Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
values |
|---|---|---|---|---|---|---|
dick and jane each saved $ 2,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 4,000 . approximately what percent less did jane save in 1990 than in 1989 ? | "1990 dick saved = $ 2200 jane saved = $ 1800 ( jane saved $ 200 less than she did the prior year ) jane saved approximately $ 200 / 2000 $ ( 10 % ) less in 1990 answer : a" | a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 % | a | multiply(subtract(const_1, subtract(const_2, add(divide(10, const_100), const_1))), const_100) | divide(n3,const_100)|add(#0,const_1)|subtract(const_2,#1)|subtract(const_1,#2)|multiply(#3,const_100)| | general |
tough and tricky questions : exponents . if 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y , then x + y = | here is my solution . 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y here rhs 49 ^ x * 27 ^ y = 7 ^ ( 2 x ) * 3 ^ ( 3 y ) equating powers on both sides - - > 3 x - 1 = 2 x , thus x = 1 and 4 y - 3 = 3 y giving y = 3 so , x + y = 4 option : b | a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 5 | b | add(1, 3) | add(n1,n2) | general |
a candidate got 35 % of the votes polled and he lost to his rival by 2250 votes . how many votes were cast ? | 35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2250 100 % - - - - - - - - - ? = > 7500 answer : a | a ) 7500 , b ) 3388 , c ) 2665 , d ) 2888 , e ) 2661 | a | divide(2250, subtract(subtract(const_1, divide(35, const_100)), divide(35, const_100))) | divide(n0,const_100)|subtract(const_1,#0)|subtract(#1,#0)|divide(n1,#2) | gain |
find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg . | "req = 60 : 90 = 2 : 3 answer b" | a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 3 : 5 , e ) 4 : 5 | b | divide(subtract(6.30, 5.70), subtract(7.20, 6.30)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)| | other |
a volume of 11248 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ? | "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 11248 l can be kept in ( 11248 / 4 ) hemispheres ans . 2812 answer : a" | a ) 2812 , b ) 8231 , c ) 2734 , d ) 4222 , e ) 4254 | a | divide(11248, 4) | divide(n0,n1)| | geometry |
b completes a work in 6 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ? | "1 / 5 + 1 / 10 = 3 / 10 10 / 3 = 3.33 days answer : a" | a ) 3.33 days , b ) 4.33 days , c ) 5.33 days , d ) 6.33 days , e ) 7.33 days | a | divide(multiply(10, 6), add(6, 10)) | add(n0,n1)|multiply(n0,n1)|divide(#1,#0)| | physics |
a man can row upstream at 20 kmph and downstream at 28 kmph , and then find the speed of the man in still water ? | "us = 20 ds = 28 m = ( 28 + 20 ) / 2 = 24 answer : a" | a ) 24 , b ) 37 , c ) 30 , d ) 27 , e ) 18 | a | divide(add(20, 28), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
if x and y are integers such that x ^ 2 = 2 y and xy = 256 , then x β y = ? | "here x and y are integers . x ^ 2 = 2 y , xy = 256 . substitute ( x ^ 2 ) / 2 = y in xy = > x ^ 3 = 256 * 2 = > x ^ 3 = 512 . here x ^ 3 is positive , x is also positive . x = 8 then y = 32 . x - y = - 24 so option b is correct" | a ) - 30 , b ) - 24 , c ) - 5 , d ) 5 , e ) 20 | b | subtract(power(multiply(256, 2), const_0_33), divide(256, power(multiply(256, 2), const_0_33))) | multiply(n1,n2)|power(#0,const_0_33)|divide(n2,#1)|subtract(#1,#2)| | general |
if a tire rotates at 400 revolutions per minute when the car is traveling 144 km / h , what is the circumference of the tire ? | "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 144,000 m : c is the circumference c = 6 meters correct answer b" | a ) 2 meters , b ) 6 meters , c ) 5 meters , d ) 3 meters , e ) 7 meters | b | multiply(divide(144, multiply(multiply(multiply(const_2, const_3), const_10), 400)), const_1000) | multiply(const_2,const_3)|multiply(#0,const_10)|multiply(n0,#1)|divide(n1,#2)|multiply(#3,const_1000)| | physics |
the average of runs of a cricket player of 10 innings was 18 . how many runs must he make in his next innings so as to increase his average of runs by 4 ? | "average after 11 innings = 22 required number of runs = ( 33 * 11 ) - ( 18 * 10 ) = 242 - 180 = 62 . answer : c" | a ) 87 , b ) 16 , c ) 62 , d ) 76 , e ) 17 | c | subtract(multiply(add(10, const_1), add(4, 18)), multiply(10, 18)) | add(n0,const_1)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | general |
if a = 105 and a ^ 3 = 21 * 25 * 15 * b , what is the value of b ? | "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 15 = 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 2 * 5 ^ 3 * 7 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 2 * 5 ^ 3 * 7 b = 3 * 7 ^ 2 = 3 * 49 = 147 correct an... | a ) 35 , b ) 42 , c ) 45 , d ) 147 , e ) 54 | d | divide(power(105, 3), multiply(multiply(21, 25), 15)) | multiply(n2,n3)|power(n0,n1)|multiply(n4,#0)|divide(#1,#2)| | general |
if the difference of two numbers is 3 and the difference of their square is 39 , then the larger number is : | let the numbers be x and y then x 2 - y 2 = 39 and x - y = 3 we get x + y = 13 solving x - y = 3 , x + y = 13 x = 8 , y = 5 larger number 8 answer e | a ) 9 , b ) 2 , c ) 12 , d ) 14 , e ) 8 | e | add(divide(subtract(divide(39, 3), 3), const_2), 3) | divide(n1,n0)|subtract(#0,n0)|divide(#1,const_2)|add(n0,#2) | geometry |
the ratio of two numbers is 3 : 4 and their sum is 21 . the greater of the two numbers is ? | 3 : 4 total parts = 7 = 7 parts - - > 21 ( 7 Γ£ β 3 = 21 ) = 1 part - - - - > 3 ( 1 Γ£ β 3 = 4 ) = the greater of the two number is = 4 = 4 parts - - - - > 12 ( 4 Γ£ β 3 = 12 ) a | a ) 12 , b ) 14 , c ) 16 , d ) 17 , e ) 19 | a | subtract(21, divide(multiply(21, 3), add(3, 4))) | add(n0,n1)|multiply(n0,n2)|divide(#1,#0)|subtract(n2,#2) | other |
