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the diagonals of a rhombus are 18 cm and 22 cm . find its area ? | "let rate = r % and time = r years . then , 1200 x r x r / 100 = 300 12 r 2 = 300 r 2 = 25 r = 5 . answer : a" | a ) 5 , b ) 6 , c ) 18 , d ) can not be determined , e ) none of these | a | sqrt(divide(multiply(300, const_100), 1200)) | multiply(n1,const_100)|divide(#0,n0)|sqrt(#1)| | gain |
company z has 58 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday . | "multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 872 , 152,24 x sum of digits at odd places = 8 + 2 + 5 + 2 + x = 17 + x ( i ) sum of digits at even places = 7 + 1 + 2 + 4 = 14 ( ii ) ( i ) - ( ii ) = 17 + x - 14 = x - 3 hence x should be = 3 to make this a multiple of 11 ( 0 ) option c" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | multiply(multiply(multiply(add(multiply(const_3, const_10), const_1), const_2), const_4), 11) | multiply(const_10,const_3)|add(#0,const_1)|multiply(#1,const_2)|multiply(#2,const_4)|multiply(n2,#3)| | general |
the sum of the present ages of two persons a and b is 90 . if the age of a is twice that of b , find the sum of their ages 5 years hence ? | "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 20 x = 5.5 minutes answer : a" | a ) 5.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 60 | a | subtract(subtract(divide(const_60, const_2), 20), divide(const_60, divide(20, 1.5))) | divide(const_60,const_2)|divide(n2,n0)|divide(const_60,#1)|subtract(#0,n3)|subtract(#3,#2)| | physics |
the average expenditure of a labourer for 6 months was 95 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i | "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 150 2.5 h = 150 h = 60 . a is the answer ." | a ) 60 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm | a | divide(150, add(const_2, divide(50, const_100))) | divide(n0,const_100)|add(#0,const_2)|divide(n1,#1)| | gain |
in township k each property is taxed at 12 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 24,000 , by how much will the property tax increase ? | ' approximately ' could actually make such a question ambiguous . not this one though but a similar question with the answer as 9.2 days . you round off 8.89 days as 9 days and everything is fine in this question . what do you do when you get 9.2 days ? do you need 9 days or 10 days ? can you round off 9.2 as 9 even though that is what you do with numbers ? no , because in 9 days your work is not over . you do need 10 days . to finish a work machine w say you need to work full 9 days and a part of the 10 th day . if i ask you how many days do you need to complete the work , will you say 9 or 10 ? you will say 10 even if you do n ' t use the 10 th day fully = d | a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7 | d | inverse(add(inverse(divide(multiply(12, const_2), add(const_1, divide(const_1, const_2)))), inverse(divide(multiply(15, const_2), add(const_1, divide(const_1, const_2)))))) | divide(const_1,const_2)|multiply(n0,const_2)|multiply(n1,const_2)|add(#0,const_1)|divide(#1,#3)|divide(#2,#3)|inverse(#4)|inverse(#5)|add(#6,#7)|inverse(#8) | physics |
1 , 3,5 , 7,9 , . . 50 find term of sequnce | "when n is even , ( x ^ n - a ^ n ) is completely divisible by ( x - a ) . ( 17 ^ 200 - 1 ^ 200 ) is completely divisible by ( 17 + 1 ) , ( 17 ^ 200 - 1 ) is completely divisible by 18 . on dividing 17 ^ 200 by 18 , we get 1 as remainder . answer is d" | a ) 3 , b ) 8 , c ) 5 , d ) 1 , e ) 7 | d | power(17, 17) | power(n0,n0)| | general |
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 ) ? | "answer 469200 x 9999 = 469200 x ( 10000 - 1 ) = 4692000000 - 469200 = 4691100843 . option : e" | a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4691530800 | e | multiply(469200, 9999) | multiply(n0,n1)| | general |
given f ( x ) = 3 x β 5 , for what value of x does 2 * [ f ( x ) ] β 7 = f ( 3 x β 6 ) | "explanation : d = 100 + 130 = 230 s = 36 * 5 / 18 = 10 mps t = 230 / 10 = 23 sec answer : option d" | a ) 26 , b ) 72 , c ) 25 , d ) 23 , e ) 27 | d | divide(add(130, 100), multiply(36, const_0_2778)) | add(n0,n1)|multiply(n2,const_0_2778)|divide(#0,#1)| | physics |
running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 1 w widgets ? | "explanation : first six prime numbers which are between 60 and 90 = 61 , 67 , 71 , 73 , 79 , 83 average = ( 61 + 67 + 71 + 73 + 79 + 83 ) / 6 = 72.33 answer : e" | a ) 35.4 , b ) 42 , c ) 45.7 , d ) 57 , e ) 72.33 | e | add(60, const_1) | add(n0,const_1)| | general |
if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 320 , the cost of the article is | "c age x , then b age is 2 x so a age is 2 x + 2 . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 so b is 2 x = 2 ( 5 ) 2 x 5 = 10 answer : b" | a ) 12 years , b ) 10 years , c ) 8 years , d ) 14 years , e ) 16 years | b | 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 |
x does a work in 20 days . y does the same work in 30 days . in how many days they together will do the same work ? | total number of installments = 52 payment per installment for the first 22 installments = 410 payment per installment for the remaining 30 installments = 410 + 65 = 475 average = ( 22 * 410 + 30 * 475 ) / 52 = 447.50 answer a | a ) 447.5 , b ) 450 , c ) 465 , d ) 468 , e ) 475 | a | divide(add(multiply(22, 410), multiply(add(410, 65), subtract(52, 22))), 52) | add(n4,n5)|multiply(n3,n4)|subtract(n0,n3)|multiply(#0,#2)|add(#1,#3)|divide(#4,n0) | general |
for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers t are there between 6 * + 2 and 6 * + 6 , inclusive ? | "let the numbers be 5 x and 6 x . then their h . c . f = x . so , x = 4 . so , the numbers are 20 and 24 . l . c . m of 20 and 24 = 120 . answer : e" | a ) 12 , b ) 16 , c ) 24 , d ) 48 , e ) 120 | e | lcm(multiply(5, 4), multiply(6, 4)) | multiply(n0,n2)|multiply(n1,n2)|lcm(#0,#1)| | other |
a , b and c invested rs . 6500 , rs . 1300 and rs . 7800 respectively , in a partnership business . find the share of b in profit of rs . 11700 after a year ? | "easy solution : n = dq 1 + 241 2 n = 2 dq 1 + 482 - ( 1 ) 2 n = dq 2 + 102 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 380 d * some integer = 380 checking all options only ( c ) syncs with it . answer c" | a ) 370 , b ) 365 , c ) 380 , d ) 456 , e ) 460 | c | subtract(multiply(241, const_2), 102) | multiply(n0,const_2)|subtract(#0,n1)| | general |
