[
    {
        "Problem": "there are 1000 buildings in a street . a sign - maker is contracted to number the houses from 1 to 1000 . how many zeroes will he need ?",
        "Rationale": "divide as ( 1 - 100 ) ( 100 - 200 ) . . . . ( 900 - 1000 ) total 192 answer : c",
        "options": "a ) 190 , b ) 191 , c ) 192 , d ) 193 , e ) 194",
        "correct": "c",
        "annotated_formula": "add(add(divide(1000, const_10), multiply(subtract(const_10, 1), const_10)), const_2)",
        "linear_formula": "divide(n0,const_10)|subtract(const_10,n1)|multiply(#1,const_10)|add(#0,#2)|add(#3,const_2)",
        "category": "general"
    },
    {
        "Problem": "a man bought 20 shares of rs . 50 at 5 discount , the rate of dividend being 13 . the rate of interest obtained is :",
        "Rationale": "\"investment = rs . [ 20 x ( 50 - 5 ) ] = rs . 900 . face value = rs . ( 50 x 20 ) = rs . 1000 . dividend = rs . 27 x 1000 = rs . 135 . 2 100 interest obtained = 135 x 100 % = 15 % 900 view answer discuss in forum answer : c\"",
        "options": "a ) 27 % , b ) 87 % , c ) 15 % , d ) 66 % , e ) 88 %",
        "correct": "c",
        "annotated_formula": "divide(multiply(multiply(20, 50), divide(13, const_100)), multiply(20, subtract(50, 5)))",
        "linear_formula": "divide(n3,const_100)|multiply(n0,n1)|subtract(n1,n2)|multiply(#0,#1)|multiply(n0,#2)|divide(#3,#4)|",
        "category": "gain"
    },
    {
        "Problem": "? % of 360 = 108",
        "Rationale": "\"? % of 360 = 108 or , ? = 108 \u00d7 100 / 360 = 30 answer a\"",
        "options": "a ) 30 , b ) 36 , c ) 64 , d ) 72 , e ) none of these",
        "correct": "a",
        "annotated_formula": "divide(multiply(108, const_100), 360)",
        "linear_formula": "multiply(n1,const_100)|divide(#0,n0)|",
        "category": "gain"
    },
    {
        "Problem": "a corporation double its annual bonus to 100 of its employees . what percent of the employees \u2019 new bonus is the increase ?",
        "Rationale": "let the annual bonus be x . a corporation double its annual bonus . so new bonus = 2 x . increase = 2 x - x = x the increase is what percent of the employees \u2019 new bonus = ( x / 2 x ) * 100 = 50 % hence a .",
        "options": "a ) 50 % , b ) 12 % , c ) 8 % , d ) 6 % , e ) 5 %",
        "correct": "a",
        "annotated_formula": "multiply(divide(subtract(const_2, const_1), const_2), 100)",
        "linear_formula": "subtract(const_2,const_1)|divide(#0,const_2)|multiply(n0,#1)",
        "category": "general"
    },
    {
        "Problem": "a and b together do a work in 20 days . b and c together in 15 days and c and a in 12 days . then b alone can finish same work in how many days ?",
        "Rationale": "\"( a + b ) work in 1 day = 1 / 20 , ( b + c ) work in 1 days = 1 / 15 . , ( c + a ) work in 1 days = 1 / 12 ( 1 ) adding = 2 [ a + b + c ] in 1 day work = [ 1 / 20 + 1 / 15 + 1 / 12 ] = 1 / 5 ( a + b + c ) work in 1 day = 1 / 10 b work in 1 days = [ a + b + c ] work in 1 days - work of ( a + c ) in 1 days = [ 1 / 10 - 1 / 12 ] = 1 / 60 b alone finish work in 60 days answer b\"",
        "options": "a ) 50 , b ) 60 , c ) 45 , d ) 35 , e ) 48",
        "correct": "b",
        "annotated_formula": "inverse(divide(add(inverse(12), add(inverse(20), inverse(15))), const_2))",
        "linear_formula": "inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|divide(#4,const_2)|inverse(#5)|",
        "category": "physics"
    },
    {
        "Problem": "oak street begins at pine street and runs directly east for 2 kilometers until it ends when it meets maple street . oak street is intersected every 400 meters by a perpendicular street , and each of those streets other than pine street and maple street is given a number beginning at 1 st street ( one block east of pine street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of maple street . what is the highest - numbered street that intersects oak street ?",
        "Rationale": "2 km / 400 m = 5 . however , the street at the 2 - km mark is not 5 th street ; it is maple street . therefore , the highest numbered street is 4 th street . the answer is a .",
        "options": "a ) 4 th , b ) 5 th , c ) 6 th , d ) 7 th , e ) 8 th",
        "correct": "a",
        "annotated_formula": "subtract(divide(multiply(2, const_1000), 400), const_1)",
        "linear_formula": "multiply(n0,const_1000)|divide(#0,n1)|subtract(#1,const_1)",
        "category": "physics"
    },
    {
        "Problem": "the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if arthur and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?",
        "Rationale": "\"if arthur 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 $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) .\"",
        "options": "a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54",
        "correct": "b",
        "annotated_formula": "divide(subtract(multiply(const_2, multiply(80, 0.02)), multiply(multiply(160, divide(subtract(100, 25), 100)), 0.02)), const_2)",
        "linear_formula": "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)|",
        "category": "gain"
    },
    {
        "Problem": "if 6 men and 8 women can do a piece of work in 10 days while 26 men and 48 women can do the same in 2 days , the time taken by 15 men and 20 women in doing the same type of work will be ?",
        "Rationale": "let 1 man ' s 1 day ' s work = x and 1 women ' s 1 day ' s work = y . then , 6 x + 8 y = 1 and 26 x + 48 y = 1 . 10 2 solving these two equations , we get : x = 1 and y = 1 . 100 200 ( 15 men + 20 women ) ' s 1 day ' s work = 15 + 20 = 1 . 100 200 4 15 men and 20 women can do the work in 4 days . hence answer will be b",
        "options": "a ) 5 , b ) 4 , c ) 6 , d ) 7 , e ) 8",
        "correct": "b",
        "annotated_formula": "divide(multiply(add(divide(8, divide(subtract(multiply(48, 2), multiply(8, 10)), subtract(multiply(6, 10), multiply(26, 2)))), 6), 10), add(divide(20, divide(subtract(multiply(48, 2), multiply(8, 10)), subtract(multiply(6, 10), multiply(26, 2)))), 15))",
        "linear_formula": "multiply(n4,n5)|multiply(n1,n2)|multiply(n0,n2)|multiply(n3,n5)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)|divide(n1,#6)|divide(n7,#6)|add(n0,#7)|add(n6,#8)|multiply(n2,#9)|divide(#11,#10)",
        "category": "physics"
    },
    {
        "Problem": "a sum of rs . 1360 has been divided among a , b and c such that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets . b ' s share is :",
        "Rationale": "\"let c ' s share = rs . x then , b ' s share = rs . x / 4 ; a ' s share = rs . 2 / 3 * x / 4 = rs . x / 6 therefore x / 6 + x / 4 + x = 1360 17 x / 12 = 1360 x = 1360 * 12 / 17 = rs . 960 hence , b ' s share = rs . 960 / 4 = rs . 240 answer : c\"",
        "options": "a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 300 , e ) rs . 500",
        "correct": "c",
        "annotated_formula": "subtract(subtract(multiply(divide(1360, const_10), const_2), const_12), const_12)",
        "linear_formula": "divide(n0,const_10)|multiply(#0,const_2)|subtract(#1,const_12)|subtract(#2,const_12)|",
        "category": "general"
    },
    {
        "Problem": "two - third of a positive number and 16 / 216 of its reciprocal are equal . find the positive number .",
        "Rationale": "\"explanation : let the positive number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 x = \u221a 16 / 144 = 4 / 12 . answer : a\"",
        "options": "a ) 4 / 12 , b ) 4 / 17 , c ) 4 / 15 , d ) 4 / 11 , e ) 4 / 03",
        "correct": "a",
        "annotated_formula": "sqrt(divide(multiply(16, const_3), multiply(216, const_2)))",
        "linear_formula": "multiply(n0,const_3)|multiply(n1,const_2)|divide(#0,#1)|sqrt(#2)|",
        "category": "general"
    },
    {
        "Problem": "spanish language broadcast records last 90 min on each of two sides . if it takes 3 hours to translate one hour of broadcast , how long will it take to translate 16 full records ?",
        "Rationale": "records last 90 min on each of 2 sides , = = > record last 90 * 2 = 180 min = 3 hours 16 full records - - > 16 * 3 = 48 hour broadcast given , 3 hours to translate 1 hour of broadcast let x be the time required to translate 48 hour broadcast ( 16 full records ) x = 48 * 3 = 144 hours answer : a",
        "options": "a ) 144 hours , b ) 124 hours , c ) 134 hours , d ) 154 hours , e ) 164 hours",
        "correct": "a",
        "annotated_formula": "multiply(multiply(divide(multiply(90, const_2), const_60), 16), 3)",
        "linear_formula": "multiply(n0,const_2)|divide(#0,const_60)|multiply(n2,#1)|multiply(n1,#2)",
        "category": "physics"
    },
    {
        "Problem": "today is thursday . i came home from a trip 3 days before the day after last monday . how many days have i been home ?",
        "Rationale": "d 6 days the day after last monday was tuesday . if i came home 3 days before that , i came home on saturday , sunday , monday , tuesday , wednesday , and thursday = 6 days .",
        "options": "a ) 1 day , b ) 2 days , c ) 7 days , d ) 6 days , e ) 10 days",
        "correct": "d",
        "annotated_formula": "add(add(3, const_1), const_2)",
        "linear_formula": "add(n0,const_1)|add(#0,const_2)",
        "category": "physics"
    },
    {
        "Problem": "a train running at the speed of 50 km / hr crosses a post in 4 seconds . what is the length of the train ?",
        "Rationale": "\"speed = ( 54 x 5 / 18 ) = 15 m / sec . length of the train = ( speed x time ) . length of the train = 15 x 4 m = 60 m . answer : c\"",
        "options": "a ) 90 , b ) 120 , c ) 60 , d ) 95 , e ) 75",
        "correct": "c",
        "annotated_formula": "multiply(divide(multiply(50, const_1000), const_3600), 4)",
        "linear_formula": "multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|",
        "category": "physics"
    },
    {
        "Problem": "if soundharya rows 49 km upstream and 77 km down steam taking 7 hours each , then the speed of the stream",
        "Rationale": "speed upstream = 49 / 7 = 7 kmph speed down stream = 77 / 7 = 11 kmph speed of stream = \u00bd ( 11 - 7 ) = 2 kmph answer : c",
        "options": "a ) 6 kmph , b ) 5 kmph , c ) 2 kmph , d ) 3 kmph , e ) 4 kmph",
        "correct": "c",
        "annotated_formula": "divide(subtract(77, 49), multiply(7, const_2))",
        "linear_formula": "multiply(n2,const_2)|subtract(n1,n0)|divide(#1,#0)",
        "category": "physics"
    },
    {
        "Problem": "two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many t hours will it take if jim types the report and mary edits it immediately after he is done ?",
        "Rationale": "\"break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many t hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a .\"",
        "options": "a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8",
        "correct": "a",
        "annotated_formula": "add(inverse(subtract(divide(const_1, 12.5), divide(const_1, 30))), inverse(subtract(divide(const_1, 7.5), divide(const_1, 12))))",
        "linear_formula": "divide(const_1,n0)|divide(const_1,n2)|divide(const_1,n1)|divide(const_1,n3)|subtract(#0,#1)|subtract(#2,#3)|inverse(#4)|inverse(#5)|add(#6,#7)|",
        "category": "physics"
    },
    {
        "Problem": "in two triangles , the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4 . find the ratio of their bases .",
        "Rationale": "sol . let the bases of the two triangles be x and y and their heights be 3 h and 4 h respectively . then , ( ( 1 / 2 ) x xx 3 h ) / ( 1 / 2 ) x y x 4 h ) = 4 / 3 \uf0f3 x / y = ( 4 / 3 x 4 / 3 ) = 16 / 9 required ratio = 16 : 9 . ans : c",
        "options": "['a ) 2 : 3', 'b ) 4 : 5', 'c ) 16 : 9', 'd ) 7 : 9', 'e ) 8 : 5']",
        "correct": "c",
        "annotated_formula": "multiply(divide(4, 3), inverse(divide(3, 4)))",
        "linear_formula": "divide(n0,n1)|divide(n1,n0)|inverse(#1)|multiply(#0,#2)",
        "category": "geometry"
    },
    {
        "Problem": "what is the probability of drawing a queen from a deck of 52 cards ?",
        "Rationale": "\"total number of cards , n ( s ) = 52 total number of queen cards , n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 52 = 1 / 13 option b is answer\"",
        "options": "a ) 4 / 13 , b ) 1 / 13 , c ) 4 , d ) 1 , e ) 2 / 13",
        "correct": "b",
        "annotated_formula": "divide(const_2, choose(add(const_3, const_3), const_3))",
        "linear_formula": "add(const_3,const_3)|choose(#0,const_3)|divide(const_2,#1)|",
        "category": "probability"
    },
    {
        "Problem": "how many words , with or without meaning , can be formed using all letters of the word good using each letter exactly once ?",
        "Rationale": "\"the word good has exactly 4 letters which are all different . therefore the number of words that can be formed = number of permutations of 4 letters taken all at a time . = p ( 4 , 4 ) = 4 ! = 4 x 3 x 2 \u00d7 1 = 24 answer : e\"",
        "options": "a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24",
        "correct": "e",
        "annotated_formula": "factorial(const_3)",
        "linear_formula": "factorial(const_3)|",
        "category": "general"
    },
    {
        "Problem": "the ratio of the area of a square to that of the square drawn on its diagonal is",
        "Rationale": "answer : a ) 1 : 2",
        "options": "a ) 1 : 2 , b ) 1 : 0 , c ) 1 : 7 , d ) 1 : 5 , e ) 1 : 6",
        "correct": "a",
        "annotated_formula": "power(divide(const_1, sqrt(const_2)), const_2)",
        "linear_formula": "sqrt(const_2)|divide(const_1,#0)|power(#1,const_2)|",
        "category": "geometry"
    },
    {
        "Problem": "what is the probability for a family with 3 children to have a girl and two boys ( assuming the probability of having a boy or a girl is equal ) ?",
        "Rationale": "one possible case is : girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 there are 3 c 2 = 3 such cases so we should multiply by 3 . p ( one girl and two boys ) = 3 / 8 the answer is d .",
        "options": "a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 2 , d ) 3 / 8 , e ) 5 / 8",
        "correct": "d",
        "annotated_formula": "divide(subtract(const_1, multiply(power(divide(const_1, const_2), 3), const_2)), const_2)",
        "linear_formula": "divide(const_1,const_2)|power(#0,n0)|multiply(#1,const_2)|subtract(const_1,#2)|divide(#3,const_2)",
        "category": "general"
    },
    {
        "Problem": "what quantity of water should be added to reduce 9 liters of 50 % acidic liquid to 30 % acidic liquid ?",
        "Rationale": "acid in 9 liters = 50 % of 9 = 4.5 liters suppose x liters of water be added . then 4.5 liters of acid in 9 + x liters of diluted solution 30 % of 9 + x = 4.5 27 + 3 x = 45 x = 6 liters answer is a",
        "options": "a ) 6 liters , b ) 8 liters , c ) 10 liters , d ) 12 liters , e ) 15 liters",
        "correct": "a",
        "annotated_formula": "subtract(divide(multiply(multiply(9, divide(50, const_100)), const_100), 30), 9)",
        "linear_formula": "divide(n1,const_100)|multiply(n0,#0)|multiply(#1,const_100)|divide(#2,n2)|subtract(#3,n0)",
        "category": "gain"
    },
    {
        "Problem": "a man gains 20 % by selling an article for a certain price . if the sells it at double the price , the percentage of profit will be :",
        "Rationale": "\"let c . p . = rs . x . then , s . p . = rs . ( 12 % of x ) = rs . 6 x / 5 new s . p . = 2 * 6 x / 5 = rs . 12 x / 5 profit = 12 x / 5 - x = rs . 7 x / 5 profit = 7 x / 5 * 1 / x * 100 = 140 % . \\ answer : d\"",
        "options": "a ) 327 , b ) 140 , c ) 277 , d ) 178 , e ) 112",
        "correct": "d",
        "annotated_formula": "add(multiply(subtract(multiply(add(const_1, divide(20, const_100)), const_2), const_1), const_100), const_100)",
        "linear_formula": "divide(n0,const_100)|add(#0,const_1)|multiply(#1,const_2)|subtract(#2,const_1)|multiply(#3,const_100)|add(#4,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red king is drawn ?",
        "Rationale": "\"the total number of cards is 52 . the number of red kings is 2 . p ( red king ) = 2 / 52 = 1 / 26 the answer is d .\"",
        "options": "a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 13 , d ) 1 / 26 , e ) 1 / 52",
        "correct": "d",
        "annotated_formula": "divide(multiply(const_4, const_3), 52)",
        "linear_formula": "multiply(const_3,const_4)|divide(#0,n0)|",
        "category": "probability"
    },
    {
        "Problem": "rani bought more apples than oranges . she sells apples at \u20b9 23 apiece and makes 15 % profit . she sells oranges at \u20b9 10 apiece and makes 25 % profit . if she gets \u20b9 653 after selling all the apples and oranges , find her profit percentage z .",
        "Rationale": "\"given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % z = ( 97 / 556 ) * 100 = 17.4 % answer : b\"",
        "options": "a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %",
        "correct": "b",
        "annotated_formula": "multiply(divide(subtract(653, add(multiply(multiply(const_2, 10), add(multiply(const_2, 10), const_1)), multiply(divide(10, add(divide(25, const_100), const_1)), add(15, const_2)))), add(multiply(multiply(const_2, 10), add(multiply(const_2, 10), const_1)), multiply(divide(10, add(divide(25, const_100), const_1)), add(15, const_2)))), const_100)",
        "linear_formula": "add(n1,const_2)|divide(n3,const_100)|multiply(n2,const_2)|add(#2,const_1)|add(#1,const_1)|divide(n2,#4)|multiply(#3,#2)|multiply(#0,#5)|add(#6,#7)|subtract(n4,#8)|divide(#9,#8)|multiply(#10,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations . what is the ratio of their speeds ?",
        "Rationale": "in same time , they cover 110 km & 90 km respectively so ratio of their speed = 110 : 90 = 11 : 9 answer : a",
        "options": "a ) 11 : 9 , b ) 11 : 2 , c ) 91 : 9 , d ) 11 : 1 , e ) 11 : 5",
        "correct": "a",
        "annotated_formula": "inverse(divide(subtract(200, 110), 110))",
        "linear_formula": "subtract(n2,n3)|divide(#0,n3)|inverse(#1)",
        "category": "physics"
    },
    {
        "Problem": "the set s consists of 5 numbers : { 1 , 2,3 , 4,5 } . if all possible subsets including the null set are created and one subset is chosen at random , what is the probability that the subset has 4 or 5 as its largest number ?",
        "Rationale": "\"the set s has 2 ^ 5 = 32 subsets . the number 5 is in half of these subsets . thus 5 is the largest number in 16 subsets of s . of the remaining 16 subsets , 4 is an element in 8 of them . thus 4 is the largest number in 8 subsets of s . the probability that 4 or 5 is the largest number is 24 / 32 = 3 / 4 . the answer is c .\"",
        "options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 5 / 8 , e ) 11 / 16",
        "correct": "c",
        "annotated_formula": "divide(multiply(5, 4), power(const_2, 5))",
        "linear_formula": "multiply(n4,n5)|power(const_2,n0)|divide(#0,#1)|",
        "category": "probability"
    },
    {
        "Problem": "two men are going along a track rail in the opposite direction . one goods train crossed the first person in 20 sec . after 10 min the train crossed the other person who is coming in opposite direction in 18 sec . after the train has passed , when the two persons will meet ?",
        "Rationale": "explanation : let us consider that speed of train , first man and second man are respectively t , f and s . according to first given condition goods train crossed the first person moving in same direction in 20 sec . so length of the will be 20 ( t - f ) similarly train crossed the second man in 18 sec . so length of the train will be 18 ( t + s ) on comparing these two equations , we get 20 ( t - f ) = 18 ( t + s ) = > 2 t = 20 f + 18 s = > t = 10 f + 9 s now it is given that after 10 min the train crossed the other person who is coming in opposite direction . so , if we consider this way of train as l then the next equation will be l = 600 t ( here 600 is used for 10 minutes ) finally as asked in the question the time required to meet the two man after the train has passed will be given by time = ( l - 600 f ) / ( f + s ) { here 600 f is used for the distance traveled by first man in 10 minutes } = > = ( 600 t - 600 f ) / ( f + s ) = > = [ 600 ( 10 f + 9 s ) - 600 f ] / ( f + s ) = > = 600 ( 10 f + 9 s - f ) / ( f + s ) = 600 * 9 ( f + s ) / ( f + s ) = > = 600 * 9 seconds = > = 600 * 9 / 60 min = > = 90 minutes hence ( b ) is the correct answer . answer : b",
        "options": "a ) 95 minutes , b ) 90 minutes , c ) 88 minutes , d ) 95 minutes , e ) none of these",
        "correct": "b",
        "annotated_formula": "divide(multiply(multiply(const_60, 10), divide(18, const_2)), const_60)",
        "linear_formula": "divide(n2,const_2)|multiply(n1,const_60)|multiply(#0,#1)|divide(#2,const_60)",
        "category": "physics"
    },
    {
        "Problem": "what is the smallest positive integer x such that 108 x is the cube of a positive integer ?",
        "Rationale": "\"given 108 x is a perfect cube so we will take 216 = 6 * 6 * 6 108 x = 216 x = 216 / 108 = 2 correct option is a\"",
        "options": "a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 7",
        "correct": "a",
        "annotated_formula": "add(const_3, const_4)",
        "linear_formula": "add(const_3,const_4)|",
        "category": "geometry"
    },
    {
        "Problem": "8 men can dig a pit in 20 days . if a man works half as much again a s a boy , then 4 men and 9 boys can dig a similar pit in :",
        "Rationale": "explanation : 1 work done = 8 \u00d7 20 1 man = 3 / 2 boys 1 boy = 2 / 3 men then , 9 boys = 9 \u00d7 2 / 3 men = 6 men then , 4 men + 9 boys = 10 men then , 8 \u00d7 20 = 10 \u00d7 ? days ? days = 8 \u00d7 20 / 10 = 16 days . answer : option d",
        "options": "a ) 10 days , b ) 12 days , c ) 15 days , d ) 16 days , e ) 20 days",
        "correct": "d",
        "annotated_formula": "divide(multiply(multiply(8, divide(const_3, const_2)), 20), add(multiply(4, divide(const_3, const_2)), 9))",
        "linear_formula": "divide(const_3,const_2)|multiply(n0,#0)|multiply(n2,#0)|add(n3,#2)|multiply(n1,#1)|divide(#4,#3)",
        "category": "physics"
    },
    {
        "Problem": "in a throw of dice what is the probability of ge \u00e6 \u00ab ng number greater than 4",
        "Rationale": "\"explanation : number greater than 4 is 5 & 6 , so only 2 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 2 / 6 = 1 / 3 answer : b\"",
        "options": "a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these",
        "correct": "b",
        "annotated_formula": "divide(subtract(const_6, 4), const_6)",
        "linear_formula": "subtract(const_6,n0)|divide(#0,const_6)|",
        "category": "probability"
    },
    {
        "Problem": "two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team q . if team a ' s average speed was 5 mph greater than team q ' s , what was team q ' s average mph ?",
        "Rationale": "\"this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team q ' s speed was s . then team q ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team q . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team q is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct .\"",
        "options": "a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25",
        "correct": "d",
        "annotated_formula": "divide(divide(300, 5), 3)",
        "linear_formula": "divide(n0,n2)|divide(#0,n1)|",
        "category": "physics"
    },
    {
        "Problem": "a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is ?",
        "Rationale": "let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d",
        "options": "a ) 17 , b ) 98 , c ) 88 , d ) 85 , e ) 83",
        "correct": "d",
        "annotated_formula": "divide(subtract(multiply(5, subtract(12.4, 0.4)), 26), 0.4)",
        "linear_formula": "subtract(n0,n3)|multiply(n1,#0)|subtract(#1,n2)|divide(#2,n3)",
        "category": "general"
    },
    {
        "Problem": "out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many t applicants majored in political science and had a gpa higher than 3.0 ?",
        "Rationale": "\"total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) t = 20 - 15 = 5 answer : a\"",
        "options": "a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35",
        "correct": "a",
        "annotated_formula": "subtract(20, subtract(40, add(10, 15)))",
        "linear_formula": "add(n1,n4)|subtract(n0,#0)|subtract(n2,#1)|",
        "category": "general"
    },
    {
        "Problem": "a man invests some money partly in 9 % stock at 96 and partly in 12 % stock at 120 . to obtain equal dividends from both , he must invest the money in the ratio ?",
        "Rationale": "\"for an income of re . 1 in 9 % stock at 96 , investment = rs . 96 / 9 = rs . 32 / 3 for an income re . 1 in 12 % stock at 120 , investment = rs . 120 / 12 = rs . 10 . ratio of investments = ( 32 / 3 ) : 10 = 32 : 30 = 16 : 15 answer : c\"",
        "options": "a ) 16 : 18 , b ) 16 : 13 , c ) 16 : 15 , d ) 16 : 12 , e ) 16 : 11",
        "correct": "c",
        "annotated_formula": "divide(multiply(96, const_2), multiply(120, const_3))",
        "linear_formula": "multiply(n1,const_2)|multiply(n3,const_3)|divide(#0,#1)|",
        "category": "other"
    },
    {
        "Problem": "in an electric circuit , two resistors with resistances 3 ohm and 5 ohm are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is the value ?",
        "Rationale": "the wording is a bit confusing , though basically we are told that 1 / r = 1 / 3 + 1 / 5 , from which it follows that r = 15 / 8 ohms . answer : b .",
        "options": "['a ) 15 ohms', 'b ) 15 / 8 ohms', 'c ) 1 / 8 ohms', 'd ) 8 / 15 ohms', 'e ) 8 ohms']",
        "correct": "b",
        "annotated_formula": "divide(multiply(3, 5), add(3, 5))",
        "linear_formula": "add(n0,n1)|multiply(n0,n1)|divide(#1,#0)",
        "category": "geometry"
    },
    {
        "Problem": "a and b enterd into a partnership investing rs . 16000 and rs . 12000 respectively . after 3 months , a withdrew rs . 5000 while b invested rs . 5000 more . after 3 more months . c joins the business with a capital of rs . 21000 . the share of b exceeds that of c , out of a total profit of rs . 26400 after one year by",
        "Rationale": "solution a : b : c = ( 16000 x 3 + 11000 x 9 ) : ( 12000 x 3 + 17000 x 9 ) : ( 21000 x 6 ) = 147 : 180 : 126 = 7 : 9 : 6 . \u2234 difference of b and c \u2019 s shares = rs . ( 26400 x 9 / 22 - 26400 x 6 / 22 ) = rs . 3600 . answer c",
        "options": "a ) rs . 2400 , b ) rs . 3000 , c ) rs . 3600 , d ) rs . 4800 , e ) none of these",
        "correct": "c",
        "annotated_formula": "subtract(multiply(26400, divide(add(multiply(12000, 3), multiply(add(12000, 5000), subtract(const_12, 3))), add(add(add(multiply(16000, 3), multiply(subtract(16000, 5000), subtract(const_12, 3))), add(multiply(12000, 3), multiply(add(12000, 5000), subtract(const_12, 3)))), multiply(21000, subtract(subtract(const_12, 3), 3))))), multiply(26400, divide(multiply(21000, subtract(subtract(const_12, 3), 3)), add(add(add(multiply(16000, 3), multiply(subtract(16000, 5000), subtract(const_12, 3))), add(multiply(12000, 3), multiply(add(12000, 5000), subtract(const_12, 3)))), multiply(21000, subtract(subtract(const_12, 3), 3))))))",
        "linear_formula": "add(n1,n3)|multiply(n1,n2)|multiply(n0,n2)|subtract(const_12,n2)|subtract(n0,n3)|multiply(#0,#3)|multiply(#4,#3)|subtract(#3,n2)|add(#1,#5)|add(#2,#6)|multiply(n6,#7)|add(#9,#8)|add(#11,#10)|divide(#8,#12)|divide(#10,#12)|multiply(n7,#13)|multiply(n7,#14)|subtract(#15,#16)",
        "category": "general"
    },
    {
        "Problem": "if the cost price of 20 articles is equal to the selling price of 25 articles , what is the % profit or % loss made by the merchant ?",
        "Rationale": "\"explanatory answer approach : assume a value for cost price . compute cost price and selling price for the same number of articles let the cost price of 1 article be $ 1 . therefore , cost price of 20 articles = 20 * 1 = $ 20 the selling price of 25 articles = cost price of 20 articles = $ 20 . let us find the cost price of 25 articles . cost price of 25 articles = 25 * 1 = $ 25 . therefore , profit made on sale of 25 articles = selling price of 25 articles - cost price of 25 articles = 20 - 25 = - $ 5 . because the profit is in the negative , the merchant has made a loss of $ 5 . therefore , % loss = loss / cost price \u2217 100 % loss = 5 / 25 \u2217 100 = 20 % loss . choice c\"",
        "options": "a ) 25 % loss , b ) 25 % profit , c ) 20 % loss , d ) 20 % profit , e ) 5 % profit",
        "correct": "c",
        "annotated_formula": "multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 25), 20)), divide(multiply(const_100, 25), 20)))",
        "linear_formula": "multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)|divide(#2,#1)|multiply(#3,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "the ratio of two quantities is 10 : 7 . if each of the quantities is increased by 2 , their ratio changes to 15 : 11 then the greatest number is ?",
        "Rationale": "\"let the numbers be 10 x and 7 x then 10 x + 2 / 7 x + 2 = 15 / 11 110 x + 22 = 105 x + 30 5 x = 8 x = 1.6 greatest number = 10 * 1.6 = 16 answer is d\"",
        "options": "a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 20",
        "correct": "d",
        "annotated_formula": "divide(add(10, 2), add(7, 2))",
        "linear_formula": "add(n0,n2)|add(n1,n2)|divide(#0,#1)|",
        "category": "general"
    },
    {
        "Problem": "average between two sets of numbers is closer to the set with morenumbers ?",
        "Rationale": "\"if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86.3 \u00d7 90 + 2 \u00d7 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b\"",
        "options": "a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95",
        "correct": "b",
        "annotated_formula": "multiply(multiply(const_2, const_4), const_10)",
        "linear_formula": "multiply(const_2,const_4)|multiply(#0,const_10)|",
        "category": "general"
    },
    {
        "Problem": "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 b are ? a . 15 b . 18",
        "Rationale": "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 6 / 25 * 75 = 18 answer : b",
        "options": "a ) 22 , b ) 18 , c ) 99 , d ) 77 , e ) 24",
        "correct": "b",
        "annotated_formula": "multiply(divide(75, add(add(multiply(divide(2, 3), divide(2, 5)), divide(2, 5)), const_1)), divide(2, 5))",
        "linear_formula": "divide(n0,n3)|divide(n0,n1)|multiply(#1,#0)|add(#0,#2)|add(#3,const_1)|divide(n4,#4)|multiply(#5,#0)",
        "category": "general"
    },
    {
        "Problem": "in the class of 50 students , 30 speak tamil and 40 speak telugu . what is the lowest possible number of students who speak both the languages ?",
        "Rationale": "let the student who speaks tamil - x let the student who speaks telugu - y as ( xuy ) - ( xny ) = total 30 + 40 - ( xny ) = 50 = 20 c )",
        "options": "a ) a ) 8 , b ) b ) 10 , c ) c ) 20 , d ) d ) 30 , e ) e ) 32",
        "correct": "c",
        "annotated_formula": "subtract(add(40, 30), 50)",
        "linear_formula": "add(n1,n2)|subtract(#0,n0)",
        "category": "other"
    },
    {
        "Problem": "if twice of a number divided by 3 d gives 20 as the remainder , and 5 times of the same number gives 32 as the remainder . what will be the value of d ?",
        "Rationale": "remainder in second case is , 32 . so , 3 d > = 33 . so , minimum value of d should 11 . if number = 28 . double of number = 56 and take d = 12 so 56 / 36 remainder = 20 . now 5 times of number = 140 . so 140 / 36 remainder = 32 . that is , 3 d = 36 satisfy the conditions . so d = 12 . answer : b",
        "options": "a ) 11 , b ) 12 , c ) 15 , d ) 14 , e ) 18",
        "correct": "b",
        "annotated_formula": "subtract(multiply(divide(32, 5), const_2), divide(const_1, const_4))",
        "linear_formula": "divide(n3,n2)|divide(const_1,const_4)|multiply(#0,const_2)|subtract(#2,#1)",
        "category": "general"
    },
    {
        "Problem": "3 people candidates contested an election and they received 1136 , 7636 and 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?",
        "Rationale": "tot no of votes = ( 1136 + 7636 + 11628 ) = 20400 req = > ( 11628 / 20400 * 100 ) = > 57 % answer c",
        "options": "a ) 40 % , b ) 45 % , c ) 57 % , d ) 58 % , e ) 60 %",
        "correct": "c",
        "annotated_formula": "multiply(divide(11628, add(add(1136, 7636), 11628)), const_100)",
        "linear_formula": "add(n1,n2)|add(n3,#0)|divide(n3,#1)|multiply(#2,const_100)",
        "category": "general"
    },
    {
        "Problem": "a and b started a business jointly a ' s investment was thrice the investment of b and the period of his investment was two times the period of investment of b . if b received rs . 4000 as profit , then their total profit is",
        "Rationale": "\"explanation : suppose b invested rs . x for y months . then , a invested rs . 3 x for 2 y months . so , a : b = ( 3 x * 2 y ) : ( x * y ) = 6 xy : xy = 6 : 1 . b ' s profit : total profit = 1 : 7 . let the total profit be rs . x then , 1 / 7 = 4000 / x or x = 28000 . answer : b ) 28000\"",
        "options": "a ) 23477 , b ) 28000 , c ) 28877 , d ) 1987 , e ) 1771",
        "correct": "b",
        "annotated_formula": "multiply(add(multiply(const_2, const_3), const_1), 4000)",
        "linear_formula": "multiply(const_2,const_3)|add(#0,const_1)|multiply(n0,#1)|",
        "category": "general"
    },
    {
        "Problem": "the general hospital is comprised of , 3 / 5 pediatricians , 1 / 4 surgeons , and the rest are gp doctors . if 1 / 4 of the surgeons are heart surgeons , and the hospital doubles the number of gp doctors , what proportion of the hospital are now heart surgeons ?",
        "Rationale": "ped = 3 / 5 = 12 / 20 sur = 1 / 4 = 4 / 20 gp = 1 - ( 12 / 20 + 4 / 20 ) = 1 - 16 / 20 = 4 / 20 hsur = ( 1 / 4 ) ( 4 / 20 ) = 1 / 20 if gp doubled = > ( 2 ) ( 4 ) = 8 ; then , total = 12 + 4 + 8 = 24 , and 1 is hsur = > proportion = 1 / 24 . answer : d",
        "options": "a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 24 , e ) 1 / 25",
        "correct": "d",
        "annotated_formula": "divide(subtract(3, add(1, 1)), add(multiply(4, 5), 4))",
        "linear_formula": "add(n2,n2)|multiply(n1,n3)|add(n3,#1)|subtract(n0,#0)|divide(#3,#2)",
        "category": "general"
    },
    {
        "Problem": "45 pupil , out of them 12 in debate only and 22 in singing only . then how many in both ?",
        "Rationale": "the intersection for two = 45 - 12 - 22 = 11 play both games . answer : c",
        "options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13",
        "correct": "c",
        "annotated_formula": "subtract(45, add(12, 22))",
        "linear_formula": "add(n1,n2)|subtract(n0,#0)",
        "category": "other"
    },
    {
        "Problem": "of the 75 cars on a car lot , 45 have air - conditioning , 35 have power steering , and 12 have both air - conditioning and power steering . how many of the cars on the lot have neither air - conditioning nor power steering ?",
        "Rationale": "\"total - neither = all air conditioning + all power steering - both or 75 - neither = 45 + 35 - 12 = 68 . = > neither = 7 , hence a . answer : a\"",
        "options": "a ) 7 , b ) 8 , c ) 10 , d ) 15 , e ) 18",
        "correct": "a",
        "annotated_formula": "subtract(75, subtract(add(45, 35), 12))",
        "linear_formula": "add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)|",
        "category": "other"
    },
    {
        "Problem": "a corporation 5 times its annual bonus to 10 of its employees . what percent of the employees \u2019 new bonus is the increase ?",
        "Rationale": "let the annual bonus be x . a corporation triples its annual bonus . so new bonus = 5 x . increase = 5 x - x = 4 x the increase is what percent of the employees \u2019 new bonus = ( 4 x / 5 x ) * 100 = 80 % hence c .",
        "options": "a ) 12 % , b ) 18 % , c ) 80 % , d ) 20 % , e ) 15 %",
        "correct": "c",
        "annotated_formula": "multiply(divide(subtract(5, const_1), 5), const_100)",
        "linear_formula": "subtract(n0,const_1)|divide(#0,n0)|multiply(#1,const_100)",
        "category": "general"
    },
    {
        "Problem": "a certain tests consists 8 sections with 25 questions , numbered from 1 to 25 , in each section . if a student answered all of the even - numbered questions correctly and 3 / 4 of the odd - numbered questions correctly , what was the total number of questions he answered correctly ? a . 150 b . 172 c . 174 d . 175 e . 176",
        "Rationale": "each set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions . 96 + 3 / 4 \u00e2 \u02c6 \u2014 104 = 96 + 78 = 17496 + 3 / 4 \u00e2 \u02c6 \u2014 104 = 96 + 78 = 174 answer : a",
        "options": "a ) 174 , b ) 150 , c ) 180 , d ) 175 , e ) 190",
        "correct": "a",
        "annotated_formula": "add(divide(multiply(8, 25), const_2), multiply(divide(multiply(8, 25), const_2), divide(3, 4)))",
        "linear_formula": "divide(n4,n5)|multiply(n0,n1)|divide(#1,const_2)|multiply(#2,#0)|add(#2,#3)",
        "category": "general"
    },
    {
        "Problem": "a no . when divided by 221 gives a remainder 43 , what remainder will beobtained by dividing the same number 19 ?",
        "Rationale": "\"221 + 43 = 264 / 17 = 9 ( remainder ) c\"",
        "options": "a ) 3 , b ) 6 , c ) 9 , d ) 11 , e ) 15",
        "correct": "c",
        "annotated_formula": "divide(add(221, 43), 19)",
        "linear_formula": "add(n0,n1)|divide(#0,n2)|",
        "category": "general"
    },
    {
        "Problem": "tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg",
        "Rationale": "\"explanation : since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . cost of 1 kg tea of 1 st kind cost of 1 kg tea of 2 nd kind x - 153 / 22.50 = 1 = > x - 153 = 22.50 = > x = 175.50 . hence , price of the third variety = rs . 175.50 per kg . answer : c ) rs . 175.50\"",
        "options": "a ) 175.59 , b ) 175.5 , c ) 175.57 , d ) 175.52 , e ) 175.11",
        "correct": "c",
        "annotated_formula": "divide(subtract(multiply(153, add(add(1, 1), 2)), add(126, 126)), 2)",
        "linear_formula": "add(n1,n1)|add(n0,n0)|add(n3,#0)|multiply(n4,#2)|subtract(#3,#1)|divide(#4,n3)|",
        "category": "other"
    },
    {
        "Problem": "today jim is twice as old as fred , and sam is 4 years younger than fred . 4 years ago jim was 8 times as old as sam . how old is jim now ?",
        "Rationale": "we ' re asked how old jim is now . we ' re given three facts to work with : 1 ) today , jim is twice as old as fred 2 ) today , sam is 4 years younger than fred 3 ) four years ago , jim was 8 times as old as sam . let ' s test answer d : 20 if . . . . jim is currently 20 years old . . . . fred is 10 years old sam is 6 years old 4 years ago , jim was 16 and sam was 2 , so jim was 8 times sam ' s age . this is an exact match for what we were told , so this must be the answer . d",
        "options": "a ) 8 , b ) 12 , c ) 16 , d ) 20 , e ) 24",
        "correct": "d",
        "annotated_formula": "multiply(divide(subtract(multiply(8, 8), 4), subtract(8, const_2)), const_2)",
        "linear_formula": "multiply(n2,n2)|subtract(n2,const_2)|subtract(#0,n0)|divide(#2,#1)|multiply(#3,const_2)",
        "category": "general"
    },
    {
        "Problem": "a store sells 2 kinds of jelly beans mixes ( a and b ) both made up of red and yellow beans . if b contains 20 % more red beans than a but 10 % fewer yellow beans . and jar a contains twice as many red beans as yellow by what percent is the number of beans in jar b larger than the number in jar a",
        "Rationale": "a has 10 yellows 20 reds total = 30 so b has 1.2 x 20 = 24 reds 0.9 x 10 = 9 yellows total = 33 difference = 3 / 30 = 10 % answer : e",
        "options": "a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10",
        "correct": "e",
        "annotated_formula": "multiply(subtract(divide(add(add(const_100, 20), subtract(const_100, 10)), const_100), const_2), const_100)",
        "linear_formula": "add(n1,const_100)|subtract(const_100,n2)|add(#0,#1)|divide(#2,const_100)|subtract(#3,const_2)|multiply(#4,const_100)",
        "category": "general"
    },
    {
        "Problem": "find the greatest common factor ( gfc ) of 24 , 40 and 60 .",
        "Rationale": "we first write the prime factorization of each given number 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 = 23 * cubic * \u00d7 3 40 = 2 \u00d7 2 \u00d7 2 \u00d7 5 = 23 * cubic * \u00d7 5 60 = 2 \u00d7 2 \u00d7 3 \u00d7 5 = 22 * square * \u00d7 3 \u00d7 5 gfc = 22 * square * = 4 corect answer is d ) 4",
        "options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5",
        "correct": "d",
        "annotated_formula": "gcd(gcd(24, 40), 60)",
        "linear_formula": "gcd(n0,n1)|gcd(n2,#0)",
        "category": "other"
    },
    {
        "Problem": "1394 x 1394",
        "Rationale": "\"1394 x 1394 = ( 1394 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 6 ) 2 - ( 6 x 1400 x 6 ) = 1943236 . answer : option a\"",
        "options": "a ) 1943236 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these",
        "correct": "a",
        "annotated_formula": "multiply(divide(1394, 1394), const_100)",
        "linear_formula": "divide(n0,n1)|multiply(#0,const_100)|",
        "category": "general"
    },
    {
        "Problem": "a and b start a business jointly . a invests rs 16000 for 8 month and b remains in the business for 4 months . out of total profit , b claims 2 / 7 of the profit . how much money was contributed by b ?",
        "Rationale": "b claims 2 / 7 of the profit a claims remaining 5 / 7 of the profit = > a : b = 5 / 7 : 2 / 7 = 5 : 2 let the money contributed by b = b then a : b = 16000 \u00d7 8 : b \u00d7 4 therefore , 16000 \u00d7 8 : b \u00d7 4 = 5 : 2 16000 \u00d7 8 \u00d7 2 = b \u00d7 4 \u00d7 5 16000 \u00d7 2 \u00d7 2 = b \u00d7 5 3200 \u00d7 2 \u00d7 2 = b b = 12800 answer is a .",
        "options": "a ) 12800 , b ) 13000 , c ) 11500 , d ) 12500 , e ) 12000",
        "correct": "a",
        "annotated_formula": "divide(multiply(multiply(16000, 8), divide(8, 4)), multiply(4, add(4, const_1)))",
        "linear_formula": "add(n2,const_1)|divide(n1,n2)|multiply(n0,n1)|multiply(#1,#2)|multiply(n2,#0)|divide(#3,#4)",
        "category": "general"
    },
    {
        "Problem": "the second of two numbers is two less than 3 times the first . find the numbers if there sum is 82 .",
        "Rationale": "we are looking for two numbers . # 1 - x # 2 - 3 x \u00e2 \u20ac \u201c 2 the sum is 82 . # 1 + # 2 = 82 substituting x + 3 x \u00e2 \u20ac \u201c 2 = 82 4 x \u00e2 \u20ac \u201c 2 = 82 4 x = 84 x = 21 the first number is 21 , the second number is two less than three times 21 or 61 . correct answer e",
        "options": "a ) 7 - 19 , b ) 8 - 20 , c ) 10 - 16 , d ) 15 - 9 , e ) 21 - 61",
        "correct": "e",
        "annotated_formula": "subtract(divide(add(82, const_2), add(3, const_1)), subtract(multiply(3, divide(add(82, const_2), add(3, const_1))), const_2))",
        "linear_formula": "add(n1,const_2)|add(n0,const_1)|divide(#0,#1)|multiply(n0,#2)|subtract(#3,const_2)|subtract(#2,#4)",
        "category": "general"
    },
    {
        "Problem": "in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ?",
        "Rationale": "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a",
        "options": "['a ) 45', 'b ) 50', 'c ) 55', 'd ) 60', 'e ) 63']",
        "correct": "a",
        "annotated_formula": "multiply(multiply(30, const_2), divide(3, const_4))",
        "linear_formula": "divide(n3,const_4)|multiply(n2,const_2)|multiply(#0,#1)",
        "category": "other"
    },
    {
        "Problem": "a train moves with a speed of 108 kmph . its speed in metres per second is :",
        "Rationale": "\"explanation : 108 kmph = ( 108 x 5 / 18 ) m / sec = 30 m / s . answer : c\"",
        "options": "a ) 10.8 , b ) 18 , c ) 30 , d ) 38.8 , e ) none of these",
        "correct": "c",
        "annotated_formula": "multiply(108, const_0_2778)",
        "linear_formula": "multiply(n0,const_0_2778)|",
        "category": "physics"
    },
    {
        "Problem": "by how much is 50 % of 250 greater than 25 % of 400 .",
        "Rationale": "\"( 50 / 100 ) * 250 \u00e2 \u20ac \u201c ( 25 / 100 ) * 400 125 - 100 = 25 answer : b\"",
        "options": "a ) 25 , b ) 26 , c ) 29 , d ) 39 , e ) 26",
        "correct": "b",
        "annotated_formula": "subtract(multiply(250, divide(50, const_100)), multiply(divide(25, const_100), 400))",
        "linear_formula": "divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|multiply(n3,#1)|subtract(#2,#3)|",
        "category": "gain"
    },
    {
        "Problem": "in a rectangular coordinate system , if a line passes through the points ( - 15 , - 18 ) , ( 1522 ) and ( x , 2 ) then what is the value of x ?",
        "Rationale": "the slope of the line m is rise / run = 22 - ( - 18 ) / 15 - ( - 15 ) = 4 / 3 4 / 3 = 22 - 2 / 15 - x 60 - 4 x = 66 - 6 x = 0 the answer is c .",
        "options": "a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2",
        "correct": "c",
        "annotated_formula": "add(1522, 18)",
        "linear_formula": "add(n1,n2)",
        "category": "general"
    },
    {
        "Problem": "running at the same constant rate , 100 identical machines can produce a total of 500 coffee bar per minute . at this rate , how many bottles could 20 such machines produce in 2 minutes ?",
        "Rationale": "let ' s take the approach that uses the answer choices to eliminate wasted time . 500 / 100 = 5 coffee bar per minute per machine . 20 machines = 100 per minute . 2 minutes worth = 200 coffe bar . looking at the answers it is clear . . . we can only choose ( d ) the correct answer is d .",
        "options": "a ) 110 , b ) 220 , c ) 330 , d ) 200 , e ) 789",
        "correct": "d",
        "annotated_formula": "multiply(multiply(divide(500, 100), 2), 20)",
        "linear_formula": "divide(n1,n0)|multiply(n3,#0)|multiply(n2,#1)",
        "category": "gain"
    },
    {
        "Problem": "two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of b crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of b ?",
        "Rationale": "lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( b ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e",
        "options": "a ) b / 2 , b ) b , c ) 3 b / 2 , d ) 2 b , e ) 3 b",
        "correct": "e",
        "annotated_formula": "multiply(const_2, add(const_1, divide(const_1, const_2)))",
        "linear_formula": "divide(const_1,const_2)|add(#0,const_1)|multiply(#1,const_2)",
        "category": "general"
    },
    {
        "Problem": "a certain number of badges were distributed among a class of students . the student who got 1 / 6 th of the total number of badges actually got 5 times the average number of badges the others got ! how many students were there in the class ?",
        "Rationale": "detailed solution let the total students be ( n + 1 ) let total badges be x let the average of \u2018 n \u2019 students be y the student who got 1 / 6 th of x = 5 y or y = x / 30 therefore \u2018 n \u2019 students got 1 / 30 th of total share each or n * x / 30 + 1 * x / 6 = x nx + 5 x = 30 x n + 5 = 30 or n = 25 total = n + 1 = 26 correct answer : b",
        "options": "a ) 30 , b ) 26 , c ) 11 , d ) 31 , e ) 32",
        "correct": "b",
        "annotated_formula": "add(subtract(multiply(6, 5), 5), 1)",
        "linear_formula": "multiply(n1,n2)|subtract(#0,n2)|add(n0,#1)",
        "category": "general"
    },
    {
        "Problem": "tough and tricky questions : work / rate problems . a group of 4 junior lawyers require 7 hours to complete a legal research assignment . how many hours would it take a group of 3 legal assistants to complete the same research assignment assuming that a legal assistant works at two - thirds the rate of a junior lawyer ? source : chili hot gmat",
        "Rationale": "# of people times the # of hours : 4 * 7 = 28 - - > 4 lawyers do 28 worksin 7 hours . 3 * 14 / 3 = 14 - - > 3 assistants do 14 worksin 4 hours so , since the amount of work the assistants do is half the work the lawyers do , the time will be double , soans a",
        "options": "a ) 14 , b ) 10 , c ) 9 , d ) 6 , e ) 5",
        "correct": "a",
        "annotated_formula": "multiply(multiply(divide(const_2, const_3), 3), 7)",
        "linear_formula": "divide(const_2,const_3)|multiply(n2,#0)|multiply(n1,#1)",
        "category": "general"
    },
    {
        "Problem": "the difference of a larger number and a smaller number is 6 . the sum of the larger number and twice the smaller is 15 . what is the larger number ?",
        "Rationale": "let x be the larger number and y be the smaller number . x - y = 6 x + 2 ( y ) = 15 solve by substitution : y = x - 6 x + 2 ( x - 6 ) = 15 x + 2 x - 12 = 15 3 x = 27 x = 9 the larger number is 9 , so answer c is correct .",
        "options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11",
        "correct": "c",
        "annotated_formula": "divide(add(15, multiply(const_2, 6)), add(const_1, const_2))",
        "linear_formula": "add(const_1,const_2)|multiply(n0,const_2)|add(n1,#1)|divide(#2,#0)",
        "category": "general"
    },
    {
        "Problem": "the diameters of two spheres are in the ratio 1 : 2 what is the ratio of their surface area ?",
        "Rationale": "1 : 4 answer : b",
        "options": "['a ) 1 : 0', 'b ) 1 : 4', 'c ) 1 : 6', 'd ) 1 : 2', 'e ) 1 : 1']",
        "correct": "b",
        "annotated_formula": "divide(1, const_4)",
        "linear_formula": "divide(n0,const_4)",
        "category": "geometry"
    },
    {
        "Problem": "there are 3 prizes to be distributed among 10 students . if no students gets more than one prize , then this can be done in ?",
        "Rationale": "explanation : 3 prize among 10 students can be distributed in 10 c 3 ways = 120 ways . answer : d",
        "options": "a ) 10 , b ) 45 , c ) 95 , d ) 120 , e ) none of these",
        "correct": "d",
        "annotated_formula": "add(multiply(10, 3), multiply(subtract(10, const_1), 10))",
        "linear_formula": "multiply(n0,n1)|subtract(n1,const_1)|multiply(n1,#1)|add(#0,#2)",
        "category": "general"
    },
    {
        "Problem": "a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ' s contribution in the capital ?",
        "Rationale": "let b ' s capital be rs . x . { 3500 \\ 12 } / { 7 x } = { 2 } / { 3 } = > x = 9000 . answer : d",
        "options": "a ) rs . 9228 , b ) rs . 9129 , c ) rs . 9120 , d ) rs . 9000 , e ) rs . 1922",
        "correct": "d",
        "annotated_formula": "divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 5), 2))",
        "linear_formula": "multiply(n0,const_12)|subtract(const_12,n1)|multiply(n3,#0)|multiply(n2,#1)|divide(#2,#3)",
        "category": "other"
    },
    {
        "Problem": "how many of the positive factors of 24 are not factors of 27",
        "Rationale": "\"factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 27 - 1 , 3 , 9,27 comparing both , we have 6 factors of 24 which are not factors of 27 - 2,4 , 6,8 , 12,24 answer : b\"",
        "options": "a ) 2 , b ) 6 , c ) 4 , d ) 1 , e ) 5",
        "correct": "b",
        "annotated_formula": "divide(27, 24)",
        "linear_formula": "divide(n1,n0)|",
        "category": "other"
    },
    {
        "Problem": "a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - .",
        "Rationale": "\"drawing two balls of same color from seven green balls can be done in \u2077 c \u2082 ways . similarly from eight white balls two can be drawn in ways . 7 / 15 answer : e\"",
        "options": "a ) 7 / 18 , b ) 7 / 19 , c ) 7 / 11 , d ) 7 / 12 , e ) 7 / 15",
        "correct": "e",
        "annotated_formula": "add(multiply(divide(8, add(7, 8)), divide(subtract(8, const_1), subtract(add(7, 8), const_1))), multiply(divide(7, add(7, 8)), divide(subtract(7, const_1), subtract(add(7, 8), const_1))))",
        "linear_formula": "add(n0,n1)|subtract(n1,const_1)|subtract(n0,const_1)|divide(n1,#0)|divide(n0,#0)|subtract(#0,const_1)|divide(#1,#5)|divide(#2,#5)|multiply(#3,#6)|multiply(#4,#7)|add(#8,#9)|",
        "category": "other"
    },
    {
        "Problem": "a is a working partner and b is a sleeping partner in a business . a puts in 20,000 and b 90,000 . a gets 20 % of the profit for managing the business , and the rest is divided in proportion to their capitals . find the share of b in profit of 11000 .",
        "Rationale": "\"the amount a gets for managing = 20 % of rs . 11000 = 2200 remaining profit = 11000 \u2013 2200 = 8800 this is to be divided in the ratio 2 : 9 . share of b = 9 / 11 of 8800 = 7200 answer b\"",
        "options": "a ) 3500 , b ) 7200 , c ) 6800 , d ) 4800 , e ) none of these",
        "correct": "b",
        "annotated_formula": "add(divide(multiply(subtract(11000, divide(multiply(20, 11000), const_100)), add(const_2, const_3)), add(add(const_2, const_3), add(const_2, const_4))), divide(multiply(20, 11000), const_100))",
        "linear_formula": "add(const_2,const_3)|add(const_2,const_4)|multiply(n2,n3)|add(#0,#1)|divide(#2,const_100)|subtract(n3,#4)|multiply(#0,#5)|divide(#6,#3)|add(#7,#4)|",
        "category": "gain"
    },
    {
        "Problem": "a carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet . if the carpenter were to make a similar sandbox twice as long , twice as wide , and twice as high as the first sandbox , what would be the capacity , in cubic feet , of the second sandbox ?",
        "Rationale": "\"a quick note on doubling . when you double a length you have 2 * l 1 . when you double all lengths of a rectangle you have ( 2 * l 1 ) ( 2 * l 2 ) = a . an increase of 2 ^ 2 or 4 . when you double all lengths of a rectangular prism you have ( 2 * l 1 ) ( 2 * l 2 ) ( 2 * l 3 ) = v . an increase of 2 ^ 3 or 8 . this leads to the basic relationship : line : 2 * original size rectangle : 4 * original size rectangular prism : 8 * original size answer is d\"",
        "options": "a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100",
        "correct": "d",
        "annotated_formula": "multiply(power(const_2, const_3), 10)",
        "linear_formula": "power(const_2,const_3)|multiply(n0,#0)|",
        "category": "geometry"
    },
    {
        "Problem": "when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land twice on heads and twice tails ?",
        "Rationale": "must be twice on heads and twice on tails 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 answer : c",
        "options": "a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 16 , d ) 1 / 32 , e ) 1 / 2",
        "correct": "c",
        "annotated_formula": "divide(const_1, power(const_2, 4))",
        "linear_formula": "power(const_2,n0)|divide(const_1,#0)",
        "category": "general"
    },
    {
        "Problem": "the circumferences of the fore and hind - wheels of a carriage are 2 2 / 5 and 3 3 / 7 meters respectively . a chalk mark is put on the point of contact of each wheel with the ground at any given moment . how far will the carriage have travelled so that their chalk marks may be again on the ground at the same time ?",
        "Rationale": "a little reflection will show that chalk marks will touch the ground together for the first time after the wheels have passed over a distance which is the lcm of 2 2 / 5 metres and 3 3 / 7 metres . lcm of 12 / 5 metres and 24 / 7 metres = 24 metres . answer is e",
        "options": "a ) 18 metres , b ) 16 metres , c ) 38 metres , d ) 42 metres , e ) 24 metres",
        "correct": "e",
        "annotated_formula": "add(multiply(7, 3), 3)",
        "linear_formula": "multiply(n3,n5)|add(n3,#0)",
        "category": "general"
    },
    {
        "Problem": "if 5 ^ 5 \u00d7 5 ^ x = ( 125 ) ^ 4 , then what is the value of x ?",
        "Rationale": "\"5 ^ 5 \u00d7 5 ^ x = ( 125 ) ^ 4 5 ^ ( 5 + x ) = 5 ^ 12 since they have the same base we can just set the exponents equal to each other : ( 5 + x ) = 12 x = 7 ans . e ) 7\"",
        "options": "a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 7",
        "correct": "e",
        "annotated_formula": "divide(subtract(multiply(const_2, 5), 125), const_3)",
        "linear_formula": "multiply(n1,const_2)|subtract(#0,n3)|divide(#1,const_3)|",
        "category": "general"
    },
    {
        "Problem": "machine a produces 100 parts thrice as fast as machine b does . machine b produces 100 parts in 30 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 6 minutes ?",
        "Rationale": "machine b produces 100 part in 30 minutes . machine a produces 100 parts thrice as fast as b , so machine a produces 100 parts in 30 / 3 = 10 minutes . now , machine a produces 100 parts in 10 minutes which is 100 / 10 = 10 parts / minute . 10 parts x a total of 6 minutes = 60 d",
        "options": "a ) 20 , b ) 80 , c ) 40 , d ) 60 , e ) 50",
        "correct": "d",
        "annotated_formula": "multiply(multiply(divide(100, 30), const_3), 6)",
        "linear_formula": "divide(n0,n2)|multiply(#0,const_3)|multiply(n3,#1)",
        "category": "gain"
    },
    {
        "Problem": "a train 150 m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds . the speed of the second train is",
        "Rationale": "given that two trains are of same length i . e . . 150 mtrs first train passes the km stone in 15 seconds . here we have time and distance so speed = 150 / 15 = 10 m / s we need to find out the second train speed . suppose the speed of the 2 nd train is x m / s relative speed of two trains is ( 10 + x ) = = > ( 150 + 150 ) / ( 10 + x ) = 8 = = > ( 300 ) / ( 10 + x ) = 8 = = > 300 = 80 + 8 x = = > 300 - 80 = 8 x = = > 220 = 8 x : - x = 55 / 2 m / s convert m / s into km / ph ( 55 / 2 ) * ( 18 / 5 ) = 99 kmph answer : d",
        "options": "a ) 60 kmph , b ) 66 kmph , c ) 72 kmph , d ) 99 kmph , e ) 89 kmph",
        "correct": "d",
        "annotated_formula": "multiply(divide(subtract(add(150, 150), multiply(divide(150, 15), 8)), 8), const_3_6)",
        "linear_formula": "add(n0,n0)|divide(n0,n1)|multiply(n2,#1)|subtract(#0,#2)|divide(#3,n2)|multiply(#4,const_3_6)",
        "category": "physics"
    },
    {
        "Problem": "what is the max number of rectangular boxes , each measuring 5 inches by 2 inches by 7 inches , that can be packed into a rectangular packing box measuring 15 inches by 20 inches by 35 inches , if all boxes are aligned in the same direction ?",
        "Rationale": "\"the 5 inch side should be aligned to the 15 inch side ( 3 layer ) 2 inch side should be aligned to the 20 inch side . ( 10 layer ) 7 inch side should be aligned to the 35 inch side . ( 5 layer ) maximum number of rectangles = 3 * 10 * 5 = 150 answer is d\"",
