Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
values |
|---|---|---|---|---|---|---|
operation # is defined as adding a randomly selected two digit multiple of 10 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ? | "any multiple of 10 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ." | a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 % | a | divide(add(10, add(10, const_3)), const_2) | add(n1,const_3)|add(n0,#0)|divide(#1,const_2)| | general |
a room of 8 m 44 cm long and 3 m 50 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor . | "explanation : area of the room = 844 * 350 sq cm size of largest square tile = h . c . f of 844 cm and 350 cm = 2 cm area of 1 tile = 2 * 2 sq cm no . of tiles required = ( 844 * 350 ) / ( 2 * 2 ) = 73850 answer : a ) 73850" | a ) 73850 , b ) 73805 , c ) 844 , d ) 350 , e ) 2 | a | divide(multiply(add(multiply(8, const_100), 44), add(multiply(3, const_100), 50)), power(divide(add(multiply(8, const_100), 44), power(const_2, const_4)), const_2)) | multiply(n0,const_100)|multiply(n2,const_100)|power(const_2,const_4)|add(n1,#0)|add(n3,#1)|divide(#3,#2)|multiply(#3,#4)|power(#5,const_2)|divide(#6,#7)| | physics |
a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 45 kmph . when and at what distance from mumbai do the two trains meet ? | "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 45 - 40 ) = 8 hours so , the two trains meet at 6 p . m . the two trains meet 6 * 45 = 270 km away ... | a ) 287 , b ) 279 , c ) 270 , d ) 278 , e ) 379 | c | multiply(divide(multiply(40, const_1), subtract(45, 40)), 45) | multiply(n1,const_1)|subtract(n2,n1)|divide(#0,#1)|multiply(n2,#2)| | physics |
he average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 62 kg . what might be the weight of the new person ? | "explanation : total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 62 + 28 ) kg = 90 kg . answer : e" | a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 90 kg | e | add(multiply(3.5, 8), 62) | multiply(n0,n1)|add(n2,#0)| | general |
the price of a jacket is reduced by 20 % . during a special sale the price of the jacket is reduced another 25 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ? | "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 20 % , therefore bringing down the price to $ 80 . 3 ) again it is further discounted by 25 % , therefore bringing down the price to $ 60 . 4 ) now 60 has to be added byx % in order to equal the original price . 60 + ( x % ) 60 = 100 . solvin... | a ) 32.5 , b ) 35 , c ) 48.1 , d ) 65 , e ) 66.67 | e | multiply(const_100, divide(subtract(const_100, subtract(subtract(const_100, 20), multiply(subtract(const_100, 20), divide(25, const_100)))), subtract(subtract(const_100, 20), multiply(subtract(const_100, 20), divide(25, const_100))))) | divide(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|subtract(#1,#2)|subtract(const_100,#3)|divide(#4,#3)|multiply(#5,const_100)| | gain |
a cylindrical can has a radius of 3 centimeters and a height of 12 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ? | "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 3 * 12 = 72 pi answer is b ." | a ) 16 pi , b ) 72 pi , c ) 96 pi , d ) 192 pi , e ) 576 pi | b | multiply(multiply(3, 12), multiply(const_2, const_pi)) | multiply(n0,n1)|multiply(const_2,const_pi)|multiply(#0,#1)| | geometry |
a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 9.00 ? | "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 9 ( 1 / 12 ) * x = 9 x = 108 answer : e" | a ) 40 , b ) 60 , c ) 90 , d ) 120 , e ) 108 | e | divide(9.00, subtract(divide(1.00, 4), divide(0.50, 3))) | divide(n3,n2)|divide(n1,n0)|subtract(#0,#1)|divide(n4,#2)| | gain |
a man took a loan from a bank at the rate of 11 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was : | "solution principal = rs . ( 100 x 5400 / 11 x 3 ) = rs . 16363.64 . answer a" | a ) rs . 16363.64 , b ) rs . 10 , 000.64 , c ) rs . 15 , 000,64 , d ) rs . 21 , 353.64 , e ) none | a | divide(divide(multiply(5400, const_100), multiply(3, 11)), multiply(divide(const_60, const_4), const_100)) | divide(const_60,const_4)|multiply(n2,const_100)|multiply(n0,n1)|divide(#1,#2)|multiply(#0,const_100)|divide(#3,#4)| | gain |
the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 98 , what is the difference between the ages of patrick and monica ? | "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 98 x = 2 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 2 = 32 answer a" | a ) 32 , b ) 48 , c ) 45 , d ) 72 , e ) 18 | a | subtract(multiply(multiply(5, 5), divide(98, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5)))), multiply(multiply(3, 3), divide(98, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5))))) | multiply(n0,n0)|multiply(n1,n0)|multiply(n1,n3)|add(#0,#1)|add(#3,#2)|divide(n4,#4)|multiply(#5,#2)|multiply(#5,#0)|subtract(#6,#7)| | general |
three 6 faced dice are thrown together . the probability that exactly two dice show the same number on them is - . | "using question number 11 and 12 , we get the probability as 1 - ( 1 / 36 + 5 / 9 ) = 5 / 12 answer a" | a ) 5 / 12 , b ) 4 / 13 , c ) 5 / 17 , d ) 3 / 12 , e ) 8 / 9 | a | multiply(multiply(multiply(divide(const_1, 6), divide(const_1, 6)), divide(const_1, 6)), divide(const_1, 6)) | divide(const_1,n0)|multiply(#0,#0)|multiply(#0,#1)|multiply(#0,#2)| | general |
six dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 6 dots that do not form an equilateral triangle ? | the total number of ways we can choose three dots is 6 c 3 = 20 . we can form two equilateral triangles from these six dots . there are 20 - 2 = 18 combinations which do not form an equilateral triangle . the answer is a . | ['a ) 18', 'b ) 17', 'c ) 16', 'd ) 15', 'e ) 14'] | a | subtract(divide(factorial(6), multiply(factorial(const_3), factorial(const_3))), const_2) | factorial(n0)|factorial(const_3)|multiply(#1,#1)|divide(#0,#2)|subtract(#3,const_2) | geometry |
