"A": "10 / 15",
"B": "11 / 15",
"C": "12 / 15",
"D": "13 / 15",
"E": "14 / 15"
} | divide(add(const_12, const_1), multiply(3, 5)) | add(const_1,const_12)|multiply(n0,n1)|divide(#0,#1) | the probability of a student possessing a ball point pen in exam is 3 / 5 . the probability of a student not possessing a ball point pen in exam is 2 / 5 & possessing an ink pen is 2 / 3 . & not possessing an ink pen is 1 / 3 . his probability of possessing none of them = 2 / 5 * 1 / 3 = 2 / 15 his probability of possessing one of them = 1 - 2 / 15 = 13 / 15 answer : d | general |
math_qa__ETAEWQttKCG7IATO | If 200!/10^n is an integer, what is the largest possible value of n? Select.
A) 40 B) 42 C) 44 D) 48 E) 49 | <gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">200 / 5</gadget>
<output>40</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<gadget id="calculator">8 + 40</gadget>
<output>48</output>
<result>E</result> | E | 49 | If 200!/10^n is an integer, what is the largest possible value of n? | {
"A": "40",
"B": "42",
"C": "44",
"D": "48",
"E": "49"
} | add(divide(divide(200, add(const_4, const_1)), add(const_4, const_1)), divide(200, add(const_4, const_1))) | add(const_1,const_4)|divide(n0,#0)|divide(#1,#0)|add(#2,#1)| | "we have to basically count the number of 5 s withing 200 200 / 5 = 40 200 / 5 ^ 2 = 8 200 / 5 ^ 3 = 1 we know for sure that there will be at least 49 even numbers ( multiples of 2 ) within 200 so there are 49 10 s in 200 ! answer : e" | general |
math_qa__k72z5vdairbMclsF | Evaluate
248+64−−√−−−−−−−−−√
Choose the correct choice from the following
A) 14 B) 26 C) 16 D) 36 E) 46 | <gadget id="calculator">64 * 4</gadget>
<output>256</output>
<gadget id="calculator">256 - 248</gadget>
<output>8</output>
<gadget id="calculator">2 * 8</gadget>
<output>16</output>
<result>C</result> | C | 16 | Evaluate
248+64−−√−−−−−−−−−√ | {
"A": "14",
"B": "26",
"C": "16",
"D": "36",
"E": "46"
} | multiply(const_2, subtract(multiply(64, const_4), 248)) | multiply(n1,const_4)|subtract(#0,n0)|multiply(#1,const_2) | explanation : = 248 + 64 − − √ − − − − − − − − − √ = 248 + 8 − − − − − − √ = 256 − − − √ = 16 answer : c | general |
math_qa__ovpXZ5pHLSyZuy85 | Two employees X and Y are paid a total of Rs. 638 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Pick:
A) s . 250
B) s . 280
C) s . 290
D) s . 299
E) s . 300 | <gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">638 * 10</gadget>
<output>6_380</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">6_380 / 22</gadget>
<output>290</output>
<result>C</result> | C | 290 | Two employees X and Y are paid a total of Rs. 638 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? | {
"A": "s . 250",
"B": "s . 280",
"C": "s . 290",
"D": "s . 299",
"E": "s . 300"
} | divide(multiply(638, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2)) | add(const_1,const_4)|multiply(#0,const_2)|add(#1,const_1)|multiply(n0,#1)|multiply(#2,const_2)|divide(#3,#4)| | "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 638 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 638 ⇒ y [ 12 / 10 + 1 ] = 638 ⇒ 22 y / 10 = 638 ⇒ 22 y = 6380 ⇒ y = 6380 / 22 = 580 / 2 = rs . 290 c" | general |
math_qa__8TinvjRfAfdSYbTu | For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y? Choices:
A) 14 B) 12 C) 10 D) 16 E) 18 | <gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">7 + 9</gadget>
<output>16</output>
<result>D</result> | D | 16 | For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 920, what is the maximum possible sum of the length of x and the length of y? | {
"A": "14",
"B": "12",
"C": "10",
"D": "16",
"E": "18"
} | add(add(4, 3), add(add(4, 4), 1)) | add(n2,n7)|add(n2,n2)|add(n0,#1)|add(#0,#2)| | "we know that : x > 1 , y > 1 , and x + 3 y < 1000 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest noall factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( it exceeds 920 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which has length of integer is 9 . now , since x = 512 , x + 3 y < 920 so , 3 y < 408 = = > y < 136 so , y can take any value which is less than 136 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . d" | general |
math_qa__p8aM9Rq575BQFMRn | A circular grass lawn of 35 metres in radius has a path 7 metres wide running around it on the outside. Find the area of path. Select the correct option:
A) 1694 m 2
B) 1700 m 2
C) 1598 m 2
D) 1500 m 2
E) none of thes | <gadget id="calculator">35 + 7</gadget>
<output>42</output>
<gadget id="calculator">pi * (42 ** 2)</gadget>
<output>1764*pi = around 5_541.769441</output>
<gadget id="calculator">pi * (35 ** 2)</gadget>
<output>1225*pi = around 3_848.451001</output>
<gadget id="calculator">(1764*pi) - (1225*pi)</gadget>
<output>539*pi = around 1_693.31844</output>
<result>A</result> | A | 1,694 | A circular grass lawn of 35 metres in radius has a path 7 metres wide running around it on the outside. Find the area of path. | {
"A": "1694 m 2",
"B": "1700 m 2",
"C": "1598 m 2",
"D": "1500 m 2",
"E": "none of thes"
} | subtract(circle_area(add(35, 7)), circle_area(35)) | add(n0,n1)|circle_area(n0)|circle_area(#0)|subtract(#2,#1) | radius of a circular grass lawn ( without path ) = 35 m ∴ area = π r 2 = π ( 35 ) 2 radius of a circular grass lawn ( with path ) = 35 + 7 = 42 m ∴ area = π r 2 = π ( 42 ) 2 ∴ area of path = π ( 42 ) 2 – π ( 35 ) 2 = π ( 422 – 352 ) = π ( 42 + 35 ) ( 42 – 35 ) answer a | geometry |
math_qa__xWSwZcIZZhIJKkrE | Sonika deposited Rs.6000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much? Answers:
A) 9660 B) 6560 C) 7560 D) 9560 E) 8560 | <gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">9_200 - 6_000</gadget>
<output>3_200</output>
<gadget id="calculator">3_200 / 3</gadget>
<output>3_200/3 = around 1_066.666667</output>
<gadget id="calculator">(3_200/3) / 6_000</gadget>
<output>8/45 = around 0.177778</output>
<gadget id="calculator">(1/50) + (8/45)</gadget>
<output>89/450 = around 0.197778</output>
<gadget id="calculator">(89/450) * 6_000</gadget>
<output>3_560/3 = around 1_186.666667</output>
<gadget id="calculator">(3_560/3) * 3</gadget>
<output>3_560</output>
<gadget id="calculator">3_560 + 6_000</gadget>
<output>9_560</output>
<result>D</result> | D | 9,560 | Sonika deposited Rs.6000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much? | {
"A": "9660",
"B": "6560",
"C": "7560",
"D": "9560",
"E": "8560"
} | add(multiply(multiply(add(divide(2, const_100), divide(divide(subtract(9200, 6000), 3), 6000)), 6000), 3), 6000) | divide(n3,const_100)|subtract(n1,n0)|divide(#1,n2)|divide(#2,n0)|add(#0,#3)|multiply(n0,#4)|multiply(n2,#5)|add(n0,#6)| | "( 6000 * 3 * 2 ) / 100 = 360 9200 - - - - - - - - 9560 answer : d" | gain |
math_qa__zHTolhnALjnGqEzj | Excluding stoppages, the speed of a train is 42 kmph and including stoppages it is 27 kmph. Of how many minutes does the train stop per hour? Answers
A) 19.42
B) 20.42
C) 21.42
D) 22.42
E) 23.42 | <gadget id="calculator">27 / 42</gadget>
<output>9/14 = around 0.642857</output>
<gadget id="calculator">60 * (9/14)</gadget>
<output>270/7 = around 38.571429</output>
<gadget id="calculator">60 - (270/7)</gadget>
<output>150/7 = around 21.428571</output>
<result>C</result> | C | 21.42 | Excluding stoppages, the speed of a train is 42 kmph and including stoppages it is 27 kmph. Of how many minutes does the train stop per hour? | {
"A": "19.42",
"B": "20.42",
"C": "21.42",
"D": "22.42",
"E": "23.42"
} | subtract(const_60, multiply(const_60, divide(27, 42))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | "explanation : t = 15 / 42 * 60 = 21.42 answer : option c" | physics |
math_qa__u4Gr4YesLKeJe82S | The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 80/kg. how much did a kg of coffee cost in june ?
