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
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7 x + y = 19 , and x + 3 y = 1 . find the value of 2 x + y | add these two equations 8 x + 4 y = 20 divide by 2 ( to get 2 x + y ) answer will be d . 10 | a ) 20 , b ) 18 , c ) 11 , d ) 5 , e ) 50 | d | add(multiply(2, subtract(1, multiply(3, divide(subtract(7, 19), subtract(multiply(7, 3), const_1))))), divide(subtract(7, 19), subtract(multiply(7, 3), const_1))) | multiply(n0,n2)|subtract(n0,n1)|subtract(#0,const_1)|divide(#1,#2)|multiply(n2,#3)|subtract(n3,#4)|multiply(n4,#5)|add(#3,#6) | general |
what is the sum of the greatest common factor and the lowest common multiple of 12 and 16 ? | "prime factorization of the given numbers 12 = 2 ^ 2 * 3 48 = 2 ^ 4 * 3 greatest common factor = 4 lowest common multiple = 48 sum = 4 + 48 = 52 answer c" | a ) 19 , b ) 22 , c ) 52 , d ) 36 , e ) 38 | c | divide(multiply(12, 16), const_4) | multiply(n0,n1)|divide(#0,const_4)| | general |
the least number which must be subtracted from 909 to make it exactly divisible by 9 is : | "on dividing 909 by 9 , we get remainder = 0 therefore , required number to be subtracted = 0 answer : c" | a ) a ) 2 , b ) b ) 3 , c ) c ) 0 , d ) d ) 5 , e ) e ) 6 | c | subtract(909, multiply(add(multiply(add(const_4, const_1), const_10), add(const_4, const_2)), 9)) | add(const_2,const_4)|add(const_1,const_4)|multiply(#1,const_10)|add(#0,#2)|multiply(n1,#3)|subtract(n0,#4)| | general |
a person want to give his money of $ 3600 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ? | "b ' s share = 3600 * 3 / 9 = $ 1200 answer is b" | a ) $ 2000 , b ) $ 1200 , c ) $ 2500 , d ) $ 1800 , e ) $ 1600 | b | multiply(divide(3, add(add(2, 3), 4)), 3600) | add(n1,n2)|add(n4,#0)|divide(n1,#1)|multiply(n0,#2)| | other |
each week , harry is paid x dollars per hour for the first 24 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and ja... | "42 x = 24 x + 1.5 x ( h - 24 ) = = > 42 = 24 + 1.5 ( h - 24 ) = = > h - 24 = 18 / 1.5 = 12 = > h = 36 answer is b" | a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39 | b | add(divide(subtract(add(40, 2), 24), 1.5), 24) | add(n2,n3)|subtract(#0,n0)|divide(#1,n1)|add(n0,#2)| | general |
rs . 1600 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 85 . how much was lent at 5.00001 % ? | ( x * 5 * 1 ) / 100 + [ ( 1600 - x ) * 6 * 1 ] / 100 = 85 5 x / 100 + ( 9600 β 6 x ) / 100 = 85 = > x = 1100 answer : a | a ) 1100 , b ) 1200 , c ) 1300 , d ) 1400 , e ) 1700 | a | multiply(add(5, 6), const_100) | add(n1,n2)|multiply(#0,const_100) | gain |
a box contains 10 tablets of medicine a and 16 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted . | "the worst case scenario will be if we remove all 16 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 16 + 2 = 18 tablets . answer : d ." | a ) 12 , b ) 15 , c ) 17 , d ) 18 , e ) 21 | d | add(16, const_2) | add(n1,const_2)| | general |
for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 171 ? | "100 + 102 + . . . + 170 = 100 * 36 + ( 2 + 4 + . . . + 70 ) = 100 * 36 + 2 * ( 1 + 2 + . . . + 35 ) = 100 * 36 + 2 ( 35 ) ( 36 ) / 2 = 100 * 36 + 35 * 36 = 135 ( 36 ) = 4860 the answer is c ." | a ) 2820 , b ) 3440 , c ) 4860 , d ) 5560 , e ) 6720 | c | add(divide(subtract(subtract(171, 1), add(99, 1)), 2), 1) | add(n2,n0)|subtract(n3,n0)|subtract(#1,#0)|divide(#2,n1)|add(n0,#3)| | general |
a train 3000 m long can cross an electric pole in 120 sec and then find the speed of the train ? | "length = speed * time speed = l / t s = 3000 / 120 s = 25 m / sec speed = 25 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 90 kmph answer : a" | a ) 90 , b ) 95 , c ) 100 , d ) 105 , e ) 110 | a | divide(divide(3000, const_1000), divide(120, const_3600)) | divide(n0,const_1000)|divide(n1,const_3600)|divide(#0,#1)| | physics |
at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 500 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ? | "we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 500 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . ... | a ) 1,108 , b ) 4,100 , c ) 2,108 , d ) 2,124 , e ) 2,256 | b | multiply(divide(200, 22.95), 500) | divide(n6,n5)|multiply(n4,#0)| | general |
a can give b 60 meters start and c 120 meters start in a kilometer race . how much start can b give c in a kilometer race ? | "a runs 1000 m while b runs 940 m and c runs 880 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 880 ) / 940 = 936.17 m . b can give c = 1000 - 936.17 = 63.83 m . answer : a" | a ) 63.83 , b ) 111.67 , c ) 111.64 , d ) 111.11 , e ) 101.12 | a | subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 120)), subtract(multiply(const_100, const_10), 60))) | multiply(const_10,const_100)|subtract(#0,n1)|subtract(#0,n0)|multiply(#0,#1)|divide(#3,#2)|subtract(#0,#4)| | physics |
you have 59 cubic blocks . what is the minimum number that needs to be taken away in order to construct a solid cube with none left over ? | d 32 the next cube number below 64 ( 4 Γ 4 Γ 4 ) is 27 ( 3 Γ 3 Γ 3 ) . in order to construct a solid cube , therefore , with none left over , 59 β 27 = 32 blocks need to be taken away . | ['a ) 27', 'b ) 43', 'c ) 11', 'd ) 32', 'e ) 45'] | d | subtract(59, multiply(multiply(const_3, const_3), const_3)) | multiply(const_3,const_3)|multiply(#0,const_3)|subtract(n0,#1) | geometry |
from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 8 kilometers per hour , while ferry q takes a route that is three times longer . if ferry p is slower than ferry q by 1 kilometer per hour , how many hours longer is the journey of ferry q compared with t... | "the distance traveled by ferry p is 24 km . then the distance traveled by ferry q is 72 km . ferry q travels at a speed of 9 kph . the time of the journey for ferry q is 72 / 9 = 8 hours , which is 5 hours more than ferry p . the answer is a ." | a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 12 | a | subtract(divide(multiply(const_3, multiply(8, 3)), add(8, 1)), 3) | add(n1,n2)|multiply(n0,n1)|multiply(#1,const_3)|divide(#2,#0)|subtract(#3,n0)| | physics |