nd the area of trapezium whose parallel sides are 20 cm and 16 cm long , and the distance between them is 15 cm ? | "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 16 ) * ( 15 ) = 270 cm 2 answer : a" | a ) 270 cm 2 , b ) 275 cm 2 , c ) 280 cm 2 , d ) 285 cm 2 , e ) 290 cm 2 | a | divide(multiply(15, add(20, 16)), const_2) | add(n0,n1)|multiply(n2,#0)|divide(#1,const_2)| | physics |
how many positive integer solutions does the equation 2 x + 1 y = 100 have ? | "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 1 ) = 50 answer : c" | a ) 44 , b ) 33 , c ) 50 , d ) 35 , e ) 14 | c | divide(1, 2) | divide(n1,n0)| | general |
if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by how much ? | "unit place increased by 3 . so 6 , 16,26 , . . . . 96 . total 10 * 3 = 30 increased . ten ' s place increased by 30 . so 60,61 , . . . 69 . total 10 * 30 = 300 increased . so total varies = 300 + 30 = 330 . answer : a" | a ) 330 , b ) 360 , c ) 380 , d ) 400 , e ) 420 | a | add(multiply(multiply(subtract(9, 6), const_10), const_10), multiply(subtract(9, 6), const_10)) | subtract(n1,n0)|multiply(#0,const_10)|multiply(#1,const_10)|add(#2,#1)| | general |
a train 130 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train . | "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 130 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2340 < = > x = 73 speed of the train is 73 kmph . answer : option e" | a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 73 kmph | e | subtract(divide(130, multiply(6, const_0_2778)), 5) | multiply(n1,const_0_2778)|divide(n0,#0)|subtract(#1,n2)| | physics |
sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6700 ? | "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6700 x 6 ) - 34009 ] = rs . ( 40200 - 34009 ) = rs . 6191 answer : b" | a ) 4966 , b ) 6191 , c ) 2877 , d ) 2676 , e ) 1881 | b | multiply(subtract(divide(add(add(add(add(6835, 9927), 6855), 7230), 6562), 5), 6700), 5) | add(n0,n1)|add(n2,#0)|add(n3,#1)|add(n4,#2)|divide(#3,n5)|subtract(#4,n6)|multiply(n5,#5)| | general |
find the average of all prime numbers between 10 and 40 | "prime numbers between 10 and 40 are 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 required average = ( 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 ) / 8 = 180 / 8 = 22.5 answer is b" | a ) 15.6 , b ) 22.5 , c ) 18.6 , d ) 32.2 , e ) 26.9 | b | divide(add(add(add(10, const_1), add(add(10, const_1), const_2)), add(subtract(40, 10), subtract(40, const_2))), 10) | add(n0,const_1)|subtract(n1,n0)|subtract(n1,const_2)|add(#0,const_2)|add(#1,#2)|add(#0,#3)|add(#5,#4)|divide(#6,n0)| | general |
if y is 80 % greater than x , than x is what % less than y ? | "let x = 100 so y = 180 we want percentage change . so , ( 100 - 180 ) / 180 = - 44.44 % = 44 4 / 9 % lesser than y . hence option ( d ) ." | a ) 20 , b ) 25 , c ) 33 1 / 3 , d ) 44 4 / 9 , e ) 80 | d | multiply(divide(80, add(80, const_100)), const_100) | add(n0,const_100)|divide(n0,#0)|multiply(#1,const_100)| | general |
how many miles is 150 km ? | "93.75 miles 150 / 1.6 answer : c" | a ) 91.5 miles , b ) 92.75 miles , c ) 93.75 miles , d ) 94.5 miles , e ) 95.75 miles | c | divide(volume_cube(const_10), volume_cube(150)) | volume_cube(const_10)|volume_cube(n0)|divide(#0,#1)| | physics |
every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 108 , how many more green disks than blue disks are in the bag ? | "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 108 - - > x = 6 . g - b = 8 x - 3 x = 5 x = 30 . the answer is c ." | a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40 | c | multiply(divide(108, add(add(3, 7), 8)), subtract(8, 3)) | add(n0,n1)|subtract(n2,n0)|add(n2,#0)|divide(n3,#2)|multiply(#3,#1)| | general |
a room is 7 meters 20 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room . | "let us calculate both the length and width of the room in centimeters . length = 7 meters and 20 centimeters = 720 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each... | a ) 10 , b ) 15 , c ) 17 , d ) 19 , e ) 21 | b | divide(multiply(add(multiply(7, const_100), 20), add(multiply(4, const_100), 32)), multiply(gcd(add(multiply(7, const_100), 20), add(multiply(4, const_100), 32)), gcd(add(multiply(7, const_100), 20), add(multiply(4, const_100), 32)))) | multiply(n0,const_100)|multiply(n2,const_100)|add(n1,#0)|add(n3,#1)|gcd(#2,#3)|multiply(#2,#3)|multiply(#4,#4)|divide(#5,#6)| | general |
a number is greater than 3 but less than 8 . also the number is greater than 6 but less than 10 . what is the number ? | b 7 | a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9 | b | subtract(8, const_1) | subtract(n1,const_1) | general |
efrida and frazer who live 13 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ? | "it ' s a simple geometry problem . look at the diagram below : answer : e ." | a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11 | e | add(sqrt(divide(subtract(power(13, const_2), power(const_2, const_2)), const_2)), const_2) | power(n0,const_2)|power(const_2,const_2)|subtract(#0,#1)|divide(#2,const_2)|sqrt(#3)|add(#4,const_2)| | physics |
a cistern is filled by a tap in 8 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ? | "filling rate - leak rate = net rate 1 / 8.5 - leak rate = 1 / 9 leak rate = 2 / 17 - 1 / 9 = 1 / 153 the answer is c ." | a ) 133 , b ) 143 , c ) 153 , d ) 163 , e ) 173 | c | divide(1, subtract(divide(1, add(8, divide(1, 2))), divide(1, const_4))) | divide(n1,n2)|divide(n1,const_4)|add(n0,#0)|divide(n1,#2)|subtract(#3,#1)|divide(n1,#4)| | physics |
nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 54 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ? | "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 54 for cristina = c = 5 * t @ t = 27 , n = 135 c = 135 right answer ans : d" | a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 27 seconds , e ) 45 seconds | d | divide(54, subtract(5, 3)) | subtract(n1,n2)|divide(n0,#0)| | physics |
