Problem
stringlengths 11
628
| Rationale
stringlengths 1
2.74k
| options
stringlengths 37
137
| correct
stringclasses 5
values | annotated_formula
stringlengths 6
848
| linear_formula
stringlengths 7
357
| category
stringclasses 6
values |
---|---|---|---|---|---|---|
a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 16 days . in how many days b alone can do the work ? | "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 Γ£ β ( 100 + 31.1 ) / ( 100 Γ’ Λ β 5 ) = 138 hence , required % profit = 138 Γ’ β¬ β 100 = 38 % answer a" | a ) 38 , b ) 27.675 , c ) 30 , d ) data inadequate , e ) none of these | a | subtract(divide(multiply(add(const_100, 31.1), const_100), subtract(const_100, 5)), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,const_100)|divide(#2,#1)|subtract(#3,const_100)| | gain |
john makes $ 60 a week from his job . he earns a raise andnow makes $ 80 a week . what is the % increase ? | "s . i . = ( 1000 * 14 * 4 ) / 100 = rs . 560 c . i . = [ 1000 * ( 1 + 14 / 100 ) 4 - 1000 ] = rs . 689 difference = ( 689 - 560 ) = rs . 129 answer : a" | a ) 129 , b ) 130 , c ) 124 , d ) 133 , e ) 145 | a | subtract(subtract(multiply(1000, power(add(divide(14, const_100), const_1), 4)), 1000), multiply(multiply(1000, divide(14, const_100)), 4)) | divide(n0,const_100)|add(#0,const_1)|multiply(n1,#0)|multiply(n2,#2)|power(#1,n2)|multiply(n1,#4)|subtract(#5,n1)|subtract(#6,#3)| | gain |
a 250 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ? | "the total number of stations = 30 from 30 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 3 β° p β ways . 30 p β = 30 * 29 = 870 . answer : c" | a ) 156 , b ) 167 , c ) 870 , d ) 352 , e ) 380 | c | multiply(add(28, const_1), add(add(28, const_1), const_1)) | add(n0,const_1)|add(#0,const_1)|multiply(#0,#1)| | physics |
find the product of the local value and absolute value of 2 in 564823 | "p = 3888 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 3888 / ( 1 + 20 / 100 ) ^ 2 = 3888 / ( 6 / 5 ) ^ 2 = 2700 ( approximately ) answer is e" | a ) 2500 , b ) 2100 , c ) 3500 , d ) 3600 , e ) 2700 | e | add(3888, divide(multiply(3888, 20), const_100)) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)| | gain |
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 ) | "13 : 93 = 1 : 729 answer : e" | a ) 1 : 0 , b ) 1 : 8 , c ) 1 : 7 , d ) 1 : 2 , e ) 1 : 729 | e | divide(power(const_2.0, 9), power(const_3.0, 9)) | power(const_2.0,n1)|power(const_3.0,n1)|divide(#0,#1)| | other |
find the smallest number in gp whose sum is 38 and product is 1728 | "easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 s = - 49 . d is the answer ." | a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 51 | d | add(add(negate(26), const_1), add(add(negate(26), const_1), const_1)) | negate(n0)|add(#0,const_1)|add(#1,const_1)|add(#1,#2)| | general |
what is the greatest possible length which can be used to measure exactly the lengths 10 m 50 cm , 14 m 55 cm and 50 cm ? | "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 36 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 360 / 10,000 = 36 / 1000 = 0.036 ft the answer is a ." | a ) 0.036 , b ) 0.36 , c ) 0.6 , d ) 6 , e ) 3.6 | a | divide(volume_cylinder(6, 10), circle_area(100)) | circle_area(n0)|volume_cylinder(n2,n3)|divide(#1,#0)| | geometry |
when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 3 of the remaining balance , what will be the final balance in her bank account ? | "let x be the number of 35 ounce cans . therefore ( x + 20 ) is the number of 25 ounce cans . total volume is same , therefore 35 x = 25 ( x + 20 ) 10 x = 500 x = 50 therefore , number of 15 ounce cans = 50 + 20 = 70 ans - b" | a ) 60 , b ) 70 , c ) 80 , d ) 100 , e ) 120 | b | add(25, 20) | add(n1,n2)| | general |
if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 13 . what is the value of f ( 6 ) ? | "101 * n ^ 2 < = 10000 n ^ 2 < = 10000 / 101 which will be less than 100 since 10000 / 100 = 100 which is the square of 9 next closest value of n where n ^ 2 < = 100 is 9 ans c" | a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | c | floor(sqrt(divide(10000, 101))) | divide(n2,n0)|sqrt(#0)|floor(#1)| | general |
rahim bought 52 books for rs . 1200 from one shop and 32 books for rs . 480 from another . what is the average price he paid per book ? | "explanation : use formula for a work members Γ£ β days = constant 10 Γ£ β 4 = 5 Γ£ β a a = 8 so answer is 8 days answer : d" | a ) 10 , b ) 4 , c ) 5 , d ) 8 , e ) 6 | d | divide(const_1, multiply(divide(const_1, multiply(const_4.0, 10)), 4)) | multiply(n0,n1)|divide(const_1,#0)|multiply(n2,#1)|divide(const_1,#2)| | physics |
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 ? | "formula : ( after = 100 denominator ago = 100 numerator ) 8000 Γ£ β 80 / 100 Γ£ β 80 / 100 x 80 / 100 = 4096 answer : b" | a ) 5100 , b ) 4096 , c ) 5200 , d ) 5400 , e ) 5500 | b | subtract(subtract(8000, multiply(8000, divide(20, const_100))), multiply(subtract(8000, multiply(8000, divide(20, const_100))), divide(20, const_100))) | divide(n1,const_100)|multiply(n0,#0)|subtract(n0,#1)|multiply(#0,#2)|subtract(#2,#3)| | gain |
the average of 6 no . ' s is 3.95 . the average of 2 of them is 4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ? | "let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 140 % of rs . 1600 = 140 / 100 * 1600 = rs . 2240 . answer : e" | a ) 2000 , b ) 2778 , c ) 2299 , d ) 2778 , e ) 2240 | e | multiply(divide(add(const_100, 40), const_100), divide(add(1920, 1280), const_2)) | add(n2,const_100)|add(n0,n1)|divide(#0,const_100)|divide(#1,const_2)|multiply(#2,#3)| | gain |
if 3 ^ x = 2 , then 3 ^ ( 4 x + 3 ) = | "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 360 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 360 x = ( 10 x 4 x 360 ) / ( 6 ) x = 2400 . answer : c" | a ) 648 , b ) 1800 , c ) 2400 , d ) 10800 , e ) 10900 | c | multiply(multiply(divide(360, 6), 4), 10) | divide(n1,n0)|multiply(n3,#0)|multiply(n2,#1)| | gain |
mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8010 / - . find out the amount that he borrowed . | divide as ( 1 - 100 ) ( 100 - 200 ) . . . . ( 900 - 1000 ) total 192 answer : c | a ) 190 , b ) 191 , c ) 192 , d ) 193 , e ) 194 | c | add(add(divide(1000, const_10), multiply(subtract(const_10, 1), const_10)), const_2) | divide(n0,const_10)|subtract(const_10,n1)|multiply(#1,const_10)|add(#0,#2)|add(#3,const_2) | general |
how many liters of water must be evaporated from 50 liters of a 6 - percent sugar solution to get a 10 - percent solution ? | "investment = rs . [ 20 x ( 50 - 5 ) ] = rs . 900 . face value = rs . ( 50 x 20 ) = rs . 1000 . dividend = rs . 27 x 1000 = rs . 135 . 2 100 interest obtained = 135 x 100 % = 15 % 900 view answer discuss in forum answer : c" | a ) 27 % , b ) 87 % , c ) 15 % , d ) 66 % , e ) 88 % | c | divide(multiply(multiply(20, 50), divide(13, const_100)), multiply(20, subtract(50, 5))) | divide(n3,const_100)|multiply(n0,n1)|subtract(n1,n2)|multiply(#0,#1)|multiply(n0,#2)|divide(#3,#4)| | gain |
the average age of 36 students in a group is 13 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ? | "? % of 360 = 108 or , ? = 108 Γ 100 / 360 = 30 answer a" | a ) 30 , b ) 36 , c ) 64 , d ) 72 , e ) none of these | a | divide(multiply(108, const_100), 360) | multiply(n1,const_100)|divide(#0,n0)| | gain |
a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - . | "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 300 + 150 = 450 m required time = 450 * 2 / 25 = 36 sec answer : option b" | a ) 40 , b ) 36 , c ) 41 , d ) 42 , e ) 34 | b | divide(300, multiply(subtract(45, 150), const_0_2778)) | subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
a box contains 8 pairs of shoes ( 16 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ? | "10 ^ 29 is a 30 - digit number : 1 followed by 29 zeros . 10 ^ 29 - 41 is a 29 - digit number : 27 9 ' s and 59 at the end . the sum of the digits is 27 * 9 + 5 + 9 = 257 . the answer is a ." | a ) 257 , b ) 242 , c ) 231 , d ) 202 , e ) 187 | a | multiply(add(divide(subtract(subtract(29, 10), const_2), const_2), 10), divide(add(subtract(29, 10), const_2), const_2)) | subtract(n1,n0)|add(#0,const_2)|subtract(#0,const_2)|divide(#2,const_2)|divide(#1,const_2)|add(n0,#3)|multiply(#5,#4)| | general |
a school has received 50 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ? | "speed = ( 120 x ( 5 / 18 ) m / sec = ( 100 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 100 / 3 ) x 18 ) m = 600 m e" | a ) 560 , b ) 570 , c ) 580 , d ) 590 , e ) 600 | e | multiply(divide(multiply(120, const_1000), const_3600), 18) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
how many figures are required to number the pages the pages of a book containing 223 pages ? | "s = ( 100 + 300 ) / 45 = 400 / 45 * 18 / 5 = 32 answer : a" | a ) 32 kmph , b ) 76 kmph , c ) 34 kmph , d ) 43 kmph , e ) 40 kmph | a | divide(divide(add(100, 300), const_1000), divide(45, const_3600)) | add(n0,n1)|divide(n2,const_3600)|divide(#0,const_1000)|divide(#2,#1)| | physics |
the lcm and hcf of two numbers are 8 and 48 respectively . if one of them is 24 , find the other ? | "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 40 sell price = $ 400 + $ 40 thus , the sell price is $ 440 for each item . selling all 100 items gives the retailer . . . 100 ( $ 40 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 440 ) = $ 22 discount $ 418 = $ 400 + $ 18 now , the retailer makes a profit of just $ 18 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 18 ( x ) = $ 2,000 x = 2,000 / 18 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d" | a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226 | d | divide(multiply(100, 40), subtract(40, divide(multiply(add(divide(multiply(100, 40), 10), 40), 5), 100))) | multiply(n0,n1)|divide(#0,n2)|add(n1,#1)|multiply(n3,#2)|divide(#3,n0)|subtract(n1,#4)|divide(#0,#5)| | gain |
on dividing 123 by a number , the quotient is 7 and the remainder is 4 . find the divisor . | "age of the 15 th student = [ 15 * 14 - ( 14 * 5 + 16 * 9 ) ] = ( 210 - 214 ) = 4 years . answer : b" | a ) 3 years , b ) 4 years , c ) 5 years , d ) 6 years , e ) 7 years | b | 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 |
simplify : 0.3 * 0.3 + 0.3 * 0.3 | "the bookman had 10 hardback ad 55 - 10 = 45 paperback copies ; 14 copies were sold , hence 55 - 14 = 41 copies were left . let # of paperback copies left be p then 10 p + 20 ( 41 - p ) = 460 - - > 10 p = 360 - - > p = 36 # of paperback copies sold is 45 - 36 = 9 answer : e" | a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 9 | e | divide(subtract(subtract(add(multiply(subtract(55, 10), 10), multiply(10, 20)), 460), multiply(gcd(55, 10), 20)), 10) | gcd(n0,n1)|multiply(n1,n2)|subtract(n0,n1)|multiply(n1,#2)|multiply(n2,#0)|add(#3,#1)|subtract(#5,n5)|subtract(#6,#4)|divide(#7,n1)| | general |
a contractor undertakes to built a walls in 50 days . he employs 30 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ? | "number of statues = all the paint Γ· amount used per statue = 1 / 2 Γ· 1 / 16 = 8 / 16 * 16 / 1 = 8 / 1 = 8 answer is a ." | a ) 8 , b ) 20 , c ) 28 , d ) 14 , e ) 19 | a | divide(divide(1, 2), divide(1, 16)) | divide(n0,n1)|divide(n2,n3)|divide(#0,#1)| | general |
john purchased some shirts and trousers for $ 1550 . he paid $ 250 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ? | "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.2 ( p * x ) y = ( 1.2 / 1.25 ) x = 0.96 x which is a reduction of 4 % . the answer is c ." | a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 % | c | multiply(divide(subtract(add(25, const_100), add(20, const_100)), add(25, const_100)), const_100) | add(n0,const_100)|add(n1,const_100)|subtract(#0,#1)|divide(#2,#0)|multiply(#3,const_100)| | general |
the principal that amounts to rs . 4903 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ? | too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1000 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1000 - - > { not on display } = 1500 . according to ( i ) 2 / 3 * { total } = 1500 - - > { total } = 2250 . answer : b . | a ) 360 , b ) 2250 , c ) 540 , d ) 640 , e ) 720 | b | divide(divide(1000, subtract(const_1, divide(1, 3))), subtract(const_1, divide(1, 3))) | divide(n0,n1)|subtract(const_1,#0)|divide(n6,#1)|divide(#2,#1) | general |