n a certain flower shop , which stocks 4 types of flowers , there are 1 / 3 as many violets as carnations , and 1 / 4 as many tulips as violets . if there are equal numbers of roses and tulips , what percent of the flowers in the shop are carnations ? | given : - violets - c / 3 carnations - c tulip - c / 12 rose - c / 12 total flowers in terms of c = c / 3 + c + c / 12 + c / 12 = 18 c / 12 percentage of carnations = c / 3 c / 2 * 100 = 66.66 % answer d | a ) 62 , b ) 63 , c ) 64 , d ) 66.66 , e ) 65 | d | multiply(add(divide(1, 3), divide(1, 3)), const_100) | divide(n1,n2)|add(#0,#0)|multiply(#1,const_100) | general |
at a contest with 500 participants , 1 / 2 of the people are aged 28 to 32 . next year , the number of people aged 28 to 32 will increase by 1 / 8 . after this change , what percentage of the total 500 people will the 28 - to 32 - year - olds represent ? | "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 8 , we are multiplying it by 1 + 1 / 8 = 9 / 8 , so the answer here must be ( 1 / 2 ) * ( 9 / 8 ) = 9 / 16 = 56.25 % . ans... | a ) 33.25 % , b ) 40.25 % , c ) 50.25 % , d ) 55.25 % , e ) 56.25 % | e | multiply(divide(multiply(divide(500, 2), add(1, divide(1, 8))), 500), const_100) | divide(n1,n8)|divide(n0,n2)|add(#0,n1)|multiply(#2,#1)|divide(#3,n0)|multiply(#4,const_100)| | general |
on a purchase of $ 130 , a store offered a payment plan consisting of a $ 30 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ? | 12 * 10 + 30 = 150 . ( 30 / 130 ) * 100 = 23.1 answer : c | a ) 23.5 % , b ) 24.5 % , c ) 23.1 % , d ) 25.5 % , e ) 26.5 % | c | multiply(divide(subtract(add(multiply(10, 12), 30), multiply(10, 12)), 130), const_100) | multiply(n2,n3)|add(n1,#0)|subtract(#1,#0)|divide(#2,n0)|multiply(#3,const_100) | gain |
the largest 4 digit number exactly divisible by 66 is ? | "largest 4 - digit number = 9999 66 ) 9999 ( 151 9966 largest number : 9966 answer : d" | a ) 9935 , b ) 9939 , c ) 9944 , d ) 9966 , e ) 9960 | d | square_area(const_pi) | square_area(const_pi)| | general |
ashok secured average of 77 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ? | "explanation : number of subjects = 6 average of marks in 6 subjects = 77 therefore total marks in 6 subjects = 77 * 6 = 462 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 462 β 370 = 92 answer : c" | a ) 38 , b ) 27 , c ) 92 , d ) 17 , e ) 80 | c | subtract(multiply(77, 6), multiply(74, 5)) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)| | general |
roses can be purchased individually for $ 7.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ? | "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 7.3 = ~ 4 roses for that amount . total = 312 + 4 = 316 . answer : c ." | a ) 156 , b ) 162 , c ) 316 , d ) 324 , e ) 325 | c | add(multiply(floor(divide(680, 50)), multiply(const_12, const_2)), floor(divide(subtract(680, multiply(floor(divide(680, 50)), 50)), 7.30))) | divide(n3,n2)|multiply(const_12,const_2)|floor(#0)|multiply(n2,#2)|multiply(#2,#1)|subtract(n3,#3)|divide(#5,n0)|floor(#6)|add(#7,#4)| | general |
what is the equation of a circle of radius 5 units centered at ( 3 , 2 ) ? | the equation of a circle with center at ( a , b ) and radius r is ( x - a ) ^ 2 + ( y - b ) ^ 2 = r ^ 2 = > answer = ( x - 3 ) ^ 2 + ( y - 2 ) ^ 2 = 5 ^ 2 solving , , we get the equation in answer choice e . | ['a ) x ^ 2 + y ^ 2 + 6 x β 4 y = 23', 'b ) x ^ 2 + y ^ 2 - 6 x + 4 y = 23', 'c ) x ^ 2 + y ^ 2 + 6 x + 4 y = 23', 'd ) x ^ 2 + y ^ 2 - 6 x β 4 y = - 12', 'e ) x ^ 2 + y ^ 2 - 6 x β 4 y = 12'] | e | subtract(subtract(power(5, const_2), power(3, const_2)), power(2, const_2)) | power(n0,const_2)|power(n1,const_2)|power(n2,const_2)|subtract(#0,#1)|subtract(#3,#2) | geometry |
if the diameter of circle r is 20 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ? | "let diameter of circle r , dr = 20 and diameter of circle s , ds = 100 radius of circle r , rr = 10 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 10 / 50 ) ^ 2 = ( 2 / 10 ) ^ 2 = 4 % answer : e" | a ) 5 % , b ) 10 % , c ) 15 % , d ) 14 % , e ) 4 % | e | divide(multiply(circle_area(20), const_100), circle_area(const_100)) | circle_area(n0)|circle_area(const_100)|multiply(#0,const_100)|divide(#2,#1)| | geometry |
walking with 4 / 5 of my usual speed , i arrive at the bus stop 9 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ? | "let t = usual time = distance / usual speed t + 9 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 36 the answer is d ." | a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40 | d | divide(9, subtract(divide(5, 4), const_1)) | divide(n1,n0)|subtract(#0,const_1)|divide(n2,#1)| | physics |
what will be the length of the mini - train , if it crosses a pole in 3 sec while travelling at a speed of 75 kmph ? | explanation : d = 75 * 5 / 18 * 3 = 62.5 m answer : option e | a ) 60 m , b ) 65 m , c ) 63.5 m , d ) 64 m , e ) 62.5 m | e | multiply(multiply(75, const_0_2778), 3) | multiply(n1,const_0_2778)|multiply(n0,#0) | physics |
if 4 x = 8 y = 12 z , then what is a possible sum of positive integers x , y , and z ? | "4 x = 8 y = 12 z x = 2 y = 3 z 3 ( 2 * 3 ) = 2 ( 3 * 1 ) = 3 ( 1 * 2 ) addition = 18 + 6 + 6 = 30 answer would be multiple of 30 which is 180 answer : e" | a ) 52 , b ) 58 , c ) 84 , d ) 122 , e ) 180 | e | divide(multiply(multiply(8, 12), 4), const_4) | multiply(n1,n2)|multiply(n0,#0)|divide(#1,const_4)| | general |
find a two digit number , given that the sum of the digits is 12 and the difference of the digits is 6 . ? | "using elimination method find which of the options fit the description of the number . . . from the option only 41 meets this description sum of digits - - - 4 + 1 = 5 difference of digits - - - 4 - 1 = 3 answer a ." | a ) 41 , b ) 46 , c ) 42 , d ) 46 , e ) 47 | a | multiply(multiply(6, 6), add(6, const_4)) | add(n1,const_4)|multiply(n1,n1)|multiply(#0,#1)| | general |
it takes joey the postman 1 hours to run a 3 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 6 mile / hour , what is the speed with which joey returns ? | "let his speed for one half of the journey be 3 miles an hour let the other half be x miles an hour now , avg speed = 6 mile an hour 2 * 3 * x / 3 + x = 6 6 x = 6 x + 18 = > x = 18 e" | a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 18 | e | divide(3, subtract(divide(multiply(const_2, 3), 6), 1)) | multiply(n1,const_2)|divide(#0,n2)|subtract(#1,n0)|divide(n1,#2)| | physics |