working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 6 x boxes ? | "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combin... | a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 6 minutes , e ) 12 minutes | e | divide(multiply(6, 10), add(speed(10, 10), speed(multiply(2, 10), 5))) | multiply(n0,n3)|multiply(n0,n1)|speed(n0,n0)|speed(#1,n2)|add(#2,#3)|divide(#0,#4)| | physics |
a light flashes every 15 seconds , how many times will it flash in ? of an hour ? | "1 flash = 15 sec for 1 min = 4 flashes so for 1 hour = 4 * 60 = 240 flashes . answer : c" | a ) 550 , b ) 600 , c ) 240 , d ) 700 , e ) 750 | c | divide(const_3600, 15) | divide(const_3600,n0)| | physics |
a train running at the speed of 60 km / hr crosses a pole in 7 seconds . find the length of the train . | "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 7 = 116.67 meter . answer : a" | a ) 116.67 , b ) 882 , c ) 772 , d ) 252 , e ) 121 | a | multiply(divide(multiply(60, const_1000), const_3600), 7) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
in what time will a train 40 m long cross an electric pole , it its speed be 144 km / hr ? | "speed = 144 * 5 / 18 = 40 m / sec time taken = 40 / 40 = 1.0 sec . answer : b" | a ) 2.5 sec , b ) 1.0 sec , c ) 7.5 sec , d ) 2.3 sec , e ) 1.5 sec | b | divide(40, multiply(144, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
a certain country had a total annual expenditure of $ 1.2 x 10 ^ 12 . if the population of the country was 240 million last year , what was the per capita expenditure ? | "explanation : in scientific notation 240 million is 2.4 x 10 ^ 8 . so the per capita expenditure was : ( $ 1.2 x 10 ^ 12 ) / ( 2.4 x 10 ^ 8 ) = ( $ 1.2 ) / ( 2.4 ) x 10 ^ 12 - 8 = $ 0.5 x 10 ^ 4 = $ 5000 answer : option e" | a ) $ 500 , b ) $ 1000 , c ) $ 2000 , d ) $ 3000 , e ) $ 5000 | e | divide(multiply(1.2, power(10, 12)), multiply(240, power(10, add(const_4, const_2)))) | add(const_2,const_4)|power(n1,n2)|multiply(n0,#1)|power(n1,#0)|multiply(n3,#3)|divide(#2,#4)| | general |
in a dairy farm , 50 cows eat 50 bags of husk in 50 days . in how many days one cow will eat one bag of husk ? | "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 50 bags 50 1 ] : : 50 : x = > x β 50 β 1 = 50 β 1 β 50 = > x = 50 option d" | a ) 34 days , b ) 40 days , c ) 46 days , d ) 50 days , e ) none of these | d | multiply(divide(50, 50), 50) | divide(n0,n0)|multiply(n0,#0)| | physics |
what is the range of all the roots of | x ^ 2 - 1 | = x ? | we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 1 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 1 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 2 or x = 1 i guess range is 2 - ... | a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0 | d | sqrt(1) | sqrt(n1) | general |
one - third of rahul β s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 2 , 50000 as total savings , how much has he saved in public provident fund ? | explanation let savings in n . s . c and p . p . f . be rs . x and rs . ( 250000 β x ) respectively . then , 1 / 3 x = 1 / 2 ( 250000 - x ) = > x / 3 + x / 2 = 125000 = > 5 x / 6 = 125000 = > x = 125000 x 6 / 5 = 150000 savings in public provident fund = rs . ( 250000 β 150000 ) = rs . 100000 answer d | a ) rs . 30,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 100,000 , e ) none | d | subtract(add(multiply(2, multiply(const_100, const_1000)), 50000), divide(add(multiply(2, multiply(const_100, const_1000)), 50000), add(const_2, const_3))) | add(const_2,const_3)|multiply(const_100,const_1000)|multiply(n0,#1)|add(n1,#2)|divide(#3,#0)|subtract(#3,#4) | general |
roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 2 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ? | "distance = relative speed * time = ( 2 + 3 ) * 4 = 20 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : b" | a ) 11 , b ) 20 , c ) 77 , d ) 26 , e ) 12 | b | multiply(add(2, 3), 4) | add(n0,n1)|multiply(n2,#0)| | physics |
the proportion of water to alcohol in solution a is 4 : 1 and the proportion of water to alcohol in solution b is 3 : 1 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ? | "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 5 ) ( v / 2 ) + ( 1 / 4 ) ( v / 2 ) = v / 10 + v / 8 = 9 v / 40 . the concentration of alcohol is 9 / 40 = 22.5 % the answer is d ." | a ) 16.5 % , b ) 18.5 % , c ) 20.5 % , d ) 22.5 % , e ) 24.5 % | d | multiply(divide(add(1, 1), add(add(4, 3), add(1, 1))), const_100) | add(n1,n3)|add(n0,n2)|add(#1,#0)|divide(#0,#2)|multiply(#3,const_100)| | general |
find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm ? | "1 / 2 * 20 ( 9 + 6 ) = 150 cm 2 answer : b" | a ) 188 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2 | b | multiply(multiply(divide(const_1, const_2), add(6, 9)), 20) | add(n1,n2)|divide(const_1,const_2)|multiply(#0,#1)|multiply(n0,#2)| | geometry |
how many integers between 0 and 1000 do not contain the integer 1 | from 1 to 99 = 19 integers having 1 from 101 to 199 = all are having 1 similarly 201 - 299 , 301 - 399 , 401 - 499 , . . . . . so on , will have 19 integers having 1 answer = 1000 - ( 19 * 9 + 99 + 2 ) / / 2 is added for 100 and 1000 = 728 answer : b | a ) 727 , b ) 728 , c ) 758 , d ) 748 , e ) 792 | b | subtract(1000, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2)) | add(const_3,const_4)|multiply(const_100,const_2)|multiply(#0,const_10)|add(#1,#2)|add(#3,const_2)|subtract(n1,#4) | general |
working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 6 days ? | "4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 4 x units in 6 days therefore , we need to get to 4 x / 6 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 3 x done in... | a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8 | d | multiply(multiply(4, 3), divide(6, 6)) | divide(n1,n3)|multiply(n0,n2)|multiply(#0,#1)| | general |
