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 |
|---|---|---|---|---|---|---|
if ( 2 ^ 13 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ? | "given 2 ^ 13 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 13 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans b on comparing the power of 2 = > m = 13" | a ) 7 , b ) 13 , c ) 15 , d ) 16 , e ) 23 | b | power(divide(10, 5), const_4) | divide(n4,n3)|power(#0,const_4)| | general |
a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 36,000 , what will be the amount a receives ? | total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 β 3 x + 14000 = 50000 β 3 x = 50000 β 14000 = 36000 β x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 invest... | a ) 15120 , b ) 14500 , c ) 14900 , d ) 14300 , e ) 14000 | a | multiply(add(divide(subtract(multiply(5000, const_10), add(add(4000, 5000), 5000)), const_3), add(4000, 5000)), divide(multiply(multiply(const_3, const_12), const_1000), multiply(5000, const_10))) | add(n1,n2)|multiply(n2,const_10)|multiply(const_12,const_3)|add(n2,#0)|multiply(#2,const_1000)|divide(#4,#1)|subtract(#1,#3)|divide(#6,const_3)|add(#0,#7)|multiply(#8,#5) | general |
a glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution . if 500 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ? | "we are given that a glucose solution contains 20 grams of glucose per 1000 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of glucose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of glucose would be in the container wh... | a ) 10.00 , b ) 15.00 , c ) 11.50 , d ) 10.50 , e ) 9.75 | a | multiply(500, divide(20, 1000)) | divide(n0,n1)|multiply(n2,#0)| | physics |
right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 6 β€ x β€ 2 and 4 β€ y β€ 9 , then how many different triangles can be drawn that will meet ... | "we have the rectangle with dimensions 9 * 6 ( 9 horizontal dots and 6 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 6 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot... | a ) 54 , b ) 432 , c ) 2,160 , d ) 2,916 , e ) 148,824 | c | multiply(multiply(6, subtract(6, const_1)), multiply(9, 6)) | multiply(n0,n3)|subtract(n0,const_1)|multiply(n0,#1)|multiply(#2,#0)| | geometry |
the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 6000 , brokerage being 1 / 4 % , is : | face value = rs . 6000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 6000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs ... | a ) 83.08 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75 | a | subtract(multiply(divide(6000, 756), 10.5), divide(1, 4)) | divide(n2,n1)|divide(n3,n4)|multiply(n0,#0)|subtract(#2,#1) | gain |
the curved surface of a sphere is 64 pi cm 2 . find its radius ? | "4 Γ― β¬ r 2 = 64 = > r = 4 answer b" | a ) 1 cm , b ) 4 cm , c ) 2 cm , d ) 3 cm , e ) 5 cm | b | sqrt(divide(64, const_4)) | divide(n0,const_4)|sqrt(#0)| | physics |
a hollow iron pipe is 42 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 3 g / cm 3 , then the weight of the pipe is : | "external radius = 4 cm , internal radius = 3 cm . volume of iron = 22 / 7 x ( ( 4 square ) - ( 3 square ) ) x 42 = ( 22 / 7 ) x 7 x 1 x 42 cm 3 . = 924 cm 3 . weight of iron = ( 924 x 3 ) gm = 2772 gm = 2.772 kg answer : e" | a ) 2.172 kg , b ) 2.272 kg , c ) 2.282 kg , d ) 2.992 kg , e ) 2.772 kg | e | divide(multiply(subtract(volume_cylinder(divide(8, const_2), 42), volume_cylinder(subtract(divide(8, const_2), const_1), 42)), 8), const_1000) | divide(n1,const_2)|subtract(#0,n2)|volume_cylinder(#0,n0)|volume_cylinder(#1,n0)|subtract(#2,#3)|multiply(n3,#4)|divide(#5,const_1000)| | physics |
a shopping cart contains only apples , oranges , and pears . if there are 3 times as many oranges as apples , and 4 times as many pears as oranges , then the apples are equivalent to what fraction of the pears ? | o = 3 a p = 4 o = 12 a a = p / 12 the answer is c . | a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 12 , d ) 1 / 4 , e ) 3 / 4 | c | divide(const_1, multiply(4, 3)) | multiply(n0,n1)|divide(const_1,#0) | general |
the compound interest earned by sunil on a certain amount at the end of two years at the rate of 6 % p . a . was rs . 370.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned . | let the sum be rs . p p { [ 1 + 6 / 100 ] 2 - 1 } = 370.80 p ( 6 / 100 ) ( 2 + 6 / 100 ) = 370.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 246 / ( 0.05 ) ( 2.05 ) = 3000 . amount = rs . 3370.80 . answer : b | a ) rs . 3360.80 , b ) rs . 3370.80 , c ) rs . 3320.70 , d ) rs . 3230.80 , e ) rs . 3130.80 | b | add(divide(370.8, subtract(power(add(const_1, divide(6, const_100)), const_2), const_1)), 370.8) | divide(n0,const_100)|add(#0,const_1)|power(#1,const_2)|subtract(#2,const_1)|divide(n1,#3)|add(n1,#4) | gain |
q ' = 3 q - 3 , what is the value of ( 3 ' ) ' ? | "( 3 ' ) ' = ( 3 * 3 - 3 ) ' = 6 ' = 6 * 6 - 6 = 30 answer d" | a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 40 | d | multiply(subtract(multiply(subtract(multiply(3, 3), 3), 3), 3), subtract(3, const_1)) | multiply(n0,n2)|subtract(n2,const_1)|subtract(#0,n0)|multiply(n0,#2)|subtract(#3,n0)|multiply(#4,#1)| | general |
five equal cubes , each of side 5 cm , are placed adjacent to each other . the volume of the new solid formed will be | solution the new solid formed is a cuboid of length 25 cm , breadth 5 cm and height 5 cm β΄ volume = ( 25 x 5 x 5 ) cm 3 βΉ = βΊ 625 cm 3 answer b | ['a ) 125 cm 3', 'b ) 625 cm 3', 'c ) 15525 cm 3', 'd ) 1225 cm 3', 'e ) none'] | b | multiply(volume_cube(5), add(const_4, const_1)) | add(const_1,const_4)|volume_cube(n0)|multiply(#0,#1) | geometry |
a watch was sold at a loss of 10 % . if it was sold for rs . 180 more , there would have been a gain of 5 % . what is the cost price ? | "90 % 105 % - - - - - - - - 15 % - - - - 180 100 % - - - - ? = > rs . 1200 answer : a" | a ) rs . 1200 , b ) rs . 1100 , c ) rs . 1300 , d ) rs . 1400 , e ) rs . 1000 | a | divide(multiply(180, const_100), subtract(add(const_100, 5), subtract(const_100, 10))) | add(const_100,n2)|multiply(n1,const_100)|subtract(const_100,n0)|subtract(#0,#2)|divide(#1,#3)| | gain |