Choose the correct answer.
A) 50
B) 60
C) 80
D) 100
E) 120 | <gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(1/5) + 1</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(4/5) * (6/5)</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">80 / (24/25)</gadget>
<output>250/3 = around 83.333333</output>
<result>C</result> | C | 80 | The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 80/kg. how much did a kg of coffee cost in june ? | {
"A": "50",
"B": "60",
"C": "80",
"D": "100",
"E": "120"
} | divide(80, multiply(subtract(const_1, divide(20, const_100)), add(divide(20, const_100), const_1))) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|divide(n2,#4)| | "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 800 gm ) of tea and 1 / 2 kg ( 800 gm ) of coffee ( equal quantities ) = 80 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 80 = > x = 80 thus proved . . . option c ." | general |
math_qa__s5tGIESpzqD1Xrza | Two boys starts from the same place walking at the rate of 4.5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 9.5 km apart? Select:
A) 9.5
B) 5.5
C) 8.5
D) 9.6
E) 9.7 | <gadget id="calculator">5.5 - 4.5</gadget>
<output>1</output>
<gadget id="calculator">9.5 / 1</gadget>
<output>9.5</output>
<result>A</result> | A | 9.5 | Two boys starts from the same place walking at the rate of 4.5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 9.5 km apart? | {
"A": "9.5",
"B": "5.5",
"C": "8.5",
"D": "9.6",
"E": "9.7"
} | divide(9.5, subtract(5.5, 4.5)) | subtract(n1,n0)|divide(n2,#0) | explanation : relative speed = 5.5 - 4.5 = 1 kmph ( because they walk in the same direction ) distance = 9.5 km time = distance / speed = 9.5 / 1 = 9.5 hr answer : a | gain |
math_qa__vkrErGYh9hdtkWYL | A train is moving at 4/5 of its usual speed. The train is 45 minutes too late. What is the usual time (in hours) for the train to complete the journey?
Choose the correct choice from the following choices:
A) 1
B) 1.5
C) 2
D) 2.5
E) 3 | <gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">45 * (4/5)</gadget>
<output>36</output>
<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / (1/5)</gadget>
<output>5</output>
<gadget id="calculator">36 * 5</gadget>
<output>180</output>
<gadget id="calculator">180 / 60</gadget>
<output>3</output>
<result>E</result> | E | 3 | A train is moving at 4/5 of its usual speed. The train is 45 minutes too late. What is the usual time (in hours) for the train to complete the journey? | {
"A": "1",
"B": "1.5",
"C": "2",
"D": "2.5",
"E": "3"
} | divide(multiply(multiply(45, divide(4, 5)), inverse(subtract(const_1, divide(4, 5)))), const_60) | divide(n0,n1)|multiply(n2,#0)|subtract(const_1,#0)|inverse(#2)|multiply(#3,#1)|divide(#4,const_60) | new time = d / ( 4 v / 5 ) = 5 / 4 * usual time 45 minutes represents 1 / 4 of the usual time . the usual time is 4 * 45 minutes = 3 hours . the answer is e . | physics |
math_qa__qbgIF6UPVWs1i2jL | In a class of 52 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German? Choices:
A) 30
B) 10
C) 18
D) 28
E) 32 | <gadget id="calculator">52 + 12</gadget>
<output>64</output>
<gadget id="calculator">64 - 22</gadget>
<output>42</output>
<gadget id="calculator">42 - 12</gadget>
<output>30</output>
<result>A</result> | A | 30 | In a class of 52 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German? | {
"A": "30",
"B": "10",
"C": "18",
"D": "28",
"E": "32"
} | subtract(subtract(add(52, 12), 22), 12) | add(n0,n1)|subtract(#0,n2)|subtract(#1,n1) | total = english + german - both + neither - - > 52 = english + 22 - 12 + 0 - - > english = 42 - - > only english = english - both = 42 - 12 = 30 answer : a . | other |
math_qa__bUU8dm38FssvNnji | If the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 4, what is the ratio of apples to cucumbers? Options: A) 1 : 3 B) 2 : 5 C) 3 : 5 D) 5 : 8 E) 4 : 7 | <gadget id="calculator">5 / 2</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) / 4</gadget>
<output>5/8 = around 0.625</output>
<result>D</result> | D | 0.625 | If the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 4, what is the ratio of apples to cucumbers? | {
"A": "1 : 3",
"B": "2 : 5",
"C": "3 : 5",
"D": "5 : 8",
"E": "4 : 7"
} | divide(divide(5, 2), 4) | divide(n0,n1)|divide(#0,n3) | the ratio of bananas to cucumbers is 1 to 4 which equals 2 to 8 . the ratio of apples to bananas to cucumbers is 5 to 2 to 8 . the ratio of apples to cucumbers is 5 to 8 . the answer is d . | other |
math_qa__iFlaOFkGCKuDDuCJ | A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability L that the first ball picked up is odd numbered? Choose the correct choice from the following choices
A) 0 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 1 | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<result>D</result> | D | 0.666667 | A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability L that the first ball picked up is odd numbered? | {
"A": "0",
"B": "1 / 3",
"C": "1 / 2",
"D": "2 / 3",
"E": "1"
} | divide(const_2, 3) | divide(const_2,n3) | answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability l is 2 / 3 . d | probability |
math_qa__t4P15VrFmRuNSiV6 | The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 and that of failed candidates was 39 and that of failed candidates was 15, the no.of candidates who passed the examination is?
Select the correct option:
A) 80 B) 90 C) 100 D) 120 E) 130 | <gadget id="calculator">120 * 35</gadget>
<output>4_200</output>
<gadget id="calculator">120 * 15</gadget>
<output>1_800</output>
<gadget id="calculator">4_200 - 1_800</gadget>
<output>2_400</output>
<gadget id="calculator">39 - 15</gadget>
<output>24</output>
<gadget id="calculator">2_400 / 24</gadget>
<output>100</output>
<result>C</result> | C | 100 | The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 and that of failed candidates was 39 and that of failed candidates was 15, the no.of candidates who passed the examination is? | {
"A": "80",
"B": "90",
"C": "100",
"D": "120",
"E": "130"
} | divide(subtract(multiply(120, 35), multiply(120, 15)), subtract(39, 15)) | multiply(n0,n1)|multiply(n0,n4)|subtract(n2,n4)|subtract(#0,#1)|divide(#3,#2) | let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 ⇒ 24 y = 4200 - 1800 ∴ y = 2400 / 24 = 100 c | general |
math_qa__UAPQfjhmYYdFI4kE | Boy sells a book for Rs. 720 he gets a loss of 10 %, To gain 10%, what should be the SP? Choose the correct option.