susan can type 10 pages in 5 minutes . mary can type 5 pages in 10 minutes . working together , how many pages can they type in 30 minutes ? | susan can type 2 pages in 1 min mary can type 0.5 pages in 1 min so , both of them work together they type 2.5 pages in 1 min so , in 30 min they type ( 30 * 2.5 ) = 75 pages answer : e | a ) 15 , b ) 20 , c ) 25 , d ) 65 , e ) 75 | e | add(multiply(divide(30, 10), 5), multiply(10, divide(30, 5))) | divide(n4,n0)|divide(n4,n1)|multiply(n1,#0)|multiply(n0,#1)|add(#2,#3) | physics |
( 178 % of 1265 ) ÷ 5.96 = ? | explanation : ? = ( 178 x 1265 / 100 ) ÷ 6 = 2250 / 600 = 375 answer : option d | a ) 125 , b ) 175 , c ) 225 , d ) 375 , e ) 524 | d | divide(multiply(divide(178, const_100), 1265), 5.96) | divide(n0,const_100)|multiply(n1,#0)|divide(#1,n2) | general |
at the faculty of aerospace engineering , 312 students study random - processing methods , 234 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ? | "312 + 234 - 112 ( since 112 is counted twice ) = 434 b is the answer" | a ) 430 , b ) 434 , c ) 438 , d ) 444 , e ) 446 | b | add(subtract(312, divide(112, const_2)), subtract(234, divide(112, const_2))) | divide(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|add(#1,#2)| | other |
there are 399 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 399 = 231 answer : d" | a ) 152 , b ) 209 , c ) 57 , d ) 231 , e ) 181 | d | multiply(multiply(8, subtract(11, 8)), 11) | subtract(n2,n1)|multiply(n1,#0)|multiply(n2,#1)| | other |
after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 6100 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ? | "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 6100 = 21600 exp in % = 100 - 10 = 90 % , 21600 = 90 % saving = 10 % = 21600 x 10 / 90 = rs . 2400 answer : e" | a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) 2400 | e | subtract(divide(multiply(add(add(add(add(add(5000, 1500), 4500), 2500), 2000), 6100), const_100), subtract(const_100, 10)), add(add(add(add(add(5000, 1500), 4500), 2500), 2000), 6100)) | add(n0,n1)|subtract(const_100,n6)|add(n2,#0)|add(n3,#2)|add(n4,#3)|add(n5,#4)|multiply(#5,const_100)|divide(#6,#1)|subtract(#7,#5)| | general |
a train 825 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 90 seconds . the speed of the train is : | "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 45 = = > x = 50 km / hr . answer : d" | a ) 33 , b ) 27 , c ) 27 , d ) 50 , e ) 81 | d | divide(divide(subtract(825, multiply(multiply(5, const_0_2778), 5)), 5), const_0_2778) | multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778)| | physics |
in a hostel , the number of students decreased by 10 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the prev... | "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.9 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.9 * 1.2 ) = > f ( new ) = 0.9259 f therefore the n... | a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 7.4 % | e | multiply(subtract(const_1, divide(multiply(const_100, const_100), multiply(subtract(const_100, 10), add(const_100, 20)))), const_100) | add(n1,const_100)|multiply(const_100,const_100)|subtract(const_100,n0)|multiply(#0,#2)|divide(#1,#3)|subtract(const_1,#4)|multiply(#5,const_100)| | general |
the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 63 kmph , find the speed of the stream ? | "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 63 / 3 = 21 kmph . answer : d" | a ) 15 , b ) 19 , c ) 14 , d ) 21 , e ) 16 | d | subtract(63, divide(multiply(63, const_2), const_3)) | multiply(n0,const_2)|divide(#0,const_3)|subtract(n0,#1)| | physics |
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 rs . 6600 ? | "required difference = [ 3 ½ % of rs . 6600 ] – [ 3 1 / 3 % of rs . 6600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 6600 = 1 / 6 % of rs . 6600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 6600 ] = rs . 11 . answer is a ." | a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10 | a | divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 6600), const_100) | divide(n1,n2)|divide(n1,n0)|add(n0,#0)|add(n0,#1)|subtract(#2,#3)|multiply(n6,#4)|divide(#5,const_100)| | general |
working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 7 x boxes ? | "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combin... | a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 14 minutes , e ) 12 minutes | d | divide(multiply(7, 10), add(speed(10, 10), speed(multiply(2, 10), 5))) | multiply(n0,n3)|multiply(n0,n1)|speed(n0,n0)|speed(#1,n2)|add(#2,#3)|divide(#0,#4)| | physics |
in a shop , the profit is 320 % of the cost . if the cost increases by 25 % but the selling price remains constant , approximately what percentage of the selling price is the profit ? | "cp . = rs . 100 . = > profit = rs . 320 , s . p . = rs . 420 . new c . p . = 125 % of rs . 100 = rs . 125 new s . p . = rs . 420 . profit = rs . ( 420 - 125 ) = rs . 295 . req = ( 295 / 420 * 100 ) = = > 70 % answer a" | a ) 70 % , b ) 50 % , c ) 100 % , d ) 60 % , e ) 55 % | a | multiply(divide(subtract(add(320, const_100), add(25, const_100)), add(320, const_100)), const_100) | add(n0,const_100)|add(n1,const_100)|subtract(#0,#1)|divide(#2,#0)|multiply(#3,const_100)| | gain |
2 trains in same direction at 50 km / hr , 32 km / hr . a man in slower train observes 15 sec elapse before the faster train completely passed by him what is length of faster train ? | relative speed = 18 k / hr = 5 m / sec distance covered = length of faster train = 5 * 15 = 75 meters answer : b | a ) 65 meters , b ) 75 meters , c ) 85 meters , d ) 95 meters , e ) 55 meters | b | multiply(divide(multiply(subtract(50, 32), const_1000), const_3600), 15) | subtract(n1,n2)|multiply(#0,const_1000)|divide(#1,const_3600)|multiply(n3,#2) | physics |