        "options": "a ) 200 , b ) 350 , c ) 100 , d ) 150 , e ) 120",
        "correct": "d",
        "annotated_formula": "divide(multiply(multiply(15, 20), 35), multiply(multiply(5, 2), 7))",
        "linear_formula": "multiply(n3,n4)|multiply(n0,n1)|multiply(n5,#0)|multiply(n2,#1)|divide(#2,#3)|",
        "category": "geometry"
    },
    {
        "Problem": "at a wedding reception , 125 guests ate chicken and 75 guests ate beef . if exactly 100 guests ate only one of the two types of meat , how many guests ate both types of meat ?",
        "Rationale": "say x guests ate both types of meat . ( 125 - x ) + ( 75 - x ) = 100 - - > x = 50 . answer : e .",
        "options": "a ) 5 , b ) 100 , c ) 7 , d ) 4 , e ) 50",
        "correct": "e",
        "annotated_formula": "add(subtract(125, 100), subtract(100, 75))",
        "linear_formula": "subtract(n0,n2)|subtract(n2,n1)|add(#0,#1)",
        "category": "other"
    },
    {
        "Problem": "the average temperature for monday , tuesday and wednsday is 36.3 degrees c . the average temperature for tuesday , wednesday and thursday is 36.7 degrees c . if monday \u2019 s temperature recorded as 39 degrees c , find the thursday \u2019 s temperature ?",
        "Rationale": "explanation : mon + tue + wed temperature = 3 x 36.3 = 108.9 tue + wed temperature = 108.9 \u2013 39 = 69.9 tue + wed + thu temperature = 3 x 36.7 = 110.1 so , thursday \u2019 s temperature = 110.1 \u2013 69.9 = 40.2 degrees c answer : c",
        "options": "a ) 60.2 degrees c , b ) 50.2 degrees c , c ) 40.2 degrees c , d ) 70.2 degrees c , e ) none of these",
        "correct": "c",
        "annotated_formula": "subtract(multiply(36.7, const_3), subtract(multiply(36.3, const_3), 39))",
        "linear_formula": "multiply(n1,const_3)|multiply(n0,const_3)|subtract(#1,n2)|subtract(#0,#2)",
        "category": "general"
    },
    {
        "Problem": "a boy goes to his school from his house at a speed of 3 km / hr and returns at a speed of 2 km / hr . if he takes 5 hours in going and coming . the distance between his house and school is :",
        "Rationale": "\"sol . average speed = [ 2 * 3 * 2 / 3 + 2 ] km / hr = 12 / 5 km / hr . distance travelled = [ 12 / 5 * 5 ] km = 12 km . \u2234 distance between house and school = [ 12 / 2 ] km = 6 km . answer c\"",
        "options": "a ) 4.5 km , b ) 5.5 km , c ) 6 km , d ) 7 km , e ) none",
        "correct": "c",
        "annotated_formula": "multiply(divide(5, add(divide(3, 2), const_1)), 3)",
        "linear_formula": "divide(n0,n1)|add(#0,const_1)|divide(n2,#1)|multiply(n0,#2)|",
        "category": "physics"
    },
    {
        "Problem": "how many kilograms of sugar costing rs . 9 per kg must be mixed with 27 kg of sugar costing rs . 7 per kg so that there may be a gain of 10 % by selling the mixture at rs . 9.24 per kg ?",
        "Rationale": "by the rule of alligation : c . p . of 1 kg sugar of 1 st kind c . p . of 1 kg sugar of 2 nd kind { \\ color { blue } \\ therefore } ratio of quantities of 1 st and 2 nd kind = 14 : 6 = 7 : 3 . let x kg of sugar of 1 st kind be mixed with 27 kg of 2 nd kind . then , 7 : 3 = x : 27 or x = ( 7 x 27 / 3 ) = 63 kg . answer : d ) 63 kg",
        "options": "a ) 33 , b ) 39 , c ) 38 , d ) 63 , e ) 01",
        "correct": "d",
        "annotated_formula": "divide(subtract(multiply(27, divide(9.24, add(divide(10, const_100), const_1))), multiply(27, 7)), subtract(9, divide(9.24, add(divide(10, const_100), const_1))))",
        "linear_formula": "divide(n3,const_100)|multiply(n1,n2)|add(#0,const_1)|divide(n4,#2)|multiply(n1,#3)|subtract(n0,#3)|subtract(#4,#1)|divide(#6,#5)",
        "category": "gain"
    },
    {
        "Problem": "the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if saran and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?",
        "Rationale": "if saran 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 combinedno discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) .",
        "options": "a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54",
        "correct": "b",
        "annotated_formula": "divide(subtract(multiply(const_2, multiply(80, 0.02)), multiply(multiply(160, divide(subtract(100, 25), 100)), 0.02)), const_2)",
        "linear_formula": "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)",
        "category": "gain"
    },
    {
        "Problem": "a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ' s contribution in the capital",
        "Rationale": "\"explanation : let b contribution is x . 3500 * 12 / 7 x = 2 / 3 = > 14 x = 126000 = > x = rs 9000 option a\"",
        "options": "a ) rs 9000 , b ) rs 7000 , c ) rs 5000 , d ) rs 4000 , e ) none of these",
        "correct": "a",
        "annotated_formula": "divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 5), 2))",
        "linear_formula": "multiply(n0,const_12)|subtract(const_12,n1)|multiply(n3,#0)|multiply(n2,#1)|divide(#2,#3)|",
        "category": "other"
    },
    {
        "Problem": "a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 10 hours . if both the taps are opened simultaneously then after how much time will the cistern get filled ?",
        "Rationale": "\"net part filled in 1 hour 1 / 5 - 1 / 10 = 1 / 10 the cistern will be filled in 10 hr answer is b\"",
        "options": "a ) 20 hr , b ) 10 hr , c ) 5 hr , d ) 4 hr , e ) 15 hr",
        "correct": "b",
        "annotated_formula": "divide(const_1, subtract(divide(const_1, 5), divide(const_1, 10)))",
        "linear_formula": "divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)|",
        "category": "physics"
    },
    {
        "Problem": "the mall charges 50 cents for the first hour of parking and $ 3 for each additional hour until the customer reaches 4 hours , after that the parking fee is $ 1 per hour . if a certain customer parked his in the mall for 7 hours and 30 minutes , how much is he going to pay ?",
        "Rationale": "charges for 7 hours = ( first hour @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 ) charges for 7 hours = ( 1 @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 ) charges for 7 hours = ( $ 0.50 ) + ( $ 9 ) + ( $ 3.5 ) charges for 7 hours = ( $ 0.50 ) + ( $ 9 ) + ( $ 3.50 ) charges for 7 hours = $ 13 hence correct answer must be ( c )",
        "options": "a ) $ 11.5 . , b ) $ 12 . , c ) $ 13 . , d ) $ 14.5 , e ) $ 15 .",
        "correct": "c",
        "annotated_formula": "add(add(multiply(3, 3), multiply(add(subtract(7, 4), divide(50, const_100)), 1)), divide(50, const_100))",
        "linear_formula": "divide(n0,const_100)|multiply(n1,n1)|subtract(n4,n2)|add(#0,#2)|multiply(n3,#3)|add(#1,#4)|add(#5,#0)",
        "category": "physics"
    },
    {
        "Problem": "the number of students in each section of a school is 24 . after admitting new students , 3 new sections were started . now , the total number of sections is 16 and there are 21 students in each section . the number of new students admitted is :",
        "Rationale": "original number of sections = 16 - 3 = 13 original number of students = 24 x 13 = 312 present number of students = 21 x 16 = 336 number of new students admitted = 336 - 312 = 24 so the answer is option c ) 24 .",
        "options": "a ) 12 , b ) 42 , c ) 24 , d ) 28 , e ) 26",
        "correct": "c",
        "annotated_formula": "subtract(multiply(21, 16), multiply(24, subtract(16, 3)))",
        "linear_formula": "multiply(n2,n3)|subtract(n2,n1)|multiply(n0,#1)|subtract(#0,#2)",
        "category": "physics"
    },
    {
        "Problem": "simplify : 81 x 81 + 68 x 68 - 2 x 81 x 68 .",
        "Rationale": "= ( 81 ) ^ 2 + ( 68 ) ^ 2 \u2013 2 x 81 x 68 = a ^ 2 + b ^ 2 \u2013 2 ab , where a = 81 , b = 68 = ( a - b ) ^ 2 = ( 81 \u2013 68 ) ^ 2 = ( 13 ) ^ 2 = 169 . answer is a .",
        "options": "a ) 169 , b ) 159 , c ) 189 , d ) 179 , e ) 219",
        "correct": "a",
        "annotated_formula": "add(81, 81)",
        "linear_formula": "add(n0,n0)",
        "category": "general"
    },
    {
        "Problem": "a parallelogram has a base that is four time the size of it ' s height . the total area of this parallelogram is 2,304 sq ft . what is the height of the parallelogram ?",
        "Rationale": "4 x * x = 2304 = > x = 24 answer : c",
        "options": "['a ) 19', 'b ) 23', 'c ) 24', 'd ) 16', 'e ) 17']",
        "correct": "c",
        "annotated_formula": "sqrt(divide(add(add(multiply(const_1000, const_2), multiply(const_100, const_3)), const_4), const_4))",
        "linear_formula": "multiply(const_1000,const_2)|multiply(const_100,const_3)|add(#0,#1)|add(#2,const_4)|divide(#3,const_4)|sqrt(#4)",
        "category": "geometry"
    },
    {
        "Problem": "what is the remainder when the number w = 14 ^ 2 * 15 ^ 8 is divided by 5 ?",
        "Rationale": "\"14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus w = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )\"",
        "options": "a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5",
        "correct": "a",
        "annotated_formula": "divide(5, 5)",
        "linear_formula": "divide(n4,n4)|",
        "category": "general"
    },
    {
        "Problem": "the product of two numbers is 2028 and their h . c . f is 13 . the number of such pairs is :",
        "Rationale": "\"let the numbers be 13 a and 13 b . then , 13 a * 13 b = 2028 = > ab = 12 . now , co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) . so , the required numbers are ( 13 * 1 , 13 * 12 ) and ( 13 * 3 , 13 * 4 ) . clearly , there are 2 such pairs . answer : b\"",
        "options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5",
        "correct": "b",
        "annotated_formula": "sqrt(add(power(sqrt(subtract(13, multiply(const_2, 2028))), const_2), multiply(const_4, 2028)))",
        "linear_formula": "multiply(n0,const_4)|multiply(n0,const_2)|subtract(n1,#1)|sqrt(#2)|power(#3,const_2)|add(#0,#4)|sqrt(#5)|",
        "category": "general"
    },
    {
        "Problem": "if the average marks of 3 batches of 55 , 60 and 45 students respectively is 40 , 62 , 58 , then the average marks of all the students is",
        "Rationale": "explanation : ( 55 \u00e3 \u2014 40 ) + ( 60 \u00e3 \u2014 62 ) + ( 45 \u00e3 \u2014 58 ) / 55 + 60 + 45 8530 / 160 = 53.3 option b",
        "options": "a ) 54.48 , b ) 53.31 , c ) 54.6 , d ) 54.58 , e ) none of these",
        "correct": "b",
        "annotated_formula": "divide(add(add(multiply(55, 40), multiply(60, 62)), multiply(40, 58)), add(add(55, 60), 45))",
        "linear_formula": "add(n1,n2)|multiply(n1,n4)|multiply(n2,n5)|multiply(n4,n6)|add(#1,#2)|add(n3,#0)|add(#4,#3)|divide(#6,#5)",
        "category": "general"
    },
    {
        "Problem": "in an election contested by two parties , party d secured 12 % of the total votes more than party r . if party r got 132000 votes , by how many votes did it lose the election ?",
        "Rationale": "explanatory answer let the percentage of the total votes secured by party d be x % then the percentage of total votes secured by party r = ( x - 12 ) % as there are only two parties contesting in the election , the sum total of the votes secured by the two parties should total up to 100 % i . e . , x + x - 12 = 100 2 x - 12 = 100 or 2 x = 112 or x = 56 % . if party d got 56 % of the votes , then party got ( 56 - 12 ) = 44 % of the total votes . 44 % of the total votes = 132,000 i . e . , 44 / 100 * t = 132,000 = > t = 132000 * 100 / 44 = 300,000 votes . the margin by which party r lost the election = 12 % of the total votes = 12 % of 300,000 = 36,000 . the correct choice is ( d )",
        "options": "a ) 240000 , b ) 300000 , c ) 168000 , d ) 36000 , e ) 24,000",
        "correct": "d",
        "annotated_formula": "multiply(divide(132000, divide(subtract(const_100, 12), const_2)), 12)",
        "linear_formula": "subtract(const_100,n0)|divide(#0,const_2)|divide(n1,#1)|multiply(n0,#2)",
        "category": "general"
    },
    {
        "Problem": "a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many e ways can the test be completed if every question is unanswered ?",
        "Rationale": "\"5 choices for each of the 4 questions , thus total e of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c .\"",
        "options": "a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024",
        "correct": "c",
        "annotated_formula": "power(5, 4)",
        "linear_formula": "power(n1,n0)|",
        "category": "general"
    },
    {
        "Problem": "a and b undertake to do a piece of work for $ 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of a ?",
        "Rationale": "c ' s 1 day work = ( 1 / 3 ) - ( 1 / 6 + 1 / 8 ) = 1 / 24 a : b : c = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 a ' s share = 600 * 4 / 8 = $ 300 answer is c",
        "options": "a ) $ 100 , b ) $ 150 , c ) $ 300 , d ) $ 250 , e ) $ 350",
        "correct": "c",
        "annotated_formula": "multiply(divide(multiply(multiply(3, 8), inverse(6)), add(add(multiply(multiply(3, 8), subtract(inverse(3), add(inverse(6), inverse(8)))), multiply(multiply(3, 8), inverse(6))), multiply(multiply(3, 8), inverse(8)))), 600)",
        "linear_formula": "inverse(n1)|inverse(n3)|inverse(n2)|multiply(n2,n3)|add(#0,#2)|multiply(#0,#3)|multiply(#2,#3)|subtract(#1,#4)|multiply(#3,#7)|add(#8,#5)|add(#9,#6)|divide(#5,#10)|multiply(n0,#11)",
        "category": "physics"
    },
    {
        "Problem": "the value of x + x ( xx ) when x = 7",
        "Rationale": "x + x ( xx ) put the value of x = 7 in the above expression we get , 7 + 7 ( 77 ) = 7 + 7 ( 7 \u00e3 \u2014 7 ) = 7 + 7 ( 49 ) = 7 + 343 = 350 the answer is ( a )",
        "options": "a ) a ) 350 , b ) b ) 346 , c ) c ) 358 , d ) d ) 336 , e ) e ) 364",
        "correct": "a",
        "annotated_formula": "add(multiply(7, multiply(7, 7)), 7)",
        "linear_formula": "multiply(n0,n0)|multiply(n0,#0)|add(n0,#1)",
        "category": "general"
    },
    {
        "Problem": "find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm ?",
        "Rationale": "\"let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = \u221a ( 20 ) 2 \u2013 ( 12 ) 2 = \u221a 256 = 16 cm . so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 \u00d7 24 x 32 ) cm 2 = 384 cm 2 hence c\"",
        "options": "a ) 320 cm 2 , b ) 280 cm 2 , c ) 384 cm 2 , d ) 290 cm 2 , e ) 350 cm 2",
        "correct": "c",
        "annotated_formula": "add(multiply(multiply(divide(const_1, const_2), 24), sqrt(subtract(multiply(multiply(20, 20), const_4), multiply(24, 24)))), 24)",
        "linear_formula": "divide(const_1,const_2)|multiply(n0,n0)|multiply(n1,n1)|multiply(n1,#0)|multiply(#1,const_4)|subtract(#4,#2)|sqrt(#5)|multiply(#3,#6)|add(n1,#7)|",
        "category": "geometry"
    },
    {
        "Problem": "you need to print a document of the area 216 sq cm . condition is 3 cm margin is to be left at both top & bottom and 2 cm at the sides . what is the optimized size of your paper ?",
        "Rationale": "let us consider it is a rectangle . so area = 24 * 9 = 216 sq . cm now ( 24 - 3 * 2 ) * ( 9 - 2 * 2 ) = 18 * 5 = 90 sq . cm answer : e",
        "options": "['a ) 60 sq . cm', 'b ) 70 sq . cm', 'c ) 95 sq . cm', 'd ) 80 sq . cm', 'e ) 90 sq . cm']",
        "correct": "e",
        "annotated_formula": "multiply(subtract(divide(216, power(const_3, const_2)), multiply(3, const_2)), subtract(power(const_3, const_2), multiply(2, const_2)))",
        "linear_formula": "multiply(n1,const_2)|multiply(n2,const_2)|power(const_3,const_2)|divide(n0,#2)|subtract(#2,#1)|subtract(#3,#0)|multiply(#5,#4)",
        "category": "other"
    },
    {
        "Problem": "a number , when 35 is subtracted from it , reduces to its 80 percent . what is 4 - fifth of that number ?",
        "Rationale": "explanation : x - 35 = 80 x / 100 = > x = 175 = > 4 x / 5 = 4 x 175 / 5 = 140 . answer d",
        "options": "a ) 130 , b ) 155 , c ) 490 , d ) 140 , e ) 160",
        "correct": "d",
        "annotated_formula": "multiply(divide(4, add(const_4, const_1)), multiply(35, add(const_4, const_1)))",
        "linear_formula": "add(const_1,const_4)|divide(n2,#0)|multiply(n0,#0)|multiply(#1,#2)",
        "category": "general"
    },
    {
        "Problem": "from a pack of 52 cards , two cards are drawn together at random . what is the probability that the one is heart and other two is diamond ?",
        "Rationale": "\"solution let s be the sample space . then , n ( s ) = 52 c 3 = 22100 let e = event of getting 1 face card . n ( e ) = number of ways of choosing 1 face card out of 26 = 13 c 1 * 13 c 2 = 13 * 72 = 936 p ( e ) = n ( e ) / n ( s ) = 936 / 22100 = 234 / 5525 = 234 / 5525 . answer d\"",
        "options": "a ) 238 / 5525 , b ) 176 / 5534 , c ) 253 / 5523 , d ) 234 / 5525 , e ) 1 / 5525",
        "correct": "d",
        "annotated_formula": "divide(multiply(divide(52, const_4), divide(52, const_4)), choose(52, const_2))",
        "linear_formula": "choose(n0,const_2)|divide(n0,const_4)|multiply(#1,#1)|divide(#2,#0)|",
        "category": "probability"
    },
    {
        "Problem": "the sector of a circle has radius of 14 cm and its perimeter 50 cm . find its central angel ?",
        "Rationale": "lte central angle = x perimeter of the sector = length of the arc + 2 ( radius ) 50 = ( x / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) 50 = 88 x / 360 + 28 88 x / 360 = 22 88 x = 7920 x = 90 answer : e",
        "options": "a ) 180 o , b ) 225 o , c ) 270 o , d ) 150 o , e ) 90 o",
        "correct": "e",
        "annotated_formula": "multiply(multiply(const_2, divide(multiply(subtract(14, const_3), const_2), add(const_4, const_3))), 14)",
        "linear_formula": "add(const_3,const_4)|subtract(n0,const_3)|multiply(#1,const_2)|divide(#2,#0)|multiply(#3,const_2)|multiply(n0,#4)",
        "category": "physics"
    },
    {
        "Problem": "a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction q of the sum of the 21 numbers in the list ?",
        "Rationale": "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction q of n to the total would be 4 a / 24 a or 1 / 6 answer b",
        "options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21",
        "correct": "b",
        "annotated_formula": "divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3))",
        "linear_formula": "divide(n2,n1)|multiply(const_1,const_1)|add(n0,#0)|divide(#2,n1)|multiply(#3,const_2)|subtract(#4,n1)|subtract(#5,const_3)|divide(#1,#6)",
        "category": "general"
    },
    {
        "Problem": "the length and breadth of a rectangular courtyard is 75 m and 32 m . find the cost of leveling it at the rate of $ 3 per m 2 . also , find the distance covered by a boy to take 4 rounds of the courtyard .",
        "Rationale": "length of the courtyard = 75 m breadth of the courtyard = 32 m perimeter of the courtyard = 2 ( 75 + 32 ) m = 2 \u00d7 107 m = 214 m distance covered by the boy in taking 4 rounds = 4 \u00d7 perimeter of courtyard = 4 \u00d7 214 = 856 m we know that area of the courtyard = length \u00d7 breadth = 75 \u00d7 32 m 2 = 2400 m 2 for 1 m 2 , the cost of levelling = $ 3 for 2400 m 2 , the cost of levelling = $ 3 \u00d7 2400 = $ 7200 answer : e",
        "options": "a ) 3573 , b ) 3455 , c ) 8600 , d ) 7000 , e ) 7200",
        "correct": "e",
        "annotated_formula": "multiply(3, multiply(75, 32))",
        "linear_formula": "multiply(n0,n1)|multiply(n2,#0)",
        "category": "physics"
    },
    {
        "Problem": "a man and a boy complete a work together in 24 days . if for the last 6 days man alone does the work then it is completed in 26 days . how long the boy will take to complete the work alone ?",
        "Rationale": "explanation : ( man + boy ) \u2019 s 1 day \u2019 s work = 1 / 24 their 20 day \u2019 s work = 1 / 24 \u00d7 20 = 5 / 6 the remaining 1 / 6 work is done by the man in 6 days therefore , the man alone will finish the work in 6 \u00d7 6 days = 36 days man \u2019 s 1 day \u2019 s work = 1 / 36 therefore , boy \u2019 s 1 day \u2019 s work = 1 / 24 \u2013 1 / 36 = 3 \u2013 2 / 72 = 1 / 72 therefore , the boy alone will finish the work in 72 days . answer : option a",
        "options": "a ) 72 days , b ) 20 days , c ) 24 days , d ) 36 days , e ) 34 days",
        "correct": "a",
        "annotated_formula": "add(subtract(26, 6), multiply(26, const_2))",
        "linear_formula": "multiply(n2,const_2)|subtract(n2,n1)|add(#0,#1)",
        "category": "physics"
    },
    {
        "Problem": "mathew is planning a vacation trip to london next year from today for 5 days , he has calculated he would need about $ 3000 for expenses , including a round - trip plane ticket from l . a to london . he nets around $ 1500 monthly in gross income , after all bills are paid , he is left with about $ 350 each month free for whatever he desires . how much money would mathew need to evenly save from his $ 350 to have $ 3000 in his bank within 12 months ?",
        "Rationale": "answer is ( d ) . if mathew is left with about $ 350 after all expenses each month , he would need to divide the total expense budget to london ( $ 3000 ) by 12 months to determine how much he would need to put away every single month to hit his target . $ 3000 / 12 = $ 250 .",
        "options": "a ) $ 240 , b ) $ 350 , c ) $ 217 , d ) $ 250 , e ) $ 340",
        "correct": "d",
        "annotated_formula": "divide(3000, 12)",
        "linear_formula": "divide(n1,n6)",
        "category": "general"
    },
    {
        "Problem": "3 pounds of 05 grass seed contain 1 percent herbicide . a different type of grass seed , 20 , which contains 20 percent herbicide , will be mixed with 3 pounds of 05 grass seed . how much grass seed of type 20 should be added to the 3 pounds of 05 grass seed so that the mixture contains 15 percent herbicide ?",
        "Rationale": "05 grass seed contains 5 % herbicide and its amount is 3 pound 20 grass seed contains 20 % herbicide and its amount is x when these two types of grass seeds are mixed , their average becomes 15 % thus we have 3 ( 1 ) + x ( 20 ) / ( x + 3 ) = 15 3 + 20 x = 15 x + 45 5 x = 42 or x = 8.4 d",
        "options": "a ) 3 , b ) 3.75 , c ) 4.5 , d ) 8.4 , e ) 9",
        "correct": "d",
        "annotated_formula": "divide(subtract(multiply(15, 3), 3), subtract(20, 15))",
        "linear_formula": "multiply(n0,n10)|subtract(n3,n10)|subtract(#0,n0)|divide(#2,#1)",
        "category": "general"
    },
    {
        "Problem": "if f ( f ( n ) ) + f ( n ) = 2 n + 3 and f ( 0 ) = 1 , what is the value of f ( 2012 ) ?",
        "Rationale": "\"put n = 0 then f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 \u21d2 \u21d2 f ( 1 ) + 1 = 3 \u21d2 \u21d2 f ( 1 ) = 2 put n = 1 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 \u21d2 \u21d2 f ( 2 ) + 2 = 5 \u21d2 \u21d2 f ( 2 ) = 3 put n = 2 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 \u21d2 \u21d2 f ( 3 ) + 3 = 7 \u21d2 \u21d2 f ( 3 ) = 4 . . . . . . f ( 2012 ) = 2013 answer : c\"",
        "options": "a ) 222 , b ) 2787 , c ) 2013 , d ) 2778 , e ) 10222",
        "correct": "c",
        "annotated_formula": "add(1, 2012)",
        "linear_formula": "add(n3,n4)|",
        "category": "general"
    },
    {
        "Problem": "a certain barrel , which is a right circular cylinder , is filled to capacity with 60 gallons of oil . the first barrel is poured into a second barrel , also a right circular cylinder , which is empty . the second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel . if all of the oil in the first barrel is poured into the second barrel , how much empty capacity , in gallons , is left in the second barrel ?",
        "Rationale": "radius of first cylinder = r , diameter = 2 r , height = h radius of second cylinder = 2 r , diamter = 2 d and height = 2 h volume of first cylinder = pie ( r ^ 2 ) * h = 60 volume of second cylinder = pie ( 2 r ^ 2 ) 2 h put the value of pie ( r ^ 2 ) * h = 60 in the second cylinder , volume = pie ( r ^ 2 ) * 4 * 2 = 60 * 8 = 480 gallons empty capacity = 420 gallons answer d",
        "options": "['a ) there is no empty capacity', 'b ) 100 gallons', 'c ) 300 gallons', 'd ) 420 gallons', 'e ) 840 gallons']",
        "correct": "d",
        "annotated_formula": "subtract(multiply(60, power(const_2, const_3)), 60)",
        "linear_formula": "power(const_2,const_3)|multiply(n0,#0)|subtract(#1,n0)",
        "category": "geometry"
    },
    {
        "Problem": "concentrated apples juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches . the tubes are packed into wooden boxes , each with dimensions of 11 inches by 10 inches by 31 inches . how many tubes of concentrated apples juice , at the most , can fit into 3 wooden boxes ?",
        "Rationale": "concentrated apples juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way now , diameter of each tube = 5 inches therefore , 4 * 2 can be put in each wooden box in 3 boxes 3 * 4 * 2 can be accommodated = 24 = a",
        "options": "a ) 24 . , b ) 28 . , c ) 36 . , d ) 42 . , e ) 48 .",
        "correct": "a",
        "annotated_formula": "subtract(divide(multiply(multiply(multiply(11, 10), 31), 3), multiply(multiply(divide(multiply(add(const_10, const_1), const_2), add(const_3, const_4)), power(2.5, const_2)), 15)), 10)",
        "linear_formula": "add(const_1,const_10)|add(const_3,const_4)|multiply(n2,n3)|power(n0,const_2)|multiply(n4,#2)|multiply(#0,const_2)|divide(#5,#1)|multiply(n5,#4)|multiply(#6,#3)|multiply(n1,#8)|divide(#7,#9)|subtract(#10,n3)",
        "category": "gain"
    },
    {
        "Problem": "if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly twice in 2 consecutive flips ?",
        "Rationale": "\"total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 = 4 ways for 2 h hh , thus probability is = p ( hh ) = 1 / 4 = . 25 answer : c\"",
        "options": "a ) 0.125 , b ) 0.225 , c ) 0.25 , d ) 0.5 , e ) 0.666",
        "correct": "c",
        "annotated_formula": "multiply(power(divide(const_1, const_2), 2), 2)",
        "linear_formula": "divide(const_1,const_2)|power(#0,n0)|multiply(n0,#1)|",
        "category": "general"
    },
    {
        "Problem": "in a 100 member association consisting of men and women , exactly 10 % of men and exactly 20 % women are homeowners . what is the maximum number of members who are homeowners ?",
        "Rationale": "\"solution simple out of 100 10 % are male i . e 10 and 20 % are female i . e 20 , so total homeowner is 30 . now min number homeowner is 10 and max is 30 so question ask us to find maximum and 29 has maximum value among all option . so ans is 29 . ans : a\"",
        "options": "a ) 29 , b ) 27 , c ) 25 , d ) 23 , e ) 21",
        "correct": "a",
        "annotated_formula": "add(multiply(multiply(divide(20, const_100), 10), multiply(divide(20, const_100), 10)), divide(subtract(100, 10), 10))",
        "linear_formula": "divide(n2,const_100)|subtract(n0,n1)|divide(#1,n1)|multiply(n1,#0)|multiply(#3,#3)|add(#2,#4)|",
        "category": "gain"
    },
    {
        "Problem": "in the coordinate plane , a circle centered on point ( - 3 , 4 ) passes through point ( 1 , 1 ) . what is the area of the circle ?",
        "Rationale": "\"r ^ 2 = ( - 3 - 1 ) ^ 2 + ( 4 - 1 ) ^ 2 = 16 + 9 = 25 area of circle = \u03c0 r ^ 2 = 25 \u03c0 answer : c\"",
        "options": "a ) 9 \u03c0 , b ) 18 \u03c0 , c ) 25 \u03c0 , d ) 37 \u03c0 , e ) 41 \u03c0",
        "correct": "c",
        "annotated_formula": "circle_area(sqrt(add(power(subtract(3, 1), const_2), power(add(1, 4), const_2))))",
        "linear_formula": "add(n1,n2)|subtract(n0,n2)|power(#1,const_2)|power(#0,const_2)|add(#2,#3)|sqrt(#4)|circle_area(#5)|",
        "category": "geometry"
    },
    {
        "Problem": "1 , 3,5 , 7,9 , . . 50 find term of sequnce",
        "Rationale": "\"this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n \u2212 1 ) l ) sn = 12 n ( 2 a + ( n \u2212 1 ) l ) s 50 = 12 \u00d7 50 \u00d7 ( 2 \u00d7 1 + ( 50 \u2212 1 ) \u00d7 2 ) s 50 = 12 \u00d7 50 \u00d7 ( 2 \u00d7 1 + ( 50 \u2212 1 ) \u00d7 2 ) = 25 \u00d7 ( 2 + 49 \u00d7 2 ) = 25 \u00d7 ( 2 + 49 \u00d7 2 ) = 25 \u00d7 ( 2 + 98 ) = 25 \u00d7 ( 2 + 98 ) = 2500 = 2500 . e\"",
        "options": "a ) 1230 , b ) 1300 , c ) 1500 , d ) 1679 , e ) 2500",
        "correct": "e",
        "annotated_formula": "subtract(negate(50), multiply(subtract(3,5, 7,9), divide(subtract(3,5, 7,9), subtract(1, 3,5))))",
        "linear_formula": "negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)|",
        "category": "general"
    },
    {
        "Problem": "if the arithmetic mean of seventy 5 numbers is calculated , it is 35 . if each number is increased by 5 , then mean of new number is ?",
        "Rationale": "a . m . of 75 numbers = 35 sum of 75 numbers = 75 * 35 = 2625 total increase = 75 * 5 = 375 increased sum = 2625 + 375 = 3000 increased average = 3000 / 75 = 40 . answer : b",
        "options": "a ) 87 , b ) 40 , c ) 37 , d ) 28 , e ) 26",
        "correct": "b",
        "annotated_formula": "add(35, 5)",
        "linear_formula": "add(n0,n1)",
        "category": "general"
    },
    {
        "Problem": "a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts 6 hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?",
        "Rationale": "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 6 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 6 + t ) = 40 * t t = 18 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 18 / 60 = 12 hrs time taken by a = 6 + t = 6 + 18 = 24 hrs time taken by k = 12 hrs so k starts 24 - 12 = 12 hrs after a . ( answer d )",
        "options": "a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 12 , e ) e ) 5",
        "correct": "d",
        "annotated_formula": "divide(multiply(30, add(6, divide(multiply(30, 6), subtract(40, 30)))), 60)",
        "linear_formula": "multiply(n0,n3)|subtract(n1,n0)|divide(#0,#1)|add(n3,#2)|multiply(n0,#3)|divide(#4,n2)",
        "category": "physics"
    },
    {
        "Problem": "in an exam 80 % of the boys and 40 % of the girls passed . the number of girls who passed is 120 , which is 2 / 3 rd of the number of boys who failed . what is the total number of students who appeared for the exam ?",
        "Rationale": "let the number of boys = x , number of girls = y 40 y / 100 = 120 y = 300 120 = 2 / 3 * 20 x / 100 = 2 x / 15 x = 900 total = x + y = 300 + 900 = 1200 answer : a",
        "options": "a ) 1200 , b ) 380 , c ) 3800 , d ) 2180 , e ) 3180",
        "correct": "a",
        "annotated_formula": "add(divide(120, multiply(divide(subtract(const_100, 80), const_100), divide(2, 3))), divide(120, divide(40, const_100)))",
        "linear_formula": "divide(n3,n4)|divide(n1,const_100)|subtract(const_100,n0)|divide(#2,const_100)|divide(n2,#1)|multiply(#3,#0)|divide(n2,#5)|add(#6,#4)",
        "category": "general"
    },
    {
        "Problem": "the marked price of a book is 20 % more than the cost price . after the book is sold , the vendor realizes that he had wrongly raised the cost price by a margin of 25 % . if the marked price of the book is rs . 30 , what is the original cost price of the book ?",
        "Rationale": "let the incorrect cost price be c 1 and let the original cost price be c 2 . marked price of book is rs . 30 . it is 20 % more than c 1 . therefore , ( 120 / 100 ) x c 1 = 30 or c 1 = 25 . c 1 is more than c 2 margin of 25 % . or c 1 = ( 125 / 100 ) c 2 therefore , c 2 = ( 100 / 125 ) x 25 = rs 20 answer : d",
        "options": "a ) rs . 30 , b ) rs . 25 , c ) rs . 45 , d ) rs . 20 , e ) rs . 10",
        "correct": "d",
        "annotated_formula": "divide(divide(30, add(const_1, divide(20, const_100))), add(const_1, divide(25, const_100)))",
        "linear_formula": "divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|add(#1,const_1)|divide(n2,#2)|divide(#4,#3)",
        "category": "gain"
    },
    {
        "Problem": "if annual decrease in the population of a town is 5 % and the present number of people is 40000 what will the population be in 2 years ?",
        "Rationale": "population in 2 years = 40000 ( 1 - 5 / 100 ) ^ 2 = 40000 * 19 * 19 / 20 * 20 = 36100 answer is c",
        "options": "a ) 24560 , b ) 26450 , c ) 36100 , d ) 38920 , e ) 45200",
        "correct": "c",
        "annotated_formula": "multiply(power(divide(subtract(const_100, 5), const_100), 2), 40000)",
        "linear_formula": "subtract(const_100,n0)|divide(#0,const_100)|power(#1,n2)|multiply(n1,#2)",
        "category": "gain"
    },
    {
        "Problem": "find the missing figures : ? % of 25 = 20125",
        "Rationale": "\"let x % of 25 = 2.125 . then , ( x / 100 ) * 25 = 2.125 x = ( 2.125 * 4 ) = 8.5 . answer is e .\"",
        "options": "a ) 4.5 , b ) 6.5 , c ) 2.5 , d ) 7.5 , e ) 8.5",
        "correct": "e",
        "annotated_formula": "divide(20125, divide(25, const_100))",
        "linear_formula": "divide(n0,const_100)|divide(n1,#0)|",
        "category": "gain"
    },
    {
        "Problem": "two trains leave the train station at the same time . one train , on the blue line , heads east - while the other , on the red line , heads west . if the train on the blue line averages 40 km / hr and the other train averages 40 km / hr - how long will it take for the trains to be 100 km apart ?",
        "Rationale": "each train is averaging 40 km / hour in an opposite direction . after 1 hour , they will be 80 km apart , and after 1.25 hours , they will be 100 km apart . ( 80 * 1.25 = 100 ) answer is d",
        "options": "a ) 2 hours , b ) 2.25 hours , c ) 1 hour , d ) 1.25 hours , e ) not enough information",
        "correct": "d",
        "annotated_formula": "divide(divide(100, const_2), 40)",
        "linear_formula": "divide(n2,const_2)|divide(#0,n0)",
        "category": "general"
    },
    {
        "Problem": "what is the greatest possible length which can be used to measure exactly the lengths 10 m 50 cm , 14 m 55 cm and 50 cm ?",
        "Rationale": "\"required length = hcf of 1050 cm , 1455 cm , 50 cm = 5 cm answer is e\"",
        "options": "a ) 20 cm , b ) 24 cm , c ) 30 cm , d ) 10 cm , e ) 5 cm",
        "correct": "e",
        "annotated_formula": "multiply(55, const_4)",
        "linear_formula": "multiply(n3,const_4)|",
        "category": "physics"
    },
    {
        "Problem": "at scratch and dents rent - a - car , it costs $ 34.95 a day plus $ 0.23 per mile to rent a car . at rent - a - lemon , the charge is $ 25.00 a day plus $ 1.31 per mile . if you need to rent a car for 3 days , how many miles ( to nearest tenth ) must you drive for a car from both agencies to cost the same amount ?",
        "Rationale": "for sad : saddaily = $ 34.95 / day sadmile = $ 0.23 / mile for ral : raldaily = $ 25.00 / day ralmile = $ 1.31 / mile we want the raltotal = sadtotal , so we get ( raldaily * days ) + ( ralmile * miles ) = ( saddaily * days ) + ( sadmile * miles ) = > miles = ( ( saddaily * days ) - ( raldaily * days ) ) / ( ralmiles - sadmiles ) = ( ( saddaily - raldaily ) * days ) / ( ralmiles - sadmiles ) miles = ( ( $ 34.95 * 3 ) - ( $ 25.00 * 3 ) ) / ( $ 1.31 - $ 0.23 ) = 27.6 miles c . 27.6 miles",
        "options": "a ) 25.7 miles , b ) 26.2 miles , c ) 27.6 miles , d ) 27.9 miles , e ) 29.9 miles",
        "correct": "c",
        "annotated_formula": "divide(subtract(multiply(34.95, 3), multiply(25, 3)), subtract(1.31, 0.23))",
        "linear_formula": "multiply(n0,n4)|multiply(n2,n4)|subtract(n3,n1)|subtract(#0,#1)|divide(#3,#2)",
        "category": "general"
    },
    {
        "Problem": "average of 15 results is 43 . if the average of first 7 results is 41 and average of last 7 results is 45 then find the eighth result ?",
        "Rationale": "option ' c '",
        "options": "a ) 41 , b ) 39 , c ) 43 , d ) 45 , e ) 47",
        "correct": "c",
        "annotated_formula": "subtract(multiply(15, 43), add(multiply(7, 41), multiply(7, 45)))",
        "linear_formula": "multiply(n0,n1)|multiply(n2,n3)|multiply(n2,n5)|add(#1,#2)|subtract(#0,#3)",
        "category": "general"
    },
    {
        "Problem": "a sprinter starts running on a circular path of radius r metres . her average speed ( in metres / minute ) is \u03c0 r during the first 30 seconds , \u03c0 r / 2 during next one minute , \u03c0 r / 4 during next 2 minutes , \u03c0 r / 8 during next 4 minutes , and so on . what is the ratio of the time taken for the nth round to that for the previous round ?",
        "Rationale": "explanation : there is more than 1 way to approach the solution ; however , i will detail the easiest way to go about it here . we want to find the ratio of time taken for nth round : time taken for ( n - 1 ) th round it will be same as finding the ratio of time taken for 2 nd round : time taken for 1 st round . 1 round = circumference of the circle = 2 \u03c0 r 1 st round : speed = \u03c0 r for 30 seconds . so , total distance travelled = \u03c0 r / 2 . speed = \u03c0 r / 2 for 1 minute . so , total distance travelled = \u03c0 r / 2 . speed = \u03c0 r / 4 for 2 minutes . so , total distance travelled = \u03c0 r / 2 . speed = \u03c0 r / 8 for 4 minutes . so , total distance travelled = \u03c0 r / 2 . so , for a distance of 2 \u03c0 r , time taken is 7.5 minutes . 2 nd round : speed = \u03c0 r / 16 for 8 minutes . so , total distance travelled = \u03c0 r / 2 . speed = \u03c0 r / 32 for 16 minutes . so , total distance travelled = \u03c0 r / 2 . speed = \u03c0 r / 64 for 32 minutes . so , total distance travelled = \u03c0 r / 2 . speed = \u03c0 r / 128 for 64 minutes . so , total distance travelled = \u03c0 r / 2 . so , for a distance of 2 \u03c0 r , time taken is 120 minutes . ratio is 120 : 7.5 = 16 : 1 . answer : c",
        "options": "a ) 4 , b ) 8 , c ) 16 , d ) 32 , e ) 36",
        "correct": "c",
        "annotated_formula": "power(2, 4)",
        "linear_formula": "power(n1,n2)",
        "category": "physics"
    },
    {
        "Problem": "the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 \u03c0 \u00b7 r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams t ?",
        "Rationale": "\"weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )\"",
        "options": "a ) t = 16 , b ) t = 32 , c ) t = 64 , d ) 128 , e ) 512",
        "correct": "b",
        "annotated_formula": "multiply(8, 4)",
        "linear_formula": "multiply(n0,n3)|",
        "category": "geometry"
    },
    {
        "Problem": "an enterprising businessman earns an income of re 5 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 10 th day of business , he earns an income of :",
        "Rationale": "2 nd day he earns = 3 ( 2 \u2013 5 ) 3 rd day he earns = 3 ( 3 \u2013 5 ) on 20 th day he earns 3 ( 20 - 5 ) = 45 rupees answer : d",
        "options": "a ) 21 , b ) 22 , c ) 20 , d ) 45 , e ) 30",
        "correct": "d",
        "annotated_formula": "subtract(multiply(5, 10), 5)",
        "linear_formula": "multiply(n0,n1)|subtract(#0,n0)",
        "category": "physics"
    },
    {
        "Problem": "two goods train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively find the time taken by the slower train to pass the driver of the faster one .",
        "Rationale": "solution relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec total distance covered = ( 500 + 500 ) m = 1000 m required time = ( 1000 x 6 / 125 ) sec = 48 sec answer c",
        "options": "a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) none",
        "correct": "c",
        "annotated_formula": "multiply(divide(500, divide(multiply(const_1000, add(45, 30)), const_3600)), const_2)",
        "linear_formula": "add(n1,n2)|multiply(#0,const_1000)|divide(#1,const_3600)|divide(n0,#2)|multiply(#3,const_2)",
        "category": "physics"
    },
    {
        "Problem": "if x / 5 + 9 / x = 14 / 5 , what are the values of 3 x - 7 ?",
        "Rationale": "i got the same thing b is the answer 8 or 20",
        "options": "a ) 8 and 9 , b ) 8 and 20 , c ) 17 and 21 , d ) 12 and 29 , e ) 17 and 29",
        "correct": "b",
        "annotated_formula": "add(multiply(subtract(add(subtract(9, 5), sqrt(subtract(power(subtract(9, 5), 5), multiply(5, multiply(9, 5))))), 3), const_10), subtract(subtract(subtract(9, 5), sqrt(subtract(power(subtract(9, 5), 5), multiply(5, multiply(9, 5))))), 3))",
        "linear_formula": "multiply(n0,n1)|subtract(n1,n0)|multiply(n0,#0)|power(#1,n3)|subtract(#3,#2)|sqrt(#4)|add(#5,#1)|subtract(#1,#5)|subtract(#6,n4)|subtract(#7,n4)|multiply(#8,const_10)|add(#10,#9)|",
        "category": "general"
    },
    {
        "Problem": "a closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity . when the tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . when the tank is placed on its side on level ground , what is the height , in feet , of the surface of the water above the ground ?",
        "Rationale": "36 pie cubic feet of water and its filled to half tank ' s capacity . . . volume of tank = 72 pie cubic feet height of tank = 4 * 2 = 8 feet ( since tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . ) 72 pie = pie * r 2 * 8 r 2 = 9 r = 3 feet answer : d",
        "options": "['a ) 0 feet', 'b ) 1 feet', 'c ) 2 feet', 'd ) 3 feet', 'e ) 4 feet']",
        "correct": "d",
        "annotated_formula": "sqrt(divide(divide(multiply(36, const_pi), 4), const_pi))",
        "linear_formula": "multiply(n0,const_pi)|divide(#0,n1)|divide(#1,const_pi)|sqrt(#2)",
        "category": "geometry"
    },
    {
        "Problem": "the ratio of two speeds of two trains is 3 to 4 . if each of the trains slows its speed 5 km / hr , what will be the ratio of these two train speeds ?",
        "Rationale": "3 / 4 = 3 x / 4 x we need to find out ( 3 x + 5 ) / ( 4 x + 5 ) off course we can not solve this to arrive at any rational number hence e .",
        "options": "a ) 3 / 4 , b ) 8 / 9 , c ) 18 / 19 , d ) 23 / 24 , e ) it can not be determined from the information given",
        "correct": "e",
        "annotated_formula": "divide(3, 4)",
        "linear_formula": "divide(n0,n1)",
        "category": "other"
    },
    {
        "Problem": "a box contain the number of balls which is as much times greater than 15 as much times lesser than 240 . the no . of ball is ?",
        "Rationale": "\"answer let the number be x . x / 15 = 240 / x x ^ 2 = 240 * 15 = 3600 x = \u221a 3600 = 60 correct option : c\"",
        "options": "a ) 48 , b ) 75 , c ) 60 , d ) 54 , e ) 45",
        "correct": "c",
        "annotated_formula": "divide(add(240, 15), const_2)",
        "linear_formula": "add(n0,n1)|divide(#0,const_2)|",
        "category": "general"
    },
    {
        "Problem": "5 years ago , the average age of a and b was 15 years . average age of a , b and c today is 20 years . how old will c be after 14 years ?",
        "Rationale": "explanation : ( a + b ) , five years ago = ( 15 * 2 ) = 30 years . ( a + b ) , now = ( 30 + 5 * 2 ) years = 40 years . ( a + b + c ) , now = ( 20 x 3 ) years = 60 years . c , now = ( 60 - 40 ) years = 20 years . c , after 14 years = ( 20 + 14 ) years = 34 years . answer : b",
        "options": "a ) 30 , b ) 34 , c ) 40 , d ) 50 , e ) 60",
        "correct": "b",
        "annotated_formula": "add(subtract(multiply(20, const_3), add(add(multiply(15, const_2), 5), 5)), 14)",
        "linear_formula": "multiply(n2,const_3)|multiply(n1,const_2)|add(n0,#1)|add(n0,#2)|subtract(#0,#3)|add(n3,#4)",
        "category": "general"
    },
    {
        "Problem": "one fourth of a solution that was 10 % sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?",
        "Rationale": "\"say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.16 - - > x = 0.34 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.16 - - > x = 0.34 . answer : a .\"",
        "options": "a ) 34 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 %",
        "correct": "a",
        "annotated_formula": "multiply(divide(subtract(multiply(const_100, divide(16, const_100)), multiply(subtract(const_100, multiply(divide(const_1, const_4), const_100)), divide(10, const_100))), multiply(divide(const_1, const_4), const_100)), const_100)",
        "linear_formula": "divide(n1,const_100)|divide(n0,const_100)|divide(const_1,const_4)|multiply(#0,const_100)|multiply(#2,const_100)|subtract(const_100,#4)|multiply(#1,#5)|subtract(#3,#6)|divide(#7,#4)|multiply(#8,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a black card and the second card is a king or queen ?",
        "Rationale": "\"p ( black card ) = 1 / 2 p ( king or queen ) = 2 / 13 p ( black card then a king / queen ) = 1 / 2 * 2 / 13 = 1 / 13 the answer is b .\"",
        "options": "a ) 1 / 52 , b ) 1 / 13 , c ) 1 / 26 , d ) 3 / 26 , e ) 17 / 26",
        "correct": "b",
        "annotated_formula": "multiply(divide(add(multiply(const_3, const_4), const_1), const_52), divide(const_2, const_52))",
        "linear_formula": "divide(const_2,const_52)|multiply(const_3,const_4)|add(#1,const_1)|divide(#2,const_52)|multiply(#3,#0)|",
        "category": "probability"
    },
    {
        "Problem": "a man whose bowling average is 22.2 , takes 4 wickets for 36 runs and thereby decreases his average by 1.2 . the number of wickets , taken by him before his last match is :",
        "Rationale": "\"explanation : let the number of wickets taken before the last match is x . then , ( 22.2 x + 36 ) / ( x + 4 ) = 21 = > 22.2 x + 36 = 21 x + 84 = > 1.2 x = 48 = > x = 48 / 1.2 = 40 answer : d\"",
        "options": "a ) 14 , b ) 22 , c ) 38 , d ) 40 , e ) 50",
        "correct": "d",
        "annotated_formula": "divide(subtract(multiply(floor(22.2), 4), 36), subtract(22.2, floor(22.2)))",
        "linear_formula": "floor(n0)|multiply(n1,#0)|subtract(n0,#0)|subtract(#1,n2)|divide(#3,#2)|",
        "category": "general"
    },
    {
        "Problem": "susan drives from city a to city b . after two hours of driving she noticed that she covered 80 km and calculated that , if she continued driving at the same speed , she would end up been 15 minutes late . so she increased her speed by 10 km / hr and she arrived at city b 36 minutes earlier than she planned . find the distance between cities a and b .",
        "Rationale": "let xx be the distance between a and b . since susan covered 80 km in 2 hours , her speed was v = 802 = 40 v = 802 = 40 km / hr . if she continued at the same speed she would be 1515 minutes late , i . e . the planned time on the road is x 40 \u2212 1560 x 40 \u2212 1560 hr . the rest of the distance is ( x \u2212 80 ) ( x \u2212 80 ) km . v = 40 + 10 = 50 v = 40 + 10 = 50 km / hr . so , she covered the distance between a and b in 2 + x \u2212 80502 + x \u2212 8050 hr , and it was 36 min less than planned . therefore , the planned time was 2 + x \u2212 8050 + 36602 + x \u2212 8050 + 3660 . when we equalize the expressions for the scheduled time , we get the equation : x 40 \u2212 1560 = 2 + x \u2212 8050 + 3660 x 40 \u2212 1560 = 2 + x \u2212 8050 + 3660 x \u2212 1040 = 100 + x \u2212 80 + 3050 x \u2212 1040 = 100 + x \u2212 80 + 3050 x \u2212 104 = x + 505 x \u2212 104 = x + 505 5 x \u2212 50 = 4 x + 2005 x \u2212 50 = 4 x + 200 x = 250 x = 250 so , the distance between cities a and b is 250 km . answer : c",
        "options": "a ) 223 , b ) 376 , c ) 250 , d ) 378 , e ) 271",
        "correct": "c",
        "annotated_formula": "add(divide(subtract(add(subtract(divide(36, const_60), divide(80, add(divide(80, const_2), 10))), const_2), divide(15, const_60)), subtract(divide(const_1, divide(80, const_2)), divide(const_1, add(divide(80, const_2), 10)))), const_100)",
        "linear_formula": "divide(n3,const_60)|divide(n0,const_2)|divide(n1,const_60)|add(n2,#1)|divide(const_1,#1)|divide(n0,#3)|divide(const_1,#3)|subtract(#0,#5)|subtract(#4,#6)|add(#7,const_2)|subtract(#9,#2)|divide(#10,#8)|add(#11,const_100)",
        "category": "physics"
    },
    {
        "Problem": "what is the product of all the possible values of x if x ^ 2 + 5 x + 6 ?",
        "Rationale": "explanation : = > y = x ^ 2 + 5 x + 6 = > y = ( x + 2 ) ( x + 3 ) = > x = - 2 , x = - 3 product x = ( - 2 ) ( - 3 ) = 6 answer option 6 answer : d",
        "options": "a ) 12 , b ) 18 , c ) 15 , d ) 6 , e ) 9",
        "correct": "d",
        "annotated_formula": "divide(6, const_1)",
        "linear_formula": "divide(n2,const_1)",
        "category": "general"
    },
    {
        "Problem": "mr . das decided to walk down the escalator of a mall . he found that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stair she would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom , find out the height of the stair way insteps ?",
        "Rationale": "here when he step down 26 steps he has 30 seconds for remaining steps . if he step down 34 stairs he has only 18 sec . 30 - 18 = 12 12 secs for 8 steps . . 18 secs for 12 steps . 12 + 34 = 46 so ans is 46 . . answer : b",
        "options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9",
        "correct": "b",
        "annotated_formula": "subtract(add(multiply(divide(subtract(34, 26), subtract(30, 18)), 30), 26), multiply(const_4, const_10))",
        "linear_formula": "multiply(const_10,const_4)|subtract(n2,n0)|subtract(n1,n3)|divide(#1,#2)|multiply(n1,#3)|add(n0,#4)|subtract(#5,#0)",
        "category": "physics"
    },
    {
        "Problem": "a man has $ 480 in the denominations of one - dollar , 5 - dollar notes and 10 - dollar . the number of dollars of each denomination is equal . what is the total number of dollar that he has ?",
        "Rationale": "c $ 90 let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 .",
        "options": "a ) 50 , b ) 60 , c ) 90 , d ) 48 , e ) 67",
        "correct": "c",
        "annotated_formula": "add(divide(multiply(480, 10), const_60), 10)",
        "linear_formula": "multiply(n0,n2)|divide(#0,const_60)|add(n2,#1)",
        "category": "general"
    },
    {
        "Problem": "a , b and c can do a work in 7 , 14 and 21 days respectively . they completed the work and got rs . 242 . what is the share of c ?",
        "Rationale": "\"the ratio of their working rates = 1 / 7 : 1 / 14 : 1 / 21 = 6 : 3 : 2 . since , they work together , the share of c = 2 / 11 * 242 = rs . 44 \\ answer : b\"",
        "options": "a ) 33 , b ) 44 , c ) 55 , d ) 77 , e ) 99",
        "correct": "b",
        "annotated_formula": "multiply(242, divide(inverse(14), add(inverse(21), add(inverse(7), inverse(14)))))",
        "linear_formula": "inverse(n1)|inverse(n0)|inverse(n2)|add(#1,#0)|add(#3,#2)|divide(#0,#4)|multiply(n3,#5)|",
        "category": "physics"
    },
    {
        "Problem": "kavi spends 50 % of his monthly salary on food and saves 80 % of the remaining amount . if his monthly salary is rs . 19000 , how much money does he save every month ?",
        "Rationale": "explanation : kavi ' s monthly income = rs . 19,000 he spends 50 % on food . the total money spent on food = 50 / 100 * 19000 = rs . 9500 now , his monthly remaining income = rs . 19000 \u2013 rs . 9500 = rs . 9500 out of rs . 9500 , he saves 40 % . amount saved = 40 / 100 * 9500 = rs . 3800 answer : d",
        "options": "a ) rs . 2000 , b ) rs . 600 , c ) rs . 8000 , d ) rs . 3800 , e ) rs . 1200",
        "correct": "d",
        "annotated_formula": "divide(divide(multiply(divide(multiply(19000, 50), const_100), 80), const_100), const_2)",
        "linear_formula": "multiply(n0,n2)|divide(#0,const_100)|multiply(n1,#1)|divide(#2,const_100)|divide(#3,const_2)",
        "category": "gain"
    },
    {
        "Problem": "a boatman selling a boat along river flow . if he sell boat in steal water at 3 m / sec and flow of river is 2 m / sec . how much time he will take to sell 100 m .",
        "Rationale": "net speed = 3 + 2 = 5 m / sec distance = 100 m time = 100 / 5 = 20 sec answer d",
        "options": "a ) 30 , b ) 10 , c ) 15 , d ) 20 , e ) 25",
        "correct": "d",
        "annotated_formula": "divide(100, add(3, 2))",
        "linear_formula": "add(n0,n1)|divide(n2,#0)",
        "category": "physics"
    },
    {
        "Problem": "evaluate 35 % of 450 + 45 % of 350",
        "Rationale": "\"explanation : = ( 35 / 100 ) * 450 + ( 45 / 100 ) * 350 = 315 option c\"",
        "options": "a ) 232 , b ) 242 , c ) 315 , d ) 262 , e ) 272",
        "correct": "c",
        "annotated_formula": "divide(35, divide(450, 35))",
        "linear_formula": "divide(n1,n0)|divide(n0,#0)|",
        "category": "gain"
    },
    {
        "Problem": "a bullock cart has to cover a distance of 80 km in 10 hrs . if it covers half of the journey in 3 / 5 th time . what should be its speed to cover the remaining distance in the time left .",
        "Rationale": "a 10 kmph time left = 10 - 3 / 5 * 10 = 4 hr 10 km / h speed = 40 km / 4 hr = 10 kmph",
        "options": "a ) 10 kmph , b ) 20 kmph , c ) 30 kmph , d ) 40 kmph , e ) 50 kmph",
        "correct": "a",
        "annotated_formula": "divide(divide(80, const_2), subtract(10, multiply(divide(10, 5), 3)))",
        "linear_formula": "divide(n0,const_2)|divide(n1,n3)|multiply(n2,#1)|subtract(n1,#2)|divide(#0,#3)",
        "category": "physics"
    },
    {
        "Problem": "a furniture manufacturer has two machines , but only one can be used at a time . machine w is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine w can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?",
        "Rationale": "' approximately ' could actually make such a question ambiguous . not this one though but a similar question with the answer as 9.2 days . you round off 8.89 days as 9 days and everything is fine in this question . what do you do when you get 9.2 days ? do you need 9 days or 10 days ? can you round off 9.2 as 9 even though that is what you do with numbers ? no , because in 9 days your work is not over . you do need 10 days . to finish a work machine w say you need to work full 9 days and a part of the 10 th day . if i ask you how many days do you need to complete the work , will you say 9 or 10 ? you will say 10 even if you do n ' t use the 10 th day fully = d",
        "options": "a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7",
        "correct": "d",
        "annotated_formula": "inverse(add(inverse(divide(multiply(12, const_2), add(const_1, divide(const_1, const_2)))), inverse(divide(multiply(15, const_2), add(const_1, divide(const_1, const_2))))))",
        "linear_formula": "divide(const_1,const_2)|multiply(n0,const_2)|multiply(n1,const_2)|add(#0,const_1)|divide(#1,#3)|divide(#2,#3)|inverse(#4)|inverse(#5)|add(#6,#7)|inverse(#8)",
        "category": "physics"
    },
    {
        "Problem": "what will be the remainder when 17 ^ 200 is divided by 18 ?",
        "Rationale": "\"when n is even , ( x ^ n - a ^ n ) is completely divisible by ( x - a ) . ( 17 ^ 200 - 1 ^ 200 ) is completely divisible by ( 17 + 1 ) , ( 17 ^ 200 - 1 ) is completely divisible by 18 . on dividing 17 ^ 200 by 18 , we get 1 as remainder . answer is d\"",
        "options": "a ) 3 , b ) 8 , c ) 5 , d ) 1 , e ) 7",
        "correct": "d",
        "annotated_formula": "power(17, 17)",
        "linear_formula": "power(n0,n0)|",
        "category": "general"
    },
    {
        "Problem": "a is two years older than b who is twice as old as c . if the total ages of a , b and c be 27 . what is the age of b ?",
        "Rationale": "\"c age x , then b age is 2 x so a age is 2 x + 2 . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 so b is 2 x = 2 ( 5 ) 2 x 5 = 10 answer : b\"",
        "options": "a ) 12 years , b ) 10 years , c ) 8 years , d ) 14 years , e ) 16 years",
        "correct": "b",
        "annotated_formula": "divide(multiply(subtract(27, const_2), const_2), add(const_4, const_1))",
        "linear_formula": "add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)|",
        "category": "general"
    },
    {
        "Problem": "s is a positive integer and multiple of 2 ; p = 4 ^ s , what is the remainder when p is divided by 10 ?",
        "Rationale": "it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the s is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , s must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since s must be an even integer , the units digit of p = 4 ^ s will always be 6 . consequently , the remainder when p = 4 ^ s is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : s = 2 - - > p = 4 ^ z = 16 - - > s / 10 = 1 with a remainder of 6 s = 4 - - > p = 4 ^ z = 256 - - > s / 10 = 25 with a remainder of 6 s = 6 - - > p = 4 ^ z = 4096 - - > s / 10 = 409 with a remainder of 6 s = 8 - - > p = 4 ^ z = 65536 - - > s / 10 = 6553 with a remainder of 6 answer : b .",
        "options": "a ) 10 , b ) 6 , c ) 4 , d ) 0 , e ) it can not be determined",
        "correct": "b",
        "annotated_formula": "reminder(power(4, 2), 10)",
        "linear_formula": "power(n1,n0)|reminder(#0,n2)",
        "category": "general"
    },
    {
        "Problem": "there is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save . auggie was very curious to test this theory . auggie spent all of his money in 5 stores . in each store , he spent rs . 4 more than one - half of what he had when he went in . how many rupees did auggie have when he entered the first store ?",
        "Rationale": "amount left = 0.5 x \u2212 4 for fifth store this is zero . so x = 8 . that means he entered fifth store with 8 . now for fourth store , amount left = 8 so 0.5 x \u2212 4 = 8 \u21d2 x = 24 for third store , amount left = 24 so 12 x \u2212 4 = 24 \u21d2 x = 56 for second store , amount left = 56 so 0.5 x \u2212 4 = 56 \u21d2 x = 120 for first store , amount left = 120 so 0.5 x \u2212 4 = 120 \u21d2 x = 248 so he entered first store with 248 . answer : a",
        "options": "a ) 248 , b ) 120 , c ) 252 , d ) 250 , e ) 350",
        "correct": "a",
        "annotated_formula": "multiply(add(multiply(add(multiply(add(multiply(add(multiply(4, const_2), 4), const_2), 4), const_2), 4), const_2), 4), const_2)",
        "linear_formula": "multiply(n1,const_2)|add(n1,#0)|multiply(#1,const_2)|add(n1,#2)|multiply(#3,const_2)|add(n1,#4)|multiply(#5,const_2)|add(n1,#6)|multiply(#7,const_2)",
        "category": "general"
    },
    {
        "Problem": "3 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire cost of the car , then the share of each of the remaining persons increased by :",
        "Rationale": "original share of 1 person = 1 / 3 new share of 1 person = 1 / 2 increase = ( 1 / 2 - 1 / 3 = 1 / 6 ) therefore , required fraction = ( 1 / 6 ) / ( 1 / 3 ) = ( 1 / 6 ) x ( 3 / 1 ) = 1 / 2 answer is a .",
        "options": "a ) 1 / 2 , b ) 2 / 7 , c ) 3 / 2 , d ) 4 / 7 , e ) none of them",
        "correct": "a",
        "annotated_formula": "divide(subtract(divide(const_1, const_2), divide(const_1, 3)), divide(const_1, 3))",
        "linear_formula": "divide(const_1,const_2)|divide(const_1,n0)|subtract(#0,#1)|divide(#2,#1)",
        "category": "general"
    },
    {
        "Problem": "the sum of the even numbers between 1 and k is 79 * 80 , where k is an odd number , then k =",
        "Rationale": "\"the number of terms in this set would be : n = ( k - 1 ) / 2 ( as k is odd ) last term : k - 1 average would be first term + last term / 2 = ( 2 + k - 1 ) / 2 = ( k + 1 ) / 2 also average : sum / number of terms = 79 * 80 / ( ( k - 1 ) / 2 ) = 158 * 80 / ( k - 1 ) ( k + 1 ) / 2 = 158 * 80 / ( k - 1 ) - - > ( k - 1 ) ( k + 1 ) = 158 * 160 - - > k = 159 answer e .\"",
