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jack and jill work at a hospital with 4 other workers . for an internal review , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ? | "very easy question . 2 variables and 2 easy equations . xy = 4 - - - > x = 4 / y - ( i ) x / y = 16 - - - > replacing ( i ) here - - - > 4 / ( y ^ 2 ) = 16 - - - > y ^ 2 = 4 / 16 = 1 / 4 - - - > y = 1 / 2 or - 1 / 2 the question states that x and y are positive integers . therefore , y = 1 / 2 is the answer . answer a ." | a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6 | a | sqrt(divide(4, 16)) | divide(n0,n1)|sqrt(#0)| | general |
( 3 x + 2 ) ( 2 x - 1 ) = ax ^ 2 + kx + n . what is the value of a - n + k ? | "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x Γ’ β¬ β y x = ( ds + us ) / 2 y = ( ds Γ’ β¬ β us ) / 2 in the above problem ds = 6 ; us = 2 x = ( 6 + 2 ) / 2 = 8 / 2 = 4 km / hr y = ( 6 - 2 ) / 2 = 4 / 2 = 2 km / hr answer : e" | a ) 4 , 3 , b ) 4 , 4 , c ) 3 , 3 , d ) 4 , 5 , e ) 4 , 2 | e | divide(add(divide(48, 24), divide(24, 4)), const_2) | divide(n2,n3)|divide(n0,n1)|add(#0,#1)|divide(#2,const_2)| | physics |
a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 60 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . ) | "when the storm deposited 115 billion gallons , volume of water in the reservoir = 280 + 120 = 400 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 400 / 0.5 = 800 billion gallons therefore percentage of reservoir that was full before the storm = ( 280 / 800 ) * 100 = 35 % option c" | a ) 45 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 % | c | multiply(divide(280, divide(add(120, 280), divide(50, const_100))), const_100) | add(n0,n2)|divide(n1,const_100)|divide(#0,#1)|divide(n2,#2)|multiply(#3,const_100)| | general |
a train is 410 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length | "each row contains 14 plants . leaving 2 corner plants , 12 plants in between have ( 12 x 2 ) metres & 1 metre on each side is left . length = ( 24 + 2 ) m = 26 m . answer : d" | a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m | d | add(add(multiply(subtract(14, const_1), 2), divide(12, 2)), divide(12, 2)) | divide(n0,n2)|subtract(n1,const_1)|multiply(n2,#1)|add(#0,#2)|add(#3,#0)| | physics |
what is x if x + 5 y = 24 and y = 2 ? | "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 86 thus m = 688 - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 688 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 16 ans : e" | a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16 | e | divide(subtract(multiply(90, 8), multiply(86, 8)), subtract(92, 90)) | multiply(n0,n1)|multiply(n1,n2)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2)| | general |
one night a certain hotel rented 3 / 5 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ? | "800 - - - - 180 100 - - - - ? = > 35 % answer : c" | a ) 22 , b ) 20 , c ) 35 , d ) 88 , e ) 11 | c | multiply(divide(subtract(1080, 800), 800), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
how many 3 digit number formed by using 23 , 45 , 67 once such that number is divisible by 15 . | "solution for an income of rs . 1 in 12 % stock at 108 , investment = rs . ( 108 / 12 ) = rs . 9 . for an income of rs . 1 in 10 % stock at 60 , investment = rs . ( 60 / 10 ) = rs . 6 . β΄ ratio of investments = 9 : 6 = 3 : 2 answer b" | a ) 3 : 4 , b ) 3 : 2 , c ) 4 : 5 , d ) 16 : 15 , e ) none | b | divide(multiply(108, const_2), multiply(60, const_3)) | multiply(n1,const_2)|multiply(n3,const_3)|divide(#0,#1)| | other |
what is the smallest positive integer x , such that 1,152 x is a perfect cube ? | ": speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 6 = 100 meter answer : c" | a ) 150 , b ) 278 , c ) 100 , d ) 776 , e ) 191 | c | multiply(divide(multiply(60, const_1000), const_3600), 6) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
a train 110 m long is running with a speed of 30 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ? | "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 8 % interest = ( 8 / 100 ) * 35 = 2.8 $ total amount that laura owes a year later = 35 + 2.8 = 37.8 $ answer d" | a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 37.8 , e ) $ 38.80 | d | add(multiply(divide(8, const_100), 35), 35) | divide(n0,const_100)|multiply(n1,#0)|add(n1,#1)| | general |
a envelop weight 8.5 gm , if 820 of these envelop are sent with an advertisement mail . how much wieght ? | explanation : 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 β 900 = 600 a | a ) a ) 600 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500 | a | subtract(multiply(const_10, 150), add(multiply(3, 100), multiply(4, 150))) | multiply(n3,const_10)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|subtract(#0,#3) | general |
what is the smallest number which , when increased by 9 , is divisible by 7 , 8 , and 24 ? | "50 pages typed 1 x 40 pages typed 2 x ( original + one revision ) 10 pages typed 3 x ( original + two revisions ) 50 ( 6 ) + 40 ( 6 + 4 ) + 10 ( 6 + 4 + 4 ) = 300 + 400 + 140 = 840 answer - b" | a ) $ 850 , b ) $ 840 , c ) $ 860 , d ) $ 870 , e ) $ 880 | b | add(add(multiply(100, 6), multiply(40, 4)), multiply(multiply(10, 4), const_2)) | multiply(n0,n2)|multiply(n1,n3)|multiply(n1,n4)|add(#0,#1)|multiply(#2,const_2)|add(#3,#4)| | general |
the ages of two persons differ by 16 years . if 6 years ago , the elder one be 3 times as old as the younger one , find their present ages . | let x be the number of additional games the gambler needs to play . 0.4 ( 30 ) + 0.7 x = 0.6 ( x + 30 ) 0.1 x = 6 x = 60 the answer is e . | a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60 | e | divide(subtract(multiply(30, divide(60, const_100)), multiply(30, divide(40, const_100))), subtract(divide(70, const_100), divide(60, const_100))) | divide(n3,const_100)|divide(n0,const_100)|divide(n2,const_100)|multiply(n1,#0)|multiply(n1,#1)|subtract(#2,#0)|subtract(#3,#4)|divide(#6,#5) | gain |
sonika deposited rs . 7000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ? | "the rooms which were not rented is 1 / 5 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 1 / 5 ) = 1 = 100 % the answer is e ." | a ) 60 % , b ) 70 % , c ) 80 % , d ) 90 % , e ) 100 % | e | multiply(divide(multiply(subtract(const_1, divide(2, 4)), multiply(divide(4, 5), const_100)), subtract(const_100, multiply(divide(4, 5), const_100))), const_100) | divide(n0,n1)|divide(n2,n0)|multiply(#0,const_100)|subtract(const_1,#1)|multiply(#2,#3)|subtract(const_100,#2)|divide(#4,#5)|multiply(#6,const_100)| | gain |
