Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and other digits are correct , then the correct answer would be : | "987 = 3 x 7 x 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 - - > sum of digits = 28 , not divisible by 3 555181 sum of digits = 25 , not divisible by 3 555681 is divisible by each one of 3 , 7 , 47 . 556581 sum of digits = 30 , not divisible by 7 555581 sum of digits = 29 , not divi... | a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) 555581 | c | multiply(subtract(subtract(divide(559981, 987), const_4), const_0_33), 987) | divide(n1,n0)|subtract(#0,const_4)|subtract(#1,const_0_33)|multiply(n0,#2)| | other |
given f ( x ) = 2 x – 3 , for what value of x does 2 * [ f ( x ) ] – 11 = f ( x – 2 ) ? | "2 ( 2 x - 3 ) - 11 = 2 ( x - 2 ) - 3 2 x = 10 x = 5 the answer is d ." | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | d | divide(subtract(add(multiply(2, 3), 11), add(multiply(2, 2), 3)), subtract(multiply(2, 2), multiply(2, const_1))) | multiply(n1,n2)|multiply(n4,n0)|multiply(n0,n2)|multiply(n0,const_1)|add(n3,#0)|add(n1,#1)|subtract(#2,#3)|subtract(#4,#5)|divide(#7,#6)| | general |
pipe a fills a tank of capacity 750 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute a... | "in one cycle they fill 40 + 30 - 20 = 50 liters 750 = 50 * n = > n = 15 here n = number of cycles . total time = 15 * 3 = 45 as in one cycle there are 3 minutes . thus 45 minutes answer : a" | a ) 45 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these | a | multiply(divide(750, subtract(add(40, 30), 20)), const_3) | add(n1,n2)|subtract(#0,n3)|divide(n0,#1)|multiply(#2,const_3)| | physics |
the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 21 ? | "$ 21 = 3 * $ 6 + $ 3 the number of doughnuts is 3 * 12 + 3 = 39 the answer is d ." | a ) 33 , b ) 35 , c ) 37 , d ) 39 , e ) 41 | d | multiply(divide(21, 6), const_12) | divide(n2,n1)|multiply(#0,const_12)| | general |
all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 150 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial qua... | "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 150 liters was transferred from cont... | a ) 1200 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372 | a | divide(150, subtract(inverse(const_2), subtract(const_1, divide(62.5, const_100)))) | divide(n0,const_100)|inverse(const_2)|subtract(const_1,#0)|subtract(#1,#2)|divide(n1,#3)| | general |
a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 17 seconds . what is the length of the platform in meters ? | "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 17 * 20 = 340 = length of train length of platform = 600 - 340 = 260 answer : b" | a ) 240 meters , b ) 260 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined | b | subtract(multiply(divide(multiply(72, const_1000), const_3600), 30), multiply(divide(multiply(72, const_1000), const_3600), 17)) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|multiply(n2,#1)|subtract(#2,#3)| | physics |
two numbers have a h . c . f of 14 and a product of two numbers is 2562 . find the l . c . m of the two numbers ? | "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2562 / 14 = 183 . answer : e" | a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 183 | e | divide(2562, 14) | divide(n1,n0)| | physics |
a can complete a work in 10 days and b can do the same work in 5 days . if a after doing 2 days , leaves the work , find in how many days b will do the remaining work ? | "the required answer = ( 10 - 2 ) * 5 / 10 = 40 / 10 = 4 days answer is b" | a ) 2 days , b ) 4 days , c ) 6 days , d ) 7 days , e ) 10 days | b | add(multiply(10, 2), divide(10, 2)) | divide(n0,n2)|multiply(n0,n2)|add(#0,#1)| | physics |
let the number which when multiplied by 13 is increased by 180 . | "solution let the number be x . then , 13 x - x = 180 ‹ = › 12 x = 180 x ‹ = › 15 . answer c" | a ) 14 , b ) 20 , c ) 15 , d ) 28 , e ) 30 | c | divide(180, subtract(13, const_1)) | subtract(n0,const_1)|divide(n1,#0)| | general |
the diagonals of a rhombus are 20 cm and 25 cm . find its area ? | "1 / 2 * 20 * 25 = 250 answer : c" | a ) 158 , b ) 129 , c ) 250 , d ) 123 , e ) 117 | c | rhombus_area(20, 25) | rhombus_area(n0,n1)| | geometry |
10 ^ ( 655 ) ã · 10 ^ ( 652 ) = ? | "10 ^ ( 655 ) ã · 10 ^ ( 652 ) = 10 ^ ( 655 - 652 ) = 10 ^ 3 = 1000 answer : e" | a ) 1 , b ) 100 , c ) 10000 , d ) 100000 , e ) 1000 | e | power(10, subtract(655, 652)) | subtract(n1,n3)|power(n0,#0)| | general |
if 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ? | if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so... | a ) 110 , b ) 130 , c ) 150 , d ) 170 , e ) 190 | e | divide(factorial(20), multiply(factorial(subtract(20, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4) | physics |
the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 12 km / hr respectively . they will meet for the first time in ? | "clearly , the two will meet when they are 1000 m apart to be 20 + 12 = 32 km apart , they take 1 hour to be 1000 m apart , they take 32 * 1000 / 1000 = 32 min . answer is a" | a ) 32 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min | a | add(20, 12) | add(n1,n2)| | general |
an escalator moves towards the top level at the rate of 15 ft . sec and its length is 180 feet . if a person walks on the moving escalator at the rate of 3 feet per second towards the top level , how much time does he take to cover the entire length . | "explanation : time taken to cover the entire length = tot . dist / resultant speed = 180 / ( 15 + 3 ) = 10 sec answer : e" | a ) 12 sec , b ) 20 sec , c ) 15 sec , d ) 18 sec , e ) 10 sec | e | divide(180, add(15, 3)) | add(n0,n2)|divide(n1,#0)| | gain |
a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 335,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ? | "0.04 x + 0.09 y = 335000 [ 1 ] 0.04 x = 0.80 * 335000 = 268000 [ 2 ] 268000 + 0.09 y = 320000 - - > 0.09 y = 67000 [ 3 ] 268000 / 12 = 22333.3333 [ 4 ] 67000 / 12 = 5583.333 [ 5 ] adding [ 4,5 ] we get : 27916 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.395 , ans a" | a ) $ 1,395 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796 | a | subtract(9, multiply(4, const_2)) | multiply(n0,const_2)|subtract(n1,#0)| | general |