a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 585.75 . how many boxes of plain cookies did she sell ? | "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 132000 = 6 / 11 . 6 / 11 is a little above 6 / 12 = 1 / 2 . thus , our answer is just a little above 35 . answer : d" | a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 % | d | multiply(divide(add(multiply(divide(30, const_100), 60000), multiply(divide(40, const_100), 72000)), add(72000, 60000)), const_100) | add(n2,n3)|divide(n0,const_100)|divide(n1,const_100)|multiply(n2,#1)|multiply(n3,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)| | gain |
find the value of 201834 x 99999 = m ? | "area of the floor = ( 5.5 Γ£ β 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 900 Γ£ β 22 ) = rs . 19800 answer : option a" | a ) s . 19,800 , b ) s . 15,600 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900 | a | multiply(900, multiply(5.5, 4)) | multiply(n0,n1)|multiply(n2,#0)| | physics |
if 36 men can do a piece of work in 25 hours , in how mwny hours will 15 men do it ? | "30 % of 1000 = 300 worked for 15 hours payment @ 5 / hr total payment = 300 * 15 * 5 = 22500 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 22500 + 100000 + 40000 + 15000 = 1775000 hence , answer is d" | a ) $ 180,000 , b ) $ 185,000 , c ) $ 190,000 , d ) $ 177,500 , e ) $ 205,000 | d | multiply(add(divide(1, 15), 1), divide(multiply(1000, divide(add(add(multiply(add(multiply(divide(const_3, const_2), multiply(5, 15)), multiply(40, 5)), subtract(15, add(const_3, 5))), multiply(multiply(40, 5), 5)), multiply(multiply(5, 15), const_3)), 15)), 1000)) | add(n1,const_3)|divide(n3,n6)|divide(const_3,const_2)|multiply(n1,n6)|multiply(n1,n2)|add(n3,#1)|multiply(#2,#3)|multiply(n1,#4)|multiply(#3,const_3)|subtract(n6,#0)|add(#6,#4)|multiply(#10,#9)|add(#11,#7)|add(#12,#8)|divide(#13,n6)|multiply(n0,#14)|divide(#15,n0)|multiply(#5,#16)| | general |
half a number plus 7 is 11 . what is the number ? | let the annual bonus be x . a corporation double its annual bonus . so new bonus = 2 x . increase = 2 x - x = x the increase is what percent of the employees β new bonus = ( x / 2 x ) * 100 = 50 % hence a . | a ) 50 % , b ) 12 % , c ) 8 % , d ) 6 % , e ) 5 % | a | multiply(divide(subtract(const_2, const_1), const_2), 100) | subtract(const_2,const_1)|divide(#0,const_2)|multiply(n0,#1) | general |
the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if x 20 = 190 , what is the value of x ? | "( a + b ) work in 1 day = 1 / 20 , ( b + c ) work in 1 days = 1 / 15 . , ( c + a ) work in 1 days = 1 / 12 ( 1 ) adding = 2 [ a + b + c ] in 1 day work = [ 1 / 20 + 1 / 15 + 1 / 12 ] = 1 / 5 ( a + b + c ) work in 1 day = 1 / 10 b work in 1 days = [ a + b + c ] work in 1 days - work of ( a + c ) in 1 days = [ 1 / 10 - 1 / 12 ] = 1 / 60 b alone finish work in 60 days answer b" | a ) 50 , b ) 60 , c ) 45 , d ) 35 , e ) 48 | b | inverse(divide(add(inverse(12), add(inverse(20), inverse(15))), const_2)) | inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|divide(#4,const_2)|inverse(#5)| | physics |
a man is walking at a speed of 10 km per hour . after every kilometre , he takes rest for 6 minutes . how much time will be take to cover a distance of 6 kilometres ? | "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 16 = 76 * 5 / 18 t = 2500 / 9 * 18 / 380 = 13.15 sec . answer : d" | a ) 10.11 , b ) 8.11 , c ) 77.2 , d ) 13.15 , e ) 22.22 | d | multiply(multiply(multiply(const_0_2778, subtract(60, 16)), 50), inverse(multiply(const_0_2778, add(60, 16)))) | add(n0,n1)|subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(#1,const_0_2778)|inverse(#2)|multiply(n2,#3)|multiply(#4,#5)| | physics |
two numbers are respectively 50 % and 20 % more than a third number . the percentage that is first of the second is ? | "explanation : 30 x = 50 y x : y = 30 : 50 = 3 : 5 answer : b" | a ) 4 : 5 , b ) 3 : 5 , c ) 3 : 7 , d ) 3 : 2 , e ) 4 : 5 | b | divide(30, 50) | divide(n0,n1)| | general |
the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 6 minutes , then the area of the park ( in sq . m ) is : | "300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 34 = 86 sq m of the wallpaper overlaps in three layers . 86 sq m makes two extra layers hence the area over which it makes two extra layers is 43 sq m . answer ( a ) ." | a ) 43 square meters , b ) 36 square meters , c ) 42 square meters , d ) 83.3 square meters , e ) 120 square meters | a | divide(subtract(subtract(300, 180), 34), const_2) | subtract(n0,n1)|subtract(#0,n2)|divide(#1,const_2)| | geometry |
a glass was filled with 24 ounces of water , and 0.06 ounce of the water evaporated each day during a 12 - day period . what percent of the original amount of water evaporated during this period ? | "the total number of ways to choose 6 managers is 9 c 6 = 84 we need to subtract the number of groups which include the two managers , which is 7 c 4 = 35 . 84 - 35 = 49 the answer is e ." | a ) 36 , b ) 40 , c ) 42 , d ) 45 , e ) 49 | e | subtract(choose(9, 6), choose(subtract(9, 2), 2)) | choose(n1,n0)|subtract(n1,n2)|choose(#1,n2)|subtract(#0,#2)| | probability |
find the length of the wire required to go 14 times round a square field containing 5625 m 2 . | "original price = 100 cp = 80 s = 80 * ( 140 / 100 ) = 112 100 - 112 = 12 % answer : c" | a ) 82 % , b ) 52 % , c ) 12 % , d ) 19 % , e ) 22 % | c | multiply(subtract(divide(divide(multiply(subtract(const_100, 20), add(const_100, 40)), const_100), const_100), const_1), const_100) | add(n1,const_100)|subtract(const_100,n0)|multiply(#0,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,const_1)|multiply(#5,const_100)| | gain |