if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 15.00 / day for each additional week , how much does it cost to stay for 23 days ? | "the ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b can do work in x days then 10 : 13 : : 23 : x x = ( 23 * 13 ) / 10 x = 299 / 10 a ' s 1 day ' s work = 1 / 23 b ' s 1 day ' s work = 10 / 299 ( a + b ) ' s 1 day ' s work = 1 / 23 + 10 / 299 = 23 / 299 = 1 / 13 a and b together can do work in 13 days answer ( b )" | a ) 25 days , b ) 13 days , c ) 14 days , d ) 20 days , e ) 15 days | b | inverse(add(divide(const_1, 23), divide(const_1, multiply(add(divide(30, const_100), const_1), 23)))) | divide(const_1,n1)|divide(n0,const_100)|add(#1,const_1)|multiply(n1,#2)|divide(const_1,#3)|add(#0,#4)|inverse(#5)| | physics |
what annual payment will discharge a debt of rs . 1125 due in 2 years at the rate of 5 % compound interest ? | "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 6 % reduction in employees lead to 94 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 94 employees is 94 * 1100 = 103400 now the new salary is more than previous salary by x % . x = ( 103400 / 100000 ) * 100 = 103.4 % so the answer is d" | a ) 98.5 % , b ) 100.0 % , c ) 102.8 % , d ) 103.4 % , e ) 105.0 % | d | divide(multiply(add(const_100, multiply(const_100, 10)), add(subtract(const_100, 6), const_4)), multiply(const_100, 10)) | multiply(n1,const_100)|subtract(const_100,n0)|add(#0,const_100)|add(#1,const_4)|multiply(#2,#3)|divide(#4,#0)| | general |
the product of x and y is a constant . if the value of x is increased by 60 % , by what percentage must the value of y be decreased ? | "total age of 10 students = 10 * 20 = 200 and the total age of 16 students = 21 * 15 = 315 . let the average age of 2 new students be x . therefore total age of the new students = 2 x . so total age of 12 student = 200 + 5 x = 315 , x = 23 hence , the correct answer is a ." | a ) 23 , b ) 21 , c ) 19.5 , d ) 20 , e ) 22.5 | a | divide(subtract(multiply(add(20, 1), add(20, 1)), multiply(20, 10)), 2) | add(n1,n3)|multiply(n0,n1)|multiply(#0,#0)|subtract(#2,#1)|divide(#3,n2)| | general |
if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 284 pounds . what is jake β s present weight , in pounds ? | "reduce 1 - 100 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 - - 85 - - 95 are valid multiples . add them - - > 500 e" | a ) 180 , b ) 245 , c ) 320 , d ) 405 , e ) 500 | e | divide(multiply(100, multiply(const_3, 5)), 5) | multiply(n2,const_3)|multiply(n1,#0)|divide(#1,n2)| | general |
in a basketball game , dhoni scored 30 points more than dravid , but only half as many points as shewag . if the 3 players scored a combined total of 150 points , how many points did dhoni score ? | "2 * 22 / 7 * 6 = 37.7 37.7 * 3 1 / 2 = rs . 131.95 answer : a" | a ) 131.95 , b ) 132.9 , c ) 140.33 , d ) 123.4 , e ) 190.4 | a | multiply(circumface(divide(12, const_2)), 3.50) | divide(n0,const_2)|circumface(#0)|multiply(n1,#1)| | physics |
if a mixture is 5 β 9 alcohol by volume and 4 β 9 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ? | "explanation : as there is meal for 70 adults and 28 have their meal , the meal left can be catered to 42 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 42 adults = 54 children hence , the meal can be catered to 54 children . answer : b" | a ) 33 , b ) 54 , c ) 18 , d ) 17 , e ) 01 | b | multiply(subtract(70, 28), divide(90, 70)) | divide(n3,n1)|subtract(n1,n4)|multiply(#0,#1)| | general |
the price of an article is cut by 10 % . to restore it to the former value . the new price must be increased by ? | "let weight of side of beef before processing = x ( 75 / 100 ) * x = 540 = > x = ( 540 * 100 ) / 75 = 720 answer c" | a ) 191 , b ) 355 , c ) 720 , d ) 840 , e ) 1,560 | c | divide(multiply(540, const_100), subtract(const_100, 25)) | multiply(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)| | gain |
jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 4 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ? | one case is : 1 / 3 * 1 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 2 ^ 3 / 3 ^ 5 we have 5 ! / 2 ! * 3 ! = 10 such cases so , 2 ^ 3 * 10 / 3 ^ 5 = 80 / 243 answer : d . | a ) 5 / 243 , b ) 25 / 243 , c ) 64 / 243 , d ) 80 / 243 , e ) 16 / 17 | d | subtract(1, divide(const_2, const_3)) | divide(const_2,const_3)|subtract(n0,#0) | general |
if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ? | "940 * ( 30 / 100 ) = 282 - - - - 6 ? - - - - 1 = > rs . 47 answer : b" | a ) 72 , b ) 47 , c ) 40 , d ) 28 , e ) 20 | b | divide(divide(multiply(940, 30), const_100), 6) | multiply(n0,n2)|divide(#0,const_100)|divide(#1,n1)| | gain |
a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000.00001 more . at the end of the year , their profits amounted to rs . 714 find the share of a . | "5 / 6 * 3 / 2 * 6 / 5 = 3 / 2 3 : 2 answer : d" | a ) 1 : 1 , b ) 1 : 87 , c ) 1 : 6 , d ) 3 : 2 , e ) 1 : 2 | d | divide(divide(multiply(5, 3), multiply(6, 2)), divide(multiply(3, 6), multiply(2, 5))) | multiply(n0,n2)|multiply(n1,n3)|multiply(n2,n4)|multiply(n3,n5)|divide(#0,#1)|divide(#2,#3)|divide(#4,#5)| | other |
alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1081 . find the cost of each ice - cream cup ? | assume the revenue in 2000 to be 100 . then in 2003 it would be 130 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 130 ) / 130 = 50 / 130 = 39 % answer : e . | a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 39 % | e | multiply(divide(subtract(add(const_1, divide(80, const_100)), add(const_1, divide(30, const_100))), add(const_1, divide(30, const_100))), const_100) | divide(n3,const_100)|divide(n0,const_100)|add(#0,const_1)|add(#1,const_1)|subtract(#2,#3)|divide(#4,#3)|multiply(#5,const_100) | gain |
when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that the merchant paid was $ 109.90 , what was the total value of the item ? | "95 % - - - - 8 152 % - - - - ? 95 / 152 * 8 = 5 answer : a" | a ) 5 , b ) 8 , c ) 7 , d ) 4 , e ) 2 | a | divide(multiply(subtract(const_100, 5), 8), add(const_100, 52)) | add(n2,const_100)|subtract(const_100,n0)|multiply(n1,#1)|divide(#2,#0)| | gain |