a train 200 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ? | "s = ( 200 + 300 ) / 45 = 500 / 45 * 18 / 5 = 40 answer : d" | a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50 | d | divide(divide(add(200, 300), const_1000), divide(45, const_3600)) | add(n0,n1)|divide(n2,const_3600)|divide(#0,const_1000)|divide(#2,#1)| | physics |
john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 72000 , what is their combined tax rate ? | "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 128000 = 72 / 128 = 9 ... | a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 % | d | multiply(divide(add(multiply(divide(30, const_100), 56000), multiply(divide(40, const_100), 72000)), add(72000, 56000)), const_100) | add(n2,n3)|divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#1)|multiply(n3,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)| | gain |
john ' s bank ' s saving amount is decreased 30 % due to loan payment and current balance is rs . 7000 . find the actual balance before deduction ? | "cp * ( 70 / 100 ) = 7000 cp = 100 * 100 = > cp = 10000 answer : e" | a ) 8000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 10000 | e | add(divide(multiply(7000, 30), const_100), 7000) | multiply(n0,n1)|divide(#0,const_100)|add(n1,#1)| | gain |
during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 6 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ? | kim purchased 20 gallons of gas . she paid for 6 + 0.9 * 14 = 18.6 gallons , so the overall discount she got was 1.4 / 20 = 7 % . isabella purchased 25 gallons of gas . she paid for 6 + 0.9 * 19 = 23.1 gallons , so the overall discount she got was 1.9 / 25 = 7.6 % . 7.6 is 7.6 / 7 * 100 = 109 % of 7 . answer : c . | a ) 80 % , b ) 100 % , c ) 109 % , d ) 120 % , e ) 140 % | c | multiply(divide(multiply(subtract(const_1, divide(add(divide(multiply(add(10, subtract(10, const_1)), subtract(const_100, const_10)), const_100), 6), 25)), const_100), multiply(subtract(const_1, divide(add(6, divide(multiply(add(10, const_4), subtract(const_100, const_10)), const_100)), 20)), const_100)), const_100) | add(n0,const_4)|subtract(n0,const_1)|subtract(const_100,const_10)|add(n0,#1)|multiply(#0,#2)|divide(#4,const_100)|multiply(#3,#2)|add(n1,#5)|divide(#6,const_100)|add(n1,#8)|divide(#7,n2)|divide(#9,n3)|subtract(const_1,#10)|multiply(#12,const_100)|subtract(const_1,#11)|multiply(#14,const_100)|divide(#15,#13)|multiply(#1... | gain |
a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 3 : 2 : 4 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ? | "originally ( 4 / 9 ) * 1350 = 600 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 600 = 150 more acres were planted with tobacco . the answer is b ." | a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450 | b | subtract(multiply(add(add(multiply(const_100, const_10), multiply(const_3, const_100)), multiply(3, const_10)), divide(3, add(add(3, 2), 2))), multiply(add(add(multiply(const_100, const_10), multiply(const_3, const_100)), multiply(3, const_10)), divide(2, add(add(3, 2), 2)))) | add(n1,n2)|multiply(const_10,const_100)|multiply(const_100,const_3)|multiply(n1,const_10)|add(#1,#2)|add(n2,#0)|add(#4,#3)|divide(n1,#5)|divide(n2,#5)|multiply(#6,#7)|multiply(#6,#8)|subtract(#9,#10)| | other |
if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability w that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ? | only ( x + y ) ( x - y ) pair will give the form x ^ 2 - ( by ) ^ 2 the probability of selecting these two pairs are 1 / 4 * 1 / 3 = 1 / 12 , assuming x + y is picked first , then x - y , but x - y can be picked first followed by x + y . so the probability w = 1 / 12 * 2 = 1 / 6 ans e | a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) w = 1 / 6 | e | divide(const_1, divide(divide(factorial(4), factorial(const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|divide(#0,#1)|divide(#2,#1)|divide(const_1,#3) | general |
if 4 men working 10 hours a day earn rs . 1200 per week , then 9 men working 6 hours a day will earn how much per week ? | "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1200 : x hence 4 * 10 * x = 9 * 6 * 1200 or x = 9 * 6 * 1200 / 4 * 10 = 1620 answer : c" | a ) rs 840 , b ) rs 1320 , c ) rs 1620 , d ) rs 1680 , e ) none of these | c | multiply(divide(multiply(9, 6), multiply(4, 10)), 1200) | multiply(n3,n4)|multiply(n0,n1)|divide(#0,#1)|multiply(n2,#2)| | physics |
a test has 180 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain g... | "a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 p... | a ) 29 , b ) 33 , c ) 35 , d ) 40 , e ) 42 | a | add(add(divide(subtract(180, 40), 5), 1), 1) | subtract(n0,n5)|divide(#0,n1)|add(#1,n2)|add(#2,n2)| | general |
jean drew a gumball at random from a jar of pink and blue gumballs . since the gumball she selected was blue and she wanted a pink one , she replaced it and drew another . the second gumball also happened to be blue and she replaced it as well . if the probability of her drawing the two blue gumballs was 16 / 49 what i... | "the probability of drawing a pink gumball both times is the same . the probability that she drew two blue gumballs = 16 / 49 = ( 4 / 7 ) * ( 4 / 7 ) therefore probability that the next one she draws is pink = 3 / 7 option ( c )" | a ) 1 / 49 , b ) 4 / 7 , c ) 3 / 7 , d ) 16 / 49 , e ) 40 / 49 | c | subtract(const_1, sqrt(divide(16, 49))) | divide(n0,n1)|sqrt(#0)|subtract(const_1,#1)| | general |
if x is 25 percent greater than 88 , then x = | "x = 88 * 1.25 = 110 so the answer is a ." | a ) 110 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108 | a | add(88, multiply(divide(25, const_100), 88)) | divide(n0,const_100)|multiply(n1,#0)|add(n1,#1)| | general |
a cistern 8 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ? | "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 8 x 1.25 ) + 8 x 4 ] = 62 the answer is d ." | a ) 40 , b ) 48 , c ) 54 , d ) 62 , e ) 76 | d | add(add(multiply(8, 4), multiply(const_2, multiply(4, add(1, divide(25, const_100))))), multiply(const_2, multiply(8, add(1, divide(25, const_100))))) | divide(n3,const_100)|multiply(n0,n1)|add(n2,#0)|multiply(n1,#2)|multiply(n0,#2)|multiply(#3,const_2)|multiply(#4,const_2)|add(#1,#5)|add(#7,#6)| | physics |