lionel left his house and walked towards walt ' s house , 48 miles away . four hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 2 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ? | "in the first 4 hours lionel at the rate of 2 miles per hour covered distance = rate * time = 4 * 2 = 8 miles . so , the distance between him and walt was 48 - 8 = 40 miles when walt left his house . now , their combined rate to cover this distance was 2 + 6 = 8 miles per hour , hence they will meet ( they will cover t... | a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 28 | b | multiply(2, add(divide(subtract(48, multiply(2, 2)), add(6, 2)), 2)) | add(n1,n2)|multiply(n1,n1)|subtract(n0,#1)|divide(#2,#0)|add(#3,n1)|multiply(n1,#4)| | physics |
x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 13860 ? | "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = ... | a ) 4032 , b ) 4000 , c ) 3250 , d ) 3825 , e ) 3985 | a | multiply(multiply(48000, subtract(multiply(const_3, 4), 4)), divide(13860, add(add(multiply(36000, multiply(const_3, 4)), multiply(42000, multiply(const_3, 4))), multiply(48000, subtract(multiply(const_3, 4), 4))))) | multiply(const_3,n2)|multiply(n0,#0)|multiply(n1,#0)|subtract(#0,n2)|add(#1,#2)|multiply(n3,#3)|add(#4,#5)|divide(n4,#6)|multiply(#7,#5)| | gain |
a cyclist traveled for two days . on the second day the cyclist traveled 3 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling , what was her average speed on the second day ? | "solution : d = 280 mi t = 12 hrs day 1 time = t 1 day 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs day 1 rate = r 1 day 2 rate = r 2 r 1 - r 2 = 10 mph i . e . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 i . e . 280 = 8 r 2 + 4 ( 10 + r 2 ) i .... | a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph | b | divide(subtract(280, multiply(divide(subtract(12, 3), const_2), 10)), add(divide(subtract(12, 3), const_2), add(divide(subtract(12, 3), const_2), 3))) | subtract(n3,n0)|divide(#0,const_2)|add(n0,#1)|multiply(n1,#1)|add(#2,#1)|subtract(n2,#3)|divide(#5,#4)| | physics |
from the digits 2 , 3 , 4 , 5 , 6 and 7 , how many 5 - digit numbers can be formed that have distinct digits and are multiples of 12 ? | detailed solution any multiple of 12 should be a multiple of 4 and 3 . first , let us look at the constraint for a number being a multiple of 3 . sum of the digits should be a multiple of 3 . sum of all numbers from 2 to 7 is 27 . so , if we have to drop a digit and still retain a multiple of 3 , we should drop either ... | a ) 36 , b ) 60 , c ) 84 , d ) 72 , e ) 86 | b | add(multiply(factorial(subtract(5, const_2)), multiply(const_2, const_3)), multiply(const_4, factorial(subtract(5, const_2)))) | multiply(const_2,const_3)|subtract(n3,const_2)|factorial(#1)|multiply(#2,#0)|multiply(#2,const_4)|add(#3,#4) | general |
what is the least common multiple of 8,12 , 32,14 | "the given numbers are 8,12 , 32,14 thus the l . c . m is 2 * 2 * 2 * 1 * 3 * 4 * 7 = 672 the answer is a" | a ) 672 , b ) 682 , c ) 328 , d ) 964 , e ) 285 | a | multiply(add(8,12, const_1), const_2) | add(n0,const_1)|multiply(#0,const_2)| | general |
the difference between the local value and the face value of 8 in the numeral 96348621 is | "explanation : ( local value of 8 ) - ( face value of 8 ) = ( 8000 - 8 ) = 7992 e )" | a ) 6992 , b ) 6982 , c ) 7982 , d ) 7972 , e ) 7992 | e | subtract(multiply(8, const_1000), 8) | multiply(n0,const_1000)|subtract(#0,n0)| | general |
find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.80 a kg to produce a mixture worth rs . 6.30 a kg ? | "solution required ratio = 50 : 90 = 5 : 9 answer a" | a ) 5 : 9 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) none of these | a | divide(subtract(6.30, 5.80), subtract(7.20, 6.30)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)| | other |
three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 15 minutes . if a , b & c are kept open successively for 4 minute each , how soon will the tank be filled ? | in three minute 1 / 20 + 1 / 30 - 1 / 15 = 1 / 60 part is filled 12 min - - - - - - - - 1 / 60 parts x min - - - - - - - - - 1 part ( full ) x = 720 min = 12 hours answer : b | a ) 2 hours , b ) 12 hours , c ) 3 hours , d ) 5 hours , e ) 6 hours | b | add(add(4, 4), 4) | add(n3,n3)|add(n3,#0) | physics |
when positive integer x is divided by 8 , the quotient is y and the remainder is 2 . when 2 x is divided by 7 , the quotient is 2 y and the remainder is 4 . what is the value of 6 y – x ? | "( 1 ) x = 8 y + 2 ( 2 ) 2 x = 14 y + 4 ( 2 ) - ( 1 ) : x = 6 y + 2 6 y - x = - 2 the answer is c ." | a ) - 1 , b ) 1 , c ) - 2 , d ) 2 , e ) - 3 | c | subtract(multiply(6, divide(subtract(multiply(2, 2), 4), subtract(multiply(7, 2), multiply(2, 8)))), add(multiply(8, divide(subtract(multiply(2, 2), 4), subtract(multiply(7, 2), multiply(2, 8)))), 2)) | multiply(n1,n2)|multiply(n3,n4)|multiply(n0,n2)|subtract(#0,n5)|subtract(#1,#2)|divide(#3,#4)|multiply(n6,#5)|multiply(n0,#5)|add(n1,#7)|subtract(#6,#8)| | general |
if n = 2 ^ 0.15 and n ^ b = 32 , b must equal | "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 5 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 5 b = 100 / 3 answer : d" | a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 100 / 3 , e ) 80 / 3 | d | divide(log(32), log(power(2, 0.15))) | log(n2)|power(n0,n1)|log(#1)|divide(#0,#2)| | general |
a man is 25 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is | "explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 25 ) years = > ( x + 25 ) + 2 = 2 ( x + 2 ) = > x + 27 = 2 x + 4 so , x = 23 . answer : e" | a ) 21 , b ) 22 , c ) 20 , d ) 18 , e ) 23 | e | divide(subtract(25, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | general |
