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set q consists of integers { 3 , - 8 , y , 19 , - 6 } and set b consists of integers { k , - 3 , 0 , 16 , - 5 , 9 } . number l represents the median of set q , number m represents mode of set b and number z = l ^ m . if y is an integer greater than 21 , for what value of k will z be a divisor of 26 ? | "the 5 inch side should be aligned to the 15 inch side ( 3 layer ) 2 inch side should be aligned to the 20 inch side . ( 10 layer ) 7 inch side should be aligned to the 35 inch side . ( 5 layer ) maximum number of rectangles = 3 * 10 * 5 = 150 answer is d" | a ) 200 , b ) 350 , c ) 100 , d ) 150 , e ) 120 | d | divide(multiply(multiply(15, 20), 35), multiply(multiply(5, 2), 7)) | multiply(n3,n4)|multiply(n0,n1)|multiply(n5,#0)|multiply(n2,#1)|divide(#2,#3)| | geometry |
if p ( a ) = 0.4 , p ( b ) = 0.6 and p ( a ∪ b ) = 0.8 . what is the value of p ( a ∩ b ' ) = ? | "p = 288 ( 100 / 5 ) ^ 2 = > p = 7200 answer : d" | a ) 2277 , b ) 2667 , c ) 3600 , d ) 7200 , e ) 1811 | d | divide(288, subtract(power(add(divide(20, const_100), const_1), 2), add(multiply(divide(20, const_100), 2), const_1))) | divide(n1,const_100)|add(#0,const_1)|multiply(n0,#0)|add(#2,const_1)|power(#1,n0)|subtract(#4,#3)|divide(n2,#5)| | gain |
points a , b , and , c have xy - coordinates ( 20 ) , ( 812 ) , and ( 140 ) , respectively . points x , y , and z have xy - coordinates ( 60 ) , ( 84 ) , and ( 100 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ? | "we assume that 867 is 100 % assume ' x ' is value we looking for here , 867 = 100 % and x % = 63.2 therefore , 100 / x = 867 / 63.2 100 / x = 13.71 x = 7.29 c" | a ) 6.9 , b ) 8.99 , c ) 7.29 , d ) 7.98 , e ) 9.21 | c | multiply(divide(63.2, 867), const_100) | divide(n0,n1)|multiply(#0,const_100)| | gain |
find the l . c . m of 15 , 18 , 28 and 30 . | "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 15 work done by p , q and r in 1 day = 1 / 10 + 1 / 15 = 1 / 6 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 1 / 6 = > work done by p in 1 day = 1 / 12 = > work done by q and r in 1 day = 1 / 12 hence work done by q in 1 day = 1 / 12 â € “ 1 / 15 = 1 / 60 so q alone can do the work in 60 days answer is e ." | a ) 20 , b ) 22 , c ) 25 , d ) 27 , e ) 60 | e | divide(const_1, subtract(divide(add(divide(const_1, 10), divide(const_1, 15)), const_2), divide(const_1, 15))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(#2,const_2)|subtract(#3,#1)|divide(const_1,#4)| | physics |
country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 12,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ? | "lets work with the data given to us . we know that there ratio of cats to dogs is 6 : 12 or cats 6 dogs 12 we can write number of cats as 6 x and number of dogs as 12 x and we know that 12 x - 6 x = 24 ( therefore 6 x = 24 = > x = 4 ) then # of dogs = 12 x 4 = 48 answer is b" | a ) 50 , b ) 48 , c ) 52 , d ) 54 , e ) 56 | b | multiply(24, 12) | multiply(n1,n2)| | other |
if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2160 less than the principal . what was the principal ? | "1 / 80 + 1 / 40 = 0.0375 days answer : d" | a ) 1.0875 days , b ) 0.1875 days , c ) 0.0675 days , d ) 0.0375 days , e ) 0.0775 days | d | inverse(add(inverse(80), inverse(40))) | inverse(n0)|inverse(n1)|add(#0,#1)|inverse(#2)| | physics |
by selling 10 pencils for a rupee a man loses 25 % . how many for a rupee should he sell in order to gain 25 % ? | for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.80 . let x be the price per pound for the steak . then 0.8 x = 180 x = 180 / 0.8 = $ 2.25 the answer is c . | a ) $ 2.05 , b ) $ 2.15 , c ) $ 2.25 , d ) $ 2.35 , e ) $ 2.45 | c | divide(1.8, add(multiply(const_0_25, const_2), multiply(const_0_33, const_1))) | multiply(const_0_25,const_2)|multiply(const_0_33,const_1)|add(#0,#1)|divide(n0,#2) | general |
by weight , liquid x makes up 1.5 percent of solution p and 6.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ? | "the number of exhaustive outcomes is 36 . let e be the event of getting a prime number on both the dice . p ( e ) = 8 / 36 = 2 / 9 . c )" | a ) 5 / 9 , b ) 1 / 9 , c ) 2 / 9 , d ) 4 / 9 , e ) 7 / 9 | c | divide(const_6, multiply(const_6, const_6)) | multiply(const_6,const_6)|divide(const_6,#0)| | other |
a cat leaps 5 leaps for every 4 leaps of a dog , but 2 leaps of the dog are equal to 3 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ? | say x guests ate both types of meat . ( 125 - x ) + ( 75 - x ) = 100 - - > x = 50 . answer : e . | a ) 5 , b ) 100 , c ) 7 , d ) 4 , e ) 50 | e | add(subtract(125, 100), subtract(100, 75)) | subtract(n0,n2)|subtract(n2,n1)|add(#0,#1) | other |
a group of men decided to do a work in 20 days , but 8 of them became absent . if the rest of the group did the work in 28 days , find the original number of men ? | explanation : mon + tue + wed temperature = 3 x 36.3 = 108.9 tue + wed temperature = 108.9 – 39 = 69.9 tue + wed + thu temperature = 3 x 36.7 = 110.1 so , thursday ’ s temperature = 110.1 – 69.9 = 40.2 degrees c answer : c | a ) 60.2 degrees c , b ) 50.2 degrees c , c ) 40.2 degrees c , d ) 70.2 degrees c , e ) none of these | c | subtract(multiply(36.7, const_3), subtract(multiply(36.3, const_3), 39)) | multiply(n1,const_3)|multiply(n0,const_3)|subtract(#1,n2)|subtract(#0,#2) | general |
how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ? | "originally ( 3 / 9 ) * 1350 = 450 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 450 = 300 more acres were planted with tobacco . the answer is d ." | a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450 | d | subtract(multiply(add(add(multiply(const_100, const_10), multiply(const_3, const_100)), multiply(4, const_10)), divide(4, add(add(4, 2), 2))), multiply(add(add(multiply(const_100, const_10), multiply(const_3, const_100)), multiply(4, const_10)), divide(2, add(add(4, 2), 2)))) | add(n1,n2)|multiply(const_10,const_100)|multiply(const_100,const_3)|multiply(n1,const_10)|add(#1,#2)|add(n2,#0)|add(#4,#3)|divide(n1,#5)|divide(n2,#5)|multiply(#6,#7)|multiply(#6,#8)|subtract(#9,#10)| | other |
a train running at the speed of 50 km / hr crosses a post in 4 seconds . what is the length of the train ? | "first recognize you only need to consider the first three digits ( because the second three are just the first three flipped ) there are 900 possibilities for the first three digits of a 6 digit number , 100 - 999 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 900 = 500 answer : c" | a ) 400 , b ) 450 , c ) 500 , d ) 900 , e ) 2500 | c | divide(power(const_10, divide(6, const_2)), const_2) | divide(n1,const_2)|power(const_10,#0)|divide(#1,const_2)| | general |