what is the units digit of ( 3 ^ 5 ) ( 4 ^ 13 ) ? | the total number of stations = 34 from 34 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 34 p 2 ways . 34 p 2 = 34 * 33 = 1122 answer : d | a ) 1800 , b ) 1820 , c ) 1150 , d ) 1122 , e ) 1900 | d | multiply(add(32, const_2), subtract(add(32, const_2), const_1)) | add(n0,const_2)|subtract(#0,const_1)|multiply(#0,#1) | physics |
last year the range of the annual bonus of the 100 employees at company x was $ 20000 . if the annual bonus of each of the 100 employees this year is 10 percent greater than it was last year , what is the range of the annual bonus of the 100 employees this year ? | "explanation : a and b 1 day ' s work = 1 / 4 a alone can do 1 day ' s work = 1 / 12 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 4 ) - ( 1 / 12 ) = 6 days answer : option a" | a ) 6 days , b ) 8 days , c ) 12 days , d ) 10 days , e ) 5 days | a | add(inverse(subtract(divide(const_1, 4), divide(const_1, 12))), divide(const_2, add(const_2, const_3))) | add(const_2,const_3)|divide(const_1,n0)|divide(const_1,n1)|divide(const_2,#0)|subtract(#1,#2)|inverse(#4)|add(#3,#5)| | physics |
in what time will a train 100 m long cross an electric pole , it its speed be 90 km / hr ? | "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 1.9 = 3 km = 3000 m . required time = 3000 * 3 / 125 = 72 sec . answer : b" | a ) 99 , b ) 72 , c ) 48 , d ) 96 , e ) 22 | b | subtract(divide(multiply(1.10, const_1000), divide(multiply(60, const_1000), const_3600)), divide(multiply(1.9, const_1000), divide(multiply(90, const_1000), const_3600))) | multiply(n2,const_1000)|multiply(n0,const_1000)|multiply(n3,const_1000)|multiply(n1,const_1000)|divide(#1,const_3600)|divide(#3,const_3600)|divide(#0,#4)|divide(#2,#5)|subtract(#6,#7)| | physics |
the cost price of a radio is rs . 2550 and it was sold for rs . 2130 , find the loss % ? | "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 5 = 19 the answer is a ." | a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27 | a | add(add(11, divide(subtract(11, 5), 2)), 5) | subtract(n4,n0)|divide(#0,n1)|add(n4,#1)|add(n2,#2)| | physics |
in a can , there is a mixture of milk and water in the ratio 3 : 2 . if the can is filled with an additional 6 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ? | "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 288 / 32 = 9 m / s distance covered by b in 4 seconds = speed Γ£ β time = 9 Γ£ β 4 = 36 metre i . e . , a beat b by 36 metre answer is e" | a ) 38 metre , b ) 28 metre , c ) 23 metre , d ) 15 metre , e ) 36 metre | e | subtract(288, multiply(divide(288, 32), 28)) | divide(n0,n2)|multiply(n1,#0)|subtract(n0,#1)| | physics |
24 oz of juice p and 25 oz of juice t are mixed to make smothies x and y . the ratio of p to t in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ? | "= ( 417 ) ^ 2 + ( 383 ) ^ 2 = ( 400 + 17 ) ^ 2 + ( 400 - 17 ) ^ 2 = 2 [ ( 400 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 160000 + 289 ] = 2 x 160289 = 320578 answer is a" | a ) 320578 , b ) 80578 , c ) 80698 , d ) 81268 , e ) none of them | a | multiply(417, power(417, 383)) | power(n1,n2)|multiply(n0,#0)| | general |
24 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ? | "any x and y satisfying x / y = 7 / 4 should give the same value for ( x + y ) / ( x - y ) . say x = 7 and y = 4 , then ( x + y ) / ( x - y ) = ( 7 + 4 ) / ( 7 - 4 ) = 11 / 3 . answer : b ." | a ) 5 , b ) 11 / 3 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 5 | b | divide(add(7, 4), subtract(7, 4)) | add(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | general |
there are two groups of students in the sixth grade . there are 45 students in group a , and 55 students in group b . if , on a particular day , 20 % of the students in group a forget their homework , and 40 % of the students in group b forget their homework , then what percentage of the sixth graders forgot their homework ? | "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.5 ) = $ 7 ( as the charge is 0.5 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 7 = 8 answer is e ." | a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 8.00 | e | add(1.00, multiply(subtract(divide(1.00, divide(1, 5)), 1), 0.50)) | divide(n1,n2)|divide(n6,#0)|subtract(#1,n1)|multiply(n3,#2)|add(n0,#3)| | general |
how many of the positive factors of 24 are not factors of 27 | "let us assume x = 1 and y = 37.5 then 1.5 ( x ) = 0.04 ( y ) that is 1.5 ( 1 ) = 0.04 ( 37.5 ) = 1.5 = 1.5 therfore from given equation ( 37.5 - 1 ) ( 37.5 + 1 ) = ( 36.5 ) ( 38.5 ) = 1405.25 answer : a" | a ) 1405.25 , b ) 1305.25 , c ) 1205.25 , d ) 1505.25 , e ) 1605.25 | a | divide(subtract(divide(multiply(1.5, const_100), const_2), const_2), add(divide(multiply(1.5, const_100), const_2), const_2)) | multiply(n0,const_100)|divide(#0,const_2)|add(#1,const_2)|subtract(#1,const_2)|divide(#3,#2)| | general |
how many diagonals does a 58 - sided convex polygon have ? | "say a 100 families existed in 1956 then the number of families owning a computer in 1956 - 25 number of families owning computer in 1960 = 25 * 115 / 100 = 28.75 number of families in 1960 = 105 the percentage = 28.75 / 105 * 100 = 27.38 % . option : e" | a ) 50 % , b ) 51.22 % , c ) 5.26 % , d ) 7.20 % , e ) 27.38 % | e | multiply(const_100, divide(divide(multiply(add(15, const_100), 25), const_100), add(const_100, 5))) | add(n3,const_100)|add(n5,const_100)|multiply(n1,#0)|divide(#2,const_100)|divide(#3,#1)|multiply(#4,const_100)| | general |
walking with 4 / 5 of my usual speed , i miss the bus by 7 minutes . what is my usual time ? | "sol . sp = rs 100 : then cp = rs 91 : profit = rs 9 . profit = { ( 9 / 91 ) * 100 } % = 9.89 % answer is a ." | a ) 9.89 % , b ) 8.90 % , c ) 9.00 % , d ) 8.00 % , e ) 9.27 % | a | multiply(divide(subtract(const_100, 91), 91), const_100) | subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
the overall age of x and y is 11 year greater than the overall age of y and z . z is how many decades younger that x ? | "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 24 41 - - - - ? = > rs . 123 answer : d" | a ) 288 , b ) 262 , c ) 72 , d ) 123 , e ) 267 | d | multiply(divide(24, 40), add(add(const_100, 65), 40)) | add(n0,const_100)|divide(n2,n1)|add(n1,#0)|multiply(#2,#1)| | general |