A) 430 B) 880 C) 550 D) 590 E) 600 | <gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">720 / (9/10)</gadget>
<output>800</output>
<gadget id="calculator">800 * (1/10)</gadget>
<output>80</output>
<gadget id="calculator">800 + 80</gadget>
<output>880</output>
<result>B</result> | B | 880 | Boy sells a book for Rs. 720 he gets a loss of 10 %, To gain 10%, what should be the SP? | {
"A": "430",
"B": "880",
"C": "550",
"D": "590",
"E": "600"
} | add(divide(720, subtract(const_1, divide(10, const_100))), multiply(divide(720, subtract(const_1, divide(10, const_100))), divide(10, const_100))) | divide(n1,const_100)|divide(n2,const_100)|subtract(const_1,#0)|divide(n0,#2)|multiply(#3,#1)|add(#3,#4)| | "cost price = 720 / 90 x 100 = 800 to gain 10 % = 800 x 10 / 100 = 80 sp = cp + gain = 800 + 80 = 880 answer : b" | gain |
math_qa__sunZWdTqHrb3LGA9 | Renu can do a piece of work in 5 days, but with the help of her friend Suma , she can do it in 4 days. In what time Suma can do it alone? Options
A) 10 B) 12 C) 14 D) 15 E) 20 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/4) - (1/5)</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 / (1/20)</gadget>
<output>20</output>
<result>E</result> | E | 20 | Renu can do a piece of work in 5 days, but with the help of her friend Suma , she can do it in 4 days. In what time Suma can do it alone? | {
"A": "10",
"B": "12",
"C": "14",
"D": "15",
"E": "20"
} | inverse(subtract(divide(const_1, 4), divide(const_1, 5))) | divide(const_1,n1)|divide(const_1,n0)|subtract(#0,#1)|inverse(#2)| | "renu â € ™ s one day â € ™ s work = 1 / 5 suma â € ™ s one day â € ™ s work = 1 / 4 - 1 / 5 = 1 / 20 suma can do it alone in 20 days . answer : e" | physics |
math_qa__jKLo3FOaLBync02G | The compounded ratio of (2 : 3), (6: 11) and (11 :2) is : Select:
A) 1 : 2 B) 5 : 9 C) 2 : 1 D) 11 : 24 E) none | <gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">6 / 11</gadget>
<output>6/11 = around 0.545455</output>
<gadget id="calculator">(2/3) * (6/11)</gadget>
<output>4/11 = around 0.363636</output>
<gadget id="calculator">11 / 2</gadget>
<output>11/2 = around 5.5</output>
<gadget id="calculator">(4/11) * (11/2)</gadget>
<output>2</output>
<result>C</result> | C | 2 | The compounded ratio of (2 : 3), (6: 11) and (11 :2) is : | {
"A": "1 : 2",
"B": "5 : 9",
"C": "2 : 1",
"D": "11 : 24",
"E": "none"
} | multiply(multiply(divide(2, 3), divide(6, 11)), divide(11, 2)) | divide(n3,n0)|divide(n0,n1)|divide(n2,n3)|multiply(#1,#2)|multiply(#0,#3) | answer : option c 2 / 3 : 6 / 11 : 11 / 2 = 2 : 1 | other |
math_qa__r7yKxwIqA1pGBH6h | In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number P and the smallest possible number of students that could have taken both geometry and biology? Select the correct option
A) 144 B) 119 C) 113 D) 88 E) 31 | <gadget id="calculator">144 + 119</gadget>
<output>263</output>
<gadget id="calculator">263 - 232</gadget>
<output>31</output>
<gadget id="calculator">119 - 31</gadget>
<output>88</output>
<result>D</result> | D | 88 | In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number P and the smallest possible number of students that could have taken both geometry and biology? | {
"A": "144",
"B": "119",
"C": "113",
"D": "88",
"E": "31"
} | subtract(119, subtract(add(144, 119), 232)) | add(n1,n2)|subtract(#0,n0)|subtract(n2,#1)| | "official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number of students p that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ." | other |
math_qa__w0lJJ2xuGFfossHu | The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people V who purchased only book A? Choose the correct choice from the following answers:
A) 250
B) 500
C) 750
D) 1000
E) 1500 | <gadget id="calculator">500 / 2</gadget>
<output>250</output>
<gadget id="calculator">500 + 250</gadget>
<output>750</output>
<gadget id="calculator">750 * 2</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 - 500</gadget>
<output>1_000</output>
<result>D</result> | D | 1,000 | The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people V who purchased only book A? | {
"A": "250",
"B": "500",
"C": "750",
"D": "1000",
"E": "1500"
} | subtract(multiply(add(500, divide(500, const_2)), const_2), 500) | divide(n0,const_2)|add(n0,#0)|multiply(#1,const_2)|subtract(#2,n0)| | "this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , v = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000" | other |
math_qa__fqXuxbVPVehX4zJp | In a recent election, Geoff received 1 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3000 more votes to win the election, what is the value of x ? Choose the most appropriate option
A) 50 B) 54 C) 56 D) 51 E) 63 | <gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">50 + 1</gadget>
<output>51</output>
<result>D</result> | D | 51 | In a recent election, Geoff received 1 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3000 more votes to win the election, what is the value of x ? | {
"A": "50",
"B": "54",
"C": "56",
"D": "51",
"E": "63"
} | add(divide(const_100, const_2), 1) | divide(const_100,const_2)|add(n0,#0)| | "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 60 votes he needs 3571 more votes so : 60 + 3000 = 3060 now what ' s the problem wants ? ? a x % . . . . . . . . 3060 is what % of total votes 6000 . . . . . . . . translating : 3060 = x / 100 * 6000 - - - x = 51 % . . . . . . . . . . d" | gain |
math_qa__scqriySBSOl3kHBB | Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability E that Jane will be on the same committee as Albert? Choose the correct choice from the following answers
A) 12 %
B) 20 %
C) 33 %
D) 40 %
E) 50 % | <gadget id="calculator">binomial(4, 1)</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">binomial(6, 3)</gadget>
<output>20</output>
<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>D</result> | D | 40 | Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability E that Jane will be on the same committee as Albert? | {
"A": "12 %",
"B": "20 %",
"C": "33 %",
"D": "40 %",
"E": "50 %"
} | multiply(divide(multiply(choose(const_4, const_1), const_2), choose(6, 3)), multiply(multiply(const_5, const_5), const_4)) | choose(const_4,const_1)|choose(n0,n1)|multiply(const_5,const_5)|multiply(#0,const_2)|multiply(#2,const_4)|divide(#3,#1)|multiply(#5,#4)| | "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability e = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d" | probability |
math_qa__owG6enQROeX1qngl | If 40% of a certain number is 160, then what is 20% of that number? Choose the correct choice from the following answers:
A) 75
B) 100
C) 120
D) 30
E) 80 | <gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">160 / (2/5)</gadget>
<output>400</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">400 * (1/5)</gadget>
<output>80</output>
<result>E</result> | E | 80 | If 40% of a certain number is 160, then what is 20% of that number? | {
"A": "75",
"B": "100",
"C": "120",
"D": "30",
"E": "80"
} | multiply(divide(160, divide(40, const_100)), divide(20, const_100)) | divide(n0,const_100)|divide(n2,const_100)|divide(n1,#0)|multiply(#2,#1)| | "explanation : 40 % = 40 * 4 = 160 20 % = 20 * 4 = 80 answer : option e" | gain |
math_qa__fVLcMG0tTTus8WG9 | workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.15 lacs . How many workers were they? Choose the correct option:
A) 300 B) 230 C) 500 D) 560 E) 590 | <gadget id="calculator">3.15 - 3</gadget>
<output>0.15</output>
<gadget id="calculator">0.15 * 1_000</gadget>
<output>150</output>
<gadget id="calculator">150 * 100</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 / 50</gadget>
<output>300</output>
<result>A</result> | A | 300 | workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.15 lacs . How many workers were they? | {
"A": "300",
"B": "230",
"C": "500",
"D": "560",
"E": "590"
} | divide(multiply(multiply(subtract(3.15, 3), const_1000), const_100), 50) | subtract(n2,n0)|multiply(#0,const_1000)|multiply(#1,const_100)|divide(#2,n1)| | "n * 50 = ( 315000 - 300000 ) = 15000 n = 15000 / 50 = 300 a" | general |
math_qa__gCXvkBHStfnhSsZg | There are 7 players in a bowling team with an average weight of 112 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? Pick one
A) 115 kg . B) 110 kg . C) 106 kg . D) 105 kg . E) 100 kg . | <gadget id="calculator">7 * 112</gadget>
<output>784</output>
<gadget id="calculator">110 + 60</gadget>
<output>170</output>
<gadget id="calculator">784 + 170</gadget>
<output>954</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">954 / 9</gadget>
<output>106</output>
<result>C</result> | C | 106 | There are 7 players in a bowling team with an average weight of 112 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? | {
"A": "115 kg .",
"B": "110 kg .",
"C": "106 kg .",
"D": "105 kg .",
"E": "100 kg ."