evaluate : 60 - 12 * 3 * 2 = ? | "a 2400 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 6000 - r ) = > 3 r = 12000 - 2 r = > 5 r = 12000 = > r = 2400 ." | a ) 2400 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 1930 | a | divide(multiply(6000, multiply(const_2, const_2)), add(add(multiply(divide(multiply(const_2, const_2), const_3), const_3), multiply(const_1, const_3)), multiply(const_1, const_3))) | multiply(const_2,const_2)|multiply(const_1,const_3)|divide(#0,const_3)|multiply(n0,#0)|multiply(#2,const_3)|add(#4,#1)|add(#5,#1)|divide(#3,#6)| | general |
the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 8 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ? | "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 15 ) = 331 times . answer : e" | a ) 380 times , b ) 381 times , c ) 382 times , d ) 392 times , e ) 331 times | e | divide(add(add(const_2, 47), multiply(add(20, add(const_2, const_60)), const_60)), 15) | add(n6,const_2)|add(const_2,const_60)|add(n5,#1)|multiply(#2,const_60)|add(#0,#3)|divide(#4,n0)| | general |
two good train each 750 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one . | "sol . average speed = [ 2 * 3 * 2 / 3 + 2 ] km / hr = 12 / 5 km / hr . distance travelled = [ 12 / 5 * 5 ] km = 12 km . ∴ distance between house and school = [ 12 / 2 ] km = 6 km . answer c" | a ) 4.5 km , b ) 5.5 km , c ) 6 km , d ) 7 km , e ) none | c | multiply(divide(5, add(divide(3, 2), const_1)), 3) | divide(n0,n1)|add(#0,const_1)|divide(n2,#1)|multiply(n0,#2)| | physics |
a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 10 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ? | "number of passengers on flight = 120 number of female passengers = . 6 * 120 = 72 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 72 - 8 = 64 answer d" | a ) 44 , b ) 48 , c ) 50 , d ) 64 , e ) 56 | d | subtract(multiply(120, divide(60, const_100)), subtract(multiply(120, divide(10, const_100)), divide(multiply(120, divide(10, const_100)), 3))) | divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#0)|multiply(n0,#1)|divide(#3,n5)|subtract(#3,#4)|subtract(#2,#5)| | gain |
today jim is twice as old as fred , and sam is 4 years younger than fred . 4 years ago jim was 8 times as old as sam . how old is jim now ? | "radius / side = 2 / 7 â ‡ ’ area of circle / area of square = 4 / 49 answer : d" | a ) 2 : 1 , b ) 4 : 7 , c ) 8 : 77 , d ) 4 : 49 , e ) none | d | power(divide(2, 7), 2) | divide(n0,n1)|power(#0,n0)| | geometry |
tim and é lan are 60 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ? | by the rule of alligation : c . p . of 1 kg sugar of 1 st kind c . p . of 1 kg sugar of 2 nd kind { \ color { blue } \ therefore } ratio of quantities of 1 st and 2 nd kind = 14 : 6 = 7 : 3 . let x kg of sugar of 1 st kind be mixed with 27 kg of 2 nd kind . then , 7 : 3 = x : 27 or x = ( 7 x 27 / 3 ) = 63 kg . answer : d ) 63 kg | a ) 33 , b ) 39 , c ) 38 , d ) 63 , e ) 01 | d | divide(subtract(multiply(27, divide(9.24, add(divide(10, const_100), const_1))), multiply(27, 7)), subtract(9, divide(9.24, add(divide(10, const_100), const_1)))) | divide(n3,const_100)|multiply(n1,n2)|add(#0,const_1)|divide(n4,#2)|multiply(n1,#3)|subtract(n0,#3)|subtract(#4,#1)|divide(#6,#5) | gain |
a person bought 135 glass bowls at a rate of rs . 15 per bowl . he sold 115 of them at rs . 18 and the remaining broke . what is the percentage gain for a ? | "s . i for 5 years = ( 1020 - 820 ) = rs . 200 . s . i . for 2 years = 200 / 5 * 2 = rs . 80 . principal = ( 820 - 80 ) = rs . 740 . answer : d" | a ) rs . 440 , b ) rs . 500 , c ) rs . 540 , d ) rs . 740 , e ) rs . 840 | d | subtract(820, multiply(divide(subtract(1020, 820), 5), 2)) | subtract(n2,n0)|divide(#0,n3)|multiply(n1,#1)|subtract(n0,#2)| | general |
there are 3000 students in a school and among them 20 % of them attends chess class . 40 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ? | "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 60 x = 48.7 hence , the correct option is e" | a ) 39.55 $ , b ) 40.63 $ , c ) 41.63 $ , d ) 42.15 $ , e ) 48.7 $ | e | divide(60, add(divide(add(7, 15), const_100), const_1)) | add(n1,n2)|divide(#0,const_100)|add(#1,const_1)|divide(n0,#2)| | general |
the smallest value of n , for which 2 n is not a prime number , is | sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 21000 + 35000 ) = 66000 - s 6000 = rs . 10000 e | a ) rs . 8000 , b ) rs . 9000 , c ) rs . 9800 , d ) rs . 9900 , e ) rs . 10000 | e | add(subtract(42000, divide(multiply(21000, 5), 3)), subtract(divide(multiply(42000, 4), 7), 21000)) | multiply(n4,n7)|multiply(n1,n6)|divide(#0,n3)|divide(#1,n2)|subtract(n6,#2)|subtract(#3,n7)|add(#4,#5) | general |
one - third of 600 is what percent of 120 ? | "solution required numbers are 102 , 018,114 , . . . . 996 . this is an a . p with a = 102 , d = 6 . let the number of its terms be n . then a + ( n - 1 ) d ‹ = › 102 + ( n - 1 ) × 6 = 996 ‹ = › n = 150 . answer b" | a ) 149 , b ) 150 , c ) 151 , d ) 166 , e ) none | b | add(multiply(const_100, 6), const_100) | multiply(n0,const_100)|add(#0,const_100)| | general |
the distance between 2 cities a and b is 1000 km . a train starts from a at 12 p . m . and travels towards b at 100 km / hr . another starts from b at 1 p . m . and travels towards a at 150 km / hr . at what time do they meet ? | "speed of boat in still water = 12 km / hr speed of the stream = 4 km / hr speed downstream = ( 12 + 4 ) = 16 km / hr time taken to travel 68 km downstream = 68 ⁄ 16 = 17 ⁄ 4 = 4.25 hours answer is a" | a ) 4.25 hr , b ) 5.25 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr | a | divide(68, add(12, 4)) | add(n0,n1)|divide(n2,#0)| | physics |
tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 52 people bought tickets to the concert , what was the total revenue from ticket sales ? | if saran and david submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combinedno discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) . | a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54 | b | divide(subtract(multiply(const_2, multiply(80, 0.02)), multiply(multiply(160, divide(subtract(100, 25), 100)), 0.02)), const_2) | multiply(n0,n3)|subtract(n2,n1)|divide(#1,n2)|multiply(#0,const_2)|multiply(n4,#2)|multiply(n0,#4)|subtract(#3,#5)|divide(#6,const_2) | gain |