a train 80 m in length crosses a telegraph post in 6 seconds . the speed of the train is ? | "s = 80 / 6 * 18 / 5 = 48 kmph answer : d" | a ) 16 kmph , b ) 88 kmph , c ) 54 kmph , d ) 48 kmph , e ) 19 kmph | d | multiply(const_3_6, divide(80, 6)) | divide(n0,n1)|multiply(#0,const_3_6)| | physics |
a man can row upstream at 7 kmph and downstream at 33 kmph , and then find the speed of the man in still water ? | "us = 7 ds = 33 m = ( 33 + 7 ) / 2 = 20 answer : d" | a ) 11 , b ) 77 , c ) 30 , d ) 20 , e ) 34 | d | divide(add(7, 33), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
in a class of 150 students 55 speak english ΝΎ 85 speak telugu and 30 speak neither english nor telugu how many speak both english and telugu ? | total = 150 english = 55 telugu = 85 none / neither english nor telugu = 30 no . of students who speak only one or both = 150 - 30 = 120 so , 120 stud ' s can speak english or telugu or both . then , no . of stud ' s speak only english = 120 - 85 ( telugu ) = 35 ` ` ` ` ` ` ` ` ` ` telugu = 120 - 55 = 65 remaining 120 ... | a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50 | b | subtract(add(55, 85), subtract(150, 30)) | add(n1,n2)|subtract(n0,n3)|subtract(#0,#1) | other |
of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 110 geese survived the first year and if no more than one goose hatched from each egg , how many ... | "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first y... | a ) 280 , b ) 400 , c ) 540 , d ) 550 , e ) 840 | d | divide(divide(divide(110, subtract(const_1, divide(3, 5))), divide(3, 4)), divide(2, 3)) | divide(n1,n5)|divide(n1,n3)|divide(n0,n1)|subtract(const_1,#0)|divide(n6,#3)|divide(#4,#1)|divide(#5,#2)| | general |
a library has an average of 510 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is : | "explanation : since the month begins with a sunday , to there will be five sundays in the month . required average = ( 510 Γ 5 + 240 Γ 25 / 30 ) = 8550 / 30 = 285 answer : d" | a ) 250 , b ) 276 , c ) 280 , d ) 285 , e ) 295 | d | divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 510), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 240)), 30) | add(const_3,const_4)|divide(n2,#0)|floor(#1)|add(#2,const_1)|multiply(n0,#3)|subtract(n2,#3)|multiply(n1,#5)|add(#4,#6)|divide(#7,n2)| | general |
the price of a t . v . set worth rs . 15000 is to be paid in 20 installments of rs . 1500 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ? | "money paid in cash = rs . 1500 balance payment = ( 15000 - 1500 ) = rs . 13500 . answer : c" | a ) 29997 , b ) 28088 , c ) 13500 , d ) 19000 , e ) 2799 | c | subtract(15000, 1500) | subtract(n0,n2)| | gain |
a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 5 cubic feet . if a large block has three times the width , twice the depth , and half the length of a normal block , what is the volume of cheese in a large block in cubic feet ? | "volume of cube = lbh = 5 new cube l , b , h are increases of 3 b , 2 h and a decrease of . 5 l new volume of cube = . 5 l * 3 b * 2 h = 3 * lbh = 3 * 5 = 15 answer : c" | a ) 10 , b ) 30 , c ) 15 , d ) 20 , e ) 25 | c | multiply(multiply(multiply(const_2, const_2), const_2), 5) | multiply(const_2,const_2)|multiply(#0,const_2)|multiply(n0,#1)| | geometry |
after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 60 % full . if the original contents of the reservoir totaled 240 billion gallons , the reservoir was approximately what percentage full before the storm ? | "when the storm deposited 120 billion gallons , volume of water in the reservoir = 240 + 120 = 360 billion gallons if this is only 60 % of the capacity of the reservoir , the total capacity of the reservoir = 360 / 0.6 = 600 billion gallons therefore percentage of reservoir that was full before the storm = ( 240 / 600 ... | a ) 40 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 % | c | multiply(divide(240, divide(add(120, 240), divide(60, const_100))), const_100) | add(n0,n2)|divide(n1,const_100)|divide(#0,#1)|divide(n2,#2)|multiply(#3,const_100)| | general |
the average of first six prime numbers greater than 65 is ? | "67 + 71 + 73 + 79 + 83 + 89 = 462 / 6 = 77 answer : b" | a ) 55 , b ) 77 , c ) 56 , d ) 67 , e ) 98 | b | add(65, const_1) | add(n0,const_1)| | general |
crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 25 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it ... | "deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $... | a ) $ 75 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 100 | a | subtract(divide(50, divide(50, const_100)), multiply(divide(50, divide(50, const_100)), divide(25, const_100))) | divide(n1,const_100)|divide(n0,const_100)|divide(n1,#0)|multiply(#2,#1)|subtract(#2,#3)| | general |
' a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the addition of the maximum and minimum possible values of ' a + b ' ? | "possible values of a and b can be 5,4 ; 4,5 ( which are same for a + b ) and 1,20 ; 20,1 ( same result for a + b ) so 21 + 9 = 30 . ans b ." | a ) 28 , b ) 30 , c ) 22 , d ) 20 , e ) 32 | b | subtract(add(divide(20, const_4), const_4), add(divide(20, const_4), const_4)) | divide(n0,const_4)|add(#0,const_4)|subtract(#1,#1)| | general |
what is the area of an equilateral triangle whose one side length is 70 ? | - > the area of an equilateral triangle with one side length of a is β 3 a 2 / 4 . thus , β 3 ( 70 ^ 2 ) / 4 = 1225 β 3 and the answer is e . | a ) 825 β 3 , b ) 925 β 3 , c ) 1025 β 3 , d ) 1125 β 3 , e ) 1225 β 3 | e | triangle_area_three_edges(70, 70, 70) | triangle_area_three_edges(n0,n0,n0)| | geometry |