        "options": "a ) 79 , b ) 80 , c ) 81 , d ) 157 , e ) 159",
        "correct": "e",
        "annotated_formula": "add(multiply(79, const_2), 1)",
        "linear_formula": "multiply(n1,const_2)|add(#0,n0)|",
        "category": "general"
    },
    {
        "Problem": "ele , the circus elephant , is currently 3 times older than lyn , the circus lion . in 15 years from now , lyn the circus lion will be exactly half as old as ele , the circus elephant . how old is ele today ?",
        "Rationale": "ele , the circus elephant , is currently three times older than lyn , the circus lion . ele = 3 * lyn usually , ages are integers so there is a good possibility that the age of ele is 45 ( the only option that is a multiple of 3 ) . then age of lyn would be 15 . in 15 yrs , ele would be 60 and lyn would be 30 - so lyn would be half as old as ele . answer ( d )",
        "options": "a ) 40 , b ) 48 , c ) 43 , d ) 45 , e ) 41",
        "correct": "d",
        "annotated_formula": "multiply(subtract(multiply(const_2, 15), 15), 3)",
        "linear_formula": "multiply(n1,const_2)|subtract(#0,n1)|multiply(n0,#1)",
        "category": "general"
    },
    {
        "Problem": "a right circular cone is exactly fitted inside a cube in such away that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube . if the volume of the cube is 343 cc , what approximately is the volume of the cone ?",
        "Rationale": "edge of the cube = 3 \u221a 334 = 7 cm \u2234 radius of cone = 3.5 cm height = 7 cm volume of cone = 1 \u2044 3 \u03c0 r 2 h 1 \u2044 3 \u03c0 r 2 h = 1 \u2044 3 \u00d7 22 \u2044 7 \u00d7 ( 3.5 ) 2 \u00d7 7 = 1 \u2044 3 \u00d7 22 \u00d7 12.25 \u2248 90 sec answer b",
        "options": "['a ) 80 cc', 'b ) 90 cc', 'c ) 110 cc', 'd ) 105 cc', 'e ) 100 cc']",
        "correct": "b",
        "annotated_formula": "volume_cone(divide(cube_edge_by_volume(343), const_2), cube_edge_by_volume(343))",
        "linear_formula": "cube_edge_by_volume(n0)|divide(#0,const_2)|volume_cone(#1,#0)",
        "category": "geometry"
    },
    {
        "Problem": "the area of a rhombus is equal to the area of a rectangle whose length is 20 cm and the breadth is 10 cm . if one of the diagonals is 32 cm what is the length of other diagonal ?",
        "Rationale": "area of rectangle = 20 x 10 = 200 cm \u00e2 \u00b2 let ' l ' the length of other diagonal = 0.5 x 32 xl = 200 which gives x = 12.5 cm answer : b",
        "options": "['a ) 10', 'b ) 12.5', 'c ) 15', 'd ) 16', 'e ) 17.5']",
        "correct": "b",
        "annotated_formula": "divide(multiply(rectangle_area(20, 10), const_2), 32)",
        "linear_formula": "rectangle_area(n0,n1)|multiply(#0,const_2)|divide(#1,n2)",
        "category": "geometry"
    },
    {
        "Problem": "a line has a slope of 3 / 4 and intersects the point w ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?",
        "Rationale": "\"assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point w of intersection is ( 40,0 ) . a is the correct answer .\"",
        "options": "a ) ( 40,0 ) , b ) ( 30,0 ) , c ) ( 0,40 ) , d ) ( 40,30 ) , e ) ( 0,30 )",
        "correct": "a",
        "annotated_formula": "multiply(negate(divide(subtract(negate(39), multiply(negate(12), divide(3, 4))), divide(3, 4))), const_10)",
        "linear_formula": "divide(n0,n1)|negate(n3)|negate(n2)|multiply(#0,#2)|subtract(#1,#3)|divide(#4,#0)|negate(#5)|multiply(#6,const_10)|",
        "category": "general"
    },
    {
        "Problem": "how long does a truck of 200 m long traveling at 60 kmph takes to cross a bridge of 180 m in length ?",
        "Rationale": "d = 200 + 180 = 380 m s = 60 * 5 / 18 = 50 / 3 t = 380 * 3 / 50 = 22.8 sec answer : c",
        "options": "a ) 36.7 , b ) 26.8 , c ) 22.8 , d ) 21.1 , e ) 16.2",
        "correct": "c",
        "annotated_formula": "divide(add(200, 180), multiply(60, const_0_2778))",
        "linear_formula": "add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)",
        "category": "physics"
    },
    {
        "Problem": "difference between the length & breadth of a rectangle is 10 m . if its perimeter is 206 m , then its area is ?",
        "Rationale": "solving the two equations , we get : l = 30 and b = 40 . area = ( l x b ) = ( 30 x 40 ) m 2 = 1200 m ^ 2 d",
        "options": "['a ) 2400 m ^ 2', 'b ) 1500 m ^ 2', 'c ) 2520 m ^ 2', 'd ) 1200 m ^ 2', 'e ) 2580 m ^ 2']",
        "correct": "d",
        "annotated_formula": "multiply(multiply(10, const_4), multiply(10, const_3))",
        "linear_formula": "multiply(n0,const_4)|multiply(n0,const_3)|multiply(#0,#1)",
        "category": "geometry"
    },
    {
        "Problem": "1370 , 1320 , x , - 180 , - 6430",
        "Rationale": "\"1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a .\"",
        "options": "a ) 1070 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830",
        "correct": "a",
        "annotated_formula": "subtract(negate(6430), multiply(subtract(1320, 180), divide(subtract(1320, 180), subtract(1370, 1320))))",
        "linear_formula": "negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)|",
        "category": "general"
    },
    {
        "Problem": "sum of two numbers is 63 . their difference is 1 / 8 of their sum . their l . c . m is",
        "Rationale": "\"explanation : let the numbers be x and y according to the problem x + y = 63 x - y = 1 / 8 ( x + y ) x - y = 1 / 8 * 63 , x - y = 9 2 x = 72 , x = 36 and y = 27 l . c . m of 36 and 27 is 351 answer : option c\"",
        "options": "a ) 231 , b ) 153 , c ) 351 , d ) 345 , e ) 355",
        "correct": "c",
        "annotated_formula": "subtract(63, divide(subtract(63, divide(1, const_2)), const_2))",
        "linear_formula": "divide(n1,const_2)|subtract(n0,#0)|divide(#1,const_2)|subtract(n0,#2)|",
        "category": "general"
    },
    {
        "Problem": "last year the price range ( per kg ) for 100 varieties of apples in wholesale market was $ 100 . if the prices of each of the 100 varieties increased by 10 percent this year over what it was last year , what is the range of the wholesale prices of the 1000 varieties of apples this year ?",
        "Rationale": "let the lowest price be x . therefore , highest price is x + 100 . now price of each variety is increased by 10 % . therefore the price will remain arranged in the same order as before . or lowest price = 1.1 x and highest = 1.1 * ( x + 100 ) or range = highest - lowest = 1.1 * ( x + 100 ) - 1.1 x = 110 , hence , c",
        "options": "a ) $ 50 , b ) $ 100 , c ) $ 110 , d ) $ 600 , e ) $ 300",
        "correct": "c",
        "annotated_formula": "multiply(100, divide(add(10, const_100), const_100))",
        "linear_formula": "add(n3,const_100)|divide(#0,const_100)|multiply(n0,#1)",
        "category": "general"
    },
    {
        "Problem": "the tailor has a 10 meter long piece of fabric for which to sew a ball room dress . she has to cuts this fabric into strips of 200 centimeters each . how long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ?",
        "Rationale": "the tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes . the answer is d",
        "options": "a ) 150 , b ) 200 , c ) 188 , d ) 245 , e ) 123",
        "correct": "d",
        "annotated_formula": "multiply(subtract(divide(multiply(10, const_1000), 200), const_1), 5)",
        "linear_formula": "multiply(n0,const_1000)|divide(#0,n1)|subtract(#1,const_1)|multiply(n3,#2)",
        "category": "physics"
    },
    {
        "Problem": "each of 3 investments has a 20 % of becoming worthless within a year of purchase , independently of what happens to the other two investments . if simone invests an equal sum k in each of these 3 investments on january 1 , the approximate chance that by the end of the year , she loses no more than 1 / 3 of her original investment is",
        "Rationale": "the problem asks for the approximate chance that no more than 1 / 3 of the original investment is lost . we can apply the \u201c 1 \u2013 x \u201d technique : what \u2019 s the chance that more than 1 / 3 of the original investment is lost ? there are two outcomes we have to separately measure : ( a ) all 3 investments become worthless . ( b ) 2 of the 3 investments become worthless , while 1 doesn \u2019 t . outcome ( a ) : the probability is ( 0.2 ) ( 0.2 ) ( 0.2 ) = 0.008 , or a little less than 1 % . outcome ( b ) : call the investments x , y , and z . the probability that x retains value , while y and z become worthless , is ( 0.8 ) ( 0.2 ) ( 0.2 ) = 0.032 . now , we have to do the same thing for the specific scenarios in which y retains value ( while x and z don \u2019 t ) and in which z retains value ( while x and y don \u2019 t ) . each of those scenarios results in the same math : 0.032 . thus , we can simply multiply 0.032 by 3 to get 0.096 , or a little less than 10 % . the sum of these two probabilities is 0.008 + 0.096 = 0.104 , or a little more than 10 % . finally , subtracting from 100 % and rounding , we find that the probability we were looking for is approximately 90 % . the correct answer is a . this problem illustrates the power of diversification in financial investments . all else being equal , it \u2019 s less risky to hold a third of your money in three uncorrelated ( independent ) but otherwise equivalent investments than to put all your eggs in one of the baskets . that said , be wary of historical correlations ! housing price changes in different us cities were not so correlated \u2014 and then they became highly correlated during the recent housing crisis ( they all fell together ) , fatally undermining spreadsheet models that assumed that these price changes were independent .",
        "options": "a ) 90 % , b ) 80 % , c ) 70 % , d ) 60 % , e ) 40 %",
        "correct": "a",
        "annotated_formula": "subtract(add(multiply(20, const_2), multiply(20, 3)), const_10)",
        "linear_formula": "multiply(n1,const_2)|multiply(n0,n1)|add(#0,#1)|subtract(#2,const_10)",
        "category": "general"
    },
    {
        "Problem": "a bank pays interest to its customers on the last day of the year . the interest paid to a customer is calculated as 10 % of the average monthly balance maintained by the customer . john is a customer at the bank . on the last day , when the interest was accumulated into his account , his bank balance doubled to $ 5080 . what is the average monthly balance maintained by john in his account during the year ?",
        "Rationale": "bank balance is doubled with accumulation of interest tp 5080 . . this means interest is 5080 / 2 = 2540 for entire year . . although since interest is 10 % of avg monthly balance , it becomes 25400 . . d",
        "options": "a ) 2840 , b ) 5680 , c ) 6840 , d ) 25400 , e ) 28400",
        "correct": "d",
        "annotated_formula": "multiply(5080, divide(10, const_2))",
        "linear_formula": "divide(n0,const_2)|multiply(n1,#0)",
        "category": "general"
    },
    {
        "Problem": "a bus 75 m long is running with a speed of 21 km / hr . in what time will it pass a woman who is walking at 3 km / hr in the direction opposite to that in which the bus is going ?",
        "Rationale": "\"speed of bus relative to woman = 21 + 3 = 24 km / hr . = 24 * 5 / 18 = 20 / 3 m / sec . time taken to pass the woman = 75 * 3 / 20 = 11.25 sec . answer : c\"",
        "options": "a ) 5.75 , b ) 7.62 , c ) 11.25 , d ) 4.25 , e ) 3.25",
        "correct": "c",
        "annotated_formula": "divide(divide(multiply(75, const_3600), add(21, 3)), const_1000)",
        "linear_formula": "add(n1,n2)|multiply(n0,const_3600)|divide(#1,#0)|divide(#2,const_1000)|",
        "category": "physics"
    },
    {
        "Problem": "what is the largest power of 3 contained in 200 !",
        "Rationale": "\"in real basic terms , we ' re asked to find all of the ' 3 s ' in 200 ! we can figure out that 200 / 3 = 66 , so we know that there are at least 66 ' 3 s ' in 200 ! while that answer is among the 5 choices , it seems a bit too ' easy ' , so let ' s do a bit more work and list out the first few numbers that we know have a ' 3 ' in them : 3 = 3 x 1 6 = 3 x 2 9 = 3 x 3 notice how both 3 and 6 have just one 3 in them , but 9 has two 3 s ( there ' s an ' extra ' 3 that we have to account for ) . this implies that there are probably other numbers that include ' extra 3 s ' that we have to figure out : to find those extra 3 s , we have to look at numbers that contain ' powers of 3 ' . . . 3 ^ 2 = 9 3 ^ 3 = 27 3 ^ 4 = 81 3 ^ 5 = 243 , but that ' s too big ( we ' re only going up to 200 ) . keep in mind that a multiple of 81 is also a multiple of 9 and 27 , so we do n ' t want to count any of those values more than once . 200 / 9 = 22 , so we know that there are at least 22 extra 3 s ( and certainly more because of the 27 and 81 ) . with the 66 3 s that we already have , those 22 extra 3 s increase the total to 88 . with the other extra 3 s , we ' ll end up with more than 88 3 s . there ' s only one answer that fits that logic . . . answer : d\"",
        "options": "a ) 88 , b ) 48 , c ) 66 , d ) 97 , e ) 39",
        "correct": "d",
        "annotated_formula": "multiply(floor(divide(power(const_10, 3), 200)), 200)",
        "linear_formula": "power(const_10,n0)|divide(#0,n1)|floor(#1)|multiply(n1,#2)|",
        "category": "other"
    },
    {
        "Problem": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with thrice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per glass on the second day ?",
        "Rationale": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 3 units of water was used to make 4 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 4 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 4 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 4 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 4 * x - - > x = $ 0.3 . answer : c .\"",
        "options": "a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45",
        "correct": "c",
        "annotated_formula": "divide(multiply(add(const_1, const_1), 0.60), add(const_1, const_2))",
        "linear_formula": "add(const_1,const_1)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)|",
        "category": "general"
    },
    {
        "Problem": "8597 - ? = 7429 - 4358",
        "Rationale": "\"d 7429 - 4358 = 3071 let 8597 - x = 3071 then , x = 8597 - 3071 = 5526\"",
        "options": "a ) 3567 , b ) 6424 , c ) 6835 , d ) 5526 , e ) none of these",
        "correct": "d",
        "annotated_formula": "subtract(multiply(divide(8597, const_100), 7429), multiply(divide(const_1, const_3), multiply(divide(8597, const_100), 7429)))",
        "linear_formula": "divide(n0,const_100)|divide(const_1,const_3)|multiply(n1,#0)|multiply(#1,#2)|subtract(#2,#3)|",
        "category": "general"
    },
    {
        "Problem": "pipe a can fill the tank in 30 minutes and pipe b can empty the tank in 90 minutes . how long it will take to fill the tank if both pipes are operating together ?",
        "Rationale": "pipe a fills 1 / 30 th of the tank in a minute and pipe b empties 1 / 90 th of the tank ( 1 / 30 ) - ( 1 / 90 ) = ( 1 / x ) 2 / 90 = 1 / x = > x = 45 answer : d",
        "options": "a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50",
        "correct": "d",
        "annotated_formula": "divide(const_1, subtract(divide(const_1, 30), divide(const_1, 90)))",
        "linear_formula": "divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)",
        "category": "physics"
    },
    {
        "Problem": "if 3 girls can do 3 times of a particular work in 3 days , then , 7 girls can do 7 times of that work in",
        "Rationale": "answer : option ' d ' that is , 1 girl can do one time of the work in 3 days . therefore , 7 girls can do 7 times work in the same 3 days itself .",
        "options": "a ) 1 1 / 5 days , b ) 2 days , c ) 2 1 / 5 days , d ) 3 days , e ) 4 days",
        "correct": "d",
        "annotated_formula": "multiply(divide(3, 3), 3)",
        "linear_formula": "divide(n0,n0)|multiply(n0,#0)",
        "category": "physics"
    },
    {
        "Problem": "arun is travelling on his cycle and has calculated to reach point a at 2 pm if he travels at 10 kmph . he will reach there at 12 noon if he travels at 15 kmph . at what speed must he travel to reach a at 1 pm ?",
        "Rationale": "let distance be x km travelling at 10 kmph reach at 2 pm travelling at 15 kmph reach at 12 noon = > time taken when travelling at 10 km - time taken when travelling at 15 km = 2 hrs x / 10 - x / 15 = 2 3 x - 2 x * 30 x = 60 time needed if travelled at 10 kmph = 60 / 10 = 6 hrs = > reach at 1 pm = > ( 6 - 1 ) = 5 hrs req speed = 60 / 5 = 12 kmph answer b",
        "options": "a ) 8 kmph , b ) 12 kmph , c ) 10 kmph , d ) 14 kmph , e ) 15 kmph",
        "correct": "b",
        "annotated_formula": "divide(add(15, 10), 2)",
        "linear_formula": "add(n1,n3)|divide(#0,n0)",
        "category": "physics"
    },
    {
        "Problem": "find the least number which when divided by 26 , 36 and 46 leaves the remainders 12 , 22 and 32 respectively .",
        "Rationale": "\"explanation : the difference between any divisor and the corresponding remainder is 14 , l . c . m of 26 , 36,46 - 14 = 10764 - 14 = 10750 answer : option b\"",
        "options": "a ) 10570 , b ) 10750 , c ) 17050 , d ) 10075 , e ) 10085",
        "correct": "b",
        "annotated_formula": "add(46, lcm(26, 36))",
        "linear_formula": "lcm(n0,n1)|add(n2,#0)|",
        "category": "general"
    },
    {
        "Problem": "a 1 k . m . long wire is held by n poles . if one pole is removed , the length of the gap becomes 12 / 3 m . what is the number of poles initially ?",
        "Rationale": "length after removing pole is 12 / 3 = 4 then before removing pole is 2 ( ' coz | 2 | 2 | is | 4 | ) i . e . gap between two poles is 2 m 1 km = 1000 m then split 1000 m by 2 m = > we have 500 sections or gaps then no . of poles is 500 + 1 st pole = 501 poles therefore n = 501 . answer : b",
        "options": "a ) 500 , b ) 501 , c ) 502 , d ) 503 , e ) 504",
        "correct": "b",
        "annotated_formula": "subtract(add(add(add(add(multiply(multiply(12, 3), const_12), const_10), multiply(const_10, const_4)), const_10), const_10), 1)",
        "linear_formula": "multiply(n1,n2)|multiply(const_10,const_4)|multiply(#0,const_12)|add(#2,const_10)|add(#3,#1)|add(#4,const_10)|add(#5,const_10)|subtract(#6,n0)",
        "category": "physics"
    },
    {
        "Problem": "a certain deep blue paint contains 45 percent blue pigment and 55 percent red pigment by weight . a certain green paint contains 35 percent blue pigment and 65 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?",
        "Rationale": "10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 55 = 2.75 grams of red pigment",
        "options": "a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 2.75 , e ) 4.5",
        "correct": "d",
        "annotated_formula": "multiply(divide(55, multiply(const_100, const_2)), 10)",
        "linear_formula": "multiply(const_100,const_2)|divide(n1,#0)|multiply(n5,#1)",
        "category": "gain"
    },
    {
        "Problem": "in the new budget the price of wheat rose by 8 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?",
        "Rationale": "reduce in consumption = r / ( 100 + r ) * 100 % = 8 / 108 * 100 = 7.41 % answer is b",
        "options": "a ) 7.5 % , b ) 7.41 % , c ) 10.9 % , d ) 12.6 % , e ) 15 %",
        "correct": "b",
        "annotated_formula": "multiply(divide(divide(8, const_100), add(divide(8, const_100), const_1)), const_100)",
        "linear_formula": "divide(n0,const_100)|add(#0,const_1)|divide(#0,#1)|multiply(#2,const_100)",
        "category": "general"
    },
    {
        "Problem": "a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction e of the sum of the 21 numbers in the list ?",
        "Rationale": "\"this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction e of n to the total would be 4 a / 24 a or 1 / 6 answer b\"",
        "options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21",
        "correct": "b",
        "annotated_formula": "divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3))",
        "linear_formula": "divide(n2,n1)|multiply(const_1,const_1)|add(n0,#0)|divide(#2,n1)|multiply(#3,const_2)|subtract(#4,n1)|subtract(#5,const_3)|divide(#1,#6)|",
        "category": "general"
    },
    {
        "Problem": "a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets euro 1000 more than d , what is b ' s share ?",
        "Rationale": "\"e euro 2000 let the shares of a , b , c and d be euro 5 x , euro 2 x , euro 4 x and euro 3 x respectively . then , 4 x - 3 x = 1000 x = 1000 . b ' s share = euro 2 x = euro ( 2 x 1000 ) = euro 2000 .\"",
        "options": "a ) euro 1000 , b ) euro 3000 , c ) euro 5000 , d ) euro 4000 , e ) euro 2000",
        "correct": "e",
        "annotated_formula": "multiply(multiply(subtract(4, 3), 1000), 3)",
        "linear_formula": "subtract(n2,n3)|multiply(n4,#0)|multiply(n3,#1)|",
        "category": "general"
    },
    {
        "Problem": "if a and b are positive integers , and a = 20 b - 15 , the greatest common divisor of a and b can not be",
        "Rationale": "\"if b is 1 , 3 , 5 , or 15 , then gcd of a and b is 1 , 3 , 5 , and 15 respectively . so , by poe the answer must be c . still : if b is a multiple of 18 , then a is 15 smaller than a multiple of 18 , so not a multiple of 18 , so both of them can not be divisive by 18 . answer : c .\"",
        "options": "a ) 1 , b ) 3 , c ) 18 , d ) 15 , e ) 5",
        "correct": "c",
        "annotated_formula": "add(divide(15, 20), const_2)",
        "linear_formula": "divide(n1,n0)|add(#0,const_2)|",
        "category": "general"
    },
    {
        "Problem": "a retailer marks her goods in such a way that the profit made by selling 50 articles is equal to the selling price of 20 articles . what is the percentage of profit made by the retailer ?",
        "Rationale": "let cost price = x profit = y selling price = x + y 50 y = 20 ( x + y ) 30 y = 20 x percentage profit = y / x \u2217 100 = 20 / 30 \u2217 100 = 66.667 answer = a",
        "options": "a ) 66.67 % , b ) 33.33 % , c ) 40 % , d ) 25 % , e ) 20 %",
        "correct": "a",
        "annotated_formula": "multiply(subtract(divide(50, subtract(50, 20)), const_1), const_100)",
        "linear_formula": "subtract(n0,n1)|divide(n0,#0)|subtract(#1,const_1)|multiply(#2,const_100)",
        "category": "gain"
    },
    {
        "Problem": "what is the angle between the minute and the hour hand of the clock which shows 12 : 24 ?",
        "Rationale": "at 12 : 24 - minute hand will be at 24 * 6 = 144 degrees from position of 12 . - hour hand will move by 2 * 6 = 12 degree during the same time so the difference between the two hands will be 144 - 12 = 132 degrees . answer : e",
        "options": "a ) 115 , b ) 120 , c ) 124 , d ) 130 , e ) 132",
        "correct": "e",
        "annotated_formula": "subtract(multiply(24, multiply(const_3, const_2)), 12)",
        "linear_formula": "multiply(const_2,const_3)|multiply(n1,#0)|subtract(#1,n0)",
        "category": "physics"
    },
    {
        "Problem": "find the value of ( 70 + 28 / 100 ) \u00d7 100",
        "Rationale": "( 7000 + 28 ) / 100 * 100 = 7028 answer : a",
        "options": "a ) 7028 , b ) 4028 , c ) 3128 , d ) 3256 , e ) 5264",
        "correct": "a",
        "annotated_formula": "multiply(add(divide(28, 100), 70), const_100)",
        "linear_formula": "divide(n1,n2)|add(n0,#0)|multiply(#1,const_100)",
        "category": "general"
    },
    {
        "Problem": "a train with 120 wagons crosses john who is going in the same direction , in 36 seconds . it travels for half an hour from the time it starts ove ( who is also riding on his horse ) coming from the opposite direction in 24 seconds . in how much time after the train has crossed the mike do the john meets to mike ? rtaking the john ( he is riding on the horse ) before it starts overtaking the mike",
        "Rationale": "let the length of the train be l metres and speeds of the train arun and sriram be r , a and s respectively , then - - - - - - - - - - ( i ) and - - - - - - - - - ( ii ) from eq . ( i ) and ( ii ) 3 ( r - a ) = 2 ( r + k ) r = 3 a + 2 k in 30 minutes ( i . e 1800 seconds ) , the train covers 1800 r ( distance ) but the arun also covers 1800 a ( distance ) in the same time . therefore distance between arun and sriram , when the train has just crossed sriram = 1800 ( r - a ) - 24 ( a + k ) time required = = ( 3600 - 24 ) = 3576 s e",
        "options": "a ) 2534 , b ) 3545 , c ) 3521 , d ) 4564 , e ) 3576",
        "correct": "e",
        "annotated_formula": "subtract(divide(multiply(subtract(divide(add(36, 24), subtract(36, 24)), const_1), multiply(multiply(const_10, const_3), const_60)), const_2), 24)",
        "linear_formula": "add(n1,n2)|multiply(const_10,const_3)|subtract(n1,n2)|divide(#0,#2)|multiply(#1,const_60)|subtract(#3,const_1)|multiply(#4,#5)|divide(#6,const_2)|subtract(#7,n2)",
        "category": "physics"
    },
    {
        "Problem": "how many internal diagonals does a pentagon ( five sided polygon ) have ?",
        "Rationale": "\"number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 5 no . of diagonals = 5 ( 5 - 3 ) / 2 = 5 ans a\"",
        "options": "a ) 5 , b ) 8 , c ) 9 , d ) 10 , e ) 12",
        "correct": "a",
        "annotated_formula": "multiply(subtract(multiply(const_2, const_4), const_3), divide(multiply(const_2, const_4), const_2))",
        "linear_formula": "multiply(const_2,const_4)|divide(#0,const_2)|subtract(#0,const_3)|multiply(#1,#2)|",
        "category": "geometry"
    },
    {
        "Problem": "10 stickers numbered 1 to 10 are placed in a bowl , mixed up thoroughly and then one sticker is drawn randomly . if it is known that the number on the drawn sticker is more than 3 , what is the probability that it is an even number ?",
        "Rationale": "let a be the event \u2018 the number on the card drawn is even \u2019 and b be the event \u2018 the number on the card drawn is greater than 3 \u2019 . we have to find p ( a | b ) . now , the sample space of the experiment is s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } then a = { 2 , 4 , 6 , 8 , 10 } , b = { 4 , 5 , 6 , 7 , 8 , 9 , 10 } and a n b = { 4 , 6 , 8 , 10 } also p ( a ) = 5 / 2 , p ( b ) = 7 / 10 and p ( a n b ) = 4 / 10 then p ( a | b ) = p ( a n b ) / p ( b ) = ( 4 / 10 ) / ( 7 / 10 ) = 4 / 7 b )",
        "options": "a ) 3 / 7 , b ) 4 / 7 , c ) 5 / 7 , d ) 7 / 11 , e ) 9 / 11",
        "correct": "b",
        "annotated_formula": "multiply(divide(const_4, 10), divide(10, subtract(10, 3)))",
        "linear_formula": "divide(const_4,n0)|subtract(n0,n3)|divide(n0,#1)|multiply(#0,#2)",
        "category": "general"
    },
    {
        "Problem": "for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score w for the exam ?",
        "Rationale": "\"a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean w = 74 . answer : a .\"",
        "options": "a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82",
        "correct": "a",
        "annotated_formula": "divide(add(multiply(58, 3), multiply(98, 2)), add(2, 3))",
        "linear_formula": "add(n1,n3)|multiply(n0,n3)|multiply(n1,n2)|add(#1,#2)|divide(#3,#0)|",
        "category": "general"
    },
    {
        "Problem": "a student travels from his house to school at 10 km / hr and reaches school 1 hour late . the next day he travels 12 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?",
        "Rationale": "let x be the distance from his house to the school . x / 10 = x / 12 + 2 6 x = 5 x + 120 x = 120 km the answer is e .",
        "options": "a ) 100 , b ) 105 , c ) 110 , d ) 115 , e ) 120",
        "correct": "e",
        "annotated_formula": "multiply(multiply(10, 12), divide(subtract(12, 10), add(1, 1)))",
        "linear_formula": "add(n1,n1)|multiply(n0,n2)|subtract(n2,n0)|divide(#2,#0)|multiply(#3,#1)",
        "category": "physics"
    },
    {
        "Problem": "in school there are some bicycles and 4 wheeler wagons . one tuesday there are 190 wheels in the campus . how many bicycles are there ?",
        "Rationale": "let no . of bicycles be x & no . of wagons be y so , 2 x + 4 y = 190 by solving , we get no . of bicycles = 39 ( wheels = > 2 * 39 = 78 ) no . of wagons = 28 ( wheels = > 4 * 28 = 112 ) answer : e",
        "options": "a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39",
        "correct": "e",
        "annotated_formula": "multiply(divide(190, add(multiply(4, const_2), const_2)), const_2)",
        "linear_formula": "multiply(n0,const_2)|add(#0,const_2)|divide(n1,#1)|multiply(#2,const_2)",
        "category": "physics"
    },
    {
        "Problem": "what is the length of the diagonal of a square whose area is 4 times of another square with diagonal as 5 v 2 cm ?",
        "Rationale": "solution : 10 v 2 area of square = 1 / 2 * ( length of diagonal ) 2 area of square 1 = * ( 5 v 2 ) 2 = 25 area of square 2 = 4 * 25 = 100 length of diagonal of square 2 = v 2 * area = v 2 * 100 = v 200 = 10 v 2 cm answer is c",
        "options": "['a ) 20 v 2', 'b ) 10', 'c ) 10 v 2', 'd ) 20', 'e ) 25']",
        "correct": "c",
        "annotated_formula": "multiply(const_10, sqrt(2))",
        "linear_formula": "sqrt(n2)|multiply(#0,const_10)",
        "category": "geometry"
    },
    {
        "Problem": "6 ^ 4 \u2212 4 ^ 4 = ?",
        "Rationale": "\"we can write the above in terms of ( a + b ) ( a - b ) 6 ^ 4 \u2212 4 ^ 4 = ( 6 ^ 2 ) 2 - ( 4 ^ 2 ) 2 = ( 6 ^ 2 \u2212 4 ^ 2 ) * ( 6 ^ 2 + 4 ^ 2 ) = ( 36 \u2212 16 ) * ( 36 + 16 ) = > 20 * 52 = 1040 ans option e .\"",
        "options": "a ) 20 , b ) 52 , c ) 104 , d ) 520 , e ) 1040",
        "correct": "e",
        "annotated_formula": "divide(power(6, 4), power(6, 4))",
        "linear_formula": "power(n0,n1)|power(n0,n3)|divide(#0,#1)|",
        "category": "general"
    },
    {
        "Problem": "find the value of ( 950 + 220 / 900 ) \u00d7 900",
        "Rationale": "\"( 855000 + 220 ) / 900 * 900 = 855000 + 220 = 855220 answer : d\"",
        "options": "a ) 854542 , b ) 856945 , c ) 758965 , d ) 855220 , e ) 826450",
        "correct": "d",
        "annotated_formula": "multiply(add(divide(220, 900), 950), 900)",
        "linear_formula": "divide(n1,n2)|add(n0,#0)|multiply(#1,n2)|",
        "category": "general"
    },
    {
        "Problem": "a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it takes 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?",
        "Rationale": "let the man ' s rate upstream be x kmph and that downstream be y kmph . then , distance covered upstream in 8 hrs 48 min = distance covered downstream in 4 hrs . 44 * x / 5 = 4 * y y = 11 / 5 * x required ratio = ( y + x ) / 2 : ( y - x ) / 2 = 8 / 5 : 3 / 5 = 8 / 3 ans - b",
        "options": "a ) 8 / 5 , b ) 8 / 3 , c ) 3 / 5 , d ) 5 / 8 , e ) 5 / 3",
        "correct": "b",
        "annotated_formula": "divide(divide(add(divide(add(divide(48, const_60), 8), 4), const_1), const_2), divide(subtract(divide(add(divide(48, const_60), 8), 4), const_1), const_2))",
        "linear_formula": "divide(n1,const_60)|add(n0,#0)|divide(#1,n2)|add(#2,const_1)|subtract(#2,const_1)|divide(#3,const_2)|divide(#4,const_2)|divide(#5,#6)",
        "category": "physics"
    },
    {
        "Problem": "mary sold boxes of butter cookies . ann sold 5 times as much as she did . 18 boxes of cookies were sold that day , how many boxes did mary sell ?",
        "Rationale": "# of boxes of cookies mary sold = x ann sold 5 times more = 5 x x + 5 x = 18 6 x = 18 x = 18 / 6 = 3 answer : a",
        "options": "a ) 3 , b ) 5 , c ) 6 , d ) 10 , e ) 18",
        "correct": "a",
        "annotated_formula": "divide(18, add(5, const_1))",
        "linear_formula": "add(n0,const_1)|divide(n1,#0)",
        "category": "general"
    },
    {
        "Problem": "there are 76 persons . 54 can read hindu , 43 can read times , 37 can read deccan and 15 can read all . if 24 can read hindu and deccan and 27 can read deccan and times then what is the number of persons who read only times and hindu .",
        "Rationale": "let ' a ' can be read hindu , let ' b ' can be read times , let ' c ' can be read deccan , from the given data : n ( aubuc ) = 76 , n ( a ) = 54 , n ( b ) = 43 , n ( c ) = 37 , n ( anbnc ) = 15 , n ( anc ) = 24 , n ( bnc ) = 27 , n ( anb ) = ? n ( aubuc ) = n ( a ) + n ( b ) + n ( c ) - n ( anb ) - n ( bnc ) - n ( anc ) + n ( anbnc ) = = > 76 = 54 + 43 + 37 - n ( anb ) - 24 - 27 + 15 = = > n ( anb ) = 54 + 43 + 37 + 15 - 24 - 27 - 76 = = > n ( anb ) = 149 - 127 = = > n ( anb ) = 22 answer : b",
        "options": "a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25",
        "correct": "b",
        "annotated_formula": "add(subtract(24, 15), subtract(27, 15))",
        "linear_formula": "subtract(n5,n4)|subtract(n6,n4)|add(#0,#1)",
        "category": "general"
    },
    {
        "Problem": "chocolate bars are sold in packages of 4 or 9 only . if mark bought 97 chocolate bars exactly , what could be the number of large packs mark bought ?",
        "Rationale": "let number of packs of four = f let number of packs of nine = n 4 f + 9 n = 97 now , we need to test for values of n . since sum 97 is odd and 4 f will always be even , n ca n ' t be even . now , we can test for values e = 2 , 4 and 6 4 * 4 + 9 * 9 = 16 + 81 = 97 answer d",
        "options": "a ) 3 , b ) 4 , c ) 8 , d ) 9 , e ) 13",
        "correct": "d",
        "annotated_formula": "divide(subtract(97, multiply(4, 4)), 9)",
        "linear_formula": "multiply(n0,n0)|subtract(n2,#0)|divide(#1,n1)",
        "category": "general"
    },
    {
        "Problem": "10 men can cut 10 trees in 2 hours . if 2 men leave the job , how many trees will be cut in 3 hours ?",
        "Rationale": "10 men - working 2 hrs - cut 10 trees 1 men - working 1 hr - cuts = 10 / 10 * 2 thus 8 men - working 3 hrs - cut = 10 * 8 * 3 / 10 * 2 = 12 trees answer is a",
        "options": "a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 20",
        "correct": "a",
        "annotated_formula": "multiply(multiply(subtract(10, 2), divide(divide(10, 2), 10)), 3)",
        "linear_formula": "divide(n0,n2)|subtract(n0,n2)|divide(#0,n0)|multiply(#2,#1)|multiply(n4,#3)",
        "category": "physics"
    },
    {
        "Problem": "a person ' s present age is one - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . how old is the mother at present ?",
        "Rationale": "\"let the mother ' s present age be x years then the person ' s present age = 2 x / 5 ( 3 x / 5 ) + 8 = 1 / 2 ( x + 8 ) 2 ( 3 x + 40 ) = 5 ( x + 8 ) x = 40 answer is e\"",
        "options": "a ) a ) 25 , b ) b ) 44 , c ) c ) 32 , d ) d ) 45 , e ) e ) 40",
        "correct": "e",
        "annotated_formula": "divide(subtract(8, add(const_2, const_3)), subtract(divide(const_1, const_2), divide(const_2, add(const_2, const_3))))",
        "linear_formula": "add(const_2,const_3)|divide(const_1,const_2)|divide(const_2,#0)|subtract(n0,#0)|subtract(#1,#2)|divide(#3,#4)|",
        "category": "general"
    },
    {
        "Problem": "find the product of the place value and face value of 3 in 5769354",
        "Rationale": "\"explanation : place value = local value face value = absolute value the place value of 3 in 5769354 is 3 x 100 = 300 the face value of 3 in 5769354 is nothing but 3 . = > 300 x 3 = 900 answer : option a\"",
        "options": "a ) 900 , b ) 9000 , c ) 90 , d ) 9 , e ) 0.9",
        "correct": "a",
        "annotated_formula": "multiply(multiply(3, const_1000), 3)",
        "linear_formula": "multiply(n0,const_1000)|multiply(n0,#0)|",
        "category": "general"
    },
    {
        "Problem": "a shopkeeper loses 15 % , if an article is sold for $ 102 . what should be the selling price of the article to gain 20 % ?",
        "Rationale": "\"c $ 144 given that sp = $ 102 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 102 ) / 85 = 20 * 6 = $ 120 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 120 * 120 ) / 100 = $ 144\"",
        "options": "a ) $ 165 , b ) $ 174 , c ) $ 144 , d ) $ 164 , e ) $ 183",
        "correct": "c",
        "annotated_formula": "add(divide(102, subtract(const_1, divide(15, const_100))), multiply(divide(102, subtract(const_1, divide(15, const_100))), divide(20, const_100)))",
        "linear_formula": "divide(n0,const_100)|divide(n2,const_100)|subtract(const_1,#0)|divide(n1,#2)|multiply(#3,#1)|add(#3,#4)|",
        "category": "gain"
    },
    {
        "Problem": "a man sells an article at 10 % gain . had be sold at for rs . 60 / - more he could have gained 20 % what is cost price of article",
        "Rationale": "first selling price = 110 % - - - - - > x rupees = sold at for rs . 60 / - = 120 % - - - - - > x + 60 rupees ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - > 60 100 % - - - - - - - > rs . 600 / - option ' b '",
        "options": "a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 760 , e ) rs . 800",
        "correct": "b",
        "annotated_formula": "multiply(divide(60, subtract(20, 10)), const_100)",
        "linear_formula": "subtract(n2,n0)|divide(n1,#0)|multiply(#1,const_100)",
        "category": "general"
    },
    {
        "Problem": "6 people can do work in 80 days how much people they required to complete the work in 16 days ?",
        "Rationale": "man and days concept . . . 6 m * 80 d = m * 16 d solve it , total no of people required is 30 ; answer : c",
        "options": "a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50",
        "correct": "c",
        "annotated_formula": "divide(multiply(6, 80), 16)",
        "linear_formula": "multiply(n0,n1)|divide(#0,n2)",
        "category": "physics"
    },
    {
        "Problem": "david and lewis leave chennai for tirupati simultaneously at 7 a . m in the morning driving in two cars at speeds of 60 mph and 80 mph respectively . as soon as lewis reaches tirupati he returns back to chennai along the same route and meets david on the way back . if the distance between the two cities is 160 miles , how far from chennai did david and lewis meet ?",
        "Rationale": "time taken by lewis to reach tirupati = 160 / 80 = 2 hours in 2 hours , david travels 60 * 2 = 120 miles so distance at which they meet should be greater than 120 miles . only b satisfies . answer is b .",
        "options": "a ) 100 mlies , b ) 120 miles , c ) 90 miles , d ) 95 miles , e ) 110 miles",
        "correct": "b",
        "annotated_formula": "multiply(const_2, 60)",
        "linear_formula": "multiply(n1,const_2)",
        "category": "physics"
    },
    {
        "Problem": "city a to city b , andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph . what was the average speed for the whole trip ?",
        "Rationale": "the total distance is 1 \u00d7 50 + 3 \u00d7 60 = 2301 \u00d7 50 + 3 \u00d7 60 = 230 . and the total time is 4 hours . hence , average speed = ( total distancetotal time ) = 2304 = 57.5 b",
        "options": "a ) 56 , b ) 57.5 , c ) 58.9 , d ) 61.4 , e ) 62",
        "correct": "b",
        "annotated_formula": "divide(add(multiply(50, 1), multiply(60, 3)), add(3, 1))",
        "linear_formula": "add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)",
        "category": "physics"
    },
    {
        "Problem": "the cost of producing x tools by a company is given by c ( x ) = 600 x + 5500 ( in $ ) a ) what is the cost of 100 tools ?",
        "Rationale": "solution c ( 100 ) = 600 * 100 + 5500 = 125500 $ answer a",
        "options": "a ) 65500 $ , b ) 125800 $ , c ) 125900 $ , d ) 6500 $ , e ) 122500 $",
        "correct": "a",
        "annotated_formula": "add(multiply(100, 600), 5500)",
        "linear_formula": "multiply(n0,n2)|add(n1,#0)",
        "category": "general"
    },
    {
        "Problem": "in an election between the two candidates , the candidates who gets 60 % of votes polled is winned by 280 votes majority . what is the total number of votes polled ?",
        "Rationale": "\"note : majority ( 20 % ) = difference in votes polled to win ( 60 % ) & defeated candidates ( 40 % ) 20 % = 60 % - 40 % 20 % - - - - - > 280 ( 20 \u00d7 14 = 280 ) 100 % - - - - - > 1400 ( 100 \u00d7 14 = 1400 ) a )\"",
        "options": "a ) 1400 , b ) 1600 , c ) 1800 , d ) 2000 , e ) 2100",
        "correct": "a",
        "annotated_formula": "divide(multiply(const_100, 280), subtract(60, subtract(const_100, 60)))",
        "linear_formula": "multiply(n1,const_100)|subtract(const_100,n0)|subtract(n0,#1)|divide(#0,#2)|",
        "category": "gain"
    },
    {
        "Problem": "the height of a cylinder is 60 cm and the diameter of its base is 5 cm . the total surface area of the cylinder is",
        "Rationale": "given h = 60 cm and r = 5 / 2 cm total surface area = 2 \u03c0 rh + 2 & pir ( power 2 ) = 2 \u03c0 r ( h + r ) = [ 2 \u00d7 22 / 7 \u00d7 5 / 2 \u00d7 ( 60 + 5 / 2 ) ] cm ( power 2 ) = [ 44 / 7 \u00d7 5 / 2 \u00d7 ( ( 120 + 5 ) / 2 ) ] cm ( power 2 ) = 22 / 7 \u00d7 5 \u00d7 125 / 2 cm ( power 2 ) = ( 55 \u00d7 125 ) / 7 cm ( power 2 ) = 6875 / 7 cm ( power 2 ) = 982.14 cm ( power 2 ) answer is c .",
        "options": "['a ) 918.14', 'b ) 981.41', 'c ) 982.14', 'd ) 928.41', 'e ) none of them']",
        "correct": "c",
        "annotated_formula": "surface_cylinder(divide(5, const_2), 60)",
        "linear_formula": "divide(n1,const_2)|surface_cylinder(#0,n0)",
        "category": "geometry"
    },
    {
        "Problem": "what will be the compound interest on rs . 25000 a \u014d er 3 years at the rate of 12 % per annum",
        "Rationale": "\"explanation : ( 25000 \u00d7 ( 1 + 12100 ) 3 ) = > 25000 \u00d7 2825 \u00d7 2825 \u00d7 2825 = > 35123.20 so compound interest will be 35123.20 - 25000 = rs 10123.20 answer : a\"",
        "options": "a ) rs 10123.20 , b ) rs 10123.30 , c ) rs 10123.40 , d ) rs 10123.50 , e ) none of these",
        "correct": "a",
        "annotated_formula": "subtract(multiply(multiply(multiply(const_4, const_100), const_100), power(add(const_1, divide(12, const_100)), 3)), multiply(multiply(const_4, const_100), const_100))",
        "linear_formula": "divide(n2,const_100)|multiply(const_100,const_4)|add(#0,const_1)|multiply(#1,const_100)|power(#2,n1)|multiply(#3,#4)|subtract(#5,#3)|",
        "category": "gain"
    },
    {
        "Problem": "a batsman scores 26 runs and increases his average from 14 to 15 . find the runs to be made if he wants top increasing the average to 19 in the same match ?",
        "Rationale": "number of runs scored more to increase the ratio by 1 is 26 - 14 = 12 to raise the average by one ( from 14 to 15 ) , he scored 12 more than the existing average . therefore , to raise the average by five ( from 14 to 19 ) , he should score 12 x 5 = 60 more than the existing average . thus he should score 14 + 60 = 74 . answer d",
        "options": "a ) 12 , b ) 18 , c ) 25 , d ) 74 , e ) 88",
        "correct": "d",
        "annotated_formula": "subtract(multiply(19, add(subtract(26, 15), const_1)), multiply(14, subtract(26, 15)))",
        "linear_formula": "subtract(n0,n2)|add(#0,const_1)|multiply(n1,#0)|multiply(n3,#1)|subtract(#3,#2)",
        "category": "general"
    },
    {
        "Problem": "a total of 520 players participated in a single tennis knock out tournament . what is the total number of matches played in the tournament ? ( knockout means if a player loses , he is out of the tournament ) . no match ends in a tie .",
        "Rationale": "there are 520 players , only 1 person wins , 519 players lose . in order to lose , you must have lost a game . 519 games . ans - b",
        "options": "a ) 511 , b ) 519 , c ) 256 , d ) 255 , e ) 1023",
        "correct": "b",
        "annotated_formula": "add(add(add(add(add(add(add(divide(divide(divide(520, const_2), const_2), const_2), add(divide(520, const_2), divide(divide(520, const_2), const_2))), divide(divide(divide(divide(520, const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2)), divide(divide(divide(divide(divide(divide(divide(divide(divide(520, const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2), const_2))",
        "linear_formula": "divide(n0,const_2)|divide(#0,const_2)|add(#0,#1)|divide(#1,const_2)|add(#2,#3)|divide(#3,const_2)|add(#4,#5)|divide(#5,const_2)|add(#6,#7)|divide(#7,const_2)|add(#8,#9)|divide(#9,const_2)|add(#10,#11)|divide(#11,const_2)|add(#12,#13)|divide(#13,const_2)|add(#14,#15)",
        "category": "general"
    },
    {
        "Problem": "solving a linear equation with several occurrences of the variable , solve for w . simplify answer as much as possible . ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22",
        "Rationale": "( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22 or , [ 7 w + 6 + 3 ( 9 w + 8 ) ] / 6 = 22 or , 7 w + 6 + 27 w + 24 = 132 or , 34 w + 30 = 132 or , 34 w = 132 - 30 or , 34 w = 102 or , w = 102 / 34 therefore , w = 3 answer : c",
        "options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5",
        "correct": "c",
        "annotated_formula": "divide(subtract(multiply(multiply(2, 6), 22), add(multiply(8, 6), multiply(2, 6))), add(multiply(9, 6), multiply(7, const_2)))",
        "linear_formula": "multiply(n1,n5)|multiply(n1,n4)|multiply(n1,n3)|multiply(n0,const_2)|add(#1,#0)|add(#2,#3)|multiply(n6,#0)|subtract(#6,#4)|divide(#7,#5)",
        "category": "general"
    },
    {
        "Problem": "the average age of 36 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . find out the teacher ' s age in years ?",
        "Rationale": "\"average age of 36 students in a group is 14 sum of the ages of 36 students = 36 \u00d7 14 when teacher ' s age is included to it , the average increases by one = > average = 15 sum of the ages of 36 students and the teacher = 37 \u00d7 15 hence teachers age = 37 \u00d7 15 - 36 \u00d7 14 = 37 \u00d7 15 - 14 ( 37 - 1 ) = 37 \u00d7 15 - 37 \u00d7 14 + 14 = 37 ( 15 - 14 ) + 14 = 37 + 14 = 51 answer is e .\"",
        "options": "a ) 50 , b ) 49 , c ) 53 , d ) 54 , e ) 51",
        "correct": "e",
        "annotated_formula": "add(36, const_1)",
        "linear_formula": "add(n0,const_1)|",
        "category": "general"
    },
    {
        "Problem": "a is 1.5 times as fast as b . a alone can do the work in 20 days . if a and b working together , in how many days will the work be completed ?",
        "Rationale": "a can finish 1 work in 20 days b can finish 1 / 1.5 work in 20 days - since a is 1.5 faster than b this means b can finish 1 work in 20 * 1.5 days = 30 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 30 / ( 20 + 30 ) = 20 * 30 / 50 = 12 days so answer is c",
        "options": "a ) 23 , b ) 22 , c ) 12 , d ) 24 , e ) 25",
        "correct": "c",
        "annotated_formula": "divide(const_1, add(divide(const_1, 20), divide(divide(const_1, 20), 1.5)))",
        "linear_formula": "divide(const_1,n1)|divide(#0,n0)|add(#0,#1)|divide(const_1,#2)",
        "category": "physics"
    },
    {
        "Problem": "if a = 1 , what is the value of \u2013 ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 ) ?",
        "Rationale": "if a = 1 , then putting values in equation = - [ ( 1 ) ^ 2 + ( 1 ) ^ 3 + ( 1 ^ 4 ) + ( 1 ^ 5 ) ] = - [ 1 + 1 + 1 + 1 ] = - 4 answer = b = - 4",
        "options": "a ) - 14 , b ) - 4 , c ) 0 , d ) 4 , e ) 14",
        "correct": "b",
        "annotated_formula": "negate(add(add(add(power(1, 2), power(1, 3)), power(1, 4)), power(1, 5)))",
        "linear_formula": "power(n0,n1)|power(n0,n2)|power(n0,n3)|power(n0,n4)|add(#0,#1)|add(#4,#2)|add(#5,#3)|negate(#6)",
        "category": "general"
    },
    {
        "Problem": "an astronomer noted that a grouping of red giant stars had an average solar mass of 8 m each , and a grouping of white dwarf stars had an average solar mass of 1.5 m each . if the astronomer calculated the total solar mass of both groupings to be 49 m , what total number of red giant stars and white dwarf stars did the astronomer note ?",
        "Rationale": "we can determine quickly that total number should range between 49 / 8 < = n < = 49 / 1.5 , so ans should be between 6 and 33 . now solving the expression 8 a + 1.5 b = 49 decreasing 49 in multiple of 8 and checking divisibility of that number by 1.5 . this way we get 2 red giants , 22 white dwarfs we get 49 , but 2 + 22 = 24 and 24 is not an option . next we get 5 red giants and 6 white dwarfs to get 49 , 5 * 8 + 6 * 1.5 = 49 hence total number is 5 + 6 = 11 ans b",
        "options": "a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14",
        "correct": "b",
        "annotated_formula": "add(divide(subtract(49, multiply(1.5, add(const_2, const_4))), 8), add(const_2, const_4))",
        "linear_formula": "add(const_2,const_4)|multiply(n1,#0)|subtract(n2,#1)|divide(#2,n0)|add(#0,#3)",
        "category": "general"
    },
    {
        "Problem": "village a \u2019 s population is 300 greater than village b ' s population . if village b \u2019 s population were reduced by 600 people , then village a \u2019 s population would be 4 times as large as village b ' s population . what is village b ' s current population ?",
        "Rationale": "a = b + 300 . a = 4 ( b - 600 ) . 4 ( b - 600 ) = b + 300 . 3 b = 2700 . b = 900 . the answer is a .",
        "options": "a ) 900 , b ) 1000 , c ) 1100 , d ) 1200 , e ) 1300",
        "correct": "a",
        "annotated_formula": "divide(add(multiply(600, 4), 300), subtract(4, const_1))",
        "linear_formula": "multiply(n1,n2)|subtract(n2,const_1)|add(n0,#0)|divide(#2,#1)",
        "category": "general"
    },
    {
        "Problem": "6 students wrote science exam . their average marks are 70 . 5 students got 65 , 75 , 55 , 72 and 69 marks respectively . therefore what is the marks of the sixth student ?",
        "Rationale": "explanation total marks of 5 students = ( 65 + 75 + 55 + 72 + 69 ) = 336 required marks = [ ( 70 x 6 ) \u2013 336 ] = ( 420 \u2013 336 ) = 84 answer a",
        "options": "a ) 84 , b ) 68 , c ) 85 , d ) 75 , e ) 42",
        "correct": "a",
        "annotated_formula": "subtract(multiply(70, 6), add(add(add(add(65, 75), 55), 72), 69))",
        "linear_formula": "add(n3,n4)|multiply(n0,n1)|add(n5,#0)|add(n6,#2)|add(n7,#3)|subtract(#1,#4)",
        "category": "general"
    },
    {
        "Problem": "the sum of 7 th and 23 rd term of a . p . is equal to the sum of 8 th , 15 th and 13 th term . find the term which is 0",
        "Rationale": "t 7 + t 23 = t 8 + t 15 + t 13 = > a + 6 d + a + 22 d = a + 7 d + a + 14 d + a + 12 d = > a + 5 d = 0 = > t 6 = 0 i . e . 6 th term is zero . answer : a",
        "options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14",
        "correct": "a",
        "annotated_formula": "subtract(add(13, add(8, 15)), add(7, 23))",
        "linear_formula": "add(n2,n3)|add(n0,n1)|add(n4,#0)|subtract(#2,#1)",
        "category": "general"
    },
    {
        "Problem": "what is the perimeter of a rectangular field whose diagonal is 5 m and length is 4 m ?",
        "Rationale": "\"sol : breadth of the rectangular plot is = 5 ^ 2 - 4 ^ 2 = 3 m therefore , perimeter of the rectangular plot = 2 ( 4 + 3 ) = 14 m c ) 14 m\"",
        "options": "a ) 20 m , b ) 15 m , c ) 14 m , d ) 10 m , e ) 25 m",
        "correct": "c",
        "annotated_formula": "divide(add(add(sqrt(subtract(power(5, const_2), power(4, const_2))), 4), add(sqrt(subtract(power(5, const_2), power(4, const_2))), 4)), 4)",
        "linear_formula": "power(n0,const_2)|power(n1,const_2)|subtract(#0,#1)|sqrt(#2)|add(n1,#3)|add(#4,#4)|divide(#5,n1)|",
        "category": "geometry"
    },
    {
        "Problem": "coconuts were purchased at 150 per 100 and sold at 2 per coconut . if 2000 coconuts were sold , what was the total profit made ?",
        "Rationale": "c . p . for one coconut = 150 \u2044 100 = 3 \u2044 2 s . p . for one coconut = 2 profit on one coconut = 2 - 3 \u2044 2 = 1 \u2044 2 \u2234 profit on 2000 coconut = 1 \u2044 2 \u00d7 2000 = 1000 answer b",
        "options": "a ) 500 , b ) 1000 , c ) 1500 , d ) 2000 , e ) none of these",
        "correct": "b",
        "annotated_formula": "multiply(2000, subtract(2, divide(150, 100)))",
        "linear_formula": "divide(n0,n1)|subtract(n2,#0)|multiply(n3,#1)",
        "category": "gain"
    },
    {
        "Problem": "what is the factorial of 5 ?",
        "Rationale": "\"c 120 120 ( 5 x 4 x 3 x 2 x 1 ) .\"",
        "options": "a ) 1 , b ) 60 , c ) 120 , d ) 130 , e ) 180",
        "correct": "c",
        "annotated_formula": "circle_area(divide(5, multiply(const_2, const_pi)))",
        "linear_formula": "multiply(const_2,const_pi)|divide(n0,#0)|circle_area(#1)|",
        "category": "other"
    },
    {
        "Problem": "when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in e hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of e ?",
        "Rationale": "\"rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * e = 1 = > x = 1 / e when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / e = 4 / 3 = > 1 / e = ( 8 - 3 ) / 6 = 5 / 6 = > e = 6 / 5 = 1 [ 1 / 5 ] answer b\"",
        "options": "a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2",
        "correct": "b",
        "annotated_formula": "add(subtract(4, 2), divide(const_1, add(2, 3)))",
        "linear_formula": "add(n0,n1)|subtract(n2,n0)|divide(const_1,#0)|add(#2,#1)|",
        "category": "physics"
    },
    {
        "Problem": "the area of a parallelogram is 72 cm ^ 2 and its altitude is twice the corresponding base . what is the length of the base ?",
        "Rationale": "let base = x cm height = 2 x cm area = x \u00e3 \u2014 2 x = 2 x ^ 2 area = x \u00e3 \u2014 2 x = 2 x ^ 2 area is given as 72 cm ^ 2 2 x ^ 2 = 72 x ^ 2 = 36 x = 6 cm answer : c",
        "options": "['a ) 1 cm', 'b ) 3 cm', 'c ) 6 cm', 'd ) 4 cm', 'e ) 2 cm']",
        "correct": "c",
        "annotated_formula": "sqrt(divide(72, const_2))",
        "linear_formula": "divide(n0,const_2)|sqrt(#0)",
        "category": "geometry"
    },
    {
        "Problem": "martin buys a pencil and a notebook for 80 cents . at the same store , gloria buys a notebook and an eraser for $ 1.15 cents , and zachary buys a pencil and an eraser for 75 cents . how many cents would it cost to buy 3 pencils , 3 notebooks , and 3 erasers ? ( assume that there is no volume discount . )",
        "Rationale": "pencil + notebook = 80 notebook + eraser = 115 pencil + eraser = 75 let ' s add all three equations . 2 pencils + 2 notebooks + 2 erasers = 270 cents the cost to buy 3 of each would be ( 3 / 2 ) ( 270 ) = 405 the answer is e .",
        "options": "a ) 325 , b ) 345 , c ) 365 , d ) 385 , e ) 405",
        "correct": "e",
        "annotated_formula": "multiply(divide(add(add(multiply(1.15, const_100), 80), 75), const_2), 3)",
        "linear_formula": "multiply(n1,const_100)|add(n0,#0)|add(n2,#1)|divide(#2,const_2)|multiply(n3,#3)",
        "category": "gain"
    },
    {
        "Problem": "if a fast song has 160 beats per minute , and a slow song has 90 beats per minute , how many minutes total would you play a fast and a slow song to have a stream of music that had a total of 1020 beats ?",
        "Rationale": "we can determine quickly that total number should range between 1020 / 160 < = n < = 1020 / 90 , so ans should be between 6 and 12 . now solving the expression 160 a + 90 b = 1020 decreasing 1020 by multiples of 160 and checking divisibility of that number by 9 , we get fast song plays for 3 minutes and slow somg plays for 6 minutes , 3 * 160 + 6 * 90 = 1020 hence total number of minutes stream of music plays is 3 + 6 = 9 minutes ans d",
        "options": "a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10",
        "correct": "d",
        "annotated_formula": "add(floor(multiply(divide(1020, add(160, 90)), const_2)), const_1)",
        "linear_formula": "add(n0,n1)|divide(n2,#0)|multiply(#1,const_2)|floor(#2)|add(#3,const_1)",
        "category": "physics"
    },
    {
        "Problem": "during the second quarter of 1984 , a total of 3 , 976000 domestic cars were sold . if this was 32 % greater than the number sold during the first quarter of 1984 , how many were sold during the first quarter ?",
        "Rationale": "let number of cars sold in 1 st quarter = x number of cars sold in 2 nd quarter = 32 % greater than the number sold during the first quarter = ( 1 + 32 / 100 ) x = 1.32 x 1.32 x = 3 , 976,000 = > x = 3 , 012,121 so , answer will be d",
        "options": "a ) 714,240 , b ) 2 , 261,760 , c ) 2 , 400,000 , d ) 3 , 012,121 , e ) 3 , 915,790",
        "correct": "d",
        "annotated_formula": "multiply(multiply(divide(divide(divide(add(multiply(3, multiply(const_1000, const_1000)), 976000), add(divide(32, const_100), const_1)), const_1000), const_100), 3), 3)",
        "linear_formula": "divide(n3,const_100)|multiply(const_1000,const_1000)|add(#0,const_1)|multiply(n1,#1)|add(n2,#3)|divide(#4,#2)|divide(#5,const_1000)|divide(#6,const_100)|multiply(n1,#7)|multiply(n1,#8)",
        "category": "gain"
    },
    {
        "Problem": "a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is",
        "Rationale": "explanation : let distance = x km and usual rate = y kmph . then , x / y - x / ( y + 3 ) = 40 / 60 - - > 2 y ( y + 3 ) = 9 x - - - - - ( i ) also , x / ( y - 2 ) - x / y = 40 / 60 - - > y ( y - 2 ) = 3 x - - - - - - - - ( ii ) on dividing ( i ) by ( ii ) , we get : x = 40 km . answer : c",
        "options": "a ) 27 , b ) 87 , c ) 40 , d ) 18 , e ) 17",
        "correct": "c",
        "annotated_formula": "multiply(multiply(divide(multiply(multiply(2, 3), 2), subtract(3, 2)), divide(40, const_60)), add(const_1, divide(divide(multiply(multiply(2, 3), 2), subtract(3, 2)), 3)))",
        "linear_formula": "divide(n1,const_60)|multiply(n0,n2)|subtract(n0,n2)|multiply(n2,#1)|divide(#3,#2)|divide(#4,n0)|multiply(#4,#0)|add(#5,const_1)|multiply(#7,#6)",
        "category": "physics"
    },
    {
        "Problem": "if the average of w , b , c , 14 and 15 is 12 . what is the average value of w , b , c and 29",
        "Rationale": "w + b + c + 14 + 15 = 12 * 5 = 60 = > w + b + c = 60 - 29 = 31 w + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d",
        "options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16",
        "correct": "d",
        "annotated_formula": "divide(add(subtract(subtract(multiply(add(const_1, const_4), 12), 15), 14), 29), const_4)",
        "linear_formula": "add(const_1,const_4)|multiply(n2,#0)|subtract(#1,n1)|subtract(#2,n0)|add(n3,#3)|divide(#4,const_4)",
        "category": "general"
    },
    {
        "Problem": "list a consists of 12 consecutive integers . if - 4 is the least integer in list a , what is the range of positive integers in list a ?",
        "Rationale": "since - 4 is the least integer in list a , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b .",