how many factors of 270 are odd numbers greater than 1 ? | "prime factors of 810 are 2 ^ 1,3 ^ 4,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 4 + 1 ) ( 1 + 1 ) = 10 since we need odd divisors other than 1 = > 10 - 1 = 9 odd divisors e is the answer" | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9 | e | divide(270, multiply(const_10, const_2)) | multiply(const_10,const_2)|divide(n0,#0)| | other |
a batsman in his 12 th innings makes a score of 65 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been β not out β ? | "let β x β be the average score after 12 th innings β 12 x = 11 Γ ( x β 2 ) + 65 β΄ x = 43 answer b" | a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46 | b | add(subtract(65, multiply(12, 2)), 2) | multiply(n0,n2)|subtract(n1,#0)|add(n2,#1)| | general |
what is the unit digit in 7 ^ 105 | "explanation : unit digit in 7 ^ 105 = unit digit in [ ( 7 ^ 4 ) 26 x 7 ] but , unit digit in ( 7 ^ 4 ) 26 = 1 unit digit in 7105 = ( 1 x 7 ) = 7 a" | a ) 7 , b ) 0 , c ) 2 , d ) 3 , e ) 5 | a | reminder(power(7, const_2), const_10) | power(n0,const_2)|reminder(#0,const_10)| | general |
if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 14 is subtracted and divided by 10 ? | "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 14 ) / 10 = ( 54 - 14 ) / 10 = 4 answer : option a" | a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3 | a | divide(subtract(add(multiply(7, 7), 5), 14), 10) | multiply(n1,n1)|add(n0,#0)|subtract(#1,n3)|divide(#2,n4)| | general |
when the number 1 y 92355 is exactly divisible by 11 , then the smallest whole number in place of y is ? | the given number = 1 y 92355 sum of the odd places = 5 + 3 + 9 + 1 = 18 sum of the even places = 5 + 2 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 18 - ( 7 + y ) = divisible by 11 11 οΏ½ y = divisible by 11 . y must be 0 , to make given number divisible by 11 . e | a ) 1 , b ) 3 , c ) 7 , d ) 9 , e ) 0 | e | subtract(1, const_1) | subtract(n0,const_1) | general |
how many liters of oil at rs . 40 per liter should be mixed with 240 liters of a second variety of oil at rs . 60 per liter so as to get a mixture whose cost is rs . 52 per liter ? | 8 : 12 = 2 : 3 if 240 lrs of the 2 nd variety taken then the 1 st variety should be taken as 160 lr answer c | a ) 120 , b ) 150 , c ) 160 , d ) 180 , e ) 200 | c | divide(subtract(multiply(240, 60), multiply(52, 240)), subtract(52, 40)) | multiply(n1,n2)|multiply(n1,n3)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2) | physics |
if w / x = 1 / 3 and w / y = 2 / 3 , then ( x + y ) / y = | "ratio 1 : 3 w = x ratio 2 : 3 w = 2 y x = 2 y ( x + y ) / y = ( 2 y + y ) / y = y ( 2 + 1 ) / y = 3 answer is d" | a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 7 | d | add(divide(divide(2, 1), divide(3, 3)), const_1) | divide(n2,n0)|divide(n3,n1)|divide(#0,#1)|add(#2,const_1)| | general |
two trains running in opposite directions cross a man standing on the platform in 25 seconds and 18 seconds respectively and they cross each other in 20 seconds . the ratio of their speeds is : | "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 25 x meters , and length of the second train = 18 y meters . ( 25 x + 18 y ) / ( x + y ) = 20 = = > 25 x + 18 y = 20 x + 20 y = = > 5 x = 2 y = = > x / y = 2 / 5 answer : option d" | a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 8 , d ) 2 : 5 , e ) 3 : 4 | d | divide(subtract(25, 20), subtract(20, 18)) | subtract(n0,n2)|subtract(n2,n1)|divide(#0,#1)| | physics |
in how many no . between 100 and 1000 at least one of their digits is 7 ? | "let ' s count the number of occurrences with only one 7 : ( 1 ) 7 xx : 1 * 9 * 9 = 81 ( 2 ) x 7 x : 8 * 1 * 9 = 72 ( 3 ) xx 7 : 8 * 9 * 1 = 72 81 + 72 + 72 = 225 at this point we can already see that the answer must be d since the choice are very dispersed . anyways , let ' s count number of occurrences with two 7 s :... | a ) 900 , b ) 648 , c ) 720 , d ) 252 , e ) 729 | d | divide(divide(1000, 100), 7) | divide(n1,n0)|divide(#0,n2)| | general |
the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ? | "let rate in r = 100 x then p = 75 x g = 100 y p = 90 y thus 75 x = 90 y or x = 1.20 y ans r = 120 y so increase = 20 % answer : b ." | a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 150 % | b | multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 25), subtract(const_100, 10)), const_100)), multiply(divide(subtract(const_100, 25), subtract(const_100, 10)), const_100)), const_100) | subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)|divide(#4,#3)|multiply(#5,const_100)| | gain |
farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 4000 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is : | "only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to (... | a ) 15 % , b ) 25 % , c ) 12.5 % , d ) 20.83 % , e ) none | d | divide(multiply(multiply(divide(500, 4000), const_100), const_100), 60) | divide(n2,n1)|multiply(#0,const_100)|multiply(#1,const_100)|divide(#2,n0)| | general |
the s . i . on a certain sum of money for 2 years at 6 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ? | "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 2 * 6 ) = rs . 3500 answer : c" | a ) 2197 , b ) 1267 , c ) 3500 , d ) 2267 , e ) 1262 | c | divide(divide(subtract(multiply(4000, power(add(const_1, divide(10, const_100)), 2)), 4000), 2), multiply(2, divide(6, const_100))) | divide(n4,const_100)|divide(n1,const_100)|add(#0,const_1)|multiply(n0,#1)|power(#2,n3)|multiply(n2,#4)|subtract(#5,n2)|divide(#6,n3)|divide(#7,#3)| | gain |
the avg weight of a , b & c is 60 kg . if d joins the group , the avg weight of the group becomes 65 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 64 kg . what is the weight of a ? | "a + b + c = 3 * 60 = 180 a + b + c + d = 4 * 65 = 260 - - - - ( i ) so , d = 80 & e = 80 + 3 = 83 b + c + d + e = 64 * 4 = 256 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 260 β 256 = 4 a = e + 4 = 83 + 4 = 87 answer : e" | a ) 56 , b ) 65 , c ) 75 , d ) 89 , e ) 87 | e | subtract(multiply(65, const_4), subtract(multiply(64, const_4), add(3, subtract(multiply(65, const_4), multiply(60, 3))))) | multiply(n1,const_4)|multiply(n3,const_4)|multiply(n0,n2)|subtract(#0,#2)|add(n2,#3)|subtract(#1,#4)|subtract(#0,#5)| | general |