during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 5 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 5 + 0.9 * 15 = 18.5 gallons , so the overall discount she got was 1.5 / 20 = 7.5 % . isabella purchased 25 gallons of gas . she paid for 5 + 0.9 * 20 = 23 gallons , so the overall discount she got was . 5 / 25 = 8 % . 8 is 8 / 7.5 * 100 = 107 % of 7.5 . answer : b ." | a ) 80 % , b ) 107 % , c ) 116.7 % , d ) 120 % , e ) 140 % | b | multiply(divide(multiply(subtract(const_1, divide(add(divide(multiply(add(10, subtract(10, const_1)), subtract(const_100, 10)), const_100), 5), 25)), const_100), multiply(subtract(const_1, divide(add(5, divide(multiply(add(10, const_4), subtract(const_100, 10)), const_100)), 20)), const_100)), const_100) | add(n0,const_4)|subtract(n0,const_1)|subtract(const_100,n0)|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(#16,cons... | gain |
jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stoc... | let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 2000 ) solving for x , we get the shares as 12000 . ans : ( option c ) | a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400 | c | add(5, 6) | add(n0,n2) | gain |
if m is a positive integer and m ^ 2 is divisible by 54 , then the largest positive integer that must divide m is ? | m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 18 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is c but if m = 54 then answer should be 16 . is the question right ? or am i missing some thing ? c | a ) 3 , b ) 6 , c ) 18 , d ) 12 , e ) 16 | c | multiply(const_3, divide(divide(54, const_3), const_3)) | divide(n1,const_3)|divide(#0,const_3)|multiply(#1,const_3) | general |
if 24 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 . s... | a ) 276 , b ) 350 , c ) 425 , d ) 512 , e ) 648 | a | divide(factorial(24), multiply(factorial(subtract(24, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)| | physics |
a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations p are possible ? | "the combinations could be p { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these ... | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) p = 8 | e | divide(240, 30) | divide(n0,n2)| | general |
in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 9,4 ) , and ( 9,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ? | "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 36 . p ( x + y < 4 ) = 8 / 36 = 2 / 9 the an... | a ) 2 / 5 , b ) 3 / 5 , c ) 3 / 7 , d ) 4 / 7 , e ) 2 / 9 | e | divide(divide(multiply(4, 4), const_2), multiply(4, add(const_1, 4))) | add(const_1,n0)|multiply(n0,n0)|divide(#1,const_2)|multiply(n0,#0)|divide(#2,#3)| | general |
for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 ? | "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 = 6 * 0 + 2 * 7.2 + 8 - 6.2 = 0 + 14.4 + 1.8 16.2 answer d" | a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 . | d | subtract(add(multiply(2, 7.2), subtract(8.4, divide(const_4, const_10))), 6.2) | divide(const_4,const_10)|multiply(n1,n4)|subtract(n5,#0)|add(#1,#2)|subtract(#3,n6)| | general |
machine a takes 100 hours to complete a certain job and starts that job at 6 am . after ten hour of working alone , machine a is joined by machine b and together they complete the job at 6 pm . how long would it have taken machine b to complete the job if it had worked alone for the entire job ? | "let us assume total job = 100 units a finishes 100 units in 100 hrs ( given ) hence a ( working rate ) = 1 units / hr now given that a works for 10 hr ( so 10 units done ) then a and b finish total work in 12 hours . hence a and b finish 90 units in 2 hours . of these 1 x 2 = 2 units were done by a . hence b did 88 un... | a ) 24.65 , b ) 22.27 , c ) 2.273 , d ) 11.62 , e ) 21.13 | c | inverse(subtract(divide(subtract(const_1, multiply(inverse(100), const_2)), subtract(subtract(multiply(6, const_2), 6), const_2)), inverse(100))) | inverse(n0)|multiply(n2,const_2)|multiply(#0,const_2)|subtract(#1,n1)|subtract(const_1,#2)|subtract(#3,const_2)|divide(#4,#5)|subtract(#6,#0)|inverse(#7)| | physics |
efrida and frazer who live 12 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ? | "it ' s a simple geometry problem . look at the diagram below : answer : d ." | a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11 | d | add(sqrt(divide(subtract(power(12, const_2), power(const_2, const_2)), const_2)), const_2) | power(n0,const_2)|power(const_2,const_2)|subtract(#0,#1)|divide(#2,const_2)|sqrt(#3)|add(#4,const_2)| | physics |
a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 7 feet and a heig... | "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 49 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 490 / 10,000 = 49 / 1000 = 0.049 ft the answer is b ." | a ) 0.07 , b ) 0.049 , c ) 0.7 , d ) 0.49 , e ) 4.9 | b | divide(volume_cylinder(7, 10), circle_area(100)) | circle_area(n0)|volume_cylinder(n2,n3)|divide(#1,#0)| | geometry |
at the end of the first quarter , the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 80 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of... | "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 80 = 25 + b + 25 b / 100 b = 44 answer ( e )" | a ) 20 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 44 % | e | multiply(subtract(divide(add(const_100, 80), add(const_100, 25)), const_1), const_100) | add(n1,const_100)|add(n0,const_100)|divide(#0,#1)|subtract(#2,const_1)|multiply(#3,const_100)| | gain |
an article is bought for rs . 1200 and sold for rs . 1300 , find the loss percent ? | "1200 - - - - 100 100 - - - - ? = > 16 2 / 3 % answer : a" | a ) 8.33 % , b ) 9.33 % , c ) 10.00 % , d ) 11.11 % , e ) 7.56 % | a | subtract(const_100, divide(multiply(1300, const_100), 1200)) | multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)| | gain |
by selling an article for $ 100 a man gains $ 20 then his gain % ? | "s . p . = $ 100 gain = $ 20 c . p . = 100 - 20 = 80 gain % = 20 / 80 * 100 = 25 % answer is a" | a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 % | a | divide(multiply(20, const_100), subtract(100, 20)) | multiply(n1,const_100)|subtract(n0,n1)|divide(#0,#1)| | gain |