at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 ¢ . how many oranges must mary put back so that the average price of the pieces o... | "if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 48 , the ratio should be 2 : 3 . mary must put back 5 oranges . the answer is e ." | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | e | divide(subtract(add(multiply(divide(subtract(multiply(60, 10), multiply(54, 10)), subtract(60, 40)), 40), multiply(subtract(10, divide(subtract(multiply(60, 10), multiply(54, 10)), subtract(60, 40))), 60)), multiply(48, 10)), subtract(60, 48)) | multiply(n1,n2)|multiply(n2,n4)|multiply(n2,n5)|subtract(n1,n0)|subtract(n1,n5)|subtract(#0,#1)|divide(#5,#3)|multiply(n0,#6)|subtract(n2,#6)|multiply(n1,#8)|add(#7,#9)|subtract(#10,#2)|divide(#11,#4)| | general |
david has $ 1800 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ? | suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b | a ) $ 200 , b ) $ 500 , c ) $ 600 , d ) $ 800 , e ) $ 1,200 | b | divide(subtract(1800, 800), const_2) | subtract(n0,n1)|divide(#0,const_2) | general |
two cylinders of the radius in the ratio 3 : 5 and heights in the ratio 10 : 9 . then find the volumes ratio ? | π r ( power 2 ) h : π r ( power 2 ) h 9 × 10 : 25 × 9 90 : 225 2 : 5 answer is e . | ['a ) 4 : 5', 'b ) 1 : 5', 'c ) 3 : 5', 'd ) 1.5 : 5', 'e ) 2 : 5'] | e | divide(multiply(power(3, const_2), 10), multiply(power(5, const_2), 9)) | power(n0,const_2)|power(n1,const_2)|multiply(n2,#0)|multiply(n3,#1)|divide(#2,#3) | geometry |
the length of the bridge , which a train 125 m long and traveling at 45 km / hr can cross in 30 sec is ? | "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 125 + x ) / 30 = 25 / 2 x = 250 m . answer : option d" | a ) 235 , b ) 240 , c ) 245 , d ) 250 , e ) 255 | d | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 125) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | physics |
angelo and isabella are both salespersons . in any given week , angelo makes $ 540 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of m... | "let the weekly sales of both = x 540 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 23000 answer : a" | a ) 23,000 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500 | a | floor(divide(divide(subtract(540, multiply(1,000, divide(8, const_100))), subtract(divide(10, const_100), divide(8, const_100))), 1,000)) | divide(n1,const_100)|divide(n3,const_100)|multiply(#0,n2)|subtract(#1,#0)|subtract(n0,#2)|divide(#4,#3)|divide(#5,n2)|floor(#6)| | general |
a computer store offers employees a 30 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 1500 dollars and marked up the price 30 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 30 % off retail price ) as ... | "cost price = 1500 profit = 30 % = 30 % of 1500 = 450 selling price = cp + profit sp = 1950 a discount of 30 % to employees means 30 % off on 1950 so 30 % of 1950 = 585 ans e" | a ) 525 , b ) 545 , c ) 565 , d ) 575 , e ) 585 | e | divide(add(divide(multiply(1500, 30), const_100), 1500), multiply(divide(1500, const_100), const_2)) | divide(n1,const_100)|multiply(n0,n1)|divide(#1,const_100)|multiply(#0,const_2)|add(n1,#2)|divide(#4,#3)| | gain |
car a runs at the speed of 65 km / hr & reaches its destination in 5 hr . car b runs at the speed of 70 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ? | sol . distance travelled by car a = 65 ã — 5 = 325 km distance travelled by car b = 70 ã — 4 = 280 km ratio = 325 / 280 = 65 : 56 e | a ) 11 : 6 , b ) 12 : 7 , c ) 13 : 7 , d ) 15 : 6 , e ) 65 : 56 | e | divide(multiply(65, 5), multiply(70, 4)) | multiply(n0,n1)|multiply(n2,n3)|divide(#0,#1) | physics |
if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 11 a + 11 b ? | "( i ) 9 a - 11 b = 70 ( ii ) 2 a + 22 b = - 70 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ." | a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4 | c | multiply(negate(multiply(divide(70, 2), 2)), 11) | divide(n2,n4)|multiply(#0,n4)|negate(#1)|multiply(n5,#2)| | general |
how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 17 ? | "so i can write this as in - 3 i + 4 < = 17 or in - 3 i < = 13 so n can have - 10 to 16 = 15 true values . . . . a" | a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19 | a | add(multiply(3, 4), const_1) | multiply(n0,n1)|add(#0,const_1)| | general |
there are 250 men and 150 women in a committee , if all will work they will complete 12 units per day , if all men work they will complete 15 units per day , how many units will women complete per day ? | i think there is a mistake in this question . if all men and women together complete 12 units , how only men can do 15 units of work a day ? forgetting about the reality , women can do - 3 units a day . answer : b | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7 | b | subtract(15, 12) | subtract(n3,n2) | physics |
the cash difference between the selling prices of an article at a profit of 10 % and 6 % is rs . 3 . the ratio of the two selling prices is ? | "let c . p . of the article be rs . x . then , required ratio = 110 % of x / 106 % of x = 110 / 106 = 55 / 53 = 55 : 53 answer : b" | a ) 52 : 56 , b ) 55 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 52 : 51 | b | divide(add(const_100, 10), add(const_100, 6)) | add(n0,const_100)|add(n1,const_100)|divide(#0,#1)| | gain |
in order to obtain an income of rs . 650 from 10 % stock at rs . 96 , one must make an investment of | to obtain rs . 10 , investment = rs . 96 . to obtain rs . 650 , investment = = rs . 6240 . answer : b | a ) 5363 , b ) 6240 , c ) 2368 , d ) 1987 , e ) 2732 | b | multiply(divide(96, 10), 650) | divide(n2,n1)|multiply(n0,#0) | gain |
there are 380 doctors and nurses in a hospital . if the ratio of the doctors to the nurses is 8 : 11 , then how many nurses are there in the hospital ? | "given , the ratio of the doctors to the nurses is 8 : 11 number of nurses = 11 / 19 x 380 = 220 answer : e" | a ) 152 , b ) 209 , c ) 57 , d ) 171 , e ) 220 | e | multiply(multiply(8, subtract(11, 8)), 11) | subtract(n2,n1)|multiply(n1,#0)|multiply(n2,#1)| | other |