a reduction of 40 % in the price of bananas would enable a man to obtain 66 more for rs . 40 , what is reduced price per dozen ? | "40 * ( 40 / 100 ) = 16 - - - 66 ? - - - 12 = > rs . 2.91 answer : b" | a ) 1.91 , b ) 2.91 , c ) 4.91 , d ) 3.91 , e ) 5.91 | b | multiply(const_12, divide(multiply(40, divide(40, const_100)), 66)) | divide(n0,const_100)|multiply(n0,#0)|divide(#1,n1)|multiply(#2,const_12)| | gain |
a car travels uphill at 30 km / hr and downhill at 80 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ? | "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 80 = 5 / 8 ; avg speed = 150 / ( 10 / 3 + 5 / 8 ) = 38 kmph answer : a" | a ) 38 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph | a | divide(add(100, 50), add(divide(100, 30), divide(50, 80))) | add(n2,n3)|divide(n2,n0)|divide(n3,n1)|add(#1,#2)|divide(#0,#3)| | general |
convert the 8 / 26 m / s into kilometers per hour ? | "8 / 26 m / s = 8 / 26 * 18 / 5 = 1 ( 1 / 10 ) = 1.1 kmph . answer : d" | a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.1 kmph . , e ) 1.9 kmph . | d | multiply(const_3_6, divide(8, 26)) | divide(n0,n1)|multiply(#0,const_3_6)| | physics |
jane and thomas are among the 7 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ? | "the total number of ways to choose 4 people from 7 is 7 c 4 = 35 . the number of committees without jane or thomas is 5 c 4 = 5 . there are 35 - 5 = 30 possible committees which include jane and / or thomas . the answer is a ." | a ) 30 , b ) 45 , c ) 55 , d ) 65 , e ) 70 | a | add(add(choose(7, const_1), choose(7, const_1)), choose(const_4, const_1)) | choose(n0,const_1)|choose(const_4,const_1)|add(#0,#0)|add(#2,#1)| | probability |
jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jack and jill will make a basket but sandy will miss ? | "the probability that jack and jill will make a basket but sandy will miss is 1 / 6 * 1 / 7 * 7 / 8 = 1 / 48 . the answer is c ." | a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 48 , d ) 1 / 96 , e ) 1 / 168 | c | multiply(multiply(divide(1, 7), divide(1, 8)), subtract(1, divide(1, 6))) | divide(n0,n3)|divide(n0,n5)|divide(n0,n1)|multiply(#0,#1)|subtract(n0,#2)|multiply(#3,#4)| | general |
you hold some gold in a vault as an investment . over the past year the price of gold increases by 42 % . in order to keep your gold in the vault , you must pay 4 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year . | "( 100 % + 42 % ) * ( 100 % - 4 % ) = 1.42 * 0.96 = 136.32 % an increase of 36.32 % your gold holdings have increased in value by 36.32 % . the answer is e" | a ) 38 % , b ) 46 % , c ) 47.68 % , d ) 44.32 % , e ) 36.32 % | e | subtract(42, divide(42, 4)) | divide(n0,n1)|subtract(n0,#0)| | gain |
calculate how many seconds it eill take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 2 , 5 , 8 and 11 seconds . ? | "lcm of 2 , 5 , 8 and 11 is 440 lcm = 440 answer : a" | a ) 440 , b ) 420 , c ) 410 , d ) 442 , e ) 422 | a | multiply(const_3, multiply(8, multiply(2, 5))) | multiply(n1,n2)|multiply(n3,#0)|multiply(#1,const_3)| | gain |
the sum of the ages of 5 children born at the intervals of 1 year each is 50 years . what is the age of the youngest child ? | "let x = the youngest child . each of the other four children will then be x + 1 , x + 2 , x + 3 , x + 4 . we know that the sum of their ages is 50 . so , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) = 50 therefore the youngest child is 8 years old answer : b" | a ) 22 , b ) 8 , c ) 10 , d ) 99 , e ) 38 | b | divide(subtract(divide(50, divide(5, 1)), multiply(subtract(5, const_1), 1)), 1) | divide(n0,n1)|subtract(n0,const_1)|divide(n2,#0)|multiply(n1,#1)|subtract(#2,#3)|divide(#4,n1)| | general |
if 15 machine can finish a job in 36 days , then how many more machines would be needed to finish the job in one - fourth less time ? | "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 t... | a ) a . 5 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16 | a | subtract(divide(multiply(15, 36), multiply(divide(const_3, const_4), 36)), 15) | divide(const_3,const_4)|multiply(n0,n1)|multiply(n1,#0)|divide(#1,#2)|subtract(#3,n0)| | general |
if a randomly selected non - negative single digit integer is added to { 2 , 3 , 6 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ? | "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the... | a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6 | c | divide(const_4, const_10) | divide(const_4,const_10)| | general |
in what time will a train 140 m long cross an electric pole , it its speed be 108 km / hr ? | "speed = 108 * 5 / 18 = 30 m / sec time taken = 140 / 30 = 4.7 sec . answer : b" | a ) 2.5 , b ) 4.7 , c ) 2.9 , d ) 2.3 , e ) 2.1 | b | divide(140, multiply(108, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
a small water pump would take 2 hours to fill an empty tank . a larger pump would take 1 / 3 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ? | "rate of the small pump is 1 / 2 tank / hour rate of the larger pump is 1 / ( 1 / 3 ) or 3 tank / hour ; combined rate of the two pumps is 1 / 2 + 3 = 7 / 2 tank / hour , together they will fill the empty tank in 1 / ( 7 / 2 ) = 2 / 7 hours ( time = job / rate ) . answer : b" | a ) 3 / 7 , b ) 2 / 7 , c ) 1 / 4 , d ) 2 / 3 , e ) 5 / 7 | b | inverse(add(inverse(2), 3)) | inverse(n0)|add(n2,#0)|inverse(#1)| | physics |