the present population of a town is 280 . population increase rate is 10 % p . a . find the population of town after 1 years ? | explanation : unit digit in 3 ^ 4 = 1 unit digit in ( 3 ^ 4 ) 16 = 1 unit digit in 3 ^ 65 = unit digit in [ ( 3 ^ 4 ) 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 6 ^ 59 = 6 unit digit in 7 ^ 4 unit digit in ( 7 ^ 4 ) 17 is 1 . unit digit in 7 ^ 71 = unit digit in [ ( 7 ^ 4 ) 17 x 73 ] = ( 1 x 3 ) = 3 required digit = unit digit in ( 3 x 6 x 3 ) = 4 e | a ) 18 , b ) 12 , c ) 69 , d ) 32 , e ) 4 | e | subtract(multiply(multiply(3, 6), 3), subtract(multiply(multiply(3, 6), 3), const_4)) | multiply(n0,n2)|multiply(n0,#0)|subtract(#1,const_4)|subtract(#1,#2) | general |
the sum of all the integers k such that β 21 < k < 24 is | "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 6 + 5 / 9 = 6.55 answer b" | a ) 4.7 kmph , b ) 6.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph | b | add(divide(1, divide(add(const_60, 48), const_60)), 6) | add(n2,const_60)|divide(#0,const_60)|divide(n1,#1)|add(n0,#2)| | physics |
the largest number of six digits | 2 km / 400 m = 5 . however , the street at the 2 - km mark is not 5 th street ; it is maple street . therefore , the highest numbered street is 4 th street . the answer is a . | a ) 4 th , b ) 5 th , c ) 6 th , d ) 7 th , e ) 8 th | a | subtract(divide(multiply(2, const_1000), 400), const_1) | multiply(n0,const_1000)|divide(#0,n1)|subtract(#1,const_1) | physics |
if two dice are thrown together , the probability of getting prime number on both dice is | "say there are 100 people in that group , then there would be 0.5 * 0.30 * 100 = 15 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 15 / 100 . answer : e" | a ) 0.16 , b ) 0.25 , c ) 0.45 , d ) 0.35 , e ) 0.15 | e | multiply(divide(50, multiply(multiply(const_5, const_5), const_4)), divide(30, multiply(multiply(const_5, const_5), const_4))) | multiply(const_5,const_5)|multiply(#0,const_4)|divide(n0,#1)|divide(n1,#1)|multiply(#2,#3)| | gain |
107 x 107 + 93 x 93 = ? | "1 / 2 * d ( 14 + 8 ) = 550 d = 50 answer : c" | a ) 76 , b ) 28 , c ) 50 , d ) 80 , e ) 25 | c | divide(divide(divide(550, divide(add(14, 8), const_2)), 8), const_2) | add(n0,n1)|divide(#0,const_2)|divide(n2,#1)|divide(#2,n1)|divide(#3,const_2)| | physics |
the ratio of spinsters to cats is 2 to 7 . if there are 40 more cats than spinsters , how many spinsters are there ? | "3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is c" | a ) 2 / 5 , b ) 7 / 5 , c ) 3 / 5 , d ) 8 / 15 , e ) 1 / 2 | c | subtract(const_1, add(add(divide(4, multiply(add(const_2, 4), 4)), divide(const_2, multiply(add(const_2, 4), 4))), divide(const_1, multiply(add(const_2, 4), 4)))) | add(const_2,n0)|multiply(n0,#0)|divide(n0,#1)|divide(const_2,#1)|divide(const_1,#1)|add(#2,#3)|add(#5,#4)|subtract(const_1,#6)| | physics |
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 ? | "let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 350 x = 50 4 x = 200 the answer is c ." | a ) $ 200 , b ) $ 225 , c ) $ 250 , d ) $ 275 , e ) $ 300 | c | multiply(divide(350, add(add(divide(const_1, const_2), const_1), const_2)), const_2) | divide(const_1,const_2)|add(#0,const_1)|add(#1,const_2)|divide(n0,#2)|multiply(#3,const_2)| | general |
jane makes toy bears . when she works with an assistant , she makes 100 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane β s output of toy bears per hour by what percent ? | "you could pick 40 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 45 . b" | a ) 10 , b ) 45 , c ) 55 , d ) 35 , e ) 65 | b | add(subtract(80, 90), subtract(50, 35)) | subtract(n2,n0)|subtract(n1,n3)|add(#0,#1)| | general |
surface area of two spheres are in the ratio 1 : 4 what is the ratio of their volumes ? | "if arthur 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 combined no 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 words , with or without meaning , can be formed using all letters of the word good using each letter exactly once ? | "expanding we have 6 x ^ 2 - 15 x + 2 x - 5 6 x ^ 2 - 13 x - 5 taking coefficients , a = 6 , k = - 13 , n = - 5 therefore a - n + k = 6 - ( - 13 ) - 5 = 19 - 5 = 14 the answer is d ." | a ) 5 , b ) 8 , c ) 9 , d ) 14 , e ) 11 | d | add(add(multiply(3, 1), multiply(5, 1)), subtract(multiply(1, 1), multiply(5, 3))) | multiply(n0,n1)|multiply(n1,n3)|multiply(n1,n1)|multiply(n0,n3)|add(#0,#1)|subtract(#2,#3)|add(#4,#5)| | general |
if 30 % of a class averages 95 % on a test , 50 % of the class averages 79 % on the test , and the remainder of the class averages 60 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) . | let 1 man ' s 1 day ' s work = x and 1 women ' s 1 day ' s work = y . then , 6 x + 8 y = 1 and 26 x + 48 y = 1 . 10 2 solving these two equations , we get : x = 1 and y = 1 . 100 200 ( 15 men + 20 women ) ' s 1 day ' s work = 15 + 20 = 1 . 100 200 4 15 men and 20 women can do the work in 4 days . hence answer will be b | a ) 5 , b ) 4 , c ) 6 , d ) 7 , e ) 8 | b | divide(multiply(add(divide(8, divide(subtract(multiply(48, 2), multiply(8, 10)), subtract(multiply(6, 10), multiply(26, 2)))), 6), 10), add(divide(20, divide(subtract(multiply(48, 2), multiply(8, 10)), subtract(multiply(6, 10), multiply(26, 2)))), 15)) | multiply(n4,n5)|multiply(n1,n2)|multiply(n0,n2)|multiply(n3,n5)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)|divide(n1,#6)|divide(n7,#6)|add(n0,#7)|add(n6,#8)|multiply(n2,#9)|divide(#11,#10) | physics |
when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 3 of the remaining balance , what will be the final balance in her bank account ? | "explanation : required number of students = h . c . f of 1345 and 775 = 5 . answer : d" | a ) 91 , b ) 10 , c ) 6 , d ) 5 , e ) none of these | d | gcd(1345, 775) | gcd(n0,n1)| | general |
a rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size . which of the following could be a length of a side of the squares ? | "let c ' s share = rs . x then , b ' s share = rs . x / 4 ; a ' s share = rs . 2 / 3 * x / 4 = rs . x / 6 therefore x / 6 + x / 4 + x = 1360 17 x / 12 = 1360 x = 1360 * 12 / 17 = rs . 960 hence , b ' s share = rs . 960 / 4 = rs . 240 answer : c" | a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 300 , e ) rs . 500 | c | subtract(subtract(multiply(divide(1360, const_10), const_2), const_12), const_12) | divide(n0,const_10)|multiply(#0,const_2)|subtract(#1,const_12)|subtract(#2,const_12)| | general |