} | divide(add(multiply(7, 112), add(110, 60)), add(7, const_2)) | add(n2,n3)|add(n0,const_2)|multiply(n0,n1)|add(#0,#2)|divide(#3,#1)| | "the new average will be = ( 112 * 7 + 110 + 60 ) / 9 = 106 kgs c is the answer" | general |
math_qa__0z08LsxHGcIwIpfv | Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 25 kg of fresh grapes? Choose the correct choice from the following options:
A) 2 kg B) 2.4 kg C) 3.12 kg D) 10 kg E) none of these | <gadget id="calculator">100 - 90</gadget>
<output>10</output>
<gadget id="calculator">10 * 25</gadget>
<output>250</output>
<gadget id="calculator">250 / 100</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">(5/2) / 80</gadget>
<output>1/32 = around 0.03125</output>
<gadget id="calculator">(1/32) * 100</gadget>
<output>25/8 = around 3.125</output>
<result>C</result> | C | 3.12 | Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 25 kg of fresh grapes? | {
"A": "2 kg",
"B": "2.4 kg",
"C": "3.12 kg",
"D": "10 kg",
"E": "none of these"
} | multiply(divide(divide(multiply(subtract(const_100, 90), 25), const_100), subtract(const_100, 20)), const_100) | subtract(const_100,n0)|subtract(const_100,n1)|multiply(n2,#0)|divide(#2,const_100)|divide(#3,#1)|multiply(#4,const_100) | the weight of non - water in 25 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 25 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 3.12 answer : c . | gain |
math_qa__cyIlK4M0VyXp8I32 | Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A? Pick:
A) 10.21 B) 10.27 C) 10.25 D) 10.23 E) 60.25 | <gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">80 * 9</gadget>
<output>720</output>
<gadget id="calculator">720 / 4</gadget>
<output>180</output>
<gadget id="calculator">350 - 180</gadget>
<output>170</output>
<gadget id="calculator">170 / 60</gadget>
<output>17/6 = around 2.833333</output>
<gadget id="calculator">(17/6) / 2</gadget>
<output>17/12 = around 1.416667</output>
<gadget id="calculator">(17/12) - 1</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">(5/12) * 60</gadget>
<output>25</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">60 + (1/4)</gadget>
<output>241/4 = around 60.25</output>
<result>E</result> | E | 60.25 | Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A? | {
"A": "10.21",
"B": "10.27",
"C": "10.25",
"D": "10.23",
"E": "60.25"
} | add(60, divide(multiply(subtract(divide(divide(subtract(350, divide(multiply(80, multiply(const_3, const_3)), const_4)), 60), 2), const_1), const_60), const_100)) | multiply(const_3,const_3)|multiply(n1,#0)|divide(#1,const_4)|subtract(n5,#2)|divide(#3,n4)|divide(#4,n2)|subtract(#5,const_1)|multiply(#6,const_60)|divide(#7,const_100)|add(n4,#8) | distance covered in 2 hrs 15 min i . e . , 2 1 / 4 hrs = 80 * 9 / 4 = 180 hrs . time taken to cover remaining distance = ( 350 - 180 ) / 60 = 17 / 6 hrs = 2 5 / 6 = 2 hrs 50 min total time taken = ( 2 hrs 15 min + 2 hrs 50 min ) = 5 hrs 5 min . so , anna reached city a at 10.25 a . m . answer : e | physics |
math_qa__7YykadBbyOBZac9x | Pencils, Pens and Exercise books in a shop are in the ratio of 10: 2 : 3. If there are 120 pencils, the number of exercise books in the shop is: Choose the correct choice from the following answers: A) 26 B) 36 C) 46 D) 56 E) 66 | <gadget id="calculator">120 / 10</gadget>
<output>12</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<result>B</result> | B | 36 | Pencils, Pens and Exercise books in a shop are in the ratio of 10: 2 : 3. If there are 120 pencils, the number of exercise books in the shop is: | {
"A": "26",
"B": "36",
"C": "46",
"D": "56",
"E": "66"
} | multiply(divide(120, 10), 3) | divide(n3,n0)|multiply(n2,#0)| | "explanation : let pencils = 10 x , pens = 2 x & exercise books = 3 x . now , 10 x = 120 hence x = 12 . number of exercise books = 3 x = 36 . answer : b" | other |
math_qa__pVwz50IHPbsxOSLg | In a group of ducks and cows, the total number of legs are 26 more than thrice the number of heads. Find the total number of cows. Choose the correct choice.