in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 45 % of all the employees are men . what % of all the employee went to the picnic ? | "total men in company 45 % means total women in company 55 % ( assume total people in company 100 % ) no of men employees attended picnic = 45 x ( 20 / 100 ) = 9 no of women employees attend picnic = 55 x ( 40 / 100 ) = 22 total percentage of employees attend the picnic = 9 + 22 = 31 % answer : a" | a ) 31 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 % | a | multiply(add(multiply(divide(45, const_100), divide(20, const_100)), multiply(divide(subtract(const_100, 45), const_100), divide(40, const_100))), const_100) | divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|subtract(const_100,n2)|divide(#3,const_100)|multiply(#0,#1)|multiply(#4,#2)|add(#5,#6)|multiply(#7,const_100)| | gain |
the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 5 : 4 : 2 . someone removes 7 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ? | "the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 7 pounds of clothes doubles the ratio of books to clothes , then 7 pounds represents half the weight of the clothes . 2 k = 7 pounds and then k = 3.5 pounds . the electronics weigh 2 ( 3.5 ) = 7 pounds . the answer is b ." | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | b | multiply(2, divide(negate(multiply(add(add(5, 4), 2), 7)), subtract(multiply(add(add(5, 4), 2), const_2), multiply(add(add(5, 4), 2), 4)))) | add(n0,n1)|add(n2,#0)|multiply(n3,#1)|multiply(#1,const_2)|multiply(n1,#1)|negate(#2)|subtract(#3,#4)|divide(#5,#6)|multiply(n2,#7)| | other |
martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 17.20 , how many discounted tickets did he buy ? | "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 17.2 0.4 x = 1.2 = > x = 3 discounted tickets = 10 - x = 7 ans : e" | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | e | subtract(multiply(10, 2.00), multiply(1.60, 10)) | multiply(n0,n1)|multiply(n0,n2)|subtract(#0,#1)| | gain |
if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 10 , what is the value of x ? | "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and ... | a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4 | c | divide(const_1, 4) | divide(const_1,n4)| | general |
if a # b = ab β b + b ^ 2 , then 2 # 3 = | "solution - simply substitute 2 and 3 in equation in the place of a and b respectively . 2 # 3 = 2 * 3 - 3 + 3 ^ 2 = 6 - 3 + 9 = 12 . ans c" | a ) 2 , b ) 8 , c ) 12 , d ) 21 , e ) 35 | c | add(subtract(multiply(2, 3), 3), power(3, 2)) | multiply(n1,n2)|power(n2,n0)|subtract(#0,n2)|add(#1,#2)| | general |
andy solves problems 70 to 125 inclusive in a math exercise . how many problems does he solve ? | 125 - 70 + 1 = 56 ' a ' is the answer | a ) 56 , b ) 52 , c ) 51 , d ) 50 , e ) 49 | a | add(subtract(125, 70), const_1) | subtract(n1,n0)|add(#0,const_1) | general |
share rs . 4200 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ? | "amount received by sanjay . 4 / 12 x 4200 = 1400 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1400 . e" | a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400 | e | subtract(divide(4200, 2), divide(4200, 6)) | divide(n0,n1)|divide(n0,n3)|subtract(#0,#1)| | other |
if k is a non - negative integer and 21 ^ k is a divisor of 435,961 then 7 ^ k - k ^ 7 = | "4 + 3 + 5 + 9 + 6 + 1 = 28 , so this number is not divisible by 3 and thus not divisible by 21 . therefore , k = 0 7 ^ k - k ^ 7 = 1 - 0 = 1 the answer is b ." | a ) 0 , b ) 1 , c ) 42 , d ) 118 , e ) 242 | b | subtract(power(7, subtract(const_1, const_1)), power(subtract(const_1, const_1), 7)) | subtract(const_1,const_1)|power(n2,#0)|power(#0,n2)|subtract(#1,#2)| | general |
maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 60 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ? | "time taken = total distance / relative speed total distance = 60 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 60 / 10 = 6 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 6 = 36 kms . . . answer - b" | a ) 16 , b ) 36 , c ) 20 , d ) 24 , e ) 30 | b | multiply(4, divide(60, add(4, 6))) | add(n1,n2)|divide(n0,#0)|multiply(n1,#1)| | physics |
a train 90 meters long completely crosses a 200 meters long bridge in 36 seconds . what is the speed of the train is ? | "s = ( 90 + 200 ) / 36 = 290 / 36 * 18 / 5 = 29 answer : a" | a ) 29 , b ) 40 , c ) 25 , d ) 66 , e ) 09 | a | divide(divide(add(90, 200), const_1000), divide(36, const_3600)) | add(n0,n1)|divide(n2,const_3600)|divide(#0,const_1000)|divide(#2,#1)| | physics |
a circular plate with a diameter of 10 inches is kept on another plate of 12 inches diameter . what fraction of the big plate ' s surface is not covered by the small plate ? | the questions asks us to find the surface which is not covered by the plate i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered... | ['a ) 11 / 36', 'b ) 23 / 10', 'c ) 5 / 14', 'd ) 22 / 11', 'e ) 3 / 4'] | a | divide(subtract(circle_area(divide(12, const_2)), circle_area(divide(10, const_2))), circle_area(divide(12, const_2))) | divide(n1,const_2)|divide(n0,const_2)|circle_area(#0)|circle_area(#1)|subtract(#2,#3)|divide(#4,#2) | geometry |
a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days b will the work get over ? | "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 there... | a ) 60 , b ) 70 , c ) b = 75 , d ) b = 80 , e ) 100 | c | divide(multiply(divide(multiply(10, 20), const_0_25), subtract(const_1, const_0_25)), subtract(10, 2)) | multiply(n1,n2)|subtract(const_1,const_0_25)|subtract(n1,n3)|divide(#0,const_0_25)|multiply(#3,#1)|divide(#4,#2)| | physics |
if the cost price is 25 % of selling price . then what is the profit percent | "explanation : let the s . p = 100 then c . p . = 25 profit = 75 profit % = ( 75 / 25 ) * 100 = 300 % answer : c" | a ) 238 , b ) 278 , c ) 300 , d ) 166 , e ) 129 | c | multiply(divide(subtract(const_100, 25), 25), const_100) | subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