calculate the ratio between x and y if 90 % of x equal to 60 % of y ? | "( 18 Γ 15 Γ 12 ) / ( 5 Γ 3 Γ 2 ) = 108 answer is c ." | a ) 106 , b ) 109 , c ) 108 , d ) 101 , e ) 104 | c | divide(multiply(multiply(18, 15), 2), multiply(multiply(5, 3), 2)) | multiply(n3,n4)|multiply(n0,n1)|multiply(n5,#0)|multiply(n2,#1)|divide(#2,#3)| | physics |
if x ^ 2 + y ^ 2 = 20 and xy = 3 , then ( x β y ) ^ 2 = | "explanation : let the positive number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 x = β 16 / 144 = 4 / 12 . answer : a" | a ) 4 / 12 , b ) 4 / 17 , c ) 4 / 15 , d ) 4 / 11 , e ) 4 / 03 | a | sqrt(divide(multiply(16, const_3), multiply(216, const_2))) | multiply(n0,const_3)|multiply(n1,const_2)|divide(#0,#1)|sqrt(#2)| | general |
a train 450 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in : | "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 d" | a ) 1235 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1489 | d | multiply(divide(subtract(1365, 15), subtract(6, const_1)), 6) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | general |
the sector of a circle has radius of 14 cm and central angle 135 o . find its perimeter ? | "7 + 11 + 13 = 31 / 3 = 10.3 answer : d" | a ) 12.6 , b ) 12.9 , c ) 22.3 , d ) 10.3 , e ) 12.7 | d | add(5, const_1) | add(n0,const_1)| | general |
a train is 435 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length | james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d | a ) 901 , b ) 989 , c ) 990 , d ) 991 , e ) 1,001 | d | subtract(add(const_1000, const_1000), multiply(add(const_1000, const_1000), 0.5)) | add(const_1000,const_1000)|multiply(n0,#0)|subtract(#0,#1) | general |
find the simple interest on $ 10000 at 7 % per annum for 12 months ? | explanation : treat 12 : 8 as 12 / 8 and x : 16 as x / 16 , treat : : as = so we get 12 / 8 = x / 16 = > 8 x = 192 = > x = 24 option b | a ) 18 , b ) 24 , c ) 28 , d ) 16 , e ) 20 | b | divide(add(multiply(8, const_3.0), 8), 16) | multiply(const_3.0,n1)|add(n1,#0)|divide(#1,n2)| | general |
55 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be : | "on dividing 3832 by 5 , we get remainder = 2 . required number be subtracted = 2 answer : b" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | subtract(3832, multiply(floor(divide(3832, 5)), 5)) | divide(n0,n1)|floor(#0)|multiply(n1,#1)|subtract(n0,#2)| | general |
alex and brian start a business with rs . 7000 each , and after 8 months , brian withdraws half of his capital . how should they share the profits at the end of the 18 months ? | "a 2 = 5625 = > a = 75 4 a = 300 300 * 14 = 4200 answer : c" | a ) 15840 , b ) 3388 , c ) 4200 , d ) 8766 , e ) 66711 | c | multiply(square_perimeter(square_edge_by_area(5625)), 14) | square_edge_by_area(n1)|square_perimeter(#0)|multiply(n0,#1)| | physics |
the number of students in each section of a school is 24 . after admitting new students , 3 new sections were started . now , the total number of sections is 16 and there are 21 students in each section . the number of new students admitted is : | "number of bricks = volume of the wall / volume of 1 brick = ( 100 x 200 x 20 ) / ( 25 x 11.25 x 6 ) = 237 . answer : option c" | a ) 5600 , b ) 6000 , c ) 237 , d ) 7200 , e ) 8600 | c | divide(multiply(multiply(multiply(1, const_100), multiply(2, const_100)), 20), multiply(multiply(25, 11.25), 6)) | multiply(n3,const_100)|multiply(n4,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(n2,#2)|multiply(n5,#3)|divide(#5,#4)| | physics |
for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 21000 , my total savings for the two - year is | records last 90 min on each of 2 sides , = = > record last 90 * 2 = 180 min = 3 hours 16 full records - - > 16 * 3 = 48 hour broadcast given , 3 hours to translate 1 hour of broadcast let x be the time required to translate 48 hour broadcast ( 16 full records ) x = 48 * 3 = 144 hours answer : a | a ) 144 hours , b ) 124 hours , c ) 134 hours , d ) 154 hours , e ) 164 hours | a | multiply(multiply(divide(multiply(90, const_2), const_60), 16), 3) | multiply(n0,const_2)|divide(#0,const_60)|multiply(n2,#1)|multiply(n1,#2) | physics |
there are 1000 students in a school and among them 10 % of them attends chess class . 10 % 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 ? | "45 * 12 : 54 * x = 2 : 1 x = 5 12 - 5 = 7 . answer : a" | a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5 | a | subtract(multiply(const_4, const_3), divide(divide(multiply(45000, multiply(const_4, const_3)), 5400), 2)) | multiply(const_3,const_4)|multiply(n0,#0)|divide(#1,n1)|divide(#2,n2)|subtract(#0,#3)| | other |
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 ? | "a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 3 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 3 ) = 7 / 12 b ' s 1 hour work = ( 7 / 12 + 1 / 2 ) = 1 / 12 b alone will take 12 hours to do the work . answer : c" | a ) 15 hours , b ) 14 hours , c ) 12 hours , d ) 74 hours , e ) 79 hours | c | divide(const_1, subtract(divide(const_1, 3), subtract(divide(const_1, 2), divide(const_1, 4)))) | divide(const_1,n1)|divide(const_1,n2)|divide(const_1,n0)|subtract(#1,#2)|subtract(#0,#3)|divide(const_1,#4)| | physics |
a tank with a volume of 45 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 5 cubic inches / min and the 2 outlet pipes empty it out at the rates of 14 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches ) | "explanation : here distance d = 650 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 39 sec . answer : d" | a ) 48 , b ) 36 , c ) 26 , d ) 39 , e ) 18 | d | divide(650, multiply(subtract(63, 3), const_0_2778)) | subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