the owner of a furniture shop charges his customer 42 % more than the cost price . if a customer paid rs . 8300 for a computer table , then what was the cost price of the computer table ? | "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 90 * 60 / 90 - 60 ] = rs . [ 90 * 60 / 30 ] = rs . 180 answer b" | a ) 210 , b ) 180 , c ) 360 , d ) 450 , e ) none | b | divide(multiply(90, 60), subtract(90, 60)) | multiply(n0,n1)|subtract(n0,n1)|divide(#0,#1)| | gain |
a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 9 more than the correct answer . find the number . | it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the s is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , s must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since s must be an even integer , the units digit of p = 4 ^ s will always be 6 . consequently , the remainder when p = 4 ^ s is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : s = 2 - - > p = 4 ^ z = 16 - - > s / 10 = 1 with a remainder of 6 s = 4 - - > p = 4 ^ z = 256 - - > s / 10 = 25 with a remainder of 6 s = 6 - - > p = 4 ^ z = 4096 - - > s / 10 = 409 with a remainder of 6 s = 8 - - > p = 4 ^ z = 65536 - - > s / 10 = 6553 with a remainder of 6 answer : b . | a ) 10 , b ) 6 , c ) 4 , d ) 0 , e ) it can not be determined | b | reminder(power(4, 2), 10) | power(n1,n0)|reminder(#0,n2) | general |
if | x - 20 | = 40 what is the sum of all the values of x . | "sol . let the numbers be x and y . then , ( x + y ) = 22 and x 2 + y 2 = 386 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 22 ) 2 - 386 = 484 - 386 = 98 xy = 49 . answer b" | a ) 40 , b ) 49 , c ) 80 , d ) 88 , e ) 90 | b | divide(subtract(power(22, const_2), 386), const_2) | power(n0,const_2)|subtract(#0,n1)|divide(#1,const_2)| | general |
after decreasing 90 % in the price of an article costs rs . 320 . find the actual cost of an article ? | "largest 4 - digit number = 9999 88 ) 9999 ( 113 88 - - - - 119 88 - - - - 319 264 - - - 55 - - - required number = ( 9999 - 55 ) = 9944 . e )" | a ) 9934 , b ) 9938 , c ) 9940 , d ) 9942 , e ) 9944 | e | square_area(const_pi) | square_area(const_pi)| | general |
jar a has 6 % more marbles than jar b . what percent of marbles from jar a need to be moved into jar b so that both jars have equal marbles ? | "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 80 % of 50 % i . e 40 % . so he completed 50 + 40 = 90 % of total trip . e" | a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90 | e | add(divide(const_100, const_2), divide(multiply(80, divide(const_100, const_2)), const_100)) | divide(const_100,const_2)|multiply(n0,#0)|divide(#1,const_100)|add(#0,#2)| | gain |
how many multiples of 5 are there between 70 and 358 ? | "( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 15 - m ) = 4 ^ ( ( 15 - m ) / 2 ) therefore , m = ( 15 - m ) / 2 2 m = 15 - m m = 5 answer d" | a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6 | d | divide(15, add(2, const_1)) | add(n0,const_1)|divide(n3,#0)| | general |
the probability that event a occurs is 0.4 , and the probability that events a and b both occur is 0.45 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event b will occur ? | "perimeter = distance covered in 10 min . = ( 15000 x 8 ) / 60 m = 2000 m . let length = 3 x metres and breadth = 4 x metres . then , 2 ( 3 x + 4 x ) = 2000 or x = 142.86 . length = 428.58 m and breadth = 571.44 m . area = ( 428.58 x 571.44 ) m 2 = 244907.76 m a" | a ) 244907.04 m , b ) 244000 m , c ) 244900 m , d ) 400000 m , e ) 154300 m | a | rectangle_area(divide(divide(multiply(multiply(divide(15, multiply(const_10, multiply(const_3, const_2))), 10), const_1000), add(3, 4)), const_2), multiply(divide(divide(multiply(multiply(divide(15, multiply(const_10, multiply(const_3, const_2))), 10), const_1000), add(3, 4)), const_2), 4)) | 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 |
find the area of a parallelogram with base 24 cm and height 12 cm ? | "let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 378 x = 54 4 x = 216 the answer is c ." | a ) $ 200 , b ) $ 208 , c ) $ 216 , d ) $ 224 , e ) $ 232 | c | multiply(divide(378, 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 |
if the average of 6 digits is 16 and the average of 4 of them is 10 , calculate the average of the remaining 2 numbers ? | "cost of 8 kg grapes = 75 Γ 8 = 600 . cost of 9 kg of mangoes = 55 Γ 9 = 495 . total cost he has to pay = 600 + 495 = 1095 . e )" | a ) a ) 1000 , b ) b ) 1055 , c ) c ) 1065 , d ) d ) 1075 , e ) e ) 1095 | e | add(multiply(8, 75), multiply(9, 55)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | gain |
a sum of money at simple interest amounts to $ 680 in 3 years and to $ 710 in 4 years . the sum is : | "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( sqrt ( 5 ) x ) ^ 2 = 5 x ^ 2 . the answer is e ." | a ) 1.5 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | e | power(sqrt(5), const_2) | sqrt(n0)|power(#0,const_2)| | geometry |
a train is 410 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length | "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 50 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 50 ml and 25 ml is 25 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 25 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 15 % . therefore , 15 out of 25 is 3 / 5 and e is the answer ." | a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 5 | e | inverse(add(divide(subtract(35, 25), subtract(50, 35)), const_1)) | subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)|add(#2,const_1)|inverse(#3)| | other |
if 2 x + y = 7 and x + 2 y = 5 , then 10 xy / 3 = ? | "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.8 ( 1.2 x ) = 0.96 x . the difference is 4 % . the answer is d ." | a ) 10 % , b ) 8 % , c ) 6 % , d ) 4 % , e ) 2 % | d | multiply(subtract(const_1, multiply(add(divide(20, const_100), const_1), divide(80, const_100))), const_100) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|multiply(#2,#1)|subtract(const_1,#3)|multiply(#4,const_100)| | general |
if 2 ^ y = 4 ^ ( 5 x + 3 ) and 3 ^ ( x - 7 ) = 9 ^ y , what is the value of x + y ? | amount left = 0.5 x β 4 for fifth store this is zero . so x = 8 . that means he entered fifth store with 8 . now for fourth store , amount left = 8 so 0.5 x β 4 = 8 β x = 24 for third store , amount left = 24 so 12 x β 4 = 24 β x = 56 for second store , amount left = 56 so 0.5 x β 4 = 56 β x = 120 for first store , amount left = 120 so 0.5 x β 4 = 120 β x = 248 so he entered first store with 248 . answer : a | a ) 248 , b ) 120 , c ) 252 , d ) 250 , e ) 350 | a | multiply(add(multiply(add(multiply(add(multiply(add(multiply(4, const_2), 4), const_2), 4), const_2), 4), const_2), 4), const_2) | multiply(n1,const_2)|add(n1,#0)|multiply(#1,const_2)|add(n1,#2)|multiply(#3,const_2)|add(n1,#4)|multiply(#5,const_2)|add(n1,#6)|multiply(#7,const_2) | general |