a number increased by 25 % gives 520 . the number is ? | "explanation : relative speed = ( 72 - 36 ) x 5 / 18 = 2 x 5 = 10 mps . distance covered in 32 sec = 32 x 10 = 320 m . the length of the faster train = 320 m . answer is d" | a ) 170 m , b ) 100 m , c ) 270 m , d ) 320 m , e ) 350 m | d | multiply(divide(subtract(72, 36), const_3_6), 32) | subtract(n0,n1)|divide(#0,const_3_6)|multiply(n2,#1)| | physics |
a train running at the speed of 120 km / hr crosses a pole in 18 seconds . what is the length of the train ? | number of ways first - place medal can be awarded to four contestants = 8 number of ways second - place medal can be awarded to contestants after awarding first - place medal = 3 therefore number of possibilities = 8 * 3 = 24 answer : e | a ) 6 , b ) 7 , c ) 12 , d ) 16 , e ) 24 | e | multiply(8, subtract(4, const_1)) | subtract(n1,const_1)|multiply(n0,#0) | general |
a and b are two multiples of 36 , and q is the set of consecutive integers between a and b , inclusive . if q contains 9 multiples of 9 , how many multiples of 4 are there in q ? | "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 Γ ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) Γ 44000 ] = rs . 12000 answer : option a" | a ) rs . 12000 , b ) rs . 13375 , c ) rs . 11750 , d ) rs . 11625 , e ) none of these | a | multiply(44000, inverse(add(add(divide(2, 3), multiply(divide(2, 3), 3)), const_1))) | divide(n1,n0)|multiply(n0,#0)|add(#0,#1)|add(#2,const_1)|inverse(#3)|multiply(n3,#4)| | gain |
bookman purchased 55 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 460 , how many paperback copies were sold ? | "solution simple out of 400 20 % are male i . e 80 and 25 % are female i . e 100 , so total homeowner is 180 . now min number homeowner is 80 and max is 180 so question ask us to find least and 81 has least value among all option . so ans is 81 . answer : a" | a ) 81 , b ) 147 , c ) 145 , d ) 143 , e ) 141 | a | add(multiply(multiply(divide(25, const_100), 20), multiply(divide(25, const_100), 20)), divide(subtract(400, 20), 20)) | divide(n2,const_100)|subtract(n0,n1)|divide(#1,n1)|multiply(n1,#0)|multiply(#3,#3)|add(#2,#4)| | general |
p and q started a business investing rs . 48,000 and rs . 24,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ? | total amount of interest is i = p / 100 * 1 [ 3 / 12 + 9 / 12 + 27 / 12 β¦ . 312 / 12 where p = 100 ; i = 1 / 12 ( 3 + 9 + β¦ . . 312 ) i = 1 / 12 ( 3 ( 312 - 1 ) ) / 3 - 1 = 531440 * 3 / 12 * 2 = rs . 66430 answer : d | a ) rs . 797160 , b ) rs . 791160 , c ) rs . 65930 , d ) rs . 66430 , e ) rs . 67430 | d | divide(multiply(subtract(power(3, const_12), const_1), 3), multiply(const_12, const_2)) | multiply(const_12,const_2)|power(n1,const_12)|subtract(#1,const_1)|multiply(n1,#2)|divide(#3,#0) | general |
what is the value of 3 x ^ 2 β 1.8 x + 0.7 for x = 0.6 ? | the top and the bottom are each single faces formed by three equilateral triangles joining , as in the diagram on the left , to make an isosceles trapezoid . top = 1 face , and bottom = 1 face . this is a four - sided figure , so there are four rectangles extending from the bottom of this prism to the congruent figure at the top . notice , in particular , the larger vertical face in the β back β of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining . total = 1 top + 1 bottom + 4 sides = 6 faces . answer = b . | a ) 4 , b ) 6 , c ) 9 , d ) 10 , e ) 12 | b | add(add(const_4, const_1), const_1) | add(const_1,const_4)|add(#0,const_1)| | geometry |
of the families in city x in 1956 , 25 percent owned a personal computer . the number of families in city x owning a computer in 1960 was 15 percent greater than it was in 1956 , and the total number of families in city x was 5 percent greater in 1956 than it was in 1960 . what percent of the families in city x owned a personal computer in 1960 ? | the area of a square whose side is 6 β ( the area of a square whose side is 4 + the area of the semi - circle whose side is 4 ) = the area of the region shaded the correct answer is b . | ['a ) 48 - 8 Ο', 'b ) 48 - 6 Ο', 'c ) 24 + 6 Ο', 'd ) 16 + 8 Ο', 'e ) 64 - 8 Ο'] | b | subtract(multiply(const_3, multiply(const_4, const_4)), multiply(6, const_pi)) | multiply(const_4,const_4)|multiply(n0,const_pi)|multiply(#0,const_3)|subtract(#2,#1) | geometry |
an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 20286 / - in 3 years at the same rate of interest . find the rate percentage ? | "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 4 * 5 ) = 5 answer : d" | a ) 50 , b ) 33 , c ) 16 , d ) 5 , e ) 14 | d | divide(5, 4) | divide(n1,n0)| | general |
a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 256 sq . feet , how many feet of fencing will be required ? | as given , after lost , the remaining 8 crates total cost = $ 40 so , 1 crate cost = 40 / 8 = 5 to get 20 % profit , 1 crate cost should be = 5 + 5 * 20 / 100 = $ 6 answer : a | a ) $ 6 , b ) $ 8 , c ) $ 10 , d ) $ 12 , e ) $ 14 | a | divide(add(40, multiply(40, divide(20, const_100))), subtract(10, 2)) | divide(n3,const_100)|subtract(n0,n2)|multiply(n1,#0)|add(n1,#2)|divide(#3,#1) | gain |
in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 90 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ? | "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 32 = 15 = > x = 180 m . answer : e" | a ) 228 , b ) 240 , c ) 887 , d ) 166 , e ) 180 | e | multiply(20, multiply(54, const_0_2778)) | multiply(n2,const_0_2778)|multiply(n1,#0)| | physics |
when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.12 , what is the value of y ? | "9.18 x + 5.17 x + 2.05 x = 16.4 x = 170 cookies x = 170 / 16.4 = 10 ( approx ) so , irin baked 10 * 9.18 cookies or 91 cookies ( approx ) % share = 91 / 170 = 53.5 approx hence , answer is d ." | a ) 0.125 % , b ) 1.25 % , c ) 12.5 % , d ) 53.5 % , e ) 0.152 % | d | multiply(divide(divide(multiply(170, 5.17), add(add(9.18, 5.17), 2.05)), 170), const_100) | add(n0,n1)|multiply(n1,n3)|add(n2,#0)|divide(#1,#2)|divide(#3,n3)|multiply(#4,const_100)| | other |