for all even integers n , h ( n ) is defined to be the sum of the even integers between 4 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ? | d 6 days the day after last monday was tuesday . if i came home 3 days before that , i came home on saturday , sunday , monday , tuesday , wednesday , and thursday = 6 days . | a ) 1 day , b ) 2 days , c ) 7 days , d ) 6 days , e ) 10 days | d | add(add(3, const_1), const_2) | add(n0,const_1)|add(#0,const_2) | physics |
the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 3 ? | "675 - - - - 425 100 - - - - ? = > = 63 % answer : c" | a ) 65 % , b ) 64 % , c ) 63 % , d ) 62 % , e ) 61 % | c | subtract(const_100, divide(multiply(1100, const_100), 675)) | multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)| | gain |
if x / 4 years ago roger was 14 years old and x / 4 years from now he will be 4 x years old , how old will he be 3 x years from now ? | "sol . speed in still water = 1 / 2 ( 19 + 5 ) kmph = 12 kmph . answer d" | a ) 2 , b ) 4 , c ) 7 , d ) 12 , e ) 15 | d | divide(add(19, 5), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
the perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters . what is the length of the yard if the area of the yard is 9 meters squared ? | "first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 46000 - 30000 = 16000 so 40 more machines . . total = 140 machines imo a . ." | a ) 140 , b ) 103 , c ) 105 , d ) 115 , e ) 120 | a | add(100, divide(subtract(multiply(multiply(multiply(add(4, 3), multiply(3, const_2)), 100), multiply(add(4, const_1), const_2)), multiply(multiply(multiply(100, 100), divide(3, 100)), 100)), multiply(multiply(100, 100), divide(4, 100)))) | add(n0,n2)|add(const_1,n2)|divide(n0,n1)|divide(n2,n1)|multiply(const_2,n0)|multiply(n1,n1)|multiply(#0,#4)|multiply(#1,const_2)|multiply(#2,#5)|multiply(#3,#5)|multiply(#6,n1)|multiply(n1,#8)|multiply(#10,#7)|subtract(#12,#11)|divide(#13,#9)|add(n1,#14)| | gain |
a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 12 miles per gallon , and from town b to town c , the car averaged 14 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ? | "d 4 9 x + x = 13 + 27 10 x = 40 = > x = 4" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | d | divide(add(27, 4), add(6, 6)) | add(n1,n3)|add(n0,n0)|divide(#0,#1)| | general |
a sprinter starts running on a circular path of radius r metres . her average speed ( in metres / minute ) is Ο r during the first 30 seconds , Ο r / 2 during next one minute , Ο r / 4 during next 2 minutes , Ο r / 8 during next 4 minutes , and so on . what is the ratio of the time taken for the nth round to that for the previous round ? | a profit of rs . 900 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 540 and 360 . difference in profit share = 540 - 360 = 180 answer : b | a ) s . 280 , b ) s . 180 , c ) s . 380 , d ) s . 50 , e ) s . 90 | b | subtract(divide(divide(900, add(divide(1, 2), divide(1, 3))), 2), divide(divide(900, add(divide(1, 2), divide(1, 3))), 3)) | divide(n1,n2)|divide(n1,n4)|add(#0,#1)|divide(n0,#2)|divide(#3,n2)|divide(#3,n4)|subtract(#4,#5) | general |
the perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters . what is the length of the yard if the area of the yard is 9 meters squared ? | "explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 β 5 x = 25 β x = 5 . hence , b ' s age = 2 x = 10 years . answer : e" | a ) 7 , b ) 9 , c ) 8 , d ) 11 , e ) 10 | e | divide(multiply(subtract(27, const_2), const_2), add(const_4, const_1)) | add(const_1,const_4)|subtract(n0,const_2)|multiply(#1,const_2)|divide(#2,#0)| | general |
a train speeds past a pole in 10 seconds and a platform 50 m long in 20 seconds . its length is : | 3 + 5 + 8 = 16 2880 / 16 = 180 so y ' s share = 3 * 180 = 540 answer : a | a ) 540 , b ) 520 , c ) 140 , d ) 560 , e ) 240 | a | multiply(divide(2880, add(add(3, 5), 8)), 3) | add(n1,n2)|add(n3,#0)|divide(n0,#1)|multiply(n1,#2) | general |
at a wedding reception , 125 guests ate chicken and 75 guests ate beef . if exactly 100 guests ate only one of the two types of meat , how many guests ate both types of meat ? | "p - 3 = 3 ( k - 3 ) and so p = 3 k - 6 p + 9 = 2 ( k + 9 ) ( 3 k - 6 ) + 9 = 2 k + 18 k = 15 p = 39 p + k = 54 the answer is d ." | a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58 | d | add(subtract(multiply(add(negate(subtract(9, multiply(9, const_2))), subtract(multiply(3, 3), 3)), 3), subtract(multiply(3, 3), 3)), add(negate(subtract(9, multiply(9, const_2))), subtract(multiply(3, 3), 3))) | multiply(n2,const_2)|multiply(n0,n1)|subtract(n2,#0)|subtract(#1,n0)|negate(#2)|add(#4,#3)|multiply(#5,n1)|subtract(#6,#3)|add(#5,#7)| | general |
three pipes of same capacity can fill a tank in 8 hours . if there are only two pipes of same capacity , the tank can be filled in . | "speed = ( 54 x 5 / 18 ) = 15 m / sec . length of the train = ( speed x time ) . length of the train = 15 x 4 m = 60 m . answer : c" | a ) 90 , b ) 120 , c ) 60 , d ) 95 , e ) 75 | c | multiply(divide(multiply(50, const_1000), const_3600), 4) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 10 of money ? | speed upstream = 49 / 7 = 7 kmph speed down stream = 77 / 7 = 11 kmph speed of stream = Β½ ( 11 - 7 ) = 2 kmph answer : c | a ) 6 kmph , b ) 5 kmph , c ) 2 kmph , d ) 3 kmph , e ) 4 kmph | c | divide(subtract(77, 49), multiply(7, const_2)) | multiply(n2,const_2)|subtract(n1,n0)|divide(#1,#0) | physics |
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 ? | is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 95 106 115 124 133 15 ways . . d | a ) 7 , b ) 8 , c ) 14 , d ) 15 , e ) 20 | d | subtract(subtract(24, 7), const_2) | subtract(n0,n2)|subtract(#0,const_2) | general |
the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years q in which the population would be doubled assuming there is no emigration or immigration is | "let the numbers be 2 x and 5 x their h . c . f . = 6 so the numbers are 2 * 6 , 5 * 6 = 12,30 l . c . m . = 60 answer is e" | a ) 20 , b ) 24 , c ) 52 , d ) 36 , e ) 60 | e | sqrt(divide(6, add(power(5, 2), add(power(2, 2), power(2, 2))))) | power(n0,n1)|power(n1,n1)|power(n2,n1)|add(#0,#1)|add(#3,#2)|divide(n3,#4)|sqrt(#5)| | other |