a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 10 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ? | "area of the poster is 2.4 x 2.4 = 5.76 1 / 2 the area = 2.88 pi * r ^ 2 = 2.88 r ^ 2 = 2.88 / pi r = sqrt ( 2.88 / pi ) answer ( b )" | a ) 1 / pi , b ) sqrt ( 2.88 / pi ) , c ) 1 , d ) 2 / sqrt ( pi ) , e ) pi / 2 | b | sqrt(divide(divide(square_area(2.4), 2), const_pi)) | square_area(n0)|divide(#0,n2)|divide(#1,const_pi)|sqrt(#2)| | geometry |
from a pack of 52 cards , two cards are drawn together at random . what is the probability that the one is heart and other two is diamond ? | "5359 x 51 = 5359 x ( 50 + 1 ) = 5359 x 50 + 5359 x 1 = 267950 + 5359 = 273309 e )" | a ) 273232 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273309 | e | multiply(divide(5359, 51), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
an empty wooden vessel weighs 20 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled . | original share of 1 person = 1 / 3 new share of 1 person = 1 / 2 increase = ( 1 / 2 - 1 / 3 = 1 / 6 ) therefore , required fraction = ( 1 / 6 ) / ( 1 / 3 ) = ( 1 / 6 ) x ( 3 / 1 ) = 1 / 2 answer is a . | a ) 1 / 2 , b ) 2 / 7 , c ) 3 / 2 , d ) 4 / 7 , e ) none of them | a | divide(subtract(divide(const_1, const_2), divide(const_1, 3)), divide(const_1, 3)) | divide(const_1,const_2)|divide(const_1,n0)|subtract(#0,#1)|divide(#2,#1) | general |
the average monthly salary of 10 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ? | solution relative speed = ( 45 - 40 ) kmph = 5 kmph = ( 5 x 5 / 18 ) m / sec = ( 25 / 18 ) m / sec time taken = ( 350 x 18 / 25 ) sec = 252 sec . answer d | a ) 72 sec , b ) 132 sec , c ) 192 sec , d ) 252 sec , e ) none | d | multiply(const_3600, divide(divide(add(200, 150), const_1000), subtract(45, 40))) | add(n0,n1)|subtract(n3,n2)|divide(#0,const_1000)|divide(#2,#1)|multiply(#3,const_3600) | physics |
the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 70 , and what number ? | "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 175 ( 35 * 5 ) profit percentage = ( 175 - 100 ) / 100 * 100 = 75 % answer : c" | a ) 80 % , b ) 50 % , c ) 75 % , d ) 40 % , e ) 53 % | c | subtract(multiply(35, add(const_4, const_1)), multiply(25, const_4)) | add(const_1,const_4)|multiply(n1,const_4)|multiply(n3,#0)|subtract(#2,#1)| | gain |
| x + 3 | β | 4 - x | = | 7 + x | how many solutions will this equation have ? | "required number = ( 75 / 2 ) / ( 1 / 8 ) = ( 75 / 2 x 8 / 1 ) = 300 . answer : a" | a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700 | a | divide(add(37, divide(1, 2)), divide(1, 8)) | divide(n0,n4)|divide(n0,n1)|add(n2,#0)|divide(#2,#1)| | general |
harkamal purchased 8 kg of grapes at the rate of 90 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ? | "suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 2 / 4 ) rq ] = 4 / 2 also , rp = rr / ( 2 / 3 ) = > 2 = rr / ( 2 / 3 ) = > rr = 4 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 2 + 4 / 3 = 13 / 3 = 1 / ( 3 / 13 ) thus running simultaneously , pipe q will drain 3 / 13 of the liquid . thus answer = a ." | a ) 3 / 13 , b ) 8 / 23 , c ) 3 / 8 , d ) 17 / 29 , e ) 3 / 4 | a | divide(multiply(2, 2), add(multiply(multiply(4, 2), const_2), multiply(2, 2))) | multiply(n0,n0)|multiply(n0,n1)|multiply(#1,const_2)|add(#2,#0)|divide(#0,#3)| | physics |
what is the characteristic of the logarithm of 0.0000134 ? | "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 5 = 8 : 10 - - > qy = 4.0 . answer : c ." | a ) 3.6 cm , b ) 2.4 cm , c ) 4.0 cm , d ) 2.16 cm , e ) 3.2 cm | c | divide(multiply(5, 8), const_10) | multiply(n1,n2)|divide(#0,const_10)| | geometry |
5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3443 , how much was it in the beginning ? | "explanation : average after 11 innings = 24 required number of runs = ( 24 * 11 ) β ( 20 * 10 ) = 264 β 200 = 64 answer : c" | a ) 22 , b ) 77 , c ) 64 , d ) 19 , e ) 17 | c | subtract(multiply(add(10, const_1), add(20, 4)), multiply(20, 10)) | add(n0,const_1)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | general |
the sum of three consecutive even numbers is 63 . find the middle number of the three ? | "ratio of the capitals of a , b and c = 20000 Γ£ β 10 + 15000 Γ£ β 2 : 20000 Γ£ β 10 + 16000 Γ£ β 2 : 20000 Γ£ β 10 + 26000 Γ£ β 2 = 230000 : 232000 : 252000 = 230 : 232 : 252 . b Γ’ β¬ β’ s share = ( 71400 Γ£ β 232 Γ’ Β β 714 ) = 23200 ; answer c" | a ) 20,000 , b ) 21,200 , c ) 23,200 , d ) 20,500 , e ) none of these | c | divide(add(multiply(subtract(const_12, 10), 4000), multiply(multiply(const_2, multiply(const_100, const_100)), 10)), multiply(const_100, const_10)) | multiply(const_100,const_100)|multiply(const_10,const_100)|subtract(const_12,n1)|multiply(n3,#2)|multiply(#0,const_2)|multiply(n1,#4)|add(#3,#5)|divide(#6,#1)| | gain |
daniel went to a shop and bought things worth rs . 25 , out of which 60 paise went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ? | "the number of terms in this set would be : n = ( k - 1 ) / 2 ( as k is odd ) last term : k - 1 average would be first term + last term / 2 = ( 2 + k - 1 ) / 2 = ( k + 1 ) / 2 also average : sum / number of terms = 79 * 80 / ( ( k - 1 ) / 2 ) = 158 * 80 / ( k - 1 ) ( k + 1 ) / 2 = 158 * 80 / ( k - 1 ) - - > ( k - 1 ) ( k + 1 ) = 158 * 160 - - > k = 159 answer e ." | a ) 79 , b ) 80 , c ) 81 , d ) 157 , e ) 159 | e | add(multiply(79, const_2), 1) | multiply(n1,const_2)|add(#0,n0)| | general |
let f ( x ) = x ^ 2 + bx + c . if f ( 3 ) = 0 and f ( - 3 ) = 0 , then b + c = | "speed = 78 * 5 / 18 = 21.7 m / sec total distance covered = 125 + 125 = 250 m . required time = 250 / 21.7 ' = 11.5 sec . answer : c" | a ) 12.7 sec , b ) 10.1 sec , c ) 11.5 sec , d ) 12.1 sec , e ) 11.7 sec | c | divide(add(125, 125), multiply(78, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | physics |
what is the angle between the 2 hands of the clock at 8 : 24 pm ? | ele , the circus elephant , is currently three times older than lyn , the circus lion . ele = 3 * lyn usually , ages are integers so there is a good possibility that the age of ele is 45 ( the only option that is a multiple of 3 ) . then age of lyn would be 15 . in 15 yrs , ele would be 60 and lyn would be 30 - so lyn would be half as old as ele . answer ( d ) | a ) 40 , b ) 48 , c ) 43 , d ) 45 , e ) 41 | d | multiply(subtract(multiply(const_2, 15), 15), 3) | multiply(n1,const_2)|subtract(#0,n1)|multiply(n0,#1) | general |