the manufacturer β s suggested retail price ( msrp ) of a certain item is $ 60 . store a sells the item for 20 percent more than the msrp . the regular price of the item at store b is 30 percent more than the msrp , but the item is currently on sale for 10 percent less than the regular price . if sales tax is 5 percent of the purchase price at both stores , what is the result when the total cost of the item at store b is subtracted from the total cost of the item at store a ? | "1 st digit can be filled up by the numbers - { 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 7 ways 2 nd digit can be filled up by the numbers - { 0 , 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways 3 rd digit can be filled up by the numbers - { 0 , 1 , 2 , 4 , 5 , 7 , 8 , 9 } = 8 ways so , total no of ways is 7 * 8 * 8 = > 3584 hence answer will be ( b )" | a ) 2401 , b ) 3584 , c ) 4096 , d ) 5040 , e ) 7200 | b | multiply(multiply(multiply(const_10, const_10), subtract(const_10, const_1)), 6) | multiply(const_10,const_10)|subtract(const_10,const_1)|multiply(#0,#1)|multiply(n1,#2)| | general |
if 36 men can do a piece of work in 25 hours , in how mwny hours will 15 men do it ? | "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 30 % = 130 % 130 % - - - - - - - > 650 ( 130 Γ£ β 5 = 650 ) 100 % - - - - - - - > 400 ( 100 Γ£ β 5 = 500 ) option ' d '" | a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600 | d | divide(650, add(const_1, divide(30, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | gain |
a man whose speed is 5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ? | "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 16.2 - answer b" | a ) 15.2 % , b ) 16.2 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 % | b | multiply(const_100, subtract(multiply(multiply(divide(add(25, const_100), const_100), divide(add(25, const_100), const_100)), divide(subtract(const_100, 25), const_100)), const_1)) | add(n0,const_100)|subtract(const_100,n0)|divide(#1,const_100)|divide(#0,const_100)|multiply(#3,#3)|multiply(#2,#4)|subtract(#5,const_1)|multiply(#6,const_100)| | general |
if soundharya rows 49 km upstream and 77 km down steam taking 7 hours each , then the speed of the stream | "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 20 * 6 / 10 = 12 days . answer : a" | a ) 12 days . , b ) 17 days . , c ) 18 days . , d ) 19 days . , e ) 20 days . | a | subtract(20, multiply(divide(20, 10), 4)) | divide(n2,n0)|multiply(n1,#0)|subtract(n2,#1)| | physics |
if x , y , and z are positive integers and 2 x = 3 y = 4 z , then the least possible value of x + y + z is | 120 and 60 are both divisible by 6 and 15 but also by 12 . so they are not the right answer . 36 and 54 are both clearly not divisible by 15 ( not correct ) 90 is both divisible by 6 and 15 but not by 12 . answer : ( d ) 90 | a ) 120 , b ) 60 , c ) 36 , d ) 90 , e ) 54 | d | multiply(6, 15) | multiply(n0,n1) | general |
the contents of a certain box consist of 14 apples and 25 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ? | "90 = ( 450 * 4 * r ) / 100 r = 5 % i = ( 450 * 6 * 5 ) / 100 = 135 450 + 135 = 585 answer : c" | a ) 227 , b ) 299 , c ) 270 , d ) 585 , e ) 271 | c | subtract(multiply(subtract(540, 450), 6), subtract(540, 450)) | subtract(n1,n0)|multiply(n3,#0)|subtract(#1,#0)| | gain |
15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 4 hrs . each would it take for 21 women if 3 women do as much work as 2 men ? | "the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r Γ£ β si ) / ( 2 Γ£ β 100 ) difference between the compound interest and simple interest = 340 - 324 = 16 ( r Γ£ β si ) / ( 2 Γ£ β 100 ) = 16 ( r Γ£ β 324 ) / ( 2 Γ£ β 100 ) = 16 r = 9.87 % answer : option c" | a ) 15 % , b ) 14.25 % , c ) 9.87 % , d ) 10.5 % , e ) 11.5 % | c | divide(multiply(const_100, subtract(subtract(340, divide(324, 2)), divide(324, 2))), divide(324, 2)) | divide(n1,n0)|subtract(n2,#0)|subtract(#1,#0)|multiply(#2,const_100)|divide(#3,#0)| | gain |
a is an integer greater than 19 but less than 32 , b is an integer greater than 29 but less than 42 , what is the range of a / b ? | "let t be the tier price , p be total price = 14000 per the given conditions : 0.10 t + 0.08 ( p - t ) = 1440 - - - - > t = 1600 . a is the correct answer ." | a ) $ 1600 , b ) $ 6000 , c ) $ 6050 , d ) $ 7050 , e ) $ 8000 | a | divide(subtract(1440, multiply(multiply(multiply(const_3, multiply(const_2, const_3)), const_1000), divide(8, const_100))), subtract(divide(10, const_100), divide(8, const_100))) | divide(n1,const_100)|divide(n0,const_100)|multiply(const_2,const_3)|multiply(#2,const_3)|subtract(#1,#0)|multiply(#3,const_1000)|multiply(#0,#5)|subtract(n3,#6)|divide(#7,#4)| | general |
john and steve are speed walkers in a race . john is 10 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john β s final push ? | "let the speed of bus be v - 20 , speed of taxi be v the bus travelled a total of 4 hrs and taxi a total of 2 hrs . hence 4 * ( v - 20 ) = 2 v 4 v - 80 = 2 v 2 v = 80 v = 40 mph e" | a ) 42 , b ) 48 , c ) 44 , d ) 50 , e ) 40 | e | divide(add(multiply(2, 20), multiply(2, 20)), subtract(add(2, 2), 2)) | add(n0,n0)|multiply(n0,n1)|add(#1,#1)|subtract(#0,n0)|divide(#2,#3)| | physics |
if a man lost 5 % by selling oranges at the rate of 8 a rupee at how many a rupee must he sell them to gain 52 % ? | "when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 10 * 24 / 60 = 4 miles and the man walks the distance mm , which is 10 * 12 / 60 = 2 mile . the difference of 4 - 2 = 2 miles ( mw ) will be covered by the man in ( 2 ) / 9 = 2 / 9 of an hour , which is ~ 13 minutes . answer a ." | a ) 13 , b ) 10 , c ) 15 , d ) 11 , e ) 9 | a | multiply(const_60, divide(multiply(divide(10, const_60), subtract(24, 12)), 12)) | divide(n2,const_60)|subtract(n1,n0)|multiply(#0,#1)|divide(#2,n0)|multiply(#3,const_60)| | physics |
john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 73000 , what is their combined tax rate ? | "| 5 x - 5 | = 100 5 x - 5 = 100 or 5 x - 5 = - 100 5 x = 105 or 5 x = - 95 x = 21 or x = - 19 sum = 21 - 19 = 2 answer is c" | a ) 1 , b ) - 2 , c ) 2 , d ) - 3 , e ) 4 | c | subtract(subtract(subtract(100, 5), add(100, 5)), 5) | add(n1,n2)|subtract(n2,n1)|subtract(#1,#0)|subtract(#2,n1)| | general |
the mean of 50 observations was 36 . it was found later that an observation 58 was wrongly taken as 43 . the corrected new mean is ? | "sol . 39 Γ· 3 = 13 . answer : d" | a ) 20 lb , b ) 30 lb , c ) 10 lb , d ) 13 lb , e ) 5 lb | d | divide(39, const_1) | divide(n0,const_1)| | general |