speed of a boat in standing water is 9 kmph and speed of the stream is 1.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ? | "speed upstream = 7.5 kmph speed downstream = 10.5 kmph total time taken = 105 / 7.5 + 105 / 10.5 = 24 hours answer is b" | a ) 12 hours , b ) 24 hours , c ) 36 hours , d ) 10 hours , e ) 15 hours | b | add(multiply(add(add(9, 1.5), subtract(9, 1.5)), 105), multiply(subtract(add(divide(105, add(9, 1.5)), divide(105, subtract(9, 1.5))), add(add(9, 1.5), subtract(9, 1.5))), const_60)) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|divide(n2,#0)|divide(n2,#1)|add(#3,#4)|multiply(n2,#2)|subtract(#5,#2)|multiply(#7,const_60)|add(#6,#8)| | physics |
the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 30 metres ? | "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 30 / 5 = 6 seconds . answer : a" | a ) 6 , b ) 8 , c ) 12 , d ) 4 , e ) 13 | a | divide(30, multiply(add(15, 3), const_0_2778)) | add(n0,n1)|multiply(#0,const_0_2778)|divide(n2,#1)| | physics |
a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 62.50 , his capital is ? | "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 62.50 32 x - 31 x = 6250 * 4 x = 25,000 . answer : b" | a ) 24,602 , b ) 25,000 , c ) 24,600 , d ) 24,628 , e ) 24,6012 | b | divide(62.50, divide(const_4, 4)) | divide(const_4,n3)|divide(n4,#0)| | gain |
harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 65 per kg . how much amount did he pay to the shopkeeper ? | "cost of 8 kg grapes = 70 Γ 8 = 560 . cost of 9 kg of mangoes = 65 Γ 9 = 585 . total cost he has to pay = 560 + 585 = 1145 . c )" | a ) a ) 1055 , b ) b ) 1075 , c ) c ) 1145 , d ) d ) 1070 , e ) e ) 1080 | c | add(multiply(8, 70), multiply(9, 65)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | gain |
it was calculated that 75 men could complete a piece of work in 20 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ? | "before : one day work = 1 / 20 one man β s one day work = 1 / ( 20 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 20 * 75 ) the total no . of days required to complete the work = ( 75 * 20 ) / 50 = 30 answer : b" | a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 40 | b | multiply(20, divide(75, 25)) | divide(n0,n2)|multiply(n1,#0)| | physics |
the number of diagonals of a polygon of n sides is given by the formula z = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ? | "z = n ( n - 3 ) z = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b" | a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | b | add(3, 2) | add(n0,n1)| | general |
divide rs . 32000 in the ratio 3 : 9 ? | "3 / 12 * 32000 = 8000 9 / 12 * 32000 = 24000 answer : e" | a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 12000 , 20007 , d ) 12000 , 20006 , e ) 8000 , 24000 | e | multiply(subtract(9, const_2), divide(32000, add(3, subtract(9, const_2)))) | subtract(n2,const_2)|add(n1,#0)|divide(n0,#1)|multiply(#2,#0)| | other |
what will be the remainder if 2 ^ 300 is divided by 4 ? | d 4 now if you go on calculating 2 ^ 300 , you will lose so much time and it might not even be feasible to carry out so long of calculations . thus we will make use of a trick here . we will calculate the remainder of each power of 2 till we come across a pattern . 2 ^ 1 divided by 4 leaves the remainder 2 . 2 ^ 2 divi... | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | d | power(2, const_2) | power(n0,const_2) | general |
a movie buff owns movies on dvd and on blu - ray in a ratio of 7 : 2 . if she buys 5 more blu - ray movies , that ratio would change to 13 : 4 . if she owns movies on no other medium , what was the original number of movies in her library before the extra purchase ? | if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 7 x and b ( d ) = 2 x now from the next line the new eqn becomes 7 x / ( 2 x + 6 ) = 13 / 4 solving it 28 x = 26 x + 78 x = 39 which means m ( d ) = 273 and ... | a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 351 | e | multiply(divide(multiply(13, add(5, const_1)), subtract(multiply(4, 7), multiply(13, 2))), add(7, 2)) | add(n0,n1)|add(n2,const_1)|multiply(n0,n4)|multiply(n1,n3)|multiply(n3,#1)|subtract(#2,#3)|divide(#4,#5)|multiply(#0,#6) | general |
three numbers are in the ratio 1.5 : 2 : 3.5 and their h . c . f is 18 . the numbers are : | "let the required numbers be 1.5 x , 2 x and 3.5 x . then , their h . c . f = x . so , x = 18 . the numbers are 27,36 , 63 . answer : e" | a ) 22,36 , 63 , b ) 27,45 , 63 , c ) 27,54 , 63 , d ) 54 , 45 , 36 , e ) 27,36 , 63 | e | add(multiply(multiply(1.5, 3.5), const_100), multiply(2, 3.5)) | multiply(n0,n2)|multiply(n1,n2)|multiply(#0,const_100)|add(#2,#1)| | other |
10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4500 , how much was it in the beginning ? | "x * ( 90 / 100 ) * ( 80 / 100 ) = 4500 x = 6250 answer : c" | a ) 5999 , b ) 6788 , c ) 6250 , d ) 4559 , e ) 6989 | c | floor(divide(4500, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 20), const_100)))) | subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,const_100)|divide(#1,const_100)|multiply(#2,#3)|divide(n2,#4)|floor(#5)| | general |
the tax on a commodity is diminished by 25 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ? | "explanation : 100 * 100 = 10000 75 * 110 = 8250 10000 - - - - - - - 1750 100 - - - - - - - ? = 17.5 % e )" | a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 17.5 % | e | subtract(const_100, divide(multiply(add(const_100, 10), subtract(const_100, 25)), const_100)) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|subtract(const_100,#3)| | general |
a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 48 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ? | "l = 48 / 12 = 4 ft w = 72 / 12 = 6 ft area of paper = 24 area of cube = 4 * side ^ 2 side of cube = 2 v of cube = 8" | a ) a 8 , b ) b 22 , c ) c 27 , d ) d 40 , e ) e 51 | a | divide(48, divide(divide(divide(volume_cube(divide(divide(sqrt(rectangle_area(48, 72)), const_3), const_2)), 12), 12), 12)) | rectangle_area(n0,n1)|sqrt(#0)|divide(#1,const_3)|divide(#2,const_2)|volume_cube(#3)|divide(#4,n3)|divide(#5,n3)|divide(#6,n3)|divide(n0,#7)| | geometry |