each person in a group of 110 investors has investments in either equities or securities or both . exactly 25 of the investors in equities have investments in securities , and exactly 40 of the investors in securities have investments in equities . how many have investments in equities ? | "explanation : let ' s son age is x , then father age is x + 30 . = > 2 ( x + 2 ) = ( x + 30 + 2 ) = > 2 x + 4 = x + 32 = > x = 28 years option a" | a ) 28 years , b ) 22 years , c ) 23 years , d ) 24 years , e ) 26 years | a | divide(subtract(30, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | general |
two trains are moving in opposite directions with speed of 60 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds | "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 394000 x \ therefore required percentage = \ inline \ frac { 800 x } { 394000 } \ times 100 = 0.20304 e" | a ) 0.20833 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.20304 | e | multiply(divide(divide(480, divide(60, const_100)), add(multiply(multiply(3, const_100), const_1000), multiply(add(multiply(const_4, const_10), const_4), const_1000))), const_100) | divide(n0,const_100)|multiply(n1,const_100)|multiply(const_10,const_4)|add(#2,const_4)|divide(n3,#0)|multiply(#1,const_1000)|multiply(#3,const_1000)|add(#5,#6)|divide(#4,#7)|multiply(#8,const_100)| | general |
a 125 meter long train crosses a man standing on the platform in 5 sec . what is the speed of the train ? | "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 110 + x ) / 30 = 25 / 2 = = > 2 ( 110 + x ) = 750 = = > x = 265 m . answer : option a" | a ) 265 , b ) 244 , c ) 245 , d ) 238 , e ) 236 | a | subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 110) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | physics |
a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 420 less than the sum lent . what was the sum lent ? | "let the distance one way be x time from home to work = x / 60 time from work to home = x / 100 total time = 2 hrs ( x / 60 ) + ( x / 100 ) = 2 solving for x , we get x = 75 time from home to work in minutes = ( 75 ) * 60 / 60 = 75 minutes ans = d" | a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78 | d | multiply(divide(multiply(100, 2), add(60, 100)), const_60) | add(n0,n1)|multiply(n1,n2)|divide(#1,#0)|multiply(#2,const_60)| | physics |
a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by a are ? | "area of square = pi * radius ^ 2 new radius = 0.5 * old radius so new area = ( 0.5 ) ^ 2 old area = > 0.25 of old area = > 25 % old area ans : c" | a ) 10 % decrease , b ) 20 % decrease , c ) 75 % decrease , d ) 40 % decrease , e ) 50 % decrease | c | subtract(const_100, multiply(power(divide(50, const_100), const_2), const_100)) | divide(n0,const_100)|power(#0,const_2)|multiply(#1,const_100)|subtract(const_100,#2)| | geometry |
two stations p and q are 155 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ? | "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 30 : x β x = ( 30 x 4 / 5 ) β x = 24 days . hence , tanya takes 16 days is complete the work . answer c" | a ) 15 , b ) 16 , c ) 14 , d ) 25 , e ) 10 | c | divide(30, add(const_1, divide(25, const_100))) | divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)| | physics |
mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.00 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ? | "3 ^ 8 - 1 = ( 3 ^ 4 - 1 ) ( 3 ^ 4 + 1 ) = 80 * 82 = 8 * 10 * 2 * 41 the answer is d ." | a ) 29 , b ) 31 , c ) 37 , d ) 41 , e ) 43 | d | floor(divide(3, divide(8, const_2))) | divide(n1,const_2)|divide(n0,#0)|floor(#1)| | general |
a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 48 now , the son age 5 years back was | "explanation : 90 x = 60 y x : y = 90 : 60 = 3 : 2 answer : c" | a ) 1 : 2 , b ) 3 : 5 , c ) 3 : 2 , d ) 3 : 4 , e ) 5 : 2 | c | divide(90, 60) | divide(n0,n1)| | general |
if 5 machines can produce 20 units in 10 hours , how long would it take 25 to produce 100 units ? | "1 / 2 * 50 ( 15 + 5 ) = 500 cm 2 answer : e" | a ) 100 cm 2 , b ) 150 cm 2 , c ) 200 cm 2 , d ) 250 cm 2 , e ) 500 cm 2 | e | multiply(multiply(divide(const_1, const_2), add(5, 15)), 50) | add(n1,n2)|divide(const_1,const_2)|multiply(#0,#1)|multiply(n0,#2)| | geometry |
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 | "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 1200 + x ) / 60 = 65 / 3 x = 100 m . answer : d" | a ) 2898 , b ) 277 , c ) 500 , d ) 100 , e ) 435 | d | divide(1200, multiply(subtract(78, 1), const_0_2778)) | subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
the average of 7 numbers is 23 . if each number be multiplied by 5 . find the average of new set of numbers ? | "7 + 11 + 13 + 17 + 19 = 67 / 5 = 13.40 answer : a" | a ) 13.4 , b ) 12.26 , c ) 12.3 , d ) 32.8 , e ) 32.4 | a | add(5, const_1) | add(n0,const_1)| | general |
a can do a piece of work in 5 days and b can do it in 4 days how long will they both work together to complete the work ? | edge of the cube = 3 β 334 = 7 cm β΄ radius of cone = 3.5 cm height = 7 cm volume of cone = 1 β 3 Ο r 2 h 1 β 3 Ο r 2 h = 1 β 3 Γ 22 β 7 Γ ( 3.5 ) 2 Γ 7 = 1 β 3 Γ 22 Γ 12.25 β 90 sec answer b | ['a ) 80 cc', 'b ) 90 cc', 'c ) 110 cc', 'd ) 105 cc', 'e ) 100 cc'] | b | volume_cone(divide(cube_edge_by_volume(343), const_2), cube_edge_by_volume(343)) | cube_edge_by_volume(n0)|divide(#0,const_2)|volume_cone(#1,#0) | geometry |
the perimeter of a triangle is 22 cm and the inradius of the triangle is 3.5 cm . what is the area of the triangle ? | "here , l = 7 and m = 28 therefore , first number = l / m x 100 % of second number = 7 / 28 x 100 % of second number = 25 % of second number answer : b" | a ) 20 % , b ) 25 % , c ) 18 % , d ) 30 % , e ) none of these | b | multiply(divide(divide(7, const_100), divide(28, const_100)), const_100) | divide(n0,const_100)|divide(n1,const_100)|divide(#0,#1)|multiply(#2,const_100)| | gain |
what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 25 % ? | "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 53 ) = > x / 2 = 30 = > x = 60 . answer : c" | a ) 18 , b ) 82 , c ) 60 , d ) 27 , e ) 29 | c | multiply(subtract(83, 53), const_2) | subtract(n0,n1)|multiply(#0,const_2)| | general |