        "options": "a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12",
        "correct": "b",
        "annotated_formula": "subtract(subtract(12, add(4, const_1)), const_1)",
        "linear_formula": "add(n1,const_1)|subtract(n0,#0)|subtract(#1,const_1)",
        "category": "general"
    },
    {
        "Problem": "convert 100 miles into inches ?",
        "Rationale": "\"1 feet = 12 inches 1 mile = 5280 feet 100 mile = 5280 * 12 * 100 = 6336000 ans : a\"",
        "options": "a ) 6336000 , b ) 6542000 , c ) 5462300 , d ) 6213000 , e ) 6120330",
        "correct": "a",
        "annotated_formula": "divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 100), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)))",
        "linear_formula": "add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2)|",
        "category": "physics"
    },
    {
        "Problem": "a room 5 m 44 cm long and 3 m 74 cm broad needs to be paved with square tiles . what will be the least number of square tiles required to cover the floor ?",
        "Rationale": "\"length = 5 m 44 cm = 544 cm breadth = 3 m 74 cm = 374 cm area = 544 * 374 hcf = 34 area of square = 34 * 34 cm 2 no of tiles req = 544 * 374 / 34 * 34 = 16 * 11 = 176 answer a\"",
        "options": "a ) 176 , b ) 124 , c ) 224 , d ) 186 , e ) 190",
        "correct": "a",
        "annotated_formula": "divide(multiply(add(multiply(5, const_100), 44), add(multiply(3, const_100), 74)), multiply(subtract(44, add(multiply(const_2, const_4), const_2)), subtract(44, add(multiply(const_2, const_4), const_2))))",
        "linear_formula": "multiply(n0,const_100)|multiply(n2,const_100)|multiply(const_2,const_4)|add(n1,#0)|add(n3,#1)|add(#2,const_2)|multiply(#3,#4)|subtract(n1,#5)|multiply(#7,#7)|divide(#6,#8)|",
        "category": "physics"
    },
    {
        "Problem": "the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 8 , is :",
        "Rationale": "\"explanation : required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 8 = 540 + 8 = 548 . answer : option d\"",
        "options": "a ) 504 , b ) 536 , c ) 544 , d ) 548 , e ) none of these",
        "correct": "d",
        "annotated_formula": "multiply(54, const_10)",
        "linear_formula": "multiply(n3,const_10)|",
        "category": "general"
    },
    {
        "Problem": "rhonda picked 2 pen from the table , if there were 7 pens on the table and 5 belongs to jill , what is the probability that the 2 pen she picked does not belong to jill ? .",
        "Rationale": "since jill owns 5 of the pen , the subset from which the 2 pens hould be chosen are the 2 pens not owned by jill fom the universe of 7 . the first pen can be one of the 2 from the 7 with probability 2 / 7 . the second pen can be one of the 1 from the 6 remaining with probability 1 / 6 , the total probability will be 2 / 7 \u00d7 1 / 6 . on cancellation , this comes to 2 / 42 . thus , the answer is b - 2 / 42 .",
        "options": "a ) 5 / 42 , b ) 2 / 42 , c ) 7 / 42 , d ) 2 / 7 , e ) 5 / 7",
        "correct": "b",
        "annotated_formula": "multiply(divide(subtract(7, 5), 7), divide(subtract(subtract(7, 5), const_1), subtract(7, const_1)))",
        "linear_formula": "subtract(n1,n2)|subtract(n1,const_1)|divide(#0,n1)|subtract(#0,const_1)|divide(#3,#1)|multiply(#2,#4)",
        "category": "probability"
    },
    {
        "Problem": "a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent w of the cost would the gross profit on the item have been if it had been sold without the discount ?",
        "Rationale": "\"let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : profit w = selling price - original cost price = > 20 % of cp = 80 % of mp - 100 % cp = > mp = 120 cp / 80 = 3 / 2 ( cp ) now if product is sold without any discount , then , profit = selling price ( without discount ) - original cost price = market price - original cost price = mp - cp = 3 / 2 cp - cp = 1 / 2 cp = 50 % of cp thus , answer should bec .\"",
        "options": "a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %",
        "correct": "c",
        "annotated_formula": "subtract(const_100, subtract(subtract(const_100, 20), 20))",
        "linear_formula": "subtract(const_100,n0)|subtract(#0,n1)|subtract(const_100,#1)|",
        "category": "gain"
    },
    {
        "Problem": "a number when divided by 4 , gives 40 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 3",
        "Rationale": "\"explanation : p \u00f7 4 = 40 = > p = 40 * 4 = 160 p / 3 = 160 / 3 = 53 , remainder = 1 answer : option a\"",
        "options": "a ) a ) 1 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7",
        "correct": "a",
        "annotated_formula": "divide(multiply(4, 40), 3)",
        "linear_formula": "multiply(n0,n1)|divide(#0,n3)|",
        "category": "general"
    },
    {
        "Problem": "the total surface area of a cuboid length 12 m , breadth 10 m and height 8 m .",
        "Rationale": "total surface area of cuboid = 2 ( lb + bh + lh ) = 2 ( 120 + 80 + 96 ) = 2 ( 296 ) = > 596 m ( power 2 ) answer is c .",
        "options": "['a ) 576', 'b ) 566', 'c ) 596', 'd ) 556', 'e ) 586']",
        "correct": "c",
        "annotated_formula": "surface_rectangular_prism(12, 10, 8)",
        "linear_formula": "surface_rectangular_prism(n0,n1,n2)",
        "category": "geometry"
    },
    {
        "Problem": "the radius of a cone is 4 m , height 5 m . find the curved surface area ?",
        "Rationale": "\"cone curved surface area = \u03c0 rl = 22 / 7 \u00d7 4 \u00d7 5 = 440 / 7 = 62 6 / 7 slant height ( l ) = \u221a r ( power 2 ) + h ( power 2 ) = \u221a 16 + 9 = \u221a 25 = 5\"",
        "options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9",
        "correct": "c",
        "annotated_formula": "volume_cone(4, 5)",
        "linear_formula": "volume_cone(n0,n1)|",
        "category": "geometry"
    },
    {
        "Problem": "among the two clocks , clock a gains 20 seconds per minute . if clock a and b are set at 2 0 ' clock , when clock a is at 7 : 20 , what does clock b show ?",
        "Rationale": "clock a gains 20 seconds per minute , 1200 seconds per hour or 20 minutes per hour . the two clocks show 2 : 00 at 2 0 ' clock at 3 : 00 - clock b is at 3 : 00 clock a is at 3 : 20 ( 1 hour + gains 20 minutes ) at 4 : 00 - clock b is at 4 : 00 clock a is at 4 : 40 ( 2 hours + gains 40 minutes ) in 4 hours the clock a gains 4 * 20 = 80 minutes or 1 hour 20 minutes if clock a is at 7 : 20 the clock b is at 6 : 00 answer is b",
        "options": "a ) 5 : 30 , b ) 6 : 00 , c ) 5 : 45 , d ) 6 : 20 , e ) 3 : 30",
        "correct": "b",
        "annotated_formula": "divide(add(add(multiply(subtract(7, 2), const_60), 20), divide(multiply(add(multiply(subtract(7, 2), const_60), 20), 20), const_60)), const_60)",
        "linear_formula": "subtract(n3,n1)|multiply(#0,const_60)|add(n0,#1)|multiply(n0,#2)|divide(#3,const_60)|add(#2,#4)|divide(#5,const_60)",
        "category": "physics"
    },
    {
        "Problem": "source : knewton a cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . what is the maximum distance , in miles , that the cyclist could travel in 5 hours ?",
        "Rationale": "we are told that : generallya cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . is it possible the cyclist to travel with maximum speed for some time ? why not , if there is right terrain for that . so , if there is long enough terrain for the maximum speed of 14 mph then the maximum distance , in miles , that the cyclist could travel in 5 hours would be 5 * 14 = 70 miles . answer : c .",
        "options": "a ) 42 , b ) 56 , c ) 70 , d ) 98 , e ) 140",
        "correct": "c",
        "annotated_formula": "multiply(14, 5)",
        "linear_formula": "multiply(n1,n2)",
        "category": "physics"
    },
    {
        "Problem": "the length of a rectangle is two - seventh of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 5929 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 25 units ?",
        "Rationale": "given that the area of the square = 5929 sq . units = > side of square = \u00e2 \u02c6 \u0161 5929 = 77 units the radius of the circle = side of the square = 77 units length of the rectangle = 2 / 7 * 77 = 22 units given that breadth = 25 units area of the rectangle = lb = 22 * 25 = 550 sq . units answer : d",
        "options": "['a ) 660 sq . units', 'b ) 440 sq . units', 'c ) 770 sq . units', 'd ) 550 sq . units', 'e ) 220 sq . units']",
        "correct": "d",
        "annotated_formula": "rectangle_area(25, multiply(sqrt(5929), divide(const_2, add(const_3, const_4))))",
        "linear_formula": "add(const_3,const_4)|sqrt(n0)|divide(const_2,#0)|multiply(#2,#1)|rectangle_area(n1,#3)",
        "category": "geometry"
    },
    {
        "Problem": "the fuel indicator in a car shows 1 / 5 th of the fuel tank as full . when 22 more liters of fuel are poured in to the tank , the indicator rests at the 3 / 4 of the full mark . find the capacity of the tank .",
        "Rationale": "x / 5 + 22 = 3 x / 4 = > x = 40 litres answer : d",
        "options": "a ) 25 litres , b ) 35 litres , c ) 30 litres , d ) 40 litres , e ) none of these",
        "correct": "d",
        "annotated_formula": "divide(22, subtract(divide(3, 4), divide(1, 5)))",
        "linear_formula": "divide(n3,n4)|divide(n0,n1)|subtract(#0,#1)|divide(n2,#2)",
        "category": "general"
    },
    {
        "Problem": "a rectangle with width 8 and diagonal 30 . find the area ?",
        "Rationale": "then the area is : 8 ' ' x 30 ' ' = 240 square inches , or 240 square units hence a",
        "options": "['a ) 240 square units', 'b ) 180 square units', 'c ) 100 square units', 'd ) 150 square units', 'e ) 160 square units']",
        "correct": "a",
        "annotated_formula": "rectangle_area(sqrt(subtract(power(30, const_2), power(8, const_2))), 8)",
        "linear_formula": "power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|sqrt(#2)|rectangle_area(n0,#3)",
        "category": "geometry"
    },
    {
        "Problem": "simplify : 250 x 250 - 100 x 100",
        "Rationale": "\"( 250 ) ^ 2 - ( 100 ) ^ 2 = ( 250 + 100 ) ( 250 - 100 ) = 350 x 150 = 52500 . answer is c .\"",
        "options": "a ) 761200 , b ) 761400 , c ) 52500 , d ) 761500 , e ) none of them",
        "correct": "c",
        "annotated_formula": "add(multiply(250, 250), multiply(100, 100))",
        "linear_formula": "multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|",
        "category": "general"
    },
    {
        "Problem": "the length of each side of an equilateral triangle having an area of 4 \u00e2 \u02c6 \u0161 3 cm 2 is ?",
        "Rationale": "explanation : \u00e2 \u02c6 \u0161 3 / 4 a 2 = 4 \u00e2 \u02c6 \u0161 3 - > a = 4 answer is d",
        "options": "['a ) 4 / 3 cm', 'b ) 3 / 4 cm', 'c ) 3 cm', 'd ) 4 cm', 'e ) 5 cm']",
        "correct": "d",
        "annotated_formula": "sqrt(divide(multiply(4, sqrt(3)), multiply(multiply(divide(const_1, 2), divide(const_1, 2)), sqrt(3))))",
        "linear_formula": "divide(const_1,n2)|sqrt(n1)|multiply(n0,#1)|multiply(#0,#0)|multiply(#3,#1)|divide(#2,#4)|sqrt(#5)",
        "category": "geometry"
    },
    {
        "Problem": "area of four walls of a room is 99 m 2 . the length and breadth of the room are 7.5 m and 3.5 m respectively . the height of the room is :",
        "Rationale": "2 ( 7.5 + 3.5 ) \u00d7 h = 99 2 ( 11 ) h = 99 22 h = 99 h = 99 / 22 = 9 / 2 = 4.5 m answer is d .",
        "options": "['a ) 2.5 m', 'b ) 3.5 m', 'c ) 1.5 m', 'd ) 4.5 m', 'e ) 5.5 m']",
        "correct": "d",
        "annotated_formula": "divide(99, add(multiply(7.5, const_2), multiply(3.5, const_2)))",
        "linear_formula": "multiply(n2,const_2)|multiply(n3,const_2)|add(#0,#1)|divide(n0,#2)",
        "category": "physics"
    },
    {
        "Problem": "if the mean of numbers 28 , x , 42 , 78 , 82 and 104 is 62 , then what is the mean of 128 , 255 , 511 , 1023 and x ?",
        "Rationale": "\"the mean of numbers 28 , x , 42 , 78 and 104 is 62 : 28 + x + 42 + 78 + 82 + 104 = 62 * 6 - - > x = 38 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 511 + 1023 + 38 ) / 5 = 391 . answer : c .\"",
        "options": "a ) 395 , b ) 275 , c ) 391 , d ) 415 , e ) 365",
        "correct": "c",
        "annotated_formula": "divide(add(add(add(add(subtract(multiply(104, add(const_4, const_1)), add(add(add(28, 42), 78), 82)), 62), 128), 255), 511), add(const_4, const_1))",
        "linear_formula": "add(const_1,const_4)|add(n0,n1)|add(n2,#1)|multiply(n4,#0)|add(n3,#2)|subtract(#3,#4)|add(n5,#5)|add(n6,#6)|add(n7,#7)|add(n8,#8)|divide(#9,#0)|",
        "category": "general"
    },
    {
        "Problem": "usc invited each south carolina high school to send up to 39 students to watch a football game . a section which has 199 seats in each row is reserved for those students . what is the least number of rows needed to guarantee that if 2006 students show up , then all students from the same high school can be seated in the same row ?",
        "Rationale": "the answer is 12 rows . if 59 schools send 34 students each , then we can sit at most 5 groups of students in the same row , so we will need 12 rows . next , 12 rows are sufficient . assume that this is not the case . suppose the groups of students are seated like this : first the largest group , then the second largest group , then the third largest group , etc . suppose we run out of space - there are not enough seats in any row to seat together the next group . suppose the first group that can not be seated together is the kth group and it consists of n students . then k 61 since any row fits at least 5 groups . also , n 2006 / k 2006 / 61 < 33 ( all groups already seated are no smaller than the kth group ) . so , n 32 . since there is not enough space in any of the 12 rows to seat the kth group , then there must be at least 168 students seated in each of the 12 rows . now , 12 \u00d7 168 = 2016 > 2006 a contradiction . so , 12 rows are sufficient . correct answer b",
        "options": "a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15",
        "correct": "b",
        "annotated_formula": "add(divide(2006, 199), const_2)",
        "linear_formula": "divide(n2,n1)|add(#0,const_2)",
        "category": "physics"
    },
    {
        "Problem": "a man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes . if the ratio between the length and breadth of the park be 3 : 2 , then its area is :",
        "Rationale": "perimeter = distance covered in 8 min = ( 12000 / 60 * 8 ) m = 1600 m let , length = 3 x meters and breadth = 2 x meters then , 2 ( 3 x + 2 x ) = 1600 or x = 160 therefore , length = 480 m and breadth = 320 m therefore , area = ( 480 * 320 ) m 2 = 153600 m 2 answer : c",
        "options": "['a ) 1536 m 2', 'b ) 15360 m 2', 'c ) 153600 m 2', 'd ) 163600 m 2', 'e ) none of these']",
        "correct": "c",
        "annotated_formula": "multiply(multiply(divide(multiply(8, divide(multiply(12, const_1000), multiply(multiply(const_3, const_2), const_10))), const_10), 2), multiply(divide(multiply(8, divide(multiply(12, const_1000), multiply(multiply(const_3, const_2), const_10))), const_10), 3))",
        "linear_formula": "multiply(n0,const_1000)|multiply(const_2,const_3)|multiply(#1,const_10)|divide(#0,#2)|multiply(n1,#3)|divide(#4,const_10)|multiply(n3,#5)|multiply(n2,#5)|multiply(#6,#7)",
        "category": "physics"
    },
    {
        "Problem": "find the value of ( 875 233 / 899 ) \u00d7 899",
        "Rationale": "\"( 875 233 / 899 ) \u00d7 899 ( 786625 + 233 ) / 899 \u00d7 899 786858 / 899 \u00d7 899 786858 c\"",
        "options": "a ) 786845 , b ) 786857 , c ) 786858 , d ) 786859 , e ) 786860",
        "correct": "c",
        "annotated_formula": "multiply(add(divide(233, 899), 875), 899)",
        "linear_formula": "divide(n1,n2)|add(n0,#0)|multiply(#1,n2)|",
        "category": "general"
    },
    {
        "Problem": "a department of 10 people - 6 men and 4 women - needs to send a team of 5 to a conference . if they want to make sure that there are no more than 3 members of the team from any one gender , how many distinct groups are possible to send ?",
        "Rationale": "they can make a team of 3 men and 2 women . the number of ways to do this is 6 c 3 * 4 c 2 = 20 * 6 = 120 they can make a team of 2 men and 3 women . the number of ways to do this is 6 c 2 * 4 c 3 = 15 * 4 = 60 the total number of distinct groups is 180 . the answer is c .",
        "options": "a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240",
        "correct": "c",
        "annotated_formula": "add(add(multiply(multiply(6, 5), 4), multiply(6, 5)), multiply(6, 5))",
        "linear_formula": "multiply(n1,n3)|multiply(n2,#0)|add(#1,#0)|add(#2,#0)",
        "category": "general"
    },
    {
        "Problem": "forks , spoons , and knives in drawer are in the ratio of 4 : 4 : 3 . if there are 16 forks , the number of knives in the drawer is :",
        "Rationale": "explanation : let forks = 4 x , spoons = 4 x & knives = 3 x . now , 4 x = 16 hence x = 4 . number of knives = 3 x = 12 . answer : c",
        "options": "a ) 8 , b ) 4 , c ) 12 , d ) 16 , e ) 14",
        "correct": "c",
        "annotated_formula": "multiply(divide(16, 4), 3)",
        "linear_formula": "divide(n3,n0)|multiply(n2,#0)",
        "category": "other"
    },
    {
        "Problem": "what is the smallest positive integer x such that 450 x is the cube of a positive integer ?",
        "Rationale": "\"450 = 2 x 3 ^ 2 x 5 ^ 2 now we need two 2 s , one 3 and one 5 to make it perfect cube . so x = 2 ^ 2 x 3 x 5 = 60 . answer is c .\"",
        "options": "a ) 2 , b ) 15 , c ) 30 , d ) 60 , e ) 120",
        "correct": "c",
        "annotated_formula": "add(const_3, const_4)",
        "linear_formula": "add(const_3,const_4)|",
        "category": "geometry"
    },
    {
        "Problem": "if two dice are thrown together , the probability of getting a doublet on the dice is",
        "Rationale": "\"the number of exhaustive outcomes is 36 . let e be the event of getting doublet on the dies is 6 / 36 = 1 / 6 p ( e ) = 1 / 6 . a )\"",
        "options": "a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2",
        "correct": "a",
        "annotated_formula": "divide(const_6, multiply(const_6, const_6))",
        "linear_formula": "multiply(const_6,const_6)|divide(const_6,#0)|",
        "category": "probability"
    },
    {
        "Problem": "it takes 10 days for digging a trench of 100 m long , 50 m broad and 10 m deep . what length of trench , 25 m broad and 15 m deep can be dug in 30 days ?",
        "Rationale": "more days , more length ( direct ) less breadth , more length ( indirect ) more depth , less length ( indirect days 10 : 30 ; breadth 25 : 50 ; : : 100 : x depth 15 : 10 ; : . 10 * 25 * 15 * x = 30 * 50 * 10 * 100 x = ( 30 * 50 * 10 * 100 ) / 10 * 25 * 15 = 400 so the required length = 400 m answer : a",
        "options": "a ) 400 m , b ) 200 m , c ) 100 m , d ) 89 m , e ) 79 m",
        "correct": "a",
        "annotated_formula": "divide(multiply(multiply(multiply(30, 50), 10), 100), multiply(15, multiply(10, 25)))",
        "linear_formula": "multiply(n2,n6)|multiply(n0,n4)|multiply(n0,#0)|multiply(n5,#1)|multiply(n1,#2)|divide(#4,#3)",
        "category": "physics"
    },
    {
        "Problem": "if the price of a certain computer increased 30 percent from a dollars to 351 dollars , then 2 a =",
        "Rationale": "\"before price increase price = a after 30 % price increase price = a + ( 30 / 100 ) * a = 1.3 a = 351 ( given ) i . e . a = 351 / 1.3 = $ 270 i . e . 2 a = 2 * 270 = 540 answer : option a\"",
        "options": "a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700",
        "correct": "a",
        "annotated_formula": "multiply(divide(351, divide(add(const_100, 30), const_100)), 2)",
        "linear_formula": "add(n0,const_100)|divide(#0,const_100)|divide(n1,#1)|multiply(n2,#2)|",
        "category": "general"
    },
    {
        "Problem": "in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability w this college graduate has a graduate degree ?",
        "Rationale": "\"in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability w of cgd / ( cg ) - > 3 / 19 answer d\"",
        "options": "a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43",
        "correct": "d",
        "annotated_formula": "divide(divide(divide(1, 8), divide(2, 3)), add(divide(divide(1, 8), divide(2, 3)), 1))",
        "linear_formula": "divide(n0,n1)|divide(n2,n3)|divide(#0,#1)|add(#2,n0)|divide(#2,#3)|",
        "category": "other"
    },
    {
        "Problem": "a bucket full of nuts was discovered by the crow living in the basement . the crow eats a sixth of the total number of nuts in 4 hours . how many hours i total will it take the crow to finish a quarter of the nuts ?",
        "Rationale": "\"in one hour , the crow eats 1 / 24 of the nuts . ( 1 / 4 ) / ( 1 / 24 ) = 6 hours the answer is a .\"",
        "options": "a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14",
        "correct": "a",
        "annotated_formula": "divide(divide(const_1, const_4), divide(divide(const_1, add(const_2, const_3)), 4))",
        "linear_formula": "add(const_2,const_3)|divide(const_1,const_4)|divide(const_1,#0)|divide(#2,n0)|divide(#1,#3)|",
        "category": "general"
    },
    {
        "Problem": "a and b can finish a work together in 12 days , and b and c together in 16 days . if a alone works for 5 days and then b alone continues for 7 days , then remaining work is done by c in 13 days . in how many days can c alone finish the complete work ?",
        "Rationale": "here lcm of 12 and 16 is taken as total work . ( becomes easy to solve ) assume total work = 48 units then workdone by ( a + b ) in one day = 48 / 12 = 4 units similarly , by ( b + c ) in one day = 48 / 16 = 3 units now according to question , a works 5 days , b for 7 days and c for 13 days to complete total work so , 5 a + 7 b + 13 c = 48 units 5 ( a + b ) + 2 ( b + c ) + 11 c = 48 units 5 * 4 + 2 * 3 + 11 c = 48 units 11 c = 22 units c = 2 units ( c does 2 units of work daily ) therefore , 48 / 2 = 24 days c requires 24 days to complete the work alone . answer d",
        "options": "a ) 22 days , b ) 21 days , c ) 25 days , d ) 24 days , e ) 23 days",
        "correct": "d",
        "annotated_formula": "divide(const_1, divide(subtract(const_1, add(divide(5, 12), divide(const_2, 16))), subtract(add(5, 13), 7)))",
        "linear_formula": "add(n2,n4)|divide(n2,n0)|divide(const_2,n1)|add(#1,#2)|subtract(#0,n3)|subtract(const_1,#3)|divide(#5,#4)|divide(const_1,#6)",
        "category": "physics"
    },
    {
        "Problem": "the ages of two person , differ by 20 years . if 5 years ag , the elder one be 5 times as old as the younger one their present ages ( in years ) are respectively",
        "Rationale": "let their ages be x and ( x + 20 ) years ( x - 5 ) * 5 = ( x + 20 - 5 ) after solving this we get x = 10 years the age of elder one = 10 + 20 = 30 years so the present ages are 30 and 10 years answer : a",
        "options": "a ) 30 , 10 , b ) 2010 , c ) 3515 , d ) 5117 , e ) 20,17",
        "correct": "a",
        "annotated_formula": "add(20, const_10)",
        "linear_formula": "add(n0,const_10)",
        "category": "general"
    },
    {
        "Problem": "the price of stock increased by 8 % last year and decreased by 6 % this year . what is the net percentage change in the price of the stock ?",
        "Rationale": "( 100 % + 8 % ) * ( 100 % - 6 % ) = 1.08 * 0.94 = 1.0152 = 101.52 % . the net percentage change in the price of the stock is ( + ) 1.52 % the answer is d",
        "options": "a ) 0.2 % , b ) 0.8 % , c ) 1.2 % , d ) 1.52 % , e ) 2 %",
        "correct": "d",
        "annotated_formula": "subtract(multiply(multiply(divide(add(const_100, 8), const_100), divide(subtract(const_100, 6), const_100)), const_100), const_100)",
        "linear_formula": "add(n0,const_100)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|multiply(#4,const_100)|subtract(#5,const_100)",
        "category": "general"
    },
    {
        "Problem": "boys and girls in a class are writing letters . there are twice as many girls as boys in the class , and each girl writes 3 more letters than each boy . if boys write 24 of the 90 total letters written by the class , how many letters does each boy write ?",
        "Rationale": "there are twice as many girls as boys in the class - - > g = 2 b . each girl writes 3 more letters than each boy - - > boys write x letters , girls write x + 3 letters . boys write 24 letters - - > bx = 24 . girls write 90 - 24 = 66 letters - - > ( 2 b ) ( x + 3 ) = 66 - - > 2 bx + 6 b = 66 - - > 2 * 24 + 6 b = 66 - - > b = 3 . bx = 24 - - > 3 x = 24 - - > x = 8 . answer : d .",
        "options": "a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12",
        "correct": "d",
        "annotated_formula": "divide(24, divide(subtract(90, multiply(3, 24)), multiply(3, const_2)))",
        "linear_formula": "multiply(n0,n1)|multiply(n0,const_2)|subtract(n2,#0)|divide(#2,#1)|divide(n1,#3)",
        "category": "general"
    },
    {
        "Problem": "a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in meters ) is :",
        "Rationale": "\"speed = ( 5 * 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 * 15 * 60 ) m = 1250 m . correct option : d\"",
        "options": "a ) 600 , b ) 750 , c ) 1000 , d ) 1250 , e ) none of these",
        "correct": "d",
        "annotated_formula": "multiply(divide(multiply(5, const_1000), const_60), 15)",
        "linear_formula": "multiply(n0,const_1000)|divide(#0,const_60)|multiply(n1,#1)|",
        "category": "physics"
    },
    {
        "Problem": "23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , ( . . . )",
        "Rationale": "\"explanation : all are prime numbers in their order , starting from 23 hence , next number is 67 answer : b\"",
        "options": "a ) 53 , b ) 67 , c ) 48 , d ) 59 , e ) 45",
        "correct": "b",
        "annotated_formula": "multiply(43, 23)",
        "linear_formula": "multiply(const_3.0,n0)|",
        "category": "general"
    },
    {
        "Problem": "adam borrowed some money at the rate of 6 % p . a . for the first two years , at the rate of 9 % p . a . for the next 3 years , and at the rate of 14 % p . a . for the period beyond 4 years . if he pays a total interest of 11900 at the end of 9 years , how much money did he borrow ?",
        "Rationale": "let the sum borrowed be x . then , ( x \u00d7 6 \u00d7 21 / 00 ) + ( x \u00d7 9 \u00d7 3 / 100 ) + ( x \u00d7 14 \u00d7 4 / 100 ) = 11900 \u21d2 ( 3 \u2044 25 x + 27 \u2044 100 x + 14 \u2044 25 x ) = 11400 \u21d2 95 \u2044 100 x = 11900 \u21d2 x = ( 11900 \u00d7 100 / 95 ) = 12526 hence , sum borrowed = 12,526 answer b",
        "options": "a ) 10,526 , b ) 12,526 , c ) 14,000 , d ) 16,000 , e ) 16,536",
        "correct": "b",
        "annotated_formula": "subtract(divide(11900, add(add(divide(multiply(6, const_2), const_100), divide(multiply(9, 3), const_100)), divide(multiply(14, 4), const_100))), multiply(const_12, const_1000))",
        "linear_formula": "multiply(n0,const_2)|multiply(n1,n2)|multiply(n3,n4)|multiply(const_1000,const_12)|divide(#0,const_100)|divide(#1,const_100)|divide(#2,const_100)|add(#4,#5)|add(#7,#6)|divide(n5,#8)|subtract(#9,#3)",
        "category": "gain"
    },
    {
        "Problem": "the two trains of lengths 400 m , 600 m respectively , running at same directions . the faster train can cross the slower train in 180 sec , the speed of the slower train is 48 km . then find the speed of the faster train ?",
        "Rationale": "length of the two trains = 600 m + 400 m speed of the first train = x speed of the second train = 48 kmph 1000 / x - 48 = 180 1000 / x - 48 * 5 / 18 = 180 50 = 9 x - 120 x = 68 kmph answer : b",
        "options": "a ) 76 kmph , b ) 68 kmph , c ) 87 kmph , d ) 56 kmph , e ) 10 kmph",
        "correct": "b",
        "annotated_formula": "add(48, multiply(divide(add(400, 600), 180), const_3_6))",
        "linear_formula": "add(n0,n1)|divide(#0,n2)|multiply(#1,const_3_6)|add(n3,#2)",
        "category": "physics"
    },
    {
        "Problem": "surface area of two spheres are in the ratio 1 : 4 what is the ratio of their volumes ?",
        "Rationale": "1 : 8 answer : b",
        "options": "['a ) 1 : 9', 'b ) 1 : 8', 'c ) 1 : 3', 'd ) 1 : 4', 'e ) 1 : 5']",
        "correct": "b",
        "annotated_formula": "power(sqrt(divide(1, 4)), const_3)",
        "linear_formula": "divide(n0,n1)|sqrt(#0)|power(#1,const_3)",
        "category": "geometry"
    },
    {
        "Problem": "two unbiased coins are tossed . what is the probability of getting at most one head ?",
        "Rationale": "\"s = { hh , tt , ht , th } e = event of getting at most one head . e = { tt , ht , th } . p ( e ) = n ( e ) / n ( s ) = 3 / 4 answer is option c\"",
        "options": "a ) 2 / 3 , b ) 1 , c ) 3 / 4 , d ) 2 , e ) 1 / 2",
        "correct": "c",
        "annotated_formula": "negate_prob(divide(const_1, power(const_2, const_3)))",
        "linear_formula": "power(const_2,const_3)|divide(const_1,#0)|negate_prob(#1)|",
        "category": "probability"
    },
    {
        "Problem": "the compound interest on a sum for 2 years is rs . 832 and the simple interest on the same sum for the same period is rs . 800 . the difference between the compound and simple interest for 3 years will be",
        "Rationale": "explanation : given that simple interest for 2 years is rs . 800 i . e . , simple interest for 1 st year is rs . 400 and simple interest for 2 nd year is also rs . 400 compound interest for 1 st year will be 400 and compound interest for 2 nd year will be 832 - 400 = 432 you can see that compound interest for 2 nd year is more than simple interest for 2 nd year by 432 - 400 = rs . 32 i . e , rs . 32 is the interest obtained for rs . 400 for 1 year rate , r = 100 \u00d7 si / pt = ( 100 \u00d7 32 ) / ( 400 \u00d7 1 ) = 8 % difference between compound and simple interest for the 3 rd year = simple interest obtained for rs . 832 = prt / 100 = ( 832 \u00d7 8 \u00d7 1 ) / 100 = rs . 66.56 total difference between the compound and simple interest for 3 years = 32 + 66.56 = rs . 98.56 answer : option b",
        "options": "a ) rs . 48 , b ) rs . 98.56 , c ) rs . 66.56 , d ) rs . 66.58 , e ) none of these",
        "correct": "b",
        "annotated_formula": "add(subtract(832, 800), multiply(832, divide(subtract(832, 800), divide(800, 2))))",
        "linear_formula": "divide(n2,n0)|subtract(n1,n2)|divide(#1,#0)|multiply(n1,#2)|add(#3,#1)",
        "category": "general"
    },
    {
        "Problem": "if a * b = 2 a - 3 b + ab , then 3 * 5 + 5 * 3 is equal to",
        "Rationale": "3 * 5 + 5 * 3 = ( 2 x 3 - 3 x 5 + 3 x 5 ) + ( 2 x 5 - 3 x 3 + 5 x 3 ) = 22 answer a 22",
        "options": "a ) 22 , b ) 25 , c ) 26 , d ) 28 , e ) 23",
        "correct": "a",
        "annotated_formula": "add(multiply(2, 3), multiply(3, 5))",
        "linear_formula": "multiply(n0,n1)|multiply(n1,n3)|add(#0,#1)",
        "category": "general"
    },
    {
        "Problem": "if 25 ^ 5 \u00d7 5 ^ ( - 1 ) = ( 125 ) ^ x , then what is the value of x ?",
        "Rationale": "25 ^ 5 \u00d7 5 ^ ( - 1 ) = ( 125 ) ^ x ( 5 ^ 2 ) ^ 5 \u00d7 5 ^ ( - 1 ) = 5 ^ 3 x 5 ^ 10 x 5 ^ ( - 1 ) = 5 ^ 3 x ; since all of the bases are the same now , we can equate the exponents in the next step 10 - 1 = 3 x 9 = 3 x x = 3 ans . b ) 3",
        "options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6",
        "correct": "b",
        "annotated_formula": "divide(subtract(multiply(const_2, 5), 1), const_3)",
        "linear_formula": "multiply(n1,const_2)|subtract(#0,n3)|divide(#1,const_3)",
        "category": "general"
    },
    {
        "Problem": "a lady starts from p towards q and realizes that at a point r , if he walks 50 km further he will be at a point s , which is as far away from r as it is from q . what is the distance between p and q if the distance between p and r is half the distance from r to q ? ( assume that p , q , r and s are all on the same straight line )",
        "Rationale": "p ___ 50 _____ r ___ 50 _____ s ____ 50 ___ q the above figure gives the locations of p , r , s & q in relation to each other . answer : a",
        "options": "a ) 150 km , b ) 200 km , c ) 250 km , d ) 125 km , e ) 155 km",
        "correct": "a",
        "annotated_formula": "add(multiply(50, const_2), divide(multiply(50, const_2), const_2))",
        "linear_formula": "multiply(n0,const_2)|divide(#0,const_2)|add(#1,#0)",
        "category": "physics"
    },
    {
        "Problem": "the sum of two numbers is 528 and their h . c . f is 33 . the number of pairs of numbers satisfying the above condition is",
        "Rationale": "\"let the required numbers be 33 a and 33 b . then 33 a + 33 b = 528 \\ inline \\ fn _ jvn \\ rightarrow a + b = 16 . now , co - primes with sum 16 are ( 1,15 ) , ( 3,13 ) , ( 5,11 ) and ( 7,9 ) . \\ inline \\ fn _ jvn \\ therefore required numbers are ( 33 x 1 , 33 x 15 ) , ( 33 x 3 , 33 x 13 ) , ( 33 x 5 , 33 x 11 ) , ( 33 x 7 , 33 x 9 ) the number of such pairs is 4 answer : a\"",
        "options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8",
        "correct": "a",
        "annotated_formula": "multiply(divide(add(528, 33), add(const_1, const_1)), subtract(divide(add(528, 33), add(const_1, const_1)), 33))",
        "linear_formula": "add(n0,n1)|add(const_1,const_1)|divide(#0,#1)|subtract(#2,n1)|multiply(#2,#3)|",
        "category": "general"
    },
    {
        "Problem": "consider the sets tn = { n , n + 1 , n + 2 , n + 3 , n + 4 ) , where n = 1 , 2 , 3 , \u2026 , 96 . how many of these sets contain 6 or any integral multiple thereof ( i . e . , any one of the numbers 6 , 12 , 18 , \u2026 ) ?",
        "Rationale": "explanation : if n = 1 , then the set t 1 = { 1 , 23 , 45 } , and it does not have 6 or any multiples . n = 2 to n = 6 has 6 in the set . n = 7 , has the set t 7 = { 7 , 89 , 1011 } , and no 6 or multiples . so 1 in every 6 members do not have 6 or multiples of 6 . so , till n = 96 , there are 16 sets of \u201c 6 members \u201d ( 16 * 6 = 96 ) and 16 sets do not have 6 or its multiples , while the remaining 80 sets have . answer : a",
        "options": "a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84",
        "correct": "a",
        "annotated_formula": "multiply(divide(add(const_2, const_3), 6), 96)",
        "linear_formula": "add(const_2,const_3)|divide(#0,n8)|multiply(n7,#1)",
        "category": "general"
    },
    {
        "Problem": "if a square mirror has a 20 - inch diagonal , what is the approximate perimeter t of the mirror , in inches ?",
        "Rationale": "\"if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter t must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b\"",
        "options": "a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120",
        "correct": "b",
        "annotated_formula": "square_perimeter(divide(20, power(add(const_1, const_1), inverse(const_2))))",
        "linear_formula": "add(const_1,const_1)|inverse(const_2)|power(#0,#1)|divide(n0,#2)|square_perimeter(#3)|",
        "category": "geometry"
    },
    {
        "Problem": "the ratio of the two natural numbers is 5 : 6 . if a certain number is added to both the numbers , the ratio becomes 7 : 8 . if the larger number exceeds the smaller number by 10 , find the number added ?",
        "Rationale": "\"let the two numbers be 5 x and 6 x . let the numbers added to both so that their ratio becomes 7 : 8 be k . ( 5 x + k ) / ( 6 x + k ) = 7 / 8 = > 40 x + 8 k = 42 x + 7 k = > k = 2 x . 6 x - 5 x = 10 = > x = 10 k = 2 x = 20 . answer : c\"",
        "options": "a ) 17 , b ) 14 , c ) 10 , d ) 16 , e ) 20",
        "correct": "c",
        "annotated_formula": "subtract(multiply(multiply(6, 6), 6), multiply(add(multiply(7, 6), 6), 8))",
        "linear_formula": "multiply(n1,n1)|add(n1,#0)|multiply(n2,#0)|multiply(n3,#1)|subtract(#2,#3)|",
        "category": "other"
    },
    {
        "Problem": "if the perimeter of a rectangular house is 1400 m , its length when its breadth is 300 m is ?",
        "Rationale": "2 ( l + 300 ) = 1400 = > l = 400 m answer : b",
        "options": "a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700",
        "correct": "b",
        "annotated_formula": "subtract(divide(1400, const_2), 300)",
        "linear_formula": "divide(n0,const_2)|subtract(#0,n1)|",
        "category": "physics"
    },
    {
        "Problem": "last year the range of the annual bonus of the 100 employees at company x was $ 20000 . if the annual bonus of each of the 100 employees this year is 10 percent greater than it was last year , what is the range of the annual bonus of the 100 employees this year ?",
        "Rationale": "let the lowest bonus be x . therefore , highest bonus is x + 20000 . now bonus of each employee is increased by 10 % . therefore the bonus will remain arranged in the same order as before . or lowest bonus = 1.1 x and highest = 1.1 * ( x + 20000 ) or range = highest - lowest = 1.1 * ( x + 20000 ) - 1.1 x = 22000 , hence , b",
        "options": "a ) $ 27000 , b ) $ 22000 , c ) $ 33000 , d ) $ 16000 , e ) $ 43000",
        "correct": "b",
        "annotated_formula": "multiply(20000, add(const_1, divide(10, const_100)))",
        "linear_formula": "divide(n3,const_100)|add(#0,const_1)|multiply(n1,#1)",
        "category": "general"
    },
    {
        "Problem": "you have to send 3000 grapes 1000 kilometers from grapecity to appleland . your truck can carry 1000 grapes at a time . every time you travel a kilometer towards appleland you must pay a tax of 1 grape but you pay nothing when going in the other direction ( towards grapecity ) . what is highest number of grapes you can get to appleland ?",
        "Rationale": "step one : first you want to make 3 trips of 1,000 grapes 333 kilometers . you will be left with 2,001 grapes and 667 kilometers to go . step two : next you want to take 2 trips of 1,000 grapes 500 kilometers . you will be left with 1,000 grapes and 167 kilometers to go ( you have to leave a grape behind ) . step three : finally , you travel the last 167 kilometers with one load of 1,000 grapes and are left with 833 grapes in appleland . correct answer is a ) 833",
        "options": "a ) 833 , b ) 765 , c ) 665 , d ) 679 , e ) 874",
        "correct": "a",
        "annotated_formula": "subtract(1000, subtract(subtract(1000, floor(divide(1000, const_3))), divide(1000, const_2)))",
        "linear_formula": "divide(n1,const_3)|divide(n1,const_2)|floor(#0)|subtract(n1,#2)|subtract(#3,#1)|subtract(n1,#4)",
        "category": "physics"
    },
    {
        "Problem": "niall ' s income is 60 % less than rex ' s income , and sam ' s income is 25 % less than niall ' s income . if rex gave 60 % of his income to sam and 40 % of his income to niall , niall ' s new income would be what fraction of sam ' s new income ?",
        "Rationale": "we can take some easy numbers and make calculations simpler . let r ( rex ' s income ) = 100 q ( niall ' s income ) = 40 % r = 40 s ( sam ' s income ) = 75 % q = ( 3 / 4 ) * 40 = 30 now , if rex gives 40 % to niall - - > q = 40 + 40 = 80 60 % given to sam - - > s = 30 + 60 = 90 the ratio is : q / s = 80 / 90 = 8 / 9 = a",
        "options": "a ) 8 / 9 , b ) 11 / 12 , c ) 8 / 13 , d ) 11 / 13 , e ) 12 / 13",
        "correct": "a",
        "annotated_formula": "divide(add(40, 40), add(add(40, 40), const_10))",
        "linear_formula": "add(n3,n3)|add(#0,const_10)|divide(#0,#1)",
        "category": "general"
    },
    {
        "Problem": "5 + 5",
        "Rationale": "d",
        "options": "a ) 9 , b ) 12 , c ) 20 , d ) 10 , e ) 0",
        "correct": "d",
        "annotated_formula": "multiply(divide(5, 5), const_100)",
        "linear_formula": "divide(n0,n1)|multiply(#0,const_100)|",
        "category": "general"
    },
    {
        "Problem": "a certain ball team has an equal number of right - and left - handed players . on a certain day , one - third of the players were absent from practice . of the players at practice that day , one - third were right handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of left handed players who were not at practice ?",
        "Rationale": "\"say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 6 absent and 12 present . of the players at practice that day , one - third were right - handed - - > 12 * 1 / 3 = 4 were right - handed and 8 left - handed . the number of right - handed players who were not at practice that day is 9 - 4 = 5 . the number of left - handed players who were not at practice that days is 9 - 8 = 1 . the ratio = 5 / 1 . answer : b\"",
        "options": "a ) 1 / 3 , b ) 5 / 1 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2",
        "correct": "b",
        "annotated_formula": "divide(subtract(divide(const_1, const_2), subtract(subtract(const_1, divide(const_1, const_3)), multiply(divide(const_1, const_3), subtract(const_1, divide(const_1, const_3))))), subtract(divide(const_1, const_2), multiply(divide(const_1, const_3), subtract(const_1, divide(const_1, const_3)))))",
        "linear_formula": "divide(const_1,const_2)|divide(const_1,const_3)|subtract(const_1,#1)|multiply(#1,#2)|subtract(#2,#3)|subtract(#0,#3)|subtract(#0,#4)|divide(#6,#5)|",
        "category": "general"
    },
    {
        "Problem": "a room is 30 m long and 24 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :",
        "Rationale": "let the height be h 2 ( 30 + 24 ) x h \u2013 2 ( 30 - 24 ) h = ( 2 ( 30 x 24 ) ) / ( 2 ( 30 + 24 ) ) = ( 30 x 24 ) / 54 = 40 / 3 m volume = 30 x 24 x 40 / 3 = 9600 m 3 answer : d",
        "options": "['a ) 9.6 m 3', 'b ) 96 m 3', 'c ) 960 m 3', 'd ) 9600 m 3', 'e ) 96000 m 3']",
        "correct": "d",
        "annotated_formula": "volume_rectangular_prism(30, 24, divide(multiply(rectangle_area(30, 24), const_2), rectangle_perimeter(30, 24)))",
        "linear_formula": "rectangle_area(n0,n1)|rectangle_perimeter(n0,n1)|multiply(#0,const_2)|divide(#2,#1)|volume_rectangular_prism(n0,n1,#3)",
        "category": "geometry"
    },
    {
        "Problem": "find the smallest number which should be multiplied with 520 to make it a perfect square",
        "Rationale": "\"explanation : 520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5 required smallest number = 2 * 13 * 5 = 130 130 is the smallest number which should be multiplied with 520 to make it a perfect square . answer : e\"",
        "options": "a ) 337 , b ) 297 , c ) 266 , d ) 116 , e ) 130",
        "correct": "e",
        "annotated_formula": "divide(divide(divide(divide(divide(520, const_3), const_3), const_4), const_4), const_4)",
        "linear_formula": "divide(n0,const_3)|divide(#0,const_3)|divide(#1,const_4)|divide(#2,const_4)|divide(#3,const_4)|",
        "category": "geometry"
    },
    {
        "Problem": "the price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980 . if its price of $ 1.20 in 1970 was 150 percent of its price in 1960 , what was its price in 1980 ?",
        "Rationale": "the price in 1970 was 150 percent of its price in 1960 , means that the percent increase was 50 % from 1960 to 1970 ( and from 1970 to 1980 ) . therefore the price in 1980 = $ 1.2 * 1.5 = $ 1.8 . answer : a .",
        "options": "a ) $ 1.80 , b ) $ 2.00 , c ) $ 2.40 , d ) $ 2.70 , e ) $ 3.00",
        "correct": "a",
        "annotated_formula": "multiply(divide(150, const_100), 1.2)",
        "linear_formula": "divide(n6,const_100)|multiply(n4,#0)",
        "category": "general"
    },
    {
        "Problem": "if c and t are positive integers , ct + c + t can not be",
        "Rationale": "let ct + t + c = x add 1 on both sides : ct + t + c + 1 = x + 1 t ( c + 1 ) + c + 1 = x + 1 ( c + 1 ) ( t + 1 ) = x + 1 minimum value of ( c + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > ct + t + s can not be 6 answer : b",
        "options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9",
        "correct": "b",
        "annotated_formula": "multiply(const_2, const_3)",
        "linear_formula": "multiply(const_2,const_3)",
        "category": "general"
    },
    {
        "Problem": "what is the least common multiple of 15 , 22 and 24 ?",
        "Rationale": "\"let us first write the numbers in the form of prime factors : 15 = 3 * 5 22 = 2 * 11 24 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 1320 option d\"",
        "options": "a ) 60 , b ) 120 , c ) 240 , d ) 1320 , e ) 1720",
        "correct": "d",
        "annotated_formula": "lcm(lcm(add(const_10, const_2), subtract(multiply(const_3, const_10), const_3)), 22)",
        "linear_formula": "add(const_10,const_2)|multiply(const_10,const_3)|subtract(#1,const_3)|lcm(#0,#2)|lcm(n1,#3)|",
        "category": "general"
    },
    {
        "Problem": "a team of 8 persons joins in a shooting competition . the best marksman scored 85 points . if he had scored 92 points , the average score for the team would have been 84 . the number of points , the team scored was :",
        "Rationale": "explanation : let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a ) 665",
        "options": "a ) 665 , b ) 376 , c ) 998 , d ) 1277 , e ) 1991",
        "correct": "a",
        "annotated_formula": "subtract(add(multiply(84, 8), 85), 92)",
        "linear_formula": "multiply(n0,n3)|add(n1,#0)|subtract(#1,n2)",
        "category": "general"
    },
    {
        "Problem": "a certain fruit stand sold apples for $ 0.70 each and guava for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?",
        "Rationale": "some multiple of 7 + some multiple of 5 should yield 63 . to get to a some multiple of 5 , we should ensure that a 3 or 8 ( 5 + 3 ) should be a multiple of 7 . 63 is a direct multiple of 7 , however in this case there wo n ' t be any guava . hence the next option is to look for a multiple of 7 that has 8 as the unit digit . 28 satisfies this hence no . of apples is 4 and no of bananas is 7 . c",
        "options": "a ) 12 , b ) 13 , c ) 11 , d ) 14 , e ) 5",
        "correct": "c",
        "annotated_formula": "add(divide(subtract(6.3, multiply(0.7, const_4)), 0.5), const_4)",
        "linear_formula": "multiply(n0,const_4)|subtract(n2,#0)|divide(#1,n1)|add(#2,const_4)",
        "category": "other"
    },
    {
        "Problem": "4 dice are thrown simultaneously on the board . find the probability which show the same face ?",
        "Rationale": "\"the total number of elementary events associated to the random experiments of throwing four dice simultaneously is : = 6 \u00d7 6 \u00d7 6 \u00d7 6 = 64 = 6 \u00d7 6 \u00d7 6 \u00d7 6 = 64 n ( s ) = 64 n ( s ) = 64 let xx be the event that all dice show the same face . x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) = 6 hence required probability , = n ( x ) n ( s ) = 664 = n ( x ) n ( s ) = 664 = 1 / 216 c\"",
        "options": "a ) 2 / 113 , b ) 3 / 117 , c ) 1 / 216 , d ) 3 / 111 , e ) 4 / 121",
        "correct": "c",
        "annotated_formula": "multiply(divide(const_3, add(const_3, const_3)), divide(const_3, add(const_3, const_3)))",
        "linear_formula": "add(const_3,const_3)|divide(const_3,#0)|multiply(#1,#1)|",
        "category": "probability"
    },
    {
        "Problem": "tough and tricky questions : word problems . operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 8 , when a # b = 100 ?",
        "Rationale": "official solution : ( b ) we know that a # b = 100 and a # b = 4 a \u00b2 + 4 b \u00b2 + 8 ab . so 4 a \u00b2 + 4 b \u00b2 + 8 ab = 100 we can see that 4 a \u00b2 + 4 b \u00b2 + 8 ab is a well - known formula for ( 2 a + 2 b ) \u00b2 . therefore ( 2 a + 2 b ) \u00b2 = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 8 = 10 / 2 + 8 = 13 . the correct answer is d",
        "options": "a ) 5 , b ) 8 , c ) 10 , d ) 13 , e ) 17",
        "correct": "d",
        "annotated_formula": "add(sqrt(divide(100, 4)), 8)",
        "linear_formula": "divide(n6,n0)|sqrt(#0)|add(n4,#1)",
        "category": "general"
    },
    {
        "Problem": "( 7 + 7 + 7 \u00f7 7 ) / ( 5 + 5 + 5 \u00f7 5 ) = ?",
        "Rationale": "\"answer given expression = ( 7 + 7 + 7 \u00f7 7 ) / ( 5 + 5 + 5 \u00f7 5 ) = ( 14 + 1 ) / ( 10 + 1 ) = 15 / 11 option : c\"",
        "options": "a ) 1 , b ) 1 / 5 , c ) 15 / 11 , d ) 3 / 11 , e ) none",
        "correct": "c",
        "annotated_formula": "subtract(divide(multiply(7, add(7, const_1)), const_2), divide(multiply(subtract(7, const_1), 7), const_2))",
        "linear_formula": "add(n3,const_1)|subtract(n0,const_1)|multiply(n3,#0)|multiply(n0,#1)|divide(#2,const_2)|divide(#3,const_2)|subtract(#4,#5)|",
        "category": "general"
    },
    {
        "Problem": "what is the least possible value of x ^ 2 - 15 where x is a positive number .",
        "Rationale": "if x is a positive integer , the lowest value would be x = 1 , because 0 is not included in the natural numbers . that ' s a technicality the gmat would not expect students to know . if x = 1 , then the expression equals - 14 . answer = ( b ) .",
        "options": "a ) - 15 , b ) - 14 , c ) - 13 , d ) - 12 , e ) - 11",
        "correct": "b",
        "annotated_formula": "subtract(subtract(const_1, const_1), 15)",
        "linear_formula": "subtract(const_1,const_1)|subtract(#0,n1)",
        "category": "general"
    },
    {
        "Problem": "the surface area of a sphere is 4 \u03c0 r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area e of that hemisphere ?",
        "Rationale": "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !",
        "options": "['a ) 6 / \u03c0', 'b ) 9 / \u03c0', 'c ) 6', 'd ) 9', 'e ) 12']",
        "correct": "d",
        "annotated_formula": "add(divide(multiply(multiply(4, const_pi), divide(3, const_pi)), 2), multiply(const_pi, divide(3, const_pi)))",
        "linear_formula": "divide(n2,const_pi)|multiply(n0,const_pi)|multiply(#0,#1)|multiply(#0,const_pi)|divide(#2,n1)|add(#4,#3)",
        "category": "geometry"
    },
    {
        "Problem": "if n is a positive integer such that n ! / ( n - 2 ) ! = 342 , find n .",
        "Rationale": "we write n ! = n * ( n - 1 ) ( n - 2 ! ) therefore n ! / ( n - 2 ) ! = n ( n - 1 ) * ( n - 2 ) ! / ( n - 2 ) ! = n ( n - 1 ) . - - > n ( n - 1 ) = 342 - - > n ^ 2 - n - 342 = 0 - - > n ^ 2 - 19 n + 18 n - 342 = 0 - - > n ( n - 19 ) + 18 ( n - 19 ) = 0 - - > ( n - 19 ) ( n + 18 ) = 0 therefore n - 19 = 0 ; n + 18 = 0 ; ( i . e ) n = 19 ; n = - 18 we want positive integer . so , n = 19 . answer : c",
        "options": "a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21",
        "correct": "c",
        "annotated_formula": "sqrt(add(342, divide(const_1, const_4)))",
        "linear_formula": "divide(const_1,const_4)|add(n1,#0)|sqrt(#1)",
        "category": "general"
    },
    {
        "Problem": "a person has 100 $ in 10 $ and 5 $ bill . if the 5 $ bill quantity is twice that of 10 $ bill . what is quantity of 10 $ .",
        "Rationale": "let amount of 10 $ be x . then amount of 5 $ be 2 x . now 5 * 2 x + 10 * x = 100 . thus x = 5 . answer : e",
        "options": "a ) 2 , b ) 6 , c ) 7 , d ) 8 , e ) 5",
        "correct": "e",
        "annotated_formula": "divide(divide(100, 10), const_2)",
        "linear_formula": "divide(n0,n1)|divide(#0,const_2)",
        "category": "general"
    },
    {
        "Problem": "eric throws 2 dice , and his score is the sum of the values shown . sandra throws one dice and her score is the square of the value shown . what is the probabilty that sandras score will be strictly higher than erics score ? ?",
        "Rationale": "sandra score can be like 1,4 , 9,16 , 25,36 eric score less then 1 - - > 0 eric score less then 4 = ( 1,1 ) , ( 1,2 ) ( 2,1 ) - - > 3 eric score less then 9 are ( 1,1 ) ( 1,2 ) ( 1,3 ) ( 1,4 ) ( 1,5 ) ( 1,6 ) ( 2,1 ) ( 2,2 ) ( 2,3 ) ( 2,4 ) ( 2,5 ) ( 2,6 ) ( 3,1 ) ( 3,2 ) ( 3,3 ) ( 3,4 ) ( 3,5 ) ( 4,1 ) ( 4,2 ) ( 4,3 ) ( 4,4 ) ( 5,1 ) ( 5,2 ) ( 5,3 ) ( 6,1 ) ( 6,2 ) - - > 26 eric score will always be less then 16 - - - > 36 eric score will always be less then 25 - - - > 36 eric score will always be less then 36 - - - > 36 total favorable outcomes = 3 + 26 + 36 + 36 + 36 = 137 total possible outcomes = 216 ( 36 * 6 ) probability = 137 / 216 answer : a",
        "options": "['a ) 137 / 216', 'b ) 137 / 218', 'c ) 137 / 217', 'd ) 136 / 216', 'e ) 138 / 216']",
        "correct": "a",
        "annotated_formula": "divide(add(add(add(add(const_3, subtract(power(multiply(2, const_3), const_2), const_10)), power(multiply(2, const_3), const_2)), power(multiply(2, const_3), const_2)), power(multiply(2, const_3), const_2)), multiply(power(multiply(2, const_3), const_2), multiply(2, const_3)))",
        "linear_formula": "multiply(n0,const_3)|power(#0,const_2)|multiply(#0,#1)|subtract(#1,const_10)|add(#3,const_3)|add(#4,#1)|add(#5,#1)|add(#6,#1)|divide(#7,#2)",
        "category": "geometry"
    },
    {
        "Problem": "recently , i decided to walk down an escalator of a tube station . i did some quick calculation in my mind . i found that if i walk down 20 ` ` 6 steps , i require thirty seconds to reach the bottom . however , if i am able to step down thirty ` ` 4 stairs , i would only require eighteen seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time i step off the last step at the bottom ?",
        "Rationale": "26 steps 30 seconds and for 34 steps only 18 seconds left to reach botto . means he covered 8 steps ( i . e . 34 - 26 ) in 12 ( i . e 30 - 18 ) seconds the spped of the boy is 8 steps in 12 seconds after further simplyfy . . 2 steps in 3 seconds after 34 steps only 18 seconds , means 12 more steps are left total steps are 34 + 12 = 46 answer : e",
        "options": "a ) 43 , b ) 44 , c ) 45 , d ) 40 , e ) 46",
        "correct": "e",
        "annotated_formula": "add(add(multiply(const_3, const_10), 4), multiply(divide(subtract(add(multiply(const_3, const_10), 4), add(20, 6)), subtract(multiply(const_3, const_10), multiply(6, const_3))), multiply(6, const_3)))",
        "linear_formula": "add(n0,n1)|multiply(const_10,const_3)|multiply(n1,const_3)|add(n2,#1)|subtract(#1,#2)|subtract(#3,#0)|divide(#5,#4)|multiply(#6,#2)|add(#3,#7)",
        "category": "physics"
    },
    {
        "Problem": "find the volume and surface area of a cuboid 16 m long , 14 m broad and 7 m high .",
        "Rationale": "volume = ( 16 x 14 x 7 ) m ^ 3 = 1568 m ^ 3 . surface area = [ 2 ( 16 x 14 + 14 x 7 + 16 x 7 ) ] cm ^ 2 = ( 2 x 434 ) cm ^ 2 = 868 cm ^ 2 . answer is d",
        "options": "['a ) 878 cm ^ 2', 'b ) 858 cm ^ 2', 'c ) 838 cm ^ 2', 'd ) 868 cm ^ 2', 'e ) none of them']",
        "correct": "d",
        "annotated_formula": "multiply(add(multiply(16, 7), add(multiply(16, 14), multiply(14, 7))), const_2)",
        "linear_formula": "multiply(n0,n1)|multiply(n1,n2)|multiply(n0,n2)|add(#0,#1)|add(#3,#2)|multiply(#4,const_2)",
        "category": "geometry"
    },
    {
        "Problem": "3 - twentieths of the members of a social club are retirees who are also bridge players , 5 - twentieths of the members are retirees , and one - half of the members are bridge players . if 120 of the members are neither retirees nor bridge players , what is the total number of members in the social club ?",
        "Rationale": "{ total } = { retirees } + { bridge players } - { both } + { neither } x = 5 / 20 * x + x / 2 - 3 / 20 * x + 120 20 x = 5 x + 10 x - 3 x + 120 * 20 ( multiply by 20 ) 12 x = 120 * 20 x = 200 . answer : c",
        "options": "a ) 240 , b ) 300 , c ) 200 , d ) 400 , e ) 480",
        "correct": "c",
        "annotated_formula": "multiply(subtract(120, multiply(5, const_4)), const_2)",
        "linear_formula": "multiply(n1,const_4)|subtract(n2,#0)|multiply(#1,const_2)",
        "category": "general"
    },
    {
        "Problem": "there are 13 clubs in a full deck of 52 cards . in a certain game , you pick a card from a standard deck of 52 cards . if the card is a club , you win . if the card is not a club , the person replaces the card to the deck , reshuffles , and draws again . the person keeps repeating that process until he picks a club , and the point is to measure how many draws it took before the person picked a club and , thereby , won . what is the probability that one will pick the first club on the forth draw or later ?",
        "Rationale": "favorable case = the club is picked in the third draw or later unfavorable cases = the club is picked in either first draw , second draw or third draws probability = favorable outcomes / total out comes also probability = 1 - ( unfavorable outcomes / total out comes ) unfavorable case 1 : probability of club picked in first draw = 13 / 52 = 1 / 4 unfavorable case 2 : probability of club picked in second draw ( i . e . first draw is not club ) = ( 39 / 52 ) * ( 13 / 52 ) = ( 3 / 4 ) * ( 1 / 4 ) = 3 / 16 unfavorable case 3 : probability of club picked in third draw ( i . e . first and 2 nd draws are not clubs ) = ( 39 / 52 ) * ( 39 / 52 ) * ( 13 / 52 ) = ( 3 / 4 ) * ( 3 / 4 ) * ( 1 / 4 ) = 9 / 64 total unfavorable probability = ( 1 / 4 ) + ( 3 / 16 ) + ( 9 / 64 ) = ( 16 / 64 ) + ( 12 / 64 ) + ( 9 / 64 ) = 37 / 64 i . e . , favorable probability = 1 - ( 37 / 64 ) = 27 / 64 answer : option e",
        "options": "a ) 1 / 2 , b ) 3 / 4 , c ) 7 / 8 , d ) 27 / 32 , e ) 27 / 64",
        "correct": "e",
        "annotated_formula": "multiply(multiply(divide(subtract(52, 13), 52), divide(subtract(52, 13), 52)), divide(subtract(52, 13), 52))",
        "linear_formula": "subtract(n1,n0)|divide(#0,n1)|multiply(#1,#1)|multiply(#1,#2)",
        "category": "probability"
    },
    {
        "Problem": "a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent e of the distribution is less than m + d ?",
        "Rationale": "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , e = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d",
        "options": "a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %",
        "correct": "d",
        "annotated_formula": "subtract(const_100, divide(subtract(const_100, 68), const_2))",
        "linear_formula": "subtract(const_100,n0)|divide(#0,const_2)|subtract(const_100,#1)",
        "category": "general"
    },
    {
        "Problem": "an electric pump can fill a tank in 3 hours . because of a leak in the tank , it took 3 hours 30 min to fill the tank . in what time the leak can drain out all the water of the tank and will make tank empty ?",
        "Rationale": "\"explanation : we can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak , as work done for 1 hour without leak = 1 / 3 work done with leak = 3 1 / 2 = 7 / 2 work done with leak in 1 hr = 2 / 7 work done by leak in 1 hr = 1 / 3 = 2 / 7 = 1 / 21 so tank will be empty by the leak in 21 hours . answer is d\"",
        "options": "a ) 10 hours , b ) 13 hours , c ) 17 hours , d ) 21 hours , e ) 25 hours",
        "correct": "d",
        "annotated_formula": "divide(3, const_1)",
        "linear_formula": "divide(n1,const_1)|",
        "category": "physics"
    },
    {