2056 x 987 = ? | "= 2056 x 987 = 2056 x ( 1000 - 13 ) = 2056 x 1000 - 2056 x 13 = 2056000 - 26728 = 2029272 answer is b" | a ) 1936372 , b ) 2029272 , c ) 1896172 , d ) 1923472 , e ) none of them | b | multiply(divide(2056, 987), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
a rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn . the area of the lawn is 2109 sq . m . what is the width of the road ? | "area of the park = 60 * 40 = 2400 m ^ 2 given area of the lawn = 2109 m ^ 2 total area of the cross roads = 2400 - 2109 = 291 m ^ 2 assume that the width of the cross road = x = area of road 1 + road 2 - common area cross road = 60 x + 40 x - x ^ 2 total area of cross road = 60 x + 40 x - x ^ 2 = 291 m ^ 2 ( x - 97 ) ... | a ) 5 m , b ) 4 m , c ) 2 m , d ) 3 m , e ) 6 m | d | divide(subtract(negate(negate(add(40, 60))), sqrt(subtract(power(const_100, const_2), multiply(multiply(const_4, const_1), subtract(multiply(60, 40), 2109))))), multiply(const_2, const_1)) | add(n0,n1)|multiply(const_1,const_4)|multiply(n0,n1)|multiply(const_1,const_2)|power(const_100,const_2)|negate(#0)|subtract(#2,n2)|multiply(#1,#6)|negate(#5)|subtract(#4,#7)|sqrt(#9)|subtract(#8,#10)|divide(#11,#3)| | geometry |
a train is moving at 6 / 7 of its usual speed . the train is 30 minutes too late . what is the usual time for the train to complete the journey ? | "new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 30 minutes represents 1 / 6 of the usual time . the usual time is 3 hours . the answer is c ." | a ) 1 hour , b ) 30 minutes , c ) 3 hours , d ) 2 hours 30 min , e ) 2 hours | c | divide(multiply(multiply(30, divide(6, 7)), inverse(subtract(const_1, divide(6, 7)))), const_60) | divide(n0,n1)|multiply(n2,#0)|subtract(const_1,#0)|inverse(#2)|multiply(#3,#1)|divide(#4,const_60)| | physics |
we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 530 . how many green hats did we buy ? | let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 530 . 6 ( 85 - g ) + 7 g = 530 . 510 - 6 g + 7 g = 530 . g = 530 - 510 = 20 . the answer is b . | a ) a ) 36 , b ) b ) 20 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44 | b | subtract(530, multiply(85, 6)) | multiply(n0,n1)|subtract(n3,#0) | general |
a volunteer organization is recruiting new members . in the fall they manage to increase their number by 5 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ? | "( 100 % + 5 % ) * ( 100 % - 19 % ) = 1.05 * . 81 = 0.8505 . 1 - 0.8505 = 14.95 % lost = - 14.95 % the answer is c the organization has lost 14.95 % of its total volunteers from fall to spring ." | a ) 16.16 % , b ) 15.15 % , c ) 14.95 % , d ) 13.33 % , e ) 12.52 % | c | subtract(const_100, multiply(multiply(add(const_1, divide(5, const_100)), subtract(const_1, divide(19, const_100))), const_100)) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5)| | general |
two cars are driving toward each other . the first car is traveling at a speed of 90 km / h , which is 50 % faster than the second car ' s speed . if the distance between the cars is 975 km , how many hours will it take until the two cars meet ? | "the speed of the first car is 90 km / h . the speed of the second car is 90 / 1.5 = 60 km / h . the two cars complete a total of 150 km each hour . the time it takes the cars to meet is 975 / 150 = 6.5 hours . the answer is b ." | a ) 6 , b ) 6.5 , c ) 7 , d ) 7.5 , e ) 8 | b | divide(add(multiply(90, const_4), multiply(divide(multiply(const_4, 90), add(const_1, const_4)), const_4)), add(90, divide(multiply(const_4, 90), add(const_1, const_4)))) | add(const_1,const_4)|multiply(n0,const_4)|divide(#1,#0)|add(n0,#2)|multiply(#2,const_4)|add(#1,#4)|divide(#5,#3)| | physics |
find the annual income derived by investing $ 6800 in 40 % stock at 136 . | "by investing $ 136 , income obtained = $ 40 . by investing $ 6800 , income obtained = $ [ ( 40 / 136 ) * 6800 ] = $ 2000 . answer b ." | a ) 550 , b ) 2000 , c ) 250 , d ) 3000 , e ) 400 | b | divide(multiply(6800, 40), 136) | multiply(n0,n1)|divide(#0,n2)| | gain |
in 1982 and 1983 , company b β s operating expenses were $ 12.0 million and $ 14.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b β s profit ( revenues minus operating expenses ) from 1982 to 1983 ? | "profit in 1982 = 15.6 - 12.0 = 3.6 profit in 1983 = 18.8 - 14.0 = 4.8 increase in profit = 4.8 - 3.6 = 1.2 percentage increase 12 * 100 / 36 = 33.33 ; answer : d" | a ) 3 % , b ) 16 2 / 3 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 % | d | subtract(const_100, divide(multiply(subtract(14.0, 12.0), const_100), subtract(18.8, 15.6))) | subtract(n3,n2)|subtract(n5,n4)|multiply(#0,const_100)|divide(#2,#1)|subtract(const_100,#3)| | general |
what is the difference between local value & face value of 7 in the numeral 65793 ? | ( local value of 7 ) - ( face value of 7 ) = ( 700 - 7 ) = 693 a | a ) 693 , b ) 656 , c ) 691 , d ) 9890 , e ) 10000 | a | subtract(multiply(7, const_100), 7) | multiply(n0,const_100)|subtract(#0,n0) | general |
mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 14 miles , how many miles was mike ' s ride ? | the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 14 ) = $ 11 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 11 0.25 * x = 8.5 x = 34 miles the answer is d . | a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36 | d | divide(subtract(add(add(2.5, 5), multiply(0.25, 14)), 2.5), 0.25) | add(n0,n3)|multiply(n1,n5)|add(#0,#1)|subtract(#2,n0)|divide(#3,n1) | general |
at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 35 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 40 km / h . if the distance between city p and city q is 335 km , at what time will the truck and the car meet each other ... | "at 2 : 00 pm , the truck and the car are 300 km apart . the truck and the car complete a distance of 75 km each hour . the time it takes to meet is 300 / 75 = 4 hours . they will meet at 6 : 00 pm . the answer is c ." | a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 30 , e ) 7 : 00 | c | divide(subtract(divide(335, 35), 1), add(1, divide(40, 35))) | divide(n4,n2)|divide(n3,n2)|add(n0,#1)|subtract(#0,n0)|divide(#3,#2)| | physics |