there are 6 people in the elevator . their average weight is 150 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person . | area of rectangle = 20 x 10 = 200 cm Γ’ Β² let ' l ' the length of other diagonal = 0.5 x 32 xl = 200 which gives x = 12.5 cm answer : b | ['a ) 10', 'b ) 12.5', 'c ) 15', 'd ) 16', 'e ) 17.5'] | b | divide(multiply(rectangle_area(20, 10), const_2), 32) | rectangle_area(n0,n1)|multiply(#0,const_2)|divide(#1,n2) | geometry |
ram and shyam start a two - length swimming race at the same moment but from opposite ends of the pool . they swim in lanes at uniform speeds , but hardy is faster than andy . they 1 st pass at a point 18.5 m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec . after setting off on the return length , the swimmers pass for the 2 nd time just 10.5 m from the shallow end . how long is the pool ? | p - 2160 = ( p * 5 * 4 ) / 100 p = 2700 answer : c | a ) 1500 , b ) 2500 , c ) 2700 , d ) 3200 , e ) 11500 | c | divide(2160, subtract(const_1, divide(multiply(4, 5), const_100))) | multiply(n0,n1)|divide(#0,const_100)|subtract(const_1,#1)|divide(n2,#2) | gain |
11 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ? | "for 40 hrs = 40 * 16 = 640 excess = 948 - 640 = 308 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 308 / 28 = 77 / 7 = 11 total hrs = 40 + 11 = 51 answer e 51" | a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 51 | e | add(40, divide(subtract(948, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100))) | add(n3,const_100)|multiply(n0,n1)|multiply(n0,#0)|subtract(n4,#1)|divide(#2,const_100)|divide(#3,#4)|add(n1,#5)| | general |
the average temperature for monday , tuesday and wednsday is 36.3 degrees c . the average temperature for tuesday , wednesday and thursday is 36.7 degrees c . if monday β s temperature recorded as 39 degrees c , find the thursday β s temperature ? | "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point w of intersection is ( 40,0 ) . a is the correct answer ." | a ) ( 40,0 ) , b ) ( 30,0 ) , c ) ( 0,40 ) , d ) ( 40,30 ) , e ) ( 0,30 ) | a | multiply(negate(divide(subtract(negate(39), multiply(negate(12), divide(3, 4))), divide(3, 4))), const_10) | divide(n0,n1)|negate(n3)|negate(n2)|multiply(#0,#2)|subtract(#1,#3)|divide(#4,#0)|negate(#5)|multiply(#6,const_10)| | general |
a bullock cart has to cover a distance of 80 km in 10 hrs . if it covers half of the journey in 3 / 5 th time . what should be its speed to cover the remaining distance in the time left . | let his total sales be x total sales - commission = $ 31100 x - [ ( 5 % of 10000 ) + 4 % of ( x - 10000 ) ] = 31100 x - 500 - ( x - 10000 ) / 25 = 31100 x = 32500 answer is b | a ) $ 30000 , b ) $ 32500 , c ) $ 35120 , d ) $ 41520 , e ) $ 25460 | b | divide(add(31100, subtract(divide(multiply(5, 10000), const_100), divide(multiply(4, 10000), const_100))), subtract(const_1, divide(4, const_100))) | divide(n2,const_100)|multiply(n0,n1)|multiply(n1,n2)|divide(#1,const_100)|divide(#2,const_100)|subtract(const_1,#0)|subtract(#3,#4)|add(n3,#6)|divide(#7,#5) | general |
the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 66 kmph ? | ( 60 / 100 ) * 50 β ( 34 / 100 ) * 30 30 - 10.2 = 19.8 answer : b | a ) 18 , b ) 19.8 , c ) 11 , d ) 17 , e ) 12 | b | subtract(divide(multiply(60, 50), const_100), divide(multiply(34, 30), const_100)) | multiply(n0,n1)|multiply(n2,n3)|divide(#0,const_100)|divide(#1,const_100)|subtract(#2,#3) | gain |
if f ( x ) = 3 x ^ 4 - 4 x ^ 3 - 2 x ^ 2 + 5 x , then f ( - 1 ) = | "m = 5 s = 2 ds = 7 us = 3 x / 7 + x / 3 = 1 x = 2.1 d = 2.1 * 2 = 4.2 answer : d" | a ) 5.75 , b ) 5.7 , c ) 5.76 , d ) 4.2 , e ) 5.71 | d | multiply(divide(multiply(add(5, 2), subtract(5, 2)), add(add(5, 2), subtract(5, 2))), const_2) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|multiply(#0,#1)|divide(#3,#2)|multiply(#4,const_2)| | physics |
the marked price of a book is 20 % more than the cost price . after the book is sold , the vendor realizes that he had wrongly raised the cost price by a margin of 25 % . if the marked price of the book is rs . 30 , what is the original cost price of the book ? | d = 200 + 180 = 380 m s = 60 * 5 / 18 = 50 / 3 t = 380 * 3 / 50 = 22.8 sec answer : c | a ) 36.7 , b ) 26.8 , c ) 22.8 , d ) 21.1 , e ) 16.2 | c | divide(add(200, 180), multiply(60, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1) | physics |
if n is the greatest positive integer for which 2 ^ n is a factor of 8 ! , then n = ? | solving the two equations , we get : l = 30 and b = 40 . area = ( l x b ) = ( 30 x 40 ) m 2 = 1200 m ^ 2 d | ['a ) 2400 m ^ 2', 'b ) 1500 m ^ 2', 'c ) 2520 m ^ 2', 'd ) 1200 m ^ 2', 'e ) 2580 m ^ 2'] | d | multiply(multiply(10, const_4), multiply(10, const_3)) | multiply(n0,const_4)|multiply(n0,const_3)|multiply(#0,#1) | geometry |
from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 13 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ? | "1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a ." | a ) 1070 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830 | a | subtract(negate(6430), multiply(subtract(1320, 180), divide(subtract(1320, 180), subtract(1370, 1320)))) | negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)| | general |
oil is poured into a tank so that the tank is being filled at the rate of 4 cubic feet per hour . if the empty rectangular tank is 9 feet long , 8 feet wide , and 5 feet deep , approximately how many hours does it take to fill the tank ? | "machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 50 so , x = 50 . hence 6 x = 6 * 50 = 300 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 300 = 3.6 hence option ( b ) ." | a ) 100 , b ) 3.6 , c ) 25 , d ) 11 , e ) 9 | b | divide(1080, multiply(divide(50, const_10), 50)) | divide(n0,const_10)|multiply(n0,#0)|divide(n1,#1)| | general |
if an integer e is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that e ( e + 1 ) ( e + 2 ) will be divisible by 8 ? | "factorization of 45 = 3 * 3 * 5 factorization of 80 = 5 * 2 ^ 4 means the smallest value of k is \ sqrt { 3 ^ 2 * 5 * 2 ^ 4 } = 3 * 5 * 2 ^ 2 k ^ 3 = 3 ^ 3 * 5 ^ 3 * 2 ^ 6 * x = 3 ^ 3 * 2 * 4000 * x where x can be any integer k ^ 3 / 4000 = 3 ^ 3 * 2 * x = 54 x which obviously has different units digit depending on x answer : d" | a ) 0 , b ) 1 , c ) 27 , d ) 54 , e ) can not be determined | d | divide(multiply(multiply(multiply(3, 2), multiply(3, 2)), multiply(3, 2)), const_4) | multiply(n6,n9)|multiply(#0,#0)|multiply(#1,#0)|divide(#2,const_4)| | general |