the sum of the first 60 positive even integers is 3,750 . what is the sum of the odd integers from 101 to 200 , inclusive ? | "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 60 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 60 positive even integers = 3750 sum of 1 st 100 odd numbers = ... | a ) 4,700 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600 | a | multiply(divide(add(200, 101), const_2), add(divide(subtract(200, 101), const_2), const_1)) | add(n2,n3)|subtract(n3,n2)|divide(#1,const_2)|divide(#0,const_2)|add(#2,const_1)|multiply(#4,#3)| | general |
a wooden cube whose edge length is 6 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least ... | there are a total of 6 * 6 * 6 = 216 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 4 * 4 * 4 = 64 cubes . the number of cubes with at least one side painted red is 216 - 64 = 152 cubes the probability that a cube has at least one side painted red is 152 / 216 which i... | ['a ) 54.9 %', 'b ) 58.7 %', 'c ) 62.5 %', 'd ) 66.3 %', 'e ) 70.4 %'] | e | multiply(const_100, subtract(const_1, divide(volume_cube(multiply(const_1, const_4)), volume_cube(6)))) | multiply(const_1,const_4)|volume_cube(n0)|volume_cube(#0)|divide(#2,#1)|subtract(const_1,#3)|multiply(#4,const_100) | geometry |
ages of two persons differ by 18 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age | "explanation : let the age of younger person is x , then elder person age is ( x + 18 ) = > 3 ( x - 6 ) = ( x + 18 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 12 = > x = 15 . so other person age is x + 18 = 33 answer : option b" | a ) 12,28 , b ) 15,33 , c ) 16,32 , d ) 18,34 , e ) 19,34 | b | subtract(divide(subtract(add(multiply(6, 6), 18), 6), subtract(6, const_1)), const_1) | multiply(n1,n1)|subtract(n1,const_1)|add(n0,#0)|subtract(#2,n1)|divide(#3,#1)|subtract(#4,const_1)| | general |
the h . c . f . of two numbers is 28 and the other two factors of their l . c . m . are 12 and 15 . the larger of the two numbers is | "solution clearly , the numbers are ( 28 x 12 ) and ( 28 x 15 ) . larger number = ( 28 x 15 ) = 420 . answer a" | a ) 420 , b ) 430 , c ) 312 , d ) 322 , e ) none | a | multiply(28, 15) | multiply(n0,n2)| | other |
in the first 8 overs of a cricket game , the run rate was only 2.3 what should be the rate in the remaining 20 overs to reach the target of 260 runs ? | "required run rate = [ 260 - ( 2.3 * 8 ) ] / 20 = 241.60 / 20 = 12.08 answer : a" | a ) 12.08 , b ) 12.18 , c ) 12.0 , d ) 6.19 , e ) 6.21 | a | divide(subtract(260, multiply(8, 2.3)), 20) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | gain |
in the first 20 overs of a cricket game , the run rate was only 4.3 . what should be the run rate in the remaining 30 overs to reach the target of 264 runs ? | "explanation : required run rate = ( 264 - ( 4.3 x 20 ) ) / 30 = 178 / 30 = 5.93 answer : a" | a ) 5.93 , b ) 6.5 , c ) 6.75 , d ) 7 , e ) 8 | a | divide(subtract(264, multiply(20, 4.3)), 30) | multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)| | gain |
at what price must an article costing rs . 150 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 30 % on the cost price ? | "cp = 150 sp = 150 * ( 130 / 100 ) = 195 mp * ( 90 / 100 ) = 195 mp = 216.67 answer : d" | a ) 62.5 , b ) 62.0 , c ) 62.6 , d ) 216.67 , e ) 62.2 | d | divide(multiply(add(150, divide(multiply(150, 30), const_100)), const_100), subtract(const_100, 10)) | multiply(n0,n2)|subtract(const_100,n1)|divide(#0,const_100)|add(n0,#2)|multiply(#3,const_100)|divide(#4,#1)| | gain |
a man can row 8 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ? | "m = 8 s = 2 ds = 10 us = 6 x / 10 + x / 6 = 1 x = 3.75 d = 3.75 * 2 = 7.5 answer : c" | a ) 5.75 , b ) 5.7 , c ) 7.5 , d ) 5.74 , e ) 5.71 | c | multiply(divide(multiply(add(8, 2), subtract(8, 2)), add(add(8, 2), subtract(8, 2))), const_2) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|multiply(#0,#1)|divide(#3,#2)|multiply(#4,const_2)| | physics |
all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes are there whose three faces are coloured ? | there are 64 small cubes , hence one side side of the big cube is 3 β 64 = 4 cm number of small cubes having three faces coloured = no . of corners = 8 answer : b | ['a ) 4', 'b ) 8', 'c ) 16', 'd ) 24', 'e ) 2'] | b | divide(divide(64, const_4), const_2) | divide(n0,const_4)|divide(#0,const_2) | geometry |
an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ? | "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1260 ) * 100 = 25 % answer e" | a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25 % | e | multiply(divide(multiply(divide(60, const_100), 525), multiply(const_100, power(const_4, const_2))), const_100) | divide(n2,const_100)|power(const_4,const_2)|multiply(n1,#0)|multiply(#1,const_100)|divide(#2,#3)|multiply(#4,const_100)| | gain |
if the sides of a square are doubled in length , the area of the original square is now how many times as large as the area of the resultant square ? | let the original square have sides of length l and the new square have sides of length 2 l . the resulting areas are l ^ 2 for the original square and 4 l ^ 2 for the new square ( as the length of the side is square to get the area ) . the original square ' s area is l ^ 2 / 4 l ^ 2 or 25 % of the new square ' s area .... | a ) 25 % , b ) 50 % , c ) 100 % , d ) 200 % , e ) 400 % | a | multiply(power(divide(const_1, const_2), const_2), const_100) | divide(const_1,const_2)|power(#0,const_2)|multiply(#1,const_100) | geometry |
there are 16 bees in the hive , then 10 more fly . how many bees are there in all ? | 16 + 10 = 26 . answer is e . | a ) 7 , b ) 33 , c ) 12 , d ) 17 , e ) 26 | e | add(16, 10) | add(n0,n1)| | general |