a license plate in the country kerrania consists of 4 digits followed by two letters . the letters a , b , and c are used only by government vehicles while the letters d through z are used by non - government vehicles . kerrania ' s intelligence agency has recently captured a message from the country gonzalia indicatin... | if it takes 10 minutes to inspect one vehicle , the # of vehicles that can be inspected in 3 hours ( 180 minutes ) = 180 / 10 = 18 . hence , for calculating the probability that the police will find the transmitter within three hours , the favorable cases = 18 . now , we need to figure out the total # of cases . the to... | a ) 18 / 79 , b ) 1 / 6 , c ) 1 / 25 , d ) 1 / 50 , e ) 1 / 900 | d | divide(divide(multiply(3, const_60), 10), multiply(power(const_10, subtract(4, const_2)), power(const_3, const_2))) | multiply(n3,const_60)|power(const_3,const_2)|subtract(n0,const_2)|divide(#0,n2)|power(const_10,#2)|multiply(#4,#1)|divide(#3,#5) | physics |
a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 61 books in the spec... | "the total number of books is 75 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 61 books , thus the number of un - returned books is 75 - 61 = 14 books . 0.35 x = 14 x = 40 the answer is d ." | a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55 | d | divide(subtract(75, 61), subtract(const_1, divide(65, const_100))) | divide(n1,const_100)|subtract(n0,n2)|subtract(const_1,#0)|divide(#1,#2)| | gain |
one - sixth of the light switches produced by a certain factory are defective . 4 - fifths of the defective switches are rejected and 1 / 15 of the non defective switches are rejected by mistake . if all the switches not rejected are sold , what percent of the switches sold by the factory are defective ? | 1 / 6 of the switches are defective . the defective switches that are not rejected are 1 / 5 * 1 / 6 = 1 / 30 = 3 / 90 of all switches . the non defective switches that are sold are 5 / 6 * 14 / 15 = 70 / 90 of all switches . the percent of switches sold that are defective is 3 / 73 which is about 4.1 % . the answer is... | a ) 1.8 % , b ) 2.9 % , c ) 4.1 % , d ) 5.6 % , e ) 6.4 % | c | subtract(multiply(divide(1, add(4, 1)), const_100), multiply(divide(4, add(4, 1)), multiply(divide(1, add(4, 1)), const_100))) | add(n0,n1)|divide(n1,#0)|divide(n0,#0)|multiply(#1,const_100)|multiply(#2,#3)|subtract(#3,#4) | general |
a man buys a cycle for rs . 1600 and sells it at a loss of 12 % . what is the selling price of the cycle ? | s . p . = 88 % of rs . 1600 = 88 / 100 x 1600 = rs . 1408 answer : d | a ) 1410 , b ) 1420 , c ) 1430 , d ) 1408 , e ) 1540 | d | divide(multiply(subtract(const_100, 12), 1600), const_100) | subtract(const_100,n1)|multiply(n0,#0)|divide(#1,const_100) | gain |
at milk factory , each employee working the second shift produced 2 / 3 as many widgets as each employee working the first shift . if the first shift has 3 / 4 as many employees , what fraction of the total widgets did the second shift produce ? | at milk factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the se... | a ) 8 / 17 , b ) 1 / 2 , c ) 8 / 9 , d ) 9 / 8 , e ) 17 / 8 | a | divide(multiply(multiply(divide(2, 3), 3), 4), add(multiply(3, 3), multiply(multiply(divide(2, 3), 3), 4))) | divide(n0,n1)|multiply(n1,n1)|multiply(n1,#0)|multiply(n3,#2)|add(#1,#3)|divide(#3,#4) | physics |
the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ? | "if steve and david submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined ` ` no discount cost ' ' . if they submit things together as one big order , they get a discount off of that... | a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54 | b | divide(subtract(multiply(const_2, multiply(80, 0.02)), multiply(multiply(160, divide(subtract(100, 25), 100)), 0.02)), const_2) | multiply(n0,n3)|subtract(n2,n1)|divide(#1,n2)|multiply(#0,const_2)|multiply(n4,#2)|multiply(n0,#4)|subtract(#3,#5)|divide(#6,const_2)| | gain |
a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is a ' s share ? | "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 a ' s share = 5 x = 5 * $ 500 = $ 2500 the answer is d ." | a ) $ 1200 , b ) $ 1600 , c ) $ 2000 , d ) $ 2500 , e ) $ 3000 | d | multiply(multiply(subtract(4, 3), 500), 3) | subtract(n2,n3)|multiply(n4,#0)|multiply(n3,#1)| | general |
when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 7 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ? | say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 7 ) ( 4 + 4 x ) or , x = 2 / 5 answer b | a ) 3 / 10 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5 | b | divide(4, subtract(multiply(subtract(6, 4), 7), 4)) | subtract(n1,n0)|multiply(n4,#0)|subtract(#1,n0)|divide(n0,#2) | general |
a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ? | "a + b + c = 500 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 500 - - - - - - - - - - - - - - - - c = 50 answer : a" | a ) 50 , b ) 88 , c ) 77 , d ) 66 , e ) 51 | a | subtract(add(200, 350), 500) | add(n1,n2)|subtract(#0,n0)| | general |
two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 18 seconds . find the length of the faster train ? | "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 18 sec = 18 * 10 = 180 m . the length of the faster train = 180 m . answer : d" | a ) 270 , b ) 277 , c ) 187 , d ) 180 , e ) 271 | d | multiply(divide(subtract(72, 36), const_3_6), 18) | subtract(n0,n1)|divide(#0,const_3_6)|multiply(n2,#1)| | physics |
matt gets a $ 1,000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 550 , how many sales has matt made ? | "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 550 = 150 + x i . e . ... | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | b | divide(subtract(1,000, const_100), subtract(550, subtract(550, 150))) | subtract(n0,const_100)|subtract(n2,n1)|subtract(n2,#1)|divide(#0,#2)| | general |
a man invested rs . 14400 in rs . 100 shares of a company at 20 % premium . if his company declares 5 % dividend at the end of the year , then how much does he get ? | explanation : number of shares = = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = = rs . 600 answer : b ) rs . 600 | a ) 234 , b ) 600 , c ) 388 , d ) 278 , e ) 129 | b | multiply(divide(14400, divide(add(20, const_100), const_100)), divide(5, const_100)) | add(n2,const_100)|divide(n3,const_100)|divide(#0,const_100)|divide(n0,#2)|multiply(#3,#1) | gain |