how many 3 digit positive integers t exist that when divided by 7 leave a remainder of 5 ? | "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional values the productivity in 1 st case is 0.5 bears / hour and in the 2 nd case it is 1 bear / hour hence the productivity is double with the assistant i . e . the increase in productivity is 200 % e" | a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 % | e | multiply(divide(10, subtract(subtract(const_100, 100), 10)), const_100) | subtract(const_100,n0)|subtract(#0,n1)|divide(n1,#1)|multiply(#2,const_100)| | physics |
a shopkeeper fixes the marked price of an item 40 % above its cost price . the percentage of discount allowed to gain 8 % is | "explanation : amount of work p can do in 1 day = 1 / 10 amount of work q can do in 1 day = 1 / 12 amount of work p and q can do in 1 day = 1 / 10 + 1 / 12 = 11 / 60 amount of work p and q can together do in 5 days = 5 × ( 11 / 60 ) = 11 / 12 fraction of work left = 1 – 11 / 12 = 1 / 12 answer : option c" | a ) 7 / 12 , b ) 5 / 12 , c ) 1 / 12 , d ) 3 / 12 , e ) 1 / 2 | c | subtract(const_1, multiply(add(divide(const_1, 12), divide(const_1, 10)), 5)) | divide(const_1,n1)|divide(const_1,n0)|add(#0,#1)|multiply(n2,#2)|subtract(const_1,#3)| | physics |
by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 250 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ? | "perimeter = distance covered in 6 min . = ( 12000 / 60 ) x 6 m = 1200 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1200 or x = 120 . length = 360 m and breadth = 240 m . area = ( 360 x 240 ) m 2 = 86400 m 2 . answer : c" | a ) 153601 , b ) 153600 , c ) 86400 , d ) 153603 , e ) 153604 | c | rectangle_area(divide(divide(multiply(multiply(divide(12, multiply(const_10, multiply(const_3, const_2))), 6), const_1000), add(3, 2)), const_2), multiply(divide(divide(multiply(multiply(divide(12, multiply(const_10, multiply(const_3, const_2))), 6), const_1000), add(3, 2)), const_2), 2)) | add(n0,n1)|multiply(const_2,const_3)|multiply(#1,const_10)|divide(n2,#2)|multiply(n3,#3)|multiply(#4,const_1000)|divide(#5,#0)|divide(#6,const_2)|multiply(n1,#7)|rectangle_area(#7,#8)| | physics |
a man can row 5 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 ? | "area of a parallelogram = base * height = 24 * 12 = 288 cm 2 answer : e" | a ) 297 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 288 cm 2 | e | multiply(24, 12) | multiply(n0,n1)| | geometry |
a towel , when bleached , lost 30 % of its length and 20 % of its breadth . what is the percentage decrease in area ? | p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 2 / 3 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 2 / 3 = 1 / 3 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 1 / 3 = 1 / 6 - - - > p ( of burning out in a six mnth period ) = 1 - 1 / 3 = 2 / 3 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 2 / 3 * 1 / 6 = 2 / 7 ans e | a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 3 , d ) 4 / 9 , e ) 2 / 7 | e | multiply(subtract(1, divide(2, 3)), subtract(1, divide(subtract(1, divide(2, 3)), 2))) | divide(n3,n4)|subtract(n6,#0)|divide(#1,n3)|subtract(n6,#2)|multiply(#1,#3) | general |
local kennel has cats and dogs in the ratio of 6 : 12 . if there are 24 fewer cats than dogs , how many dogs are in the kennel ? | "we are given that 0.05 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.05 by 20 . this gives us : 0.05 x 20 = 1 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 1 / 10 ) x 100 % ( 10 / 100 ) x 100 % = 10 % answer e" | a ) 0.002 % , b ) 0.02 % , c ) 0.2 % , d ) 2 % , e ) 10 % | e | multiply(divide(multiply(0.05, 20), 10), const_100) | multiply(n1,n2)|divide(#0,n0)|multiply(#1,const_100)| | gain |
if 7 a - 3 b = 10 b + 50 = - 12 b - 2 a , what is the value of 9 a + 9 b ? | "explanation : let b contribution is x . 3500 * 12 / 7 x = 2 / 3 = > 14 x = 126000 = > x = rs 9000 option a" | a ) rs 9000 , b ) rs 7000 , c ) rs 5000 , d ) rs 4000 , e ) none of these | a | divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 5), 2)) | multiply(n0,const_12)|subtract(const_12,n1)|multiply(n3,#0)|multiply(n2,#1)|divide(#2,#3)| | other |
a , b and c start a business each investing 10,000 . after 6 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 34,200 was recorded . find the share of b . | "explanation : required percentage = ( 16 / 5200 * 100 ) % = 3 / 10 % = 0.30 % answer : a ) . 30 %" | a ) 30 , b ) 66 , c ) 58 , d ) 29 , e ) 17 | a | multiply(divide(5.2, 16), const_100) | divide(n0,n1)|multiply(#0,const_100)| | gain |
rs . 6490 is divided so that 4 times the first share , six times the 2 nd share and twice the third share amount to the same . what is the value of the first share ? | "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 162 . ∴ x 16 x 9 / 12 x 1 / 100 } = 162 or x = 1350 . ∴ p . w . = rs . 1350 . answer b" | a ) rs . 1386 , b ) rs . 1350 , c ) rs . 1575 , d ) rs . 2268 , e ) none of these | b | add(divide(162, divide(multiply(divide(9, multiply(const_4, const_3)), 16), const_100)), 162) | multiply(const_3,const_4)|divide(n0,#0)|multiply(n1,#1)|divide(#2,const_100)|divide(n2,#3)|add(n2,#4)| | gain |
the equation of line a is y = 4 / 3 * x - 100 . what is the smallest possible distance in the xy - plane from the point with coordinates ( 0 , 0 ) to any point on line a ? | "net part filled in 1 hour 1 / 5 - 1 / 10 = 1 / 10 the cistern will be filled in 10 hr answer is b" | a ) 20 hr , b ) 10 hr , c ) 5 hr , d ) 4 hr , e ) 15 hr | b | divide(const_1, subtract(divide(const_1, 5), divide(const_1, 10))) | divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)| | physics |
the number 150 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ? | charges for 7 hours = ( first hour @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 ) charges for 7 hours = ( 1 @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 ) charges for 7 hours = ( $ 0.50 ) + ( $ 9 ) + ( $ 3.5 ) charges for 7 hours = ( $ 0.50 ) + ( $ 9 ) + ( $ 3.50 ) charges for 7 hours = $ 13 hence correct answer must be ( c ) | a ) $ 11.5 . , b ) $ 12 . , c ) $ 13 . , d ) $ 14.5 , e ) $ 15 . | c | add(add(multiply(3, 3), multiply(add(subtract(7, 4), divide(50, const_100)), 1)), divide(50, const_100)) | divide(n0,const_100)|multiply(n1,n1)|subtract(n4,n2)|add(#0,#2)|multiply(n3,#3)|add(#1,#4)|add(#5,#0) | physics |