A) 14 B) 13 C) 16 D) 8 E) 6 | <gadget id="calculator">26 / 2</gadget>
<output>13</output>
<result>B</result> | B | 13 | In a group of ducks and cows, the total number of legs are 26 more than thrice the number of heads. Find the total number of cows. | {
"A": "14",
"B": "13",
"C": "16",
"D": "8",
"E": "6"
} | divide(26, const_2) | divide(n0,const_2)| | "explanation : let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 26 more than twice the number of heads = > 2 ( d + 2 c ) = 26 + 2 ( c + d ) = > d + 2 c = 13 + c + d = > 2 c = 13 + c = > c = 13 i . e . , total number of cows = 13 answer : b" | general |
math_qa__VilgGmk5V0z4lMIv | Working alone at its constant rate, machine A produces x boxes in 5 minutes and working alone at its constant rate, machine B produces 2x boxes in 10 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes? Choose the most appropriate option: A) 3 minutes B) 7.5 minutes C) 5 minutes D) 6 minutes E) 12 minutes | <gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">5 / 5</gadget>
<output>1</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 / 10</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>
<result>B</result> | B | 7.5 | Working alone at its constant rate, machine A produces x boxes in 5 minutes and working alone at its constant rate, machine B produces 2x boxes in 10 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes? | {
"A": "3 minutes",
"B": "7.5 minutes",
"C": "5 minutes",
"D": "6 minutes",
"E": "12 minutes"
} | divide(multiply(3, 5), add(speed(5, 5), speed(multiply(2, 5), 10))) | multiply(n0,n3)|multiply(n0,n1)|speed(n0,n0)|speed(#1,n2)|add(#2,#3)|divide(#0,#4)| | "rate = work / time given rate of machine a = 2 x / 10 min machine b produces 2 x boxes in 10 min hence , machine b produces 2 x boxes in 10 min . rate of machine b = 2 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = 2 x / 10 min + rate of machine b = 2 x / 10 = 4 x / 10 now combine time = combine work needs to be done / combine rate = 3 x / 4 x * 10 = 7.5 min ans : b" | physics |
math_qa__9P8Dj6L5QJ1anVqJ | Solution A is 20% sugar and Solution B is 80% sugar. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% sugar solution? Choose the correct choice from the following options
A) 6 : 4
B) 6 : 14
C) 4 : 4
D) 4 : 6
E) 3 : 7 | <gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(4/5) - (1/2)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/10) / (3/5)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 2</gadget>
<output>1</output>
<result>C</result> | C | 1 | Solution A is 20% sugar and Solution B is 80% sugar. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% sugar solution? | {
"A": "6 : 4",
"B": "6 : 14",
"C": "4 : 4",
"D": "4 : 6",
"E": "3 : 7"
} | multiply(divide(subtract(divide(80, const_100), divide(50, const_100)), divide(60, const_100)), const_2) | divide(n1,const_100)|divide(n4,const_100)|divide(n3,const_100)|subtract(#0,#1)|divide(#3,#2)|multiply(#4,const_2) | forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 20 ) = 1 / 1 so the volume of the two solutions will be equal . answer has to be 4 : 4 = c | other |
math_qa__3jiNnGmuy4meKhJ0 | 12 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type? Choose the correct choice from the following choices:
A) 80 B) 160 C) 720 D) 1600 E) 1848 | <gadget id="calculator">factorial(12)</gadget>
<output>479_001_600</output>
<gadget id="calculator">12 - 2</gadget>
<output>10</output>
<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>
<gadget id="calculator">479_001_600 / 3_628_800</gadget>
<output>132</output>
<gadget id="calculator">132 / 2</gadget>
<output>66</output>
<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">40_320 / 720</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<gadget id="calculator">66 * 28</gadget>
<output>1_848</output>
<result>E</result> | E | 1,848 | 12 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type? | {
"A": "80",
"B": "160",
"C": "720",
"D": "1600",
"E": "1848"
} | multiply(divide(divide(factorial(12), factorial(subtract(12, 2))), 2), divide(divide(factorial(8), factorial(subtract(8, 2))), 2)) | factorial(n0)|factorial(n1)|subtract(n0,n2)|subtract(n1,n2)|factorial(#2)|factorial(#3)|divide(#0,#4)|divide(#1,#5)|divide(#6,n2)|divide(#7,n2)|multiply(#8,#9) | no . of ways of picking 2 biology books ( from 12 books ) = 12 c 2 = ( 12 * 11 ) / 2 = 66 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 66 * 28 = 1848 ( option e ) | other |
math_qa__PHq9nWMwVgLlC4Nb | The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/3 of that total. What was the price of the basic computer? Choose the correct choice from the following answers: A) 1500 B) 1600 C) 1750 D) 1900 E) 2000 | <gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 1_000</gadget>
<output>250</output>
<gadget id="calculator">250 * 10</gadget>
<output>2_500</output>
<gadget id="calculator">500 + 2_500</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 3</gadget>
<output>1_000</output>
<gadget id="calculator">2_500 - 1_000</gadget>
<output>1_500</output>
<result>A</result> | A | 1,500 | The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/3 of that total. What was the price of the basic computer? | {
"A": "1500",
"B": "1600",
"C": "1750",
"D": "1900",
"E": "2000"
} | subtract(multiply(multiply(const_0_25, const_1000), const_10), divide(add(500, multiply(multiply(const_0_25, const_1000), const_10)), 3)) | multiply(const_0_25,const_1000)|multiply(#0,const_10)|add(n1,#1)|divide(#2,n3)|subtract(#1,#3)| | "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 3 of that new total price : p = 1 / 3 * $ 3,000 = $ 1000 plug this value in the first equation : c + 1000 = $ 2,500 - - > c = $ 1,500 . answer : a ." | general |
math_qa__ScCa9NDPhOOY1eT8 | A baseball card decreased in value 20% in its first year and 20% in its second year. What was the total percent decrease of the card's value over the two years? Select the correct option: A) 28 % B) 30 % C) 32 % D) 36 % E) 72 % | <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) * (4/5)</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">(16/25) * 100</gadget>
<output>64</output>
<gadget id="calculator">100 - 64</gadget>
<output>36</output>
<result>D</result> | D | 36 | A baseball card decreased in value 20% in its first year and 20% in its second year. What was the total percent decrease of the card's value over the two years? | {
"A": "28 %",
"B": "30 %",
"C": "32 %",
"D": "36 %",
"E": "72 %"
} | subtract(const_100, multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(20, const_100))), const_100)) | divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5)| | "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.8 = 80 after second year price = 80 * 0.8 = 64 final decrease = [ ( 100 - 64 ) / 100 ] * 100 = 36 % correct answer - d" | gain |
math_qa__Z3BxeFrQMCPMweJs | 2 is what percent of 50 Pick one: A) 2 % B) 4 % C) 6 % D) 8 % E) none of these | <gadget id="calculator">2 / 50</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/25) * 100</gadget>
<output>4</output>
<result>B</result> | B | 4 | 2 is what percent of 50 | {
"A": "2 %",
"B": "4 %",
"C": "6 %",
"D": "8 %",
"E": "none of these"
} | multiply(divide(2, 50), const_100) | divide(n0,n1)|multiply(#0,const_100)| | "explanation : 2 / 50 * 100 = 1 / 25 * 100 = 4 % option b" | gain |
math_qa__HV0y6kGPPmFYpaXk | The contents of a certain box consist of 14 apples and 26 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples? Choose the correct choice:
A) 3
B) 6
C) 14
D) 17
E) 20 | <gadget id="calculator">14 + 26</gadget>
<output>40</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">14 / (7/10)</gadget>
<output>20</output>
<gadget id="calculator">40 - 20</gadget>
<output>20</output>
<result>E</result> | E | 20 | The contents of a certain box consist of 14 apples and 26 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples? | {
"A": "3",
"B": "6",
"C": "14",
"D": "17",
"E": "20"