the distance between two cities a and b is 1140 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ? | "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 1140 . therefore , 60 x + 75 ( x - 1 ) = 1140 . = > x = 9 . so , they meet at ( 8 + 9 ) i . e , 5 pm answer : d" | a ) 09 am , b ) 07 am , c ) 11 am , d ) 05 pm , e ) 03 pm | d | add(divide(add(1140, 75), add(60, 75)), 8) | add(n0,n4)|add(n2,n4)|divide(#0,#1)|add(n1,#2)| | physics |
the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 15 % , then the cost price of the article is : | "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 115 = rs . 536 answer : option d" | a ) 500 , b ) 334 , c ) 555 , d ) 536 , e ) 5598 | d | divide(multiply(divide(multiply(616, const_100), add(const_100, 10)), add(const_100, 10)), add(const_100, 15)) | add(n1,const_100)|add(n2,const_100)|multiply(n0,const_100)|divide(#2,#0)|multiply(#0,#3)|divide(#4,#1)| | gain |
pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 7 : 00 am and pipe b at 8 : 00 am , at what time will the pool be full ? | "pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 7 : 00 a . m and pipe b at 8 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 8 : 00 a . m ... | a ) 16 : 00 , b ) 18 : 00 , c ) 19 : 00 , d ) 20 : 00 , e ) 17 : 00 | e | multiply(divide(const_3, 4), divide(const_1, subtract(divide(const_1, 4), divide(const_1, 6)))) | divide(const_3,n0)|divide(const_1,n0)|divide(const_1,n1)|subtract(#1,#2)|divide(const_1,#3)|multiply(#0,#4)| | physics |
selling an kite for rs . 30 , a shop keeper gains 35 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ? | "explanation : marked price = rs . 30 c . p . = 100 / 135 * 30 = rs . 22.22 sale price = 90 % of rs . 30 = rs . 27 required gain % = 4.77 / 22.22 * 100 = 21.5 % . answer : e" | a ) 8 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 21.5 % | e | multiply(divide(subtract(multiply(divide(30, const_100), subtract(const_100, 10)), divide(multiply(30, const_100), add(35, const_100))), divide(multiply(30, const_100), add(35, const_100))), const_100) | add(n1,const_100)|divide(n0,const_100)|multiply(n0,const_100)|subtract(const_100,n2)|divide(#2,#0)|multiply(#1,#3)|subtract(#5,#4)|divide(#6,#4)|multiply(#7,const_100)| | gain |
if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 58 , what is the compound interest on the same sum at the rate and for the same time ? | "explanation : sum = ( 58 * 100 ) / ( 2 * 5 ) = rs . 580 amount = [ 580 * ( 1 + 5 / 100 ) 2 ] = rs . 639.45 c . i . = ( 639.45 - 580 ) = rs . 59.45 answer : a" | a ) s . 59.45 , b ) s . 56.22 , c ) s . 51.219 , d ) s . 59.18 , e ) s . 51.11 | a | subtract(add(add(divide(multiply(divide(58, multiply(divide(5, const_100), 2)), 5), const_100), divide(58, multiply(divide(5, const_100), 2))), divide(multiply(add(divide(multiply(divide(58, multiply(divide(5, const_100), 2)), 5), const_100), divide(58, multiply(divide(5, const_100), 2))), 5), const_100)), divide(58, m... | divide(n1,const_100)|multiply(n0,#0)|divide(n2,#1)|multiply(n1,#2)|divide(#3,const_100)|add(#4,#2)|multiply(n1,#5)|divide(#6,const_100)|add(#5,#7)|subtract(#8,#2)| | gain |
if a = 105 and a ^ 3 = 21 Γ 25 Γ 45 Γ d , what is the value of d ? | "a = 105 = 3 * 5 * 7 a ^ 3 = 21 Γ 25 Γ 45 Γ d = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x d = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x d = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x d d = 7 ^ 2 = 49 answer d" | a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54 | d | divide(power(105, 3), multiply(multiply(21, 25), 45)) | multiply(n2,n3)|power(n0,n1)|multiply(n4,#0)|divide(#1,#2)| | general |
a present value of a machine is $ 40000 . its value depletiation rate is 5 % per annum then find the machine value after 2 years ? | "p = $ 40000 r = 5 % t = 2 years machine value after 3 years = p / ( 1 - r / 100 ) ^ t = 40000 * 19 / 20 * 19 / 20 * 19 / 20 = $ 36100 answer is b" | a ) $ 36540 , b ) $ 36100 , c ) $ 29580 , d ) $ 31256 , e ) $ 41250 | b | multiply(40000, power(subtract(const_1, divide(5, const_100)), 2)) | divide(n1,const_100)|subtract(const_1,#0)|power(#1,n2)|multiply(n0,#2)| | gain |
find the compound ratio of ( 3 : 4 ) , ( 4 : 5 ) and ( 1 : 2 ) is | "required ratio = 3 / 4 * 4 / 5 * 1 / 2 = 3 / 10 = 3 : 10 answer is c" | a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 10 , d ) 4 : 10 , e ) 3 : 2 | c | multiply(divide(3, const_3.0), multiply(divide(3, 4), divide(4, 4))) | divide(n0,n3)|divide(n2,n3)|multiply(#0,#1)|multiply(#0,#2)| | other |
at veridux corporation , there are 218 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ? | "well , first let Γ’ β¬ β’ s take care of the Γ’ β¬ Ε totals Γ’ β¬ Β . the numbers in the Γ’ β¬ Ε totals Γ’ β¬ Β row must add up . if 90 are females , the other 218 Γ’ β¬ β 90 = 128 must be males . similarly , the numbers in the Γ’ β¬ Ε totals Γ’ β¬ Β column must add up . if 40 are managers , then the other 218 Γ’ β¬ β 40 = 178 must be a... | a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 47 | e | multiply(40, const_1) | multiply(n2,const_1)| | general |
find a sum for 1 st 9 prime number ' s ? | required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 ) = 100 note : 1 is not a prime number option e | a ) 25 , b ) 28 , c ) 30 , d ) 34 , e ) 100 | e | add(add(add(add(add(add(add(add(const_2, const_3), add(const_2, const_3)), add(add(const_2, const_3), const_2)), add(9, const_2)), add(add(9, const_2), const_2)), add(add(add(9, const_2), const_2), const_4)), add(add(add(add(9, const_2), const_2), const_4), const_2)), add(add(add(add(add(9, const_2), const_2), const_4)... | add(const_2,const_3)|add(n1,const_2)|add(#0,#0)|add(#0,const_2)|add(#1,const_2)|add(#2,#3)|add(#4,const_4)|add(#5,#1)|add(#6,const_2)|add(#7,#4)|add(#8,const_4)|add(#9,#6)|add(#11,#8)|add(#12,#10) | general |
if d = 1 / ( 2 ^ 3 * 5 ^ 11 ) is expressed as a terminating decimal , how many nonzero digits will d have ? | "another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 11 ) = multiply and divide by 2 ^ 8 = 2 ^ 8 / ( 2 ^ 3 * 2 ^ 8 * 5 ^ 11 ) = 2 ^ 8 / 10 ^ 11 = > non zero digits are 256 = > ans c" | a ) one , b ) two , c ) three , d ) seven , e ) ten | c | add(1, 2) | add(n0,n1)| | general |