a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 55 percent . | "total work = 20 * 6 = 120 beaver hours 12 beaver * x = 120 beaver hours x = 120 / 12 = 10 answer : a" | a ) 10 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 8 . | a | divide(multiply(6, 20), 12) | multiply(n0,n1)|divide(#0,n2)| | physics |
the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 10 minutes , then the area of the park ( in sq . m ) is : | "let x be the weight of the sister . then the student ' s weight is 2 x + 6 . x + ( 2 x + 6 ) = 126 3 x = 120 x = 40 kg then the student ' s weight is 86 kg . the answer is c ." | a ) 82 , b ) 84 , c ) 86 , d ) 88 , e ) 90 | c | subtract(126, divide(subtract(126, 6), const_3)) | subtract(n1,n0)|divide(#0,const_3)|subtract(n1,#1)| | other |
the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 2.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ? | "cost price = rs . 575 profit = 15 % of 575 = rs . 86.25 selling price = cost price + profit = 575 + 86.25 = 661.25 answer : d" | a ) 600 , b ) 277 , c ) 269 , d ) 661.25 , e ) 281 | d | add(575, multiply(575, divide(15, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)| | gain |
if 0.2 of a number is equal to 0.08 of another number , the ratio of the numbers is : | "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many t hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ." | a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8 | a | add(inverse(subtract(divide(const_1, 12.5), divide(const_1, 30))), inverse(subtract(divide(const_1, 7.5), divide(const_1, 12)))) | divide(const_1,n0)|divide(const_1,n2)|divide(const_1,n1)|divide(const_1,n3)|subtract(#0,#1)|subtract(#2,#3)|inverse(#4)|inverse(#5)|add(#6,#7)| | physics |
what is the sum of natural numbers between 60 and 100 | let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of a = 6 / 13 * 1638 = rs . 756 answer : c | a ) 656 , b ) 456 , c ) 756 , d ) 745 , e ) 720 | c | multiply(divide(1638, add(add(2, 3), 4)), 4) | add(n2,n4)|add(n6,#0)|divide(n0,#1)|multiply(n6,#2) | general |
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 ? | "explanation : trick : number is divisible by 6 , if sum of all digits is divisible by 3 and 2 , so ( 2 + 5 + 5 + 1 + 1 + 1 + 2 + * ) = 17 + * should be divisible by , 17 + 1 will be divisible by 3 , but we ca n ' t take this number because 1 is not dividable by 2 ( 2 only dividable by those numbers who contain even number at last position ) so that least number is 4 . answer : option b" | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | b | subtract(6, subtract(6, 6)) | subtract(n1,n1)|subtract(n1,#0)| | general |
you collect baseball cards . suppose you start out with 17 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ? | "the units digit of 734 ^ 100 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 83 is 3 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 83 is in the form 4 n + 3 , the units digit is 3 . then 6 + 3 = 9 . the answer is c ." | a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | c | subtract(subtract(100, 83), divide(100, add(const_1, const_10))) | add(const_1,const_10)|subtract(n1,n3)|divide(n1,#0)|subtract(#1,#2)| | 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 | sol . let the bases of the two triangles be x and y and their heights be 3 h and 4 h respectively . then , ( ( 1 / 2 ) x xx 3 h ) / ( 1 / 2 ) x y x 4 h ) = 4 / 3 ο³ x / y = ( 4 / 3 x 4 / 3 ) = 16 / 9 required ratio = 16 : 9 . ans : c | ['a ) 2 : 3', 'b ) 4 : 5', 'c ) 16 : 9', 'd ) 7 : 9', 'e ) 8 : 5'] | c | multiply(divide(4, 3), inverse(divide(3, 4))) | divide(n0,n1)|divide(n1,n0)|inverse(#1)|multiply(#0,#2) | geometry |
20 men do a work in 20 days . how many men are needed to finish the work in 10 days ? | "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 β 15 = rs . 190 cp on 40 metres = 190 x 40 = rs . 7600 profit earned on 40 metres cloth = rs . 8200 β rs . 7600 = rs . 600 . answer : option c" | a ) rs . 950 , b ) rs . 1500 , c ) rs . 600 , d ) rs . 1200 , e ) none of these | c | multiply(15, 40) | multiply(n0,n2)| | gain |
the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 900 per sq . metre . | "total number of cards , n ( s ) = 52 total number of queen cards , n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 52 = 1 / 13 option b is answer" | a ) 4 / 13 , b ) 1 / 13 , c ) 4 , d ) 1 , e ) 2 / 13 | b | divide(const_2, choose(add(const_3, const_3), const_3)) | add(const_3,const_3)|choose(#0,const_3)|divide(const_2,#1)| | probability |
20 people went to a hotel for combine dinner party 12 of them spent rs . 70 each on their dinner and rest spent 4 more than the average expenditure of all the 20 . what was the total money spent by them . | "explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 60 50 d = 20 rs = 60 β 50 = 10 t = 20 / 10 = 2 hours answer : option a" | a ) a ) 2 , b ) b ) 5 , c ) c ) 7 , d ) d ) 5 , e ) e ) 8 | a | subtract(divide(multiply(divide(const_1, const_2), 50), subtract(60, 50)), divide(const_1, const_2)) | divide(const_1,const_2)|subtract(n1,n0)|multiply(n0,#0)|divide(#2,#1)|subtract(#3,#0)| | physics |
what is the compound interest on rs . 8500 at 7.5 % p . a . compounded half - yearly for 2 1 / 2 years . | "explanation : average weight of 18 boys = 50.25 total weight of 18 boys = 50.25 Γ 18 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 Γ 8 total weight of all boys in the class = ( 50.25 Γ 18 ) + ( 45.15 Γ 8 ) total boys = 18 + 8 = 26 average weight of all the boys = ( 50.25 Γ 18 ) + ( 45.15 Γ 8 ) / 26 = 48.68077 answer : option a" | a ) 48.68077 , b ) 42.25983 , c ) 50 , d ) 51.25388 , e ) 52.25 | a | divide(add(multiply(18, 50.25), multiply(8, 45.15)), add(18, 8)) | add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|divide(#3,#0)| | general |