the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 612 . what is the banker ' s discount ? | "explanation : td = ( bg Γ 100 ) / tr = ( 612 Γ 100 ) / ( 6 Γ 12 ) = rs . 850 bg = bd β td = > 612 = bd - 850 = > bd = 612 + 850 = 1462 answer : option d" | a ) 1240 , b ) 1120 , c ) 1190 , d ) 1462 , e ) none of these | d | add(612, divide(multiply(612, const_100), multiply(12, 6))) | multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)|add(n2,#2)| | gain |
if remainder is 19 , quotient is 61 and dividend is 507 then what is divisor ? | "we know dividend = divisor * quotient + remainder = = = > 507 = divisor * 61 + 19 = = = = = > 488 / 61 = divisor = = = > divisor = 8 ans - a" | a ) 8 , b ) 18 , c ) 10 , d ) 12 , e ) 14 | a | divide(subtract(507, 19), 61) | subtract(n2,n0)|divide(#0,n1)| | general |
the average salary of raj and roshan is rs . 4000 but the average salary of raj , roshan and thomas is rs . 5000 . what is the salary of thomas ? | total salary of raj and roshan = 2 x 4000 = 8000 total salary of raj roshan and thomas = 3 x 5000 = 15000 salary of thomas = 15000 - 8000 = rs . 7000 answer : d | a ) 4000 , b ) 5000 , c ) 6000 , d ) 7000 , e ) 8000 | d | subtract(add(5000, 4000), multiply(const_1000, const_2)) | add(n0,n1)|multiply(const_1000,const_2)|subtract(#0,#1) | general |
gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 45 and the turban . find the price of the turban . | "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 45 . thus , 3434 ( 90 + x ) = 45 + x or 270 + 3 x = 180 + 4 x or x = 90 answer : d" | a ) 27 , b ) 36 , c ) 29 , d ) 90 , e ) 11 | d | subtract(multiply(divide(subtract(90, 45), subtract(const_12, 9)), const_12), 90) | subtract(n0,n2)|subtract(const_12,n1)|divide(#0,#1)|multiply(#2,const_12)|subtract(#3,n0)| | general |
the radius of a semi circle is 35 cm then its perimeter is ? | "diameter 70 cm 1 / 2 * 22 / 7 * 70 + 70 = 180 answer : b" | a ) 32.8 , b ) 180 , c ) 32.1 , d ) 32.2 , e ) 32.9 | b | add(divide(circumface(35), const_2), multiply(35, const_2)) | circumface(n0)|multiply(n0,const_2)|divide(#0,const_2)|add(#2,#1)| | physics |
an inspector rejects 0.06 % of the meters as defective . how many will he examine to reject 2 ? | "let the number of meters to be examined be x then , 0.06 % of x = 2 ( 6 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 3333 answer is e" | a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 3333 | e | divide(multiply(2, const_100), 0.06) | multiply(n1,const_100)|divide(#0,n0)| | gain |
the present worth of rs . 1404 due in two equal half - yearly installments at 8 % per annum simple interest is : | "time = 1 / 2 yr r = 8 % let pw = x si = 1404 - x x * 1 / 2 * 8 / 100 = 1404 - x . ( ref problm 10 of si , rs aggarwal ) x = 1404 * 25 / 26 hence x = 1350 answer : c" | a ) rs . 1325 , b ) rs . 1300 , c ) rs . 1350 , d ) rs . 1500 , e ) rs . 1600 | c | add(divide(divide(1404, const_2), divide(add(const_100, 8), const_100)), divide(divide(1404, const_2), divide(add(const_100, divide(8, const_2)), const_100))) | add(n1,const_100)|divide(n0,const_2)|divide(n1,const_2)|add(#2,const_100)|divide(#0,const_100)|divide(#1,#4)|divide(#3,const_100)|divide(#1,#6)|add(#5,#7)| | gain |
a train moves with a speed of 72 kmph . its speed in metres per second is | "solution speed = 72 kmph = ( 72 x 5 / 18 ) m / sec = 20 m / sec . answer d" | a ) 10.8 , b ) 18 , c ) 30 , d ) 20 , e ) none | d | multiply(72, const_0_2778) | multiply(n0,const_0_2778)| | physics |
40 % of 2 is equal to | 40 % of 2 = ( 40 / 100 ) * 2 = 0.8 answer : option b | a ) 0.2 , b ) 0.8 , c ) 0.6 , d ) 0.7 , e ) 0.9 | b | divide(multiply(40, 2), const_100) | multiply(n0,n1)|divide(#0,const_100) | gain |
how many positive integers less than 243 are multiple of 4 but not multiples of 6 ? | "240 / 4 = 60 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 60 - 20 = 40 answer : d" | a ) 20 , b ) 31 , c ) 42 , d ) 40 , e ) 64 | d | divide(factorial(subtract(add(const_4, 4), const_1)), multiply(factorial(4), 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)| | general |
a can finish a piece of work in 5 days . b can do it in 10 days . they work together for two days and then a goes away . in how many days will b finish the work ? | "a 4 days 2 / 5 + ( 2 + x ) / 10 = 1 = > x = 4 days" | a ) 4 days , b ) 6 days , c ) 7 days , d ) 1 days , e ) 3 days | a | divide(subtract(const_1, add(multiply(divide(const_1, 5), const_2), multiply(divide(const_1, 10), const_2))), divide(const_1, 10)) | divide(const_1,n0)|divide(const_1,n1)|multiply(#0,const_2)|multiply(#1,const_2)|add(#2,#3)|subtract(const_1,#4)|divide(#5,#1)| | physics |
vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6936 , how much amount did raghu invest ? | let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6936 = x = 6936 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2400 . answer : e | a ) 1287 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 2400 | e | divide(6936, add(add(multiply(subtract(const_1, divide(10, const_100)), add(const_1, divide(10, const_100))), subtract(const_1, divide(10, const_100))), const_1)) | divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#0)|multiply(#1,#2)|add(#3,#2)|add(#4,const_1)|divide(n2,#5) | general |
an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 20 - meter platform and caught it after it had traveled 59.4 meters . how many times did the ball bounce ? | "ans : 6 division of total diatance travelled will be 20 + 20 + 10 + 5 + 2.5 + 1.25 + 0.6 ans b" | a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | b | divide(divide(20, const_2), const_2) | divide(n0,const_2)|divide(#0,const_2)| | general |
a rectangular tiled patio is composed of 80 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 80 tiles , and it will still be rectangular . how many rows are in the tile patio before th... | "r * c = 80 and ( 12 + 4 ) ( c - 2 ) = 80 - - > r = 12 and c = 7 . answer : d ." | a ) 5 , b ) 6 , c ) 10 , d ) 12 , e ) 28 | d | divide(80, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(80, 2))))), 2)) | multiply(n0,n1)|negate(n2)|power(n2,n1)|multiply(n2,#0)|add(#3,#2)|sqrt(#4)|add(#1,#5)|divide(#6,n1)|divide(n0,#7)| | geometry |