a man rows downstream 32 km and 14 km upstream . if he takes 6 hours to cover each distance , then the velocity ( in kmph ) of the current is : | sol . rate downstream = [ 32 / 6 ] kmph ; rate upstream = [ 14 / 6 ] kmph . β΄ velocity of current = 1 / 2 [ 32 / 6 - 14 / 6 ] kmph = 3 / 2 kmph = 1.5 kmph . answer a | a ) 1.5 kmph , b ) 1.75 kmph , c ) 2 kmph , d ) 3 kmph , e ) none | a | divide(subtract(divide(32, 6), divide(14, 6)), const_2) | divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2) | physics |
the average weight of 10 person ' s increases by 4 kg when a new person comes in place of one of them weighing 70 kg . what is the weight of the new person ? | "total increase in weight = 10 x 4 = 40 if x is the weight of the new person , total increase in weight = x β 70 = > 40 = x - 70 = > x = 40 + 70 = 110 answer : e" | a ) 85 , b ) 86.5 , c ) 90 , d ) 88.5 , e ) 110 | e | add(multiply(10, 4), 70) | multiply(n0,n1)|add(n2,#0)| | general |
the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ? | "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 20 = rs . 4 per kg . rice can bought now at = 100 / 4 = 25 kg . answer : option c" | a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none | c | divide(const_100, divide(subtract(const_100, 20), 20)) | subtract(const_100,n0)|divide(#0,n1)|divide(const_100,#1)| | gain |
a boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream . if the speed of the boat in still water is 10 mph , the speed of the stream is | "solution speed downstreams = ( 10 + x ) mph . speed upstreams = ( 10 - x ) mph . = 18 kmph . 36 / ( 10 - x ) - 36 / ( 10 + x ) = 90 / 60 = 72 x Γ 60 = 90 ( 100 - x Β² ) x Β² + 48 x + 100 = 0 . x = 2 mph . answer a" | a ) 2 mph , b ) 2.5 mph , c ) 3 mph , d ) 4 mph , e ) none | a | divide(subtract(sqrt(add(multiply(power(10, const_2), const_4), power(multiply(divide(36, divide(90, const_60)), const_2), const_2))), multiply(divide(36, divide(90, const_60)), const_2)), const_2) | divide(n0,const_60)|power(n2,const_2)|divide(n1,#0)|multiply(#1,const_4)|multiply(#2,const_2)|power(#4,const_2)|add(#3,#5)|sqrt(#6)|subtract(#7,#4)|divide(#8,const_2)| | physics |
if 2 + 3 = 10 ; 2 + 5 = 27 ; 2 + 7 = 53 then 2 + 11 = ? | "2 ^ 0 + 3 ^ 2 = 1 + 9 = 10 2 ^ 1 + 5 ^ 2 = 2 + 25 = 27 2 ^ 2 + 7 ^ 2 = 4 + 49 = 53 and 2 ^ 3 + 11 ^ 2 = 8 + 121 = 129 answer : b" | a ) 124 , b ) 129 , c ) 128 , d ) 125 , e ) 120 | b | add(power(2, 2), power(11, 2)) | power(n9,n3)|power(n10,n0)|add(#0,#1)| | general |
if the sides of a cube are in the ratio 7 : 3 . what is the ratio of their diagonals ? | "explanation : diagonal of a cube = a β 3 where a is side a 1 : a 2 = 7 : 3 d 1 : d 2 = 7 : 3 where β 3 cancelled both side answer : d" | a ) 9 : 4 , b ) 8 : 4 , c ) 7 : 4 , d ) 7 : 3 , e ) 6 : 4 | d | divide(7, 3) | divide(n0,n1)| | geometry |
the sum of two consecutive integers is 31 . find the numbers . | "n + ( n + 1 ) = 31 2 n + 1 = 31 2 n = 30 n = 15 answer : c" | a ) 17 , 18 , b ) 7 , 8 , c ) 15 , 16 , d ) 1 , 2 , e ) 8 , 9 | c | add(add(power(add(add(divide(subtract(subtract(31, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(31, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(31, const_10), const_2), const_4), const_2), power(add... | subtract(n0,const_10)|subtract(#0,const_2)|divide(#1,const_4)|add(#2,const_2)|power(#2,const_2)|add(#3,const_2)|power(#3,const_2)|add(#5,const_2)|add(#4,#6)|power(#5,const_2)|power(#7,const_2)|add(#9,#10)|add(#11,#8)| | physics |
the average of 4 consecutive odd numbers is 24 . find the largest number | explanation : let the numbers are x , x + 2 , x + 4 , x + 6 , then = > x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) / 4 = 24 = > 4 x + 12 ) / 4 = 24 = > x + 3 = 24 = > x = 21 so largest number is 21 + 6 = 27 option b | a ) 25 , b ) 27 , c ) 29 , d ) 31 , e ) 32 | b | add(divide(multiply(4, 24), 4), const_3) | multiply(n0,n1)|divide(#0,n0)|add(#1,const_3) | general |
what is the smallest integer that is multiple of 8,7 and 20 | correct answer : e it is the lcm of 8,7 and 20 which is 280 | a ) 141 , b ) 180 , c ) 130 , d ) 122 , e ) 280 | e | lcm(lcm(multiply(const_2, const_4), add(const_3, const_4)), 20) | add(const_3,const_4)|multiply(const_2,const_4)|lcm(#0,#1)|lcm(n1,#2) | general |
by travelling at 40 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ? | "let the time taken to reach the destination be 3 x hours . total distance = 40 * 3 x = 120 x km he covered 2 / 3 * 120 x = 80 x km in 1 / 3 * 3 x = x hours so , the remaining 40 x km , he has to cover in 2 x hours . required speed = 40 x / 2 x = 20 kmph . answer : a" | a ) 20 kmph , b ) 17 kmph , c ) 15 kmph , d ) 14 kmph , e ) 13 kmph | a | divide(subtract(multiply(40, const_3), divide(multiply(multiply(40, const_3), const_2), const_3)), subtract(const_3, const_1)) | multiply(n0,const_3)|subtract(const_3,const_1)|multiply(#0,const_2)|divide(#2,const_3)|subtract(#0,#3)|divide(#4,#1)| | physics |
the present population of a town is 260 . population increase rate is 10 % p . a . find the population of town after 1 years ? | "p = 260 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 260 * ( 1 + 10 / 100 ) = 260 * ( 11 / 10 ) = 286 answer is e" | a ) 100 , b ) 120 , c ) 200 , d ) 226 , e ) 286 | e | add(260, divide(multiply(260, 10), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)| | gain |
a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 3025 . , the number of the member is the group is : | "money collected = ( 30.25 x 100 ) paise = 3025 paise . number of members = square root of 3025 = 55 . answer : option a" | a ) 55 , b ) 67 , c ) 77 , d ) 87 , e ) 97 | a | sqrt(multiply(3025, const_100)) | multiply(n0,const_100)|sqrt(#0)| | general |