        "Problem": "together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours e would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?",
        "Rationale": "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job e in 44 hours . answer : c .",
        "options": "a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .",
        "correct": "c",
        "annotated_formula": "divide(const_1, divide(add(divide(const_1, 4), divide(const_1, 11)), 15))",
        "linear_formula": "divide(const_1,n2)|divide(const_1,n5)|add(#0,#1)|divide(#2,n0)|divide(const_1,#3)",
        "category": "physics"
    },
    {
        "Problem": "ramesh has solved 108 questions in an examination . if he got only \u2018 0 \u2019 marks , then how many questions were wrong when one mark is given for each one correct answer and 1 / 3 mark is subtracted on each wrong answer .",
        "Rationale": "if ramesh attempts ' x ' questions correct and ' y ' questions wrong , then x + y = 108 - - - ( i ) & x - ( 1 / 3 ) y = 0 - - - ( ii ) on solving x = 27 , y = 81 answer : d",
        "options": "a ) 78 , b ) 79 , c ) 80 , d ) 81 , e ) 82",
        "correct": "d",
        "annotated_formula": "subtract(108, divide(multiply(divide(1, 3), 108), add(const_1, divide(1, 3))))",
        "linear_formula": "divide(n2,n3)|add(#0,const_1)|multiply(n0,#0)|divide(#2,#1)|subtract(n0,#3)",
        "category": "general"
    },
    {
        "Problem": "what is the measure of the angle x made by the diagonals of the any adjacent sides of a cube .",
        "Rationale": "\"c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be x = 60 . c\"",
        "options": "a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90",
        "correct": "c",
        "annotated_formula": "divide(const_180, const_3)",
        "linear_formula": "divide(const_180,const_3)|",
        "category": "geometry"
    },
    {
        "Problem": "the simple interest in 14 months on a certain sum at the rate of 6 per cent per annum is 250 more than the interest on the same sum at the rate of 8 per cent in 8 months . how much amount was borrowed ?",
        "Rationale": "let the amount be x . from the question , x \u00d7 14 \u00d7 6 / 1200 \u2212 x \u00d7 8 \u00d7 8 / 1200 = 250 \u2234 x = 15000 answer a",
        "options": "a ) 15000 , b ) 25000 , c ) 7500 , d ) 14500 , e ) none of these",
        "correct": "a",
        "annotated_formula": "divide(250, subtract(multiply(divide(14, const_12), divide(6, const_100)), multiply(divide(8, const_12), divide(8, const_100))))",
        "linear_formula": "divide(n0,const_12)|divide(n1,const_100)|divide(n3,const_12)|divide(n3,const_100)|multiply(#0,#1)|multiply(#2,#3)|subtract(#4,#5)|divide(n2,#6)",
        "category": "general"
    },
    {
        "Problem": "rakesh ' s mathematics test had 75 problems , 10 arithmetic , 30 algebra , 35 geometry problems . although he answered 70 % of arithmetic , 40 % of arithmetic and 60 % of geometry problems correctly , still he got less than 60 % problems right . how many more questions he would have to answer more to get passed ?",
        "Rationale": "explanation : number of questions attempted correctly = ( 70 % of 10 + 40 % of 30 + 60 % of 35 ) = 7 + 12 + 21 = 40 . questions to be answered correctly for 60 % = 60 % of total quotations = 60 % of 75 = 45 . he would have to answer 45 - 40 = 5 answer : a",
        "options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9",
        "correct": "a",
        "annotated_formula": "subtract(divide(multiply(75, 60), const_100), add(add(divide(multiply(10, 70), const_100), divide(multiply(30, 40), const_100)), divide(multiply(35, 60), const_100)))",
        "linear_formula": "multiply(n0,n6)|multiply(n1,n4)|multiply(n2,n5)|multiply(n3,n6)|divide(#0,const_100)|divide(#1,const_100)|divide(#2,const_100)|divide(#3,const_100)|add(#5,#6)|add(#8,#7)|subtract(#4,#9)",
        "category": "general"
    },
    {
        "Problem": "one day , connie plays a game with a fair 6 - sided die . connie rolls the die until she rolls a 6 , at which point the game ends . if she rolls a 6 on her first turn , connie wins 6 dollars . for each subsequent turn , connie wins 1 6 of the amount she would have won the previous turn . what is connie ' s expected earnings from the game ?",
        "Rationale": "connie has a 1 6 chance of winning 6 dollars her first turn . she has a 5 / 6 1 / 6 chance of winning 1 dollar her second turn . next , she has a 25 36 1 / 6 chance of winning 1 / 6 dollars her third turn . generalizing , connie ' s expected earnings form a geometric series with initial term 1 / 6 * 6 = 1 and common ratio 5 / 6 * 1 / 6 = 5 / 36 . hence , connie ' s expected earnings are 1 / 1 - 5 / 36 = 36 / 31 correct answer d",
        "options": "a ) 32 / 31 , b ) 33 / 31 , c ) 34 / 31 , d ) 36 / 31 , e ) 0 / 31",
        "correct": "d",
        "annotated_formula": "divide(const_1, subtract(const_1, divide(divide(subtract(6, 1), 6), 6)))",
        "linear_formula": "subtract(n0,n4)|divide(#0,n0)|divide(#1,n0)|subtract(const_1,#2)|divide(const_1,#3)",
        "category": "general"
    },
    {
        "Problem": "a man walking at 3 / 4 th of the speed , reaches his office late by 2 hours . what is the usual time ?",
        "Rationale": "at 3 / 4 th of speed he is late by ' 2 hrs ' x - 3 / 4 ( x ) = 2 x = 8 so 8 - 2 = 6 hrs ( since 2 hrs late ) answer : c",
        "options": "a ) 5 hours , b ) 3 hours , c ) 6 hours , d ) 12 hours , e ) 15 hours",
        "correct": "c",
        "annotated_formula": "divide(multiply(multiply(multiply(divide(3, 4), 2), divide(3, 4)), 2), subtract(multiply(divide(3, 4), 2), multiply(multiply(divide(3, 4), 2), divide(3, 4))))",
        "linear_formula": "divide(n0,n1)|multiply(n2,#0)|multiply(#0,#1)|multiply(n2,#2)|subtract(#1,#2)|divide(#3,#4)",
        "category": "physics"
    },
    {
        "Problem": "given a + b = 1 , find the value of 2 a + 2 b . two solutions are presented below . only one is correct , even though both yield the correct answer .",
        "Rationale": "because a + b = 1 , 2 a + 2 b = 2 ( a + b ) = 2 \u00d7 1 = 2 . correct answer d",
        "options": "a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 1",
        "correct": "d",
        "annotated_formula": "subtract(add(add(2, 1), 2), add(2, 1))",
        "linear_formula": "add(n0,n1)|add(n1,#0)|subtract(#1,#0)",
        "category": "general"
    },
    {
        "Problem": "in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of four metre is left from all sides of the boundary of the garden . what is the length of the garden ?",
        "Rationale": "\"between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 4 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 \u00e3 \u2014 2 ) + 4 + 4 = 30 meter answer is e .\"",
        "options": "a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30",
        "correct": "e",
        "annotated_formula": "add(add(multiply(subtract(12, const_1), 2), divide(10, 2)), divide(10, 2))",
        "linear_formula": "divide(n0,n2)|subtract(n1,const_1)|multiply(n2,#1)|add(#0,#2)|add(#3,#0)|",
        "category": "physics"
    },
    {
        "Problem": "the averge score of a cricketer for 10 matches is 45 runs . if the average for the first 6 matches is 48 . then find the average for the last 4 matches ?",
        "Rationale": "sum of last 4 matches = ( ( 10 \u00d7 45 ) \u2013 ( 6 \u00d7 48 ) = 162 average = 162 / 4 = 40.5 answer : d",
        "options": "a ) 43.25 , b ) 43 , c ) 38 , d ) 40.5 , e ) 36",
        "correct": "d",
        "annotated_formula": "divide(subtract(multiply(45, 10), multiply(6, 48)), 4)",
        "linear_formula": "multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4)",
        "category": "general"
    },
    {
        "Problem": "simplify : 256 x 256 - 144 x 144",
        "Rationale": "\"( 256 ) ^ 2 - ( 144 ) ^ 2 = ( 256 + 144 ) ( 256 - 144 ) = 400 x 112 = 44800 answer is b\"",
        "options": "a ) 761200 , b ) 44800 , c ) 761800 , d ) 761500 , e ) none of them",
        "correct": "b",
        "annotated_formula": "add(multiply(256, 256), multiply(144, 144))",
        "linear_formula": "multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|",
        "category": "general"
    },
    {
        "Problem": "how many bricks , each measuring 25 cm * 11.25 cm * 6 cm , will be needed to build a wall 8 m * 6 m * 22.5 m",
        "Rationale": "\"to solve this type of question , simply divide the volume of wall with the volume of brick to get the numbers of required bricks so lets solve this number of bricks = volume of wall / volume of 1 brick = 800 \u2217 600 \u2217 22.5 / 25 \u2217 11.25 \u2217 6 = 6400 answer : a\"",
        "options": "a ) 6400 , b ) 3777 , c ) 2679 , d ) 2667 , e ) 1997",
        "correct": "a",
        "annotated_formula": "divide(multiply(multiply(multiply(8, const_100), multiply(6, const_100)), 22.5), multiply(multiply(25, 11.25), 6))",
        "linear_formula": "multiply(n3,const_100)|multiply(n4,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(n2,#2)|multiply(n5,#3)|divide(#5,#4)|",
        "category": "physics"
    },
    {
        "Problem": "a farm has chickens , cows and sheep . there are 6 times the number of chickens and cows than sheep . if there are more cows than chickens or sheep , and together , cows and chickens have a total of 100 feet and heads , how many sheep live at the farm ?",
        "Rationale": "chicken - ch cows - c sheep - s ch + c = 6 s c > ch and c > s each cow has 4 legs and 1 head each chicken has 2 legs and 1 head so 5 c + 3 ch = 100 ( sum of legs and head ) there are 2 possible solutions to this equation c = 11 and ch = 9 or c = 14 and ch = 10 since from first equation where ch + c = 6 s the sum of ch and c should be divisbile by 6 . 20 is not so the only possible solution is c = 14 and ch = 10 . so s = 4 answer : d",
        "options": "a ) 5 , b ) 8 , c ) 10 , d ) 4 , e ) 17",
        "correct": "d",
        "annotated_formula": "subtract(6, const_2)",
        "linear_formula": "subtract(n0,const_2)",
        "category": "general"
    },
    {
        "Problem": "thirty percent of the members of a swim club have passed the lifesaving test . among the members who have not passed the test , 26 have taken the preparatory course and 65 have not taken the course . how many members are there in the swim club ?",
        "Rationale": "\"30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 65 + 26 = 91 members have not passed the test , thus 0.7 * total = 91 - - > total = 130 . answer : d .\"",
        "options": "a ) 60 , b ) 80 , c ) 100 , d ) 130 , e ) 140",
        "correct": "d",
        "annotated_formula": "divide(add(26, 65), divide(subtract(const_100, 65), const_100))",
        "linear_formula": "add(n0,n1)|subtract(const_100,n1)|divide(#1,const_100)|divide(#0,#2)|",
        "category": "gain"
    },
    {
        "Problem": "if a population of women in a town is 50 % of men . what is the population of men as a percentage of population of women ?",
        "Rationale": "\"we ' re told that the number of women in a town is equal to 50 % of the number of men in that town . men = 10 women = 5 we ' re asked for the number of men , as a percentage of the number of women . m / w % = 10 / 5 = 200 % answer is c\"",
        "options": "a ) 100 % , b ) 120 % , c ) 200 % , d ) 150 % , e ) 180 %",
        "correct": "c",
        "annotated_formula": "multiply(divide(const_100, 50), const_100)",
        "linear_formula": "divide(const_100,n0)|multiply(#0,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "in an examination , the percentage of students qualified to the students appeared from school ' p ' is 70 % . in school ' q ' , the number of students appeared is 30 % more than the students appeared from school ' p ' and the number of students qualified from school ' q ' is 50 % more than the students qualified from school ' p ' . what is the % of students qualified to the number of students appeared from school ' q ' ?",
        "Rationale": "explanation : number of students appeared from school ' p ' = 100 , say number of students qualified from school ' p ' = 70 and number of students appeared from school ' q ' = 130 number of students qualified from school ' q ' = 50 % more than those qualified from school ' p ' . = 70 + 35 = 105 % of students qualified to the number of students appeared from school b = 105 / 130 * 100 = 80.76 % answer : b",
        "options": "a ) 80.78 % , b ) 80.76 % , c ) 80.72 % , d ) 80.79 % , e ) 80.74 %",
        "correct": "b",
        "annotated_formula": "multiply(divide(multiply(divide(add(50, const_100), const_100), divide(70, const_100)), divide(add(30, const_100), const_100)), const_100)",
        "linear_formula": "add(n2,const_100)|add(n1,const_100)|divide(n0,const_100)|divide(#0,const_100)|divide(#1,const_100)|multiply(#3,#2)|divide(#5,#4)|multiply(#6,const_100)",
        "category": "general"
    },
    {
        "Problem": "in a shop , the profit is 320 % of the cost . if the cost increases by 25 % but the selling price remains constant , find out approximately what percentage of the selling price is the profit ?",
        "Rationale": "let the cp = 100 profit = ( 320 / 100 ) \u00d7 100 = 320 sp = cp + profit = 100 + 320 = 420 if the cost increases by 25 % , new cp = ( 125 / 100 ) \u00d7 100 = 125 selling price is constant , hence new sp = 420 profit = sp \u2013 cp = 420 \u2013 125 = 295 required percentage = ( 295 / 420 ) \u00d7 100 = 2950 / 42 = 1475 / 21 \u2248 70 answer : e",
        "options": "a ) 180 % , b ) 120 % , c ) 90 % , d ) 80 % , e ) 70 %",
        "correct": "e",
        "annotated_formula": "multiply(divide(subtract(add(320, const_100), add(25, const_100)), add(320, const_100)), const_100)",
        "linear_formula": "add(n0,const_100)|add(n1,const_100)|subtract(#0,#1)|divide(#2,#0)|multiply(#3,const_100)",
        "category": "gain"
    },
    {
        "Problem": "if log 8 x + log 8 1 / 6 = 1 / 3 , then the value of x is :",
        "Rationale": "\"log 8 x + log 8 ( 1 / 6 ) = 1 / 3 = > ( log x / log 8 ) + ( log 1 / 6 / log 8 ) = log ( 81 / 3 ) = log 2 = > log x = log 2 \u2013 log 1 / 6 = log ( 2 * 6 / 1 ) = log 12 answer : a\"",
        "options": "a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26",
        "correct": "a",
        "annotated_formula": "multiply(power(8, divide(1, 3)), 6)",
        "linear_formula": "divide(n2,n5)|power(n0,#0)|multiply(n3,#1)|",
        "category": "general"
    },
    {
        "Problem": "find the sum of first 20 multiples of 12 .",
        "Rationale": "\"sum of first 20 multiples of 12 are = ( 12 \u00d7 1 ) + ( 12 \u00d7 2 ) + ( 12 \u00d7 3 ) + . . . . . . + ( 12 \u00d7 19 ) + ( 12 \u00d7 20 ) . = 12 ( 1 + 2 + 3 + . . . . . + 20 ) use the formula : n ( n + 1 ) 2 \u21d2 12 \u00d7 ( 20 \u00d7 21 ) 2 = 2520 . answer : a\"",
        "options": "a ) 2520 , b ) 3878 , c ) 2778 , d ) 27 , e ) 911",
        "correct": "a",
        "annotated_formula": "add(divide(divide(20, divide(divide(divide(divide(divide(20, const_2), const_2), const_2), const_2), const_2)), const_2), add(const_1, sqrt(divide(divide(20, divide(divide(divide(divide(divide(20, const_2), const_2), const_2), const_2), const_2)), const_2))))",
        "linear_formula": "divide(n0,const_2)|divide(#0,const_2)|divide(#1,const_2)|divide(#2,const_2)|divide(#3,const_2)|divide(n0,#4)|divide(#5,const_2)|sqrt(#6)|add(#7,const_1)|add(#8,#6)|",
        "category": "general"
    },
    {
        "Problem": "if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips ?",
        "Rationale": "\"on the first three flips , you must get heads . whats the probability of getting heads ? its 1 / 2 so for the first three flips , your probability is ( 1 / 2 ) ^ 3 = 1 / 8 now for the last two , you want to get tails only . whats the prob of getting tails ? well , its the same as prob of getting a heads , namely , 1 / 2 for the last two flips , your probability is ( 1 / 2 ) ^ 2 = 1 / 4 so your overall probability for the event in question is 1 / 8 * 1 / 4 = 1 / 32 answer : e\"",
        "options": "a ) 3 / 5 , b ) 1 / 2 , c ) 1 / 5 , d ) 1 / 8 , e ) 1 / 32",
        "correct": "e",
        "annotated_formula": "power(divide(1, 2), 5)",
        "linear_formula": "divide(n0,n1)|power(#0,n2)|",
        "category": "probability"
    },
    {
        "Problem": "a piece of work can finish by a certain number of men in 100 days . if however , there were 10 men less , it would take 10 days more for the work to be finished . how many men were there originally ?",
        "Rationale": "originally let there be x men . less men , more days ( indirect ) : . ( x - 10 ) : x : : 100 : 110 or x - 10 / x = 100 / 110 or 11 x - 110 = 10 x or x = 110 so , originally there were 110 men . answer : d",
        "options": "a ) 75 , b ) 82 , c ) 100 , d ) 110 , e ) 120",
        "correct": "d",
        "annotated_formula": "divide(multiply(divide(add(100, 10), 10), 10), subtract(divide(add(100, 10), 10), 10))",
        "linear_formula": "add(n0,n1)|divide(#0,n1)|multiply(n1,#1)|subtract(#1,n1)|divide(#2,#3)",
        "category": "physics"
    },
    {
        "Problem": "a square is drawn inside a right - angled triangle with the two perpendicular sides as 12 cm and 8 cm . what is the side of the largest possible square that can be drawn ?",
        "Rationale": "area of triangle is 1 / 2 * 12 * 8 = 48 side of square = x the entire triangle split into two right angled triangle and one square with dimensions as follows i ) square with side x ii ) right angled triangle with perpendicular sides x and 12 - x iii ) right angled triangle with perpendicular sides 8 - x and x sum of area of all three = 48 = x 2 + 1 / 2 * x * ( 12 - x ) + 1 / 2 * x * ( 8 - x ) = 48 = x = 4.8 cm answer : a",
        "options": "['a ) 4.8 cm', 'b ) 4.4 cm', 'c ) 4.9 cm', 'd ) 5.0 cm', 'e ) 5.2 cm']",
        "correct": "a",
        "annotated_formula": "divide(divide(multiply(12, 8), const_2), const_10)",
        "linear_formula": "multiply(n0,n1)|divide(#0,const_2)|divide(#1,const_10)",
        "category": "geometry"
    },
    {
        "Problem": "the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee \u2019 s report , what is the probability that the two members selected will both be social teachers ?",
        "Rationale": "\"probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( b )\"",
        "options": "a ) 2 / 3 , b ) 1 / 12 , c ) 2 / 9 , d ) 1 / 2 , e ) 1 / 24",
        "correct": "b",
        "annotated_formula": "multiply(divide(3, add(add(3, 4), 2)), divide(2, subtract(add(add(3, 4), 2), const_1)))",
        "linear_formula": "add(n0,n1)|add(n2,#0)|divide(n0,#1)|subtract(#1,const_1)|divide(n2,#3)|multiply(#2,#4)|",
        "category": "probability"
    },
    {
        "Problem": "by how much is 70 % of 120 greater than 35 % of 200 .",
        "Rationale": "( 70 / 100 ) * 120 \u00e2 \u20ac \u201c ( 35 / 100 ) * 200 84 - 70 = 14 answer : b",
        "options": "a ) 15 , b ) 14 , c ) 13 , d ) 16 , e ) 17",
        "correct": "b",
        "annotated_formula": "subtract(multiply(120, divide(70, const_100)), multiply(divide(35, const_100), 200))",
        "linear_formula": "divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|multiply(n3,#1)|subtract(#2,#3)",
        "category": "gain"
    },
    {
        "Problem": "the cyclist going at a constant rate of 18 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 48 miles per hour . the motor - cyclist stops to wait for the cyclist 15 minutes after passing cyclist , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ?",
        "Rationale": "for the 15 minutes the motor - cyclist continues to overtake the cyclist , she is going at 30 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 18 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 30 / 18 * 15 or 25 minutes answer is ( a )",
        "options": "a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45",
        "correct": "a",
        "annotated_formula": "divide(multiply(subtract(divide(48, const_4), divide(18, const_4)), const_60), 18)",
        "linear_formula": "divide(n1,const_4)|divide(n0,const_4)|subtract(#0,#1)|multiply(#2,const_60)|divide(#3,n0)",
        "category": "physics"
    },
    {
        "Problem": "the squared value of the diagonal of a rectangle is ( 64 + b 2 ) sq cm , where b is less than 8 cm . what is the breadth of that rectangle ?",
        "Rationale": "diagonal 2 = 64 + b 2 or , 10 ( 2 ) = 64 + 6 ( 2 ) answer a",
        "options": "['a ) 6 cm', 'b ) 10 cm', 'c ) 8 cm', 'd ) data inadequate', 'e ) none of these']",
        "correct": "a",
        "annotated_formula": "subtract(sqrt(64), const_2)",
        "linear_formula": "sqrt(n0)|subtract(#0,const_2)",
        "category": "geometry"
    },
    {
        "Problem": "in a certain game , a large container is filled with red , yellow , green , and blue beads worth , respectively , 7 , 5 , 3 , and 2 points each . a number of beads are then removed from the container . if the product of the point values of the removed beads is 30 , 870000 , how many red beads were removed ?",
        "Rationale": "30 , 870,000 = 2 ^ 4 * 5 ^ 4 * 3087 = 2 ^ 4 * 3 * 5 ^ 4 * 1029 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 343 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 7 ^ 3 the answer is c .",
        "options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5",
        "correct": "c",
        "annotated_formula": "divide(multiply(3, const_1), const_1)",
        "linear_formula": "multiply(n2,const_1)|divide(#0,const_1)",
        "category": "general"
    },
    {
        "Problem": "# 88 a necklace is made by stringing q no individual beads together in the repeating pattern red bead , green bead , white bead , blue bead , and yellow bead . if the necklace design begins with a red bead and ends with a white bead , then q could equal",
        "Rationale": "you can just write out the pattern and count : rgwbyrgwbyrgwby . . . but to save time a good test taker will just look for a pattern . min # is 3 , because w is the third one . then every 5 beads another white comes , so it must be 3 + 5 + 5 + 5 . . and so on . . . 3 + 5 = 8 3 + 5 + 5 = 13 3 + 5 + 5 + 5 = 18 3 + 5 + 5 + 5 + 5 = 23 so you see it ends in either 8 or 3 . pick an answer that ends in either 8 or 3 . only one answer does , b .",
        "options": "a ) 16 , b ) 28 , c ) 41 , d ) 54 , e ) 65",
        "correct": "b",
        "annotated_formula": "add(add(add(add(add(add(divide(88, 88), const_2), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3))",
        "linear_formula": "add(const_2,const_3)|divide(n0,n0)|add(#1,const_2)|add(#2,#0)|add(#3,#0)|add(#4,#0)|add(#5,#0)|add(#6,#0)",
        "category": "general"
    },
    {
        "Problem": "you need to pick any number from ' 1 , 3 , 5 , 7 , 9 , 11 , 13 and 15 ' to make below equation true . ( ) + ( ) + ( ) = 30 can you solve it ?",
        "Rationale": "solution : 3 ! + 15 + 9 = 30 explanation : 3 ! = 3 * 2 * 1 = 6 6 + 15 + 9 = 30 answer b",
        "options": "a ) 29 , b ) 30 , c ) 31 , d ) 32 , e ) 33",
        "correct": "b",
        "annotated_formula": "add(add(11, factorial(3)), 13)",
        "linear_formula": "factorial(n1)|add(n5,#0)|add(n6,#1)",
        "category": "general"
    },
    {
        "Problem": "ram and shyam start a two - length swimming race at the same moment but from opposite ends of the pool . they swim in lanes at uniform speeds , but hardy is faster than andy . they 1 st pass at a point 18.5 m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec . after setting off on the return length , the swimmers pass for the 2 nd time just 10.5 m from the shallow end . how long is the pool ?",
        "Rationale": "let x = length of pool at first meeting , combined distance = x at second meeting , combined distance = 3 x if andy swims 18.5 m of x , then he will swim 3 * 18.5 = 55.5 m of 3 x andy ' s total distance to second meeting = x + 10.5 m x + 10.5 = 55.5 m x = 45 m e",
        "options": "a ) 65 , b ) 60 , c ) 55 , d ) 50 , e ) 45",
        "correct": "e",
        "annotated_formula": "subtract(add(multiply(18.5, const_2), 18.5), 10.5)",
        "linear_formula": "multiply(n1,const_2)|add(n1,#0)|subtract(#1,n5)",
        "category": "physics"
    },
    {
        "Problem": "little john had $ 8.50 . he spent $ 1.25 on sweets and gave to his two friends $ 1.20 and $ 2.20 . how much money was left ?",
        "Rationale": "\"john spent and gave to his two friends a total of 1.25 + 1.20 + 2.20 = $ 4.65 money left 8.50 - 4.65 = $ 3.85 correct answer is c ) $ 3.85\"",
        "options": "a ) $ 5.85 , b ) $ 6.85 , c ) $ 3.85 , d ) $ 2.85 , e ) $ 4.85",
        "correct": "c",
        "annotated_formula": "subtract(8.50, add(1.25, add(1.20, 1.20)))",
        "linear_formula": "add(n2,n2)|add(n1,#0)|subtract(n0,#1)|",
        "category": "general"
    },
    {
        "Problem": "the speed of a bus increases by 2 kmph after every one hour . if the distance travelled in the first one hour was 35 km , what was the total distance travelled in 12 hours ?",
        "Rationale": "dist 1 st hr = 35 km speed of bus by 2 kmph 2 nd hr = 37 km 3 rd hr = 39 km tot = 35 + 37 + 39 + . . . . ( 12 terms ) 12 / 2 ( 2 * 35 + ( 12 - 1 ) 2 ] = 6 * 92 = 552 answer c",
        "options": "a ) 550 , b ) 500 , c ) 552 , d ) 560 , e ) 580",
        "correct": "c",
        "annotated_formula": "multiply(divide(12, 2), add(multiply(subtract(12, const_1), 2), multiply(2, 35)))",
        "linear_formula": "divide(n2,n0)|multiply(n0,n1)|subtract(n2,const_1)|multiply(n0,#2)|add(#3,#1)|multiply(#4,#0)",
        "category": "physics"
    },
    {
        "Problem": "it will take 16 days for mary to complete a certain task alone . she worked for 8 days before she was joined by her sister . both of them completed the remaining task in 2 and half days . if her sister had joined her when she started the task , how many days would it have taken ?",
        "Rationale": "explanation : mary and her sister complete half work in 2.5 days = > they can complete whole work in 5 days answer : option d",
        "options": "a ) 6 , b ) 8 , c ) 2 , d ) 5 , e ) 4",
        "correct": "d",
        "annotated_formula": "add(divide(divide(const_1, 8), divide(const_1, 16)), const_3)",
        "linear_formula": "divide(const_1,n1)|divide(const_1,n0)|divide(#0,#1)|add(#2,const_3)",
        "category": "physics"
    },
    {
        "Problem": "shruti purchased several number of 3 articles p , q and r in the proportion 3 : 2 : 3 . if the unit costs of the articles p , q and r are 200 , rs . 90 and rs . 60 respectively , how many articles of q must have been purchased in the total purchases of rs . 4800 ?",
        "Rationale": "explanation : let the number of articles of types p , q and r be 3 a , 2 a and 3 a respectively . thus , we get , ( 200 x 3 a ) + ( 90 x 2 a ) + ( 60 x 3 a ) = 4800 960 a = 4800 a = 5 hence , the number of articles of type \u201c q \u201d = 2 x 5 = 10 answer b",
        "options": "a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16",
        "correct": "b",
        "annotated_formula": "multiply(divide(4800, add(add(multiply(3, 200), multiply(2, 90)), multiply(3, 60))), 2)",
        "linear_formula": "multiply(n0,n4)|multiply(n2,n5)|multiply(n0,n6)|add(#0,#1)|add(#3,#2)|divide(n7,#4)|multiply(n2,#5)",
        "category": "general"
    },
    {
        "Problem": "the l . c . m of two numbers is 48 . the numbers are in the ratio 2 : 3 . the sum of numbers is ?",
        "Rationale": "\"let the numbers be 2 x and 3 x . then , their l . c . m = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : c\"",
        "options": "a ) 22 , b ) 67 , c ) 40 , d ) 88 , e ) 11",
        "correct": "c",
        "annotated_formula": "divide(multiply(2, 48), 3)",
        "linear_formula": "multiply(n0,n1)|divide(#0,n2)|",
        "category": "other"
    },
    {
        "Problem": "a and b together do a work in 20 days . b and c together in 15 days and c and a in 12 days . so a , b and c together finish same work in how many days ?",
        "Rationale": "( a + b ) work in 1 day = 1 / 20 , ( b + c ) work in 1 days = 1 / 15 . , ( c + a ) work in 1 days = 1 / 12 ( 1 ) adding = 2 [ a + b + c ] in 1 day work = [ 1 / 20 + 1 / 15 + 1 / 12 ] = 1 / 5 ( a + b + c ) work in 1 day = 1 / 10 so , all three together finish work in 10 days answer d",
        "options": "a ) 12 , b ) 15 , c ) 8 , d ) 10 , e ) 11",
        "correct": "d",
        "annotated_formula": "inverse(divide(add(inverse(12), add(inverse(20), inverse(15))), const_2))",
        "linear_formula": "inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|divide(#4,const_2)|inverse(#5)",
        "category": "physics"
    },
    {
        "Problem": "the average weight of a class of 24 students is 35 kg . if the weight of the teacher be included , the average rises by 400 g . the weight of the teacher is :",
        "Rationale": "weight of the teacher = ( 35.4 x 25 - 35 x 24 ) kg = 45 kg . answer : a",
        "options": "a ) 45 , b ) 46 , c ) 47 , d ) 48 , e ) 49",
        "correct": "a",
        "annotated_formula": "subtract(multiply(add(35, divide(400, const_1000)), add(24, const_1)), multiply(24, 35))",
        "linear_formula": "add(n0,const_1)|divide(n2,const_1000)|multiply(n0,n1)|add(n1,#1)|multiply(#3,#0)|subtract(#4,#2)",
        "category": "general"
    },
    {
        "Problem": "a and b are two circles . the radius of a is four times as large as the diameter of b . what is the ratio between the areas of the circles ?",
        "Rationale": "given : the radius of a is 4 times as large as the diameter of b . = > r ( a ) = 4 * d ( b ) = 4 * 2 * r ( b ) = 8 r ( b ) . the radius are in ratio of 1 : 8 thus the area will be in the ratio of square of radius . 1 : 64 . hence d .",
        "options": "['a ) 1 : 8 .', 'b ) 1 : 2 .', 'c ) 1 : 24 .', 'd ) 1 : 64 .', 'e ) 1 : 6 .']",
        "correct": "d",
        "annotated_formula": "divide(power(const_1, const_2), power(multiply(const_2, const_4), const_2))",
        "linear_formula": "multiply(const_2,const_4)|power(const_1,const_2)|power(#0,const_2)|divide(#1,#2)",
        "category": "geometry"
    },
    {
        "Problem": "in a garden , there are 12 rows and 14 columns of mango trees . the distance between two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is",
        "Rationale": "\"each row contains 14 plants . leaving 2 corner plants , 12 plants in between have ( 12 x 2 ) metres & 1 metre on each side is left . length = ( 24 + 2 ) m = 26 m . answer : d\"",
        "options": "a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m",
        "correct": "d",
        "annotated_formula": "add(add(multiply(subtract(14, const_1), 2), divide(12, 2)), divide(12, 2))",
        "linear_formula": "divide(n0,n2)|subtract(n1,const_1)|multiply(n2,#1)|add(#0,#2)|add(#3,#0)|",
        "category": "physics"
    },
    {
        "Problem": "a is 30 % more efficient than b . how much time they will working together take to complete a job which a alone could have done in 23 days ?",
        "Rationale": "\"the ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b can do work in x days then 10 : 13 : : 23 : x x = ( 23 * 13 ) / 10 x = 299 / 10 a ' s 1 day ' s work = 1 / 23 b ' s 1 day ' s work = 10 / 299 ( a + b ) ' s 1 day ' s work = 1 / 23 + 10 / 299 = 23 / 299 = 1 / 13 a and b together can do work in 13 days answer ( b )\"",
        "options": "a ) 25 days , b ) 13 days , c ) 14 days , d ) 20 days , e ) 15 days",
        "correct": "b",
        "annotated_formula": "inverse(add(divide(const_1, 23), divide(const_1, multiply(add(divide(30, const_100), const_1), 23))))",
        "linear_formula": "divide(const_1,n1)|divide(n0,const_100)|add(#1,const_1)|multiply(n1,#2)|divide(const_1,#3)|add(#0,#4)|inverse(#5)|",
        "category": "physics"
    },
    {
        "Problem": "two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a girl sitting at window seat in the slower train in 32 seconds . find the length of the faster train ?",
        "Rationale": "\"explanation : relative speed = ( 72 - 36 ) x 5 / 18 = 2 x 5 = 10 mps . distance covered in 32 sec = 32 x 10 = 320 m . the length of the faster train = 320 m . answer is d\"",
        "options": "a ) 170 m , b ) 100 m , c ) 270 m , d ) 320 m , e ) 350 m",
        "correct": "d",
        "annotated_formula": "multiply(divide(subtract(72, 36), const_3_6), 32)",
        "linear_formula": "subtract(n0,n1)|divide(#0,const_3_6)|multiply(n2,#1)|",
        "category": "physics"
    },
    {
        "Problem": "tough and tricky questions : combinations . 8 contestants representing 4 different countries advance to the finals of a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?",
        "Rationale": "number of ways first - place medal can be awarded to four contestants = 8 number of ways second - place medal can be awarded to contestants after awarding first - place medal = 3 therefore number of possibilities = 8 * 3 = 24 answer : e",
        "options": "a ) 6 , b ) 7 , c ) 12 , d ) 16 , e ) 24",
        "correct": "e",
        "annotated_formula": "multiply(8, subtract(4, const_1))",
        "linear_formula": "subtract(n1,const_1)|multiply(n0,#0)",
        "category": "general"
    },
    {
        "Problem": "a sum of rs . 100 is lent at simple interest of 3 % p . a . for the first month , 9 % p . a . for the second month , 27 % p . a . for the third month and so on . what is the total amount of interest earned at the end of the year approximately",
        "Rationale": "total amount of interest is i = p / 100 * 1 [ 3 / 12 + 9 / 12 + 27 / 12 \u2026 . 312 / 12 where p = 100 ; i = 1 / 12 ( 3 + 9 + \u2026 . . 312 ) i = 1 / 12 ( 3 ( 312 - 1 ) ) / 3 - 1 = 531440 * 3 / 12 * 2 = rs . 66430 answer : d",
        "options": "a ) rs . 797160 , b ) rs . 791160 , c ) rs . 65930 , d ) rs . 66430 , e ) rs . 67430",
        "correct": "d",
        "annotated_formula": "divide(multiply(subtract(power(3, const_12), const_1), 3), multiply(const_12, const_2))",
        "linear_formula": "multiply(const_12,const_2)|power(n1,const_12)|subtract(#1,const_1)|multiply(n1,#2)|divide(#3,#0)",
        "category": "general"
    },
    {
        "Problem": "suppose you have three identical prisms with congruent equilateral triangles as the end - polygons . suppose you attach them by the rectangular faces so they are perfectly aligned . there will be some large faces created by two or more co - planar faces of the individual prisms : count each such large face as one . given that , how many faces does the resultant solid have ?",
        "Rationale": "the top and the bottom are each single faces formed by three equilateral triangles joining , as in the diagram on the left , to make an isosceles trapezoid . top = 1 face , and bottom = 1 face . this is a four - sided figure , so there are four rectangles extending from the bottom of this prism to the congruent figure at the top . notice , in particular , the larger vertical face in the \u201c back \u201d of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining . total = 1 top + 1 bottom + 4 sides = 6 faces . answer = b .",
        "options": "a ) 4 , b ) 6 , c ) 9 , d ) 10 , e ) 12",
        "correct": "b",
        "annotated_formula": "add(add(const_4, const_1), const_1)",
        "linear_formula": "add(const_1,const_4)|add(#0,const_1)|",
        "category": "geometry"
    },
    {
        "Problem": "the side of a square has the length of 6 . what is the area of the region shaded ?",
        "Rationale": "the area of a square whose side is 6 \u2013 ( the area of a square whose side is 4 + the area of the semi - circle whose side is 4 ) = the area of the region shaded the correct answer is b .",
        "options": "['a ) 48 - 8 \u03c0', 'b ) 48 - 6 \u03c0', 'c ) 24 + 6 \u03c0', 'd ) 16 + 8 \u03c0', 'e ) 64 - 8 \u03c0']",
        "correct": "b",
        "annotated_formula": "subtract(multiply(const_3, multiply(const_4, const_4)), multiply(6, const_pi))",
        "linear_formula": "multiply(const_4,const_4)|multiply(n0,const_pi)|multiply(#0,const_3)|subtract(#2,#1)",
        "category": "geometry"
    },
    {
        "Problem": "monica planned her birthday party . she prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra . after the party , it turned out that one of the guests did n ' t come but every one of the guests that did come ate 6 muffins and 6 muffins remained . how many guests did monica plan on ?",
        "Rationale": "let x be the number of guests . number of muffins prepared = 5 x + 2 number of muffins eaten + number of muffins remaining = number of muffins prepared 6 ( x - 1 ) + 6 = 5 x + 2 6 x = 5 x + 2 x = 2 answer : a",
        "options": "a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 7 .",
        "correct": "a",
        "annotated_formula": "divide(subtract(add(6, 6), const_2), 5)",
        "linear_formula": "add(n1,n1)|subtract(#0,const_2)|divide(#1,n0)",
        "category": "general"
    },
    {
        "Problem": "a boy rides his bicycle 10 km at an average speed of 12 km / hr and again travels 12 km at an average speed of 10 km / hr . his average speed for the entire trip is approximately ?",
        "Rationale": "total distance traveled = 10 + 12 = 22 km / hr . total time taken = 10 / 12 + 12 / 10 = 61 / 30 hrs . average speed = 22 * 30 / 61 = 10.8 km / hr . answer : b",
        "options": "a ) 10.7 km / hr , b ) 10.8 km / hr , c ) 17.8 km / hr , d ) 10.5 km / hr , e ) 30.8 km / hr",
        "correct": "b",
        "annotated_formula": "divide(add(12, 10), const_2)",
        "linear_formula": "add(n0,n1)|divide(#0,const_2)",
        "category": "general"
    },
    {
        "Problem": "if 3 ^ x = 2 , then 3 ^ ( 4 x + 3 ) =",
        "Rationale": "3 ^ x = 2 3 ^ 4 x = 2 ^ 4 3 ^ 4 x = 16 3 ^ ( 4 x + 3 ) = 3 ^ 4 x * 3 ^ 3 = 16 * 27 = 432 answer : c",
        "options": "a ) 429 , b ) 454 , c ) 432 , d ) 438 , e ) 108",
        "correct": "c",
        "annotated_formula": "power(3, add(multiply(4, divide(log(const_2), log(const_3))), 3))",
        "linear_formula": "log(const_2)|log(const_3)|divide(#0,#1)|multiply(n3,#2)|add(n0,#3)|power(n0,#4)",
        "category": "general"
    },
    {
        "Problem": "a dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25 % . find his false weight age ?",
        "Rationale": "\"25 = e / ( 1000 - e ) * 100 1000 - e = 4 e 1000 = 5 e = > e = 200 1000 - 200 = 800 answer : c\"",
        "options": "a ) 338 , b ) 278 , c ) 800 , d ) 269 , e ) 112",
        "correct": "c",
        "annotated_formula": "subtract(multiply(divide(const_100, 25), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)",
        "linear_formula": "add(const_2,const_3)|divide(const_100,n0)|multiply(#0,const_2)|multiply(#2,const_100)|multiply(#1,#3)|subtract(#4,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "the length of a train and that of a platform are equal . if with a speed of 90 kmph the train crosses the platform in one minute , then the length of the train in metres is",
        "Rationale": "\"2 x will be the distance travelled by the train if the length of the train = the length of the platform = x as distance = speed * time distance = 2 x speed in kmph = 90 speed in mps = 90 * 5 / 18 as dist = speed * time 2 x = ( 90 * 5 / 18 ) * ( 60 sec ) on solving x = 900 mts answer : d\"",
        "options": "a ) 500 , b ) 600 , c ) 750 , d ) 900 , e ) 950",
        "correct": "d",
        "annotated_formula": "divide(divide(multiply(90, const_1000), divide(const_60, const_1)), const_2)",
        "linear_formula": "divide(const_60,const_1)|multiply(n0,const_1000)|divide(#1,#0)|divide(#2,const_2)|",
        "category": "physics"
    },
    {
        "Problem": "company a imported 10,500 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 10 percent of the widgets are made of brass and of those 20 percent are painted red and 40 percent are painted blue how many brass widgets painted green were imported ?",
        "Rationale": "\"answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are red and 40 % are blue . since we know that there are only three colors , the remaining 40 % must be green . 40 % blue of 10 % brass widgets leads to 4 % green brass widgets out of the total 10,550 widgets . 10,500 / 100 * 4 = 420 . answer d .\"",
        "options": "a ) 480 , b ) 840 , c ) 1050 , d ) 420 , e ) 2100",
        "correct": "d",
        "annotated_formula": "multiply(multiply(multiply(multiply(divide(10, const_100), divide(40, const_100)), divide(add(10, const_2), 10)), const_100), const_100)",
        "linear_formula": "add(n1,const_2)|divide(n1,const_100)|divide(n3,const_100)|divide(#0,n1)|multiply(#1,#2)|multiply(#3,#4)|multiply(#5,const_100)|multiply(#6,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field .",
        "Rationale": "\"other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . ans : a\"",
        "options": "a ) 120 , b ) 147 , c ) 251 , d ) 451 , e ) 258",
        "correct": "a",
        "annotated_formula": "rectangle_area(15, sqrt(subtract(power(17, const_2), power(15, const_2))))",
        "linear_formula": "power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|sqrt(#2)|rectangle_area(n0,#3)|",
        "category": "geometry"
    },
    {
        "Problem": "a certain quantity is measured on two different scales , the t - scale and the s - scale , that are related linearly . measurements on the t - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the t - scale corresponds to a measurement of 100 on the s - scale ?",
        "Rationale": "first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that t increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , t will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c",
        "options": "a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84",
        "correct": "c",
        "annotated_formula": "add(multiply(subtract(24, 6), divide(subtract(100, 60), subtract(60, 30))), 24)",
        "linear_formula": "subtract(n4,n3)|subtract(n3,n2)|subtract(n1,n0)|divide(#0,#1)|multiply(#3,#2)|add(n1,#4)",
        "category": "general"
    },
    {
        "Problem": "the sum of two numbers is 184 . if one - third of the one exceeds one - seventh of the other by 8 , find the smaller number .",
        "Rationale": "let the numbers be x and ( 184 - x ) . then , ( x / 3 ) - ( 184 - x ) / 7 = 8 7 x - 3 ( 184 - x ) = 168 10 x = 720 , x = 72 . hence the correct answer is option a ) 72 .",
        "options": "a ) 72 , b ) 64 , c ) 84 , d ) 12 , e ) 92",
        "correct": "a",
        "annotated_formula": "divide(add(multiply(184, const_3), multiply(multiply(add(const_3, const_4), const_3), 8)), add(add(const_3, const_4), const_3))",
        "linear_formula": "add(const_3,const_4)|multiply(n0,const_3)|add(#0,const_3)|multiply(#0,const_3)|multiply(n1,#3)|add(#1,#4)|divide(#5,#2)",
        "category": "general"
    },
    {
        "Problem": "when n divided by 3 , the remainder is 2 . when n divided by 4 , the remainder is 1 what is the the remainder when divided by 16",
        "Rationale": "case 1 n = 5,8 , 11,14 , 17,20 case 2 m = 5 , 9,13 , 17,21 therefore n = 17 remainder of 17 / 16 will be 1 a",
        "options": "a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2",
        "correct": "a",
        "annotated_formula": "floor(divide(add(add(const_12, const_3), add(const_2, const_4)), 16))",
        "linear_formula": "add(const_12,const_3)|add(const_2,const_4)|add(#0,#1)|divide(#2,n4)|floor(#3)",
        "category": "general"
    },
    {
        "Problem": "if an object travels at 8 feet per second , how many feet does it travel in forty five minutes ?",
        "Rationale": "\"if an object travels at 8 feet per second it covers 8 x 60 feet in one minute , and 8 x 60 x 45 feet in forty five minutes . answer = 21600 answer : c\"",
        "options": "a ) 18000 , b ) 24000 , c ) 21600 , d ) 18000 , e ) 22000",
        "correct": "c",
        "annotated_formula": "multiply(multiply(const_3, const_60), const_60)",
        "linear_formula": "multiply(const_3,const_60)|multiply(#0,const_60)|",
        "category": "physics"
    },
    {
        "Problem": "in arun \u2019 s opinion , his weight is greater than 65 kg but less than 72 kg . his brother doest not agree with arun and he thinks that arun \u2019 s weight is greater than 60 kg but less than 70 kg . his mother \u2019 s view is that his weight can not be greater than 68 kg . if all are them are correct in their estimation , what is the average of different probable weights of arun ?",
        "Rationale": "explanation : let arun \u2019 s weight by x kg . according to arun , 65 < x < 72 according to arun \u2019 s brother , 60 < x < 70 . according to arun \u2019 s mother , x < = 68 the values satisfying all the above conditions are 66 , 67 and 68 . required average = [ 66 + 67 + 68 / 3 ] = [ 201 / 3 ] = 67 kg answer b",
        "options": "a ) 66 kg , b ) 67 kg , c ) 68 kg , d ) 69 kg , e ) none of these",
        "correct": "b",
        "annotated_formula": "divide(add(add(subtract(68, const_1), subtract(subtract(68, const_1), const_1)), 68), const_3)",
        "linear_formula": "subtract(n4,const_1)|subtract(#0,const_1)|add(#0,#1)|add(n4,#2)|divide(#3,const_3)",
        "category": "general"
    },
    {
        "Problem": "robert left from a pvt company . management hold his salary rs . 15000 / - for one month . earlier robert borrowed rs . 7280 / - from company . but robert forget that . after one month robert asked his salary and accountant gives rs . 18500 / - to him . what is the incentive amount given to robert ?",
        "Rationale": "\"total salary = rs . 15000 / - borrowed money = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - incentive amount = 18500 - 7720 = 10780 / - answer is c\"",
        "options": "a ) 9500 , b ) 12500 , c ) 10780 , d ) 10500 , e ) 8600",
        "correct": "c",
        "annotated_formula": "subtract(18500, 7280)",
        "linear_formula": "subtract(n2,n1)|",
        "category": "general"
    },
    {
        "Problem": "ramu rides his bike at an average speed of 45 km / hr and reaches his desitination in 4 hours . somu covers the same distance in 6 hours . if ramu covered his journey at an average speed which was 9 km / hr less and somu covered his journey at an average speed which was 10 km / hr more , then the difference in their times taken to reach the destination would be ( in minutes ) .",
        "Rationale": "distance travelled by ramu = 45 * 4 = 180 km somu travelled the same distance in 6 hours . his speed = 180 / 6 = 30 km / hr hence in the conditional case , ramu ' s speed = 45 - 9 = 36 km / hr and somu ' s speed = 30 + 10 = 40 km / hr . therefore travel time of ramu and somu would be 5 hours and 4.5 hours respectively . hence difference in the time taken = 0.5 hours = 30 minutes . answer : b",
        "options": "a ) 23 minutes , b ) 30 minutes , c ) 43 minutes , d ) 23 minutes , e ) 33 minutes",
        "correct": "b",
        "annotated_formula": "multiply(subtract(divide(multiply(45, 4), subtract(45, 9)), divide(multiply(45, 4), add(divide(multiply(45, 4), 6), 10))), const_60)",
        "linear_formula": "multiply(n0,n1)|subtract(n0,n3)|divide(#0,#1)|divide(#0,n2)|add(n4,#3)|divide(#0,#4)|subtract(#2,#5)|multiply(#6,const_60)",
        "category": "general"
    },
    {
        "Problem": "if \u00e2 \u20ac \u0153 * \u00e2 \u20ac \u009d is called \u00e2 \u20ac \u0153 + \u00e2 \u20ac \u009d , \u00e2 \u20ac \u0153 / \u00e2 \u20ac \u009d is called \u00e2 \u20ac \u0153 * \u00e2 \u20ac \u009d , \u00e2 \u20ac \u0153 - \u00e2 \u20ac \u009d is called \u00e2 \u20ac \u0153 / \u00e2 \u20ac \u009d , \u00e2 \u20ac \u0153 + \u00e2 \u20ac \u009d is called \u00e2 \u20ac \u0153 - \u00e2 \u20ac \u009d . 240 * 80 / 60 + 40 / 10 = ?",
        "Rationale": "\"explanation : given : 240 * 80 / 60 + 40 / 10 = ? substituting the coded symbols for mathematical operations , we get , 240 / 80 - 60 * 40 - 10 = ? 3 - 2400 - 10 = - 2407 answer : b\"",
        "options": "a ) - 2305 , b ) - 2407 , c ) 2509 , d ) - 2101 , e ) none of these",
        "correct": "b",
        "annotated_formula": "add(multiply(divide(60, 40), divide(240, 80)), 10)",
        "linear_formula": "divide(n2,n3)|divide(n0,n1)|multiply(#0,#1)|add(n4,#2)|",
        "category": "general"
    },
    {
        "Problem": "in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive r difference between n and m ?",
        "Rationale": "\"we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result r will be 8 - 5 = 3 and answer b\"",
        "options": "a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9",
        "correct": "b",
        "annotated_formula": "subtract(5, 2)",
        "linear_formula": "subtract(n1,n0)|",
        "category": "general"
    },
    {
        "Problem": "if shreehari walks in the speed of 4.5 km / hr from his house , in what time will he reach his school which is 750 m long from his house ?",
        "Rationale": "speed = 4.5 * 5 / 18 = 1.25 m / sec time taken = 750 / 1.25 = 600 sec ie . 10 mins . answer : c",
        "options": "a ) 5 , b ) 30 , c ) 10 , d ) 12 , e ) 15",
        "correct": "c",
        "annotated_formula": "multiply(divide(divide(750, const_1000), 4.5), const_60)",
        "linear_formula": "divide(n1,const_1000)|divide(#0,n0)|multiply(#1,const_60)",
        "category": "physics"
    },
    {
        "Problem": "a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is",
        "Rationale": "sol . since the month begins with a sunday , so there will be five sundays in the month . \u2234 required average = [ 510 x 5 + 240 x 25 / 30 ] = 8550 / 30 = 285 answer d",
        "options": "a ) 250 , b ) 276 , c ) 280 , d ) 285 , e ) none",
        "correct": "d",
        "annotated_formula": "divide(add(multiply(add(const_4, const_1), 510), multiply(multiply(add(const_4, const_1), add(const_4, const_1)), 240)), 30)",
        "linear_formula": "add(const_1,const_4)|multiply(n0,#0)|multiply(#0,#0)|multiply(n1,#2)|add(#1,#3)|divide(#4,n2)",
        "category": "general"
    },
    {
        "Problem": "7 m - 20 = 2 m , then m + 7 is equal to ?",
        "Rationale": "7 m - 20 = 2 m so , 5 m = 20 so , m + 7 = 11 answer : c",
        "options": "a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13",
        "correct": "c",
        "annotated_formula": "add(divide(20, subtract(7, 2)), 7)",
        "linear_formula": "subtract(n0,n2)|divide(n1,#0)|add(n0,#1)",
        "category": "general"
    },
    {
        "Problem": "which is greater than 16",
        "Rationale": "\"66 greater than 16 . answer : b\"",
        "options": "a ) 1.6 , b ) 66 , c ) 6 , d ) - 6 , e ) 6.1",
        "correct": "b",
        "annotated_formula": "divide(divide(divide(divide(divide(divide(16, const_4), const_3), const_4), const_3), const_2), const_2)",
        "linear_formula": "divide(n0,const_4)|divide(#0,const_3)|divide(#1,const_4)|divide(#2,const_3)|divide(#3,const_2)|divide(#4,const_2)|",
        "category": "general"
    },
    {
        "Problem": "two 100 multiples of 7 are chosen at random , and 300 multiples of 8 are chosen at random . approximately what percentage of the 500 selected numbers are odd ?",
        "Rationale": "two hundred multiples of seven will have 100 even and 100 odd numbers 300 multiples of eight will have all even ( being multiple of 8 ) probability of number selected being odd = total odd numbers / total available numbers probability = 100 / 500 = 0.2 = 20 % answer : option a",
        "options": "a ) 20 % , b ) 25 % , c ) 40 % , d ) 50 % , e ) 80 %",
        "correct": "a",
        "annotated_formula": "multiply(divide(100, 500), const_100)",
        "linear_formula": "divide(n0,n4)|multiply(#0,const_100)",
        "category": "general"
    },
    {
        "Problem": "j is 25 % less than p and 20 % less than t . t is x % less than p . what is the value of x ?",
        "Rationale": "\"let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( x / 100 ) ] * p i . e . 100 - x = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . x = 6.25 answer : option d\"",
        "options": "a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2",
        "correct": "d",
        "annotated_formula": "divide(multiply(25, 25), const_100)",
        "linear_formula": "multiply(n0,n0)|divide(#0,const_100)|",
        "category": "general"
    },
    {
        "Problem": "denise is trying to open a safe whose combination she does not know . if the safe has 4000 possible combinations , and she can try 75 different possibilities , what is the probability that she does not pick the one correct combination .",
        "Rationale": "when trying the first time the probability denise does n ' t pick the correct combination = 3999 / 4000 second time , as the total number of possible combinations reduced by one , not picking the right one would be 3998 / 3999 . third time 3997 / 3998 . . . and the same 75 times . so we get : 3999 / 4000 \u2217 3998 / 3999 \u2217 . . . \u2217 3925 / 39263999 / 4000 \u2217 3998 / 3999 \u2217 . . . \u2217 3925 / 3926 every denominator but the first will cancel out and every nominator but the last will cancel out as well . we ' ll get 3925 / 4000 = 157 / 160 . answer : c .",
        "options": "a ) 1 , b ) 159 / 160 , c ) 157 / 160 , d ) 4 3 / 160 , e ) 0",
        "correct": "c",
        "annotated_formula": "divide(subtract(4000, 75), 4000)",
        "linear_formula": "subtract(n0,n1)|divide(#0,n0)",
        "category": "probability"
    },
    {
        "Problem": "what percent is 36 paisa ' s of 12 rupees ?",
        "Rationale": "\"12 rupees = 1200 paisa ' s 36 / 1200 \u00d7 100 = 3 / 12 12 / 3 = 3 % b\"",
        "options": "a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %",
        "correct": "b",
        "annotated_formula": "multiply(divide(36, 12), const_100)",
        "linear_formula": "divide(n0,n1)|multiply(#0,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many q cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]",
        "Rationale": "\"main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer q = 44 . d\"",
        "options": "a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55",
        "correct": "d",
        "annotated_formula": "multiply(divide(divide(8, divide(const_1, const_2)), const_12), multiply(0.33, 100))",
        "linear_formula": "divide(const_1,const_2)|multiply(n1,n2)|divide(n0,#0)|divide(#2,const_12)|multiply(#3,#1)|",
        "category": "general"
    },
    {
        "Problem": "two spheres of their radios in the ratio 4 : 3 . find its volumes ratio ?",
        "Rationale": "sphere volume ( v ) = 4 / 3 \u03c0 r ( power 3 ) : 4 / 3 \u03c0 r ( power 3 ) = 4 ( power 3 ) : 3 ( power 3 ) = 64 : 27 answer is d .",
        "options": "['a ) 64 : 13', 'b ) 13 : 64', 'c ) 27 : 64', 'd ) 64 : 27', 'e ) none of them']",
        "correct": "d",
        "annotated_formula": "divide(volume_sphere(4), volume_sphere(3))",
        "linear_formula": "volume_sphere(n0)|volume_sphere(n1)|divide(#0,#1)",
        "category": "other"
    },
    {
        "Problem": "bhaman travelled for 15 hours . he covered the first half of the distance at 40 kmph and remaining half of the distance at 10 kmph . find the distance travelled by bhaman ?",
        "Rationale": "let the distance travelled be x km . total time = ( x / 2 ) / 40 + ( x / 2 ) / 10 = 15 = > x / 80 + x / 20 = 15 = > ( x + 4 x ) / 80 = 15 = > x = 240 km answer : a",
        "options": "a ) 240 , b ) 230 , c ) 260 , d ) 220 , e ) 340",
        "correct": "a",
        "annotated_formula": "multiply(divide(15, add(divide(multiply(const_2, 40), const_10), divide(multiply(const_2, 10), const_10))), multiply(multiply(divide(multiply(const_2, 40), const_10), divide(multiply(const_2, 10), const_10)), const_10))",
        "linear_formula": "multiply(n1,const_2)|multiply(n2,const_2)|divide(#0,const_10)|divide(#1,const_10)|add(#2,#3)|multiply(#2,#3)|divide(n0,#4)|multiply(#5,const_10)|multiply(#6,#7)",
        "category": "physics"
    },
    {
        "Problem": "three pipes of same capacity can fill a tank in 8 hours . if there are only two pipes of same capacity , the tank can be filled in .",
        "Rationale": "the part of the tank filled by three pipes in one hour = 1 / 8 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 8 = 1 / 12 . the tank can be filled in 12 hours . answer : b",
        "options": "a ) 11 hours , b ) 12 hours , c ) 15 hours , d ) 16 hours , e ) 17 hours",
        "correct": "b",
        "annotated_formula": "inverse(multiply(divide(const_2, const_3), divide(const_1, 8)))",
        "linear_formula": "divide(const_2,const_3)|divide(const_1,n0)|multiply(#0,#1)|inverse(#2)",
        "category": "physics"
    },
    {
        "Problem": "calculate the number of bricks , each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10 % of its volume is occupied by mortar ?",
        "Rationale": "explanation : let the number of bricks be ' n ' 10 x 4 / 100 x 6 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x n 10 x 4 x 6 x 90 = 15 x 2 x n = > n = 720 . answer is a",
        "options": "a ) 720 , b ) 600 , c ) 660 , d ) 6000 , e ) none of these",
        "correct": "a",
        "annotated_formula": "divide(multiply(multiply(multiply(10, divide(4, const_100)), 6), subtract(const_1, divide(10, const_100))), multiply(multiply(divide(25, const_100), divide(15, const_100)), divide(8, const_100)))",
        "linear_formula": "divide(n4,const_100)|divide(n3,const_100)|divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|multiply(n3,#0)|multiply(#3,#4)|subtract(const_1,#1)|multiply(n5,#5)|multiply(#2,#6)|multiply(#8,#7)|divide(#10,#9)",
        "category": "physics"
    },
    {
        "Problem": "if the side length of square b is three times that of square a , the area of square b is how many times the area of square a ?",
        "Rationale": "\"let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 3 x ) ^ 2 = 9 x ^ 2 . the answer is a .\"",
        "options": "a ) 9 , b ) 8 , c ) 6 , d ) 3 , e ) 2",
        "correct": "a",
        "annotated_formula": "multiply(const_4, const_4)",
        "linear_formula": "multiply(const_4,const_4)|",
        "category": "geometry"
    },
    {
        "Problem": "the lcm and hcf of two numbers are 8 and 48 respectively . if one of them is 24 , find the other ?",
        "Rationale": "hcf x lcm = product of numbers 8 x 48 = 24 x the other number other number = ( 8 x 48 ) / 24 other number = 16 answer : d",
        "options": "a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 20",
        "correct": "d",
        "annotated_formula": "divide(multiply(8, 48), 24)",
        "linear_formula": "multiply(n0,n1)|divide(#0,n2)",
        "category": "physics"
    },
    {
        "Problem": "in a party every person shakes hands with every other person . if there are 105 hands shakes , find the number of person in the party .",
        "Rationale": "\"let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . option d\"",
        "options": "a ) 14 , b ) 12 , c ) 13 , d ) 15 , e ) 16",
        "correct": "d",
        "annotated_formula": "divide(add(sqrt(add(multiply(multiply(105, const_2), const_4), const_1)), const_1), const_2)",