a 9 by 12 rectangle is inscribed in circle . what is the circumference of the circle ? | make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get s = 7.6 and q 10.8 so 10.8 / 7.6 = 2.7 / 1.9 ans : e | a ) 11 / 12 , b ) 13 / 17 , c ) 13 / 19 , d ) 12 / 19 , e ) 27 / 19 | e | divide(add(multiply(60, const_100), multiply(60, subtract(const_100, 20))), add(multiply(40, const_100), multiply(add(40, 20), 60))) | add(n0,n1)|multiply(n4,const_100)|multiply(n0,const_100)|subtract(const_100,n1)|multiply(n4,#3)|multiply(n4,#0)|add(#1,#4)|add(#2,#5)|divide(#6,#7) | general |
if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 150 % of j ? | "let p = 3 , q = 7 then 2 * 3 + 7 = 13 so 2 p + q = 13 . answer : c" | a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 16 | c | add(multiply(3, 2), 7) | multiply(n0,n2)|add(n1,#0)| | general |
a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 10 % . their gross income from sales for one month decreases by what percent ? | "# defective pens = 2 # good pens = 7 probability of the 1 st pen being good = 7 / 9 probability of the 2 nd pen being good = 6 / 8 total probability = 7 / 9 * 6 / 8 = 7 / 12 the answer is d ." | a ) 4 / 7 , b ) 5 / 9 , c ) 6 / 11 , d ) 7 / 12 , e ) 8 / 15 | d | multiply(divide(subtract(9, 2), 9), divide(subtract(subtract(9, 2), const_1), subtract(9, const_1))) | subtract(n0,n1)|subtract(n0,const_1)|divide(#0,n0)|subtract(#0,const_1)|divide(#3,#1)|multiply(#2,#4)| | general |
what is the smallest positive perfect square that is divisible by 4 , 9 , and 18 ? | "explanation : let the numbers be x and y according to the problem x + y = 63 x - y = 1 / 8 ( x + y ) x - y = 1 / 8 * 63 , x - y = 9 2 x = 72 , x = 36 and y = 27 l . c . m of 36 and 27 is 351 answer : option c" | a ) 231 , b ) 153 , c ) 351 , d ) 345 , e ) 355 | c | subtract(63, divide(subtract(63, divide(1, const_2)), const_2)) | divide(n1,const_2)|subtract(n0,#0)|divide(#1,const_2)|subtract(n0,#2)| | general |
the price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980 . if its price of $ 1.20 in 1970 was 150 percent of its price in 1960 , what was its price in 1980 ? | "explanation : let the required no of hours be x . then less men , more hours ( indirct proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 25 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 25 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 25 } { 15 } = 60 hence , 15 men can do it in 60 hours . answer : c ) 60" | a ) 22 , b ) 38 , c ) 60 , d ) 88 , e ) 72 | c | divide(multiply(36, 25), 15) | multiply(n0,n1)|divide(#0,n2)| | physics |
in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 70 liters and a truck ' s tank is 120 % bigger and they are all empty - ? | "d 5 % increase in 10 years = ( 262500 - 175000 ) = 87500 . increase % = ( 87500 / 175000 x 100 ) % = 50 % . required average = ( 50 / 10 ) % = 5 % ." | a ) 1 % , b ) 2 % , c ) 3 % , d ) 5 % , e ) 4 % | d | add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(2, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(2, const_3)), const_1000)), 1), const_10), const_100), const_4) | add(n2,const_3)|add(const_3,const_4)|multiply(const_10,const_1000)|multiply(#2,const_10)|multiply(#0,const_100)|multiply(#1,const_10)|add(#0,#5)|subtract(#3,const_1000)|multiply(#6,const_1000)|subtract(#7,const_1000)|subtract(#9,#4)|divide(#10,#8)|subtract(#11,n0)|divide(#12,const_10)|multiply(#13,const_100)|add(#14,const_4)| | general |
if a person walks at 10 km / hr instead of 8 km / hr , he would have walked 14 km more . the actual distance traveled by him is ? | let the lowest price be x . therefore , highest price is x + 100 . now price of each variety is increased by 10 % . therefore the price will remain arranged in the same order as before . or lowest price = 1.1 x and highest = 1.1 * ( x + 100 ) or range = highest - lowest = 1.1 * ( x + 100 ) - 1.1 x = 110 , hence , c | a ) $ 50 , b ) $ 100 , c ) $ 110 , d ) $ 600 , e ) $ 300 | c | multiply(100, divide(add(10, const_100), const_100)) | add(n3,const_100)|divide(#0,const_100)|multiply(n0,#1) | general |
when a certain number x is divided by 54 , the remainder is 22 . what is the remainder when x is divided by 18 ? | "explanation : let the c . p . of the article be rs . x given that % profit earned by selling article at rs . 1920 = % loss incurred by selling article at rs . 1280 ( 1920 β x / x ) β 100 = ( x β 1280 / x ) β 100 = > 1920 - x = x - 1280 = > 2 x = 3200 = > x = 1600 s . p . for 25 % profit = rs . 1600 + 25 % of rs . 1600 = rs . 1600 * ( 125 / 100 ) = rs . 2000 answer : a" | a ) rs . 2000 , b ) rs . 2200 , c ) rs . 2400 , d ) data inadequate , e ) can not be determined | a | multiply(divide(add(const_100, 25), 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 |
a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 20 km in 20 hours . how much time he would have saved if the direction of tide has not changed ? | the tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes . the answer is d | a ) 150 , b ) 200 , c ) 188 , d ) 245 , e ) 123 | d | multiply(subtract(divide(multiply(10, const_1000), 200), const_1), 5) | multiply(n0,const_1000)|divide(#0,n1)|subtract(#1,const_1)|multiply(n3,#2) | physics |
the radius of a cone is 49 m , slant height is 35 m . find the curved surface area ? | "answer = 60 / 42 * 4 = 60 / 168 = 0.3571 option d is correct" | a ) 14.7653 , b ) 0.5897 , c ) 3.6974 , d ) 0.3571 , e ) 1.2587 | d | divide(60, 42) | divide(n0,n1)| | general |
if $ 1088 are divided between worker a and worker b in the ratio 5 : 11 , what is the share that worker b will get ? | "there are five prime numbers between 30 and 50 . they are 31,37 , 41,43 and 47 . therefore the required average = ( 31 + 37 + 41 + 43 + 47 ) / 5 ο³ 199 / 5 ο³ 39.8 answer c 39.8" | a ) 18.9 , b ) 19.8 , c ) 39.8 , d ) 29.8 , e ) 20.8 | c | divide(add(add(add(30, const_1), add(add(30, const_1), const_2)), add(subtract(50, 30), subtract(50, const_2))), 30) | add(n0,const_1)|subtract(n1,n0)|subtract(n1,const_2)|add(#0,const_2)|add(#1,#2)|add(#0,#3)|add(#5,#4)|divide(#6,n0)| | general |
on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 140 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ? | "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 4720 32.5 k = 32.5 k / 100 k * 4720 = 1534 the number of valid votes polled in favour of b is 1534 . answer : a" | a ) 1534 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2991 | a | divide(subtract(multiply(subtract(const_1, divide(20, const_100)), 4720), divide(multiply(15, 4720), const_100)), const_2) | divide(n1,const_100)|multiply(n0,n2)|divide(#1,const_100)|subtract(const_1,#0)|multiply(n2,#3)|subtract(#4,#2)|divide(#5,const_2)| | general |