a man is 25 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ? | "let the son ' s present age be x years . then , man ' s present age = ( x + 25 ) years . ( x + 25 ) + 2 = 2 ( x + 2 ) x + 27 = 2 x + 4 = > x = 23 . answer : b" | a ) 11 , b ) 23 , c ) 27 , d ) 22 , e ) 91 | b | divide(subtract(25, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | general |
calculate the sum of first 89 natural numbers . | "solution we know that ( 1 + 2 + 3 + . . . . . + 89 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 89 ) = ( 89 Γ 90 / 2 ) = 4005 . answer e" | a ) 2017 , b ) 2647 , c ) 2147 , d ) 2045 , e ) 4005 | e | multiply(add(89, const_1), divide(89, const_2)) | add(n0,const_1)|divide(n0,const_2)|multiply(#0,#1)| | general |
a jogger running at 10 km / hr along side a railway track is 340 m ahead of the engine of a 120 m long train running at 46 km / hr in the same direction . in how much time will the train pass the jogger ? | "speed of train relative to jogger = 46 - 10 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 340 + 120 = 460 m . time taken = 460 / 10 = 46 sec . answer : d" | a ) 76 sec , b ) 67 sec , c ) 98 sec , d ) 46 sec , e ) 23 sec | d | divide(add(340, 120), multiply(subtract(46, 10), divide(divide(const_10, const_2), divide(subtract(46, 10), const_2)))) | add(n1,n2)|divide(const_10,const_2)|subtract(n3,n0)|divide(#2,const_2)|divide(#1,#3)|multiply(#4,#2)|divide(#0,#5)| | general |
an amount of rs . 10000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 3 / 4 % , then the amount invested at 11 % was ? | let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 10000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 10000 - x ) * 11 * 1 ] / 100 = ( 10000 * 39 / 4 * 1 / 100 ) ( 9 x + 110000 - 11 x ) / 100 = 3900 / 4 = 975 ( 9 x + 110000 - 11 x ) = 97500 x = 6250 sum invested at 9 % = rs . 6250 sum invested at 11 ... | a ) 2377 , b ) 3750 , c ) 2997 , d ) 2677 , e ) 1987 | b | divide(subtract(multiply(10000, divide(add(9, divide(3, 4)), const_100)), multiply(10000, divide(9, const_100))), subtract(divide(11, const_100), divide(9, const_100))) | divide(n4,n5)|divide(n1,const_100)|divide(n2,const_100)|add(n1,#0)|multiply(n0,#1)|subtract(#2,#1)|divide(#3,const_100)|multiply(n0,#6)|subtract(#7,#4)|divide(#8,#5) | gain |
the present population of a town is 300 . population increase rate is 10 % p . a . find the population of town after 1 years ? | p = 300 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 300 * ( 1 + 10 / 100 ) = 300 * ( 11 / 10 ) = 330 answer is e | a ) 100 , b ) 120 , c ) 200 , d ) 220 , e ) 330 | e | add(300, divide(multiply(300, 10), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1) | gain |
in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 600 m ? | "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 600 m , the number of meters by which a beats c = ( 600 * 212.5 ) / 1000 = 127... | a ) 236 , b ) 127.5 , c ) 267 , d ) 268 , e ) 281 | b | subtract(1000, divide(multiply(subtract(1000, 100), subtract(800, 100)), 800)) | subtract(n0,n1)|subtract(n2,n1)|multiply(#0,#1)|divide(#2,n2)|subtract(n0,#3)| | physics |
a powder tin has a square base with side 8 cm and height 14 cm . another tin has a circular base with diameter 8 cm and height 14 cm . the difference in their capacities is : | sol . difference in capacities = [ 8 * 8 * 14 - 22 / 7 * 4 * 4 * 14 ] cm Β³ = 192 cm Β³ answer b | ['a ) 168 cm Β³', 'b ) 192 cm Β³', 'c ) 228 cm Β³', 'd ) 236 cm Β³', 'e ) none'] | b | subtract(volume_rectangular_prism(8, 8, 14), volume_cylinder(divide(8, const_2), 14)) | divide(n0,const_2)|volume_rectangular_prism(n0,n0,n1)|volume_cylinder(#0,n1)|subtract(#1,#2) | geometry |
today david , who is 40 years old , and his daughter , who is 12 years old , celebrate their birthdays . how many years will pass before david β s age is twice his daughter β s age ? | forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . after x years passes david β s age will be ( 40 + x ) years old , and his daughter β s age will be ( 12 + x ) years old . since the david β s age is twice his daughter β s age ( 40 + x ) = 2 * ... | a ) 22 , b ) 20 , c ) 16 , d ) 18 , e ) 14 | c | add(subtract(divide(add(add(40, 12), const_2), const_2), 12), const_1) | add(n0,n1)|add(#0,const_2)|divide(#1,const_2)|subtract(#2,n1)|add(#3,const_1) | general |
( 17 ) 3.5 x ( 17 ) ? = 178 | "solution let ( 17 ) 3.5 * ( 17 ) x = 178 . then , ( 17 ) 3.5 + x = ( 17 ) 8 . β΄ 3.5 + x = 8 β x = ( 8 - 3.5 ) β x = 4.5 answer d" | a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these | d | multiply(17, 17) | multiply(n0,n2)| | general |
earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 120 envelopes | "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envelopes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 120 envelopes they will take 120 / 60 mins . i . e . , 2 mins . answer : a" | a ) 2 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes | a | divide(120, add(36, divide(36, divide(const_3, const_2)))) | divide(const_3,const_2)|divide(n0,#0)|add(n0,#1)|divide(n1,#2)| | physics |
if ( 400 ) ( 7000 ) = ( 28000 ) ( 100 ^ x ) , what is the value of x ? | ( 400 ) ( 7,000 ) = ( 2,800 ) ( 100 ^ x ) = > ( 400 ) ( 7,000 ) / 2,800 = 100 ^ x = > 100 = 100 ^ x = > 100 ^ 1 = 100 ^ x since , base is same so powers will be same too . so , x = 1 answer will be e | a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1 | e | divide(divide(multiply(400, 7000), 28000), 100) | multiply(n0,n1)|divide(#0,n2)|divide(#1,n3) | general |
having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.64 at the candy store . what is john β s weekly allowance ? | "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.64 therefore , x = $ 2.40 . answer a" | a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80 | a | divide(0.64, subtract(const_1, add(divide(3, 5), multiply(divide(const_1, 3), subtract(const_1, divide(3, 5)))))) | divide(n0,n1)|divide(const_1,n0)|subtract(const_1,#0)|multiply(#1,#2)|add(#0,#3)|subtract(const_1,#4)|divide(n2,#5)| | general |