a car is purchased on hire - purchase . the cash price is $ 24 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ? | "the word good has exactly 4 letters which are all different . therefore the number of words that can be formed = number of permutations of 4 letters taken all at a time . = p ( 4 , 4 ) = 4 ! = 4 x 3 x 2 Γ 1 = 24 answer : e" | a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24 | e | factorial(const_3) | factorial(const_3)| | 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 ? | "square ab + bc = 60 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 3600 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 40 ^ 2 = 1600 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 1600 + 2 * ab * bc = 3600 . 1600 + 2 * ab * bc = 3600 . ab * bc = 1000 . the area = 1 / 2 * ab * bc = 500 . answer : d ." | a ) 225 , b ) 450 , c ) 25 β 2 , d ) 500 , e ) 200 β 2 | d | triangle_area_three_edges(40, multiply(const_3, const_10), multiply(const_4, const_10)) | multiply(const_10,const_3)|multiply(const_10,const_4)|triangle_area_three_edges(n0,#0,#1)| | geometry |
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 ? | answer : a ) 1 : 2 | a ) 1 : 2 , b ) 1 : 0 , c ) 1 : 7 , d ) 1 : 5 , e ) 1 : 6 | a | power(divide(const_1, sqrt(const_2)), const_2) | sqrt(const_2)|divide(const_1,#0)|power(#1,const_2)| | geometry |
two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 25 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ? | out of all the 5 options , only 4487 is not divisible by 3 . all others are divisible so answer = d ( no further calculation required ) addition of any two non - divisible numbers by 3 gives the resultant divisible by 3 19 is non - divisible by 3 ; we are adding a number to that so that the resultant becomes divisible by 3 applying the above rule , it means that the number which we are going to add should be non - divisible by 3 so comes the answer = 4487 answer : d | a ) 4461 , b ) 4473 , c ) 4479 , d ) 4487 , e ) 4491 | d | add(multiply(multiply(multiply(4, 7), multiply(3, 19)), const_2), subtract(multiply(multiply(4, 7), multiply(3, 19)), multiply(const_2, const_100))) | multiply(n0,n1)|multiply(n2,n3)|multiply(const_100,const_2)|multiply(#0,#1)|multiply(#3,const_2)|subtract(#3,#2)|add(#4,#5) | general |
3 years ago , the average age of a , b and c was 27 years and that of b and c 5 years ago was 20 years . a β s present age is : | one possible case is : girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 there are 3 c 2 = 3 such cases so we should multiply by 3 . p ( one girl and two boys ) = 3 / 8 the answer is d . | a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 2 , d ) 3 / 8 , e ) 5 / 8 | d | divide(subtract(const_1, multiply(power(divide(const_1, const_2), 3), const_2)), const_2) | divide(const_1,const_2)|power(#0,n0)|multiply(#1,const_2)|subtract(const_1,#2)|divide(#3,const_2) | general |
how many of the positive factors of 24 are not factors of 27 | "let x be the length of the size 8 shoe . then 0.3 x = 9 / 5 x = 90 / 15 = 6 inches the size 15 shoe has a length of 6 + 7 / 5 = 7.4 inches the answer is b ." | a ) 6.8 , b ) 7.4 , c ) 7.7 , d ) 8.2 , e ) 8.6 | b | add(divide(multiply(divide(1, 5), subtract(17, 8)), divide(30, const_100)), multiply(subtract(15, 8), divide(1, 5))) | divide(n2,n3)|divide(n4,const_100)|subtract(n1,n0)|subtract(n5,n0)|multiply(#0,#2)|multiply(#0,#3)|divide(#4,#1)|add(#6,#5)| | general |
a is twice as fast as b . if b alone can do a piece of work in 18 days , in what time can a and b together complete the work ? | "if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 5 hence answer should be d" | a ) 1 , b ) - 1 , c ) 3 , d ) 5 , e ) 13 | d | multiply(5, const_2) | multiply(n1,const_2)| | general |
the present population of a town is 280 . population increase rate is 10 % p . a . find the population of town after 1 years ? | "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 240 ) / 9 = 500 / 9 = > x = 260 . answer : option a" | a ) 260 , b ) 250 , c ) 240 , d ) 230 , e ) 220 | a | subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 240) | add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)| | physics |
a envelop weight 8.2 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ? | think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 12 . correct answer a | ['a ) 12', 'b ) 15', 'c ) 10', 'd ) 8', 'e ) 14'] | a | sqrt(subtract(power(15, const_2), power(9, const_2))) | power(n2,const_2)|power(n1,const_2)|subtract(#0,#1)|sqrt(#2) | geometry |
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 ? | acid in 9 liters = 50 % of 9 = 4.5 liters suppose x liters of water be added . then 4.5 liters of acid in 9 + x liters of diluted solution 30 % of 9 + x = 4.5 27 + 3 x = 45 x = 6 liters answer is a | a ) 6 liters , b ) 8 liters , c ) 10 liters , d ) 12 liters , e ) 15 liters | a | subtract(divide(multiply(multiply(9, divide(50, const_100)), const_100), 30), 9) | divide(n1,const_100)|multiply(n0,#0)|multiply(#1,const_100)|divide(#2,n2)|subtract(#3,n0) | gain |
a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.3 m and its walls are 5 cm thick . the thickness of the bottom is : | "let c . p . = rs . x . then , s . p . = rs . ( 12 % of x ) = rs . 6 x / 5 new s . p . = 2 * 6 x / 5 = rs . 12 x / 5 profit = 12 x / 5 - x = rs . 7 x / 5 profit = 7 x / 5 * 1 / x * 100 = 140 % . \ answer : d" | a ) 327 , b ) 140 , c ) 277 , d ) 178 , e ) 112 | d | add(multiply(subtract(multiply(add(const_1, divide(20, const_100)), const_2), const_1), const_100), const_100) | divide(n0,const_100)|add(#0,const_1)|multiply(#1,const_2)|subtract(#2,const_1)|multiply(#3,const_100)|add(#4,const_100)| | gain |
there are 6 people in the elevator . their average weight is 170 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person . | "20 x + 46 = 21 ( x β 5 ) x = 59 answer : e" | a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59 | e | subtract(multiply(add(20, const_1), 5), 46) | add(n0,const_1)|multiply(n2,#0)|subtract(#1,n1)| | general |
if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is - . | a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 18 days whole work will be done by a in 18 * 4 / 3 = 24 days answer is b | a ) 10 , b ) 24 , c ) 60 , d ) 30 , e ) 20 | b | divide(multiply(18, 40), subtract(40, 10)) | multiply(n0,n2)|subtract(n0,n1)|divide(#0,#1) | physics |