we invested a total of $ 1,000 . we invested one part of the money at 3 % and the rest of the money at 5 % . the total investment with interest at the end of the year was $ 1,046 . how much money did we invest at 3 % ? | "let x be the money invested at 3 % . 1.03 x + 1.05 ( 1000 - x ) = 1046 . 0.02 x = 1050 - 1046 . 0.02 x = 4 . 2 x = 400 . x = 200 . the answer is a ." | a ) $ 200 , b ) $ 240 , c ) $ 280 , d ) $ 320 , e ) $ 360 | a | divide(subtract(multiply(multiply(const_100, multiply(add(const_2, const_3), const_2)), add(divide(5, const_100), const_1)), add(add(multiply(const_100, multiply(add(const_2, const_3), const_2)), multiply(multiply(add(const_2, const_3), const_2), 3)), multiply(const_2, const_3))), subtract(add(divide(5, const_100), con... | add(const_2,const_3)|divide(n2,const_100)|divide(n1,const_100)|multiply(const_2,const_3)|add(#1,const_1)|add(#2,const_1)|multiply(#0,const_2)|multiply(#6,const_100)|multiply(#6,const_4)|subtract(#4,#5)|add(#7,#8)|multiply(#4,#7)|add(#10,#3)|subtract(#11,#12)|divide(#13,#9)| | gain |
a 5 - digit number divisible by 3 is to be formed using numerical 0 , 1 , 2 , 3 , 4 and 5 without repetition . the total number e of ways this can be done is : | we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0 , 1 , 2 , 3 , 4 , 5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good ... | a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 225 | c | add(factorial(5), multiply(4, factorial(4))) | factorial(n0)|factorial(n6)|multiply(n6,#1)|add(#0,#2) | general |
the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 700 per sq . metre . | "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 800 ã — 22 ) = rs . 15400 answer : option b" | a ) s . 15,550 , b ) s . 15,400 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900 | b | multiply(700, multiply(5.5, 4)) | multiply(n0,n1)|multiply(n2,#0)| | physics |
a car takes 6 hours to cover a distance of 270 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | "time = 6 distence = 270 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 270 / 9 = 30 kmph d )" | a ) 10 kmph , b ) 20 kmph , c ) 25 kmph , d ) 30 kmph , e ) 27 kmph | d | divide(270, divide(multiply(6, 3), 2)) | multiply(n0,n2)|divide(#0,n3)|divide(n1,#1)| | physics |
at a supermarket , john spent 1 / 5 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 11 on candy , how much did john spend at the supermarket ? | "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 5 of his money on fresh fruits and vegetables , or ( 1 / 5 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t .... | a ) $ 20 , b ) $ 30 , c ) $ 50 , d ) $ 90 , e ) $ 110 | b | divide(11, subtract(1, add(add(divide(1, 10), divide(1, 3)), divide(1, 5)))) | divide(n0,n5)|divide(n0,n3)|divide(n0,n1)|add(#0,#1)|add(#3,#2)|subtract(n0,#4)|divide(n6,#5)| | general |
a and b finish the job in 15 days . while a , b and c can finish it in 12 days . c alone will finish the job in | "explanation : 12 = ( 15 * x ) / ( 15 + x ) 180 + 12 x = 15 x 3 x = 180 x = 60 answer : option c" | a ) 40 days , b ) 30 days , c ) 60 days , d ) 70 days , e ) 50 days | c | divide(multiply(12, 15), subtract(15, 12)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | physics |
one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 250 cm when it touches the floor on third time . what is the value of the original height ? | "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = ... | a ) 80 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm | c | divide(250, add(const_2, divide(50, const_100))) | divide(n0,const_100)|add(#0,const_2)|divide(n1,#1)| | gain |
a number divided by 44 leaves remainder 17 what is the remainder when same number divided by 8 | "add 44 + 17 = 61 now 61 divided by 8 so we get 5 as reaminder answer : a" | a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 11 | a | divide(subtract(17, 8), subtract(17, 8)) | subtract(n1,n2)|divide(#0,#0)| | general |
a baker makes chocolate cookies and peanut cookies . his recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6 . if he makes exactly 96 cookies , what is the minimum number of chocolate chip cookies he makes ? | "7 c + 6 p = 96 we need to maximize p to minimize c so that the eq is also satisfied try substitution for cp to solve so that eqn is satisfied the least value of c for which equation gets satisfied is 5 i . e . 7 * 6 + 6 * 9 = 42 + 54 = 96 hence e is the answer" | a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 42 | e | multiply(divide(subtract(96, reminder(96, add(7, 6))), add(7, 6)), 7) | add(n0,n1)|reminder(n2,#0)|subtract(n2,#1)|divide(#2,#0)|multiply(n0,#3)| | general |
in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 75 percent of the registered voters who are democrats and 30 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are e... | "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.75 = 45 democrats are expected to vote for candidate a ; 40 * 0.30 = 12 republicans are expected to vote for candidate a . thus total of 45 + 12 = 57 registered voters are expected to vote for candidate a ... | a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 % | e | add(multiply(60, divide(75, const_100)), multiply(subtract(const_100, 60), divide(30, const_100))) | divide(n1,const_100)|divide(n2,const_100)|subtract(const_100,n0)|multiply(n0,#0)|multiply(#1,#2)|add(#3,#4)| | gain |
a rectangular tank needs to be coated with insulation . the tank has dimensions of 4 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ? | "the total surface area is 2 ( 2 * 4 + 4 * 5 + 2 * 5 ) = 76 square feet the total cost is 76 * $ 20 = $ 1520 the answer is a ." | a ) $ 1520 , b ) $ 1640 , c ) $ 1780 , d ) $ 1850 , e ) $ 1960 | a | multiply(surface_rectangular_prism(4, 5, 2), 20) | surface_rectangular_prism(n0,n1,n2)|multiply(n3,#0)| | geometry |
a reduction of 10 % in the price of salt enables a lady to obtain 20 kgs more for rs . 400 , find the original price per kg ? | "answer : 400 * ( 10 / 100 ) = 40 - - - 20 ? - - - 1 = > rs . 2 400 - - - 360 ? - - - 2 = > rs . 2.22 . answer : c" | a ) 2.0 , b ) 2.8 , c ) 2.2 , d ) 2.5 , e ) 3.0 | c | multiply(divide(divide(multiply(divide(10, const_100), 400), 20), multiply(divide(10, const_100), 400)), const_100) | divide(n0,const_100)|multiply(n2,#0)|divide(#1,n1)|divide(#2,#1)|multiply(#3,const_100)| | gain |