the maximum numbers of students among them 891 pens and 810 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is | olution required number of students . = h . c . f of 891 and 810 . Γ’ β¬ ΒΉ = Γ’ β¬ ΒΊ 81 . answer b | a ) 91 , b ) 81 , c ) 1001 , d ) 1911 , e ) none | b | subtract(891, 810) | subtract(n0,n1) | general |
what is the slope of a line on a standard xy - plane that passes through the point ( 1 , 3 ) and ( 4 , β 3 ) ? | plug the values for the coordinates into the formula for the slope of a line : slope = y 2 - y 1 / x 2 - x 1 = - 3 - 3 / 4 - 1 = - 6 / 3 = - 2 correct answer c ) - 2 | a ) - 1 , b ) 2 , c ) - 2 , d ) 1 / 2 , e ) - 1 / 2 | c | divide(subtract(negate(3), 3), subtract(4, 1)) | negate(n1)|subtract(n2,n0)|subtract(#0,n1)|divide(#2,#1) | general |
the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 124 different signs . if the company used 122 of the signs fully and two remained unused , how many additional area codes can be created if the company u... | "ok let ' s take a crack at this one . so basically we have 144 ^ 2 - 142 ^ 2 so then ( 144 + 142 ) ( 144 - 142 ) ( 246 ) ( 2 ) = 492 answer : c" | a ) 246 , b ) 248 , c ) 492 , d ) 15,128 , e ) 30,256 | c | multiply(multiply(122, subtract(124, 122)), subtract(124, 122)) | subtract(n1,n2)|multiply(n2,#0)|multiply(#1,#0)| | general |
pipe a can fill a tank in 5 hours . due to a leak at the bottom , it takes 10 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ? | "let the leak can empty the full tank in x hours 1 / 5 - 1 / x = 1 / 10 = > 1 / x = 1 / 5 - 1 / 10 = 1 / 10 = > x = 10 . answer : b" | a ) 67 , b ) 10 , c ) 18 , d ) 26 , e ) 12 | b | divide(multiply(10, 5), subtract(10, 5)) | multiply(n0,n1)|subtract(n1,n0)|divide(#0,#1)| | physics |
a large box contains 20 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ? | "the number of chocolate bars is equal to 20 * 25 = 500 correct answer b" | a ) 250 , b ) 500 , c ) 450 , d ) 550 , e ) 650 | b | multiply(20, 25) | multiply(n0,n1)| | general |
find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 . | "p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c" | a ) 240 / 1587 , b ) 240 / 1545 , c ) 240 / 1547 , d ) 240 / 1542 , e ) 240 / 1512 | c | multiply(divide(divide(5, 34), divide(7, 48)), divide(2, 13)) | divide(n2,n3)|divide(n4,n5)|divide(n0,n1)|divide(#0,#1)|multiply(#3,#2)| | other |
if 40 % of a number is greater than 80 % of 5 by 2 , what is the number ? | "explanation : 40 / 100 * x - 80 / 100 * 5 = 2 40 / 100 * x - 4 = 2 40 / 100 * x = 6 x = 6 * 100 / 40 x = 15 answer : option b" | a ) 3 , b ) 15 , c ) 20 , d ) 2 , e ) 5 | b | multiply(const_100, divide(add(2, multiply(divide(5, const_100), 80)), 40)) | divide(n2,const_100)|multiply(n1,#0)|add(n3,#1)|divide(#2,n0)|multiply(#3,const_100)| | gain |
each week , harry is paid x dollars per hour for the first 30 hours and 2 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 1.5 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and ja... | "james worked for 41 hours hence he earned 40 * x + 1 * 1.5 x = 41.5 x dollars ; we know that harry also earned the same 41.5 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 11.5 x additional dollars . since for each additional hour he gets 3 x dollars then he worked for 11.5 x / 2 x = 5.75 ad... | a ) 35.75 , b ) 36 , c ) 37 , d ) 38 , e ) 39 | a | add(divide(subtract(add(40, 1.5), 30), 2), 30) | add(n2,n3)|subtract(#0,n0)|divide(#1,n1)|add(n0,#2)| | general |
in a group of 80 people , 45 have visited iceland and 33 have visited norway . if 41 people have visited both iceland and norway , how many people have visited neither country ? | "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 80 = 45 + 33 - 41 + ( # in neither group ) = 33 the prompt gives you all of t... | a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34 | d | subtract(80, subtract(add(45, 33), 41)) | add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)| | other |
seven 6 faced dice are thrown together . the probability that all the three show the same number on them is ? | "the three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 * 6 = 279936 ways . hence the probability is 6 / 279936 = 1 / 46656 answer : b" | a ) 1 / 32 , b ) 1 / 46656 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34 | b | 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)| | probability |
the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 8000 , brokerage being 1 / 4 % , is : | "face value = rs . 8000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 8000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs... | a ) 110.86 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75 | a | subtract(multiply(divide(8000, 756), 10.5), divide(1, 4)) | divide(n2,n1)|divide(n3,n4)|multiply(n0,#0)|subtract(#2,#1)| | gain |
p starts a business with rs . 4000 . after 4 months , q joins with p as his partner . after a year , the profit is divided in the ratio 2 : 3 . q ' s contribution in the capital is ? | solution : let ' s q ' s capital is x . p : q = ( 4000 * 12 ) : ( x : 8 ) = 2 : 3 . so q ' s share = ( 4000 * 12 / 8 x ) = 2 / 3 = > x = ( 4000 * 12 * 3 ) / ( 2 * 8 ) = rs . 9000 answer : option e | a ) rs . 7000 , b ) rs . 11000 , c ) rs . 8000 , d ) rs . 10000 , e ) rs . 9000 | e | divide(divide(multiply(3, multiply(4000, const_12)), 2), subtract(const_12, 4)) | multiply(n0,const_12)|subtract(const_12,n1)|multiply(n3,#0)|divide(#2,n2)|divide(#3,#1) | other |
what is the probability of getting exactly 1 head in a single throw of five fair coins ? | "one possible case is htttt . p ( htttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 1 = 5 possible cases . p ( 1 head ) = 5 * 1 / 32 = 5 / 32 the answer is d ." | a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 32 , e ) 7 / 32 | d | divide(const_2, choose(add(const_3, const_3), const_3)) | add(const_3,const_3)|choose(#0,const_3)|divide(const_2,#1)| | probability |