john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 50 miles per hour , what is v in miles per hour ? | hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 50 = > v = 20 ... | a ) 20 , b ) 40 , c ) 50 , d ) 55 , e ) 70 | a | multiply(subtract(const_100, 80), subtract(divide(const_100, 50), divide(80, 80))) | divide(const_100,n2)|divide(n0,n0)|subtract(const_100,n0)|subtract(#0,#1)|multiply(#2,#3) | physics |
john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 5 % and the mobile phone at a profit of 10 % . overall how much he make a profit . | let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 5 / 100 ) = 15000 - 750 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 750 + 800 = rs . 50 as this is positive , an overall profit of rs . 50 was made . d | a ) s . 90 , b ) s . 120 , c ) s . 200 , d ) s . 50 , e ) s . 290 | d | subtract(multiply(10, divide(8000, const_100)), multiply(5, divide(15000, const_100))) | divide(n1,const_100)|divide(n0,const_100)|multiply(n3,#0)|multiply(n2,#1)|subtract(#2,#3) | gain |
the manufacturing cost of a shoe is rs . 230 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains | "explanation : total cost of a watch = 230 + ( 500 / 100 ) = 235 . gain = 20 % = > sp = 1.2 cp = 1.2 x 235 = 282 answer : a" | a ) s 282 , b ) s 216 , c ) s 220 , d ) s 210 , e ) s 217 | a | add(add(230, divide(500, 100)), multiply(divide(20, 100), add(230, divide(500, 100)))) | divide(n1,n2)|divide(n3,n2)|add(n0,#0)|multiply(#2,#1)|add(#2,#3)| | gain |
we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 15 , and the difference between the total number of stra... | "let x be the number of blueberries in each blue box . then there are x + 15 strawberries in each red box . x + ( x + 15 ) = 87 x = 36 the answer is e ." | a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36 | e | divide(subtract(87, 15), const_2) | subtract(n1,n0)|divide(#0,const_2)| | general |
suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 700 ( before payroll deductions ) ? | "total pay = 40 * $ 12.50 + $ 0.16 * x = 700 x = 200 / 0.16 = 1250 the answer is b ." | a ) 1220 , b ) 1250 , c ) 1280 , d ) 1310 , e ) 1340 | b | divide(subtract(700, multiply(12.50, 40)), 0.16) | multiply(n0,n2)|subtract(n3,#0)|divide(#1,n1)| | physics |
how many positive integers less than 500 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ? | "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 3 5 5 number of possibilities = 4 * 4 * 4 = 64 . then , just add up the number of 1 digits numbers = 4 , so total is 64 + 4 = 68 . answer : d" | a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84 | d | divide(factorial(subtract(add(const_4, 1), const_1)), multiply(factorial(1), factorial(subtract(const_4, const_1)))) | add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)| | probability |
a rope of which a calf is tied is increased from 12 m to 25 m , how much additional grassy ground shall it graze ? | "π ( 252 – 122 ) = 1511.71 answer : d" | a ) 1400 , b ) 141.71 , c ) 1210 , d ) 1511.71 , e ) 1500 | d | multiply(subtract(power(25, const_2), power(const_10, const_2)), divide(add(multiply(12, const_2), const_2), add(const_4, const_3))) | add(const_3,const_4)|multiply(const_10,const_2)|power(n1,const_2)|power(n0,const_2)|add(#1,const_2)|subtract(#2,#3)|divide(#4,#0)|multiply(#6,#5)| | general |
two pipes a and b can fill a tank in 30 and 60 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ? | "part filled by a in 1 min . = 1 / 30 part filled by b in 1 min . = 1 / 60 part filled by ( a + b ) in 1 min . = 1 / 30 + 1 / 60 = 1 / 20 . both the pipes can fill the tank in 20 minutes . answer : b" | a ) 10 , b ) 20 , c ) 30 , d ) 24 , e ) 25 | b | add(multiply(30, const_100), multiply(multiply(subtract(const_1, multiply(add(divide(const_1, 30), divide(const_1, 60)), const_2)), 30), const_60)) | divide(const_1,n0)|divide(const_1,n1)|multiply(n0,const_100)|add(#0,#1)|multiply(#3,const_2)|subtract(const_1,#4)|multiply(n0,#5)|multiply(#6,const_60)|add(#2,#7)| | physics |
by selling 22 pencils for a rupee a man loses 40 % . how many for a rupee should he sell in order to gain 40 % ? | "60 % - - - 22 140 % - - - ? 60 / 140 * 22 = 9.43 answer : c" | a ) 8.56 , b ) 9.35 , c ) 9.43 , d ) 6.56 , e ) 5.5 | c | multiply(divide(const_1, multiply(add(const_100, 40), divide(const_1, subtract(const_100, 40)))), 22) | add(n2,const_100)|subtract(const_100,n1)|divide(const_1,#1)|multiply(#0,#2)|divide(const_1,#3)|multiply(n0,#4)| | gain |
the difference between the place values of two threes in the numerical 40378273 is | "required difference = ( 300000 - 3 ) = 299997 . answer is b" | a ) 29997 , b ) 299997 , c ) 297 , d ) 0 , e ) none of them | b | divide(add(40378273, const_1), const_2) | add(n0,const_1)|divide(#0,const_2)| | general |
if m = 3 ^ n , what is the greatest value of n for which m is a factor of 22 ! | "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 , 18,21 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 21 = 3 x 7 - > 1 - - - - count 3 ' s = 9 so answer is 9 answer : c" | a ) 8 , b ) 10 , c ) 9 , d ) 14 , e ) 16 | c | add(floor(divide(22, 3)), floor(divide(22, power(3, const_2)))) | divide(n1,n0)|power(n0,const_2)|divide(n1,#1)|floor(#0)|floor(#2)|add(#3,#4)| | other |
a shopkeeper sold an book offering a discount of 5 % and earned a profit of 14 % . what would have been the percentage of profit earned if no discount was offered ? | "let c . p . be $ 100 . then , s . p . = $ 114 let marked price be $ x . then , 95 / 100 x = 114 x = 114 / 95 = $ 120 now , s . p . = $ 120 , c . p . = $ 100 profit % = 20 % . b" | a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150 | b | multiply(const_100, divide(add(const_100, 14), subtract(const_100, 5))) | add(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)|multiply(#2,const_100)| | gain |