in the rectangular coordinate system point o has coordinates ( 0,0 ) and point b has coordinates ( 5,5 ) and if point a is equidistant from points o and b and the area of the triangle oab is 16 , which of the following are the possible coordinates of point a . | area . pngsince a is equidistant from points o and b , then it must be somewhere on the green line ( perpendicular bisector of ob ) . ( 2 , - 6 ) and ( 2,6 ) are not on that line . if a is at ( 0,5 ) or ( 5,0 ) , then the area is 1 / 2 * 5 * 5 = 25 / 2 . thus a must be at ( 2,6 ) . answer : d . | ['a ) ( - 2,6 )', 'b ) ( 0,4 )', 'c ) ( 2 , - 6 )', 'd ) ( 2,6 )', 'e ) ( 4,0 )'] | d | rectangle_area(subtract(16, const_3), const_2) | subtract(n2,const_3)|rectangle_area(#0,const_2) | geometry |
the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 2 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ? | "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 2 = rs . 1812 answer : b" | a ) s . 4528 , b ) s . 1812 , c ) s . 4527 , d ) s . 4530 , e ) s . 4521 | b | multiply(subtract(subtract(multiply(multiply(const_2, 12), add(15, 25)), multiply(6, 3)), multiply(3, multiply(4, 3))), 2) | add(n0,n1)|multiply(n2,const_2)|multiply(n4,n5)|multiply(n5,n6)|multiply(#0,#1)|multiply(n5,#3)|subtract(#4,#2)|subtract(#6,#5)|multiply(n3,#7)| | geometry |
what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 300 ? | "36 = 3 ^ 2 * 2 ^ 2 . 36 ^ 300 = 3 ^ 600 * 2 ^ 600 the answer is d ." | a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900 | d | multiply(subtract(36, 300), 300) | subtract(n1,n2)|multiply(n2,#0)| | other |
huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 8 inches on a side and costs $ 10 , and a large pizza that measures 12 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if t... | "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 8 * 8 = 64 ) for the small pizza and ( 12 * 12 = 144 ) for the large pizza . in total sq inches that would be ( 64 + 144 ) * 2 = 416 sq inches . in the second case if they pool their money together they can buy 3 ... | a ) 5 square inches , b ) 10 square inches , c ) 16 square inches , d ) 25 square inches , e ) 350 square inches | c | subtract(multiply(power(12, const_2), const_3), add(add(power(8, const_2), power(12, const_2)), add(power(8, const_2), power(12, const_2)))) | power(n2,const_2)|power(n0,const_2)|add(#1,#0)|multiply(#0,const_3)|add(#2,#2)|subtract(#3,#4)| | geometry |
30 men can do a work in 40 days . when should 16 men leave the work so that the entire work is completed in 40 days after they leave the work ? | "total work to be done = 30 * 40 = 1200 let 16 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 16 * 40 ) = 1200 40 p = 560 = > p = 14 days answer : b" | a ) 87 days , b ) 14 days , c ) 55 days , d ) 44 days , e ) 22 days | b | divide(subtract(multiply(30, 40), multiply(40, 16)), 40) | multiply(n0,n1)|multiply(n1,n2)|subtract(#0,#1)|divide(#2,n1)| | physics |
what is the normal price of an article sold at $ 126 after two successive discounts of 10 % and 20 % ? | "0.8 * 0.9 * cost price = $ 126 cost price = $ 175 the answer is c ." | a ) $ 155 , b ) $ 165 , c ) $ 175 , d ) $ 185 , e ) $ 195 | c | divide(126, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 20), const_100))) | subtract(const_100,n1)|subtract(const_100,n2)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|divide(n0,#4)| | gain |
two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 40 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of | answer : d . | a ) 18 % , b ) 20 % , c ) 21 % , d ) 33 % , e ) can not be determined | d | add(divide(multiply(40, 4), 2), add(40, 5)) | add(n4,n8)|multiply(n4,n6)|divide(#1,n1)|add(#0,#2)| | general |
there are 280 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers . | as per question stem 2 / 5 m ( portion of men employees who are managers ) + 280 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 280 = 2 / 5 t , or 2 / 5 ( t - m ) = 280 , from here we get that t - m = 700 , that would be ... | a ) 600 , b ) 650 , c ) 700 , d ) 750 , e ) none of these | c | divide(280, divide(2, 5)) | divide(n1,n2)|divide(n0,#0)| | general |
the average monthly income of p and q is rs . 2050 . the average monthly income of q and r is rs . 5250 and the average monthly income of p and r is rs . 6200 . the monthly income of p is : | "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 2050 x 2 ) = 4100 . . . . ( i ) q + r = ( 5250 x 2 ) = 10500 . . . . ( ii ) p + r = ( 6200 x 2 ) = 12400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 27000 or p + q + r = 13500 . . . ... | a ) 3050 , b ) 3000 , c ) 4000 , d ) 4050 , e ) 3100 | b | subtract(add(2050, 6200), 5250) | add(n0,n2)|subtract(#0,n1)| | general |
running at the same constant rate , 16 identical machines can produce a total of 32 shirt per minute . at this rate , how many shirt could 8 such machines produce in 10 minutes ? | "let ' s take the approach that uses the answer choices to eliminate wasted time . 32 / 16 = 2 shirt per minute per machine . 8 machines = 16 per minute . 10 minutes worth = 160 shirt . looking at the answers it is clear . . . we can only choose ( d ) the correct answer is d ." | a ) 911 , b ) 100 , c ) 101 , d ) 160 , e ) 785 | d | multiply(multiply(divide(32, 16), 10), 8) | divide(n1,n0)|multiply(n3,#0)|multiply(n2,#1)| | gain |
a certain cube floating in a bucket of water has between 70 and 85 percent of its volume below the surface of the water . if between 8 and 20 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately | "if sides are 7 , vol = 7 ^ 3 = 343 70 % = 240.1 , 85 % = 291.55 so vol above water , between 102.9 and 51.45 - - > too big if side are 4 , vol = 64 70 % = 44.8 , 85 % = 54.4 vol above water between 19.2 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 70 % = 87.5 , . 85 % = 106.25 vol ab... | a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9 | a | cube_edge_by_volume(divide(multiply(20, const_100), subtract(const_100, 70))) | multiply(n3,const_100)|subtract(const_100,n0)|divide(#0,#1)|cube_edge_by_volume(#2)| | geometry |