        "linear_formula": "multiply(n0,const_2)|multiply(#0,const_4)|add(#1,const_1)|sqrt(#2)|add(#3,const_1)|divide(#4,const_2)|",
        "category": "general"
    },
    {
        "Problem": "a lawn is in the form of a rectangle having its sides in the ratio 2 : 3 . the area of the lawn is ( 1 / 6 ) hectares . find the length and breadth of the lawn .",
        "Rationale": "let length = 2 x meters and breadth = 3 x meter . now , area = ( 1 / 6 ) x 1000 m 2 = 5000 / 3 m 2 so , 2 x * 3 x = 5000 / 3 < = > x 2 = 2500 / 9 < = > x = 50 / 3 therefore length = 2 x = ( 100 / 3 ) m = 33 ( 1 / 3 ) m and breadth = 3 x = 3 ( 50 / 3 ) m = 50 m . answer is a",
        "options": "['a ) 50', 'b ) 30', 'c ) 20', 'd ) 40', 'e ) 10']",
        "correct": "a",
        "annotated_formula": "divide(multiply(divide(multiply(const_10, const_1000), 6), 3), const_100)",
        "linear_formula": "multiply(const_10,const_1000)|divide(#0,n3)|multiply(n1,#1)|divide(#2,const_100)",
        "category": "geometry"
    },
    {
        "Problem": "3 years ago , the average age of a , b and c was 27 years and that of b and c 5 years ago was 20 years . a \u2019 s present age is :",
        "Rationale": "explanation : sum of the present ages of a , b and c = ( 27 \u00d7 3 + 3 \u00d7 3 ) years = 90 years . sum of the present ages of b and c = ( 20 \u00d7 2 + 5 \u00d7 2 ) years = 50 years . a ' s present age = 90 \u2013 50 = 40 years . answer : c",
        "options": "a ) 22 , b ) 88 , c ) 40 , d ) 87 , e ) 17",
        "correct": "c",
        "annotated_formula": "subtract(add(multiply(27, 3), multiply(3, 3)), add(multiply(20, const_2), multiply(5, const_2)))",
        "linear_formula": "multiply(n0,n1)|multiply(n0,n0)|multiply(n3,const_2)|multiply(n2,const_2)|add(#0,#1)|add(#2,#3)|subtract(#4,#5)",
        "category": "general"
    },
    {
        "Problem": "a is thrice as good as workman as b and therefore is able to finish a job in 60 days less than b . working together , they can do it in :",
        "Rationale": "ratio of times taken by a and b = 1 : 3 . the time difference is ( 3 - 1 ) 2 days while b take 3 days and a takes 1 day . if difference of time is 2 days , b takes 3 days . if difference of time is 60 days , b takes ( 3 / 2 * 60 ) = 90 days so , a takes 30 days to do the work . a ' s 1 day ' s work = 1 / 30 b ' s 1 day ' s work = 1 / 90 ( a + b ) ' s 1 day ' s work = ( 1 / 30 + 1 / 90 ) = 4 / 90 = 2 / 45 a and b together can do the work in 45 / 2 = 22 1 / 2 days answer = b",
        "options": "a ) 20 days , b ) 22 1 / 2 days , c ) 24 days , d ) 25 days , e ) 30 days",
        "correct": "b",
        "annotated_formula": "multiply(add(const_4, const_1), divide(const_1, add(divide(const_1, divide(60, const_2)), divide(const_1, add(divide(60, const_2), 60)))))",
        "linear_formula": "add(const_1,const_4)|divide(n0,const_2)|add(n0,#1)|divide(const_1,#1)|divide(const_1,#2)|add(#3,#4)|divide(const_1,#5)|multiply(#0,#6)",
        "category": "physics"
    },
    {
        "Problem": "what is the difference between the largest number and the least number written with the figures 3 , 4 , 7 , 0 , 3 ?",
        "Rationale": "\"74330 largest 30347 smallest - - - - - - - - - - - - - 43983 answer : c\"",
        "options": "a ) 70983 , b ) 43893 , c ) 43983 , d ) 43883 , e ) 43823",
        "correct": "c",
        "annotated_formula": "subtract(add(add(add(multiply(multiply(3, const_100), const_10), multiply(0, const_100)), multiply(4, const_10)), 7), add(add(add(const_1000, multiply(4, const_100)), multiply(0, const_10)), 3))",
        "linear_formula": "multiply(n0,const_100)|multiply(n3,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)|",
        "category": "general"
    },
    {
        "Problem": "the average of 5 consecutive even numbers a , b , c , d and e is 20 . what percent of e is d ?",
        "Rationale": "explanation : in such a case the middle number ( c ) is the average \u2234 c = 20 and d = 22 and e = 24 required percentage = 22 / 24 x 100 = 91.7 answer : option b",
        "options": "a ) 90.1 , b ) 91.7 , c ) 97.1 , d ) 101.1 , e ) 107.1",
        "correct": "b",
        "annotated_formula": "multiply(divide(add(add(add(subtract(20, divide(add(add(add(const_2, multiply(const_2, const_2)), multiply(const_2, const_3)), multiply(const_2, const_4)), 5)), const_2), const_2), const_2), add(add(add(add(subtract(20, divide(add(add(add(const_2, multiply(const_2, const_2)), multiply(const_2, const_3)), multiply(const_2, const_4)), 5)), const_2), const_2), const_2), const_2)), const_100)",
        "linear_formula": "multiply(const_2,const_2)|multiply(const_2,const_3)|multiply(const_2,const_4)|add(#0,const_2)|add(#3,#1)|add(#4,#2)|divide(#5,n0)|subtract(n1,#6)|add(#7,const_2)|add(#8,const_2)|add(#9,const_2)|add(#10,const_2)|divide(#10,#11)|multiply(#12,const_100)",
        "category": "general"
    },
    {
        "Problem": "a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 10 % . their gross income from sales for one month decreases by what percent ?",
        "Rationale": "\"let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.1 x = 0.99 * ( p * x ) , a decrease of 1 % . the answer is a .\"",
        "options": "a ) 1 % , b ) 3 % , c ) 5 % , d ) 7 % , e ) 9 %",
        "correct": "a",
        "annotated_formula": "subtract(subtract(10, 10), divide(10, 10))",
        "linear_formula": "divide(n1,n0)|subtract(n1,n0)|subtract(#1,#0)|",
        "category": "gain"
    },
    {
        "Problem": "on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per f glass on the second day ?",
        "Rationale": "\"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d .\"",
        "options": "a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45",
        "correct": "d",
        "annotated_formula": "divide(multiply(add(const_1, const_1), 0.60), add(const_1, const_2))",
        "linear_formula": "add(const_1,const_1)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)|",
        "category": "general"
    },
    {
        "Problem": "assume all pieces of rope are equal . if 44 pieces of rope measure a feet , how long would b pieces of rope be in inches ?",
        "Rationale": "44 ropes measure a feet or 12 * a inches 1 rope will measure = 12 * a / 44 = 6 * a / 22 = 3 * a / 11 b piece of rope measure = b * 3 * a / 11 = 3 ab / 11 hence , the answer is e .",
        "options": "a ) 44 / ab , b ) 11 / 3 ab , c ) 6 / 11 ab , d ) ab / 44 , e ) 3 ab / 11",
        "correct": "e",
        "annotated_formula": "divide(const_12, 44)",
        "linear_formula": "divide(const_12,n0)",
        "category": "general"
    },
    {
        "Problem": "18800 / 470 / 20",
        "Rationale": "\"explanation : 18800 / 470 / 20 = ( 18800 / 470 ) / 20 = 40 / 20 = 2 answer : b\"",
        "options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5",
        "correct": "b",
        "annotated_formula": "divide(18800, 470)",
        "linear_formula": "divide(n0,n1)|",
        "category": "general"
    },
    {
        "Problem": "in the seaside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?",
        "Rationale": "given there are 50 students in the seaside summer camp , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . imo option a is correct .",
        "options": "a ) 50 . , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .",
        "correct": "a",
        "annotated_formula": "subtract(divide(multiply(subtract(50, divide(multiply(90, 50), const_100)), const_100), 5), 50)",
        "linear_formula": "multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(#2,const_100)|divide(#3,n2)|subtract(#4,n0)",
        "category": "general"
    },
    {
        "Problem": "the average price of 3 items of furniture is rs . 15000 . if their prices are in the ratio 2 : 4 : 8 , the price of the cheapest item is ?",
        "Rationale": "let their prices be 3 x , 5 x and 7 x . then , 2 x + 6 x + 8 x = ( 15000 * 3 ) or x = 2812.5 . cost of cheapest item = 2 x = rs . 5625 . answer : c",
        "options": "a ) 2379 , b ) 2889 , c ) 5625 , d ) 9000 , e ) 28311",
        "correct": "c",
        "annotated_formula": "divide(multiply(3, 15000), 8)",
        "linear_formula": "multiply(n0,n1)|divide(#0,n4)",
        "category": "general"
    },
    {
        "Problem": "in a group of 15 people , 8 read english , 7 read french while 3 of them read none of these two . how many of them read french and english both ?",
        "Rationale": "in the following venn diagram , f and e represent people who read french and english respectively . now , [ f + ( { f \u2229 e } ) + e ] = 15 - 3 ( or ) f + e + ( f \u2229 e ) = 12 . . . . . . ( 1 ) also , f + ( f \u2229 e ) = 7 ; e + ( f \u2229 e ) = 8 . by adding , f + e + 2 ( f \u2229 e ) = 15 - - - - - - - - - - ( 2 ) by subtracting ( 1 ) from ( 2 ) , we get ( f \u2229 e ) = 3 . \u2234 3 of them read both french and english . answer : b",
        "options": "a ) 2 , b ) 3 , c ) 4 , d ) 7 , e ) 5",
        "correct": "b",
        "annotated_formula": "subtract(add(8, 7), subtract(15, 3))",
        "linear_formula": "add(n1,n2)|subtract(n0,n3)|subtract(#0,#1)",
        "category": "other"
    },
    {
        "Problem": "miller street begins at baker street and runs directly east for 4.5 kilometers until it ends when it meets turner street . miller street is intersected every 250 meters by a perpendicular street , and each of those streets other than baker street and turner street is given a number beginning at 1 st street ( one block east of baker street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of turner street . what is the highest - numbered street that intersects miller street ?",
        "Rationale": "4.5 km / 250 m = 18 . however , the street at the 4.5 - km mark is not 18 th street ; it is turner street . therefore , the highest numbered street is 17 th street . the answer is c .",
        "options": "a ) 15 th , b ) 16 th , c ) 17 th , d ) 18 th , e ) 19 th",
        "correct": "c",
        "annotated_formula": "subtract(divide(4.5, divide(250, const_1000)), 1)",
        "linear_formula": "divide(n1,const_1000)|divide(n0,#0)|subtract(#1,n2)",
        "category": "physics"
    },
    {
        "Problem": "the pressure someone experiences as he or she dives deeper and deeper in the ocean increases linearly . on the surface , the pressure is close to 15 pounds per square inch . 33 feet below the surface , the pressure is 30 pounds . if 25000 pounds per sq inch can crush your bones , what depth is extremely dangerous for humans ?",
        "Rationale": "solution : first , model the pressure ( p ) in terms of depth ( d ) with a linear equation . we will find the equation p = md + b use ( 0 , 15 ) and ( 33 , 30 ) to find m m = 30 - 15 / 33 - 0 m = 15 / 33 = 0.45 p = 0.45 d + b use ( 0 , 15 ) to find b 15 = 0.45 \u00d7 0 + b 15 = b p = 0.45 d + 15 25000 = 0.45 d + 15 25000 - 15 = 0.45 d + 15 - 15 24985 = 0.45 d d = 24985 / 0.45 = 55522 feet answer a",
        "options": "['a ) 55522 feet', 'b ) 45522 feet', 'c ) 35522 feet', 'd ) 25522 feet', 'e ) none']",
        "correct": "a",
        "annotated_formula": "divide(divide(subtract(25000, 15), divide(subtract(30, 15), multiply(33, multiply(const_4, const_3)))), multiply(const_4, const_3))",
        "linear_formula": "multiply(const_3,const_4)|subtract(n3,n0)|subtract(n2,n0)|multiply(n1,#0)|divide(#2,#3)|divide(#1,#4)|divide(#5,#0)",
        "category": "geometry"
    },
    {
        "Problem": "in a class total 34 students , 16 are have a brother , 15 are have sisters , 9 students do n ' t have either brothers or sisters . find the number of students having both brother and sisters .",
        "Rationale": "total number of students = 34 let a be the number of students have a brothers . let b be the number of students have a sisters . aub = number of students have either brothers or sisters = 34 - 9 = 25 n ( aub ) = n ( a ) + n ( b ) - n ( anb ) 25 = 16 + 15 - n ( anb ) n ( anb ) = 31 - 25 n ( anb ) = 6 the number of students having both brother and sisters = 6 answer : c",
        "options": "a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8",
        "correct": "c",
        "annotated_formula": "subtract(add(16, 15), subtract(34, 9))",
        "linear_formula": "add(n1,n2)|subtract(n0,n3)|subtract(#0,#1)",
        "category": "other"
    },
    {
        "Problem": "two numbers are less than a third number by 40 % and 47 % respectively . how much per cent is the second number less than the first ?",
        "Rationale": "\"here , x = 40 and y = 47 therefore second number = [ [ ( 100 - y ) / ( 100 - x ) ] x 100 ] % of first number = [ [ ( 100 - 47 ) / ( 100 - 40 ) ] x 100 ] % of first number i . e , 88.3 % of the first . answer : b\"",
        "options": "a ) 95 % , b ) 88 % , c ) 85 % , d ) 90 % , e ) none of these",
        "correct": "b",
        "annotated_formula": "multiply(subtract(add(40, const_1), 40), const_10)",
        "linear_formula": "add(n0,const_1)|subtract(#0,n0)|multiply(#1,const_10)|",
        "category": "general"
    },
    {
        "Problem": "shahrukh starts from barabanki to fatehpur , 1 hour after ajay starts . shahrukh meets kajol 1.5 hours after shahrukh starts . if the speed of shahrukh is at least 20 km / h faster than the speed of kajol . what is the minimum speed of shahrukh to overtake ajay , before he meets kajol ?",
        "Rationale": "explanation : let t be the time after kajol starts , when she meets ajay , then \\ inline t = \\ frac { 300 } { ( x + y ) } this should be less than 2.5 or ( x + y ) > 120 since y = \\ inline \\ frac { 3 x } { 2 } \\ inline \\ rightarrow y > 72 this ( y > 72 ) is greater than 67.5 km / h and hence shahrukh will always overtake ajay before he meets kajol . answer : d",
        "options": "a ) 32 , b ) 21 , c ) 27 , d ) none of these , e ) 18",
        "correct": "d",
        "annotated_formula": "divide(subtract(multiply(multiply(20, const_3), const_10), multiply(20, const_3)), add(const_3, add(const_4, const_1)))",
        "linear_formula": "add(const_1,const_4)|multiply(n2,const_3)|add(#0,const_3)|multiply(#1,const_10)|subtract(#3,#1)|divide(#4,#2)",
        "category": "physics"
    },
    {
        "Problem": "1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 \u00f7 ( 1 \u00f7 1 ) } ] = ?",
        "Rationale": "explanation : 1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 \u00f7 ( 1 \u00f7 1 ) } ] = 1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 \u00f7 1 } ] = 1 \u00f7 [ 1 + 1 \u00f7 { 1 + 1 } ] = 1 \u00f7 [ 1 + 1 \u00f7 2 ] = 1 \u00f7 [ 1 + ( 1 / 2 ) ] = 1 \u00f7 3 / 2 = 1 \u00d7 3 / 2 = 1 \u00d7 2 / 3 = 2 / 3 answer : option c",
        "options": "a ) 5 / 3 , b ) 4 / 3 , c ) 2 / 3 , d ) 1 / 3 , e ) 1 / 5",
        "correct": "c",
        "annotated_formula": "divide(1, add(1, divide(1, add(1, divide(1, 1)))))",
        "linear_formula": "divide(n0,n0)|add(n0,#0)|divide(n0,#1)|add(n0,#2)|divide(n0,#3)",
        "category": "general"
    },
    {
        "Problem": "a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes bil can make using this recipe ?",
        "Rationale": "\"less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a\"",
        "options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9",
        "correct": "a",
        "annotated_formula": "min(min(divide(15, add(2, divide(1, 2))), floor(divide(16, add(divide(3, 4), 2)))), divide(8, add(divide(1, 3), 1)))",
        "linear_formula": "divide(n1,n4)|divide(n1,n0)|divide(n4,n5)|add(n1,#0)|add(n0,#1)|add(n0,#2)|divide(n11,#3)|divide(n9,#4)|divide(n10,#5)|floor(#8)|min(#7,#9)|min(#6,#10)|",
        "category": "general"
    },
    {
        "Problem": "a train running at a speed of 60 kmph crosses a pole in 18 seconds . what is the length of the train ?",
        "Rationale": "60 kmph = 50 / 3 m / sec 50 / 3 * 18 = 300 m answer : b",
        "options": "a ) 120 m , b ) 300 m , c ) 190 m , d ) 150 m , e ) 160 m",
        "correct": "b",
        "annotated_formula": "multiply(divide(multiply(60, const_1000), const_3600), 18)",
        "linear_formula": "multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)",
        "category": "physics"
    },
    {
        "Problem": "a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x \u2013 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number w of people surveyed by the company ?",
        "Rationale": "\"100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d .\"",
        "options": "a ) 46 , b ) 80 , c ) w . 90 , d ) w . 100 , e ) 200",
        "correct": "d",
        "annotated_formula": "add(subtract(divide(add(add(subtract(const_100, 23), 23), 20), const_2), 20), divide(add(add(subtract(const_100, 23), 23), 20), const_2))",
        "linear_formula": "subtract(const_100,n1)|add(n1,#0)|add(n0,#1)|divide(#2,const_2)|subtract(#3,n0)|add(#3,#4)|",
        "category": "other"
    },
    {
        "Problem": "when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of t ?",
        "Rationale": "\"a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . t * 23 + 39 = 25 * ( t + 1 ) t = 7 ans . ( a )\"",
        "options": "a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11",
        "correct": "a",
        "annotated_formula": "subtract(divide(subtract(39, 15), add(2, 1)), 1)",
        "linear_formula": "add(n1,n3)|subtract(n0,n2)|divide(#1,#0)|subtract(#2,n3)|",
        "category": "general"
    },
    {
        "Problem": "the average earning of a person for the first 4 days of a week is rs 18 and for the last 4 days is rs 22 . if he earns rs 20 on the fourth day , his average earning for the whole week is ?",
        "Rationale": "total earning for the week = rs ( 4 \u00d7 18 + 4 \u00d7 22 - 20 ) = rs 140 average earning = rs 140 / 7 = rs 20 . answer : c",
        "options": "a ) rs 18.95 , b ) rs 16 , c ) rs 20 , d ) rs 25.71 , e ) none of these",
        "correct": "c",
        "annotated_formula": "divide(subtract(add(multiply(4, 18), multiply(4, 22)), 20), add(const_4, const_3))",
        "linear_formula": "add(const_3,const_4)|multiply(n0,n1)|multiply(n0,n3)|add(#1,#2)|subtract(#3,n4)|divide(#4,#0)",
        "category": "general"
    },
    {
        "Problem": "3 different containers contain 50 litres , 100 litres and 150 litres of mixture of milk and water respectively . what is the biggest measure can measure all the different quantities exactly ?",
        "Rationale": "m 1 = 50 litres m 2 = 100 litres m 3 = 150 litres required measurement = h . c . f . of m 1 , m 2 , m 3 = 50 litres answer is d",
        "options": "a ) 120 litres , b ) 57 litres , c ) 60 litres , d ) 50 litres , e ) 100 litres",
        "correct": "d",
        "annotated_formula": "gcd(gcd(50, 100), 150)",
        "linear_formula": "gcd(n1,n2)|gcd(n3,#0)",
        "category": "physics"
    },
    {
        "Problem": "marty ' s pizza shop guarantees that their pizzas all have at least 75 % of the surface area covered with toppings , with a crust of uniform width surrounding them . if you order their best seller \u2013 a circular pizza with a diameter of 16 inches \u2013 what is the maximum width you can expect to see for the crust ?",
        "Rationale": "total area = 8 * 8 * pi radius = 64 pi surface = . 75 * 64 * pi = 48 pi radius of surface = 4 sqrt ( 3 ) ~ 6.8 radius width = 8 - 6.8 = 1.2 answer : b",
        "options": "['a ) 0.8 inches', 'b ) 1.1 inches', 'c ) 1.6 inches', 'd ) 2.0 inches', 'e ) 2.5 inches']",
        "correct": "b",
        "annotated_formula": "divide(subtract(16, multiply(sqrt(divide(divide(multiply(circle_area(divide(16, const_2)), 75), const_100), const_pi)), const_2)), const_2)",
        "linear_formula": "divide(n1,const_2)|circle_area(#0)|multiply(n0,#1)|divide(#2,const_100)|divide(#3,const_pi)|sqrt(#4)|multiply(#5,const_2)|subtract(n1,#6)|divide(#7,const_2)",
        "category": "geometry"
    },
    {
        "Problem": "compute all real solutions to 16 x + 4 x + 1 - 96 = 0",
        "Rationale": "if we substitute y = 4 x , we have y 2 + 4 y - 96 = 0 , so y = - 4 or y = 8 . the first does not map to a real solution , while the second maps to x = 3 / 2 correct answer a",
        "options": "a ) 3 / 2 , b ) 3 / 3 , c ) 2 / 4 , d ) 4 / 4 , e ) 4 / 5",
        "correct": "a",
        "annotated_formula": "divide(subtract(4, 1), subtract(subtract(4, 1), 1))",
        "linear_formula": "subtract(n1,n2)|subtract(#0,n2)|divide(#0,#1)",
        "category": "general"
    },
    {
        "Problem": "each person in a group of 110 investors has investments in either equities or securities or both . exactly 25 of the investors in equities have investments in securities , and exactly 40 of the investors in securities have investments in equities . how many have investments in equities ?",
        "Rationale": "explanation : the investors can be categorized into three groups : ( 1 ) those who have investments in equities only . ( 2 ) those who have investments in securities only . ( 3 ) those who have investments in both equities and securities . let x , y , and z denote the number of people in the respective categories . since the total number of investors is 110 , we have : - = > x + y + z = 110 - - - - - - - - - - - - - ( 1 ) . also , the number of people with investments in equities is x + z and the number of people with investments in securities is y + z . since exactly 25 % of the investors in equities have investments in securities , we have the equation = > ( 25 / 100 ) \u00d7 ( x + z ) = z . = > ( 25 / 100 ) \u00d7 x = 75 z / 100 . = > x = 3 z . - - - - - - - - - - - - - - ( 2 ) since exactly 40 % of the investors in securities have investments in equities , we have the equation = > ( 40 / 100 ) \u00d7 ( y + z ) = z . = > ( y + z ) = 5 z / 2 . = > y = 3 z / 2 . - - - - - - - - - - - - - - - - - ( 3 ) substituting equations ( 2 ) and ( 3 ) into equation ( 1 ) gives : - = > 3 z + ( 3 z / 2 ) + z = 110 . = > 11 z / 2 = 110 . = > z = 110 \u00d7 2 / 11 = 20 . hence , the number of people with investments in equities is : = > x + z = 3 z + z = 3 \u00d7 20 + 20 = 60 + 20 = 80 . answer : b",
        "options": "a ) 65 , b ) 80 , c ) 120 , d ) 180 , e ) 190",
        "correct": "b",
        "annotated_formula": "multiply(divide(110, add(add(multiply(divide(divide(40, const_100), divide(25, const_100)), divide(25, const_100)), subtract(const_1, multiply(divide(divide(40, const_100), divide(25, const_100)), divide(25, const_100)))), subtract(divide(divide(40, const_100), divide(25, const_100)), multiply(divide(divide(40, const_100), divide(25, const_100)), divide(25, const_100))))), divide(divide(40, const_100), divide(25, const_100)))",
        "linear_formula": "divide(n2,const_100)|divide(n1,const_100)|divide(#0,#1)|multiply(#2,#1)|subtract(const_1,#3)|subtract(#2,#3)|add(#3,#4)|add(#6,#5)|divide(n0,#7)|multiply(#8,#2)",
        "category": "other"
    },
    {
        "Problem": "an angry arjun carried some arrows for fighting with bheeshm . with half the arrows , he cut down the arrows thrown by bheeshm on him and with 6 other arrows he killed the chariot driver of bheeshm . with one arrow each he knocked down respectively the chariot , the flag and the bow of bheeshm . finally , with one more than 4 times the square root of arrows he laid bheeshm unconscious on an arrow bed . find the total number of arrows arjun had .",
        "Rationale": "x / 2 + 6 + 3 + 1 + 4 sqrt ( x ) = x x / 2 + 10 + 4 sqrt ( x ) = x 4 sqrt ( x ) = x / 2 - 10 squaring on both sides 16 x = x \u00b2 / 4 + 100 - 10 x simplifying x \u00b2 - 104 x + 400 = 0 x = 100 , 4 x = 4 is not possible therefore x = 100 answer : b",
        "options": "a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130",
        "correct": "b",
        "annotated_formula": "power(add(6, 4), const_2)",
        "linear_formula": "add(n0,n1)|power(#0,const_2)",
        "category": "general"
    },
    {
        "Problem": "when tom works alone he chops 3 lb . salad in 2 minutes , and when tammy works alone she chops 2 lb . salad in 3 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tom is what percent greater than the quantifying chopped by tommy ? .",
        "Rationale": "\"tammy chops 4 lbs in 6 minutes tom chops 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : c\"",
        "options": "a ) 44 % , b ) 100 % , c ) 125 % , d ) 225 % , e ) 400 %",
        "correct": "c",
        "annotated_formula": "multiply(divide(subtract(divide(2, 3), divide(const_2.0, 2)), divide(3, 2)), const_100)",
        "linear_formula": "divide(const_3.0,const_2.0)|divide(const_2.0,n1)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100)|",
        "category": "physics"
    },
    {
        "Problem": "the radius of a circular wheel is 1.75 m , how many revolutions will it make in traveling 1 km ?",
        "Rationale": "2 * 22 / 7 * 1.75 * x = 11000 x = 1000 answer : a",
        "options": "['a ) 1000', 'b ) 2788', 'c ) 2677', 'd ) 2899', 'e ) 2771']",
        "correct": "a",
        "annotated_formula": "divide(multiply(multiply(multiply(const_pi, const_2), 1.75), const_1000), add(1, const_10))",
        "linear_formula": "add(n1,const_10)|multiply(const_2,const_pi)|multiply(n0,#1)|multiply(#2,const_1000)|divide(#3,#0)",
        "category": "physics"
    },
    {
        "Problem": "if the radius of a cylinder is doubled and so is the height , what is the new volume of the cylinder divided by the old one ?",
        "Rationale": "let the radius be r and the the height be h . new radius = 2 r and height = 2 h . area ( new ) : area ( old ) = pi \u2217 ( 2 r ) ^ 2 \u2217 2 h / pi \u2217 r ^ 2 \u2217 h = 8 : 1 . hence the answer is a .",
        "options": "['a ) 8 .', 'b ) 2', 'c ) 6', 'd ) 4', 'e ) 10']",
        "correct": "a",
        "annotated_formula": "divide(volume_cylinder(multiply(const_1, const_2), multiply(const_1, const_2)), volume_cylinder(const_1, const_1))",
        "linear_formula": "multiply(const_1,const_2)|volume_cylinder(const_1,const_1)|volume_cylinder(#0,#0)|divide(#2,#1)",
        "category": "geometry"
    },
    {
        "Problem": "the average of first six multiples of 3 is",
        "Rationale": "\"solution average = 3 ( 1 + 2 + 3 + 4 + 5 + 6 ) / 6 = 63 / 6 . = 10.5 . answer a\"",
        "options": "a ) 10.5 , b ) 6 , c ) 9 , d ) 12 , e ) 15",
        "correct": "a",
        "annotated_formula": "add(3, const_1)",
        "linear_formula": "add(n0,const_1)|",
        "category": "general"
    },
    {
        "Problem": "the product of two numbers is 192 and the sum of these two numbers is 28 . what is the smaller of these two numbers ?",
        "Rationale": "\"solution let the number be x and ( 28 - x ) = then , x ( 28 - x ) = 192 \u2039 = \u203a x 2 - 28 x + 192 = 0 . \u2039 = \u203a ( x - 16 ) ( x - 12 ) = 0 \u2039 = \u203a x = 16 or x = 12 . answer b\"",
        "options": "a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 16",
        "correct": "b",
        "annotated_formula": "sqrt(add(power(sqrt(subtract(28, multiply(const_2, 192))), const_2), multiply(const_4, 192)))",
        "linear_formula": "multiply(n0,const_4)|multiply(n0,const_2)|subtract(n1,#1)|sqrt(#2)|power(#3,const_2)|add(#0,#4)|sqrt(#5)|",
        "category": "general"
    },
    {
        "Problem": "oil is poured into a tank so that the tank is being filled at the rate of 4 cubic feet per hour . if the empty rectangular tank is 9 feet long , 8 feet wide , and 5 feet deep , approximately how many hours does it take to fill the tank ?",
        "Rationale": "the volume the tank is : length * width * depth = 9 * 8 * 5 = 360 cubic feet . 360 cubic feet / 4 cubic feet per hour = 90 hours . it will take 90 hours to fill the tank . the answer is d .",
        "options": "['a ) 60', 'b ) 70', 'c ) 80', 'd ) 90', 'e ) 100']",
        "correct": "d",
        "annotated_formula": "divide(volume_rectangular_prism(9, 8, 5), 4)",
        "linear_formula": "volume_rectangular_prism(n1,n2,n3)|divide(#0,n0)",
        "category": "physics"
    },
    {
        "Problem": "the speed of a boat in still water is 15 km / hr and the rate of the current is 3 km / hr . the distance travelled downstream in 12 minutes is",
        "Rationale": "\"speed downstream = ( 15 + 3 ) km / hr = 18 km / hr . distance travelled = ( 18 x 12 / 60 ) hours = 3.6 km . answer d\"",
        "options": "a ) 1.2 km , b ) 1.8 km , c ) 2.4 km , d ) 3.6 km , e ) none",
        "correct": "d",
        "annotated_formula": "multiply(divide(12, const_60), add(15, 3))",
        "linear_formula": "add(n0,n1)|divide(n2,const_60)|multiply(#0,#1)|",
        "category": "physics"
    },
    {
        "Problem": "a certain animal in the zoo has consumed 39 pounds of food in 6 days . if it continues to eat at the same rate , in how many more days will its total consumption be 117 pounds ?",
        "Rationale": "ans is c : 39 pounds - - > 6 days 117 pounds - - > x days x = 117 * 6 / 39 = 18 the animal has already consumed food in 6 days so the the number of days for it ' s total consumption be 117 pounds is 18 - 6 = 12",
        "options": "a ) 8 , b ) 7 , c ) 12 , d ) 9 , e ) none of the above",
        "correct": "c",
        "annotated_formula": "subtract(divide(117, divide(39, 6)), 6)",
        "linear_formula": "divide(n0,n1)|divide(n2,#0)|subtract(#1,n1)",
        "category": "general"
    },
    {
        "Problem": "a set of consecutive positive integers beginning with 1 is written on the blackboard . a student came along and erased one number . the average of the remaining numbers is 35 * 7 / 17 . what was the number erased ?",
        "Rationale": "explanation : let the higher number be n and x be the number erased . then ( ( n ( n + 1 ) / 2 ) + x ) / ( n + 1 ) = 35 * 7 / 17 = 602 / 17 hence , n = 69 and x = 7 satisfy the above conditions . answer : a",
        "options": "a ) 7 , b ) 8 , c ) 6 , d ) 5 , e ) 4",
        "correct": "a",
        "annotated_formula": "subtract(multiply(divide(floor(multiply(add(35, divide(7, 17)), const_2)), const_2), subtract(floor(multiply(add(35, divide(7, 17)), const_2)), const_1)), multiply(add(35, divide(7, 17)), subtract(subtract(floor(multiply(add(35, divide(7, 17)), const_2)), const_1), 1)))",
        "linear_formula": "divide(n2,n3)|add(n1,#0)|multiply(#1,const_2)|floor(#2)|divide(#3,const_2)|subtract(#3,const_1)|multiply(#4,#5)|subtract(#5,n0)|multiply(#1,#7)|subtract(#6,#8)",
        "category": "general"
    },
    {
        "Problem": "the lengths of the diagonals of a rhombus are 20 and 48 meters . find the perimeter of the rhombus ?",
        "Rationale": "below is shown a rhombus with the given diagonals . consider the right triangle boc and apply pythagora ' s theorem as follows bc 2 = 10 ^ 2 + 24 ^ 2 and evaluate bc bc = 26 meters . we now evaluate the perimeter p as follows : p = 4 * 26 = 104 meters . answer is d",
        "options": "['a ) 150 merters', 'b ) 125 meters', 'c ) 96 meters', 'd ) 104 meters', 'e ) 152 meters']",
        "correct": "d",
        "annotated_formula": "power(divide(20, const_2), const_2)",
        "linear_formula": "divide(n0,const_2)|power(#0,const_2)",
        "category": "geometry"
    },
    {
        "Problem": "during the first two weeks of june , the total rainfall in springdale was 40 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall in inches during the second week of june ?",
        "Rationale": "let x be the rainfall in the first week . then 1.5 x was the rainfall in the second week . 2.5 x = 40 x = 16 the rainfall during the second week was 1.5 * 16 = 24 inches the answer is d .",
        "options": "a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27",
        "correct": "d",
        "annotated_formula": "multiply(divide(40, add(const_1, 1.5)), 1.5)",
        "linear_formula": "add(n1,const_1)|divide(n0,#0)|multiply(n1,#1)",
        "category": "general"
    },
    {
        "Problem": "two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days . the number of days required by 1 man to complete the work is",
        "Rationale": "two men and 7 children complete a certain piece of work in 4 days or 8 men and 28 children complete a certain piece of work in 1 days 4 men and 4 children complete the same work in only 3 days . or 12 men and 12 children complete the same work in only 3 days . so 8 men + 28 children = 12 men + 12 children 1 man = 4 children 4 men and 4 children complete the same work in only 3 days or 4 men and 1 man ( in place of 4 children ) complete the same work in only 3 days or 5 men complete the same work in 3 days or 1 man will complete the same work in 5 * 3 = 15 days answer : b",
        "options": "a ) 60 days , b ) 15 days , c ) 6 days , d ) 51 days , e ) 50 days",
        "correct": "b",
        "annotated_formula": "divide(subtract(multiply(7, 4), add(4, 4)), subtract(divide(7, 3), 1))",
        "linear_formula": "add(n1,n1)|divide(n0,n4)|multiply(n0,n1)|subtract(#2,#0)|subtract(#1,n5)|divide(#3,#4)",
        "category": "physics"
    },
    {
        "Problem": "the total surface area of a solid hemisphere of diameter 14 cm , is :",
        "Rationale": "sol . total surface area = 3 \u220f r \u00b2 = [ 3 * 22 / 7 * 7 * 7 ] cm \u00b2 = 462 cm \u00b2 answer a",
        "options": "['a ) 462 cm \u00b2', 'b ) 530 cm \u00b2', 'c ) 1345 cm \u00b2', 'd ) 1788 cm \u00b2', 'e ) none']",
        "correct": "a",
        "annotated_formula": "multiply(multiply(const_3, const_pi), power(divide(14, const_2), const_2))",
        "linear_formula": "divide(n0,const_2)|multiply(const_3,const_pi)|power(#0,const_2)|multiply(#1,#2)",
        "category": "geometry"
    },
    {
        "Problem": "15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container h ?",
        "Rationale": "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct .",
        "options": "a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42",
        "correct": "c",
        "annotated_formula": "divide(15, subtract(const_1, sqrt(divide(9, add(9, 16)))))",
        "linear_formula": "add(n2,n3)|divide(n2,#0)|sqrt(#1)|subtract(const_1,#2)|divide(n0,#3)",
        "category": "general"
    },
    {
        "Problem": "a dog breeder currently has 9 breeding dogs . 6 of the dogs have exactly 1 littermate , and 3 of the dogs have exactly 2 littermates . if 2 dogs are selected at random , what is the probability e that both selected dogs are not littermates ?",
        "Rationale": "\"we have three pairs of dogs for the 6 with exactly one littermate , and one triplet , with each having exactly two littermates . so , in fact there are two types of dogs : those with one littermate - say a , and the others with two littermates - b . work with probabilities : choosing two dogs , we can have either one dog of type b or none ( we can not have two dogs both of type b ) . the probability of choosing one dog of type b and one of type a is 3 / 9 * 6 / 8 * 2 = 1 / 2 ( the factor of 2 for the two possibilities ba and ab ) . the probability e of choosing two dogs of type a which are not littermates is 6 / 9 * 4 / 8 = 1 / 3 ( choose one a , then another a which is n ' t the previous one ' s littermate ) . the required probability is 1 / 2 + 1 / 3 = 5 / 6 . find the probability for the complementary event : choose aa or bb . probability of choosing two dogs of type a who are littermates is 6 / 9 * 1 / 8 = 1 / 12 . probability of choosing two dogs of type b ( who necessarily are littermates ) is 3 / 9 * 2 / 8 = 1 / 12 . again , we obtain 1 - ( 1 / 12 + 1 / 12 ) = 5 / 6 . answer : c\"",
        "options": "a ) 1 / 6 , b ) 2 / 9 , c ) 5 / 6 , d ) 7 / 9 , e ) 8 / 9",
        "correct": "c",
        "annotated_formula": "divide(const_5, 6)",
        "linear_formula": "divide(const_5,n1)|",
        "category": "other"
    },
    {
        "Problem": "tanks p and b are each in the shape of a right circular cylinder . the interior of tank p has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank p is what percent of the capacity of tank b ?",
        "Rationale": "b . for p , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 10 = 160 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi p / b = 160 pi / 200 pi = 0.8",
        "options": "['a ) 75 %', 'b ) 80 %', 'c ) 100 %', 'd ) 120 %', 'e ) 125 %']",
        "correct": "b",
        "annotated_formula": "multiply(divide(volume_cylinder(divide(divide(8, const_2), const_pi), 10), volume_cylinder(divide(divide(10, const_2), const_pi), 8)), const_100)",
        "linear_formula": "divide(n1,const_2)|divide(n0,const_2)|divide(#0,const_pi)|divide(#1,const_pi)|volume_cylinder(#2,n0)|volume_cylinder(#3,n1)|divide(#4,#5)|multiply(#6,const_100)",
        "category": "physics"
    },
    {
        "Problem": "what quantity of water should be added to reduce 20 liters of 80 % acidic liquid to 20 % acidic liquid ?",
        "Rationale": "\"acid in 20 liters = 80 % of 20 = 16 liters suppose x liters of water be added . then 16 liters of acid in 20 + x liters of diluted solution 20 % of 20 + x = 16 20 + x = 80 x = 60 liters answer is c\"",
        "options": "a ) 30 liters , b ) 50 liters , c ) 60 liters , d ) 70 liters , e ) 80 liters",
        "correct": "c",
        "annotated_formula": "subtract(divide(multiply(multiply(20, divide(80, const_100)), const_100), 20), 20)",
        "linear_formula": "divide(n1,const_100)|multiply(n0,#0)|multiply(#1,const_100)|divide(#2,n2)|subtract(#3,n0)|",
        "category": "gain"
    },
    {
        "Problem": "mr . shah decided to walk down the escalator of a tube station . he found \u00e2 that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stairs he would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins \u00e2 to descend to the time he steps off the last step at the bottom , find out the height of the stair way in steps ?",
        "Rationale": "( s 1 * t 2 ~ s 2 * t 1 ) / ( t 2 ~ t 1 ) = ( 26 * 18 ~ 34 * 30 ) / ( 18 ~ 30 ) = 46 answer : c",
        "options": "a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48",
        "correct": "c",
        "annotated_formula": "add(26, multiply(divide(subtract(34, 26), subtract(30, 18)), 30))",
        "linear_formula": "subtract(n2,n0)|subtract(n1,n3)|divide(#0,#1)|multiply(n1,#2)|add(n0,#3)",
        "category": "physics"
    },
    {
        "Problem": "what is 15 percent of rs . 34 ?",
        "Rationale": "\"sol . 15 % of rs . 34 = rs . ( 15 / 100 x 34 ) = rs . 5.10 answer d\"",
        "options": "a ) rs . 3.40 , b ) rs . 3.75 , c ) rs . 4.50 , d ) rs . 5.10 , e ) none",
        "correct": "d",
        "annotated_formula": "divide(multiply(15, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100)",
        "linear_formula": "add(const_2,const_3)|add(const_3,const_4)|add(const_3,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#3,const_100)|multiply(#1,#0)|multiply(#4,#5)|multiply(#6,#4)|add(#7,#8)|add(#9,#2)|multiply(n0,#10)|divide(#11,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "a reduction of 10 % in the price of tea enables a dealer to purchase 25 kg more tea for rs . 22500 . what is the reduced price per kg of tea ?",
        "Rationale": "solution : 1 st method : let the original price of tea be rs . x / kg . after reduction the price becomes = x - 10 % of x = 9 x / 10 per kg . now , ( 22500 / ( 9 x / 10 ) ) - 22500 / x = 25 or , 22500 [ 10 / 9 x - 1 / x ] = 25 or , 25 * 9 x = 22500 ; or , x = ( 22500 / 2589 ) = rs . 100 . hence , new price = 90 per kg . thought process method : let the original price be rs . 100 per kg , he get tea = 22500 / 100 = 225 kg . after reduction the price becomes = 90 per kg , he get tea = 22500 / 90 = 250 kg . so , reduction price is rs . 90 per kg as it enables him to buy 25 kg of more tea . answer : option c",
        "options": "a ) rs . 70 , b ) rs . 80 , c ) rs . 90 , d ) rs . 100 , e ) none",
        "correct": "c",
        "annotated_formula": "divide(divide(multiply(22500, subtract(divide(const_100, subtract(const_100, 10)), const_1)), 25), divide(const_100, subtract(const_100, 10)))",
        "linear_formula": "subtract(const_100,n0)|divide(const_100,#0)|subtract(#1,const_1)|multiply(n2,#2)|divide(#3,n1)|divide(#4,#1)",
        "category": "gain"
    },
    {
        "Problem": "at 12 : 30 , the hour hand and the minute hand of a clock form an angle of",
        "Rationale": "\"answer : 180 degree answer : e\"",
        "options": "a ) 120 \u00b0 , b ) 135 \u00b0 , c ) 125 \u00b0 , d ) 150 \u00b0 , e ) 180 \u00b0",
        "correct": "e",
        "annotated_formula": "subtract(multiply(multiply(multiply(const_60, 12), const_2), divide(30, const_60)), multiply(divide(divide(multiply(multiply(const_60, 12), const_2), 12), const_4), add(divide(30, const_60), 12)))",
        "linear_formula": "divide(n1,const_60)|multiply(n0,const_60)|add(n0,#0)|multiply(#1,const_2)|divide(#3,n0)|multiply(#0,#3)|divide(#4,const_4)|multiply(#2,#6)|subtract(#5,#7)|",
        "category": "physics"
    },
    {
        "Problem": "a businessman earns $ 26800 in december , thus decreasing his average annual ( january to december ) earnings by $ 1200 . his average annual earnings would be source : cmat preparation",
        "Rationale": "( x - 26,800 ) / 11 - x / 12 = 1,200 x = 480,000 x / 12 = 40,000 answer : c .",
        "options": "a ) $ 29000 , b ) $ 33500 , c ) $ 40000 , d ) $ 41000 , e ) $ 42300",
        "correct": "c",
        "annotated_formula": "add(26800, multiply(const_12, 1200))",
        "linear_formula": "multiply(n1,const_12)|add(n0,#0)",
        "category": "general"
    },
    {
        "Problem": "a sum of rs . 66000 is divided into 3 parts such that the simple interests accrued on them for 6 , two and 11 years respectively may be equal . find the amount deposited for 11 years .",
        "Rationale": "let the amounts be x , y , z in ascending order of value . as the interest rate and interest accrued are same for 2 years 6 years and 11 years i . e . 2 x = 6 y = 11 z = k . l . c . m . of 2 , 611 = 66 so x : y : z : = 33000 : 11000 : 6000 the amount deposited for 11 years = 6000 answer : e",
        "options": "a ) 6500 , b ) 2000 , c ) 4500 , d ) 3000 , e ) 6000",
        "correct": "e",
        "annotated_formula": "multiply(multiply(6, const_10), const_100)",
        "linear_formula": "multiply(n2,const_10)|multiply(#0,const_100)",
        "category": "general"
    },
    {
        "Problem": "in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what percent z of all the people in smithtown are left - handed women ?",
        "Rationale": "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c",
        "options": "a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %",
        "correct": "c",
        "annotated_formula": "multiply(divide(subtract(multiply(2, divide(add(3, 1), add(3, 2))), subtract(3, multiply(3, divide(add(3, 1), add(3, 2))))), add(3, 1)), const_100)",
        "linear_formula": "add(n0,n1)|add(n0,n3)|divide(#0,#1)|multiply(n3,#2)|multiply(n0,#2)|subtract(n0,#4)|subtract(#3,#5)|divide(#6,#0)|multiply(#7,const_100)",
        "category": "general"
    },
    {
        "Problem": "the average age of 20 men in the class is 15.6 years . 5 new men join and the new average becomes 14.56 years . what was the average age of 5 new men ?",
        "Rationale": "total age of 20 men = 15.6 x 20 = 312 now , total age of 25 men = 364 . total age of five men added later = 364 - 312 = 52 . hence , the total average of five men = 52 / 5 = 10.4 answer : d",
        "options": "a ) 15.5 , b ) 15.4 , c ) 15.25 , d ) 10.4 , e ) 15.6",
        "correct": "d",
        "annotated_formula": "divide(subtract(multiply(add(20, 5), 14.56), multiply(20, 15.6)), 5)",
        "linear_formula": "add(n0,n2)|multiply(n0,n1)|multiply(n3,#0)|subtract(#2,#1)|divide(#3,n2)",
        "category": "general"
    },
    {
        "Problem": "the sum of the squares of three consecutive natural number is 2030 . what is the middle number ?",
        "Rationale": "\"let the numbers be x , x + 1 and x + 2 x 2 + ( x + 1 ) 2 + ( x + 2 ) 2 = 2030 3 x 2 + 6 x - 2025 = 0 ( x + 27 ) ( x - 25 ) = 0 x = 25 the middle number is 26 answer b 26\"",
        "options": "a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29",
        "correct": "b",
        "annotated_formula": "divide(subtract(sqrt(add(multiply(subtract(2030, const_1), const_4), const_1)), const_1), const_2)",
        "linear_formula": "subtract(n0,const_1)|multiply(#0,const_4)|add(#1,const_1)|sqrt(#2)|subtract(#3,const_1)|divide(#4,const_2)|",
        "category": "physics"
    },
    {
        "Problem": "in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each train running with a speed of 60 kmph being 130 m and 120 m in length respectively ?",
        "Rationale": "\"d = 130 m + 120 m = 250 m * 1 / 1000 = 0.25 kms rs = 60 + 60 = 120 kmph t = ( 0.25 / 120 ) * 3600 = 7.5 sec answer : e\"",
        "options": "a ) 6.9 sec , b ) 7.1 sec , c ) 7.2 sec , d ) 7.4 sec , e ) 7.5 sec",
        "correct": "e",
        "annotated_formula": "divide(add(60, 60), multiply(add(130, 130), const_0_2778))",
        "linear_formula": "add(n0,n0)|add(n1,n1)|multiply(#1,const_0_2778)|divide(#0,#2)|",
        "category": "physics"
    },
    {
        "Problem": "rob also compared the empire state building and the petronas towers . what is the height difference between the two if the empire state building is 435 m tall and the petronas towers is 458 m tall ?",
        "Rationale": "458 - 435 = 23 . answer is c .",
        "options": "a ) 9 , b ) 17 , c ) 23 , d ) 45 , e ) 12",
        "correct": "c",
        "annotated_formula": "subtract(458, 435)",
        "linear_formula": "subtract(n1,n0)",
        "category": "physics"
    },
    {
        "Problem": "from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a red king ?",
        "Rationale": "p ( club ) = 1 / 4 p ( red king ) = 1 / 26 p ( club then a red king ) = 1 / 4 * 1 / 26 = 1 / 104 the answer is e .",
        "options": "a ) 1 / 13 , b ) 1 / 15 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 104",
        "correct": "e",
        "annotated_formula": "multiply(divide(add(multiply(const_3, const_4), const_1), const_52), divide(const_2, const_52))",
        "linear_formula": "divide(const_2,const_52)|multiply(const_3,const_4)|add(#1,const_1)|divide(#2,const_52)|multiply(#3,#0)",
        "category": "probability"
    },
    {
        "Problem": "a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many cubes are painted on only 2 faces ?",
        "Rationale": "the mini - cubes with 2 painted sides are all on the edge of the cube , in the ` ` middle ' ' of the edge . there are 4 in front , 4 in back and 4 more on the ` ` strip ' ' that runs around the left / top / right / bottom of the cube . 4 + 4 + 4 = 12 . answer a",
        "options": "['a ) 12', 'b ) 8', 'c ) 6', 'd ) 10', 'e ) 16']",
        "correct": "a",
        "annotated_formula": "multiply(const_4, power(27, divide(const_1, const_3)))",
        "linear_formula": "divide(const_1,const_3)|power(n0,#0)|multiply(#1,const_4)",
        "category": "geometry"
    },
    {
        "Problem": "the cost price of 20 articles is the same as the selling price of x articles . if the profit is 25 % , find out the value of x",
        "Rationale": "\"explanation : let the cost price of one article = rs . 1 cp of x articles = rs . x cp of 20 articles = 20 selling price of x articles = 20 profit = 25 % [ given ] \u21d2 ( sp \u2212 cp / cp ) = 25 / 100 = 1 / 4 \u21d2 ( 20 \u2212 x ) / x = 1 / 4 \u21d2 80 \u2212 4 x = x \u21d2 5 x = 80 option d \u21d2 x = 805 = 16\"",
        "options": "a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17",
        "correct": "d",
        "annotated_formula": "divide(multiply(20, const_4), add(const_4, const_1))",
        "linear_formula": "add(const_1,const_4)|multiply(n0,const_4)|divide(#1,#0)|",
        "category": "gain"
    },
    {
        "Problem": "company t produces two kinds of stereos : basic and deluxe . of the stereos produced by company t last month , 2 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?",
        "Rationale": "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 7 / 5 = 7 - - > total time for both of them would be 10 + 7 = 17 - - > deluxe / total = 7 / 17 . b",
        "options": "a ) 5 / 17 , b ) 7 / 17 , c ) 4 / 17 , d ) 3 / 17 , e ) 5",
        "correct": "b",
        "annotated_formula": "divide(multiply(5, divide(7, 5)), add(multiply(multiply(2, 5), const_1), multiply(5, divide(7, 5))))",
        "linear_formula": "divide(n2,n3)|multiply(n0,n3)|multiply(n3,#0)|multiply(#1,const_1)|add(#3,#2)|divide(#2,#4)",
        "category": "general"
    },
    {
        "Problem": "calculate the area of a triangle , if the sides of are 52 cm , 48 cm and 20 cm , what is its area ?",
        "Rationale": "\"the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a\"",
        "options": "a ) 480 cm 2 , b ) 580 cm 2 , c ) 380 cm 2 , d ) 180 cm 2 , e ) 280 cm 2",
        "correct": "a",
        "annotated_formula": "multiply(divide(48, const_2), 20)",
        "linear_formula": "divide(n1,const_2)|multiply(n2,#0)|",
        "category": "geometry"
    },
    {
        "Problem": "a truck covers a distance of 550 metres in 1 minute whereas a train covers a distance of 33 kms in 45 minutes . what is the ratio of their speed ?",
        "Rationale": "\"explanation : speed of the truck = distance / time = 550 / 1 = 550 meters / minute speed of the train = distance / time = 33 / 45 km / minute = 33000 / 45 meters / minut speed of the truck / speed of the train = 550 / ( 33000 / 45 ) = ( 550 \u00d7 45 ) / 33000 = ( 55 \u00d7 45 ) / 3300 = ( 11 \u00d7 45 ) / 660 = ( 11 \u00d7 9 ) / 132 = 9 / 12 = 34 hence , speed of the truck : speed of the train = 3 : 4 answer : option d\"",
        "options": "a ) 3 : 7 , b ) 4 : 7 , c ) 1 : 4 , d ) 3 : 4 , e ) 2 : 5",
        "correct": "d",
        "annotated_formula": "divide(550, multiply(divide(33, 45), const_1000))",
        "linear_formula": "divide(n2,n3)|multiply(#0,const_1000)|divide(n0,#1)|",
        "category": "physics"
    },
    {
        "Problem": "a sum of money is distributed among a , b , c , d in the proportion of 6 : 4 : 8 : 5 . if c gets $ 3000 more than d , what is the b ' s share ?",
        "Rationale": "\"let the shares of a , b , c , d are 6 x , 4 x , 8 x , 5 x 8 x - 5 x = 3000 3 x = 3000 , x = 1000 b ' s share = 4 x = $ 4000 answer is d\"",
        "options": "a ) $ 2000 , b ) $ 6000 , c ) $ 1000 , d ) $ 4000 , e ) $ 5000",
        "correct": "d",
        "annotated_formula": "divide(multiply(divide(multiply(add(3000, 3000), 5), 8), 4), 5)",
        "linear_formula": "add(n4,n4)|multiply(n3,#0)|divide(#1,n2)|multiply(n1,#2)|divide(#3,n3)|",
        "category": "general"
    },
    {
        "Problem": "there are 50 boys in a class . their average weight is 45 kg . when one boy leaves the class , the average reduces by 100 g . find the weight of the boy who left the class .",
        "Rationale": "here one boy is excluded and final average of the group decreases . \u2234 change in average is ( \u2013 ) ve = \u2013 0.1 kg . using the formula sum of the quantities excluded = ( changein no . ofquantities \u00d7 origina laverage ) + ( changeinaverage \u00d7 final no . ofquantities ) \u21d2 weight of the boy who left = ( 1 \u00d7 45 ) \u2013 ( \u2013 0.1 \u00d7 49 ) = 49.9 kg answer c",
        "options": "a ) 40.9 kg , b ) 42.9 kg , c ) 49.9 kg , d ) 39.9 kg , e ) none of these",
        "correct": "c",
        "annotated_formula": "add(45, divide(multiply(subtract(50, const_1), 100), const_1000))",
        "linear_formula": "subtract(n0,const_1)|multiply(n2,#0)|divide(#1,const_1000)|add(n1,#2)",
        "category": "general"
    },
    {
        "Problem": "a university cafeteria offers 6 flavors of pizza - pork , gobi - manjurian , pepperoni , chicken , hawaiian and vegetarian . if a customer has an option ( but not the obligation ) to add extra cheese , mushrooms or both to any kind of pizza , how many different pizza varieties are available ?",
        "Rationale": "6 flavours * 6 choices = 6 c 1 * 6 c 1 = 6 * 6 = 36 = d",
        "options": "a ) 4 , b ) 8 , c ) 12 , d ) 36 , e ) 32",
        "correct": "d",
        "annotated_formula": "multiply(6, 6)",
        "linear_formula": "multiply(n0,n0)",
        "category": "general"
    },
    {
        "Problem": "in a zoo , the ratio of the number of cheetahs to the number 4 then what is the increase in the number of pandas ?",
        "Rationale": "one short cut to solve the problem is c : p = 1 : 3 c increased to 5 = > 1 : 3 = 5 : x = > x = 15 = > p increased by 12 b is the answer",
        "options": "a ) 2 , b ) 12 , c ) 5 , d ) 10 , e ) 15",
        "correct": "b",
        "annotated_formula": "subtract(multiply(4, 4), const_4)",
        "linear_formula": "multiply(n0,n0)|subtract(#0,const_4)",
        "category": "other"
    },
    {
        "Problem": "rs . 6490 is divided so that 4 times the first share , six times the 2 nd share and twice the third share amount to the same . what is the value of the first share ?",
        "Rationale": "\"a + b + c = 6490 4 a = 6 b = 2 c = x a : b : c = 1 / 4 : 1 / 6 : 1 / 2 = 3 : 2 : 6 3 / 11 * 6490 = rs 1770 answer : e\"",
        "options": "a ) s 6490 , b ) s 1880 , c ) s 1660 , d ) s 1550 , e ) s 1770",
        "correct": "e",
        "annotated_formula": "multiply(4, divide(6490, add(add(4, 2), const_3)))",
        "linear_formula": "add(n1,n2)|add(#0,const_3)|divide(n0,#1)|multiply(n1,#2)|",
        "category": "general"
    },
    {
        "Problem": "the average salary per month of 55 employees in a company is rs 8500 . if the managers salary is added , the average salary increases to rs 8800 , what is the salary of the manager ?",
        "Rationale": "explanation : salary of the manager = ( 56 * 8800 - 55 * 8500 ) = 25300 answer : d",
        "options": "a ) 10000 , b ) 12000 , c ) 23000 , d ) 25300 , e ) 45000",
        "correct": "d",
        "annotated_formula": "subtract(multiply(add(55, const_1), 8800), multiply(55, 8500))",
        "linear_formula": "add(n0,const_1)|multiply(n0,n1)|multiply(n2,#0)|subtract(#2,#1)",
        "category": "general"
    },
    {
        "Problem": "there are 24 students in a seventh grade class . they decided to plant birches and roses at the school ' s backyard . while each girl planted 3 roses , every three boys planted 1 birch . by the end of the day they planted 2424 plants . how many birches were planted ?",
        "Rationale": "\"let x be the number of roses . then the number of birches is 24 \u2212 x , and the number of boys is 3 \u00d7 ( 24 \u2212 x ) . if each girl planted 3 roses , there are x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 \u2212 x ) = 24 x + 9 ( 24 \u2212 x ) = 3 \u22c5 24 x + 216 \u2212 9 x = 72 216 \u2212 72 = 8 x 1448 = x 1 x = 18 so , students planted 18 roses and 24 - x = 24 - 18 = 6 birches . correct answer is d ) 6\"",
        "options": "a ) 2 , b ) 5 , c ) 8 , d ) 6 , e ) 4",
        "correct": "d",
        "annotated_formula": "divide(subtract(multiply(3, 24), 24), subtract(multiply(3, 3), 1))",
        "linear_formula": "multiply(n0,n1)|multiply(n1,n1)|subtract(#0,n0)|subtract(#1,n2)|divide(#2,#3)|",
        "category": "physics"
    },
    {
        "Problem": "in a simultaneous throw of pair of dice . find the probability of getting the total more than 7",
        "Rationale": "here n ( s ) = ( 6 * 6 ) = 36 let e = event of getting a total more than 7 = { ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } p ( e ) = n ( e ) / n ( s ) = 15 / 36 = 5 / 12 option c",
        "options": "a ) 5 / 7 , b ) 4 / 7 , c ) 5 / 12 , d ) 4 / 7 , e ) 1 / 6",
        "correct": "c",
        "annotated_formula": "divide(add(add(7, const_4), const_4), multiply(add(const_4, const_2), add(const_4, const_2)))",
        "linear_formula": "add(n0,const_4)|add(const_2,const_4)|add(#0,const_4)|multiply(#1,#1)|divide(#2,#3)",
        "category": "general"
    },
    {
        "Problem": "a green grocer received a boxful of tomatoes and on opening the box found that several had gone bad . he then counted them up so that he could make a formal complaint and found that 68 were mouldy , which was 16 per cent of the total contents of the box . how many tomatoes were in the box ?",
        "Rationale": "b 425 ( 68 \u00e3 \u00b7 16 ) \u00e3 \u2014 100",
        "options": "a ) 336 , b ) 425 , c ) 275 , d ) 235 , e ) 689",
        "correct": "b",
        "annotated_formula": "subtract(multiply(multiply(68, const_4), const_2), const_100)",
        "linear_formula": "multiply(n0,const_4)|multiply(#0,const_2)|subtract(#1,const_100)",
        "category": "general"
    },
    {
        "Problem": "how many boxes do we need if we have to carry 250 apples into boxes that each hold 25 apples ?",
        "Rationale": "sol . apples 250 each carries 25 = 250 / 25 = 10 answer : d",
        "options": "a ) a ) 9 , b ) b ) 5 , c ) c ) 7 , d ) d ) 10 , e ) e ) none of the above",
        "correct": "d",
        "annotated_formula": "divide(250, 25)",
        "linear_formula": "divide(n0,n1)",
        "category": "general"
    },
    {
        "Problem": "the diameter of a circle is 4 / \u03c0 . find the circumference of the circle .",
        "Rationale": "circumference = 2 * pi * r = 2 * pi * 4 / pi = > 8 a",
        "options": "['a ) 8', 'b ) 4 \u03c0', 'c ) 4', 'd ) 6', 'e ) 5']",
        "correct": "a",
        "annotated_formula": "circumface(divide(4, const_pi))",
        "linear_formula": "divide(n0,const_pi)|circumface(#0)",
        "category": "geometry"
    },
    {
        "Problem": "simplify : 0.3 * 0.3 + 0.3 * 0.3",
        "Rationale": "\"given exp . = 0.3 * 0.3 + ( 0.3 * 0.3 ) = 0.09 + 0.09 = 0.18 answer is c .\"",
        "options": "a ) 0.52 , b ) 0.42 , c ) 0.18 , d ) 0.64 , e ) 0.46",
        "correct": "c",
        "annotated_formula": "add(multiply(0.3, 0.3), multiply(0.3, 0.3))",
        "linear_formula": "multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|",
        "category": "general"
    },
    {
        "Problem": "{ - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number will be a solution to the equation ( x - 4 ) ( x + 9 ) ( 2 x + 5 ) = 0 ?",
        "Rationale": "x = - 2.5 prob = 1 / 12 answer - a",
        "options": "a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2",
        "correct": "a",
        "annotated_formula": "divide(1, multiply(6, 2))",
        "linear_formula": "multiply(n1,n14)|divide(n5,#0)",
        "category": "general"
    },
    {
        "Problem": "find the value of ( 20 c 18 ) * ( 20 c 20 )",
        "Rationale": "\"20 c 20 = 1 ( 20 c 2 ) * ( 20 c 20 ) = 20 ! * 1 / 18 ! = 20 * 19 * 18 ! / 18 ! = 20 * 19 * 1 = 380 answer : b\"",
        "options": "a ) 400 , b ) 380 , c ) 360 , d ) 350 , e ) 330",
        "correct": "b",
        "annotated_formula": "multiply(add(divide(18, 20), 20), 20)",
        "linear_formula": "divide(n1,n2)|add(n0,#0)|multiply(#1,n2)|",
        "category": "general"
    },
    {
        "Problem": "find the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1 : 2 ?",
        "Rationale": "1 : 2 answer : a",
        "options": "['a ) 1 : 2', 'b ) 2 : 3', 'c ) 2 : 9', 'd ) 2 : 1', 'e ) 2 : 2']",