in 1996 , the property tax of a community is increased by 6 % over the 1995 tax . an additional surcharge of $ 200 is also added for a special project . if the petersons ' 1996 tax totals $ 2108 , find their property tax for the year 1995 | tax for the year 1996 = 2108 surcharge add : 200 ie 2000 - 200 = 1800 1800 * 6 % = 108 + 2000 = 2108 so the answer is b | a ) 1600 , b ) 1800 , c ) 1900 , d ) 2000 , e ) 2500 | b | divide(subtract(2108, 200), add(const_1, divide(6, const_100))) | divide(n1,const_100)|subtract(n5,n3)|add(#0,const_1)|divide(#1,#2) | general |
in an election , candidate douglas won 64 percent of the total vote in counties x and y . he won 76 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ? | "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 76 % voted means 76 * 200 = 152 votes combined for xy has 300 voters and voted 64 % so total votes = 192 balance votes = 192 - 152 = 40 as y has 100 voters so 40 votes means 40 % of votes required ans e" | a ) 10 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 % | e | multiply(divide(subtract(divide(64, const_100), multiply(divide(76, const_100), divide(2, const_3))), divide(1, const_3)), const_100) | divide(n0,const_100)|divide(n1,const_100)|divide(n2,const_3)|divide(n3,const_3)|multiply(#1,#2)|subtract(#0,#4)|divide(#5,#3)|multiply(#6,const_100)| | general |
how many seconds will a 900 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ? | "let length of tunnel is x meter distance = 900 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 900 + x = ( 65 / 3 ) * 60 900 + x = 20 * 65 = 1300 x = 1300 - 900 = 400 meters answer : d" | a ) 287 , b ) 288 , c ) 500 , d ) 400 , e ) 121 | d | multiply(multiply(subtract(divide(900, multiply(subtract(63, 3), const_0_2778)), const_1), const_10), const_2) | subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)|subtract(#2,const_1)|multiply(#3,const_10)|multiply(#4,const_2)| | physics |
16 * 16 * 16 * 16 * 16 = 4 ^ ? | 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 * 4 ^ 2 = 4 ^ ( 2 + 2 + 2 + 2 + 2 ) = 4 ^ 10 answer : 10 option : c | a ) 8 , b ) 6 , c ) 10 , d ) 4 , e ) 3 | c | max(4, const_10) | max(n5,const_10) | general |
fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.82 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is ... | "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.82 9.9 - 45 x + 36 x = 8.82 9 x = 1.08 x = 0.12 the answer is d ." | a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 % | d | multiply(subtract(divide(22, const_100), divide(subtract(8.82, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(15, 3), multiply(18, 2)))), const_100) | divide(n6,const_100)|multiply(n1,n5)|multiply(n0,n4)|multiply(#0,#1)|subtract(#2,#1)|subtract(n2,#3)|divide(#5,#4)|subtract(#0,#6)|multiply(#7,const_100)| | gain |
when average age of 25 members are 0 , how many members greater than 0 ? | "average of 25 numbers = 0 . sum of 25 numbers ( 0 x 25 ) = 0 . it is quite possible that 24 of these numbers may be positive and if their sum is a then 25 th number is ( - a ) answer is 24 ( b )" | a ) 17 , b ) 24 , c ) 21 , d ) 23 , e ) 25 | b | subtract(25, const_1) | subtract(n0,const_1)| | general |
the length of the bridge , which a train 130 metres long and travelling at 45 km / hr can cross in 30 seconds , is : | "given , length of the train = 130 meters speed of the train = 45 km / hr = 45 * 518 m / sec = 252 m / sec time = 30 secs let the length of the bridge be x meters . the distance travelled by the train while crossing the bridge will be sum of the length of train and length of the bridge = ( x + 130 ) meters so , 252 = x... | a ) 200 meters , b ) 225 meters , c ) 245 meters , d ) 250 meters , e ) 300 meters | c | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 130) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | physics |
sakshi can do a piece of work in 10 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work : | "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 10 : x β x = ( 10 x 4 / 5 ) β x = 8 days . hence , tanya takes 8 days is complete the work . answer a" | a ) 8 , b ) 16 , c ) 18 , d ) 25 , e ) 10 | a | divide(10, add(const_1, divide(25, const_100))) | divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)| | physics |
there were two candidates in an election . winner candidate received 65 % of votes and won the election by 300 votes . find the number of votes casted to the winning candidate ? | "w = 65 % l = 35 % 65 % - 35 % = 30 % 30 % - - - - - - - - 300 65 % - - - - - - - - ? = > 650 answer : d" | a ) 228 , b ) 744 , c ) 255 , d ) 650 , e ) 231 | d | divide(multiply(divide(300, divide(subtract(65, subtract(const_100, 65)), const_100)), 65), const_100) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)| | gain |
a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 6.00 ? | "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 6 ( 1 / 12 ) * x = 6 x = 72 answer : a" | a ) 72 , b ) 60 , c ) 90 , d ) 120 , e ) 240 | a | divide(6.00, subtract(divide(1.00, 4), divide(0.50, 3))) | divide(n3,n2)|divide(n1,n0)|subtract(#0,#1)|divide(n4,#2)| | gain |
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 3,571 more votes to win the election , what is the value of x ? | "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 + 3571 = 3631 now what ' s the problem wants ? ? a x % . . . . . . . . 3631 is what % of total votes 6000... | a ) 50 , b ) 54 , c ) 56 , d ) 60 , e ) 60.5 | e | add(divide(const_100, const_2), 1) | divide(const_100,const_2)|add(n0,#0)| | gain |
what is the value of 3 x ^ 2 β 1.8 x + 0.4 for x = 0.6 ? | "3 x ^ 2 - 1.8 x + 0.4 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.4 = 0 + 0.4 = 0.4 answer : c" | a ) β 0.3 , b ) 0 , c ) 0.4 , d ) 1.08 , e ) 2.46 | c | subtract(multiply(divide(divide(subtract(power(3, 2), power(1.8, 0.4)), const_1000), const_1000), 3), divide(divide(subtract(power(3, 2), power(1.8, 0.4)), const_1000), const_1000)) | power(n0,n1)|power(n2,n3)|subtract(#0,#1)|divide(#2,const_1000)|divide(#3,const_1000)|multiply(n0,#4)|subtract(#5,#4)| | general |