a number of 41 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ? | "to maximize # of boxes we should minimize marbles per box : 12 * 3 + 1 * 5 = 41 - - > 12 + 1 = 13 . answer : a ." | a ) 13 , b ) 12 , c ) 15 , d ) 16 , e ) 17 | a | divide(41, 3) | divide(n0,n1)| | general |
the sum of the present age of henry and jill is 41 . what is their present ages if 7 years ago henry was twice the age of jill ? | let the age of jill 7 years ago be x , age of henry be 2 x x + 7 + 2 x + 7 = 41 x = 9 present ages will be 16 and 25 answer : a | a ) and 25 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these | a | subtract(41, divide(add(41, 7), const_3)) | add(n0,n1)|divide(#0,const_3)|subtract(n0,#1) | general |
set x consists of the integers from 0 to 12 , inclusive , while set y consists of the integers from 6 to 10 , inclusive . how many distinct integers do belong to the both sets at the same time ? | "x = { 0 , 1,2 , 3,4 , 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } y = { 6 , 7 , 8 , 9 , 10 } common elements = { 6 , 7 , 8 , 9 , 10 } = 5 elements answer : option c ." | a ) 4 , b ) 10 , c ) 5 , d ) 9 , e ) 8 | c | add(subtract(12, 0), 0) | subtract(n1,n0)|add(#0,n0)| | other |
a watch was sold at a loss of 10 % . if it was sold for rs . 500 more , there would have been a gain of 10 % . what is the cost price ? | "90 % 110 % - - - - - - - - 20 % - - - - 500 100 % - - - - ? = > rs . 2500 answer : c" | a ) 1000 , b ) 2998 , c ) 2500 , d ) 2788 , e ) 2991 | c | divide(multiply(500, const_100), subtract(add(const_100, 10), subtract(const_100, 10))) | add(const_100,n2)|multiply(n1,const_100)|subtract(const_100,n0)|subtract(#0,#2)|divide(#1,#3)| | gain |
what is the area of a square field whose diagonal of length 26 m ? | "d 2 / 2 = ( 26 * 26 ) / 2 = 338 answer : c" | a ) 287 , b ) 269 , c ) 338 , d ) 200 , e ) 230 | c | divide(square_area(26), const_2) | square_area(n0)|divide(#0,const_2)| | geometry |
a book is bought for $ 600 and sold for $ 624 . what is the profit in percentage ? | "624 / 600 = 1.04 the answer is b ." | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | b | multiply(divide(subtract(624, 600), 600), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
a store owner estimates that the average price of type a products will increase by 35 % next year and that the price of type b products will increase by 20 % next year . this year , the total amount aid for type a products was $ 3500 and the total price paid for type b products was $ 6300 . according to the store owner... | "cost of type a products next year = 1.35 * 3500 = 4725 cost of type b products next year = 1.2 * 6300 = 7560 total 4725 + 7560 = 12285 answer : d" | a ) $ 14,755 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 12,285 , e ) $ 17,155 | d | multiply(divide(const_3, const_4), const_1000) | divide(const_3,const_4)|multiply(#0,const_1000)| | general |
a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by a are ? | "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 4 / 25 * 75 = 12 answer : e" | a ) 11 , b ) 18 , c ) 13 , d ) 17 , e ) 12 | e | multiply(divide(75, add(add(divide(2, 3), divide(5, 2)), 2)), 5) | divide(n0,n1)|divide(n3,n0)|add(#0,#1)|add(#2,n0)|divide(n4,#3)|multiply(n3,#4)| | general |
two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 10 seconds . find the length of the faster train ? | "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 10 * 10 = 100 m . the length of the faster train = 100 m . answer : c" | a ) 270 , b ) 288 , c ) 100 , d ) 299 , e ) 126 | c | multiply(divide(subtract(72, 36), const_3_6), 10) | subtract(n0,n1)|divide(#0,const_3_6)|multiply(n2,#1)| | physics |
a trader sells 78 meters of cloth for rs . 6788 at the profit of rs . 29 per metre of cloth . what is the cost price of one metre of cloth ? | "sp of 1 m of cloth = 6788 / 78 = rs . 87 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 87 - rs . 29 = rs . 58 . answer : d" | a ) 22 , b ) 75 , c ) 60 , d ) 58 , e ) 11 | d | subtract(divide(6788, 78), 29) | divide(n1,n0)|subtract(#0,n2)| | physics |
by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 50 % ? | "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 50 % = 50 % of 640 = rs . 320 sp = cp - loss = 640 - 320 = rs . 320 answer : c" | a ) s . 429 , b ) s . 480 , c ) s . 320 , d ) s . 128 , e ) s . 419 | c | subtract(divide(multiply(800, const_100), add(25, const_100)), divide(multiply(divide(multiply(800, const_100), add(25, const_100)), 50), const_100)) | add(n1,const_100)|multiply(n0,const_100)|divide(#1,#0)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | gain |
a ( 8 , w ^ 2 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 17 . what is the value of w ? | "y = x ^ 2 + 17 w ^ 2 = 8 ^ 2 + 17 w ^ 2 = 81 w = 9 answer e" | a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 . | e | power(subtract(power(8, 2), 17), divide(17, 8)) | divide(n3,n0)|power(n0,n2)|subtract(#1,n3)|power(#2,#0)| | general |
on a certain transatlantic crossing , 40 percent of a ship β s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship β s passengers held round - trip tickets ? | let t be the total number of passengers . let x be the number of people with round trip tickets . 0.4 t had round trip tickets and took their cars . 0.5 x had round trip tickets and took their cars . 0.5 x = 0.4 t x = 0.8 t the answer is d . | a ) 40 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 % | d | divide(40, subtract(const_1, divide(50, const_100))) | divide(n1,const_100)|subtract(const_1,#0)|divide(n0,#1) | gain |
if log 2 = 0.30103 , the number of digits in 2128 is . | log ( 2128 ) = 128 log ( 2 ) = 128 Γ 0.30103 β 38.4 ie , its characteristic = 38 hence , number of digits in 2128 = 38 + 1 = 39 answer : option b | a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 56 | b | multiply(0.30103, subtract(2128, multiply(const_2, const_1000))) | multiply(const_1000,const_2)|subtract(n2,#0)|multiply(n1,#1) | other |
bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 40 white marbles . how many red marbles could be in bag a ? | "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 3 let w in bag b be 4 k w = 30 = 6 k + 4 k = > k = 40 / 10 = 4 total red ' s in bag a will be 2 k = 8 a" | a ) 8 , b ) 3 , c ) 4 , d ) 6 , e ) 8 | a | divide(40, add(multiply(3, 2), 4)) | multiply(n1,n2)|add(n5,#0)|divide(n6,#1)| | other |