three table runners have a combined area of 212 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ? | "total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 212 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 212 - 24 - 140 all three = 24 answer : c" | a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches | c | divide(subtract(subtract(212, 24), multiply(175, divide(80, const_100))), const_2) | divide(n1,const_100)|subtract(n0,n3)|multiply(n2,#0)|subtract(#1,#2)|divide(#3,const_2)| | geometry |
two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 75 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ? | "relative speed = 45 + 75 = 120 km / hr . 120 * 5 / 18 = 100 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 100 = 30 sec . answer : b" | a ) 48 , b ) 30 , c ) 26 , d ) 23 , e ) 12 | b | add(45, 75) | add(n1,n2)| | physics |
patty ran a marathon at an average speed of 3 mph for some time and then at an average speed of 6 mph for the rest of the marathon . if she made no stops during the run and her average speed for the entire marathon was 5 mph , for what fraction of the total time did she run at 3 mph ? | we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire marathon was 5 mph , she ran at 6 mph for a longer duration . 2 1 3 - - 5 - - - - 6 this shows that you can divide the entire journey in 3 equal parts . th... | a ) 1 / 5 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 1 / 3 | e | divide(subtract(6, 5), subtract(6, 3)) | subtract(n1,n2)|subtract(n1,n0)|divide(#0,#1) | general |
kamal obtained 66 , 65 , 77 , 62 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ? | sol . average = 66 + 65 + 77 + 62 + 75 / 5 ) = ( 345 / 5 ) = 69 . answer b | a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) none | b | divide(add(add(add(add(66, 65), 77), 62), 75), add(const_1, const_4)) | add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1) | general |
a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 25 % more recliners . what is the percentage increase of the gross ? | "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 25 % more ie . , 125 recliners hence her sales tields 125 * 80 = $ 10000 increase in sales = 10000 - 10000 = $ 0 so % increase = 0 * 100 / 10000 = 0 % a is... | a ) 00 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 50 % | a | subtract(multiply(multiply(subtract(const_1, divide(20, const_100)), add(const_1, divide(25, const_100))), const_100), const_100) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(#5,const_100)| | general |
a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 750 more than that by the previous schema , his sales were worth ? | "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 750 x = 6000 answer : b" | a ) s . 4,000 , b ) s . 6,000 , c ) s . 30,000 , d ) s . 40,000 , e ) s . 50,000 | b | subtract(multiply(5, const_4), const_12) | multiply(n0,const_4)|subtract(#0,const_12)| | general |
what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 22 ? | "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 3 : 6 = 1 : 2" | a ) 10 : 7 , b ) 9 : 8 , c ) 1 : 2 , d ) 13 : 11 , e ) 14 : 8 | c | divide(subtract(25, 22), subtract(22, 16)) | subtract(n1,n2)|subtract(n2,n0)|divide(#0,#1)| | general |
calculate how long it will take a swimmer to swim a distance of 7 km against the current of a river which flows at 2.5 km / hr , given that he can swim in still water at 4.4 km / h | "swim in still water at = 4.4 speed of river = 2.5 us = 4.4 - 2.5 = 1.9 distance = 7 t = 7 / 1.9 = 3.67 answer : d" | a ) 6.67 , b ) 1.67 , c ) 2.67 , d ) 3.67 , e ) 4.67 | d | divide(7, subtract(4.4, 2.5)) | subtract(n2,n1)|divide(n0,#0)| | gain |
a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 200 . the cost for 1 bat and 6 balls is $ 220 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 210 for the purchase ? | imo it should be c that is 3 reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 200 1 b + 6 c = 220 solving both we get b that is bat = 40 and c that is ball = 30 new equation 210 to be divided in equal 3 b + 3 c = 210 3 * 40 + 3 * 30 = 210 120 + 90 = 210 | ['a ) 1', 'b ) 2', 'c ) 3', 'd ) 4', 'e ) 5'] | c | divide(210, add(subtract(220, multiply(6, divide(subtract(220, divide(200, const_2)), 4))), divide(subtract(220, divide(200, const_2)), 4))) | divide(n2,const_2)|subtract(n5,#0)|divide(#1,n1)|multiply(n4,#2)|subtract(n5,#3)|add(#2,#4)|divide(n6,#5) | geometry |
if the product of the integers from 1 to n is divisible by 686 , what is the least possible value of n ? | "686 = 7 x 7 x 7 x 2 n must include at least 7 , 2 * 7 , and 3 * 7 . the answer is c ." | a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35 | c | multiply(divide(divide(divide(686, const_3), add(const_3, const_4)), add(const_3, const_4)), const_3) | add(const_3,const_4)|divide(n1,const_3)|divide(#1,#0)|divide(#2,#0)|multiply(#3,const_3)| | general |
find the area of a parallelogram with base 12 cm and height 18 cm . | "area of a parallelogram = base * height = 12 * 18 = 216 cm 2 answer : option b" | a ) 200 , b ) 216 , c ) 345 , d ) 244 , e ) 242 | b | multiply(12, 18) | multiply(n0,n1)| | geometry |
if a number p is prime , and 2 p + 4 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ? | "1 / 6 = 0.1666666 . . . ( a repeating pattern one digit long ) a" | a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9 | a | subtract(divide(subtract(add(166, 1), 4), 2), subtract(divide(subtract(add(166, 1), 4), 2), 1)) | add(n2,n4)|subtract(#0,n1)|divide(#1,n0)|subtract(#2,n2)|subtract(#2,#3)| | general |
a train 110 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is | speed of train relative to man : 110 / 6 * 18 / 5 km / hr = 66 km / hr let speed of train = x therefore x + 6 = 66 x = 66 - 6 x = 60 km / hr answer : b | a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 82 kmph | b | divide(divide(subtract(110, multiply(multiply(6, const_0_2778), 6)), 6), const_0_2778) | multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778) | physics |