the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 14 times the probability that both events a and b occur . what is the probabil... | "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 14 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 14 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 14 * 2 b * b ... | a ) 77 / 2 , b ) 1 / 7 , c ) 78 / 85 , d ) 1 / 5 , e ) 47 / 85 | d | multiply(divide(add(const_2, const_1), add(multiply(14, const_2), const_2)), const_2) | add(const_1,const_2)|multiply(n1,const_2)|add(#1,const_2)|divide(#0,#2)|multiply(#3,const_2)| | general |
three numbers are in the ratio of 3 : 4 : 6 and their product is 1944 . the largest of these numbers is | "solution let the numbers be 3 x , 4 x and 6 x . then , 3 x × 4 x × 6 x = 1944 ‹ = › 72 x 3 = 1944 ‹ = › x 3 = 27 ‹ = › x = 3 therefore , largest number = 6 x = 18 . answer c" | a ) 6 , b ) 12 , c ) 18 , d ) 26 , e ) 28 | c | multiply(3, 6) | multiply(n0,n2)| | other |
two stations p and q are 200 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ? | "assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 200 = > 20 x + 25 ( x - 1 ) = 200 = > 45 x = 225 = > x = 5 means , they meet after 5 hours after 7 am , ie , they ... | a ) 10 am , b ) 12 noon , c ) 10.30 am , d ) 12.30 am , e ) 11 am | b | add(divide(add(200, 25), add(20, 25)), 7) | add(n0,n4)|add(n2,n4)|divide(#0,#1)|add(n1,#2)| | physics |
walking at 1 / 3 th of its usual speed a cab is 20 mnts late . find its usual time to cover the journey ? | "new speed = 1 / 3 th of usual speed new time = 3 of usual time 3 ut - ut = 20 m 2 ut = 20 m ut = 10 m answer is a" | a ) 10 m , b ) 15 m , c ) 20 m , d ) 25 m , e ) 12 m | a | multiply(1, 20) | multiply(n0,n2)| | physics |
there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 17 days more ? | "760 - - - - 22 760 - - - - 20 x - - - - - 17 x * 17 = 760 * 20 x = 894 760 - - - - - - - 134 answer : e" | a ) 89 men , b ) 120 men , c ) 90 men , d ) 60 men , e ) 134 men | e | subtract(divide(multiply(760, subtract(22, const_2)), 17), 760) | subtract(n1,const_2)|multiply(n0,#0)|divide(#1,n2)|subtract(#2,n0)| | physics |
find large number from below question the difference of two numbers is 1015 . on dividing the larger number by the smaller , we get 9 as quotient and the 15 as remainder | "let the smaller number be x . then larger number = ( x + 1015 ) . x + 1015 = 9 x + 15 8 x = 1000 x = 125 large number = 125 + 1015 = 1140 answer : d" | a ) 1209 , b ) 1324 , c ) 1245 , d ) 1140 , e ) 1635 | d | multiply(divide(subtract(1015, 15), subtract(9, const_1)), 9) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | general |
a store owner estimates that the average price of type a products will increase by 35 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owne... | "cost of type a products next year = 1.35 * 4500 = 6075 cost of type b products next year = 1.1 * 8300 = 9130 total 6075 + 9130 = 15205 option b" | a ) $ 14,755 , b ) $ 15,205 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155 | b | multiply(divide(const_3, const_4), const_1000) | divide(const_3,const_4)|multiply(#0,const_1000)| | general |
in a classroom , the average age of boys ( b ) is g and the average age of girls ( g ) is b . the average age of all is b + g . at the time of calculation , the class teacher , who is 42 years old was also present in the class . can you find the value of b + g ? | a b + g = 8 for b in range ( 199 ) : for g in range ( 199 ) : sum 1 = 2 * b * g + 42 sum 2 = ( b + g ) * ( b + g + 1 ) if ( sum 1 = = sum 2 ) : print ( b , g , sum 1 ) ( b , g ) = ( 35 ) = > b + g = 8 | a ) 8 , b ) 3 , c ) 7 , d ) 9 , e ) 10 | a | add(divide(subtract(floor(divide(add(sqrt(add(multiply(42, const_4), const_2)), const_1), const_2)), const_1), const_2), divide(subtract(sqrt(subtract(add(multiply(42, const_4), const_2), power(floor(divide(add(sqrt(add(multiply(42, const_4), const_2)), const_1), const_2)), const_2))), const_1), const_2)) | multiply(n0,const_4)|add(#0,const_2)|sqrt(#1)|add(#2,const_1)|divide(#3,const_2)|floor(#4)|power(#5,const_2)|subtract(#5,const_1)|divide(#7,const_2)|subtract(#1,#6)|sqrt(#9)|subtract(#10,const_1)|divide(#11,const_2)|add(#8,#12) | general |
mr . tom invested in fund x and fund y . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund x paid 23 % and fund y paid 17 % . the interest earned in fund y was exactly $ 200 greater than the interest earned in fund x . how much did ms . tom invest in fund x ? | x + y = 100000 0.17 y = 0.23 a + 200 take away decimals first : 17 y = 23 x + 20000 isolate first equation to solve for x ( your goal ) : y = 100000 - y plug in for b : 17 ( 100000 - x ) = 23 x + 20000 1 , 700000 - 17 x = 23 x + 20000 1 , 680000 = 40 x 1 , 680000 / 40 = x x = 42000 = answer choice c | a ) $ 32000 , b ) $ 36000 , c ) $ 42000 , d ) $ 44000 , e ) $ 45000 | c | divide(subtract(multiply(divide(17, const_100), 100000), 200), add(divide(17, const_100), divide(23, const_100))) | divide(n2,const_100)|divide(n1,const_100)|add(#0,#1)|multiply(n0,#0)|subtract(#3,n3)|divide(#4,#2) | gain |
what is the rate percent when the simple interest on rs . 800 amount to rs . 176 in 4 years ? | "176 = ( 180 * 4 * r ) / 100 r = 5.5 % answer : e" | a ) 5 % , b ) 8 % , c ) 3 % , d ) 9 % , e ) 5.5 % | e | divide(multiply(const_100, 176), multiply(800, 4)) | multiply(n1,const_100)|multiply(n0,n2)|divide(#0,#1)| | gain |
a 6 litre sol is 35 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ? | "35 % of 6 = 2.1 50 % of 6 = 3 shortage is 0.9 so we need to have 0.9 / 50 % to get 50 % alcohol content . = 1.8 d" | a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 1.8 , e ) e . 5.4 | d | subtract(6, multiply(const_2, multiply(divide(35, const_100), 6))) | divide(n1,const_100)|multiply(n0,#0)|multiply(#1,const_2)|subtract(n0,#2)| | gain |
sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 170 . if the ratio of his marks in english and maths is 1 : 4 , find his marks in science ? | s : e = 1 : 3 e : m = 1 : 4 - - - - - - - - - - - - s : e : m = 1 : 4 : 12 1 / 17 * 170 = 17 answer : a | a ) 17 , b ) 77 , c ) 66 , d ) 55 , e ) 31 | a | add(add(add(multiply(1, const_3), 1), multiply(multiply(1, const_3), add(multiply(1, const_3), 1))), 1) | multiply(n1,const_3)|add(n1,#0)|multiply(#1,#0)|add(#1,#2)|add(n1,#3) | general |