900 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ? | explanation : suppose y invested rs . y . then 40000 / y = 2 / 3 or y = 60000 . answer : c ) 60000 | a ) 33488 , b ) 63809 , c ) 60000 , d ) 37887 , e ) 77824 | c | multiply(divide(multiply(40000, add(2, 3)), 2), divide(3, add(2, 3))) | add(n0,n1)|divide(n1,#0)|multiply(n2,#0)|divide(#2,n0)|multiply(#3,#1) | gain |
if n is a positive integer such that n ! / ( n - 2 ) ! = 342 , find n . | "a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 4 meters from either end . the probability of this is 8 / 12 = 2 / 3 . the answer is b ." | a ) 1 / 6 , b ) 2 / 3 , c ) 3 / 10 , d ) 1 / 3 , e ) 2 / 5 | b | multiply(const_2, divide(const_2, 12)) | divide(const_2,n0)|multiply(#0,const_2)| | geometry |
17 : 71 : : 18 : ? | sp = 1.34 * 245 = 328 answer : a | a ) 328 , b ) 320 , c ) 300 , d ) 207 , e ) 310 | a | add(245, multiply(245, divide(34, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1) | gain |
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 ? | "assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 155 = > 20 x + 25 ( x - 1 ) = 155 = > 45 x = 180 = > x = 4 means , they meet after 3 hours after 7 am , ie , they meet at 11 am answer is e ." | a ) 10 am , b ) 12 am , c ) 10.30 am , d ) 12.30 am , e ) 11 am | e | add(divide(add(155, 25), add(20, 25)), 7) | add(n0,n4)|add(n2,n4)|divide(#0,#1)|add(n1,#2)| | physics |
the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 13 and 31 inclusive . | "a 23 years let the average age of the whole team by x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . so , average age of the team is 23 years" | a ) 23 years , b ) 20 years , c ) 25 years , d ) 22 years , e ) 28 years | a | divide(subtract(add(26, add(26, 3)), multiply(3, 3)), const_2) | add(n1,n2)|multiply(n2,n2)|add(n1,#0)|subtract(#2,#1)|divide(#3,const_2)| | general |
employees of a certain company are each to receive a unique 9 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , and 8 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ? | original number of sections = 16 - 3 = 13 original number of students = 24 x 13 = 312 present number of students = 21 x 16 = 336 number of new students admitted = 336 - 312 = 24 so the answer is option c ) 24 . | a ) 12 , b ) 42 , c ) 24 , d ) 28 , e ) 26 | c | subtract(multiply(21, 16), multiply(24, subtract(16, 3))) | multiply(n2,n3)|subtract(n2,n1)|multiply(n0,#1)|subtract(#0,#2) | physics |
in a class of 60 students , 20 did not opt for math . 15 did not opt for science and 5 did not opt for either . how many students of the class opted for both math and science ? | = ( 81 ) ^ 2 + ( 68 ) ^ 2 – 2 x 81 x 68 = a ^ 2 + b ^ 2 – 2 ab , where a = 81 , b = 68 = ( a - b ) ^ 2 = ( 81 – 68 ) ^ 2 = ( 13 ) ^ 2 = 169 . answer is a . | a ) 169 , b ) 159 , c ) 189 , d ) 179 , e ) 219 | a | add(81, 81) | add(n0,n0) | general |
if henry were to add 6 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 ? | "= > - 24 * ( 30 - 1 ) + 1240 ; = > - ( 24 * 30 ) + 24 + 1240 ; = > - 720 + 1264 = 544 . correct option : c" | a ) - 544 , b ) 584 , c ) 544 , d ) 345 , e ) none of these | c | add(multiply(negate(24), 29), 1240) | negate(n0)|multiply(n1,#0)|add(n2,#1)| | general |
r is the set of positive odd integers less than 100 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? | "the total amount of alcohol is 0.25 ( 4 ) + 0.11 ( 3 ) = 1.33 liters . the percentage is 1.33 / 7 = 133 / 700 = 19 / 100 which is 19 % the answer is c ." | a ) 18.2 % , b ) 18.6 % , c ) 19.0 % , d ) 19.4 % , e ) 19.8 % | c | multiply(divide(add(multiply(4, divide(25, const_100)), multiply(divide(11, const_100), multiply(4, divide(25, const_100)))), add(4, 3)), const_100) | add(n0,n2)|divide(n1,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(#2,#3)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)| | general |
the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 18 positive perfect squares ? | ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 13750 × 16 / 55 = rs . 4000 . share of z in the profit is rs . 4000 . option b | a ) 3200 , b ) 4000 , c ) 3250 , d ) 3825 , e ) 3985 | b | multiply(multiply(48000, subtract(multiply(const_3, const_4), const_4)), divide(13750, add(add(multiply(36000, multiply(const_3, const_4)), multiply(42000, multiply(const_3, const_4))), multiply(48000, subtract(multiply(const_3, const_4), const_4))))) | multiply(const_3,const_4)|multiply(n0,#0)|multiply(n1,#0)|subtract(#0,const_4)|add(#1,#2)|multiply(n3,#3)|add(#4,#5)|divide(n4,#6)|multiply(#7,#5) | gain |
3 different containers contain 50 litres , 100 litres and 150 litres of mixture of milk and water respectively . what is the biggest measure can measure all the different quantities exactly ? | "machine b : takes x hours to produce 550 sprockets machine a : takes ( x + 10 ) hours to produce 550 sprockets machine b : in 1 hour , b makes 550 / x sprockets machine a : in 1 hour , a makes 550 / ( x + 10 ) sprockets equating : 1.1 ( 550 / ( x + 10 ) ) = 550 / x 605 / ( x + 10 ) = 550 / x 605 x = 550 x + 5500 55 x = 5500 x = 100 a makes 550 / ( 110 ) = 5 sprockets per hour answer : b" | a ) 6 , b ) 5 , c ) 7 , d ) 8 , e ) 9 | b | divide(550, divide(multiply(multiply(10, 550), divide(add(const_100, 10), const_100)), subtract(multiply(550, divide(add(const_100, 10), const_100)), 550))) | add(n1,const_100)|multiply(n0,n1)|divide(#0,const_100)|multiply(#2,#1)|multiply(n0,#2)|subtract(#4,n0)|divide(#3,#5)|divide(n0,#6)| | gain |
the angle between the minute hand and the hour hand of a clock when the time is 7.30 , is | "b 13.2 sec d = 100 + 120 = 220 m s = 60 * 5 / 18 = 50 / 3 t = 220 * 3 / 50 = 13.2 sec answer is b" | a ) 15.8 sec , b ) 13.2 sec , c ) 12.4 sec , d ) 16.8 sec , e ) 11.8 sec | b | divide(add(100, 120), multiply(60, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | physics |
if a farmer sells 15 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 25 more chickens , he will run out of feed 3 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ? | after the reservoir is filled to 7.5 gallons the amount of water is at 55 % - which means that 45 % of the reservoir is empty . to figure out what that 45 % is approximate : 7.5 gallons / 55 percent = x gallons / 45 percent , therefore , x = 6.136 gallons , answer choices e , b , c , d are below 6.136 . we know that the reservoir must be short more than 6.136 gallons , therefore , the only possible choice is a . | a ) 6.9 , b ) 1.4 , c ) 2.5 , d ) 3.0 , e ) 4.4 | a | divide(divide(multiply(7.5, const_100), 55), const_2) | multiply(n1,const_100)|divide(#0,n2)|divide(#1,const_2) | general |