} | subtract(add(14, 26), divide(14, divide(70, const_100))) | add(n0,n1)|divide(n2,const_100)|divide(n0,#1)|subtract(#0,#2)| | "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 26 oranges , so to get to 6 oranges , we should remove 26 - 6 = 20 oranges . answer e" | general |
math_qa__d1iliDFcucGRBBOb | Light glows for every 20 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am. Choose the correct choice from the following answers:
A) 380 times B) 381 times C) 382 times D) 248 times E) 482 times | <gadget id="calculator">2 + 47</gadget>
<output>49</output>
<gadget id="calculator">2 + 60</gadget>
<output>62</output>
<gadget id="calculator">20 + 62</gadget>
<output>82</output>
<gadget id="calculator">82 * 60</gadget>
<output>4_920</output>
<gadget id="calculator">49 + 4_920</gadget>
<output>4_969</output>
<gadget id="calculator">4_969 / 20</gadget>
<output>4_969/20 = around 248.45</output>
<result>D</result> | D | 248 | Light glows for every 20 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am. | {
"A": "380 times",
"B": "381 times",
"C": "382 times",
"D": "248 times",
"E": "482 times"
} | divide(add(add(const_2, 47), multiply(add(20, add(const_2, const_60)), const_60)), 20) | add(n6,const_2)|add(const_2,const_60)|add(n5,#1)|multiply(#2,const_60)|add(#0,#3)|divide(#4,n0)| | "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 20 ) = 248 times . answer : d" | general |
math_qa__DKFOo0kGZrEMIaCS | Each week, Harry is paid x dollars per hour for the first 18 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? Choose one
A) 34 B) 36 C) 37 D) 38 E) 39 | <gadget id="calculator">40 + 2</gadget>
<output>42</output>
<gadget id="calculator">42 - 18</gadget>
<output>24</output>
<gadget id="calculator">24 / 1.5</gadget>
<output>16</output>
<gadget id="calculator">16 + 18</gadget>
<output>34</output>
<result>A</result> | A | 34 | Each week, Harry is paid x dollars per hour for the first 18 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ? | {
"A": "34",
"B": "36",
"C": "37",
"D": "38",
"E": "39"
} | add(divide(subtract(add(40, 2), 18), 1.5), 18) | add(n2,n3)|subtract(#0,n0)|divide(#1,n1)|add(n0,#2)| | "42 x = 18 x + 1.5 x ( h - 18 ) = = > 42 = 18 + 1.5 ( h - 18 ) = = > h - 18 = 24 / 1.5 = 16 = = > h = 34 answer is a" | general |
math_qa__zTmftVFIztsWu3Lz | A student committee on academic integrity has 72 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there? Select
A) 7
B) 8
C) 9
D) 10
E) 11 | <gadget id="calculator">4 * 72</gadget>
<output>288</output>
<gadget id="calculator">-1</gadget>
<output>-1</output>
<gadget id="calculator">(-1) ** 2</gadget>
<output>1</output>
<gadget id="calculator">288 + 1</gadget>
<output>289</output>
<gadget id="calculator">289 ** (1/2)</gadget>
<output>17</output>
<gadget id="calculator">1 + 17</gadget>
<output>18</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<result>C</result> | C | 9 | A student committee on academic integrity has 72 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there? | {
"A": "7",
"B": "8",
"C": "9",
"D": "10",
"E": "11"
} | divide(add(const_1, sqrt(add(multiply(const_4, 72), power(negate(const_1), const_2)))), const_2) | multiply(n0,const_4)|negate(const_1)|power(#1,const_2)|add(#0,#2)|sqrt(#3)|add(#4,const_1)|divide(#5,const_2)| | "xc 1 * ( x - 1 ) c 1 = 72 x ^ 2 - x - 72 = 0 ( x - 9 ) ( x + 8 ) = 0 x = 9 , - 8 - 8 ca n ' t possible . c" | other |
math_qa__5q6UUwris7w6qcCo | A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 3 m, the volume of the box (in m3) is: Choose one.
A) 3780
B) 5120
C) 6420
D) 8960
E) 7960 | <gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">48 - 6</gadget>
<output>42</output>
<gadget id="calculator">36 - 6</gadget>
<output>30</output>
<gadget id="calculator">42 * 30 * 3</gadget>
<output>3_780</output>
<result>A</result> | A | 3,780 | A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 3 m, the volume of the box (in m3) is: | {
"A": "3780",
"B": "5120",
"C": "6420",
"D": "8960",
"E": "7960"
} | volume_rectangular_prism(subtract(48, multiply(3, const_2)), subtract(36, multiply(3, const_2)), 3) | multiply(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|volume_rectangular_prism(n2,#1,#2)| | "clearly , l = ( 48 - 6 ) m = 42 m , b = ( 36 - 6 ) m = 30 m , h = 8 m . volume of the box = ( 42 x 30 x 3 ) m 3 = 3780 m 3 . answer : option a" | geometry |
math_qa__4WfL4ZFOg5BUDuCd | In a certain village, 20 litres of water are required per household per month. At this rate, if there are 10 households in the village, how long (in months) will 2000 litres of water last? Choose the most appropriate option
A) 5
B) 2
C) 10
D) 1
E) 12 | <gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">2_000 / 200</gadget>
<output>10</output>
<result>C</result> | C | 10 | In a certain village, 20 litres of water are required per household per month. At this rate, if there are 10 households in the village, how long (in months) will 2000 litres of water last? | {
"A": "5",
"B": "2",
"C": "10",
"D": "1",
"E": "12"
} | divide(2000, multiply(20, 10)) | multiply(n0,n1)|divide(n2,#0) | i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 20 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 20 * 10 = 200 ( m * n ) water available is 2000 ( p ) it will last 10 months ( p / m * n ) ans : c | gain |
math_qa__Pftnu47AEFmKYhnV | If x+|x|+y=5 and x+|y|-y=6 what is x+y=? Pick:
A) 1
B) - 1
C) 3
D) 12
E) 13 | <gadget id="calculator">6 * 2</gadget>
<output>12</output>
<result>D</result> | D | 12 | If x+|x|+y=5 and x+|y|-y=6 what is x+y=? | {
"A": "1",
"B": "- 1",
"C": "3",
"D": "12",
"E": "13"
} | multiply(6, const_2) | multiply(n1,const_2) | if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 12 hence answer should be d | general |
math_qa__Nk2WwhdXwvEHHwYi | a certain clock rings two notes at quarter past the hour , 4 notes at half past , and 6 notes at 3 - quarters past . on the hour , it rings 8 notes plus an additional number of notes equal to whatever hour it is . how many notes will the clock ring from 1 : 00 p . m . through 5 : 00 p . m . , including the rings at 1 : 00 and 5 : 00 ? Choose the most appropriate option: A) 87 B) 95 C) 102 D) 103 E) 115 | <gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">9 + 10</gadget>
<output>19</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">19 + 11</gadget>
<output>30</output>
<gadget id="calculator">11 + 1</gadget>
<output>12</output>
<gadget id="calculator">30 + 12</gadget>
<output>42</output>
<gadget id="calculator">12 + 1</gadget>
<output>13</output>
<gadget id="calculator">42 + 13</gadget>
<output>55</output>
<gadget id="calculator">12 + 12</gadget>
<output>24</output>
<gadget id="calculator">24 + 12</gadget>
<output>36</output>
<gadget id="calculator">36 + 12</gadget>
<output>48</output>
<gadget id="calculator">55 + 48</gadget>
<output>103</output>
<result>D</result> | D | 103 | a certain clock rings two notes at quarter past the hour , 4 notes at half past , and 6 notes at 3 - quarters past . on the hour , it rings 8 notes plus an additional number of notes equal to whatever hour it is . how many notes will the clock ring from 1 : 00 p . m . through 5 : 00 p . m . , including the rings at 1 : 00 and 5 : 00 ? | {
"A": "87",
"B": "95",
"C": "102",
"D": "103",
"E": "115"
} | add(add(add(add(add(add(8, 1), add(add(8, 1), 1)), add(add(add(8, 1), 1), 1)), add(add(add(add(8, 1), 1), 1), 1)), add(add(add(add(add(8, 1), 1), 1), 1), 1)), add(add(add(add(add(add(add(8, 1), 1), 1), 1), add(add(add(add(8, 1), 1), 1), 1)), add(add(add(add(8, 1), 1), 1), 1)), add(add(add(add(8, 1), 1), 1), 1))) | add(n3,n4)|add(n4,#0)|add(#0,#1)|add(n4,#1)|add(#2,#3)|add(n4,#3)|add(#4,#5)|add(n4,#5)|add(#5,#5)|add(#6,#7)|add(#8,#5)|add(#10,#5)|add(#9,#11) | form 1 pm to 5 pm . excluding the actual hour chime we have 20 ( 1 pm ) + 20 ( 2 pm ) + 20 ( 3 pm ) + 20 ( 4 pm ) + 8 ( 5 pm ) = 88 now the hour chimes are 1 + 2 + 3 + 4 + 5 = 15 total = 88 + 15 = 103 answer d . | general |
math_qa__t2U7CpUrxqJKeW2Q | The total age of A and B is 13 years more than the total age of B and C. C is how many years younger than A?