by selling 20 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ? | "worker b will get 11 / 16 = 68.75 % the answer is d ." | a ) 62.45 % , b ) 64.55 % , c ) 66.65 % , d ) 68.75 % , e ) 70.85 % | d | divide(1088, add(5, 11)) | add(n1,n2)|divide(n0,#0)| | other |
the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 15 % ? | "20 + 24 + 6 * 2 = 56 / 2 = 28 answer : e" | a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28 | e | divide(add(add(20, 24), multiply(6, 2)), const_2) | add(n2,n3)|multiply(n0,n1)|add(#0,#1)|divide(#2,const_2)| | general |
the average of first six multiples of 3 is | official solution : ( b ) we know that a # b = 100 and a # b = 4 a Β² + 4 b Β² + 8 ab . so 4 a Β² + 4 b Β² + 8 ab = 100 we can see that 4 a Β² + 4 b Β² + 8 ab is a well - known formula for ( 2 a + 2 b ) Β² . therefore ( 2 a + 2 b ) Β² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 4 = 10 / 2 + 4 = 9 . the correct answer is b . | a ) 5 , b ) 9 , c ) 10 , d ) 13 , e ) 17 | b | add(sqrt(divide(100, 4)), 4) | divide(n6,n0)|sqrt(#0)|add(n0,#1) | general |
the sum of all the integers s such that - 26 < s < 24 is | "area = 5.5 Γ 3.75 sq . metre . cost for 1 sq . metre . = $ 500 hence , total cost = 5.5 Γ 3.75 Γ 500 = $ 10312.50 a" | a ) $ 10312.50 , b ) $ 13512.50 , c ) $ 16512.50 , d ) $ 14512.50 , e ) $ 18512.50 | a | multiply(500, multiply(5.5, 3.75)) | multiply(n0,n1)|multiply(n2,#0)| | physics |
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 - . | "we have : l = 20 ft and lb = 10 sq . ft . so , b = 0.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 1 ) ft = 21 ft . answer : d" | a ) 34 , b ) 40 , c ) 68 , d ) 21 , e ) 78 | d | add(multiply(divide(10, 20), const_2), 20) | divide(n1,n0)|multiply(#0,const_2)|add(n0,#1)| | geometry |
denise is trying to open a safe whose combination she does not know . if the safe has 4000 possible combinations , and she can try 75 different possibilities , what is the probability that she does not pick the one correct combination . | the problem asks for the approximate chance that no more than 1 / 3 of the original investment is lost . we can apply the β 1 β x β technique : what β s the chance that more than 1 / 3 of the original investment is lost ? there are two outcomes we have to separately measure : ( a ) all 3 investments become worthless . ( b ) 2 of the 3 investments become worthless , while 1 doesn β t . outcome ( a ) : the probability is ( 0.2 ) ( 0.2 ) ( 0.2 ) = 0.008 , or a little less than 1 % . outcome ( b ) : call the investments x , y , and z . the probability that x retains value , while y and z become worthless , is ( 0.8 ) ( 0.2 ) ( 0.2 ) = 0.032 . now , we have to do the same thing for the specific scenarios in which y retains value ( while x and z don β t ) and in which z retains value ( while x and y don β t ) . each of those scenarios results in the same math : 0.032 . thus , we can simply multiply 0.032 by 3 to get 0.096 , or a little less than 10 % . the sum of these two probabilities is 0.008 + 0.096 = 0.104 , or a little more than 10 % . finally , subtracting from 100 % and rounding , we find that the probability we were looking for is approximately 90 % . the correct answer is a . this problem illustrates the power of diversification in financial investments . all else being equal , it β s less risky to hold a third of your money in three uncorrelated ( independent ) but otherwise equivalent investments than to put all your eggs in one of the baskets . that said , be wary of historical correlations ! housing price changes in different us cities were not so correlated β and then they became highly correlated during the recent housing crisis ( they all fell together ) , fatally undermining spreadsheet models that assumed that these price changes were independent . | a ) 90 % , b ) 80 % , c ) 70 % , d ) 60 % , e ) 40 % | a | subtract(add(multiply(20, const_2), multiply(20, 3)), const_10) | multiply(n1,const_2)|multiply(n0,n1)|add(#0,#1)|subtract(#2,const_10) | general |
if n is a prime number greater than 17 , what is the remainder when n ^ 2 is divided by 12 ? | "multiples of 4 less than 250 = { 4 , 8,12 , . . . . . . 248 } = 62 numbers multiples of 4 which are multiples of 3 too = { 12 , 24,36 . . . . . 240 } = 20 numbers so required number = 62 - 20 = 42 choice c" | a ) 20 , b ) 31 , c ) 42 , d ) 53 , e ) 64 | c | divide(factorial(subtract(add(const_4, 4), const_1)), multiply(factorial(4), factorial(subtract(const_4, const_1)))) | add(n1,const_4)|factorial(n1)|subtract(const_4,const_1)|factorial(#2)|subtract(#0,const_1)|factorial(#4)|multiply(#1,#3)|divide(#5,#6)| | general |
what is the remainder when the number w = 14 ^ 2 * 15 ^ 8 is divided by 5 ? | to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 50 tons will be 100,000 pounds from the answer choices : let max number of vehicles be 62 total weight will be = 62 * 1600 = 99200 pounds , which is lesser than the maximum weight allowed . ans : d | a ) 23 , b ) 41 , c ) 48 , d ) 62 , e ) 86 | d | divide(multiply(multiply(50, const_2), const_1000), add(add(add(add(add(add(const_1000, const_100), const_100), const_100), const_100), const_100), const_100)) | add(const_100,const_1000)|multiply(n0,const_2)|add(#0,const_100)|multiply(#1,const_1000)|add(#2,const_100)|add(#4,const_100)|add(#5,const_100)|add(#6,const_100)|divide(#3,#7) | general |
# 88 a necklace is made by stringing q no individual beads together in the repeating pattern red bead , green bead , white bead , blue bead , and yellow bead . if the necklace design begins with a red bead and ends with a white bead , then q could equal | "d = 8 d d = d a β 2 = 8 d a β 2 = d a = 8 d / β 2 a = d / β 2 = > 8 : 1 answer : d" | a ) 3 : 6 , b ) 3 : 3 , c ) 3 : 8 , d ) 8 : 1 , e ) 3 : 2 | d | divide(8, divide(8, 8)) | divide(n0,n0)|divide(n0,#0)| | geometry |
the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 6 per metre approximately | bank balance is doubled with accumulation of interest tp 5080 . . this means interest is 5080 / 2 = 2540 for entire year . . although since interest is 10 % of avg monthly balance , it becomes 25400 . . d | a ) 2840 , b ) 5680 , c ) 6840 , d ) 25400 , e ) 28400 | d | multiply(5080, divide(10, const_2)) | divide(n0,const_2)|multiply(n1,#0) | general |
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 ? | "speed of bus relative to woman = 21 + 3 = 24 km / hr . = 24 * 5 / 18 = 20 / 3 m / sec . time taken to pass the woman = 75 * 3 / 20 = 11.25 sec . answer : c" | a ) 5.75 , b ) 7.62 , c ) 11.25 , d ) 4.25 , e ) 3.25 | c | divide(divide(multiply(75, const_3600), add(21, 3)), const_1000) | add(n1,n2)|multiply(n0,const_3600)|divide(#1,#0)|divide(#2,const_1000)| | physics |