the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 7 students ? | "u dont need to go through all this what u have with u is 100 p + 200 c = $ 4.50 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 0.90 therefore oa is a" | a ) $ . 90 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60 | a | multiply(divide(20, 100), 4.50) | divide(n3,n0)|multiply(n2,#0)| | gain |
if a and b are positive integers , and a = 20 b - 15 , the greatest common divisor of a and b can not be | "( 1 / 2 + 1 / 3 ) t = 2 t = 12 / 5 answer : c" | a ) 8 / 15 , b ) 4 / 3 , c ) 12 / 5 , d ) 9 / 4 , e ) 15 / 4 | c | multiply(divide(const_1, add(divide(const_1, 2), divide(const_1, 3))), 2) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)|multiply(#3,n0)| | physics |
the population of a village is 13400 . it increases annually at the rate of 21 % p . a . what will be its population after 2 years ? | "a takes time 1.20 minutes = 80 sec b takes time 1.30 minutes = 90 sec diffrence = 90 - 80 = 10 sec now we are to find distance covered in 10 sec by b 90 sec = 30 m 1 sec = 30 m 10 sec = 10 x 30 = 300 m answer : d" | a ) 90 m , b ) 30 m , c ) 120 m , d ) 300 m , e ) 190 m | d | subtract(multiply(const_2.0, const_1000), multiply(divide(multiply(2.7, const_1000), add(multiply(1, const_60), 30)), add(multiply(2.7, const_60), 20))) | multiply(n0,const_1000)|multiply(n1,const_60)|multiply(n3,const_60)|add(n2,#1)|add(n4,#2)|divide(#0,#4)|multiply(#3,#5)|subtract(#0,#6)| | physics |
the grade point average of the entire class is 88 . if the average of one third of the class is 94 , what is the average of the rest of the class ? | "5 * 5 answer : a" | a ) 1 , b ) 5 , c ) 4 , d ) 6 , e ) 8 | a | add(power(const_2, const_2), const_2) | power(const_2,const_2)|add(#0,const_2)| | other |
find large number from below question the difference of two numbers is 1380 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder | 4 x * x = 2304 = > x = 24 answer : c | ['a ) 19', 'b ) 23', 'c ) 24', 'd ) 16', 'e ) 17'] | c | sqrt(divide(add(add(multiply(const_1000, const_2), multiply(const_100, const_3)), const_4), const_4)) | multiply(const_1000,const_2)|multiply(const_100,const_3)|add(#0,#1)|add(#2,const_4)|divide(#3,const_4)|sqrt(#4) | geometry |
what is the angle between the hands of a clock when time is 10 : 30 ? | "d = 150 + 170 = 320 m s = 60 * 5 / 18 = 50 / 3 t = 320 * 3 / 50 = 19.2 sec answer : b" | a ) 16.5 , b ) 19.2 , c ) 16.4 , d ) 16.8 , e ) 16.1 | b | divide(add(150, 170), multiply(60, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | physics |
car x began traveling at an average speed of 35 miles per hour . after 36 minutes , car y began traveling at an average speed of 38 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ? | "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 4 ) / 2 = 3.5 , thus the number selected must be 4 or greater . for the range to remain the same , the number must be between 2 and 7 inclusive . to satisfy both conditions , the number selected must be 4 , 5 , 6 , or 7 . the probability is 4 / 10 = 0.4 the answer is c ." | a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6 | c | divide(const_4, const_10) | divide(const_4,const_10)| | general |
an engine moves at the speed of 90 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 9 coaches are attached speed decreases to 78 kmph . what will be the speed of train when 25 coaches are attached . | "14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus w = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )" | a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5 | a | divide(5, 5) | divide(n4,n4)| | general |
if y > 0 , ( 10 y ) / 20 + ( 3 y ) / 10 is what percent of y ? | "let the numbers be 13 a and 13 b . then , 13 a * 13 b = 2028 = > ab = 12 . now , co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) . so , the required numbers are ( 13 * 1 , 13 * 12 ) and ( 13 * 3 , 13 * 4 ) . clearly , there are 2 such pairs . answer : b" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | sqrt(add(power(sqrt(subtract(13, multiply(const_2, 2028))), const_2), multiply(const_4, 2028))) | multiply(n0,const_4)|multiply(n0,const_2)|subtract(n1,#1)|sqrt(#2)|power(#3,const_2)|add(#0,#4)|sqrt(#5)| | general |
if 45 % of z is 60 % of y and y is 75 % of x , what percent of x is z ? | "let x be the number he chose , then 6 ⋅ x − 250 = 122 6 x = 372 x = 62 correct answer d" | a ) 59 , b ) 60 , c ) 61 , d ) 62 , e ) 63 | d | divide(add(122, 250), 6) | add(n1,n2)|divide(#0,n0)| | general |
if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 23 , find the value of ab . | "prime numbers between 30 and 50 are 37 , 41 , 43 , 47 required average = ( 37 + 41 + 43 + 47 ) / 4 = 168 / 4 = 42 answer is b" | a ) 15 , b ) 42 , c ) 45 , d ) 34 , e ) 26 | b | divide(add(add(add(30, const_1), add(add(const_4.0, const_1), const_2)), add(subtract(50, const_4.0), subtract(50, const_2))), 30) | add(n0,const_1)|subtract(n1,const_4.0)|subtract(n1,const_2)|add(#0,const_2)|add(#1,#2)|add(#0,#3)|add(#5,#4)|divide(#6,const_4)| | general |
an article with cost price of 245 is sold at 34 % profit . what is the selling price ? | explanation : ( 55 ã — 40 ) + ( 60 ã — 62 ) + ( 45 ã — 58 ) / 55 + 60 + 45 8530 / 160 = 53.3 option b | a ) 54.48 , b ) 53.31 , c ) 54.6 , d ) 54.58 , e ) none of these | b | divide(add(add(multiply(55, 40), multiply(60, 62)), multiply(40, 58)), add(add(55, 60), 45)) | add(n1,n2)|multiply(n1,n4)|multiply(n2,n5)|multiply(n4,n6)|add(#1,#2)|add(n3,#0)|add(#4,#3)|divide(#6,#5) | general |
p software has coding line 5 % more than n , n software has coding line 1 / 2 more than m . m software has 100 lines of coding . find p lines . | "in an arithmetic progression , the nth term is given by tn = a + ( n - 1 ) d here tn = 65 , a = - 60 , d = 1 hence , 65 = - 60 + ( n - 1 ) or n = 126 sum of n terms can be calculated by sn = n / 2 ( a + l ) a = first term , l = last term , n = no . of terms sn = 126 * ( - 60 + 65 ) / 2 sn = 126 * 5 / 2 = 315 answer : a" | a ) 315 , b ) 215 , c ) 115 , d ) 165 , e ) 765 | a | divide(multiply(60, 65), const_4) | multiply(n0,n1)|divide(#0,const_4)| | general |