a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , the how old is b ? | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 x = 6 . hence , b ' s age = 2 x = 12 years . b )" | a ) 10 years , b ) 12 years , c ) 14 years , d ) 15 years , e ) 16 years | b | divide(multiply(subtract(32, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)| | general |
a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 45000 rs , what is the value of buzness ? | "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 45000 - > x = 150000 answer : b" | a ) 150000 , b ) 90000 , c ) 85000 , d ) 190000 , e ) 250000 | b | divide(45000, multiply(divide(2, 3), divide(3, 4))) | divide(n0,n1)|divide(n1,n3)|multiply(#0,#1)|divide(n4,#2)| | general |
in a certain company , the formula for maximizing profits is p = - 25 x ^ 2 + 7500 x , , where p is profit and x is the number of machines the company operates in its factory . what value for x will maximize p ? this one is from integratedlearning . here ' s what i did : the oa states : to find a maximum or minimum val... | recognize that 25 is a factor of 7500 . if we take this out , we have two parts to the equation : - x ^ 2300 x one part of the equation brings our value down , whereas the other part brings our value up . at this point , we can test the numbers in the answer choice . notice that they are very straight forward to square... | a ) 10 , b ) 50 , c ) 150 , d ) 200 , e ) 300 | c | divide(divide(7500, multiply(const_2, sqrt(25))), sqrt(25)) | sqrt(n0)|multiply(#0,const_2)|divide(n2,#1)|divide(#2,#0) | general |
in the coordinate plane , one of the vertices of a square is the point ( - 5 , - 4 ) . if the diagonals of that square intersect at point ( 3 , 2 ) , what is the area of that square ? | "one point ( - 5 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 5 - 3 = - 8 is the midpoint of the square - - > whole side 16 , 16 * 16 = 256 d" | a ) 100 , b ) 225 , c ) 169 , d ) 256 , e ) 324 | d | multiply(multiply(5, 3), multiply(5, 3)) | multiply(n0,n2)|multiply(#0,#0)| | geometry |
the cost of the paint is rs . 30 per kg . if 1 kg of paint covers 18 sq . ft , how much will it cost to paint outside of a cube having 6 feet each side | "explanation : surface area of a cube = 6 x 6 ^ 2 = 216 sq . ft quantity of paint required = ( 216 / 18 ) = 12 kg cost of painting = 30 x 18 = rs . 540 answer : c" | a ) rs . 962 , b ) rs . 672 , c ) rs . 540 , d ) rs . 876 , e ) none of these | c | multiply(divide(surface_cube(6), 18), 30) | surface_cube(n3)|divide(#0,n2)|multiply(n0,#1)| | geometry |
what is the smallest number which when diminished by 18 , is divisible 8 , 14 , 26 and 28 ? | "required number = ( lcm of 8 , 14 , 26 and 28 ) + 18 = 728 + 18 = 746 option a" | a ) 746 , b ) 750 , c ) 789 , d ) 678 , e ) 897 | a | add(lcm(lcm(8, 14), lcm(26, 28)), 18) | lcm(n1,n2)|lcm(n3,n4)|lcm(#0,#1)|add(n0,#2)| | general |
in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 11 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture . | "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 11 ) = 36 / 20 = 9 / 5 . answer : d ." | a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 9 / 5 , e ) 3 / 2 | d | divide(subtract(45, divide(45, add(4, 1))), add(divide(45, add(4, 1)), 11)) | add(n1,n2)|divide(n0,#0)|add(n3,#1)|subtract(n0,#1)|divide(#3,#2)| | general |
two men started from the same place walk at the rate of 5 kmph and 5.5 kmph respectively . what time will they take to be 8.5 km apart , if they walk in the same direction ? | "to be 0.5 km apart they take 1 hour to be 8.5 km apart they take = 1 / 0.5 * 8.5 = 17 hours answer is c" | a ) 10 hours , b ) 12 hours , c ) 17 hours , d ) 15 hours , e ) 20 hours | c | divide(subtract(5.5, 5), 8.5) | subtract(n1,n0)|divide(#0,n2)| | gain |
? % of 360 = 162 | "? % of 360 = 162 or , ? = 162 × 100 / 360 = 45 answer c" | a ) 277 , b ) 36 , c ) 45 , d ) 72 , e ) none of these | c | divide(multiply(162, const_100), 360) | multiply(n1,const_100)|divide(#0,n0)| | gain |
how many factors does 35 ^ 2 have ? | "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 6 * 4 = 24 answer c ." | a ) 2 , b ) 8 , c ) 24 , d ) 25 , e ) 26 | c | divide(35, multiply(const_10, const_2)) | multiply(const_10,const_2)|divide(n0,#0)| | other |
at an elementary school , 60 % of the faculty members are women and 60 % of the faculty members are married . if 3 / 4 of the men are single , what fraction of the men are married ? | - - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 30 - - - - - 10 - - - - - - - - - 40 total - - - - - - - - - - - - - 40 - - - - - 60 - - - - - - - - 100 need married man / total man , so 10 / 40 = 1 / 4 e | a ) 3 / 4 , b ) 2 / 5 , c ) 4 / 5 , d ) 2 / 3 , e ) 1 / 4 | e | subtract(const_1, divide(3, 4)) | divide(n2,n3)|subtract(const_1,#0) | gain |
p , q , r enter into a partnership & their share are in the ratio 1 / 2 : 1 / 3 : 1 / 4 , after two months , p withdraws half of the capitals & after 10 months , a profit of rs 378 is divided among them . what is r ' s share ? | explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 r ' s... | a ) 108 , b ) 120 , c ) 134 , d ) 144 , e ) none of these | a | divide(multiply(378, multiply(3, 2)), multiply(add(4, 3), 3)) | add(n3,n5)|multiply(n1,n3)|multiply(n7,#1)|multiply(n3,#0)|divide(#2,#3) | general |
light glows for every 18 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am | "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 18 = 276 . so total 277 times light ll glow answer : b" | a ) 281 , b ) 277 , c ) 283 , d ) 384 , e ) 385 | b | divide(add(add(const_2, 47), multiply(add(20, add(const_2, const_60)), const_60)), 18) | add(n6,const_2)|add(const_2,const_60)|add(n5,#1)|multiply(#2,const_60)|add(#0,#3)|divide(#4,n0)| | physics |
find the smallest number which leaves 2235 , 48 and 61 as remainders when divided by 26 , 39 , 52 and 65 respectively . | answer : d | a ) 67 , b ) 26 , c ) 99 , d ) 26 , e ) 91 | d | add(divide(48, const_2), const_2) | divide(n1,const_2)|add(#0,const_2) | general |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.