Choose one: A) 13 B) 24 C) c is elder than a D) data inadequate E) none | <gadget id="calculator">13 * 1</gadget>
<output>13</output>
<result>A</result> | A | 13 | The total age of A and B is 13 years more than the total age of B and C. C is how many years younger than A? | {
"A": "13",
"B": "24",
"C": "c is elder than a",
"D": "data inadequate",
"E": "none"
} | multiply(13, const_1) | multiply(n0,const_1)| | "solution [ ( a + b ) - ( b + c ) ] = 13 â € ¹ = â € º a - c = 13 . answer a" | general |
math_qa__tIWyvGdQU9bxzwil | If the product of 6 integers is negative, at most how many of the integers can be negative? Options
A) 2 B) 3 C) 4 D) 5 E) 6 | <gadget id="calculator">6 - 1</gadget>
<output>5</output>
<result>D</result> | D | 5 | If the product of 6 integers is negative, at most how many of the integers can be negative? | {
"A": "2",
"B": "3",
"C": "4",
"D": "5",
"E": "6"
} | subtract(6, const_1) | subtract(n0,const_1)| | "product of even number of - ve numbers is positive so it cant be 6 . answer : d" | general |
math_qa__CoJ5Ory91CnllJNU | There is a 50% chance Jen will visit Chile this year, while there is a 50% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both? Select
A) 25.0 % B) 50.0 % C) 62.5 % D) 75.0 % E) 80.0 % | <gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * (1/2)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>B</result> | B | 50 | There is a 50% chance Jen will visit Chile this year, while there is a 50% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both? | {
"A": "25.0 %",
"B": "50.0 %",
"C": "62.5 %",
"D": "75.0 %",
"E": "80.0 %"
} | multiply(add(multiply(divide(subtract(power(multiply(const_2, const_5), const_2), 50), power(multiply(const_2, const_5), const_2)), divide(50, power(multiply(const_2, const_5), const_2))), multiply(divide(50, power(multiply(const_2, const_5), const_2)), divide(50, power(multiply(const_2, const_5), const_2)))), power(multiply(const_2, const_5), const_2)) | multiply(const_2,const_5)|power(#0,const_2)|divide(n1,#1)|divide(n0,#1)|subtract(#1,n0)|divide(#4,#1)|multiply(#3,#2)|multiply(#5,#2)|add(#7,#6)|multiply(#8,#1)| | "p ( chile and not madagascar ) = 0.5 * 0.5 = 0.25 p ( madagascar and not chile ) = 0.5 * 0.5 = 0.25 total probability = 0.25 + 0.25 = 0.5 = 50 % the answer is b ." | probability |
math_qa__1IG1G3R89ZrodI0t | A pipe takes a hours to fill the tank. But because of a leakage it took 7 times of its original time. Find the time taken by the leakage to empty the tank Choose the correct answer
A) 50 min B) 60 min C) 90 min D) 80 min E) 70 min | <gadget id="calculator">1 * 7</gadget>
<output>7</output>
<gadget id="calculator">10 * 7</gadget>
<output>70</output>
<result>E</result> | E | 70 | A pipe takes a hours to fill the tank. But because of a leakage it took 7 times of its original time. Find the time taken by the leakage to empty the tank | {
"A": "50 min",
"B": "60 min",
"C": "90 min",
"D": "80 min",
"E": "70 min"
} | multiply(const_10, multiply(const_1, 7)) | multiply(n0,const_1)|multiply(#0,const_10) | pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 420 x = 70 min answer : e | physics |
math_qa__sZSLQ8a11vYCdJis | At Chennai it rained as much on Tuesday as on all the others days of the week combined. If the average rainfall for the whole week was 3 cm. How much did it rain on Tuesday? Choose the correct choice from the following choices:
A) 2.625 cm B) 3 cm C) 10.5 cm D) 15 cm E) none of these | <gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">3 * 7</gadget>
<output>21</output>
<gadget id="calculator">21 / 2</gadget>
<output>21/2 = around 10.5</output>
<result>C</result> | C | 10.5 | At Chennai it rained as much on Tuesday as on all the others days of the week combined. If the average rainfall for the whole week was 3 cm. How much did it rain on Tuesday? | {
"A": "2.625 cm",
"B": "3 cm",
"C": "10.5 cm",
"D": "15 cm",
"E": "none of these"
} | divide(multiply(3, add(const_3, const_4)), const_2) | add(const_3,const_4)|multiply(n0,#0)|divide(#1,const_2) | total rainfall = 3 x 7 = 21 cm hence , rainfall received on tuesday = 21 / 2 ( as it rained as much on tuesday as on all the others days of the week combined ) = 10.5 cm . answer : c | general |
math_qa__EyPyoGajqZkzX91P | (3*10^2)*(4*10^-2)=? Pick one: A) 14 B) 12 C) 1200 D) 1.2 E) 14.11 | <gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">-2</gadget>
<output>-2</output>
<gadget id="calculator">10 ** (-2)</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">4 * (1/100)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">300 * (1/25)</gadget>
<output>12</output>
<result>B</result> | B | 12 | (3*10^2)*(4*10^-2)=? | {
"A": "14",
"B": "12",
"C": "1200",
"D": "1.2",
"E": "14.11"
} | multiply(multiply(3, power(10, 2)), multiply(4, power(10, negate(2)))) | negate(n2)|power(n1,n2)|multiply(n0,#1)|power(n1,#0)|multiply(n3,#3)|multiply(#2,#4) | 3 * 10 ^ 2 = 300 4 * 10 ^ - 2 = 0.04 ( 3 * 10 ^ 2 ) * ( 4 * 10 ^ - 2 ) = 300 * 0.04 = 12.00 the answer is option b | general |
math_qa__sKxi2wC2pKvI1bhD | Natasha climbs up a hill, and descends along the same way she went up. It takes her 3 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 3 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top? Choose the correct choice.
A) 1.5 B) 2.5 C) 3.75 D) 5 E) 7.5 | <gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) / 3</gadget>
<output>5/2 = around 2.5</output>
<result>B</result> | B | 2.5 | Natasha climbs up a hill, and descends along the same way she went up. It takes her 3 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 3 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top? | {
"A": "1.5",
"B": "2.5",
"C": "3.75",
"D": "5",
"E": "7.5"
} | divide(divide(multiply(add(3, 2), 3), 2), 3) | add(n0,n1)|multiply(n2,#0)|divide(#1,n1)|divide(#2,n0)| | "lets assume distance to top as x , so the total distance travelled by natasha = 2 x total time taken = 3 + 2 = 5 hrs avg speed = total dist / total time taken = 2 x / 5 avg speed of complete journey is given as = 3 hrs 2 x / 5 = 3 x = 7.5 miles avg speed while climbing = distance / time = 7.5 / 3 = 2.5 option b" | physics |
math_qa__Ow3qEDHbrNFUMiti | The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years K in which the population would be doubled assuming there is no emigration or immigration is Choices.