a man walking at a rate of 15 km / hr crosses a bridge in 35 minutes . the length of the bridge is ? | "a = first number l = last number sn = n / 2 [ a + l ] between 60 and 100 numbers = 41 = > 100 - 60 = 40 + 1 = 41 sn = 41 / 2 ã — 160 = 41 ã — 80 = 3280 answer : e" | a ) 4800 , b ) 4860 , c ) 5000 , d ) 5500 , e ) 3280 | e | add(100, const_1) | add(n1,const_1)| | general |
andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.82 . what is the median gasoline price ? | explanatory answer let the percentage of the total votes secured by party d be x % then the percentage of total votes secured by party r = ( x - 12 ) % as there are only two parties contesting in the election , the sum total of the votes secured by the two parties should total up to 100 % i . e . , x + x - 12 = 100 2 x - 12 = 100 or 2 x = 112 or x = 56 % . if party d got 56 % of the votes , then party got ( 56 - 12 ) = 44 % of the total votes . 44 % of the total votes = 132,000 i . e . , 44 / 100 * t = 132,000 = > t = 132000 * 100 / 44 = 300,000 votes . the margin by which party r lost the election = 12 % of the total votes = 12 % of 300,000 = 36,000 . the correct choice is ( d ) | a ) 240000 , b ) 300000 , c ) 168000 , d ) 36000 , e ) 24,000 | d | multiply(divide(132000, divide(subtract(const_100, 12), const_2)), 12) | subtract(const_100,n0)|divide(#0,const_2)|divide(n1,#1)|multiply(n0,#2) | general |
sum of 36 odd numbers is ? | "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 26 / 25 ) x ( 32 / 33 ) y = ( 344 / 341 ) ( xy ) error in measurement = ( 344 / 341 ) xy - xy = ( 3 / 341 ) xy error percentage = [ ( 3 / 341 ) xy ( 1 / xy ) 100 ] % = ( 22 / 25 ) % = 0.88 % . answer is e ." | a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.88 % | e | subtract(subtract(4, 3), divide(multiply(4, 3), const_100)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,const_100)|subtract(#1,#2)| | geometry |
25 is subtracted from 75.00001 % of a number , the result is 50 . find the number ? | "5 choices for each of the 4 questions , thus total e of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c ." | a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024 | c | power(5, 4) | power(n1,n0)| | general |
a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 36 instead of 86 then find the correct average marks up to two decimal places . | c ' s 1 day work = ( 1 / 3 ) - ( 1 / 6 + 1 / 8 ) = 1 / 24 a : b : c = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 a ' s share = 600 * 4 / 8 = $ 300 answer is c | a ) $ 100 , b ) $ 150 , c ) $ 300 , d ) $ 250 , e ) $ 350 | c | multiply(divide(multiply(multiply(3, 8), inverse(6)), add(add(multiply(multiply(3, 8), subtract(inverse(3), add(inverse(6), inverse(8)))), multiply(multiply(3, 8), inverse(6))), multiply(multiply(3, 8), inverse(8)))), 600) | inverse(n1)|inverse(n3)|inverse(n2)|multiply(n2,n3)|add(#0,#2)|multiply(#0,#3)|multiply(#2,#3)|subtract(#1,#4)|multiply(#3,#7)|add(#8,#5)|add(#9,#6)|divide(#5,#10)|multiply(n0,#11) | physics |
a certain number of two digits is 3 times the sum of its digits and if 45 be added to it , the degits are reversed . the number is . | "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 660 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 660 â ‡ ’ y [ 12 / 10 + 1 ] = 660 â ‡ ’ 22 y / 10 = 660 â ‡ ’ 22 y = 6600 â ‡ ’ y = 6600 / 22 = 600 / 2 = rs . 300 e" | a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 300 | e | divide(multiply(660, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2)) | add(const_1,const_4)|multiply(#0,const_2)|add(#1,const_1)|multiply(n0,#1)|multiply(#2,const_2)|divide(#3,#4)| | general |
uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 10 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ? | "c if we calculate we will get 10749" | a ) 2449 , b ) 10449 , c ) 10749 , d ) 10449 , e ) 6468 | c | subtract(multiply(divide(54671, const_100), 10456), multiply(divide(const_1, const_3), multiply(divide(54671, const_100), 10456))) | divide(n0,const_100)|divide(const_1,const_3)|multiply(n1,#0)|multiply(#1,#2)|subtract(#2,#3)| | general |
the ratio of the area of a square to that of the square drawn on its diagonal is | "speed = ( 120 + 80 ) km / h ( because direction is opposite hence relative velocity is added ) = 500 / 9 m / s time = 9 sec let the lenght of second train is x total distance covered = 250 + x therefore , d = speed * time thus 250 + x = 500 / 9 * 9 x = 500 - 250 = 250 m answer : c" | a ) 230 m , b ) 240 m , c ) 250 m , d ) 260 m , e ) 270 m | c | subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 250) | add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)| | physics |
find the average of all the numbers between 6 and 34 which are divisible by 5 . | x + x ( xx ) put the value of x = 7 in the above expression we get , 7 + 7 ( 77 ) = 7 + 7 ( 7 ã — 7 ) = 7 + 7 ( 49 ) = 7 + 343 = 350 the answer is ( a ) | a ) a ) 350 , b ) b ) 346 , c ) c ) 358 , d ) d ) 336 , e ) e ) 364 | a | add(multiply(7, multiply(7, 7)), 7) | multiply(n0,n0)|multiply(n0,#0)|add(n0,#1) | general |
salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 20 % vinegar , dressing p comprises what percentage of the new dressing ? | "the class borrowed a total of 40 * 2 = 80 books . the 25 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 11 * 2 = 34 . to maximize the number of books borrowed by 1 student , let ' s assume that 14 students borrowed 3 books and 1 student borrowed the rest . 80 - 34 - 3 * 14 = 4 the maximum number of books borrowed by any student is 4 . the answer is b ." | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | b | subtract(multiply(40, 2), add(multiply(subtract(subtract(40, add(add(multiply(12, 1), 11), 2)), 1), 3), add(multiply(12, 1), multiply(11, 2)))) | multiply(n0,n1)|multiply(n2,n3)|multiply(n1,n4)|add(#1,#2)|add(n4,#1)|add(n1,#4)|subtract(n0,#5)|subtract(#6,n3)|multiply(n6,#7)|add(#3,#8)|subtract(#0,#9)| | general |
a certain farmer pays $ 70 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 605 feet ? ( 43,560 square feet = 1 acre ) | t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 12 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ) ( t + m ) b | a ) 16 , b ) 12 , c ) 2 , d ) 6 , e ) 14 | b | add(const_10, 2) | add(n1,const_10) | general |
what is the angle between the minute and the hour hand of the clock which shows 12 : 24 ? | set a contains 12,14 , 16 . . . 50 set b contains 112 , 114 , 116 . . . 150 number of terms in each set = 20 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 20 = 2000 answer a | a ) 2000 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325 | a | multiply(subtract(112, 12), add(divide(subtract(50, 12), const_2), const_1)) | subtract(n1,n0)|subtract(n2,n0)|divide(#0,const_2)|add(#2,const_1)|multiply(#3,#1) | general |