in a class of 50 students , 20 play baseball , 15 play cricket and 11 play football . 7 play both baseball and cricket , 4 play cricket and football and 5 play baseball and football . if 18 students do not play any of these given sports , how many students play exactly two of these sports ? | "actual price = 500 + 50 = $ 550 saving = 10 / 550 * 100 = 100 / 55 = 1.8 % approximately answer is e" | a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 1.8 % | e | add(floor(multiply(divide(50, add(50, 500)), 500)), const_1) | add(n0,n1)|divide(n0,#0)|multiply(#1,n1)|floor(#2)|add(#3,const_1)| | general |
the length of a rectangular floor is more than its breadth by 200 % . if rs . 450 is required to paint the floor at the rate of rs . 5 per sq m , then what would be the length of the floor ? | "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 20 % of 850 = 170 . answer : b" | a ) 58 , b ) 170 , c ) 95 , d ) 100 , e ) 120 | b | divide(multiply(510, add(const_4, const_1)), add(const_1, const_2)) | add(const_1,const_4)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)| | general |
circular gears l and r start to rotate at the same time at the same rate . gear l makes 20 complete revolutions per minute and gear r makes 60 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 8 more revolutions than gear l ? | let x be the number of guests . number of muffins prepared = 5 x + 2 number of muffins eaten + number of muffins remaining = number of muffins prepared 6 ( x - 1 ) + 6 = 5 x + 2 6 x = 5 x + 2 x = 2 answer : a | a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 7 . | a | divide(subtract(add(6, 6), const_2), 5) | add(n1,n1)|subtract(#0,const_2)|divide(#1,n0) | general |
a cube of side one meter length is cut into small cubes of side 20 cm each . how many such small cubes can be obtained ? | total distance traveled = 10 + 12 = 22 km / hr . total time taken = 10 / 12 + 12 / 10 = 61 / 30 hrs . average speed = 22 * 30 / 61 = 10.8 km / hr . answer : b | a ) 10.7 km / hr , b ) 10.8 km / hr , c ) 17.8 km / hr , d ) 10.5 km / hr , e ) 30.8 km / hr | b | divide(add(12, 10), const_2) | add(n0,n1)|divide(#0,const_2) | general |
the product of x and y is a constant . if the value of x is increased by 40 % , by what percentage must the value of y be decreased ? | 3 ^ x = 2 3 ^ 4 x = 2 ^ 4 3 ^ 4 x = 16 3 ^ ( 4 x + 3 ) = 3 ^ 4 x * 3 ^ 3 = 16 * 27 = 432 answer : c | a ) 429 , b ) 454 , c ) 432 , d ) 438 , e ) 108 | c | power(3, add(multiply(4, divide(log(const_2), log(const_3))), 3)) | log(const_2)|log(const_3)|divide(#0,#1)|multiply(n3,#2)|add(n0,#3)|power(n0,#4) | general |
if n is a positive integer such that n ! / ( n - 2 ) ! = 342 , find n . | "they meet every 360 / 7 + 8 = 24 sec answer is d" | a ) 20 sec , b ) 15 sec , c ) 30 sec , d ) 24 sec , e ) 1 min | d | divide(360, add(8, 7)) | add(n0,n1)|divide(n2,#0)| | physics |
10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ? | "total savings = s amount spent on stereo = ( 1 / 3 ) s amount spent on television = ( 1 - 1 / 3 ) ( 1 / 3 ) s = ( 2 / 3 ) * ( 1 / 3 ) * s = ( 2 / 9 ) s ( stereo + tv ) / total savings = s ( 1 / 3 + 2 / 9 ) / s = 5 / 9 answer : c" | a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 9 , d ) 1 / 2 , e ) 7 / 12 | c | divide(1, 3) | divide(n0,n1)| | general |
how much 60 % of 50 is greater than 34 % of 30 ? | "y = 0.5 * 0.5 * x = x / 4 y % * x = 36 ( y / 100 ) * x = 36 ( x / 400 ) * x = 36 x ^ 2 = 36 * 400 x = 120 the answer is e ." | a ) 80 , b ) 96 , c ) 100 , d ) 108 , e ) 120 | e | multiply(multiply(divide(50, 36), divide(50, 36)), const_1000) | divide(n0,n2)|divide(n1,n2)|multiply(#0,#1)|multiply(#2,const_1000)| | general |
a man and a boy complete a work together in 24 days . if for the last 6 days man alone does the work then it is completed in 26 days . how long the boy will take to complete the work alone ? | "time = 6 distence = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph c )" | a ) 40 kmph , b ) 50 kmph , c ) 60 kmph , d ) 75 kmph , e ) 860 kmph | c | divide(540, multiply(divide(3, 2), 6)) | divide(n2,n3)|multiply(n0,#0)|divide(n1,#1)| | physics |
a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets euro 1000 more than d , what is b ' s share ? | "p ( missing all 3 ) = ( 2 / 3 ) ^ 3 = 8 / 27 p ( success on at least one attempt ) = 1 - 8 / 27 = 19 / 27 the answer is d ." | a ) 1 / 3 , b ) 5 / 9 , c ) 7 / 9 , d ) 19 / 27 , e ) 23 / 27 | d | subtract(const_1, power(divide(const_1, 3), 3)) | divide(const_1,n0)|power(#0,n1)|subtract(const_1,#1)| | probability |
what is the unit digit in 7105 ? | "90 feet / 2 seconds = 45 feet / second ( 45 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 30.68 ( approximately ) the answer is a ." | a ) 30.68 , b ) 32.34 , c ) 34.56 , d ) 36.72 , e ) 38.95 | a | divide(divide(90, 5280), multiply(2, divide(1, const_3600))) | divide(n0,n3)|divide(n2,const_3600)|multiply(n1,#1)|divide(#0,#2)| | physics |
three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 34 square meters . what is the area that is covered with three layers of wallpaper ? | "25 = e / ( 1000 - e ) * 100 1000 - e = 4 e 1000 = 5 e = > e = 200 1000 - 200 = 800 answer : c" | a ) 338 , b ) 278 , c ) 800 , d ) 269 , e ) 112 | c | subtract(multiply(divide(const_100, 25), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100) | add(const_2,const_3)|divide(const_100,n0)|multiply(#0,const_2)|multiply(#2,const_100)|multiply(#1,#3)|subtract(#4,const_100)| | gain |
carol spends 1 / 3 of her savings on a stereo and 1 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ? | "16.02 Γ£ β 0.1 = 1.602 the answer is c ." | a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these | c | multiply(divide(16.02, 0.1), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 1000 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ? | "formula : ( after = 100 denominator ago = 100 numerator ) 13400 Γ 121 / 100 Γ 121 / 100 = 19619 c" | a ) 10000 , b ) 12000 , c ) 19619 , d ) 18989 , e ) 14400 | c | multiply(13400, power(add(const_1, divide(21, const_100)), 2)) | divide(n1,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)| | gain |
a , b and c rents a pasture for rs . 899 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ? | "sol . sp = rs 100 : then cp = rs 90 : profit = rs 10 . profit = { ( 10 / 90 ) * 100 } % = 1.11 % answer is b ." | a ) 1.10 % , b ) 1.11 % , c ) 1.15 % , d ) 1.17 % , e ) 1.27 % | b | multiply(divide(subtract(const_100, 90), 90), const_100) | subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