- 64 * 29 + 468 = ? | = > - 64 * ( 30 - 1 ) + 468 ; = > - ( 64 * 30 ) + 64 + 468 ; = > - 1920 + 532 = - 1388 . correct option : d | a ) 1430 , b ) 1302 , c ) - 2801 , d ) - 1388 , e ) none of these | d | add(multiply(negate(64), 29), 468) | negate(n0)|multiply(n1,#0)|add(n2,#1) | general |
there are 70 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ? | "x + ( x - 14 ) = 70 - - > x = 42 . answer : c ." | a ) 20 , b ) 31 , c ) 42 , d ) 53 , e ) 64 | c | divide(add(70, 14), const_2) | add(n0,n1)|divide(#0,const_2)| | general |
a is twice as good a work man as b and together they finish the work in 14 days . in how many days a alone can finish the work ? | "wc = 2 : 1 2 x + x = 1 / 14 = > x = 1 / 42 2 x = 1 / 21 a can do the work in 21 days . answer : b" | a ) 12 , b ) 21 , c ) 77 , d ) 99 , e ) 22 | b | inverse(divide(inverse(14), add(const_2, const_1))) | add(const_1,const_2)|inverse(n0)|divide(#1,#0)|inverse(#2)| | physics |
find the least number must be subtracted from 165826 so that remaining no . is divisible by 4 ? | "on dividing 165826 by 4 we get the remainder 2 , so 2 should be subtracted b" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | subtract(165826, multiply(floor(divide(165826, 4)), 4)) | divide(n0,n1)|floor(#0)|multiply(n1,#1)|subtract(n0,#2)| | general |
hcf and lcm two numbers are 14 and 396 respectively . if one of the numbers is 36 , then the other number is ? | "14 * 396 = 36 * x x = 154 answer : c" | a ) 36 , b ) 66 , c ) 154 , d ) 264 , e ) 364 | c | divide(multiply(14, 396), 36) | multiply(n0,n1)|divide(#0,n2)| | physics |
a train 240 m long is running at a speed of 60 km / hr . in what time will it pass a bridge 240 m long ? | "total length = 240 + 240 = 480 speed = 60 km / h = ( 60 * 5 ) / 18 = 50 / 3 m / s time = ( 480 * 3 ) / 50 = 28.8 sec . answer : a" | a ) 28.8 sec , b ) 20.33 sec , c ) 60 sec , d ) 48 sec , e ) 49 sec | a | divide(240, multiply(subtract(60, 240), const_0_2778)) | subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 2 x km . | "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 2 x / ( x / 8 ) = 16 kmph answer : a" | a ) 16 kmph , b ) 20 kmph , c ) 25 kmph , d ) 30 kmph , e ) 35 kmph | a | divide(multiply(40, 2), add(divide(40, 40), divide(multiply(2, 40), 20))) | divide(n0,n0)|multiply(n0,n3)|multiply(n0,n1)|divide(#2,n2)|add(#0,#3)|divide(#1,#4)| | general |
if x and y are positive integers , and y = x ^ 2 + 8 , the greatest common divisor of a and b can not be | if x is 1 , 2 , 4 , or 8 , then gcd of x and y is 1 , 2 , 4 , and 8 respectively . so , by poe the answer must be a . still : if x is a multiple of 9 , then y is 8 greater than a multiple of 9 , so not a multiple of 9 , so both of them can not be divisive by 9 . answer : a . | a ) 9 , b ) 1 , c ) 2 , d ) 4 , e ) 8 | a | add(8, const_1) | add(n1,const_1) | general |
a light flashes every 12 seconds , how many times will it flash in ? of an hour ? | "1 flash = 12 sec for 1 min = 5 flashes so for 1 hour = 5 * 60 = 300 flashes . answer : b" | a ) 550 , b ) 300 , c ) 650 , d ) 700 , e ) 750 | b | divide(const_3600, 12) | divide(const_3600,n0)| | physics |
some of the 68 % solution of acid was removed and this was replaced with an equal amount of 11 % solution of acid . as a result , a 35 % solution of acid was obtained . what fraction of the original solution was replaced ? | "let x be the fraction of the original solution that was replaced . 0.68 * ( 1 - x ) + 0.11 ( x ) = 0.35 0.57 x = 0.33 x = 33 / 57 = 11 / 19 the answer is e ." | a ) 7 / 11 , b ) 7 / 17 , c ) 8 / 17 , d ) 8 / 19 , e ) 11 / 19 | e | divide(35, add(68, 11)) | add(n0,n1)|divide(n2,#0)| | gain |
how many natural numbers between 23 and 137 are divisible by 7 ? | "solution : these numbers are 28 , 35 , 42 , β¦ . , 133 . this is in a . p . in which a = 28 , d = ( 35 - 28 ) = 7 and l = 133 . let the number of there terms be n . then , tn = 133 a + ( n - 1 ) d = 133 by solving this we will get n = 16 . answer c" | a ) 12 , b ) 17 , c ) 16 , d ) 13 , e ) 15 | c | add(divide(subtract(subtract(137, const_4), add(23, const_1)), 7), const_1) | add(n0,const_1)|subtract(n1,const_4)|subtract(#1,#0)|divide(#2,n2)|add(#3,const_1)| | general |
ages of two sisters differ by 9 years . if 5 years ago , the elder one was twice as old the younger one , find their present age | explanation : let the age of younger sister be x , then elder sister ' s age is ( x + 9 ) = > 2 ( x - 5 ) = ( x + 9 - 5 ) [ 5 years before ] = > 2 x - 10 = x + 4 = > x = 14 . so older sister ' s age is x + 9 = 23 answer : option b | a ) 1228 , b ) 1423 , c ) 1632 , d ) 1834 , e ) 1932 | b | divide(add(9, subtract(multiply(5, const_2), 5)), add(9, add(9, subtract(multiply(5, const_2), 5)))) | multiply(n1,const_2)|subtract(#0,n1)|add(n0,#1)|add(n0,#2)|divide(#2,#3) | general |
in the storage room of a certain bakery , the ratio of sugar to flour is 3 to 6 , and the ratio of flour to baking soda is 5 to 1 . if there were 30 more pounds of baking soda in the room , the ratio of flour to baking soda would be 4 to 1 . how many pounds of sugar are stored in the room ? | "sugar : flour = 3 : 6 = 1 : 2 = 5 : 10 flour : soda = 5 : 1 = 10 : 2 ; thus we have that sugar : flour : soda = 5 x : 10 x : 2 x . also given that 10 x / ( 2 x + 30 ) = 4 / 1 - - > x = 60 - - > sugar = 5 x = 30 . answer : a" | a ) 30 , b ) 50 , c ) 60 , d ) 45 , e ) 70 | a | multiply(divide(3, 6), multiply(5, divide(multiply(4, 30), subtract(5, 4)))) | divide(n0,n1)|multiply(n4,n5)|subtract(n2,n5)|divide(#1,#2)|multiply(n2,#3)|multiply(#0,#4)| | general |
there are 100 students in a certain geometry class . if one half of the students are boys and one fifth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ? | total students = 100 one half of the students are boys = 1 / 2 * 100 = 50 one fifth of the boys are under six feet tall = 1 / 5 * 50 = 10 . . . therefore number of boys in the class under six feet tall = 10 . . . answer b . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 5 of 1 / 2 of to... | a ) 6 , b ) 10 , c ) 18 , d ) 24 , e ) 27 | b | divide(divide(100, const_2), add(const_1, const_4)) | add(const_1,const_4)|divide(n0,const_2)|divide(#1,#0) | general |