a , band c can do a piece of work in 11 days , 20 days and 20 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ? | "let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 15 is twice 7.5 then the area will be double which means 100 % greater . the answer is c ." | a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 % | c | multiply(divide(subtract(multiply(rectangle_area(11, 15), const_2), multiply(rectangle_area(7.5, 11), const_2)), rectangle_area(11, 15)), const_100) | rectangle_area(n0,n1)|rectangle_area(n0,n2)|multiply(#0,const_2)|multiply(#1,const_2)|subtract(#2,#3)|divide(#4,#0)|multiply(#5,const_100)| | geometry |
each child has 4 crayons and 14 apples . if there are 9 children , how many crayons are there in total ? | "10 ^ 2 + 7 ^ 2 + 1 ^ 2 = 150 = = = > sum of these 3 integers = 10 + 7 + 1 = 18 b" | a ) 17 , b ) 18 , c ) 15 , d ) 14 , e ) 13 | b | add(add(add(const_4, 3), add(3, const_2)), 3) | add(n1,const_4)|add(const_2,n1)|add(#0,#1)|add(n1,#2)| | geometry |
how many seconds will a 200 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ? | "let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 24 x 32 ) cm 2 = 384 cm 2 hence c" | a ) 320 cm 2 , b ) 280 cm 2 , c ) 384 cm 2 , d ) 290 cm 2 , e ) 350 cm 2 | c | add(multiply(multiply(divide(const_1, const_2), 24), sqrt(subtract(multiply(multiply(20, 20), const_4), multiply(24, 24)))), 24) | divide(const_1,const_2)|multiply(n0,n0)|multiply(n1,n1)|multiply(n1,#0)|multiply(#1,const_4)|subtract(#4,#2)|sqrt(#5)|multiply(#3,#6)|add(n1,#7)| | geometry |
a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is | "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 2 + x + 5 + 7 = 16 + x least value of x may be 2 therefore 16 + 2 = 18 is divisible by 3 . answer : option a" | a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4 | a | divide(divide(divide(lcm(22, 57), 57), const_4), const_4) | lcm(n0,n1)|divide(#0,n1)|divide(#1,const_4)|divide(#2,const_4)| | general |
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 | "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 120 tagged deers comprise 10 % of total # of deers - - > total # of deers = 120 * 10 = 1,200 answer : a" | a ) 1,200 , b ) 750 , c ) 1,250 , d ) 1,500 , e ) 2,500 | a | multiply(50, 5) | multiply(n1,n3)| | general |
jane and ashley take 8 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s working for four extra days on her own to complete the project . how long did it take to finish the project ? | "let the c . p of each article be re 1 . then , s . p of 7 articles = c . p of 10 articles = rs . 10 now , c . p of 7 articles = rs . 7 , s . p of 7 articles = rs 10 gain = rs ( 10 - 7 ) = rs 3 . gain % = ( 3 / 7 × 100 ) % = 43 % answer : d" | a ) 93 % , b ) 23 % , c ) 33 % , d ) 43 % , e ) 53 % | d | subtract(7, 10) | subtract(n0,n1)| | gain |
if you write down all the numbers from 1 to 100 , then how many times do you write 3 ? | "let the number of boys and girls be 2 x and 7 x total students = 360 number of girls in the school = 7 * 360 / 9 = 280 answer is e" | a ) 150 , b ) 250 , c ) 300 , d ) 370 , e ) 280 | e | multiply(divide(360, const_3), const_2.0) | divide(n2,const_3)|multiply(const_2.0,#0)| | other |
in a lottery there are 100 prizes and 300 blanks . a lottery is drawn at random . what is the probability of getting a prize ? | "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 30 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 15 cents . fraction of spirit is 1 / 2 . 15 = k * ( 1 / 2 ) k = 30 cost per liter = 30 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 30 * ( 1 / 3 ) * 3 = 50 cents b . 30 cents" | a ) 13 , b ) 30 , c ) 50 , d ) 51 , e ) 52 | b | multiply(multiply(30, divide(1, add(1, 2))), add(1, 2)) | add(n0,n4)|divide(n0,#0)|multiply(n2,#1)|multiply(#0,#2)| | geometry |
a train of 40 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ? | let us consider it is a rectangle . so area = 24 * 9 = 216 sq . cm now ( 24 - 3 * 2 ) * ( 9 - 2 * 2 ) = 18 * 5 = 90 sq . cm answer : e | ['a ) 60 sq . cm', 'b ) 70 sq . cm', 'c ) 95 sq . cm', 'd ) 80 sq . cm', 'e ) 90 sq . cm'] | e | multiply(subtract(divide(216, power(const_3, const_2)), multiply(3, const_2)), subtract(power(const_3, const_2), multiply(2, const_2))) | multiply(n1,const_2)|multiply(n2,const_2)|power(const_3,const_2)|divide(n0,#2)|subtract(#2,#1)|subtract(#3,#0)|multiply(#5,#4) | other |
if the cost price of 20 articles is same as the selling price of 25 articles . find the gain or loss percentage ? | "explanation : average = ( 2 + 4 + 6 + 8 + 10 + 12 ) / 2 = 42 / 2 = 21 option b" | a ) 15 , b ) 21 , c ) 25 , d ) 30 , e ) 35 | b | divide(add(add(add(multiply(2, const_3), add(2, multiply(2, const_2))), multiply(2, const_4)), multiply(add(const_4, const_1), 2)), 2) | add(const_1,const_4)|multiply(n2,const_2)|multiply(n2,const_3)|multiply(n2,const_4)|add(n2,#1)|multiply(n2,#0)|add(#4,#2)|add(#6,#3)|add(#7,#5)|divide(#8,n2)| | general |
after 6 games , team b had an average of 75 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ? | "any x and y satisfying x / y = 5 / 3 should give the same value for ( x + y ) / ( x - y ) . say x = 5 and y = 3 , then ( x + y ) / ( x - y ) = ( 5 + 3 ) / ( 5 - 3 ) = 4 . answer : a ." | a ) 4 , b ) 1 / 5 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 5 | a | divide(add(5, 3), subtract(5, 3)) | add(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | general |
if the wheel is 14 cm then the number of revolutions to cover a distance of 2288 cm is ? | explanation : x - 35 = 80 x / 100 = > x = 175 = > 4 x / 5 = 4 x 175 / 5 = 140 . answer d | a ) 130 , b ) 155 , c ) 490 , d ) 140 , e ) 160 | d | multiply(divide(4, add(const_4, const_1)), multiply(35, add(const_4, const_1))) | add(const_1,const_4)|divide(n2,#0)|multiply(n0,#0)|multiply(#1,#2) | general |
speed of a boat in standing water is 10 kmph and speed of the stream is 2.5 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 ? | "the actual answer is obtained by multiplying 140 % by 70 % and subtracting 100 % from this total . that is : 140 % × 70 % = 98 % ; 98 % − 100 % = - 2 % . answer : b" | a ) − 5 % , b ) − 2 % , c ) 15 % , d ) 20 % , e ) 80 % | b | multiply(subtract(multiply(add(const_1, divide(40, const_100)), subtract(const_1, divide(30, const_100))), const_1), const_100) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|subtract(#4,const_1)|multiply(#5,const_100)| | gain |