        "correct": "a",
        "annotated_formula": "divide(1, 2)",
        "linear_formula": "divide(n0,n1)",
        "category": "geometry"
    },
    {
        "Problem": "4 men and 6 women can complete a work in 8 days , while 3 men and 7 women can complete it in 10 days . in how many days will 10 women complete it ?",
        "Rationale": "\"let 1 man ' s 1 day work = x and 1 woman ' s 1 day work = y . then , 4 x + 6 y = 1 / 8 and 3 x + 7 y = 1 / 10 solving these two equations , we get : x = 11 / 400 and y = 1 / 400 1 woman ' s 1 day work = ( 1 / 400 * 10 ) = 1 / 40 . hence , 10 women will complete the work in 40 days . answer : b\"",
        "options": "a ) 21 days , b ) 40 days , c ) 27 days , d ) 18 days , e ) 17 days",
        "correct": "b",
        "annotated_formula": "inverse(multiply(divide(subtract(divide(const_1, 10), multiply(3, divide(subtract(divide(const_1, 8), multiply(divide(6, 7), divide(const_1, 10))), subtract(4, multiply(3, divide(6, 7)))))), 7), 8))",
        "linear_formula": "divide(const_1,n5)|divide(const_1,n2)|divide(n1,n4)|multiply(#2,#0)|multiply(n3,#2)|subtract(#1,#3)|subtract(n0,#4)|divide(#5,#6)|multiply(n3,#7)|subtract(#0,#8)|divide(#9,n4)|multiply(n2,#10)|inverse(#11)|",
        "category": "physics"
    },
    {
        "Problem": "3 men and 7 women can complete a work in 10 days . but 4 men and 6 women need 8 days to complete the same work . in how many days will 10 women complete the same work ?",
        "Rationale": "explanation : work done by 4 men and 6 women in 1 day = 1 / 8 work done by 3 men and 7 women in 1 day = 1 / 10 let 1 man does m work in 1 day and 1 woman does w work in 1 day . the above equations can be written as 4 m + 6 w = 1 / 8 - - - ( 1 ) 3 m + 7 w = 1 / 10 - - - ( 2 ) solving equation ( 1 ) and ( 2 ) , we get m = 11 / 400 and w = 1 / 400 amount of work 10 women can do in a day = 10 \u00d7 ( 1 / 400 ) = 1 / 40 ie , 10 women can complete the work in 40 days answer : option b",
        "options": "a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10",
        "correct": "b",
        "annotated_formula": "inverse(multiply(divide(subtract(divide(const_1, 8), multiply(4, divide(subtract(divide(const_1, 10), multiply(divide(7, 6), divide(const_1, 8))), subtract(3, multiply(4, divide(7, 6)))))), 6), 10))",
        "linear_formula": "divide(const_1,n5)|divide(const_1,n2)|divide(n1,n4)|multiply(#2,#0)|multiply(n3,#2)|subtract(#1,#3)|subtract(n0,#4)|divide(#5,#6)|multiply(n3,#7)|subtract(#0,#8)|divide(#9,n4)|multiply(n2,#10)|inverse(#11)",
        "category": "physics"
    },
    {
        "Problem": "what is the characteristic of the logarithm of 0.0000134 ?",
        "Rationale": "log ( 0.0000134 ) . since there are four zeros between the decimal point and the first significant digit , the characteristic is \u2013 5 . answer : b",
        "options": "a ) 5 , b ) - 5 , c ) 6 , d ) - 6 , e ) 7",
        "correct": "b",
        "annotated_formula": "floor(divide(log(0.0000134), log(const_10)))",
        "linear_formula": "log(n0)|log(const_10)|divide(#0,#1)|floor(#2)",
        "category": "other"
    },
    {
        "Problem": "in the game of dubblefud , red chips , blue chips and green chips are each worth 2 , 4 and 5 points respectively . in a certain selection of chips , the product of the point values of the chips is 16000 . if the number of blue chips in this selection doubles the number of green chips , how many red chips are in the selection ?",
        "Rationale": "this is equivalent to : - 2 x * 4 y * 5 z = 16000 y / 2 = z ( given ) 2 x * 4 y * 5 y / 2 = 16000 2 x * y ^ 2 = 16000 / 10 2 x * y ^ 2 = 1600 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 2 as 2 * 2 * y ^ 2 = 1600 y ^ 2 = 400 y = 20 number of red chips = 2 hence b",
        "options": "a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5",
        "correct": "b",
        "annotated_formula": "divide(multiply(multiply(power(2, 4), power(2, const_3)), power(5, const_3)), multiply(power(const_2, multiply(2, const_3)), power(5, const_3)))",
        "linear_formula": "multiply(n0,const_3)|power(n0,n1)|power(n0,const_3)|power(n2,const_3)|multiply(#1,#2)|power(const_2,#0)|multiply(#4,#3)|multiply(#5,#3)|divide(#6,#7)",
        "category": "general"
    },
    {
        "Problem": "on average , the boys in the class have 20 pencils and the girls have 38 pencils . if the overall class average is 30 pencils , what is the ratio of boys to girls in the class ?",
        "Rationale": "( 38 g + 20 b ) / ( g + b ) = 30 38 g + 20 b = 30 ( g + b ) 8 g = 10 b b / g = 4 / 5 the answer is d .",
        "options": "a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6",
        "correct": "d",
        "annotated_formula": "divide(30, 38)",
        "linear_formula": "divide(n2,n1)",
        "category": "general"
    },
    {
        "Problem": "what is the sum of all the odd numbers between 24 and 50 , inclusive ?",
        "Rationale": "\"to solve this problem , all you have to do is take every even number between 24 and 50 and add them together . so we have 25 + 27 + 29 + 31 + 33 + 35 + 37 + 39 + 41 + 43 + 45 + 47 + 49 , which is 481 . final answer : b\"",
        "options": "a ) 592 , b ) 481 , c ) 330 , d ) 475 , e ) 483",
        "correct": "b",
        "annotated_formula": "add(add(add(add(add(add(const_12, const_2), const_1), add(add(const_12, const_2), add(add(add(add(add(const_2, const_4), const_4), subtract(const_10, const_1)), add(add(const_2, const_4), const_4)), add(const_10, const_2)))), add(add(add(const_12, const_2), const_1), const_1)), 24), add(const_2, const_4))",
        "linear_formula": "add(const_12,const_2)|add(const_2,const_4)|add(const_10,const_2)|subtract(const_10,const_1)|add(#0,const_1)|add(#1,const_4)|add(#5,#3)|add(#4,const_1)|add(#6,#5)|add(#8,#2)|add(#0,#9)|add(#4,#10)|add(#11,#7)|add(n0,#12)|add(#13,#1)|",
        "category": "general"
    },
    {
        "Problem": "if the average of r , b , c , 14 and 15 is 12 . what is the average value of r , b , c and 29",
        "Rationale": "r + b + c + 14 + 15 = 12 * 5 = 60 = > r + b + c = 60 - 29 = 31 r + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d",
        "options": "a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16",
        "correct": "d",
        "annotated_formula": "divide(add(subtract(multiply(add(const_4, const_1), 12), add(14, 15)), 29), const_4)",
        "linear_formula": "add(const_1,const_4)|add(n0,n1)|multiply(n2,#0)|subtract(#2,#1)|add(n3,#3)|divide(#4,const_4)",
        "category": "general"
    },
    {
        "Problem": "what is the angle between the 2 hands of the clock at 8 : 24 pm ?",
        "Rationale": "\"required angle = 240 \u2013 24 \u00d7 ( 11 / 2 ) = 240 \u2013 132 = 108 \u00b0 answer d\"",
        "options": "a ) 100 \u00b0 , b ) 107 \u00b0 , c ) 106 \u00b0 , d ) 108 \u00b0 , e ) none of these",
        "correct": "d",
        "annotated_formula": "subtract(multiply(8, multiply(const_3, const_2)), 2)",
        "linear_formula": "multiply(const_2,const_3)|multiply(n1,#0)|subtract(#1,n0)|",
        "category": "geometry"
    },
    {
        "Problem": "two friends c and d leave point c and point d simultaneously and travel towards point d and point c on the same route at their respective constant speeds . they meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively . how long will d take to cover the entire journey between point d and point c ?",
        "Rationale": "let x per minute be the speed of c and y per minute be the speed of d . after meeting at a point , c travels for 32 mins and d travels for 50 mins . so distance covered by each of them post point of crossing c = 32 x and d = 50 y the distance covered by c and d before they cross each would be distance covered by d and c post crossing respectively . therefore distance covered by d before he meets c = 32 x time taken by d cover 32 x distance = 32 x / y mins therefore total time taken by d = 32 x / y + 50 mins . . . . . . . . . . . . . . . . . i we need to find value of x in terms of y to arrive at final answer . total distance = 32 x + 50 y combined speed of c and d = x + y therefore time taken before c and d meet en - route = ( 32 x + 50 y ) / ( x + y ) time taken by d reach destination after meeting c = 50 mins total travel time for d = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 mins . . . . . . . . . . . . . . . . . . . ii equate i and ii 32 x / y + 50 = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 ( 32 x + 50 y ) / y = ( 82 x + 100 y ) / ( x + y ) 32 x ^ 2 + 50 xy + 32 xy + 50 y ^ 2 = 82 xy + 100 y ^ 2 32 x ^ 2 + 82 xy - 82 xy + 50 y ^ 2 - 100 y ^ 2 = 0 32 x ^ 2 - 50 y ^ 2 = 0 32 x ^ 2 = 50 y ^ 2 16 x ^ 2 = 25 y ^ 2 taking square root . . ( since x and y denote speed , square root ca n ' t be negative ) 4 x = 5 y y = 4 x / 5 . . . . . . . . . . . . iii substitute in i = 32 x / ( 4 x / 5 ) + 50 = 32 x * 5 / 4 x + 50 = 40 + 50 = 90 mins a",
        "options": "a ) 90 , b ) 80 , c ) 75 , d ) 60 , e ) 65",
        "correct": "a",
        "annotated_formula": "add(sqrt(multiply(50, 32)), 50)",
        "linear_formula": "multiply(n0,n1)|sqrt(#0)|add(n1,#1)",
        "category": "physics"
    },
    {
        "Problem": "in a class of 50 students , 20 play baseball , 15 play cricket and 11 play football . 7 play both baseball and cricket , 4 play cricket and football and 5 play baseball and football . if 18 students do not play any of these given sports , how many students play exactly two of these sports ?",
        "Rationale": "notice that 7 play both baseball and cricket does not mean that out of those 7 , some does not play football too . the same for cricket / football and baseball / football . [ color = # ffff 00 ] { total } = { baseball } + { cricket } + { football } - { hc + ch + hf } + { all three } + { neither } for more checkadvanced overlapping sets problems [ / color ] 50 = 20 + 15 + 11 - ( 7 + 4 + 5 ) + { all three } + 18 - - > { all three } = 2 ; those who play only baseball and cricket are 7 - 2 = 5 ; those who play only cricket and football are 4 - 2 = 2 ; those who play only baseball and football are 5 - 2 = 3 ; hence , 5 + 2 + 3 = 10 students play exactly two of these sports . answer : a .",
        "options": "a ) 10 , b ) 46 , c ) 67 , d ) 68 , e ) 446",
        "correct": "a",
        "annotated_formula": "add(subtract(5, subtract(50, add(subtract(add(add(20, 15), 11), add(add(7, 4), 5)), 18))), add(subtract(7, subtract(50, add(subtract(add(add(20, 15), 11), add(add(7, 4), 5)), 18))), subtract(4, subtract(50, add(subtract(add(add(20, 15), 11), add(add(7, 4), 5)), 18)))))",
        "linear_formula": "add(n1,n2)|add(n4,n5)|add(n3,#0)|add(n6,#1)|subtract(#2,#3)|add(n7,#4)|subtract(n0,#5)|subtract(n4,#6)|subtract(n5,#6)|subtract(n6,#6)|add(#7,#8)|add(#10,#9)",
        "category": "other"
    },
    {
        "Problem": "what will be the area of a semi - circle of 14 metres diameter ?",
        "Rationale": "area of semicircle = \u00bd \u03c0 r 2 = \u00bd \u00d7 22 \u2044 7 \u00d7 7 \u00d7 7 = 77 m 2 answer b",
        "options": "['a ) 154 sq metres', 'b ) 77 sq metres', 'c ) 308 sq metres', 'd ) 22 sq metres', 'e ) none of these']",
        "correct": "b",
        "annotated_formula": "divide(circle_area(divide(14, const_2)), const_2)",
        "linear_formula": "divide(n0,const_2)|circle_area(#0)|divide(#1,const_2)",
        "category": "geometry"
    },
    {
        "Problem": "it takes ten minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video , rounded to the nearest hundredth ?",
        "Rationale": "\"the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 10 ) = 1 / 600 of the video per second . the combined rate is 1 / 15 + 1 / 600 = 41 / 600 of the video per second . the time required to load the video is 600 / 41 = 14.63 seconds . the answer is d .\"",
        "options": "a ) 13.42 , b ) 13.86 , c ) 14.25 , d ) 14.63 , e ) 14.88",
        "correct": "d",
        "annotated_formula": "subtract(inverse(add(inverse(multiply(add(add(const_2, const_3), const_4), const_60)), inverse(add(multiply(const_3, const_4), const_3)))), divide(subtract(multiply(multiply(const_4, const_4), const_3), const_2), multiply(const_100, const_100)))",
        "linear_formula": "add(const_2,const_3)|multiply(const_3,const_4)|multiply(const_4,const_4)|multiply(const_100,const_100)|add(#0,const_4)|add(#1,const_3)|multiply(#2,const_3)|inverse(#5)|multiply(#4,const_60)|subtract(#6,const_2)|divide(#9,#3)|inverse(#8)|add(#11,#7)|inverse(#12)|subtract(#13,#10)|",
        "category": "physics"
    },
    {
        "Problem": "a certain scholarship committee awarded scholarships in the amounts of $ 1250 , $ 2500 and $ 4000 . the committee awarded twice as many $ 2500 scholarships as $ 4000 and it awarded 3 times as many $ 1250 scholarships as $ 2500 scholarships . if the total of $ 75000 was awarded in $ 1250 scholarships , how many $ 4000 scholarships were awarded ?",
        "Rationale": "since the starting point is given as the $ 4000 scholarship , assume $ 4000 scholarships to be x by the given information , $ 2500 scholarships = 2 x and $ 1250 scholarships = 6 x gievn : total $ 1250 scholarships = $ 75000 6 x * 1250 = 75000 solve for x = 10 option d",
        "options": "a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 15",
        "correct": "d",
        "annotated_formula": "divide(divide(75000, 1250), multiply(const_2, 3))",
        "linear_formula": "divide(n8,n0)|multiply(n5,const_2)|divide(#0,#1)",
        "category": "general"
    },
    {
        "Problem": "1 = 5,2 = 25,3 = 253,4 = 150,5 = 225 then 150 = ?",
        "Rationale": "\"1 = 5,2 = 25,3 = 253,4 = 150,5 = 225 then 150 = ? 150 = 4 check the fourth eqn . answer : c\"",
        "options": "a ) 1 , b ) 255 , c ) 4 , d ) 445 , e ) 235",
        "correct": "c",
        "annotated_formula": "divide(subtract(subtract(225, multiply(multiply(add(const_4, const_2), add(const_4, const_2)), const_10)), 1), const_2)",
        "linear_formula": "add(const_2,const_4)|multiply(#0,#0)|multiply(#1,const_10)|subtract(n5,#2)|subtract(#3,n0)|divide(#4,const_2)|",
        "category": "general"
    },
    {
        "Problem": "if pintu is coded as 79523 in a certain code language , how would you code mumbo in the same language ?",
        "Rationale": "\"1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . mumbo is 43426 . . . answer : a\"",
        "options": "a ) 43426 , b ) 14236 , c ) 13436 , d ) 14263 , e ) 15263",
        "correct": "a",
        "annotated_formula": "divide(79523, add(const_3, const_3))",
        "linear_formula": "add(const_3,const_3)|divide(n0,#0)|",
        "category": "general"
    },
    {
        "Problem": "paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to paul and 40 % of his income to quentin , paul ' s new income would be what fraction of quentin ' s new income ?",
        "Rationale": "\"make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get p = 12 and q 8.8 so 12 / 8.8 = 3 / 2.2 ans : d\"",
        "options": "a ) 11 / 12 , b ) 13 / 17 , c ) 13 / 19 , d ) 15 / 11 , e ) 11 / 19",
        "correct": "d",
        "annotated_formula": "divide(add(multiply(40, const_100), multiply(40, subtract(const_100, 20))), add(multiply(40, const_100), multiply(add(40, 20), 40)))",
        "linear_formula": "add(n0,n1)|multiply(n4,const_100)|multiply(n0,const_100)|subtract(const_100,n1)|multiply(n4,#3)|multiply(n4,#0)|add(#1,#4)|add(#2,#5)|divide(#6,#7)|",
        "category": "general"
    },
    {
        "Problem": "if 6 - 12 / x = 7 - 7 / x , then x =",
        "Rationale": "\"we ' re given the equation 6 - 12 / x = 7 - 7 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we need to multiply both sides of the equation by x , giving us . . . 6 x - 12 x / x = 7 x - 7 x / x we can then eliminate that denominator , which gives us . . . . 6 x - 12 = 7 x - 7 - 5 = x a\"",
        "options": "a ) - 5 , b ) 19 , c ) - 7 / 5 , d ) 1 , e ) 5 / 6",
        "correct": "a",
        "annotated_formula": "divide(add(7, 12), subtract(6, 7))",
        "linear_formula": "add(n3,n1)|subtract(n0,n2)|divide(#0,#1)|",
        "category": "general"
    },
    {
        "Problem": "| x + 3 | \u2013 | 4 - x | = | 8 + x | how many s solutions will this equation have ?",
        "Rationale": "\"| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a\"",
        "options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4",
        "correct": "a",
        "annotated_formula": "divide(multiply(add(4, 3), const_2), 8)",
        "linear_formula": "add(n0,n1)|multiply(#0,const_2)|divide(#1,n2)|",
        "category": "general"
    },
    {
        "Problem": "49 \u00e3 \u2014 49 \u00e3 \u2014 49 = 7 ^ ?",
        "Rationale": "\"49 \u00e3 \u2014 49 \u00e3 \u2014 49 = 7 ? or , 7 ( 2 ) \u00e3 \u2014 7 ( 2 ) \u00e3 \u2014 7 ( 2 ) = 7 ? or 7 ( 6 ) = 7 ? or , ? = 6 answer d\"",
        "options": "a ) 4 , b ) 7 , c ) 8 , d ) 6 , e ) none of these",
        "correct": "d",
        "annotated_formula": "add(subtract(power(49, const_2), 49), subtract(power(49, const_2), 49))",
        "linear_formula": "power(n0,const_2)|power(n2,const_2)|subtract(#0,n0)|subtract(#1,n2)|add(#2,#3)|",
        "category": "general"
    },
    {
        "Problem": "a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 1 , - 4 ) . what is the smallest possible area of that circle ?",
        "Rationale": "\"the distance between the two points is sqrt ( 20 ) . radius = sqrt ( 20 ) / 2 area = pi * ( sqrt ( 20 ) / 2 ) ^ 2 d . 5 \u03c0\"",
        "options": "a ) 13 \u03c0 , b ) 26 \u03c0 , c ) 262 \u221a \u03c0 , d ) 5 \u03c0 , e ) 64 \u03c0",
        "correct": "d",
        "annotated_formula": "square_area(divide(sqrt(add(multiply(add(3, 1), add(3, 1)), multiply(add(2, 4), add(2, 4)))), 2))",
        "linear_formula": "add(n0,n2)|add(n1,n3)|multiply(#0,#0)|multiply(#1,#1)|add(#2,#3)|sqrt(#4)|divide(#5,n1)|square_area(#6)|",
        "category": "geometry"
    },
    {
        "Problem": "the distance between two cities a and b is 330 km . a train starts from a at 8 a . m . and travels 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 ?",
        "Rationale": "\"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 ] = 330 60 x + 75 ( x - 1 ) = 330 = > x = 3 so , they meet at ( 8 + 3 ) i . e . , 11 a . m . answer : c\"",
        "options": "a ) 12 , b ) 10 , c ) 11 , d ) 09 , e ) 03",
        "correct": "c",
        "annotated_formula": "add(divide(add(330, 75), add(60, 75)), 8)",
        "linear_formula": "add(n0,n4)|add(n2,n4)|divide(#0,#1)|add(n1,#2)|",
        "category": "physics"
    },
    {
        "Problem": "there are two numbers . if 10 % of the first number is added to the second number , then the second number increases to its 6 - fifth . what is the ratio of the first number to the second number ?",
        "Rationale": "let the two numbers be x and y . ( 1 / 10 ) * x + y = ( 6 / 5 ) * y ( 1 / 10 ) * x = ( 1 / 5 ) * y x / y = 2 / 1 = 2 / 1 the answer is e .",
        "options": "a ) 3 : 2 , b ) 4 : 3 , c ) 8 : 7 , d ) 5 : 8 , e ) 2 : 1",
        "correct": "e",
        "annotated_formula": "divide(divide(const_1, divide(10, const_2)), divide(const_1, 10))",
        "linear_formula": "divide(n0,const_2)|divide(const_1,n0)|divide(const_1,#0)|divide(#2,#1)",
        "category": "general"
    },
    {
        "Problem": "what is the average of xx , 2 x 2 x , and 66 ?",
        "Rationale": "\"by the definition of an average , we get : x + 2 x + 63 = 3 x + 63 x + 2 x + 63 = 3 x + 63 = 3 ( x + 2 ) 3 = x + 2 . = 3 ( x + 2 ) 3 = x + 2 . hence , the answer is x + 2 x + 2 or option c\"",
        "options": "a ) x + 2 , b ) x + 2 x , c ) x + 2 x + 2 , d ) 2 x + 2 , e ) x + 2 x - 2",
        "correct": "c",
        "annotated_formula": "multiply(divide(divide(multiply(2, add(2, const_1)), const_2), 2), 2)",
        "linear_formula": "add(n0,const_1)|multiply(n0,#0)|divide(#1,const_2)|divide(#2,n0)|multiply(n1,#3)|",
        "category": "general"
    },
    {
        "Problem": "10 men can complete a work in 7 days . but 10 women need 14 days to complete the same work . how many days will 5 men and 10 women need to complete the work ?",
        "Rationale": "work done by 10 men in 1 day = 1 / 7 work done by 1 man in 1 day = ( 1 / 7 ) / 10 = 1 / 70 work done by 10 women in 1 day = 1 / 14 work done by 1 woman in 1 day = 1 / 140 work done by 5 men and 10 women in 1 day = 5 \u00d7 ( 1 / 70 ) + 10 \u00d7 ( 1 / 140 ) = 5 / 70 + 10 / 140 = 1 / 7 = 5 men and 10 women can complete the work in 7 days answer : option c",
        "options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 10",
        "correct": "c",
        "annotated_formula": "inverse(add(multiply(10, inverse(multiply(14, 10))), multiply(5, divide(inverse(7), 10))))",
        "linear_formula": "inverse(n1)|multiply(n0,n3)|divide(#0,n0)|inverse(#1)|multiply(n0,#3)|multiply(n4,#2)|add(#4,#5)|inverse(#6)",
        "category": "physics"
    },
    {
        "Problem": "all numbers from 1 to 200 ( in decimal system ) are written in base 6 and base 7 systems . how many of the numbers will have a non - zero units digit in both base 6 and base 7 notations ?",
        "Rationale": "detailed solution if a number written in base 6 ends with a zero , it should be a multiple of 6 . in other words , the question wants us to find all numbers from 1 to 200 that are not multiples of 6 or 7 . there are 33 multiples of 6 less than 201 . there are 28 multiples of 7 less than 201 . there are 4 multiples of 6 & 7 ( or multiple of 42 ) from 1 to 200 . so , total multiples of 6 or 7 less than 201 = 33 + 28 - 4 = 57 . number of numbers with non - zero units digit = 200 - 57 = 143 . correct answer : a",
        "options": "['a ) 143', 'b ) 200', 'c ) 157', 'd ) 122', 'e ) 132']",
        "correct": "a",
        "annotated_formula": "subtract(200, subtract(add(divide(200, 6), divide(200, 7)), divide(200, multiply(6, 7))))",
        "linear_formula": "divide(n1,n2)|divide(n1,n3)|multiply(n2,n3)|add(#0,#1)|divide(n1,#2)|subtract(#3,#4)|subtract(n1,#5)",
        "category": "other"
    },
    {
        "Problem": "an urn contains 6 red , 5 blue and 2 green marbles . if 2 marbles are picked at random , what is the probability that both are red ?",
        "Rationale": "option ( b ) is correct p ( both are red ) , 6 c 2 / 13 c 2 = 5 / 26 answer b",
        "options": "a ) 6 / 13 , b ) 5 / 26 , c ) 6 / 26 , d ) 9 / 26 , e ) 10 / 27",
        "correct": "b",
        "annotated_formula": "divide(divide(multiply(6, 5), const_2), divide(multiply(add(add(6, 5), 2), subtract(add(add(6, 5), 2), const_1)), const_2))",
        "linear_formula": "add(n0,n1)|multiply(n0,n1)|add(n2,#0)|divide(#1,const_2)|subtract(#2,const_1)|multiply(#2,#4)|divide(#5,const_2)|divide(#3,#6)",
        "category": "other"
    },
    {
        "Problem": "solve below question 2 x + 1 = - 15",
        "Rationale": "\"2 x + 1 = - 15 x = - 8 a\"",
        "options": "a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7",
        "correct": "a",
        "annotated_formula": "divide(negate(add(15, 1)), 2)",
        "linear_formula": "add(n1,n2)|negate(#0)|divide(#1,n0)|",
        "category": "general"
    },
    {
        "Problem": "q is as much younger than r as he is older than t . if the sum of the ages of r and t is 50 years , what is definitely the difference between r and q ' s age ?",
        "Rationale": "explanation : given r \u2013 q = q \u2013 t and r + t = 50 which gives q = 25 as the difference between r & q and q & t is same so answer is 25 years answer : c",
        "options": "a ) 23 , b ) 28 , c ) 25 , d ) 19 , e ) 11",
        "correct": "c",
        "annotated_formula": "divide(50, const_2)",
        "linear_formula": "divide(n0,const_2)",
        "category": "general"
    },
    {
        "Problem": "in objective test a correct ans score 4 marks and on a wrong ans 2 marks are - - - . a student score 480 marks from 150 question . how many ans were correct ?",
        "Rationale": "let x be the correct answer and y be the wrong answer so the total number of questions is ( x + y ) = 150 = > 4 x - 2 y = 480 = > 6 x = 780 hence x = 130 answer : b",
        "options": "a ) 120 , b ) 130 , c ) 110 , d ) 150 , e ) 180",
        "correct": "b",
        "annotated_formula": "divide(add(480, multiply(150, 2)), add(4, 2))",
        "linear_formula": "add(n0,n1)|multiply(n1,n3)|add(n2,#1)|divide(#2,#0)",
        "category": "general"
    },
    {
        "Problem": "a , b and c invests rs . 6000 , rs . 5000 and rs . 3000 in a business . after one year c removed his money ; a and b continued the business for two more year . if the net profit after 3 years be rs . 4206 , then c ' s share in the profit is ?",
        "Rationale": "\"6 * 36 : 5 * 36 : 3 * 12 6 : 5 : 1 1 / 12 * 4206 = 350.50 answer : d\"",
        "options": "a ) 276 , b ) 289 , c ) 400 , d ) 350.5 , e ) 300",
        "correct": "d",
        "annotated_formula": "multiply(divide(6000, add(6000, add(multiply(5000, 3), multiply(3000, 3)))), 6000)",
        "linear_formula": "multiply(n1,n3)|multiply(n2,n3)|add(#0,#1)|add(n0,#2)|divide(n0,#3)|multiply(n0,#4)|",
        "category": "gain"
    },
    {
        "Problem": "the population of a town increased from 50000 to 80000 in a decade . the average percent increase of population per year is :",
        "Rationale": "solution increase in 10 year = ( 80000 - 50000 ) = 30000 . increase % = ( 30000 / 50000 x 100 ) % = 60 % \u00e2 \u02c6 \u00b4 required average = ( 60 / 10 ) % = 6 % answer c",
        "options": "a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none of these",
        "correct": "c",
        "annotated_formula": "divide(multiply(divide(subtract(80000, 50000), 50000), const_100), const_10)",
        "linear_formula": "subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)|divide(#2,const_10)",
        "category": "general"
    },
    {
        "Problem": "what is the probability that when a hand o f 6 cards is drawn from a well shuffled deck of 52 cards , it contains 2 queen ?",
        "Rationale": "ncr = n ! / ( n - r ) ! r ! total number of possible hands = 52 c 6 52 c 6 = ( 52 ! ) / ( ( 52 - 6 ) ! \u00d7 6 ! ) 52 c 6 = 61075560 . number of hands with 2 queen and 4 non - queen cards = 4 c 2 \u00d7 48 c 4 4 c 2 = ( 4 ! ) / ( 2 ! \u00d7 2 ! ) = 6 . 48 c 4 = ( 48 ! ) / ( 44 ! \u00d7 4 ! ) = 3 \u00d7 47 \u00d7 46 \u00d7 45 = 291870 ( other 2 cards must be chosen from the rest 48 cards ) p ( 2 queen ) = ( 4 c 2 \u00d7 48 c 4 ) / 52 c 6 = 29187 / 1017926 c",
        "options": "a ) 1 / 23445 , b ) 113 / 22434 , c ) 29187 by 1017926 , d ) 1017926 / 29187 , e ) none of these",
        "correct": "c",
        "annotated_formula": "divide(multiply(choose(const_4, 2), choose(subtract(52, const_4), subtract(6, 2))), choose(52, 6))",
        "linear_formula": "choose(const_4,n2)|choose(n1,n0)|subtract(n1,const_4)|subtract(n0,n2)|choose(#2,#3)|multiply(#0,#4)|divide(#5,#1)",
        "category": "probability"
    },
    {
        "Problem": "three cubes of iron whose edges are 6 cm , 8 cm and 10 cm respectively are melted and formed into a single cube . the edge of the new cube formed is",
        "Rationale": "sol . volume of the new cube = ( 63 + 83 + 103 ) cm 3 = 1728 cm 3 . let the edge of the new cube be a cm . \u2234 a 3 = 1728 \u21d2 a = 12 . answer b",
        "options": "['a ) 10 cm', 'b ) 12 cm', 'c ) 16 cm', 'd ) 18 cm', 'e ) none']",
        "correct": "b",
        "annotated_formula": "cube_edge_by_volume(add(volume_cube(10), add(volume_cube(6), volume_cube(8))))",
        "linear_formula": "volume_cube(n0)|volume_cube(n1)|volume_cube(n2)|add(#0,#1)|add(#3,#2)|cube_edge_by_volume(#4)",
        "category": "physics"
    },
    {
        "Problem": "if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ?",
        "Rationale": "( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) has one appearance of 3 ( in the 6 ) and no appearances of 5 . thus n must include at least 3 ^ 2 * 5 ^ 2 = 9 * 25 = 225 the answer is e .",
        "options": "a ) 75 , b ) 125 , c ) 145 , d ) 175 , e ) 225",
        "correct": "e",
        "annotated_formula": "add(add(add(add(add(multiply(multiply(5, 7), 2), multiply(multiply(5, 7), 2)), multiply(multiply(5, 7), 2)), 7), const_4), const_4)",
        "linear_formula": "multiply(n0,n7)|multiply(n1,#0)|add(#1,#1)|add(#2,#1)|add(n7,#3)|add(#4,const_4)|add(#5,const_4)",
        "category": "other"
    },
    {
        "Problem": "if p ( a ) = 0.4 , p ( b ) = 0.6 and p ( a \u222a b ) = 0.8 . what is the value of p ( a \u2229 b ' ) = ?",
        "Rationale": "\"solution : p ( a \u222a b ) = p ( a ) + p ( b ) - p ( a \u2229 b ' ) = > 0.8 = 0.4 - p ( a \u2229 b ) = > p ( a \u2229 b ) = 0.2 p ( a \u2229 b ' ) = p ( a ) - p ( a \u2229 b ) = 0.4 - 0.2 = 0.2 answer b\"",
        "options": "a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) none",
        "correct": "b",
        "annotated_formula": "multiply(multiply(0.4, 0.8), const_10)",
        "linear_formula": "multiply(n0,n2)|multiply(#0,const_10)|",
        "category": "general"
    },
    {
        "Problem": "evaluate : 980 x 436 + 980 x 764",
        "Rationale": "\"980 x 436 + 980 x 764 = 986 x ( 436 + 664 ) = 986 x 1200 = 117600 . answer is a .\"",
        "options": "a ) 1176000 , b ) 968000 , c ) 978000 , d ) 117000 , e ) none of them",
        "correct": "a",
        "annotated_formula": "subtract(980, multiply(multiply(436, 980), 764))",
        "linear_formula": "multiply(n1,n2)|multiply(n3,#0)|subtract(n0,#1)|",
        "category": "general"
    },
    {
        "Problem": "how many terminating zeroes r does 200 ! have ?",
        "Rationale": "you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c",
        "options": "a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64",
        "correct": "c",
        "annotated_formula": "add(divide(200, add(const_4, const_1)), divide(200, multiply(add(const_4, const_1), add(const_4, const_1))))",
        "linear_formula": "add(const_1,const_4)|divide(n0,#0)|multiply(#0,#0)|divide(n0,#2)|add(#1,#3)|",
        "category": "other"
    },
    {
        "Problem": "a girl walking at the rate of 9 km per hour crosses a square field diagonally in 12 seconds . the area of the field is :",
        "Rationale": "distance covered in ( 9 \u00d7 1000 ) / ( 3600 ) \u00d7 12 = 30 m diagonal of squarre field = 30 m . area of square field = 30 ( power ) 2 / 2 = 900 / 2 = 450 sq . m answer is c .",
        "options": "['a ) 430 sq . m', 'b ) 425 sq . m', 'c ) 450 sq . m', 'd ) 475 sq . m', 'e ) 350 sq . m']",
        "correct": "c",
        "annotated_formula": "divide(multiply(multiply(12, divide(multiply(9, const_1000), multiply(const_360, const_10))), multiply(12, divide(multiply(9, const_1000), multiply(const_360, const_10)))), const_2)",
        "linear_formula": "multiply(n0,const_1000)|multiply(const_10,const_360)|divide(#0,#1)|multiply(n1,#2)|multiply(#3,#3)|divide(#4,const_2)",
        "category": "geometry"
    },
    {
        "Problem": "the price of an article is cut by 10 % . to restore it to the former value . the new price must be increased by ?",
        "Rationale": "answer let original price = rs . 100 . then , new price = rs . 90 . \u2234 increased on rs . 90 = rs . 10 required increase % = ( 10 x 100 ) / 90 % = 111 / 9 % correct option : c",
        "options": "a ) 10 % , b ) 9 1 / 11 , c ) 11 1 / 9 , d ) 11 % , e ) none of these",
        "correct": "c",
        "annotated_formula": "add(subtract(const_100, subtract(const_100, 10)), const_2)",
        "linear_formula": "subtract(const_100,n0)|subtract(const_100,#0)|add(#1,const_2)",
        "category": "gain"
    },
    {
        "Problem": "in a certain group of 10 developers , 4 developers code only in python and the rest program in either ruby on rails or php - but not both . if a developer organization is to choose a 3 - member team , which must have at least 1 developer who codes in python , how many different programming teams can be chosen ?",
        "Rationale": "two ways . . . 1 ) total ways = 10 c 3 = 10 ! / 7 ! 3 ! = 120 . . ways without python developer = 6 c 3 = 6 ! / 3 ! 3 ! = 20 . . ways of at least one python developer = 120 - 20 = 100 . . 2 ) ways of selecting only one = 4 * 6 c 2 = 4 * 15 = 60 . . ways of selecting only two = 4 c 2 * 6 c 1 = 6 * 6 = 36 . . ways of selecting all three = 4 c 3 = 4 = 4 . . total = 60 + 36 + 4 = 100 . . . answer : a",
        "options": "a ) 100 , b ) 40 , c ) 66 , d ) 80 , e ) 75",
        "correct": "a",
        "annotated_formula": "subtract(divide(factorial(10), multiply(factorial(subtract(10, 3)), factorial(3))), divide(factorial(subtract(10, 4)), multiply(factorial(3), factorial(3))))",
        "linear_formula": "factorial(n0)|factorial(n2)|subtract(n0,n2)|subtract(n0,n1)|factorial(#2)|factorial(#3)|multiply(#1,#1)|divide(#5,#6)|multiply(#4,#1)|divide(#0,#8)|subtract(#9,#7)",
        "category": "other"
    },
    {
        "Problem": "a number is mistakenly divided by 5 instead of being multiplied by 5 . find the percentage change in the result due t this mistake .",
        "Rationale": "lets take a number 20 20 / 5 = 4 20 * 5 = 100 diff = 100 - 4 = 96 % answer : a",
        "options": "a ) 96 % , b ) 95 % , c ) 2400 % , d ) 200 % , e ) 400 %",
        "correct": "a",
        "annotated_formula": "multiply(subtract(multiply(5, 5), const_1), divide(const_100, multiply(5, 5)))",
        "linear_formula": "multiply(n0,n0)|divide(const_100,#0)|subtract(#0,const_1)|multiply(#1,#2)",
        "category": "general"
    },
    {
        "Problem": "the first , second and third terms of the proportion are 56 , 16 , 49 . find the fourth term .",
        "Rationale": "explanation : let the fourth term be x . thus 56 , 16 , 49 , x are in proportion . product of extreme terms = 56 x product of mean terms = 16 x 49 since , the numbers make up a proportion therefore , 56 x = 16 49 or , x = ( 16 49 ) / 56 or , x = 14 therefore , the fourth term of the proportion is 14 . answer : b",
        "options": "a ) 10 , b ) 14 , c ) 40 , d ) 50 , e ) 60",
        "correct": "b",
        "annotated_formula": "divide(multiply(49, 16), 56)",
        "linear_formula": "multiply(n1,n2)|divide(#0,n0)",
        "category": "physics"
    },
    {
        "Problem": "determine the value of 3 * 27 / 31 + 81 / 93",
        "Rationale": "solution : both fractions should be reduced before performing arithmetic operations . we get 3 * 27 / 31 + 3.27 / 3.31 = 3 * 27 / 31 + 27 / 31 = 4 * 27 / 31 = 151 / 31 answer d",
        "options": "a ) 0 , b ) 156 / 31 , c ) 123 / 31 , d ) 151 / 31 , e ) none",
        "correct": "d",
        "annotated_formula": "divide(add(subtract(add(81, multiply(27, 3)), subtract(93, 81)), const_1), 31)",
        "linear_formula": "multiply(n0,n1)|subtract(n4,n3)|add(n3,#0)|subtract(#2,#1)|add(#3,const_1)|divide(#4,n2)",
        "category": "general"
    },
    {
        "Problem": "in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds e in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?",
        "Rationale": "\"1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out e : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b\"",
        "options": "a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %",
        "correct": "b",
        "annotated_formula": "add(const_10, divide(add(25, 25), const_2))",
        "linear_formula": "add(n2,n2)|divide(#0,const_2)|add(#1,const_10)|",
        "category": "general"
    },
    {
        "Problem": "what is the smallest integer t greater than 1 that leaves a remainder of 1 when divided by any of the integers 6 , 8 , and 10 ?",
        "Rationale": "or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder t as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 6,8 and 10 is 121 . c",
        "options": "a ) 21 , b ) 41 , c ) t = 121 , d ) 241 , e ) 481",
        "correct": "c",
        "annotated_formula": "add(lcm(lcm(6, 8), 10), 1)",
        "linear_formula": "lcm(n2,n3)|lcm(n4,#0)|add(n0,#1)",
        "category": "general"
    },
    {
        "Problem": "in bangalore there is a well known science institute . during a visit i asked two of the men to tell me their ages . one replied , ' one of our ages subtracted from the other ' s equal 30 . ' then the other man spoke . ' our ages multiplied together equal 1624 . ' what were their ages ?",
        "Rationale": "e their ages were respectively 58 and 28",
        "options": "a ) 60 and 23 , b ) 66 and 25 , c ) 29 and 56 , d ) 71 and 43 , e ) 58 and 28",
        "correct": "e",
        "annotated_formula": "divide(divide(multiply(1624, 30), const_4), const_2)",
        "linear_formula": "multiply(n0,n1)|divide(#0,const_4)|divide(#1,const_2)",
        "category": "general"
    },
    {
        "Problem": "a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what w percent of the list price is the lowest possible sale price ?",
        "Rationale": "\"let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which w is 40 % of 80 hence , d is the answer\"",
        "options": "a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50",
        "correct": "d",
        "annotated_formula": "divide(80, const_2)",
        "linear_formula": "divide(n3,const_2)|",
        "category": "general"
    },
    {
        "Problem": "5 years ago , the average age of a , b , c and d was 45 years . with e joining them now , the average of all the 5 is 50 years . the age of e is ?",
        "Rationale": "solution 5 years ago average age of a , b , c , d = 45 years = > 5 years ago total age of a , b , c , d = 45 x 4 = 180 years = > total present age of a , b , c , d = 180 + 5 x 4 = 200 years if e ' s present age is x years = 200 + x / 5 = 50 x = 50 years . answer a",
        "options": "a ) 50 , b ) 47 , c ) 48 , d ) 49 , e ) 46",
        "correct": "a",
        "annotated_formula": "subtract(multiply(50, 5), add(multiply(45, multiply(const_2, const_2)), multiply(5, const_4)))",
        "linear_formula": "multiply(n0,n3)|multiply(const_2,const_2)|multiply(n0,const_4)|multiply(n1,#1)|add(#3,#2)|subtract(#0,#4)",
        "category": "general"
    },
    {
        "Problem": "there are 15 slate rocks , 20 pumice rocks , and 10 granite rocks randomly distributed in a certain field . if 2 rocks are to be chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?",
        "Rationale": "\"total no of rocks = 45 probability of choosing 1 st slate rock = 15 / 45 probability of choosing 2 nd slate rock = 14 / 44 ( without replacement ) so combined probability = 15 / 45 * 14 / 44 = 7 / 66 so , answer d .\"",
        "options": "a ) 1 / 3 , b ) 7 / 22 , c ) 1 / 9 , d ) 7 / 66 , e ) 2 / 45",
        "correct": "d",
        "annotated_formula": "multiply(divide(15, add(add(15, 20), 10)), divide(subtract(15, const_1), subtract(add(add(15, 20), 10), const_1)))",
        "linear_formula": "add(n0,n1)|subtract(n0,const_1)|add(n2,#0)|divide(n0,#2)|subtract(#2,const_1)|divide(#1,#4)|multiply(#3,#5)|",
        "category": "other"
    },
    {
        "Problem": "a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously then after how much time will the cistern get filled ?",
        "Rationale": "\"net part filled in 1 hour 1 / 4 - 1 / 9 = 5 / 36 the cistern will be filled in 36 / 5 hr = 7.2 hr answer is d\"",
        "options": "a ) 6 hr , b ) 5.6 hr , c ) 9.5 hr , d ) 7.2 hr , e ) 4 hr",
        "correct": "d",
        "annotated_formula": "divide(const_1, subtract(divide(const_1, 4), divide(const_1, 9)))",
        "linear_formula": "divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)|",
        "category": "physics"
    },
    {
        "Problem": "7 carpet - weavers can weave 7 carpets in 7 days . at the same rate , how many carpets would be woven by 14 carpet - weavers in 14 days ?",
        "Rationale": "explanation : solution : let the required number of carpets be x . more weavers , more carpets ( direct proportion ) more days , more carpets ( direct proportion ) weavers 7 : 14 } : : 7 : x days 7 : 14 . ' . 7 * 7 * x = 14 * 14 * 7 < = > x = 14 * 14 * 7 / 7 * 7 = 28 . answer : b",
        "options": "a ) 14 , b ) 28 , c ) 21 , d ) 35 , e ) none of these",
        "correct": "b",
        "annotated_formula": "add(14, add(7, 7))",
        "linear_formula": "add(n0,n0)|add(n3,#0)",
        "category": "gain"
    },
    {
        "Problem": "two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every fourth , starting with the fourth , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ?",
        "Rationale": "widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 96 - 4 ) / 4 ) + 1 = 23 + 1 = 24 widgets inspected by both : ( ( 96 / 12 ) + 1 = 9 total : 19 + 24 - 9 = 34 hence , widgets not inspected : 98 - 34 = 64 option d",
        "options": "a ) 66 , b ) 68 , c ) 70 , d ) 64 , e ) 72",
        "correct": "d",
        "annotated_formula": "subtract(98, subtract(add(floor(divide(98, add(const_4, const_1))), floor(divide(98, const_4))), floor(divide(98, add(const_10, add(const_4, const_1))))))",
        "linear_formula": "add(const_1,const_4)|divide(n0,const_4)|add(#0,const_10)|divide(n0,#0)|floor(#1)|divide(n0,#2)|floor(#3)|add(#6,#4)|floor(#5)|subtract(#7,#8)|subtract(n0,#9)",
        "category": "other"
    },
    {
        "Problem": "the speed of a car increases by 2 kms after every one hour . if the distance travelled in the first one hour was 35 kms , what was the total distance travelled in 12 hours ?",
        "Rationale": "\"total distance travelled in 12 hours = ( 35 + 37 + 39 + . . . upto 12 terms ) . this is an a . p . with first term , a = 35 , number of terms , n = 12 , common difference d = 2 required distance = 12 / 2 ( 2 * 35 + ( 12 - 1 ) * 2 ) = 6 ( 70 + 22 ) = 552 km . correct option : c\"",
        "options": "a ) 456 kms , b ) 482 kms , c ) 552 kms , d ) 556 kms , e ) none of these",
        "correct": "c",
        "annotated_formula": "multiply(add(multiply(2, 35), multiply(subtract(12, const_1), 2)), divide(12, 2))",
        "linear_formula": "divide(n2,n0)|multiply(n0,n1)|subtract(n2,const_1)|multiply(n0,#2)|add(#1,#3)|multiply(#4,#0)|",
        "category": "physics"
    },
    {
        "Problem": "evaluate : 11110 + 24 * 3 * 10 = ?",
        "Rationale": "\"according to order of operations , 24 ? 3 ? 10 ( division and multiplication ) is done first from left to right 24 / 2 = 8 * 10 = 80 hence 11110 + 24 * 3 * 10 = 11110 + 80 = 11190 correct answer c\"",
        "options": "a ) 90111 , b ) 52631 , c ) 11190 , d ) 65321 , e ) 11133",
        "correct": "c",
        "annotated_formula": "subtract(11110, multiply(multiply(24, 3), 10))",
        "linear_formula": "multiply(n1,n2)|multiply(n3,#0)|subtract(n0,#1)|",
        "category": "general"
    },
    {
        "Problem": "if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of $ 8400 ?",
        "Rationale": "\"required difference = [ 3 1 / 2 % of $ 8400 ] \u2013 [ 3 1 / 3 % of $ 8400 ] = [ ( 7 / 20 ) - ( 10 / 3 ) ] % of $ 8400 = 1 / 6 % of $ 8400 = $ [ ( 1 / 6 ) * ( 1 / 100 ) * 8400 ] = $ 14 . answer a .\"",
        "options": "a ) 14 , b ) 24 , c ) 34 , d ) 12 , e ) 13",
        "correct": "a",
        "annotated_formula": "divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 8400), const_100)",
        "linear_formula": "divide(n1,n2)|divide(n1,n0)|add(n0,#0)|add(n0,#1)|subtract(#2,#3)|multiply(n6,#4)|divide(#5,const_100)|",
        "category": "general"
    },
    {
        "Problem": "a boy goes to his school from his house at a speed of 3 km / hr and return at a speed of 2 km / hr . if he takes 5 hours in going and coming , the distance between his house and school is ?",
        "Rationale": "average speed = 2 * 3 * 2 / 3 + 2 = 12 / 5 km / hr distance traveled = 12 / 5 * 5 = 12 km distance between house and school = 12 / 2 = 6 km answer is b",
        "options": "a ) 5 km , b ) 6 km , c ) 10 km , d ) 12 km , e ) 8 km",
        "correct": "b",
        "annotated_formula": "multiply(divide(5, add(divide(3, 2), const_1)), 3)",
        "linear_formula": "divide(n0,n1)|add(#0,const_1)|divide(n2,#1)|multiply(n0,#2)",
        "category": "physics"
    },
    {
        "Problem": "cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost q is what percent of the original cost ?",
        "Rationale": "\"original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600\"",
        "options": "a ) q = 200 , b ) q = 600 , c ) q = 800 , d ) q = 1600 , e ) q = 50",
        "correct": "d",
        "annotated_formula": "multiply(power(const_2, 4), const_100)",
        "linear_formula": "power(const_2,n0)|multiply(#0,const_100)|",
        "category": "general"
    },
    {
        "Problem": "if the complement of a certain angle is 7 times the measure of that certain angle , then what is the measure of that certain angle ?",
        "Rationale": "thecomplementof angle a is the angle which , when added to angle a , gives 90 degrees . the two acute angles of a right triangle are complements , for example . the original angle is x , so the complement is 7 x , and together , these add up to 90 degrees . x + 7 x = 90 8 x = 90 x = 11.25 \u00b0 answer = ( e )",
        "options": "a ) 45 \u00b0 , b ) 30 \u00b0 , c ) 22.5 \u00b0 , d ) 18 \u00b0 , e ) 11.25 \u00b0",
        "correct": "e",
        "annotated_formula": "divide(subtract(const_100, const_10), add(7, const_1))",
        "linear_formula": "add(n0,const_1)|subtract(const_100,const_10)|divide(#1,#0)",
        "category": "geometry"
    },
    {
        "Problem": "3251 + 587 + 369 - ? = 3007",
        "Rationale": "let 4207 - x = 3007 then x = 4207 - 3007 = 1200 answer is d",
        "options": "a ) 1250 , b ) 1300 , c ) 1375 , d ) 1200 , e ) none of them",
        "correct": "d",
        "annotated_formula": "subtract(add(add(3251, 587), 369), 3007)",
        "linear_formula": "add(n0,n1)|add(n2,#0)|subtract(#1,n3)",
        "category": "general"
    },
    {
        "Problem": "the manufacturer \u2019 s suggested retail price ( msrp ) of a certain item is $ 60 . store a sells the item for 20 percent more than the msrp . the regular price of the item at store b is 30 percent more than the msrp , but the item is currently on sale for 10 percent less than the regular price . if sales tax is 5 percent of the purchase price at both stores , what is the result when the total cost of the item at store b is subtracted from the total cost of the item at store a ?",
        "Rationale": "msrp = 60 price at store a = 60 \u2217 120100 = 72 = 60 \u2217 120100 = 72 price at store b = 60 \u2217 130100 \u2217 90100 = 70.2 = 60 \u2217 130100 \u2217 90100 = 70.2 difference = 72.0 - 70.2 = 1.8 sales tax applicable = 5 % on both = 1.8 + 0.09 = 1.89 answer = d",
        "options": "a ) $ 0 , b ) $ 0.63 , c ) $ 1.80 , d ) $ 1.89 , e ) $ 2.10",
        "correct": "d",
        "annotated_formula": "subtract(multiply(60, divide(add(const_100, 20), const_100)), multiply(divide(subtract(const_100, 10), const_100), multiply(divide(add(const_100, 30), const_100), 60)))",
        "linear_formula": "add(n1,const_100)|add(n2,const_100)|subtract(const_100,n3)|divide(#0,const_100)|divide(#2,const_100)|divide(#1,const_100)|multiply(n0,#3)|multiply(n0,#5)|multiply(#4,#7)|subtract(#6,#8)",
        "category": "general"
    },
    {
        "Problem": "in certain code ' twice ' is written as ' 34 $ 5 \u03b4 ' and ' wears ' is written as ' 4 \u03b4 29 % ' . how is ' seat ' written in that code ?",
        "Rationale": "answer : option b",
        "options": "a ) 22 , b ) 23 , c ) 697 , d ) 66 p , e ) 82",
        "correct": "b",
        "annotated_formula": "subtract(subtract(29, 5), const_1)",
        "linear_formula": "subtract(n3,n1)|subtract(#0,const_1)",
        "category": "gain"
    },
    {
        "Problem": "two pipes a and b can fill a cistern in 10 and 15 minutes respectively . both fill pipes are opened together , but at the end of 3 minutes , \u2018 b \u2019 is turned off . how much time will the cistern take to fill ?",
        "Rationale": "in one min , ( a + b ) fill the cistern = 1 \u2044 10 + 1 \u2044 15 = 1 \u2044 6 th in 3 min , ( a + b ) fill the cistern = 3 \u2044 6 = 1 \u2044 2 th remaining part = 1 - 1 \u2044 2 = 1 \u2044 2 \u2235 1 \u2044 10 th part filled by a in one min . \u2234 1 \u2044 2 nd part filled by a in 10 \u00d7 1 \u2044 2 = 5 min . \u2234 total time = 3 + 5 = 8 min . answer b",
        "options": "a ) 6 min , b ) 8 min , c ) 10 min , d ) 12 min , e ) none of these",
        "correct": "b",
        "annotated_formula": "add(multiply(10, subtract(const_1, multiply(add(inverse(10), inverse(15)), const_3))), 3)",
        "linear_formula": "inverse(n0)|inverse(n1)|add(#0,#1)|multiply(#2,const_3)|subtract(const_1,#3)|multiply(n0,#4)|add(n2,#5)",
        "category": "physics"
    },
    {
        "Problem": "if o is the center of the circle in the figure above and the area of the unshaded sector is 5 , what is the area of the shaded region ?",
        "Rationale": "60 / 360 = 1 / 6 1 / 6 of total area = 5 5 / 6 of total area = 5 * 5 = 25 answer : d",
        "options": "['a ) 25 / \u221a \u03c0', 'b ) 30 / \u221a \u03c0', 'c ) 20', 'd ) 25', 'e ) 30']",
        "correct": "d",
        "annotated_formula": "power(5, const_2)",
        "linear_formula": "power(n0,const_2)",
        "category": "geometry"
    },
    {
        "Problem": "a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area w covered by the two roads ?",
        "Rationale": "\"area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads w = 1000 + 600 - 25 = 1575 answer : option c\"",
        "options": "a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625",
        "correct": "c",
        "annotated_formula": "add(rectangle_area(200, 5), rectangle_area(120, 5))",
        "linear_formula": "rectangle_area(n0,n2)|rectangle_area(n1,n2)|add(#0,#1)|",
        "category": "geometry"
    },
    {
        "Problem": "if a and b together can finish a work in 16 days . a can finish same work alone in 24 days then b alone can finish same work alone in how many days ?",
        "Rationale": "( a + b ) work in 1 day = 1 / 16 , a work in 1 day = 1 / 24 b work in 1 day = [ 1 / 16 - 1 / 24 ] = 1 / 48 . b alone can finish same work in 48 days . answer b",
        "options": "a ) 30 days , b ) 48 days , c ) 40 days , d ) 36 days , e ) 50 days",
        "correct": "b",
        "annotated_formula": "inverse(subtract(inverse(16), inverse(24)))",
        "linear_formula": "inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2)",
        "category": "physics"
    },
    {
        "Problem": "if 5 a + 7 b = m , where a and b are positive integers , what is the largest possible value of m for which exactly one pair of integers ( a , b ) makes the equation true ?",
        "Rationale": "5 * a 1 + 7 * b 1 = m 5 * a 2 + 7 * b 2 = m 5 * ( a 1 - a 2 ) = 7 * ( b 2 - b 1 ) since we are dealing with integers we can assume that a 1 - a 2 = 7 * q and b 2 - b 1 = 5 * q where q is integer , so whenever we get a pair for ( a ; b ) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa , subtracting 7 from a and adding 5 to b . lets check how it works for our numbers , starting from the largest : e ) 74 = 5 * 12 + 7 * 2 ( a 1 = 12 , b 1 = 2 ) , subtract 7 from a and add 5 to b respectively , so a 2 = 5 and b 2 = 7 , second pair - bad d ) 70 = 5 * 7 + 7 * 5 ( a 1 = 7 , b 1 = 5 ) , if we add 7 toawe will have to subtract 5 from b but b ca n ' t be 0 , so - no pair , if we subtract 7 froma , we ' ll get a = 0 which also is n ' t allowed - no pair , thus this is the only pair for ( a ; b ) that works , good ! , thus d is the answer",
        "options": "a ) 35 , b ) 48 , c ) 69 , d ) 70 , e ) 74",
        "correct": "d",
        "annotated_formula": "add(multiply(7, add(const_3, const_4)), multiply(5, const_4))",
        "linear_formula": "add(const_3,const_4)|multiply(n0,const_4)|multiply(n1,#0)|add(#2,#1)",
        "category": "general"
    },
    {
        "Problem": "a man speaks truth 3 out of 4 times . he throws a die and reports it to be a 6 . what is the probability of it being a 6 ?",
        "Rationale": "explanation : there are two cases 1 ) he is telling truth that the die reports 6 , its probability = 3 / 4 * 1 / 6 = 1 / 8 2 ) he is telling lie that the die reports 6 , its probability = 1 / 4 * 5 / 6 = 5 / 24 so required probability = ( 1 / 8 ) / ( 1 / 8 ) + ( 5 / 24 ) = ( 1 / 8 ) / ( 1 / 3 ) = 3 / 8 hencer ( d ) is the correct answer answer : d",
        "options": "a ) 3 / 5 , b ) 1 / 2 , c ) 3 / 4 , d ) 3 / 8 , e ) 3 / 6",
        "correct": "d",
        "annotated_formula": "divide(multiply(divide(3, 4), divide(const_1, 6)), add(multiply(divide(3, 4), divide(const_1, 6)), multiply(divide(const_1, const_4), divide(const_5, 6))))",
        "linear_formula": "divide(n0,n1)|divide(const_1,n2)|divide(const_1,const_4)|divide(const_5,n2)|multiply(#0,#1)|multiply(#2,#3)|add(#4,#5)|divide(#4,#6)",
        "category": "probability"
    },
    {
        "Problem": "on a sum of money , simple interest for 2 years is rs 660 and compound interest is rs 696.30 , the rate of interest being the same in both cases .",
        "Rationale": "explanation : difference between c . i and s . i for 2 years = 36.30 s . i . for one year = 330 . s . i . on rs 330 for one year = 36.30 so r % = \\ frac { 100 * 36.30 } { 330 * 1 } = 11 % answer : d",
        "options": "a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) none of these",
        "correct": "d",
        "annotated_formula": "multiply(divide(multiply(subtract(696.3, 660), 2), 660), const_100)",
        "linear_formula": "subtract(n2,n1)|multiply(n0,#0)|divide(#1,n1)|multiply(#2,const_100)",
        "category": "gain"
    },
    {
        "Problem": "the ages of two persons differ by 16 years . if 6 years ago , the elder one be 3 times as old as the younger one , find their present ages .",
        "Rationale": "\"explanation : sol . let the age of the younger person be xx years then , age of the elder person = ( x + 16 ) ( x + 16 ) years \u00e2 \u02c6 \u00b4 \u00e2 \u02c6 \u00b4 3 ( x \u00e2 \u02c6 \u2019 6 ) = ( x + 16 \u00e2 \u02c6 \u2019 6 ) 3 ( x - 6 ) = ( x + 16 - 6 ) \u00e2 \u2021 \u201d 3 x \u00e2 \u02c6 \u2019 18 = x + 10 \u00e2 \u2021 \u201d 3 x - 18 = x + 10 \u00e2 \u2021 \u201d 2 x = 28 \u00e2 \u2021 \u201d 2 x = 28 \u00e2 \u2021 \u201d x = 14 \u00e2 \u2021 \u201d x = 14 hence , their present age are 14 years and 30 years . answer is d\"",
        "options": "a ) 10 years and 18 years , b ) 18 years and 26 years , c ) 20 years and 28 years , d ) 14 years and 30 years , e ) 16 years and 25 years",
        "correct": "d",
        "annotated_formula": "subtract(add(divide(multiply(16, 6), subtract(6, const_1)), 6), 16)",
        "linear_formula": "multiply(n0,n1)|subtract(n1,const_1)|divide(#0,#1)|add(n1,#2)|subtract(#3,n0)|",
        "category": "general"
    },
    {
        "Problem": "an athlete takes 10 seconds to run 100 m . what is his avg . speed in miles per hour ?",
        "Rationale": "his average speed is 10 m / s . which is 36 km / hr . but 36 km = 22.37 miles . the average speed of the athlete is 22.37 mph answer : a",
        "options": "a ) 22.37 , b ) 26.66 , c ) 24.35 , d ) 36.0 , e ) 42.44",
        "correct": "a",
        "annotated_formula": "divide(multiply(divide(100, const_1000), const_0_6), divide(10, const_3600))",
        "linear_formula": "divide(n1,const_1000)|divide(n0,const_3600)|multiply(#0,const_0_6)|divide(#2,#1)",
        "category": "physics"
    },
    {
        "Problem": "what is the max number of rectangular boxes , each measuring 4 inches by 6 inches by 10 inches , that can be packed into a rectangular packing box measuring 16 inches by 18 inches by 30 inches , if all boxes are aligned in the same direction ?",
        "Rationale": "the 4 inch side should be aligned to the 16 inch side ( 4 layer ) 6 inch side should be aligned to the 18 inch side . ( 3 layer ) and 10 inch side should be aligned to the 30 inch side . ( 3 layer ) maximum number of rectangles = 4 * 3 * 3 = 36 answer is a",
        "options": "['a ) 36', 'b ) 14', 'c ) 12', 'd ) 15', 'e ) 11']",
        "correct": "a",
        "annotated_formula": "divide(multiply(multiply(16, 18), 30), multiply(multiply(4, 6), 10))",
        "linear_formula": "multiply(n3,n4)|multiply(n0,n1)|multiply(n5,#0)|multiply(n2,#1)|divide(#2,#3)",
        "category": "geometry"
    },
    {
        "Problem": "how many seconds will a 500 m long train take to cros a man walking with a speed of 3 kmph in the direction of the moving train if the speed of the train is 63 kmph",
        "Rationale": "time = distance ( here length of the train ) / relative speed ( 63 - 3 ) thus time = 500 / 60 * 5 / 18 = 500 * 18 / 60 * 5 = 30 seconds answer : b",
        "options": "a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 50",
        "correct": "b",
        "annotated_formula": "divide(500, divide(subtract(63, 3), const_3_6))",
        "linear_formula": "subtract(n2,n1)|divide(#0,const_3_6)|divide(n0,#1)",
        "category": "physics"
    },
    {
        "Problem": "a batsman had a certain average of runs for 16 innings . in the 17 th innings , he made a score of 87 runs thereby increasing his average by 3 . what is his average after 17 innings ?",
        "Rationale": "explanation : assume his initial average = xx his total runs after 16 innings = 16 xx after scoring 87 runs his average got increased by 3 to xx + 3 so his total runs after 17 innings = 17 \u00d7 ( xx + 3 ) but it was given that the difference in the total scores after 16 innings and 17 innings = 87 therefore 17 \u00d7 ( x + 3 ) \u2212 16 x = 87 \u21d2 x = 3617 \u00d7 ( x + 3 ) \u2212 16 x = 87 \u21d2 x = 36 his new average = 36 + 3 = 39 answer : a",
        "options": "a ) 39 , b ) 88 , c ) 266 , d ) 278 , e ) 221",
        "correct": "a",
        "annotated_formula": "add(subtract(87, multiply(17, 3)), 3)",
        "linear_formula": "multiply(n1,n3)|subtract(n2,#0)|add(n3,#1)",
        "category": "general"
    },
    {
        "Problem": "if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is - .",
        "Rationale": "\"explanation : p ( s \u1d1c k ) = p ( s ) + p ( k ) - p ( s \u2229 k ) , where s denotes spade and k denotes king . p ( s \u1d1c k ) = 13 / 52 + 4 / 52 - 1 / 52 = 4 / 13 answer : b\"",
        "options": "a ) 2 / 10 , b ) 4 / 13 , c ) 3 / 5 , d ) 9 / 7 , e ) 1 / 4",
        "correct": "b",
        "annotated_formula": "add(divide(const_3, const_52), divide(divide(const_52, const_4), const_52))",
        "linear_formula": "divide(const_3,const_52)|divide(const_52,const_4)|divide(#1,const_52)|add(#0,#2)|",
        "category": "probability"
    },
    {
        "Problem": "3 friends james , david and charlie divide $ 1230 amongs them in such a way that if $ 5 , $ 10 and $ 15 are removed from the sums that james , david and charlie received respectively , then the share of the sums that they got will be in the ratio of 9 : 10 : 11 . how much did charlie receive ?",
        "Rationale": "a + b + c = 1230 given ratio 9 : 10 : 11 let us say the shares of a , b , c deducting 5 , 1015 be a , b , c a + b + c = 1230 - 30 = 1200 = 30 k c share = ( 1200 x 30 ) / 60 = 600 c = charlie share = 600 + 15 = 615 option e",