the area of a parallelogram is 72 sq m and its altitude is twice the corresponding base . then the length of the base is ? | "least number of cubes will be required when the cubes that could fit in are biggest . 7 is the biggest number that could divide all three , 49 , 21 and 14 . thus side of cube must be 7 , and total number of cubes = 49 / 7 * 21 / 7 * 14 / 7 = 42 ans b it is ." | a ) 17 , b ) 42 , c ) 54 , d ) 108 , e ) 864 | b | divide(multiply(multiply(49, 21), 14), volume_cube(divide(14, const_2))) | divide(n2,const_2)|multiply(n0,n1)|multiply(n2,#1)|volume_cube(#0)|divide(#2,#3)| | geometry |
how many multiples of 2 are less than 2400 , and also multiples of 8 ? | "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 2000 = $ 3720 the total price is $ 4000 + $ 2850 + $ 3720 = $ 10,570 the answer is d ." | a ) $ 7,360 , b ) $ 8,540 , c ) $ 9,720 , d ) $ 10,570 , e ) $ 11,680 | d | multiply(multiply(2, const_3), const_100) | multiply(n4,const_3)|multiply(#0,const_100)| | gain |
in a party every person shakes hands with every other person . if there were a total of 190 handshakes in the party then what is the number of persons present in the party ? | "( 7000 * 3 * 2 ) / 100 = 420 9200 - - - - - - - - 9620 answer : c" | a ) 9680 , b ) 2277 , c ) 9620 , d ) 2774 , e ) 1212 | c | add(multiply(multiply(add(divide(2, const_100), divide(divide(subtract(9200, 7000), 3), 7000)), 7000), 3), 7000) | divide(n3,const_100)|subtract(n1,n0)|divide(#1,n2)|divide(#2,n0)|add(#0,#3)|multiply(n0,#4)|multiply(n2,#5)|add(n0,#6)| | gain |
a man two flats for $ 675958 each . on one he gains 16 % while on the other he loses 16 % . how much does he gain or lose in the whole transaction ? | "we have the ratio of a β s speed and b β s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 13 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn β t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 13 meters ) to reach the finish line . so b should get a head start of 7 / 20 th of the race . answer ( d )" | a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 7 / 20 , e ) 3 / 10 | d | divide(subtract(20, 13), 20) | subtract(n0,n1)|divide(#0,n0)| | general |
the ratio of 2 numbers is 2 : 5 and their h . c . f . is 6 . their l . c . m . is ? | "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 4 : 1 ( webs ) 1 : 9 } : : x : 3 Γ’ β‘ β 4 Γ£ β 1 Γ£ β 9 = 1 Γ£ β 3 Γ£ β x Γ’ β‘ β x = 12 answer : option b" | a ) 9 , b ) 12 , c ) 27 , d ) 24 , e ) 16 | b | multiply(1, 4) | multiply(n0,n3)| | physics |
the total of 324 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is | explanation : largest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 Γ· 600 = 16 , remainder = 399 hence , largest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : a | a ) 9600 , b ) 5200 , c ) 362 , d ) 958 , e ) 258 | a | subtract(subtract(multiply(const_100, const_100), const_1), reminder(subtract(multiply(const_100, const_100), const_1), lcm(lcm(lcm(15, 25), 40), 75))) | lcm(n1,n2)|multiply(const_100,const_100)|lcm(n3,#0)|subtract(#1,const_1)|lcm(n4,#2)|reminder(#3,#4)|subtract(#3,#5) | general |
two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 48 seconds . find the length of the faster train ? | "let the side of the square plot be a ft . a 2 = 64 = > a = 8 length of the fence = perimeter of the plot = 4 a = 32 ft . cost of building the fence = 32 * 58 = rs . 1856 . answer : d" | a ) 3944 , b ) 2882 , c ) 2999 , d ) 1856 , e ) 2121 | d | multiply(square_perimeter(sqrt(64)), 58) | sqrt(n0)|square_perimeter(#0)|multiply(n1,#1)| | geometry |
if the l . c . m of two numbers is 720 and their product is 38880 , find the h . c . f of the numbers . | "20 % of 6 = 1.2 50 % of 6 = 3 shortage is 1.8 so we need to have 1.8 / 50 % to get 50 % alcohol content . = 3.6 d" | a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 3.6 , e ) e . 5.4 | d | subtract(6, multiply(const_2, multiply(divide(20, const_100), 6))) | divide(n1,const_100)|multiply(n0,#0)|multiply(#1,const_2)|subtract(n0,#2)| | gain |
the charge for a single room at hotel p is 30 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ? | "( 45 / 100 ) z = ( 60 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 60 / 100 ) * ( 3 / 4 ) x i . e . z = ( 60 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1 ) x = ( 100 / 100 ) x i . e . z is 100 % of x answer : option c" | a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 50 | c | multiply(divide(divide(75, const_100), divide(divide(45, const_100), divide(60, const_100))), const_100) | divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|divide(#1,#2)|divide(#0,#3)|multiply(#4,const_100)| | gain |
a certain number of badges were distributed among a class of students . the student who got 1 / 6 th of the total number of badges actually got 5 times the average number of badges the others got ! how many students were there in the class ? | in the range 800 - 900 : 1 choice for the first digit : 8 ; 5 choices for the third digit : 1 , 3 , 5 , 7 , 9 ( as the number is odd ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 5 * 8 = 40 . in the range 900 - 999 : 1 choice for the first digit : 9 ; 4 choices for the third digit : 1 , 3 , 5 , 7 ( 9 is out as it ' s the first digit ) ; 8 choices for the second digit : 10 digits - first digit - third digit = 8 digits . 1 * 4 * 8 = 32 . total : 40 + 32 = 72 . answer : c | a ) 40 , b ) 56 , c ) 72 , d ) 81 , e ) 104 | c | add(multiply(add(3, add(const_3, const_2)), const_4), multiply(multiply(const_1, add(const_3, const_2)), add(3, add(const_3, const_2)))) | add(const_2,const_3)|add(n0,#0)|multiply(#0,const_1)|multiply(#1,const_4)|multiply(#1,#2)|add(#3,#4) | general |
in 1990 the budgets for projects q and v were $ 500,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ? | "let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 40 x = 8 and the number of spinsters is 2 ( 8 ) = 16 . the answer is b ." | a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22 | b | multiply(divide(40, subtract(7, 2)), 2) | subtract(n1,n0)|divide(n2,#0)|multiply(n0,#1)| | other |