solve the equation for x : 6 x - 27 + 3 x = 4 + 9 - x | explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 415 * 5 + 325 * 25 ) / 30 = 10200 / 30 = 340 answer : e ) 340 | a ) 140 , b ) 240 , c ) 260 , d ) 280 , e ) 340 | e | divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 425), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 325)), 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 |
a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ? | "solution let s be the sample space . then , n ( s ) = 52 c 3 = 22100 let e = event of getting 1 face card . n ( e ) = number of ways of choosing 1 face card out of 26 = 13 c 1 * 13 c 2 = 13 * 72 = 936 p ( e ) = n ( e ) / n ( s ) = 936 / 22100 = 234 / 5525 = 234 / 5525 . answer d" | a ) 238 / 5525 , b ) 176 / 5534 , c ) 253 / 5523 , d ) 234 / 5525 , e ) 1 / 5525 | d | divide(multiply(divide(52, const_4), divide(52, const_4)), choose(52, const_2)) | choose(n0,const_2)|divide(n0,const_4)|multiply(#1,#1)|divide(#2,#0)| | probability |
excluding stoppages , the speed of a bus is 84 kmph and including stoppages , it is 70 kmph . for how many minutes does the bus stop per hour ? | lte central angle = x perimeter of the sector = length of the arc + 2 ( radius ) 50 = ( x / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) 50 = 88 x / 360 + 28 88 x / 360 = 22 88 x = 7920 x = 90 answer : e | a ) 180 o , b ) 225 o , c ) 270 o , d ) 150 o , e ) 90 o | e | multiply(multiply(const_2, divide(multiply(subtract(14, const_3), const_2), add(const_4, const_3))), 14) | add(const_3,const_4)|subtract(n0,const_3)|multiply(#1,const_2)|divide(#2,#0)|multiply(#3,const_2)|multiply(n0,#4) | physics |
if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 160 , how much more remains to be paid ? | this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction q of n to the total would be 4 a / 24 a or 1 / 6 answer b | a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21 | b | divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3)) | divide(n2,n1)|multiply(const_1,const_1)|add(n0,#0)|divide(#2,n1)|multiply(#3,const_2)|subtract(#4,n1)|subtract(#5,const_3)|divide(#1,#6) | general |
a square is drawn inside a right - angled triangle with the two perpendicular sides as 12 cm and 8 cm . what is the side of the largest possible square that can be drawn ? | 12 men 120 acres 16 days 36 men ? 32 days 120 * 36 / 12 * 32 / 16 120 * 3 * 2 120 * 6 = 720 answer : d | a ) 269 , b ) 512 , c ) 369 , d ) 720 , e ) 450 | d | multiply(120, multiply(divide(36, 12), divide(32, 16))) | divide(n3,n0)|divide(n4,n2)|multiply(#0,#1)|multiply(n1,#2) | physics |
at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 203 ? | "total fish = x percentage of second catch = ( 4 / 50 ) * 100 = 8 % so , x * 8 % = 50 x = 625 ans d ." | a ) 200 , b ) 325 , c ) 565 , d ) 625 , e ) 700 | d | divide(50, divide(4, 50)) | divide(n2,n1)|divide(n0,#0)| | gain |
8 , 12 , 18 , 27 , 40.5 , ( . . . ) | "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 6 / 25 * 75 = 18 answer : b" | a ) 11 , b ) 18 , c ) 99 , d ) 77 , e ) 51 | b | multiply(divide(75, add(add(divide(2, 3), divide(5, 2)), 2)), 5) | divide(n0,n1)|divide(n3,n0)|add(#0,#1)|add(#2,n0)|divide(n4,#3)|multiply(n3,#4)| | general |
a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 36 . find the profit percentage ? | "answer we have , m x n = 8 x 200 = 1600 â ˆ ´ 1 / m + 1 / n = ( m + n ) / mn = 84 / 1600 = 3 / 50 correct option : b" | a ) 1 / 35 , b ) 3 / 50 , c ) 5 / 37 , d ) 2 / 35 , e ) none | b | divide(84, multiply(8, 200)) | multiply(n0,n1)|divide(n2,#0)| | general |
find how many positive integers less than 10000 are there such thatthe sum of the digits of the no . is divisible by 3 ? | "let the number of meters to be examined be x then , 0.04 % of x = 2 ( 4 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 5000 answer is d" | a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2500 , d ) d ) 5000 , e ) e ) 3100 | d | divide(multiply(2, const_100), 0.04) | multiply(n1,const_100)|divide(#0,n0)| | gain |
meena wrote all the numbers from 1 to 59,999 inclusive . how many digits did she write in total ? | "increase = ( 40 / 50 ) * 100 = ( 4 / 5 ) * 100 = 80 % . d" | a ) 15 % , b ) 16.66 % , c ) 17.8 % , d ) 80 % , e ) 21 % | d | multiply(divide(subtract(90, 50), 50), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many e ways can the test be completed if every question is unanswered ? | "let the son ' s present age be x years . then , ( 48 - x ) = x x = 24 . son ' s age 5 years back = ( 24 - 5 ) = 19 years answer : d" | a ) 14 , b ) 17 , c ) 11 , d ) 19 , e ) 99 | d | subtract(divide(48, const_2), 5) | divide(n0,const_2)|subtract(#0,n1)| | general |
a shopkeeper sold an article offering a discount of 5 % and earned a profit of 31.1 % . what would have been the percentage of profit earned if no discount had been offered ? | "us = 25 ds = 43 m = ( 43 + 25 ) / 2 = 34 answer : b" | a ) 86 , b ) 34 , c ) 30 , d ) 15 , e ) 17 | b | divide(add(25, 43), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
the smallest number when increased by ` ` 1 ` ` is exactly divisible by 2 , 8 , 24 , 36 is : | "there will be two cases x - 20 = 40 and x - 20 = - 40 solve for x = > x = 40 + 20 = > x = 60 or x = - 40 + 20 = > x = - 20 the sum of both values will be 60 + - 20 = 40 answer is d" | a ) 0 , b ) 60 , c ) - 80 , d ) 40 , e ) 80 | d | subtract(add(40, 20), subtract(40, 20)) | add(n0,n1)|subtract(n1,n0)|subtract(#0,#1)| | general |
niall ' s income is 60 % less than rex ' s income , and sam ' s income is 25 % less than niall ' s income . if rex gave 60 % of his income to sam and 40 % of his income to niall , niall ' s new income would be what fraction of sam ' s new income ? | "ans is e given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 12 ) + ( x / 14 ) ) = 15 ( formula avg speed = total distance / total time )" | a ) 13 , b ) 13.5 , c ) 14 , d ) 14.5 , e ) 15 | e | divide(add(multiply(14, const_10), divide(multiply(14, const_10), const_2)), add(divide(multiply(14, const_10), 12), divide(divide(multiply(14, const_10), const_2), 14))) | multiply(n1,const_10)|divide(#0,const_2)|divide(#0,n0)|add(#1,#0)|divide(#1,n1)|add(#2,#4)|divide(#3,#5)| | general |