if 6 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ? | "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 6 c 2 for vertical 8 c 2 total parallelogram is 6 c 2 * 8 c 2 = 15 * 28 = 420 answer : c" | a ) 80 , b ) 63 , c ) 420 , d ) 160 , e ) 1260 | c | multiply(divide(multiply(6, subtract(6, const_1)), const_2), divide(multiply(8, subtract(8, const_1)), const_2)) | subtract(n0,const_1)|subtract(n1,const_1)|multiply(n0,#0)|multiply(n1,#1)|divide(#2,const_2)|divide(#3,const_2)|multiply(#4,#5)| | physics |
what is the remainder if 7 ^ 8 is divided by 100 ? | "7 ^ 8 can be written as ( 7 ^ 4 ) ^ 2 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 2 by 100 , the reminder is 1 ^ 2 = 1 answer : b" | a ) 7 , b ) 1 , c ) 9 , d ) 10 , e ) 11 | b | subtract(divide(100, const_2), multiply(7, 7)) | divide(n2,const_2)|multiply(n0,n0)|subtract(#0,#1)| | general |
65 % of x = 20 % of 617.50 . find the value of x ? | "65 % of x = 20 % of 615.50 then , 65 / 100 * x = 20 / 100 * 6175 / 10 x = 190 answer is b" | a ) 100 , b ) 190 , c ) 150 , d ) 180 , e ) 199 | b | divide(multiply(multiply(divide(617.50, const_100), 20), const_100), 65) | divide(n2,const_100)|multiply(n1,#0)|multiply(#1,const_100)|divide(#2,n0)| | general |
find the smallest number of five digits exactly divisible by 24 , 48,64 and 88 . | "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 24,48 , 64,88 i . e 2012 , on dividing 10000 by 2012 , we get 60 as remainder . therefore , required number = 10000 + ( 2012 â € “ 60 ) = 11952 . answer is a ." | a ) 11952 , b ) 11852 , c ) 11752 , d ) 11652 , e ) 11552 | a | add(subtract(multiply(const_10, multiply(const_100, const_100)), const_100), 48,64) | multiply(const_100,const_100)|multiply(#0,const_10)|subtract(#1,const_100)|add(n1,#2)| | general |
how many numbers from 12 to 82 are exactly divisible by 6 ? | "option ' d ' 12 / 6 = 2 and 82 / 6 = 13 = = > 13 - 2 = 11 numbers" | a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12 | d | add(divide(subtract(multiply(floor(divide(82, 6)), 6), multiply(add(floor(divide(12, 6)), const_1), 6)), 6), const_1) | divide(n1,n2)|divide(n0,n2)|floor(#0)|floor(#1)|add(#3,const_1)|multiply(n2,#2)|multiply(n2,#4)|subtract(#5,#6)|divide(#7,n2)|add(#8,const_1)| | general |
10 men and 15 women finish a work in 6 days . one man alone finishes that work in 100 days . in how many days will a woman finish the work ? | 15 women ' s work of a day = 1 ⁄ 6 - 1 ⁄ 10 ⇒ 1 ⁄ 15 part ∴ for 1 whole part a woman will take = 15 × 15 = 225 days . answer d | a ) 125 days , b ) 150 days , c ) 90 days , d ) 225 days , e ) none of these | d | inverse(divide(subtract(divide(const_1, 6), multiply(10, divide(const_1, 100))), 15)) | divide(const_1,n2)|divide(const_1,n3)|multiply(n0,#1)|subtract(#0,#2)|divide(#3,n1)|inverse(#4) | physics |
a certain quantity is measured on two different scales , the r - scale and the s - scale , that are related linearly . measurements on the r - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the r - scale corresponds to a measurement of 100 on the s - scal... | question says they are both related linearly so they the relationships can be represented by standard linear definition y = mx + b . let s scale = y . and r scale = x . 30 = 6 m + b eqn 1 60 = 24 m + b eqn 2 eqn 2 - eqn 1 = > 30 = 18 m = > m = 5 / 3 solving for b using either equation gives us b = 20 linear relationshi... | a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84 | c | add(divide(multiply(subtract(100, 60), subtract(24, 6)), 30), 24) | subtract(n4,n3)|subtract(n1,n0)|multiply(#0,#1)|divide(#2,n2)|add(n1,#3) | general |
a fruit seller had some apples . he sells 30 % and still has 420 apples . originally , he had ? | "answer â ˆ µ 70 % of n = 420 â ˆ ´ n = ( 420 x 100 ) / 70 = 600 correct option : b" | a ) 30 apples , b ) 600 apples , c ) 420 apples , d ) 70 apples , e ) none | b | original_price_before_loss(30, 420) | original_price_before_loss(n0,n1)| | gain |
a family x went for a vacation . unfortunately it rained for 13 days when they were there . but whenever it rained in the mornings , they had clear afternoons and vice versa . in all they enjoyed 11 mornings and 12 afternoons . how many days did they stay there totally ? | explanation : clearly 11 mornings and 12 afternoons = 23 half days = > since 13 days raining means 13 half days . = > so 23 - 13 = 10 halfdays ( not effecetd by rain ) = > so 10 halfdays = 5 fulldays hence , total no . of days = 13 + 5 = 18 days answer : b | a ) 16 , b ) 18 , c ) 20 , d ) 13 , e ) 14 | b | add(13, divide(subtract(add(11, 12), 13), const_2)) | add(n1,n2)|subtract(#0,n0)|divide(#1,const_2)|add(n0,#2) | general |
what is 92 % of 4 / 5 ? | "92 % * ( 4 / 5 ) = 0.92 * 0.8 = 0.736 answer : c" | a ) 6.9 , b ) 69.0 , c ) 0.736 , d ) 0.6859 , e ) 0.69 | c | divide(multiply(92, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100) | add(const_2,const_3)|add(const_3,const_4)|add(const_3,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#3,const_100)|multiply(#1,#0)|multiply(#4,#5)|multiply(#6,#4)|add(#7,#8)|add(#9,#2)|multiply(n0,#10)|divide(#11,const_100)| | gain |
a textile manufacturing firm employees 125 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 125 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spr... | "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 124 / 125 ) â ˆ ’ 1... | a ) 13000 , b ) 7000 , c ) 10000 , d ) 2800 , e ) none of these | d | subtract(subtract(multiply(multiply(5, const_1000), const_100), add(multiply(75000, const_2), 75000)), subtract(subtract(multiply(divide(subtract(125, 1), 125), multiply(multiply(5, const_1000), const_100)), multiply(multiply(75000, const_2), divide(subtract(125, 1), 125))), 75000)) | multiply(n2,const_1000)|multiply(n6,const_2)|subtract(n0,n4)|add(n6,#1)|divide(#2,n0)|multiply(#0,const_100)|multiply(#4,#5)|multiply(#4,#1)|subtract(#5,#3)|subtract(#6,#7)|subtract(#9,n6)|subtract(#8,#10)| | general |
a milk man has 20 liters of milk . if he mixes 25 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is : | "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 45 % . answer : b" | a ) 20 % , b ) 45 % , c ) 33.33 % , d ) 18 % , e ) none of these | b | multiply(divide(subtract(multiply(add(add(add(20, 25), const_10), add(divide(25, const_2), const_3)), 18), multiply(20, 18)), multiply(20, 18)), const_100) | add(n1,n2)|divide(n1,const_2)|multiply(n0,n3)|add(#0,const_10)|add(#1,const_3)|add(#3,#4)|multiply(n3,#5)|subtract(#6,#2)|divide(#7,#2)|multiply(#8,const_100)| | gain |