2500 - ( 1002 / 20.04 ) = ? | "2500 - 50 = 2450 answer : d" | a ) 2984 , b ) 2983 , c ) 2982 , d ) 2450 , e ) none of these | d | subtract(2500, divide(1002, 20.04)) | divide(n1,n2)|subtract(n0,#0)| | general |
what is the probability of getting equilateral triangles from the vertices of regular hexagon ? | total no . of triangles that can b made with the vetices hexagon = 6 c 3 = 20 no . of possible outcomes i . e . no . of equality triangles = 2 . . ' . probability = 2 / 20 = 1 / 10 answer : a | a ) 1 / 10 , b ) 2 / 10 , c ) 3 / 10 , d ) 4 / 10 , e ) 5 / 10 | a | divide(const_2, choose(add(const_3, const_3), const_3)) | add(const_3,const_3)|choose(#0,const_3)|divide(const_2,#1) | geometry |
solomon taken a loan rs . 15000 / - from co - operative society with an interest @ 11.5 % per month . at the same time he deposited rs . 10000 / - as fixed deposit with an interest @ 9.5 % per month . after one week sam asked the manager to calculate the interest to be paid . what is the interest amount for 7 days ? | loan amount : rs . 15000 / - @ 11.5 % interest per month = 15000 / - * 11.5 % = rs . 1725 interest for one day = 1725 / 30 = 57.50 interest for 7 days is = 57.50 * 7 = 403 fd amount is = rs . 10000 / - @ 9.5 % interest per month = 10000 * 9.5 % = 950 / - interest for 7 days = 950 / 30 * 7 = 222 interest amount to be pa... | a ) a ) 165 , b ) b ) 220 , c ) c ) 310 , d ) d ) 185 , e ) e ) 181 | e | subtract(multiply(7, divide(divide(multiply(15000, 11.5), const_100), multiply(const_3, const_10))), multiply(divide(divide(multiply(10000, 9.5), const_100), multiply(const_3, const_10)), 7)) | multiply(n0,n1)|multiply(const_10,const_3)|multiply(n2,n3)|divide(#0,const_100)|divide(#2,const_100)|divide(#3,#1)|divide(#4,#1)|multiply(n4,#5)|multiply(n4,#6)|subtract(#7,#8) | general |
the sum of the first 50 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ? | "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 50 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 50 positive even integers = 2550 sum of 1 st 100 odd numbers = ... | a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600 | b | multiply(divide(add(200, 101), const_2), add(divide(subtract(200, 101), const_2), const_1)) | add(n2,n3)|subtract(n3,n2)|divide(#1,const_2)|divide(#0,const_2)|add(#2,const_1)|multiply(#4,#3)| | general |
johnny makes $ 2.35 per hour at his work . if he works 5 hours , how much money will he earn ? | 2.35 * 5 = 11.75 . answer is e . | a ) $ 30 , b ) $ 54 , c ) $ 28.50 , d ) $ 12 , e ) $ 11.75 | e | multiply(2.35, 5) | multiply(n0,n1)| | physics |
a and b together can plough a field in 10 hours but by himself a requires 15 hours . how long would b take to plough the same field ? | if a and b together can do a piece of work in x days and a alone can do the same work in y days , then b alone can do the same work in x y / y β x days . therefore , the no . of hours required by b = 10 Γ 15 / 15 β 10 = 150 / 5 = 30 hours . answer : c | a ) 10 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours | c | inverse(subtract(inverse(10), inverse(15))) | inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2) | physics |
the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 576 feet squared , what is the difference between the length and the width of the roof ? | "let the width = x x * 4 x = 576 x ^ 2 = 144 x = 12 length = 4 * 12 = 48 difference = 48 - 12 = 36 c is the answer" | a ) 38 . , b ) 40 . , c ) 36 . , d ) 44 . , e ) 46 . | c | subtract(multiply(sqrt(divide(576, 4)), 4), sqrt(divide(576, 4))) | divide(n1,n0)|sqrt(#0)|multiply(#1,n0)|subtract(#2,#1)| | geometry |
if two girls starting from same point , walking in the opposite directions with 7 km / hr and 3 km / hr as average speeds respectively . then the distance between them after 12 hours is ? | explanation : total distance = distance traveled by person a + distance traveled by person b = ( 7 Γ£ β 12 ) + ( 3 Γ£ β 12 ) = 84 + 36 = 120 km answer : a | a ) 120 , b ) 121 , c ) 122 , d ) 123 , e ) 124 | a | multiply(add(7, 3), 12) | add(n0,n1)|multiply(n2,#0) | physics |
two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 7 days ? | "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 7 days = 7 ( 1 / 18 ) = 7 / 18 . answer b" | a ) 2 / 5 , b ) 7 / 18 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 6 | b | multiply(7, add(divide(const_1, 30), divide(const_1, 45))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)| | physics |
how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 32 percent alcohol ? | "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 32 % of ( 100 + x ... | a ) 7 / 2 , b ) 5 , c ) 20 / 3 , d ) 8 , e ) 300 / 17 | e | divide(100, add(const_4, const_3)) | add(const_3,const_4)|divide(n0,#0)| | general |
24 men working 8 hours a day can finish a work in 10 days . working at the rate of 10 hours a day , the number of men required to finish the same work in 6 days is | m 1 Γ d 1 Γ t 1 Γ w 2 = m 2 Γ d 2 Γ t 2 Γ w 1 24 Γ 10 Γ 8 Γ 1 = m 2 Γ 6 Γ 10 Γ 1 β m 2 = 24 Γ 10 Γ 8 / 6 Γ 10 = 32 men answer d | a ) 30 , b ) 36 , c ) 34 , d ) 32 , e ) none of these | d | divide(multiply(10, multiply(24, 8)), multiply(10, 6)) | multiply(n0,n1)|multiply(n2,n4)|multiply(n2,#0)|divide(#2,#1) | physics |
n and m are each 3 - digit integers . each of the numbers 3,4 , 5 , 6 , 7 , and 8 is a digit of either n or m . what is the smallest possible positive difference between n and m ? | "you have 6 digits : 3 , 4 , 5 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as sma... | a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131 | b | subtract(subtract(const_100, multiply(subtract(8, 3,4), const_10)), const_1) | subtract(n5,n1)|multiply(#0,const_10)|subtract(const_100,#1)|subtract(#2,const_1)| | general |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.