the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 10 and 11 . the larger of the two numbers is : | "33 1 / 3 % = 1 / 3 1 / 3 Γ 240 = 80 a )" | a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130 | a | divide(multiply(add(33, divide(1, 3)), 240), const_100) | divide(n1,n2)|add(n0,#0)|multiply(n3,#1)|divide(#2,const_100)| | gain |
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 125 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ? | "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 30 tickets = 30 * 26 = 780 revenue generated from sales of 60 tickets = 120 + 340 + 780 = 1240 $ answer e" | a ) $ 600 , b ) $ 740 , c ) $ 850 , d ) $ 980 , e ) $ 1,240 | e | multiply(add(add(subtract(subtract(60, 20), 10), multiply(subtract(const_1, divide(40, const_100)), 10)), multiply(subtract(const_1, divide(15, const_100)), 20)), 20) | divide(n2,const_100)|divide(n4,const_100)|subtract(n5,n0)|subtract(const_1,#0)|subtract(#2,n1)|subtract(const_1,#1)|multiply(n1,#3)|multiply(n0,#5)|add(#6,#4)|add(#8,#7)|multiply(n0,#9)| | gain |
a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 174 , how many hours overtime did he work ? | "x ^ 2 + 5 x - 6 = ( x + 6 ) ( x - 1 ) = 0 then x = - 6 or x = 1 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 1 . the answer is b ." | a ) - 1 , b ) 1 , c ) 4 , d ) - 6 , e ) 6 | b | divide(add(4, 6), add(2, 5)) | add(n2,n6)|add(n0,n5)|divide(#0,#1)| | general |
find the value of 201834 x 99999 = m ? | "first pump drains 1 / 2 of the tank in 7 hours so 14 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 14 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 14 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 14 + 1 / a ) = 1 / 2 solving u get a = 14 / 13 = 1.1 hence answer is b" | a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours | b | divide(const_1, subtract(const_1, divide(const_1, multiply(7, const_2)))) | multiply(n0,const_2)|divide(const_1,#0)|subtract(const_1,#1)|divide(const_1,#2)| | physics |
in 1979 approximately 1 / 3 of the 32.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ? | "18 * 18 = 324 sq m answer : d" | a ) 225 sq m , b ) 186 sq m , c ) 586 sq m , d ) 324 sq m , e ) 296 sq m | d | square_area(18) | square_area(n0)| | geometry |
in objective test a correct ans score 4 marks and on a wrong ans 2 marks are - - - . a student score 480 marks from 150 question . how many ans were correct ? | "( 80 / 100 ) * 40 Γ’ β¬ β ( 4 / 5 ) * 30 32 - 24 = 8 answer : c" | a ) 12 , b ) 27 , c ) 8 , d ) 12 , e ) 81 | c | subtract(multiply(40, divide(80, const_100)), multiply(divide(4, 5), 30)) | divide(n0,const_100)|divide(n2,n3)|multiply(n1,#0)|multiply(n4,#1)|subtract(#2,#3)| | general |
if a 5 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ? | "the odd numbers less than 60 are 1 , 3,5 , . . . 59 some of them are equal to product of 5 and odd number hence odd multiples of 5 which are less than 60 are 5,15 , 25,35 , 45,55 ( total = 6 ) ; answer : b" | a ) 4 , b ) 6 , c ) 11 , d ) 12 , e ) 15 | b | divide(divide(60, 5), const_2) | divide(n0,n1)|divide(#0,const_2)| | general |
a 12 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ? | "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 18 - x ) + x + 2 = 30 37 - 2 x + x = 30 37 - x = 30 x = 7 so 7 members play both badminton and tennis . a" | a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | a | subtract(add(add(17, 18), 2), 30) | add(n1,n2)|add(n3,#0)|subtract(#1,n0)| | other |
ramesh has solved 108 questions in an examination . if he got only β 0 β marks , then how many questions were wrong when one mark is given for each one correct answer and 1 / 3 mark is subtracted on each wrong answer . | "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 3 + 3 ) = > 6 k = k + 4 = > k = 4 / 5 ans c it is !" | a ) 3 / 4 , b ) 1 , c ) 4 / 5 , d ) 2 , e ) 7 / 2 | c | divide(4, 3) | divide(n1,n2)| | general |
the present population of a town is 3888 . population increase rate is 20 % p . a . find the population of town before 2 years ? | "2 x will be the distance travelled by the train if the length of the train = the length of the platform = x as distance = speed * time distance = 2 x speed in kmph = 90 speed in mps = 90 * 5 / 18 as dist = speed * time 2 x = ( 90 * 5 / 18 ) * ( 60 sec ) on solving x = 900 mts answer : d" | a ) 500 , b ) 600 , c ) 750 , d ) 900 , e ) 950 | d | divide(divide(multiply(90, const_1000), divide(const_60, const_1)), const_2) | divide(const_60,const_1)|multiply(n0,const_1000)|divide(#1,#0)|divide(#2,const_2)| | physics |
in township k each property is taxed at 12 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 24,000 , by how much will the property tax increase ? | "4 x + 2 = 5 y + 2 . . . . . . . . . . . ie : 4 x - 5 y = 0 x , y must be > 1 and y is even ie ( 2 , 4,6 , . . etc ) if y = 2 thus x is fraction if y = 4 thus x = 5 n = 22 if y = 6 thus x = not possible fraction if y = 8 thus x = 10 n = 42 summation 22 + 42 = 64 c" | a ) 33 , b ) 46 , c ) 49 , d ) 53 , e ) 86 | c | add(add(multiply(5, const_2), 2), add(multiply(5, multiply(const_2, 2)), 2)) | multiply(n2,const_2)|multiply(const_2,n3)|add(n3,#0)|multiply(n2,#1)|add(n3,#3)|add(#2,#4)| | general |
in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 90 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ? | the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 140 tagged deers comprise 10 % of total # of deers - - > total # of deers = 140 * 10 = 1,400 . answer : d . | a ) 150 , b ) 750 , c ) 1,250 , d ) 1,400 , e ) 2,500 | d | multiply(50, 5) | multiply(n1,n3) | general |
reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 300 as interest at the end of the loan period , what was the rate of interest ? | "machine a can produce 100 * 30 / 15 = 200 copies and , machine b can produce 150 * 30 / 10 = 450 copies total producing 650 copies . c is the answer" | a ) 250 , b ) 425 , c ) 650 , d ) 700 , e ) 750 | c | multiply(add(divide(100, 15), divide(150, 10)), 30) | divide(n0,n1)|divide(n2,n3)|add(#0,#1)|multiply(n4,#2)| | physics |
barbata invests $ 2600 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ? | "age of the 15 th student = [ 15 * 16 - ( 14 * 5 + 16 * 9 ) ] = ( 240 - 214 ) = 26 years . answer : c" | a ) 11 years , b ) 17 years , c ) 26 years , d ) 14 years , e ) 12 years | c | subtract(multiply(15, 15), add(multiply(5, 14), multiply(9, 16))) | multiply(n0,n0)|multiply(n2,n3)|multiply(n4,n5)|add(#1,#2)|subtract(#0,#3)| | general |