the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ? | "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 130 and $ 160 respectively . charles earns $ 30 more than robin who earns $ 130 . therefore , charles ' wage is 30 / 130 * 100 = 23.07 % . correct choice is ( a )" | a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 100 % | a | multiply(divide(subtract(add(const_100, 60), add(const_100, 30)), add(const_100, 30)), const_100) | add(n1,const_100)|add(n0,const_100)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100)| | general |
find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 60 = x ? | a ) 1 | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | a | floor(add(reminder(add(subtract(multiply(divide(47, const_100), 1442), multiply(divide(36, const_100), 1412)), 60), const_10), const_1)) | divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|multiply(n3,#1)|subtract(#2,#3)|add(n4,#4)|reminder(#5,const_10)|add(#6,const_1)|floor(#7)| | general |
how many times are the hands of a clock at right angle in 6 hours ? | "in 12 hours , they are at right angles 22 times . in 6 hours , they are at right angles 11 times . answer : option c" | a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | c | divide(multiply(multiply(multiply(const_12, const_2), 6), subtract(multiply(const_12, const_4), const_4)), multiply(const_12, const_2)) | multiply(const_12,const_2)|multiply(const_12,const_4)|multiply(n0,#0)|subtract(#1,const_4)|multiply(#2,#3)|divide(#4,#0)| | physics |
a and b can do a piece of work in 4 days , b and c in 6 days , c and a in 3 days . how long will c take to do it ? | "2 c = 1 / 6 + 1 / 3 β 1 / 4 = 1 / 4 c = 1 / 8 = > 8 days answer : a" | a ) 8 days , b ) 10 days , c ) 12 days , d ) 4 days , e ) 12 days | a | divide(multiply(4, const_3), subtract(divide(add(divide(multiply(4, const_3), 3), add(divide(multiply(4, const_3), 4), divide(multiply(4, const_3), 6))), const_2), divide(multiply(4, const_3), 4))) | multiply(n0,const_3)|divide(#0,n0)|divide(#0,n1)|divide(#0,n2)|add(#1,#2)|add(#4,#3)|divide(#5,const_2)|subtract(#6,#1)|divide(#0,#7)| | physics |
45 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ? | "no of employees = 100 ( say ) men = 45 women = 55 men speaking french = 0.6 * 45 = 27 employees speaking french = 0.55 * 100 = 55 therefore women speaking french = 55 - 42 = 13 and women not speaking french = 55 - 13 = 42 % of women not speaking french = 42 / 55 * 100 = 76.36 % answer c" | a ) 4 % , b ) 10 % , c ) 76.36 % , d ) 90.16 % , e ) 20 % | c | multiply(divide(subtract(divide(subtract(const_100, 45), const_100), subtract(divide(40, const_100), multiply(divide(45, const_100), divide(60, const_100)))), divide(subtract(const_100, 45), const_100)), const_100) | divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|subtract(const_100,n0)|divide(#3,const_100)|multiply(#1,#2)|subtract(#0,#5)|subtract(#4,#6)|divide(#7,#4)|multiply(#8,const_100)| | gain |
a person spent rs . 6,040 from his salary on food and 5,000 on house rent . after that he was left with 80 % of his monthly salary . what is his monthly salary ? | "total money spent on food and house rent = 6,040 + 5,000 = 11,040 which is 100 - 80 = 20 % of his monthly salary β΄ his salary = 11040 x 100 / 20 = 55200 answer : a" | a ) 55,200 , b ) 65,200 , c ) 75,200 , d ) 85,200 , e ) 95,200 | a | divide(add(multiply(add(const_4, const_1), const_100), 80), sqrt(const_100)) | add(const_1,const_4)|sqrt(const_100)|multiply(#0,const_100)|add(n2,#2)|divide(#3,#1)| | gain |
if henry were to add 5 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ? | 7 / 8 x - 3 / 4 x = 5 galls 1 / 8 * x = 5 gallons x = 40 gallons answer : b | a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 96 | b | multiply(5, divide(const_1, subtract(divide(7, 8), divide(3, 4)))) | divide(n3,n4)|divide(n1,n2)|subtract(#0,#1)|divide(const_1,#2)|multiply(n0,#3) | general |
the number of singles that a baseball player hit increased 11 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 1 percent . if the total number of singles and doubles that she hit increased 2 percent from her first season to her second seaso... | "soln : - 1.11 s + 0.99 d = 1.02 [ s + d ] 0.09 s = 0.03 d s / d = 1 / 3 answer : a" | a ) 1 : 3 , b ) 9 : 11 , c ) 1 : 1 , d ) 2 : 1 , e ) 11 : 3 | a | divide(subtract(const_100, 1), add(const_100, 11)) | add(n0,const_100)|subtract(const_100,n1)|divide(#1,#0)| | general |
trail mix consists of chex cereal , m & m ' s , raisins , and assorted nuts . if one serving consists of 4 cups chex cereal , 3 cups m & m ' s , 2 cups rains , and 4 cups assorted nuts , and the ratio of the chex is doubled to to the m & m ' s , what is the ratio of chex to the rest of the dish ? | the answer to this question is way too long for such a simple question , but there ' s really not enough information to tell , so the answer is e . | a ) 10 : 5 , b ) 15 : 9 , c ) 7 : 17 , d ) 19 : 23 , e ) not enough information given for the answer | e | divide(4, add(add(add(4, 3), 2), 4)) | add(n0,n1)|add(n2,#0)|add(n0,#1)|divide(n0,#2) | general |
which is the least number that must be subtracted from 1856 so that the remainder when divided by 7 , 12 , 16 is 6 ? | "first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 6 will be { 336 + 6 , 336 x 2 + 6 , 336 x 3 + 6 , . . . } the largest such number less than or equal to 1856 is 33... | a ) 168 , b ) 172 , c ) 170 , d ) 174 , e ) 176 | c | subtract(1856, add(6, multiply(gcd(1856, lcm(lcm(7, 12), 16)), lcm(lcm(7, 12), 16)))) | lcm(n1,n2)|lcm(n3,#0)|gcd(n0,#1)|multiply(#2,#1)|add(n4,#3)|subtract(n0,#4)| | general |
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