A) 20 B) k = 25 C) 30 D) k = 35 E) 40 | <gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">39.4 - 19.4</gadget>
<output>20</output>
<gadget id="calculator">20 / 1_000</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/50) * 100</gadget>
<output>2</output>
<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<result>D</result> | D | 35 | The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years K in which the population would be doubled assuming there is no emigration or immigration is | {
"A": "20",
"B": "k = 25",
"C": "30",
"D": "k = 35",
"E": "40"
} | divide(subtract(const_100, multiply(const_10, const_3)), multiply(divide(subtract(39.4, 19.4), 1000), const_100)) | multiply(const_10,const_3)|subtract(n1,n2)|divide(#1,n0)|subtract(const_100,#0)|multiply(#2,const_100)|divide(#3,#4)| | "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ." | general |
math_qa__BiUgNdb490fcDnn8 | Susan made a block with small cubes of 8 cubic cm volume to make a block ,3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block? Pick:
A) 113 B) 114 C) 115 D) 116 E) 117 | <gadget id="calculator">1 * 9</gadget>
<output>9</output>
<gadget id="calculator">9 * 5</gadget>
<output>45</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">45 - 21</gadget>
<output>24</output>
<gadget id="calculator">24 + 45</gadget>
<output>69</output>
<gadget id="calculator">45 + 69</gadget>
<output>114</output>
<result>B</result> | B | 114 | Susan made a block with small cubes of 8 cubic cm volume to make a block ,3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block? | {
"A": "113",
"B": "114",
"C": "115",
"D": "116",
"E": "117"
} | add(multiply(multiply(const_1, 9), 5), add(subtract(multiply(multiply(const_1, 9), 5), multiply(add(const_4, const_3), const_3)), multiply(multiply(const_1, 9), 5))) | add(const_3,const_4)|multiply(n2,const_1)|multiply(n3,#1)|multiply(#0,const_3)|subtract(#2,#3)|add(#2,#4)|add(#5,#2) | the total volume ( in terms of number of cubes ) of the solid = 3 * 9 * 5 = 135 the total volume ( in terms of number of cubes ) of the hollow = ( 3 - 2 ) * ( 9 - 2 ) * ( 5 - 2 ) = 21 so number of cubes required = 135 - 21 = 114 answer : b | geometry |
math_qa__VqaIsNtSHEd13kX2 | A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is: Choose the correct choice from the following answers:
A) 32
B) 50
C) 40
D) 20
E) 10 | <gadget id="calculator">83 - 63</gadget>
<output>20</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<result>C</result> | C | 40 | A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is: | {
"A": "32",
"B": "50",
"C": "40",
"D": "20",
"E": "10"
} | multiply(subtract(83, 63), const_2) | subtract(n0,n1)|multiply(#0,const_2)| | "let there be x pupils in the class . total increase in marks = x x 1 / 2 = x / 2 x / 2 = ( 83 - 63 ) x / 2 = 20 x = 40 . answer : c" | general |
math_qa__v3T5fG6p2VtEwChm | In how many ways can 21 books on English and 19 books on French be placed in a row on a shelf so that two books on French May not be Together ?
Choose the correct choice from the following
A) 3990 B) 1540 C) 1995 D) 3672 E) none of these | <gadget id="calculator">21 - 1</gadget>
<output>20</output>
<gadget id="calculator">binomial(20, 3)</gadget>
<output>1_140</output>
<gadget id="calculator">factorial(20) / factorial(20 - 2)</gadget>
<output>380</output>
<gadget id="calculator">1_140 + 380</gadget>
<output>1_520</output>
<gadget id="calculator">binomial(20, 1)</gadget>
<output>20</output>
<gadget id="calculator">1_520 + 20</gadget>
<output>1_540</output>
<result>B</result> | B | 1,540 | In how many ways can 21 books on English and 19 books on French be placed in a row on a shelf so that two books on French May not be Together ? | {
"A": "3990",
"B": "1540",
"C": "1995",
"D": "3672",
"E": "none of these"
} | add(add(choose(subtract(21, const_1), const_3), permutation(subtract(21, const_1), const_2)), choose(subtract(21, const_1), const_1)) | subtract(n0,const_1)|choose(#0,const_3)|choose(#0,const_1)|permutation(#0,const_2)|add(#1,#3)|add(#4,#2)| | "in order that two books on french are never together , we must place all books as under x e x e x e x e x e . . . . . x e x where e denotes the position of an english book and x that of a french book . since there are 21 books on english , the number of places marked x are therefore , 22 . now , 19 places out of 22 can be chosen in 22 c 19 = 22 c 3 = ( 22 x 21 x 20 ) / ( 3 x 2 x 1 ) = 1540 ways answer b ." | probability |
math_qa__cvxgUPzilbW2He46 | 120 is what percent of 40 ? Choose the correct choice from the following answers:
A) 5 % B) 20 % C) 50 % D) 300 % E) 500 % | <gadget id="calculator">120 / 40</gadget>
<output>3</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<result>D</result> | D | 300 | 120 is what percent of 40 ? | {
"A": "5 %",
"B": "20 %",
"C": "50 %",
"D": "300 %",
"E": "500 %"
} | multiply(divide(120, 40), const_100) | divide(n0,n1)|multiply(#0,const_100)| | "40 * x = 120 - - > x = 3 - - > 3 expressed as percent is 300 % . answer : d ." | gain |
math_qa__83WJxY0n415Yg6Pz | Which is the smallest no which divides 2880 and gives a perfect square? Options:
A) 4
B) 9
C) 3
D) 5
E) 7 | <gadget id="calculator">2_880 / 4</gadget>
<output>720</output>
<gadget id="calculator">720 / 3</gadget>
<output>240</output>
<gadget id="calculator">240 / 4</gadget>
<output>60</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>D</result> | D | 5 | Which is the smallest no which divides 2880 and gives a perfect square? | {
"A": "4",
"B": "9",
"C": "3",
"D": "5",
"E": "7"
} | divide(divide(divide(divide(divide(divide(2880, const_4), const_3), const_4), const_3), const_2), const_2) | divide(n0,const_4)|divide(#0,const_3)|divide(#1,const_4)|divide(#2,const_3)|divide(#3,const_2)|divide(#4,const_2) | 2880 = 20 * 144 ( because w . k . t 144 is perfect square ) = 2 * 10 * 144 = 2 * 2 * 5 * 144 = 4 * 5 * 144 ( here 4 and 144 are perfect square ) so the smallest number is 5 answer : d | geometry |
math_qa__XmZ1WGx8DfrZacoj | 4.036 divided by 0.02 gives : Choose the correct choice from the following options: A) 10.09 B) 1.06 C) 10.06 D) 201.8 E) 100.9 | <gadget id="calculator">4.036 / 0.02</gadget>
<output>201.8</output>
<result>D</result> | D | 201.8 | 4.036 divided by 0.02 gives : | {
"A": "10.09",
"B": "1.06",
"C": "10.06",
"D": "201.8",
"E": "100.9"
} | divide(4.036, 0.02) | divide(n0,n1)| | "= 4.036 / 0.02 = 403.6 / 2 = 201.8 answer is d ." | general |
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