if a person walks at 5 km / hr instead of 4 km / hr , he would have walked 6 km more . the actual distance traveled by him is ? | "let the actual distance traveled be x km . then , x / 4 = ( x + 6 ) / 5 x - 24 = > x = 24 km . answer : d" | a ) 14 , b ) 20 , c ) 18 , d ) 24 , e ) 21 | d | multiply(4, divide(6, subtract(5, 4))) | subtract(n0,n1)|divide(n2,#0)|multiply(n1,#1)| | general |
if tim had lunch at $ 60.80 and he gave 20 % tip , how much did he spend ? | the tip is 20 % of what he paid for lunch . hence tip = 20 % of 60.80 = ( 20 / 100 ) * 60.80 = $ 12.16 total spent 60.80 + 12.16 = $ 72.96 correct answer c | a ) $ 30.60 , b ) $ 60.60 , c ) $ 72.96 , d ) $ 40.60 , e ) $ 50.60 | c | add(60.8, divide(multiply(60.8, 20), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1) | gain |
when asked what the time is , a person answered that the amount of time left is 1 / 3 of the time already completed . what is the time . | "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 β x = 1 / 3 x β x = 18 time is 6 pm answer : e" | a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 8 pm , e ) 6 pm | e | subtract(multiply(const_2, const_12), divide(multiply(1, const_12), add(divide(1, 3), const_1))) | divide(const_2.0,n1)|multiply(const_12,n0)|add(#0,const_1)|divide(#1,#2)|subtract(#1,#3)| | general |
a ladder 18 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 6 feet from the base of the wall . if the top of the ladder slips down 4 feet , how many feet will the bottom of the ladder slip ? | "18 ^ 2 - 6 ^ 2 = 288 it means that the height is equal to 16.9 . since the top of the ladder slips down 4 feet , then the height of the wall = 16.9 - 4 = 12.9 the bottom = sqrt ( 18 ^ 2 - 12.9 ^ 2 ) = sqrt ( 324 - 166.41 ) = 12.5 ans is a" | a ) 12.5 , b ) 15 , c ) 18 , d ) 19 , e ) 25 | a | sqrt(subtract(power(18, const_2), power(subtract(sqrt(subtract(power(18, const_2), power(6, const_2))), 4), const_2))) | power(n0,const_2)|power(n1,const_2)|subtract(#0,#1)|sqrt(#2)|subtract(#3,n2)|power(#4,const_2)|subtract(#0,#5)|sqrt(#6)| | gain |
if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be even ? | "in order to make even nos . by multiplication , we should have even * odd , odd * even or even * even total even nos . possible by multiplying nos . from the 2 sets : ( 1 * 6 ) ; 2 * any of the three from set b ; 3 * 6 ; & 4 * any of the three from set b 1 + 3 + 1 + 3 = 8 total possibilities = 4 * 3 = 12 p ( event ) =... | a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6 | d | divide(power(2, 2), multiply(choose(4, 2), choose(2, 1))) | choose(n3,n1)|choose(n1,n0)|power(n1,n1)|multiply(#0,#1)|divide(#2,#3)| | probability |
johnny makes $ 3.25 per hour at his work . if he works 8 hours , how much money will he earn ? | 3.25 * 8 = 26 . answer is c . | a ) $ 30 , b ) $ 54 , c ) $ 26 , d ) $ 12 , e ) $ 9.60 | c | multiply(3.25, 8) | multiply(n0,n1)| | physics |
an article is bought for rs . 1280 and sold for rs . 900 , find the loss percent ? | "1280 - - - - 380 100 - - - - ? = > 29 % answer : b" | a ) 28 % , b ) 29 % , c ) 16 % , d ) 26 % , e ) 32 % | b | subtract(const_100, divide(multiply(900, const_100), 1280)) | multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)| | gain |
what is the rate percent when the simple interest on rs . 800 amount to rs . 160 in 3 years ? | "160 = ( 800 * 3 * r ) / 100 r = 6.6 % answer : b" | a ) 5 % , b ) 6.6 % , c ) 9 % , d ) 2 % , e ) 4 % | b | divide(multiply(const_100, 160), multiply(800, 3)) | multiply(n1,const_100)|multiply(n0,n2)|divide(#0,#1)| | gain |
solve below question 2 x + 1 = - 17 | "1 . subtract 1 from both sides : 2 x + 1 - 1 = - 17 - 1 2 . simplify both sides : 2 x = - 18 3 . divide both sides by 2 : 4 . simplify both sides : x = - 9 b" | a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7 | b | divide(negate(add(17, 1)), 2) | add(n1,n2)|negate(#0)|divide(#1,n0)| | general |
what is the difference between the largest number and the least number written with the digits 9 , 3 , 1 , 2 ? | "explanation : 1239 9321 - - - - - - - - - - - - 8082 answer : d" | a ) 6084 , b ) 3788 , c ) 2077 , d ) 8082 , e ) 1812 | d | subtract(add(add(add(multiply(multiply(9, const_100), const_10), multiply(const_4.0, const_100)), multiply(3, const_10)), 1), add(add(add(const_1000, multiply(3, const_100)), multiply(2, const_10)), 9)) | multiply(n0,const_100)|multiply(const_4.0,const_100)|multiply(n1,const_10)|multiply(n1,const_100)|multiply(n3,const_10)|add(#3,const_1000)|multiply(#0,const_10)|add(#6,#1)|add(#5,#4)|add(#7,#2)|add(n0,#8)|add(n2,#9)|subtract(#11,#10)| | general |
if m and n are positive integer , and 1800 m = n ^ 3 , what is the least possible value of m ? | 1800 * m = n ^ 3 m = n ^ 3 / 1800 = n ^ 3 / ( 3 ^ 2 * 5 ^ 2 * 2 ^ 3 ) so n has to be 3 * 5 * 2 so that n ^ 3 is divisible by 1800 . so m = ( 2 * 3 * 5 ) ^ 3 / ( 3 ^ 2 * 5 ^ 2 * 2 ^ 3 ) m = 15 answer : c | a ) 2 , b ) 3 , c ) 15 , d ) 30 , e ) 45 | c | floor(power(multiply(1800, const_2), const_0_33)) | multiply(n0,const_2)|power(#0,const_0_33)|floor(#1) | general |
the moon revolves around the earth at a speed of approximately 1.04 kilometers per second . this approximate speed is how many kilometers per hour ? | "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.04 * 3600 = 3744 kilometers per hour . option c is correct" | a ) 60 , b ) 61.2 , c ) 3,744 , d ) 3,600 , e ) 3,672 | c | multiply(1.04, const_3600) | multiply(n0,const_3600)| | physics |
rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total ... | "for 100 - 30 - 10 = 60 pages only cost is 6 $ per page for the first time page is typed - 60 * 5 = 300 $ ; for 30 pages the cost is : first time 6 $ + 3 $ of the first revision - 30 * ( 6 + 3 ) = 270 $ ; for 10 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 10 ( 6 + 3 + 3... | a ) $ 690 , b ) $ 620 , c ) $ 650 , d ) $ 640 , e ) $ 770 | a | add(add(multiply(100, 6), multiply(30, 3)), multiply(multiply(10, 3), const_2)) | multiply(n0,n2)|multiply(n1,n3)|multiply(n1,n4)|add(#0,#1)|multiply(#2,const_2)|add(#3,#4)| | general |
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