        "options": "a ) $ 600 , b ) $ 575 , c ) $ 550 , d ) $ 580 , e ) $ 615",
        "correct": "e",
        "annotated_formula": "add(add(add(add(add(multiply(11, divide(subtract(1230, add(add(5, 10), 15)), add(add(9, 10), 11))), 15), divide(subtract(1230, add(add(5, 10), 15)), add(add(9, 10), 11))), divide(subtract(1230, add(add(5, 10), 15)), add(add(9, 10), 11))), divide(subtract(1230, add(add(5, 10), 15)), add(add(9, 10), 11))), divide(subtract(1230, add(add(5, 10), 15)), add(add(9, 10), 11)))",
        "linear_formula": "add(n2,n3)|add(n3,n5)|add(n4,#0)|add(n7,#1)|subtract(n1,#2)|divide(#4,#3)|multiply(n7,#5)|add(n4,#6)|add(#7,#5)|add(#8,#5)|add(#9,#5)|add(#10,#5)",
        "category": "general"
    },
    {
        "Problem": "calculate the area of a triangle , if the sides of are 39 cm , 36 cm and 15 cm , what is its area ?",
        "Rationale": "\"the triangle with sides 39 cm , 36 cm and 15 is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : e\"",
        "options": "a ) 570 cm 2 , b ) 370 cm 2 , c ) 170 cm 2 , d ) 271 cm 2 , e ) 270 cm 2",
        "correct": "e",
        "annotated_formula": "multiply(divide(36, const_2), 15)",
        "linear_formula": "divide(n1,const_2)|multiply(n2,#0)|",
        "category": "geometry"
    },
    {
        "Problem": "one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in ?",
        "Rationale": "\"let the slower pipe alone fill the tank in x minutes then , faster pipe will fill it in x / 3 minutes 1 / x + 3 / x = 1 / 36 4 / x = 1 / 36 x = 144 min answer is a\"",
        "options": "a ) 144 min , b ) 250 min , c ) 196 min , d ) 100 min , e ) 112 min",
        "correct": "a",
        "annotated_formula": "multiply(add(const_1, const_4), 36)",
        "linear_formula": "add(const_1,const_4)|multiply(n0,#0)|",
        "category": "physics"
    },
    {
        "Problem": "the average of 5 consecutive odd numbers a , b , c , d and e is 33 . what percent of a is d ?",
        "Rationale": "explanation : in such a case the middle number ( c ) is the average \u2234 c = 33 and a = 31 and d = 35 required percentage = 31 / 35 x 100 = 88.6 answer : option b",
        "options": "a ) 86.8 , b ) 88.6 , c ) 89.2 , d ) 90.1 , e ) 92.2",
        "correct": "b",
        "annotated_formula": "multiply(const_100, divide(divide(multiply(33, 5), 5), add(add(add(divide(multiply(33, 5), 5), const_2), const_2), const_2)))",
        "linear_formula": "multiply(n0,n1)|divide(#0,n0)|add(#1,const_2)|add(#2,const_2)|add(#3,const_2)|divide(#1,#4)|multiply(#5,const_100)",
        "category": "general"
    },
    {
        "Problem": "the volumes of two cubes are in the ratio 27 : 125 , what shall be the ratio of their surface areas ?",
        "Rationale": "a 13 : a 23 = 27 : 125 a 1 : a 2 = 3 : 5 6 a 12 : 6 a 22 a 12 : a 22 = 9 : 25 answer : c",
        "options": "['a ) 6 : 25', 'b ) 3 : 5', 'c ) 9 : 25', 'd ) 16 : 25', 'e ) 19 : 25']",
        "correct": "c",
        "annotated_formula": "divide(surface_cube(divide(divide(27, const_3), const_3)), surface_cube(divide(125, divide(125, add(const_4, const_1)))))",
        "linear_formula": "add(const_1,const_4)|divide(n0,const_3)|divide(#1,const_3)|divide(n1,#0)|divide(n1,#3)|surface_cube(#2)|surface_cube(#4)|divide(#5,#6)",
        "category": "geometry"
    },
    {
        "Problem": "bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - .",
        "Rationale": "explanation : drawing two balls of same color from seven green balls can be done in \u00e2 \u0081 \u00b7 c \u00e2 \u201a \u201a ways . similarly from eight white balls two can be drawn in \u00e2 \u0081 \u00b8 c \u00e2 \u201a \u201a ways . p = \u00e2 \u0081 \u00b7 c \u00e2 \u201a \u201a / \u00e2 \u00b9 \u00e2 \u0081 \u00b5 c \u00e2 \u201a \u201a + \u00e2 \u0081 \u00b8 c \u00e2 \u201a \u201a / \u00e2 \u00b9 \u00e2 \u0081 \u00b5 c \u00e2 \u201a \u201a = 7 / 15 a",
        "options": "a ) 7 / 15 , b ) 2 / 8 , c ) 7 / 11 , d ) 13 / 5 , e ) 87",
        "correct": "a",
        "annotated_formula": "divide(add(divide(factorial(7), multiply(factorial(subtract(7, const_2)), factorial(const_2))), divide(factorial(8), multiply(factorial(subtract(8, const_2)), factorial(const_2)))), divide(factorial(add(7, 8)), multiply(factorial(subtract(add(7, 8), const_2)), factorial(const_2))))",
        "linear_formula": "add(n0,n1)|factorial(n0)|factorial(const_2)|factorial(n1)|subtract(n0,const_2)|subtract(n1,const_2)|factorial(#4)|factorial(#5)|factorial(#0)|subtract(#0,const_2)|factorial(#9)|multiply(#6,#2)|multiply(#7,#2)|divide(#1,#11)|divide(#3,#12)|multiply(#10,#2)|add(#13,#14)|divide(#8,#15)|divide(#16,#17)",
        "category": "other"
    },
    {
        "Problem": "subtracting 30 from a number , the remainder is one fourth of the number . find the number ?",
        "Rationale": "explanation : 3 / 4 x = 30 = > x = 40 answer : c",
        "options": "a ) 29 , b ) 88 , c ) 40 , d ) 28 , e ) 27",
        "correct": "c",
        "annotated_formula": "divide(30, subtract(const_1, divide(const_1, const_4)))",
        "linear_formula": "divide(const_1,const_4)|subtract(const_1,#0)|divide(n0,#1)",
        "category": "general"
    },
    {
        "Problem": "the sum of four consecutive even integers is 1284 . the greatest of them is :",
        "Rationale": "\"sol . let the four integers be x , x + 2 , x + 4 and x + 6 then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) = 1284 \u21d4 4 x = 1272 \u21d4 x = 318 \u2234 greatest integer = x + 6 = 324 . answer a\"",
        "options": "a ) 324 , b ) 342 , c ) 364 , d ) 382 , e ) none",
        "correct": "a",
        "annotated_formula": "add(add(power(add(add(divide(subtract(subtract(1284, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(1284, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(1284, const_10), const_2), const_4), const_2), power(add(divide(subtract(subtract(1284, const_10), const_2), const_4), const_2), const_2)))",
        "linear_formula": "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)|",
        "category": "physics"
    },
    {
        "Problem": "if a train runs at 40 kmph , it reach its destination late by 11 minutes but if it runs at 50 kmph it is late by 5 minutes only . the correct time for a train to complete its journey is ? let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min",
        "Rationale": "let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min answer ( a )",
        "options": "a ) 19 min , b ) 19 hrs , c ) 52 min , d ) 126 min , e ) 52 min",
        "correct": "a",
        "annotated_formula": "divide(subtract(multiply(multiply(60, 40), 11), multiply(multiply(60, 50), 5)), subtract(multiply(60, 50), multiply(60, 40)))",
        "linear_formula": "multiply(n0,n9)|multiply(n2,n9)|multiply(n1,#0)|multiply(n3,#1)|subtract(#1,#0)|subtract(#2,#3)|divide(#5,#4)",
        "category": "general"
    },
    {
        "Problem": "alex and brian start a business with rs . 7000 each , and after 8 months , brian withdraws half of his capital . how should they share the profits at the end of the 18 months ?",
        "Rationale": "alex invests rs . 7000 for 18 months , but brian invests rs . 7000 for the first 8 months and then withdraws rs . 3500 . so , the investment of brian for remaining 10 months is rs . 3500 only . alex : brian 7000 * 18 : ( 7000 * 8 ) + ( 3500 * 10 ) 126000 : 91000 alex : brian = 18 : 13 answer : e",
        "options": "a ) 5 : 4 , b ) 4 : 3 , c ) 18 : 11 , d ) 3 : 2 , e ) 18 : 13",
        "correct": "e",
        "annotated_formula": "divide(18, add(const_12, const_1))",
        "linear_formula": "add(const_1,const_12)|divide(n2,#0)",
        "category": "gain"
    },
    {
        "Problem": "a sum of money is distributed among a , b , c , d in the proportion of 1 : 3 : 4 : 2 . if c gets $ 500 more than d , what is the b ' s share ?",
        "Rationale": "let the shares of a , b , c , d are x , 3 x , 4 x , 2 x 4 x - 2 x = 500 x = 250 b ' s share = 3 x = $ 750 answer is c",
        "options": "a ) $ 450 , b ) $ 500 , c ) $ 750 , d ) $ 800 , e ) $ 840",
        "correct": "c",
        "annotated_formula": "divide(multiply(divide(multiply(add(500, 500), 2), 4), 3), 2)",
        "linear_formula": "add(n4,n4)|multiply(n3,#0)|divide(#1,n2)|multiply(n1,#2)|divide(#3,n3)",
        "category": "general"
    },
    {
        "Problem": "if there are thrice as many women as men in a group and an equal number of men and women do not own cars - a group that is 30 % of the total . what fraction of the total is men who own cars ?",
        "Rationale": "consider a group of 100 men and 300 women , a total of 400 people . 30 % of them , which is 120 , form a group of people who do n ' t own a car . half of them are men , and the other half are women , more precisely 60 . it means that there are 100 - 60 = 40 men who own a car , and this represents 40 / 400 = 1 / 10 of the total . answer d",
        "options": "a ) 3 \u2044 20 , b ) 11 \u2044 60 , c ) 9 \u2044 40 , d ) 1 \u2044 10 , e ) 11 \u2044 20",
        "correct": "d",
        "annotated_formula": "divide(const_1, divide(30, const_3))",
        "linear_formula": "divide(n0,const_3)|divide(const_1,#0)",
        "category": "general"
    },
    {
        "Problem": "a man is 24 years older than his son . in three years , his age will be twice the age of his son . the present age of the son is",
        "Rationale": "\"solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba ( x + 24 ) + 3 = 2 ( x + 3 ) \u00e2 \u20ac \u00b9 = \u00e2 \u20ac \u00ba x + 27 = 2 x + 6 x = 21 . answer d\"",
        "options": "a ) 14 years , b ) 18 years , c ) 20 years , d ) 21 years , e ) none",
        "correct": "d",
        "annotated_formula": "divide(subtract(24, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1))",
        "linear_formula": "multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)|",
        "category": "general"
    },
    {
        "Problem": "a man covers a certain distance q in a train . if the train moved 4 km / hr faster , it would take 30 min less . if it moved 2 km / hr slower , it would take 20 mins more . find the distance ?",
        "Rationale": "not really . when you solve the 2 equation above , you get , 6 t - 4 / 3 = 5 r / 6 from simplifying equation 1 4 t - 2 = r / 2 from simplifying equation 2 you can now multiply equation 2 by 5 to get 5 ( 4 t - 2 = r / 2 ) = 20 t - 10 = 5 r / 2 and then subtract this new equation from equation 1 to get t = 3 , followed by r = 20 to give you distance q = r * t = 20 * 3 = 60 km . d",
        "options": "a ) 200 km , b ) 50 km , c ) 20 km , d ) 60 km , e ) 80 km",
        "correct": "d",
        "annotated_formula": "multiply(divide(subtract(multiply(4, 2), 4), const_2), 30)",
        "linear_formula": "multiply(n0,n2)|subtract(#0,n0)|divide(#1,const_2)|multiply(n1,#2)",
        "category": "general"
    },
    {
        "Problem": "if the a radio is sold for rs 490 and sold for rs 465.50 . find loss % .",
        "Rationale": "\"sol . cp = rs 490 , sp = 465.50 . loss = rs ( 490 - 465.50 ) = rs 24.50 . loss % = [ ( 24.50 / 490 ) * 100 ] % = 5 % answer is b .\"",
        "options": "a ) 4 % , b ) 5 % , c ) 6 % , d ) 3 % , e ) 5.5 %",
        "correct": "b",
        "annotated_formula": "multiply(divide(subtract(490, 465.50), 490), const_100)",
        "linear_formula": "subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years q in which the population would be doubled assuming there is no emigration or immigration is",
        "Rationale": "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d",
        "options": "a ) q = 20 , b ) q = 25 , c ) q = 30 , d ) q = 35 , e ) 40",
        "correct": "d",
        "annotated_formula": "divide(subtract(const_100, multiply(const_10, const_3)), multiply(divide(subtract(39.4, 19.4), 1000), const_100))",
        "linear_formula": "multiply(const_10,const_3)|subtract(n1,n2)|divide(#1,n0)|subtract(const_100,#0)|multiply(#2,const_100)|divide(#3,#4)",
        "category": "general"
    },
    {
        "Problem": "a pyramid has a square base of 6 cm , and the four lateral faces are four congruent equilateral triangles . what is the total surface area of the pyramid in square cm ?",
        "Rationale": "first of all , of course , the base has an area of 36 . for the lateral surfaces , it would be helpful to remember the formula for the area of an equilateral triangle . the area of one equilateral triangle is a = ( s ^ 2 * sqrt { 3 } ) / 4 . we know the side of the equilateral triangle must be the same as the square : s = 6 . thus , one of these equilateral triangles has an area of a = ( 6 ^ 2 * sqrt { 3 } ) / 4 = 9 * sqrt { 3 } . there are four identical triangles , so their combined area is a = 36 * sqrt { 3 } . now , add the square base , for a total surface area of a = 36 + 36 * sqrt { 3 } . answer = b",
        "options": "['a ) 36 + 18 * sqrt ( 3 )', 'b ) 36 + 36 * sqrt ( 3 )', 'c ) 72', 'd ) 72 + 36 * sqrt ( 3 )', 'e ) 72 + 72 * sqrt ( 3 )']",
        "correct": "b",
        "annotated_formula": "add(multiply(divide(multiply(6, sqrt(subtract(square_area(6), power(const_3, const_2)))), const_2), const_4), square_area(6))",
        "linear_formula": "power(const_3,const_2)|square_area(n0)|subtract(#1,#0)|sqrt(#2)|multiply(n0,#3)|divide(#4,const_2)|multiply(#5,const_4)|add(#6,#1)",
        "category": "geometry"
    },
    {
        "Problem": "find the smallest number in gp whose sum is 38 and product is 1728",
        "Rationale": "\"let x , y , z be the numbers in geometric progression ? y ^ 2 = xz x + y + z = 38 xyz = 1728 xyz = xzy = y ^ 2 y = y ^ 3 = 1728 y = 12 y ^ 2 = xz = 144 z = 144 / x x + y + z = x + 12 + 144 / x = 38 x ^ 2 + 12 x + 144 = 38 x x ^ 2 - 26 x + 144 = 0 ( x - 18 ) ( x - 8 ) = 0 x = 8,18 if x = 8 , z = 38 - 8 - 12 = 18 the numbers are 8,12 , 18 their sum is 38 their product is 1,728 the smallest number is 8 answer : d\"",
        "options": "a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9",
        "correct": "d",
        "annotated_formula": "multiply(divide(divide(divide(divide(38, const_1000), const_3), const_3), const_3), divide(divide(divide(divide(38, const_1000), const_3), const_3), const_3))",
        "linear_formula": "divide(n0,const_1000)|divide(#0,const_3)|divide(#1,const_3)|divide(#2,const_3)|multiply(#3,#3)|",
        "category": "general"
    },
    {
        "Problem": "in a fuel station the service costs $ 1.50 per car , every liter of fuel costs 0.35 $ . assuming that you own 3 limos and 2 fleet vans and all fuel tanks are empty . how much will it cost to fuel all cars together if a limo tank is 32 liters and an fleet van tank is 75 % bigger ?",
        "Rationale": "\"lots of calculations . 1.50 * 4 + 3 * . 35 * 32 + 2 * ( 7 / 4 ) * 32 * . 35 answer = $ 78.80 the correct option is a\"",
        "options": "a ) $ 78.80 , b ) $ 79.80 , c ) $ 78.90 , d ) $ 79.90 , e ) $ 77.80",
        "correct": "a",
        "annotated_formula": "multiply(multiply(0.35, 2), 3)",
        "linear_formula": "multiply(n1,n3)|multiply(n2,#0)|",
        "category": "general"
    },
    {
        "Problem": "a , b and c can do a piece of work in 7 days , 14 days and 28 days respectively . how long will they take to finish the work , if all the three work together ?",
        "Rationale": "\"1 / 7 + 1 / 14 + 1 / 28 = 7 / 28 = 1 / 4 all three can finish the work in 4 days answer : a\"",
        "options": "a ) 4 , b ) 9 , c ) 2 , d ) 11 , e ) none",
        "correct": "a",
        "annotated_formula": "inverse(add(inverse(28), add(inverse(7), inverse(14))))",
        "linear_formula": "inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|inverse(#4)|",
        "category": "physics"
    },
    {
        "Problem": "lamp a flashes every 6 seconds , lamp b flashes every 8 seconds , lamp c flashes every 10 seconds . at a certain instant of time all 3 lamps flash simultaneously . during the period of 6 minutes after that how many times will exactly two lamps flash ? ( please include any flash of exactly two lights which occurs at the 6 minute mark . )",
        "Rationale": "6 minutes is 360 seconds . lamp a and lamp b will flash together every 24 seconds . 360 / 24 = 15 . in the time period , lamp a and lamp b will flash together 15 times . lamp a and lamp c will flash together every 30 seconds . 360 / 30 = 12 . in the time period , lamp a and lamp c will flash together 12 times . lamp b and lamp c will flash together every 40 seconds . 360 / 40 = 9 . in the time period , lamp b and lamp c will flash together 9 times . all three lights will flash together every 2 * 2 * 2 * 3 * 5 = 120 seconds . 360 / 120 = 3 . we have counted these triple flashes three times , so we need to subtract three times the number of times that all three lights flash together . the number of times that exactly two lights flash together is 15 + 12 + 9 - 9 = 27 times . the answer is d .",
        "options": "a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28",
        "correct": "d",
        "annotated_formula": "subtract(add(add(divide(multiply(6, const_60), lcm(6, 8)), divide(multiply(6, const_60), lcm(6, 10))), divide(multiply(6, const_60), lcm(8, 10))), multiply(divide(multiply(6, const_60), lcm(lcm(6, 8), 10)), 3))",
        "linear_formula": "lcm(n0,n1)|lcm(n0,n2)|lcm(n1,n2)|multiply(n0,const_60)|divide(#3,#0)|divide(#3,#1)|divide(#3,#2)|lcm(n2,#0)|add(#4,#5)|divide(#3,#7)|add(#8,#6)|multiply(n3,#9)|subtract(#10,#11)",
        "category": "physics"
    },
    {
        "Problem": "the bus fare for two persons for travelling between agra and aligarh id 4 - thirds the train fare between the same places for one person . the total fare paid by 6 persons travelling by bus and 8 persons travelling by train between the two places is rs . 1512 . find the train fare between the two places for one person ?",
        "Rationale": "let the train fare between the two places for one person be rs . t bus fare between the two places for two persons rs . 4 / 3 t = > 6 / 2 ( 4 / 3 t ) + 8 ( t ) = 1512 = > 12 t = 1512 = > t = 126 . answer : a",
        "options": "a ) rs . 126 , b ) rs . 132 , c ) rs . 120 , d ) rs . 114 , e ) none of these",
        "correct": "a",
        "annotated_formula": "divide(1512, add(multiply(divide(6, const_2), divide(4, const_3)), 8))",
        "linear_formula": "divide(n1,const_2)|divide(n0,const_3)|multiply(#0,#1)|add(n2,#2)|divide(n3,#3)",
        "category": "general"
    },
    {
        "Problem": "a goods bullet train runs at the speed of 72 km / hr and crosses a 250 m long platform in 26 seconds . what is the length of the goods bullet train ?",
        "Rationale": "e 270 m",
        "options": "a ) 220 m , b ) 250 m , c ) 280 m , d ) 210 m , e ) 270 m",
        "correct": "e",
        "annotated_formula": "subtract(multiply(multiply(72, const_0_2778), 26), 250)",
        "linear_formula": "multiply(n0,const_0_2778)|multiply(n2,#0)|subtract(#1,n1)",
        "category": "physics"
    },
    {
        "Problem": "find the sum 3 / 10 + 5 / 100 + 8 / 1000 in decimal form ?",
        "Rationale": "answer 3 / 10 + 5 / 100 + 8 / 1000 = 0.3 + 0.05 + 0.008 = 0.358 correct option : b",
        "options": "a ) 0.853 , b ) 0.358 , c ) 3.58 , d ) 8.35 , e ) none",
        "correct": "b",
        "annotated_formula": "add(divide(8, 1000), add(divide(3, 10), divide(5, 100)))",
        "linear_formula": "divide(n0,n1)|divide(n2,n3)|divide(n4,n5)|add(#0,#1)|add(#3,#2)",
        "category": "general"
    },
    {
        "Problem": "prints a page 40 pg per min . if the printed for 2 hours except 20 min . where there was an paper jam , how many page did it print",
        "Rationale": "40 pages - - - - - - - > 1 min 2 hrs except 20 mints means = 2 * 60 = 120 - 20 = 100 mints i . e . , 100 * 40 = 4,000 pages printed . answer : a",
        "options": "a ) 4,000 , b ) 12,880 , c ) 14,880 , d ) 8,880 , e ) 18,880",
        "correct": "a",
        "annotated_formula": "divide(multiply(subtract(multiply(2, const_60), 20), 40), multiply(const_10, const_100))",
        "linear_formula": "multiply(n1,const_60)|multiply(const_10,const_100)|subtract(#0,n2)|multiply(n0,#2)|divide(#3,#1)",
        "category": "general"
    },
    {
        "Problem": "during a thanksgiving weekend , a car rental company rented 6 - tenths of their vehicles , including two - fifths of the 4 wds that it had . if 40 % of the vehicles are 4 wds , then what percent of the vehicles that were not rented were not 4 wds ?",
        "Rationale": "4 / 10 of all the vehicles were not rented . ( 3 / 5 ) ( 2 / 5 ) = 6 / 25 of all the vehicles are 4 wds that were not rented . ( 6 / 25 ) / ( 4 / 10 ) = 3 / 5 is the fraction of non - rented vehicles that were 4 wds 1 - 3 / 5 = 40 % of non - rented vehicles were not 4 wds . the answer is c .",
        "options": "a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %",
        "correct": "c",
        "annotated_formula": "multiply(divide(divide(multiply(const_2, 40), add(const_3, const_2)), 40), const_100)",
        "linear_formula": "add(const_2,const_3)|multiply(n2,const_2)|divide(#1,#0)|divide(#2,n2)|multiply(#3,const_100)",
        "category": "gain"
    },
    {
        "Problem": "a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm ^ 3 , then the weight of the pipe is :",
        "Rationale": "\"external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 x [ ( 4 ) ^ 2 - ( 3 ) ^ 2 ] x 21 ) cm ^ 3 ( 22 / 7 x 7 x 1 x 21 ) cm ^ 3 462 cm ^ 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b\"",
        "options": "a ) 3.6 kg , b ) 3.696 kg , c ) 36 kg , d ) 36.9 kg , e ) 3.06 kg",
        "correct": "b",
        "annotated_formula": "divide(multiply(subtract(volume_cylinder(divide(8, const_2), 21), volume_cylinder(subtract(divide(8, const_2), 1), 21)), 8), const_1000)",
        "linear_formula": "divide(n1,const_2)|subtract(#0,n2)|volume_cylinder(#0,n0)|volume_cylinder(#1,n0)|subtract(#2,#3)|multiply(n1,#4)|divide(#5,const_1000)|",
        "category": "general"
    },
    {
        "Problem": "mr . jones gave 40 % of the money he had to his wife . he also gave 20 % of the remaining amount to his 3 sons . and half of the amount now left was spent on miscellaneous items and the remaining amount of rs . 12000 was deposited in the bank . how much money did mr . jones have initially ?",
        "Rationale": "explanation : let the initial amount be x , amount given to his wife = ( 40 / 100 ) x = 2 x / 5 balance = ( x - ( 2 x / 5 ) ) = 3 x / 5 amount given to his wife = ( 20 / 100 ) * ( 3 x / 5 ) = 3 x / 25 balance = 3 x / 5 - 3 x / 25 = 12 x / 25 amountt spent on miscellaneous items = ( 1 / 2 ) * ( 12 x / 25 ) = 6 x / 25 which is equal to 12000 hence , = > 6 x / 25 = 12000 = > x = 50000 answer : c",
        "options": "a ) 40000 , b ) 45000 , c ) 50000 , d ) 62000 , e ) none of these",
        "correct": "c",
        "annotated_formula": "divide(12000, multiply(divide(divide(const_100, const_2), const_100), multiply(subtract(const_1, divide(40, const_100)), subtract(const_1, divide(20, const_100)))))",
        "linear_formula": "divide(const_100,const_2)|divide(n0,const_100)|divide(n1,const_100)|divide(#0,const_100)|subtract(const_1,#1)|subtract(const_1,#2)|multiply(#4,#5)|multiply(#3,#6)|divide(n3,#7)",
        "category": "gain"
    },
    {
        "Problem": "find the compound interest on rs . 10000 at 12 % rate of interest for 1 year , compounded half - yearly",
        "Rationale": "\"amount with ci = 10000 [ 1 + ( 12 / 2 * 100 ) ] 2 = rs . 11236 therefore , ci = 11236 \u2013 10000 = rs . 1236 answer : b\"",
        "options": "a ) rs . 1036 , b ) rs . 1236 , c ) rs . 1186 , d ) rs . 1206 , e ) rs . 1226",
        "correct": "b",
        "annotated_formula": "subtract(multiply(power(add(const_1, divide(divide(12, const_4), const_100)), const_3), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100))), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100)))",
        "linear_formula": "divide(n1,const_4)|multiply(const_4,const_4)|sqrt(const_100)|divide(#0,const_100)|multiply(#1,const_100)|add(#3,const_1)|multiply(#4,#2)|power(#5,const_3)|multiply(#6,#7)|subtract(#8,#6)|",
        "category": "gain"
    },
    {
        "Problem": "3 candidates contested an election and received 1000 , 2000 and 4000 votes respectively . what percentage of the total votes did the winning candidate got ?",
        "Rationale": "total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 required percentage = 4000 / 7000 * 100 = 57 % ( approximately ) answer : option c",
        "options": "a ) 30 % , b ) 50 % , c ) 57 % , d ) 62 % , e ) 75 %",
        "correct": "c",
        "annotated_formula": "multiply(divide(4000, add(add(1000, 2000), 4000)), const_100)",
        "linear_formula": "add(n1,n2)|add(n3,#0)|divide(n3,#1)|multiply(#2,const_100)",
        "category": "general"
    },
    {
        "Problem": "for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score r for the exam ?",
        "Rationale": "\"a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean r = 74 . answer : a .\"",
        "options": "a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82",
        "correct": "a",
        "annotated_formula": "divide(add(multiply(58, 3), multiply(98, 2)), add(2, 3))",
        "linear_formula": "add(n1,n3)|multiply(n0,n3)|multiply(n1,n2)|add(#1,#2)|divide(#3,#0)|",
        "category": "general"
    },
    {
        "Problem": "it costs $ 2 for the first 15 minutes to use the bumper cars at a fair ground . after the first 15 minutes it costs $ 6 per hour . if a certain customer uses the bumper cars for 3 hours and 25 minutes , how much will it cost him ?",
        "Rationale": "3 hrs 25 min = 205 min first 15 min - - - - - - > $ 2 time left is 190 min . . . now , 60 min costs $ 6 1 min costs $ 6 / 60 190 min costs $ 6 / 60 * 190 = > $ 19 so , total cost will be $ 19 + $ 2 = > $ 21 the answer will be ( d ) $ 21",
        "options": "a ) $ 22 , b ) $ 3 , c ) $ 15 , d ) $ 21 , e ) $ 30",
        "correct": "d",
        "annotated_formula": "add(multiply(divide(6, const_60), subtract(add(multiply(3, const_60), 25), 15)), 2)",
        "linear_formula": "divide(n3,const_60)|multiply(n4,const_60)|add(n5,#1)|subtract(#2,n1)|multiply(#0,#3)|add(n0,#4)",
        "category": "physics"
    },
    {
        "Problem": "john and andrew can finish the work 9 days if they work together . they worked together for 6 days and then andrew left . john finished the remaining work in another 6 days . in how many days john alone can finish the work ?",
        "Rationale": "amount of work done by john and andrew in 1 day = 1 / 9 amount of work done by john and andrew in 6 days = 6 \u00e3 \u2014 ( 1 / 9 ) = 2 / 3 remaining work \u00e2 \u20ac \u201c 1 \u00e2 \u20ac \u201c 2 / 3 = 1 / 3 john completes 1 / 3 work in 6 days amount of work john can do in 1 day = ( 1 / 3 ) / 6 = 1 / 18 = > john can complete the work in 18 days answer : c",
        "options": "a ) 30 days , b ) 60 days , c ) 18 days , d ) 80 days , e ) 90 days",
        "correct": "c",
        "annotated_formula": "divide(6, subtract(const_1, divide(6, 9)))",
        "linear_formula": "divide(n1,n0)|subtract(const_1,#0)|divide(n1,#1)",
        "category": "physics"
    },
    {
        "Problem": "if 100 cats kill 100 mice in 100 days , then 4 cats would kill 4 mice in how many days ?",
        "Rationale": "as 100 cats kill 100 mice in 100 days 1 cats kill 1 mouse in 100 days then 4 cats kill 4 mice in 100 days answer : d",
        "options": "a ) 1 day , b ) 4 days , c ) 40 days , d ) 100 days , e ) 50 days",
        "correct": "d",
        "annotated_formula": "divide(multiply(multiply(4, 100), 100), multiply(100, 4))",
        "linear_formula": "multiply(n0,n3)|multiply(n0,#0)|divide(#1,#0)",
        "category": "physics"
    },
    {
        "Problem": "of the 55 cars on a car lot , 40 have air - conditioning , 25 have power windows , and 12 have both air - conditioning and power windows . how many of the cars on the lot have neither air - conditioning nor power windows ?",
        "Rationale": "total - neither = all air conditioning + all power windows - both or 55 - neither = 40 + 25 - 12 = 53 . = > neither = 2 , hence d . answer : d",
        "options": "a ) 15 , b ) 8 , c ) 10 , d ) 2 , e ) 18",
        "correct": "d",
        "annotated_formula": "subtract(55, subtract(add(40, 25), 12))",
        "linear_formula": "add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)",
        "category": "other"
    },
    {
        "Problem": "if two - third of a bucket is filled in 6 minute then the time taken to fill the bucket completely will be .",
        "Rationale": "\"2 / 3 filled in 6 mint 1 / 3 filled in 3 mint thn 2 / 3 + 1 / 3 = 6 + 3 = 9 minutes answer : d\"",
        "options": "a ) 90 seconds , b ) 70 seconds , c ) 60 seconds , d ) 9 minutes , e ) 120 seconds",
        "correct": "d",
        "annotated_formula": "multiply(divide(6, const_2), const_3)",
        "linear_formula": "divide(n0,const_2)|multiply(#0,const_3)|",
        "category": "physics"
    },
    {
        "Problem": "at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses w at the restaurant ? ( assume that all boxes are filled to capacity . )",
        "Rationale": "\"most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e\"",
        "options": "a ) 96 , b ) 240 , c ) w = 256 , d ) w = 384 , e ) w = 480",
        "correct": "e",
        "annotated_formula": "multiply(multiply(16, const_2), 15)",
        "linear_formula": "multiply(n1,const_2)|multiply(n2,#0)|",
        "category": "general"
    },
    {
        "Problem": "alice and bob drive at constant speeds toward each other on a highway . alice drives at a constant speed of 30 km per hour . at a certain time they pass by each other , and then keep driving away from each other , maintaining their constant speeds . if alice is 100 km away from bob at 7 am , and also 100 km away from bob at 11 am , then how fast is bob driving ( in kilometers per hour ) ?",
        "Rationale": "alice and bob complete 200 km / 4 hours = 50 km / hour bob ' s speed is 50 - 30 = 20 km / hour the answer is a .",
        "options": "a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36",
        "correct": "a",
        "annotated_formula": "subtract(divide(add(100, 100), subtract(11, 7)), 30)",
        "linear_formula": "add(n1,n1)|subtract(n4,n2)|divide(#0,#1)|subtract(#2,n0)",
        "category": "physics"
    },
    {
        "Problem": "in what time will a train 100 metres long cross an electic pole , if its speed be 144 km / hr ?",
        "Rationale": "\"sol . speed = [ 144 x 5 / 18 ] m / sec = 40 m / sec . time taken = ( 100 / 40 ) sec = 2.5 sec . answer a\"",
        "options": "a ) 2.5 sec , b ) 4.25 sec , c ) 5 sec , d ) 12.5 sec , e ) none",
        "correct": "a",
        "annotated_formula": "divide(100, multiply(144, const_0_2778))",
        "linear_formula": "multiply(n1,const_0_2778)|divide(n0,#0)|",
        "category": "physics"
    },
    {
        "Problem": "what is the remainder when 50 ! is divided by 16 ^ 8 ? ?",
        "Rationale": "\"16 raise to 8 = 2 raise to 32 , now highest power of 2 divisible by 50 ! is 25 + 12 + 6 + 3 + 1 = 47 since 2 raise to 47 is divisible , 2 raise to 32 also will be divisible answer : a\"",
        "options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4",
        "correct": "a",
        "annotated_formula": "reminder(multiply(16, 50), 8)",
        "linear_formula": "multiply(n0,n1)|reminder(#0,n2)|",
        "category": "general"
    },
    {
        "Problem": "if the cost price of 140 pencils is equal to the selling price of 100 pencils , the gain percent is",
        "Rationale": "\"let c . p . of each pencil be re . 1 . then , c . p . of 100 pencils = rs . 100 ; s . p . of 100 pencils = rs . 140 . gain % = 40 / 100 * 100 = 40 % answer : e\"",
        "options": "a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40",
        "correct": "e",
        "annotated_formula": "divide(const_100, divide(100, subtract(140, 100)))",
        "linear_formula": "subtract(n0,n1)|divide(n1,#0)|divide(const_100,#1)|",
        "category": "gain"
    },
    {
        "Problem": "a mixture of sand and cement contains , 3 parts of sand and 5 parts of cement . how much of the mixture must be substituted with sand to make the mixture half sand and half cement ?",
        "Rationale": "we have total of 8 parts : 3 parts of sand and 5 parts of cement . in order there to be half sand and half cement ( 4 parts of sand and 4 parts of cement ) , we should remove 1 part of cement . with 1 part of cement comes 3 / 5 parts of sand , so we should remove 1 + 3 / 5 = 8 / 5 part of the mixture , which is ( 8 / 5 ) / 8 = 1 / 5 of the mixture . answer : c .",
        "options": "a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 7 , e ) 1 / 8",
        "correct": "c",
        "annotated_formula": "divide(add(const_1, divide(3, 5)), add(5, 3))",
        "linear_formula": "add(n0,n1)|divide(n0,n1)|add(#1,const_1)|divide(#2,#0)",
        "category": "general"
    },
    {
        "Problem": "a mixture contains milk and water in the ratio 5 : 2 . on adding 10 liters of water , the ratio of milk to water becomes 5 : 3 . the quantity of milk in the original mixture is ?",
        "Rationale": "\"milk : water = 5 : 2 5 x : 2 x + 10 = 5 : 3 3 [ 5 x ] = 5 [ 2 x + 10 ] 15 x = 10 x + 50 15 x - 10 x = 50 x = 10 the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 x = 70 short cut method : milk : water = 5 : 2 after adding 10 liters of water milk : water = 5 : 3 milk is same but water increse 10 liters then the water ratio is increse 1 parts 1 part - - - - - > 10 liters the quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 7 parts - - - - - > 70 liters ( answer is = 70 ) short cut method - 2 : for only milk problems milk : water 5 : 2 5 : 3 milk ratio same but water ratio 1 part incress per 10 liters 1 part of ratio - - - - - - - > 10 liters 7 part of ratio - - - - - - - > 70 liters c )\"",
        "options": "a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70",
        "correct": "c",
        "annotated_formula": "divide(multiply(10, divide(const_2.0, const_3.0)), subtract(divide(3, add(5, 2)), multiply(divide(2, add(5, 2)), divide(2, 5))))",
        "linear_formula": "add(n4,n1)|divide(n3,n4)|divide(n0,#0)|divide(n1,#0)|multiply(n2,#1)|multiply(#3,#1)|subtract(#2,#5)|divide(#4,#6)|",
        "category": "general"
    },
    {
        "Problem": "students of 3 different classes appeared in common examination . pass average of 10 students of first class was 45 % , pass average of 15 students of second class was 60 % and pass average of 25 students of third class was 80 % then what will be the pass average of all students of 3 classes ?",
        "Rationale": "solution : sum of pass students of first , second and third class , = ( 45 % of 10 ) + ( 60 % of 15 ) + ( 80 % of 25 ) = 4.5 + 9 + 20 = 33.5 total students appeared , = 10 + 15 + 25 = 50 pass average , = 33.5 * 100 / 50 = 67 % . answer : option c",
        "options": "a ) 74 % , b ) 75 % , c ) 67 % , d ) 72 % , e ) none",
        "correct": "c",
        "annotated_formula": "divide(multiply(add(add(divide(multiply(10, 45), const_100), divide(multiply(15, 60), const_100)), divide(multiply(25, 80), const_100)), const_100), add(add(10, 15), 25))",
        "linear_formula": "add(n1,n3)|multiply(n1,n2)|multiply(n3,n4)|multiply(n5,n6)|add(n5,#0)|divide(#1,const_100)|divide(#2,const_100)|divide(#3,const_100)|add(#5,#6)|add(#8,#7)|multiply(#9,const_100)|divide(#10,#4)",
        "category": "general"
    },
    {
        "Problem": "34.94 + 240.016 + 23.98 = ?",
        "Rationale": "34.94 240.016 + 23.98 - - - - - - - - 298.936 answer is a .",
        "options": "a ) 298.936 , b ) 298.694 , c ) 289.496 , d ) 289.469 , e ) 298.964",
        "correct": "a",
        "annotated_formula": "add(add(34.94, 240.016), 23.98)",
        "linear_formula": "add(n0,n1)|add(n2,#0)",
        "category": "general"
    },
    {
        "Problem": "meera purchased two 3 items from a shop . total price for 3 items is rs . 2000 / - she have given rs . 3000 / - what is the balance amount meera got ?",
        "Rationale": "total cost of items : 2000 / - amount paid : 3000 / - balance receivable : 3000 - 2000 = 1000 / - answer is b",
        "options": "a ) 650 , b ) 1000 , c ) 1500 , d ) 800 , e ) 750",
        "correct": "b",
        "annotated_formula": "subtract(3000, 2000)",
        "linear_formula": "subtract(n3,n2)",
        "category": "general"
    },
    {
        "Problem": "what is the smallest integer e greater than 1 that leaves a remainder of 1 when divided by any of the integers 6 , 8 , and 10 ?",
        "Rationale": "or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder e as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 68 and 10 is 121 . c",
        "options": "a ) 21 , b ) 41 , c ) e = 121 , d ) 241 , e ) 481",
        "correct": "c",
        "annotated_formula": "add(lcm(10, lcm(6, 8)), const_1)",
        "linear_formula": "lcm(n2,n3)|lcm(n4,#0)|add(#1,const_1)",
        "category": "general"
    },
    {
        "Problem": "in 60 litres mixture milk and water are in the ratio 3 : 1 . after adding how many liters of water its ratio will become 3 : 2",
        "Rationale": "\"milk quantity = 3 / 4 * 60 = 45 water quantity = 60 - 45 = 15 new ratio of m : w = 45 : 15 + x = 3 : 2 45 + 3 x = 90 x = 15 answer is b\"",
        "options": "a ) 1 , b ) 15 , c ) 7 , d ) 5 , e ) 12",
        "correct": "b",
        "annotated_formula": "multiply(subtract(divide(multiply(divide(3, add(3, 1)), 60), divide(3, add(3, 2))), 60), divide(add(const_10, 1), const_10))",
        "linear_formula": "add(const_10,n2)|add(n1,n2)|add(n1,n4)|divide(#0,const_10)|divide(n1,#1)|divide(n1,#2)|multiply(n0,#4)|divide(#6,#5)|subtract(#7,n0)|multiply(#3,#8)|",
        "category": "general"
    },
    {
        "Problem": "ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio r of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?",
        "Rationale": "\"say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio r of ann ' s time to bob ' s time is 3 : 2 . answer : b .\"",
        "options": "a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8",
        "correct": "b",
        "annotated_formula": "divide(const_2, add(const_1, divide(const_1, const_3)))",
        "linear_formula": "divide(const_1,const_3)|add(#0,const_1)|divide(const_2,#1)|",
        "category": "general"
    },
    {
        "Problem": "if length of a rectangle is equal to side of a square and breadth of rectangle is half of length . if area of square is 36 sq . m . calculate the area of rectangle ?",
        "Rationale": "side of square = \u221a 36 = 6 m . length = 6 m and breadth = 3 m area of rectangle = 6 * 3 = 18 sq . m answer a",
        "options": "['a ) 18', 'b ) 20', 'c ) 27', 'd ) 32', 'e ) 25']",
        "correct": "a",
        "annotated_formula": "multiply(sqrt(36), divide(sqrt(36), const_2))",
        "linear_formula": "sqrt(n0)|divide(#0,const_2)|multiply(#1,#0)",
        "category": "geometry"
    },
    {
        "Problem": "in a basketball game , dhoni scored 30 points more than dravid , but only half as many points as shewag . if the 3 players scored a combined total of 150 points , how many points did dhoni score ?",
        "Rationale": "let dravid scored point = x then dhoni scored = x + 30 shewag scored = 2 * ( x + 30 ) = 2 x + 60 as given , x + x + 30 + 2 x + 60 = 150 points 4 x + 90 = 150 x = 150 - 90 / 4 = 15 so dhoni scored = x + 30 i . e ) 15 + 30 = 45 answer : e",
        "options": "a ) 50 , b ) 52 , c ) 35 , d ) 40 , e ) 45",
        "correct": "e",
        "annotated_formula": "divide(add(150, 30), add(add(const_2, const_1), const_1))",
        "linear_formula": "add(n0,n2)|add(const_1,const_2)|add(#1,const_1)|divide(#0,#2)",
        "category": "general"
    },
    {
        "Problem": "on a partly cloudy day , milton decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction of the total distance did he cover while the sun was shining on him ?",
        "Rationale": "if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : d",
        "options": "a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 7 , e ) 1 / 3",
        "correct": "d",
        "annotated_formula": "divide(1, divide(add(add(2.8, add(2.8, 2.8)), add(2.8, 2.8)), const_2))",
        "linear_formula": "add(n1,n1)|add(n1,#0)|add(#1,#0)|divide(#2,const_2)|divide(n0,#3)",
        "category": "general"
    },
    {
        "Problem": "if 35 % of a number is 12 less than 50 % of that number , then the number is ?",
        "Rationale": "\"let the number be x . then , 50 % of x - 35 % of x = 12 50 / 100 x - 35 / 100 x = 12 x = ( 12 * 100 ) / 15 = 80 . answer : d\"",
        "options": "a ) 40 , b ) 50 , c ) 60 , d ) 80 , e ) 70",
        "correct": "d",
        "annotated_formula": "divide(12, divide(subtract(50, 35), const_100))",
        "linear_formula": "subtract(n2,n0)|divide(#0,const_100)|divide(n1,#1)|",
        "category": "gain"
    },
    {
        "Problem": "the average of 10 consecutive odd numbers is 22 . what is the sum of the first 3 numbers ?",
        "Rationale": "\"22 = ( n + n + 2 + n + 4 + . . . + ( n + 18 ) ) / 10 22 = ( 10 n + ( 2 + 4 + . . . + 18 ) ) / 10 220 = 10 n + 2 ( 1 + 2 + . . . + 9 ) 220 = 10 n + 2 ( 9 ) ( 10 ) / 2 220 = 10 n + 90 220 - 90 = 10 n 130 = 10 n n = 13 so the first three numbers are 13 , 15 , 17 13 + 15 + 17 = 45 option b\"",
        "options": "a ) 13 , b ) 45 , c ) 17 , d ) 220 , e ) 90",
        "correct": "b",
        "annotated_formula": "add(divide(subtract(multiply(22, 10), add(add(add(add(const_1, add(add(add(add(add(const_1, const_2), const_1), const_1), const_1), const_1)), const_1), const_1), add(add(add(add(const_1, add(add(add(add(add(const_1, const_2), const_1), const_1), const_1), const_1)), const_1), const_1), const_1))), 10), add(add(add(add(const_1, const_2), const_1), const_1), const_1))",
        "linear_formula": "add(const_1,const_2)|multiply(n0,n1)|add(#0,const_1)|add(#2,const_1)|add(#3,const_1)|add(#4,const_1)|add(#5,const_1)|add(#6,const_1)|add(#7,const_1)|add(#8,const_1)|add(#8,#9)|subtract(#1,#10)|divide(#11,n0)|add(#4,#12)|",
        "category": "general"
    },
    {
        "Problem": "4 out of 8 employees are capable of doing a certain task . sixty percent of the 5 employees , including the 4 who are capable , are assigned to a project involving this task . what percentage of employees assigned to the project are not capable ?",
        "Rationale": "given 50 % of 8 employees including 4 who are capable of doing task . 60 % of 5 employeees = 50 / 100 * 4 = 4 employees = = = > 4 employees who are capable of doing the task and no one employee who is not capable . percentage of employees assigned who are not capable answer : e",
        "options": "a ) 43.33 % , b ) 33.33 % , c ) 13.33 % , d ) 38.33 % , e ) none",
        "correct": "e",
        "annotated_formula": "multiply(divide(subtract(5, 4), 5), const_100)",
        "linear_formula": "subtract(n2,n0)|divide(#0,n2)|multiply(#1,const_100)",
        "category": "general"
    },
    {
        "Problem": "the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places",
        "Rationale": "\"let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( \u220f ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : option e\"",
        "options": "a ) 34 , b ) 35 , c ) 56 , d ) 67 , e ) 23.57",
        "correct": "e",
        "annotated_formula": "divide(circumface(divide(square_edge_by_perimeter(rectangle_perimeter(16, 14)), const_2)), const_2)",
        "linear_formula": "rectangle_perimeter(n0,n1)|square_edge_by_perimeter(#0)|divide(#1,const_2)|circumface(#2)|divide(#3,const_2)|",
        "category": "geometry"
    },
    {
        "Problem": "a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be :",
        "Rationale": "\"let height of the building be x meters 40.25 : 28.75 : : 17.5 < = > 40.25 x x = 28.75 x 17.5 x = 28.75 x 17.5 / 40.25 x = 12.5 answer : option b\"",
        "options": "a ) 10 m , b ) 12.5 m , c ) 17.5 m , d ) 21.25 m , e ) none",
        "correct": "b",
        "annotated_formula": "multiply(28.75, divide(17.5, 40.25))",
        "linear_formula": "divide(n0,n1)|multiply(n2,#0)|",
        "category": "physics"
    },
    {
        "Problem": "the l . c . m of 22 , 54 , 108 , 135 and 198 is",
        "Rationale": "answer : c ) 5940",
        "options": "a ) 5942 , b ) 2887 , c ) 5940 , d ) 2888 , e ) 28881",
        "correct": "c",
        "annotated_formula": "multiply(multiply(multiply(multiply(const_2, const_2), multiply(multiply(const_3, const_3), const_3)), divide(divide(divide(135, const_3), const_3), const_3)), divide(22, const_2))",
        "linear_formula": "divide(n0,const_2)|divide(n3,const_3)|multiply(const_2,const_2)|multiply(const_3,const_3)|divide(#1,const_3)|multiply(#3,const_3)|divide(#4,const_3)|multiply(#2,#5)|multiply(#6,#7)|multiply(#0,#8)",
        "category": "physics"
    },
    {
        "Problem": "a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction t of the sum of the 21 numbers in the list ?",
        "Rationale": "\"this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction t of n to the total would be 4 a / 24 a or 1 / 6 answer b\"",
        "options": "a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21",
        "correct": "b",
        "annotated_formula": "divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3))",
        "linear_formula": "divide(n2,n1)|multiply(const_1,const_1)|add(n0,#0)|divide(#2,n1)|multiply(#3,const_2)|subtract(#4,n1)|subtract(#5,const_3)|divide(#1,#6)|",
        "category": "general"
    },
    {
        "Problem": "if ' a ' completes a piece of work in 3 days , which ' b ' completes it in 5 days and ' c ' takes 10 days to complete the same work . how long will they take to complete the work , if they work together ?",
        "Rationale": "explanation : hint : a ' s one day work = 1 / 3 b ' s one day work = 1 / 5 c ' s one day work = 1 / 10 ( a + b + c ) ' s one day work = 1 / 3 + 1 / 5 + 1 / 10 = 1 / 1.5 hence , a , b & c together will take 1.5 days to complete the work . answer is a",
        "options": "a ) 1.5 days , b ) 4.5 days , c ) 7 days , d ) 9.8 days , e ) 9 days",
        "correct": "a",
        "annotated_formula": "add(subtract(3, const_2), divide(5, 10))",
        "linear_formula": "divide(n1,n2)|subtract(n0,const_2)|add(#0,#1)",
        "category": "physics"
    },
    {
        "Problem": "if a * b = 2 a - 3 b + ab , then 3 * 5 + 5 * 3 is equal to :",
        "Rationale": "\"explanation : 3 * 5 + 5 * 3 = ( 2 * 3 - 3 * 5 + 3 * 5 ) + ( 2 * 5 - 3 * 3 + 5 * 3 ) = ( 6 + 10 - 9 + 15 ) = 22 . answer : a ) 22\"",
        "options": "a ) 22 , b ) 37 , c ) 38 , d ) 398 , e ) 72",
        "correct": "a",
        "annotated_formula": "add(multiply(2, 3), multiply(3, 5))",
        "linear_formula": "multiply(n0,n1)|multiply(n1,n3)|add(#0,#1)|",
        "category": "general"
    },
    {
        "Problem": "the ratio of the ages of maala and kala is 3 : 5 . the total of their ages is 3.2 decades . the proportion of their ages after 0.8 decades will be [ 1 decade = 10 years ]",
        "Rationale": "let , maala \u2019 s age = 3 a and kala \u2019 s age = 5 a then 3 a + 5 a = 32 a = 4 maala \u2019 s age = 12 years and kala \u2019 s age = 20 years proportion of their ages after 8 is = ( 12 + 8 ) : ( 20 + 8 ) = 20 : 28 = 5 : 7 answer : b",
        "options": "a ) 6 : 5 , b ) 5 : 7 , c ) 4 : 5 , d ) 7 : 9 , e ) 3 : 6",
        "correct": "b",
        "annotated_formula": "divide(add(multiply(divide(multiply(3.2, 10), add(3, 5)), 3), multiply(0.8, 10)), add(multiply(5, divide(multiply(3.2, 10), add(3, 5))), multiply(0.8, 10)))",
        "linear_formula": "add(n0,n1)|multiply(n2,n5)|multiply(n3,n5)|divide(#1,#0)|multiply(n0,#3)|multiply(n1,#3)|add(#4,#2)|add(#5,#2)|divide(#6,#7)",
        "category": "general"
    },
    {
        "Problem": "a rectangular box measures internally 1.6 m long , 1 m broad and 60 cm deep . the number of cubical box each of edge 20 cm that can be packed inside the box is :",
        "Rationale": "\"explanation : number of blocks = ( 160 x 100 x 60 / 20 x 20 x 20 ) = 120 answer : d\"",
        "options": "a ) 30 , b ) 60 , c ) 90 , d ) 120 , e ) 140",
        "correct": "d",
        "annotated_formula": "volume_rectangular_prism(divide(1.6, divide(20, const_100)), divide(1, divide(20, const_100)), divide(divide(60, const_100), divide(20, const_100)))",
        "linear_formula": "divide(n3,const_100)|divide(n2,const_100)|divide(n0,#0)|divide(n1,#0)|divide(#1,#0)|volume_rectangular_prism(#2,#3,#4)|",
        "category": "physics"
    },
    {
        "Problem": "bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p & q , having each turn together to fill the empty drum ?",
        "Rationale": "if caoacity of q is x units , then capacity of p is 3 x and capacity of drum is 60 * 3 x = 180 x . it will take 180 x / 4 x = 45 turns it will take for both the buckets p & q , having each turn together to fill the empty drum . answer : a",
        "options": "a ) 45 , b ) 53 , c ) 54 , d ) 46 , e ) 63",
        "correct": "a",
        "annotated_formula": "divide(const_1, add(divide(const_1, 60), divide(const_1, multiply(60, const_3))))",
        "linear_formula": "divide(const_1,n0)|multiply(n0,const_3)|divide(const_1,#1)|add(#0,#2)|divide(const_1,#3)",
        "category": "other"
    },
    {
        "Problem": "find compound interest on rs . 7500 at 4 % per year for 2 years , compounded annually .",
        "Rationale": "\"amount = rs [ 7500 * ( 1 + ( 4 / 100 ) 2 ] = rs ( 7500 * ( 26 / 25 ) * ( 26 / 25 ) ) = rs . 8112 . therefore , compound interest = rs . ( 8112 - 7500 ) = rs . 612 . answer is e .\"",
        "options": "a ) 812 , b ) 712 , c ) 412 , d ) 512 , e ) 612",
        "correct": "e",
        "annotated_formula": "subtract(add(add(7500, divide(multiply(7500, 4), const_100)), divide(multiply(add(7500, divide(multiply(7500, 4), const_100)), 4), const_100)), 7500)",
        "linear_formula": "multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)|multiply(n1,#2)|divide(#3,const_100)|add(#2,#4)|subtract(#5,n0)|",
        "category": "gain"
    },
    {
        "Problem": "6 computers , each working at the same constant rate , together can process a certain amount of data in 9 days . how many additional computers , each working at the same constant rate , will be needed to process the same amount of data in 6 days ?",
        "Rationale": "explanation : if six computers require 9 days to process the data , thats a total of 54 computer - days the product of 6 and 9 . if you change the number of computers or the number of days , 54 will have to remain the product , whether that means 54 days of one computer or one day with 54 computers . in 6 days , the number of computers is : 6 c = 54 c = 9 9 computers is 3 more than the 6 that it took to do the job in 9 days , so the correct choice is ( a ) .",
        "options": "a ) 3 , b ) 5 , c ) 6 , d ) 9 , e ) 12",
        "correct": "a",
        "annotated_formula": "subtract(divide(multiply(6, divide(const_1, 6)), divide(const_1, 9)), 6)",
        "linear_formula": "divide(const_1,n0)|divide(const_1,n1)|multiply(n0,#0)|divide(#2,#1)|subtract(#3,n0)",
        "category": "physics"
    },
    {
        "Problem": "determine the value of ( 27 / 31 * 31 / 27 ) * 3",
        "Rationale": "\"solution : both fractions should be reduced before performing arithmetic operations . we get ( 27 / 31 * 31 / 27 ) 3 = 1 * 3 = 3 answer d\"",
        "options": "a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) none",
        "correct": "d",
        "annotated_formula": "divide(add(subtract(add(27, multiply(31, 27)), subtract(3, 27)), const_1), 31)",
        "linear_formula": "multiply(n0,n1)|subtract(n4,n3)|add(n3,#0)|subtract(#2,#1)|add(#3,const_1)|divide(#4,n2)|",
        "category": "general"
    },
    {
        "Problem": "a rectangular grassy plot 110 m by 65 cm has a gravel path . 5 cm wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . mt",
        "Rationale": "\"explanation : area of theplot = 110 * 65 = 7150 sq m area of the plot excluding the path = ( 110 - 5 ) * ( 65 - 5 ) = 6300 sq m area of the path = 7150 - 6300 = 850 sq m cost of gravelling the path = 850 * 80 / 100 = 680 rs answer : a ) 680 rs\"",
        "options": "a ) 680 , b ) 378 , c ) 267 , d ) 299 , e ) 271",
        "correct": "a",
        "annotated_formula": "multiply(divide(80, const_100), subtract(multiply(110, 65), multiply(subtract(110, 5), subtract(65, 5))))",
        "linear_formula": "divide(n3,const_100)|multiply(n0,n1)|subtract(n0,n2)|subtract(n1,n2)|multiply(#2,#3)|subtract(#1,#4)|multiply(#0,#5)|",
        "category": "physics"
    },
    {
        "Problem": "in 12 pumps can raise 1218 tons of water in 11 days of 9 hrs each , how many pumps will raise 2030 tons of water in 12 days of 11 hrs each ?",
        "Rationale": "explanation : pumps work time 12 1218 99 x 2030 132 = > 1218 / ( 912 * 99 ) = 2020 / ( x \u00d7 132 ) = > x = 15 pumps answer : option b",
        "options": "a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 22",
        "correct": "b",
        "annotated_formula": "divide(multiply(multiply(multiply(12, 11), 9), 2030), multiply(multiply(12, 11), 1218))",
        "linear_formula": "multiply(n0,n2)|multiply(n3,#0)|multiply(n1,#0)|multiply(n4,#1)|divide(#3,#2)",
        "category": "physics"
    },
    {
        "Problem": "one of the longest sides of the triangle is 20 m , the other side is 10 m . area of the triangle is 80 m ^ 2 . what is the another side of the triangle ?",
        "Rationale": "base of triangle is 20 and area is 80 therefore height = 2 * 80 / 20 = 8 . now one side of triangle is of 10 . so we can get the point were the base is divided by applying pythagoras therm so division pt = sqrt ( 10 ^ 2 - 8 ^ 2 ) = sqrt ( 36 ) = 6 threfore other half is 14 . now second side = sqrt ( 14 ^ 2 + 8 ^ 2 ) = sqrt ( 260 ) = 2 sqrt ( 65 ) answer : e",
        "options": "['a ) 2 sqrt ( 61 )', 'b ) 2 sqrt ( 62 )', 'c ) 2 sqrt ( 63 )', 'd ) 2 sqrt ( 64 )', 'e ) 2 sqrt ( 65 )']",
        "correct": "e",
        "annotated_formula": "sqrt(add(power(divide(multiply(80, const_2), 20), const_2), power(subtract(20, sqrt(subtract(power(10, const_2), power(divide(multiply(80, const_2), 20), const_2)))), const_2)))",
        "linear_formula": "multiply(n2,const_2)|power(n1,const_2)|divide(#0,n0)|power(#2,const_2)|subtract(#1,#3)|sqrt(#4)|subtract(n0,#5)|power(#6,const_2)|add(#3,#7)|sqrt(#8)",
        "category": "geometry"
    },
    {
        "Problem": "anne earned $ 3 an hour baby - sitting , and $ 4 an hour working in the garden . last week she did baby - sitting for 5 hours and garden work for 3 hours . how much more money does she need to buy a game that costs $ 35 ?",
        "Rationale": "5 x $ 3 = $ 15 for baby - sitting 3 x $ 4 = $ 12 for garden work $ 15 + $ 12 = $ 27 she has $ 35 - $ 27 = $ 8 more needed to buy the game correct answer a",
        "options": "a ) $ 8 , b ) $ 12 , c ) $ 6 , d ) $ 21 , e ) $ 10",
        "correct": "a",
        "annotated_formula": "subtract(35, add(multiply(5, 3), multiply(3, 4)))",
        "linear_formula": "multiply(n0,n2)|multiply(n0,n1)|add(#0,#1)|subtract(n4,#2)",
        "category": "general"
    },
    {
        "Problem": "if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 4 flips and not on the last flip ?",
        "Rationale": "( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 32 answer : b",
        "options": "a ) 1 / 8 , b ) 1 / 32 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 16",
        "correct": "b",
        "annotated_formula": "divide(const_1, power(2, 5))",
        "linear_formula": "power(n1,n2)|divide(const_1,#0)",
        "category": "probability"
    },
    {
        "Problem": "two brothers take the same route to school on their bicycles , one gets to school in 25 minutes and the second one gets to school in 36 minutes . the ratio of their speeds is",
        "Rationale": "solution let us name the brothers as a and b . = ( a ' s speed ) : ( b ' s speed ) = \u00e2 \u02c6 \u0161 b : \u00e2 \u02c6 \u0161 a = \u00e2 \u02c6 \u0161 25 : \u00e2 \u02c6 \u0161 36 = 5 : 6 answer d",
        "options": "a ) 4 : 5 , b ) 1 : 2 , c ) 6 : 7 , d ) 5 : 6 , e ) none",
        "correct": "d",
        "annotated_formula": "divide(sqrt(25), sqrt(36))",
        "linear_formula": "sqrt(n0)|sqrt(n1)|divide(#0,#1)",
        "category": "physics"
    },
    {
        "Problem": "the ratio of the cost price and the selling price is 4 : 5 . the profit percent is ?",
        "Rationale": "\"let c . p . = rs . 4 x . then , s . p . = rs . 5 x gain = ( 5 x - 4 x ) = rs . x gain % = ( x * 100 ) / 4 x = 25 % . answer : c\"",
        "options": "a ) 17 , b ) 56 , c ) 25 , d ) 28 , e ) 12",
        "correct": "c",
        "annotated_formula": "multiply(subtract(divide(5, 4), const_1), const_100)",
        "linear_formula": "divide(n1,n0)|subtract(#0,const_1)|multiply(#1,const_100)|",
        "category": "gain"
    },
    {
        "Problem": "what is the value of ( 44444445 * 88888885 * 44444442 + 44444438 ) / 44444444 ^ 2",
        "Rationale": "\"ans : a let x = 44444444 ( x + 1 ) \u00d7 ( 2 x \u2212 3 ) \u00d7 ( x \u2212 2 ) + ( x \u2212 6 ) x 2 ( x + 1 ) \u00d7 ( 2 x \u2212 3 ) \u00d7 ( x \u2212 2 ) + ( x \u2212 6 ) x 2 ( x 2 \u2212 x \u2212 2 ) \u00d7 ( 2 x \u2212 3 ) + ( x \u2212 6 ) x 2 ( x 2 \u2212 x \u2212 2 ) \u00d7 ( 2 x \u2212 3 ) + ( x \u2212 6 ) x 2 2 x 3 \u2212 2 x 2 \u2212 4 x \u2212 3 x 2 + 3 x + 6 + x \u2212 6 x 22 x 3 \u2212 2 x 2 \u2212 4 x \u2212 3 x 2 + 3 x + 6 + x \u2212 6 x 2 2 x 3 \u2212 5 x 2 x 2 = 2 x \u2212 52 x 3 \u2212 5 x 2 x 2 = 2 x \u2212 5 substituting the value of x in 2 x - 5 , we get 88888883 answer : a\"",
        "options": "a ) 88888883 , b ) 88888827 , c ) 16992677 , d ) 88888237 , e ) 88888182",
        "correct": "a",
        "annotated_formula": "power(44444445, negate(88888885))",
        "linear_formula": "negate(n1)|power(n0,#0)|",
        "category": "general"
    },
    {
        "Problem": "4 shepherds were watching over the flocks and they were commenting on how many sheep they each had . if ram had 3 more sheep than he would have one less than rahul . wheras akar has the same number as the other 3 shepherds put togeher . if john had 3 less sheep he would have exactly trile the number of ram . if they were evenly distributed if they would each have 11 seep how many sheep did ram have ?",
        "Rationale": "akar has = ram + rahul + john after evenly distribution each has 11 . so , total no . is 44 so , akar has = 22 & ram + rahul + john = 22 also ram = rahul - 4 & john - 3 = 3 * ram solving these we get the sol . answer : b",
        "options": "a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6",
        "correct": "b",
        "annotated_formula": "divide(subtract(multiply(11, const_2), add(4, 3)), add(4, const_1))",
        "linear_formula": "add(n0,n1)|add(n0,const_1)|multiply(n4,const_2)|subtract(#2,#0)|divide(#3,#1)",
        "category": "general"
    }
]