a thief is spotted by a policeman from a distance of 100 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ? | "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 100 m / 1000 ) x 1 / 2 hr = 1 / 20 hr . in 1 / 20 hrs , the thief covers a distance of 8 x 1 / 20 km = 2 / 5 km = 400 m answer is c ." | a ) 350 m , b ) 200 m , c ) 400 m , d ) 500 m , e ) none of them | c | divide(multiply(100, 8), subtract(10, 8)) | multiply(n0,n1)|subtract(n2,n1)|divide(#0,#1)| | physics |
a major airplane manufacturer announced the sale of 150 small airliners at $ 125 million each , 75 medium sized airliners at $ 175 million each , and 60 large airliners at $ 220 million each . what percentage of the company ' s income came from large and medium airliners ? | answer is ( money from mid and large plane ) / ( total money from all the planes ) x 100 = ( 175 ∗ 75 + 220 ∗ 60 ) / ( 125 ∗ 150 + 175 ∗ 75 + 220 ∗ 60 ) ∗ 100 ( 175 ∗ 75 + 220 ∗ 60 ) / ( 125 ∗ 150 + 175 ∗ 75 + 220 ∗ 60 ) ∗ 100 = 58.4 % you could just multiply add divide to get answer . however sometimes its much better... | a ) 29 % , b ) 41 % , c ) 58 % , d ) 69 % , e ) 70 % | c | multiply(divide(add(multiply(75, 175), multiply(60, 220)), add(add(multiply(75, 175), multiply(60, 220)), multiply(150, 125))), const_100) | multiply(n2,n3)|multiply(n4,n5)|multiply(n0,n1)|add(#0,#1)|add(#3,#2)|divide(#3,#4)|multiply(#5,const_100) | gain |
if 75 percent of a class answered the first question on a certain test correctly , 30 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ? | "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have... | a ) 25 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 % | a | subtract(add(add(75, 30), 20), const_100) | add(n0,n1)|add(n2,#0)|subtract(#1,const_100)| | other |
what is the decimal equivalent of ( 1 / 4 ) ^ 4 ? | "( 1 / 4 ) ^ 4 = 1 / 256 = 0.0039 answer : a" | a ) 0.0039 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5 | a | power(divide(1, 4), 4) | divide(n0,n1)|power(#0,n2)| | general |
( ( a + b ) / c ) / 2 in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 5 . what is the least possible value of the expression ? | ( ( a + b ) / c ) / 2 = ( a + b ) / 2 c the expression will have the least value when numerator ( a + b ) is the smallest . = ( 2 + 3 ) / 2 * 5 = 5 / 10 answer b | a ) 2 / 10 , b ) 5 / 10 , c ) 10 / 5 , d ) 7 / 6 , e ) 6 / 7 | b | divide(5, const_10) | divide(n3,const_10) | general |
85 % of the population of a city is 85000 . the total population of the city is ? | "x * ( 85 / 100 ) = 85000 x = 1000 * 100 x = 100000 answer : c" | a ) 95000 , b ) 97500 , c ) 100000 , d ) 105000 , e ) 102500 | c | multiply(divide(const_100, 85), 85000) | divide(const_100,n0)|multiply(n1,#0)| | gain |
if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 ? | it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 22 , 24 , 26 , 27 , 30 , 33 , 35 , 42 , . . . numbers less than median are 22 , 24 , 26 , 27 . . the median of these numbers = center of 24 and 26 ... | a ) 33 , b ) 28 , c ) 27 , d ) 24 , e ) 25 | e | divide(add(24, 26), const_2) | add(n1,n4)|divide(#0,const_2) | general |
what is the perimeter of a square with area 9 p ^ 2 / 64 ? | area of square , ( side ) ^ 2 = ( 3 p / 8 ) ^ 2 therefore side of the square = 3 p / 8 perimeter of square = 4 * side = 4 * ( 3 p / 8 ) = 3 p / 2 answer is a . | ['a ) 3 p / 2', 'b ) 3 p ^ 2 / 4', 'c ) 3 p', 'd ) 3 p ^ 2', 'e ) 4 p / 3'] | a | multiply(divide(sqrt(9), sqrt(64)), const_4) | sqrt(n0)|sqrt(n2)|divide(#0,#1)|multiply(#2,const_4) | geometry |
14 . the sum and the product of two numbers are 25 and 144 respectively , the difference of the number is ? | x + y = 25 xy = 144 ( x - y ) 2 = ( x + y ) 2 â € “ 4 xy ( x - y ) 2 = 625 â € “ 576 = > ( x â € “ y ) = 7 answer : a | a ) 7 , b ) 9 , c ) 8 , d ) 5 , e ) 4 | a | subtract(subtract(subtract(power(25, const_2), multiply(144, const_2)), multiply(144, const_2)), subtract(subtract(subtract(subtract(power(25, const_2), multiply(144, const_2)), multiply(144, const_2)), const_4), const_3)) | multiply(n2,const_2)|power(n1,const_2)|subtract(#1,#0)|subtract(#2,#0)|subtract(#3,const_4)|subtract(#4,const_3)|subtract(#3,#5) | general |
( x ) + 1789 + 9011 - 7819 = 90510 . calculate the value of x | "x + 1789 + 9011 - 7819 = 90510 = x + 1789 + 9011 = 90510 + 7819 = x + 10800 = 98329 = x = 98329 - 10800 = 87529 answer is c" | a ) 87501 , b ) 87599 , c ) 87529 , d ) 87520 , e ) 87521 | c | multiply(subtract(subtract(add(90510, 7819), 9011), 1789), divide(const_60, const_2)) | add(n2,n3)|divide(const_60,const_2)|subtract(#0,n1)|subtract(#2,n0)|multiply(#1,#3)| | general |
an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2500 , what will be the difference between q and r ' s share ? | "4 - - - 2100 5 - - - ? = > 2625 answer : d" | a ) 2225 , b ) 2325 , c ) 2425 , d ) 2625 , e ) 2525 | d | multiply(subtract(12, 7), divide(2500, subtract(7, 3))) | subtract(n1,n0)|subtract(n2,n1)|divide(n3,#0)|multiply(#2,#1)| | general |
a certain industrial loom weaves 0.132 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ? | "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.132 : 15 : : 1 : x = > 0.132 * x = 15 = > x = 15 / 0.132 = > x = 114 answer : a" | a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118 | a | divide(15, 0.132) | divide(n1,n0)| | physics |
if x is a number such that x ^ 2 + 4 x - 5 = 0 and x ^ 2 + x - 20 = 0 , then x = | x ^ 2 + 4 x - 5 = ( x + 5 ) ( x - 1 ) = 0 then x = - 5 or x = 1 . x ^ 2 + x - 20 = ( x - 4 ) ( x + 5 ) = 0 then x = 4 or x = - 5 . thus x = - 5 . the answer is d . | a ) 1 , b ) - 4 , c ) 4 , d ) - 5 , e ) 5 | d | multiply(4, 4) | multiply(n1,n1) | general |
the rate at which a sum becomes 4 times of itself in 15 years at s . i . , will be : | sol . let sum = x . then , s . i . = 3 x ∴ rate = [ 100 * s . i . / p * t ] = [ 100 * 3 x / x * 15 ] % = 20 % . answer c | a ) 10 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) none | c | divide(multiply(const_3, const_100), 15) | multiply(const_100,const_3)|divide(#0,n1) | general |
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