x and y are both integers . if x / y = 59.60 , then what is the sum of all the possible two digit remainders of x / y ? | "in real basic terms , we ' re asked to find all of the ' 3 s ' in 200 ! we can figure out that 200 / 3 = 66 , so we know that there are at least 66 ' 3 s ' in 200 ! while that answer is among the 5 choices , it seems a bit too ' easy ' , so let ' s do a bit more work and list out the first few numbers that we know have a ' 3 ' in them : 3 = 3 x 1 6 = 3 x 2 9 = 3 x 3 notice how both 3 and 6 have just one 3 in them , but 9 has two 3 s ( there ' s an ' extra ' 3 that we have to account for ) . this implies that there are probably other numbers that include ' extra 3 s ' that we have to figure out : to find those extra 3 s , we have to look at numbers that contain ' powers of 3 ' . . . 3 ^ 2 = 9 3 ^ 3 = 27 3 ^ 4 = 81 3 ^ 5 = 243 , but that ' s too big ( we ' re only going up to 200 ) . keep in mind that a multiple of 81 is also a multiple of 9 and 27 , so we do n ' t want to count any of those values more than once . 200 / 9 = 22 , so we know that there are at least 22 extra 3 s ( and certainly more because of the 27 and 81 ) . with the 66 3 s that we already have , those 22 extra 3 s increase the total to 88 . with the other extra 3 s , we ' ll end up with more than 88 3 s . there ' s only one answer that fits that logic . . . answer : d" | a ) 88 , b ) 48 , c ) 66 , d ) 97 , e ) 39 | d | multiply(floor(divide(power(const_10, 3), 200)), 200) | power(const_10,n0)|divide(#0,n1)|floor(#1)|multiply(n1,#2)| | other |
sum of 19 odd numbers is ? | "explanation : ( 40 + 60 + 70 + 80 + 80 / 5 ) = 66 option a" | a ) 66 , b ) 75 , c ) 80 , d ) 85 , e ) 90 | a | divide(add(add(add(add(40, 60), 70), 80), 80), add(const_4, const_1)) | add(n0,n1)|add(const_1,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)| | general |
jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 7 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ? | "the time it takes bob to drive to city b is 100 / 40 = 2.5 hours . alice needs to take less than 2 hours for the trip . alice needs to exceed a constant speed of 100 / 2 = 50 miles per hour . the answer is c ." | a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 54 | c | divide(100, subtract(divide(100, 40), divide(30, const_60))) | divide(n0,n1)|divide(n2,const_60)|subtract(#0,#1)|divide(n0,#2)| | physics |
a train 520 m long can cross an electric pole in 20 sec and then find the speed of the train ? | "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 3 units of water was used to make 4 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 4 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 4 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 4 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 4 * x - - > x = $ 0.3 . answer : c ." | a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45 | c | divide(multiply(add(const_1, const_1), 0.60), add(const_1, const_2)) | add(const_1,const_1)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)| | general |
in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 170 m . then , a wins by : | "d 7429 - 4358 = 3071 let 8597 - x = 3071 then , x = 8597 - 3071 = 5526" | a ) 3567 , b ) 6424 , c ) 6835 , d ) 5526 , e ) none of these | d | subtract(multiply(divide(8597, const_100), 7429), multiply(divide(const_1, const_3), multiply(divide(8597, const_100), 7429))) | divide(n0,const_100)|divide(const_1,const_3)|multiply(n1,#0)|multiply(#1,#2)|subtract(#2,#3)| | general |
the s . i . on a certain sum of money for 5 years at 6 % per annum is half the c . i . on rs . 3000 for 2 years at 15 % per annum . the sum placed on s . i . is ? | "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 } ( less than 24 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 } ( less than 24 ) 17 is the only common number in both the sets . hence k = 17 answer : d" | a ) 2 , b ) 5 , c ) 6 , d ) 3 , e ) 8 | d | reminder(add(const_12, 5), 7) | add(n0,const_12)|reminder(#0,n5)| | general |
two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 20 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 20 miles ahead of the black car , how many hours will it take the black car to overtake the red car ? | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 = > x = 6 hence , b ' s age = 2 x = 12 years . answer : e" | a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12 | e | multiply(divide(subtract(32, const_2), add(const_3, const_2)), const_2) | add(const_2,const_3)|subtract(n0,const_2)|divide(#1,#0)|multiply(#2,const_2)| | general |
alex takes a loan of $ 8,000 to buy a used truck at the rate of 9 % simple interest . calculate the annual interest to be paid for the loan amount . | "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 20 = 12.1 sec . answer : b" | a ) 12.6 , b ) 12.0 , c ) 12.1 , d ) 12.3 , e ) 12.2 | b | divide(add(110, 132), multiply(72, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | physics |
if the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is ? | "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 6 = 120 m . answer : c" | a ) 298 , b ) 288 , c ) 120 , d ) 776 , e ) 991 | c | divide(const_100.0, subtract(divide(const_100.0, 10), 6)) | divide(const_100.0,n1)|subtract(#0,n2)|divide(const_100.0,#1)| | physics |
how many 7 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 1234321 . | "even i got 96 % j = 100 t = 100 * 0.4 = 40 m = 40 * 1.6 = 64 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 64 * 100 / 100 = 64 ans : c" | a ) 124 % , b ) b . 120 % , c ) 64 % , d ) 80 % , e ) 64 % | c | add(subtract(const_100, 60), multiply(subtract(const_100, 60), divide(60, const_100))) | divide(n0,const_100)|subtract(const_100,n1)|multiply(#0,#1)|add(#2,#1)| | general |
simplify : 81 x 81 + 68 x 68 - 2 x 81 x 68 . | "no . of ways of picking 2 biology books ( from 11 books ) = 11 c 2 = ( 11 * 10 ) / 2 = 55 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 55 * 28 = 1540 ( option e )" | a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 1540 | e | multiply(divide(divide(factorial(11), factorial(subtract(11, 2))), 2), divide(divide(factorial(8), factorial(subtract(8, 2))), 2)) | factorial(n0)|factorial(n1)|subtract(n0,n2)|subtract(n1,n2)|factorial(#2)|factorial(#3)|divide(#0,#4)|divide(#1,#5)|divide(#6,n2)|divide(#7,n2)|multiply(#8,#9)| | other |
what is the greatest prime factor of 2 ^ 8 - 1 ? | pipe a fills 1 / 30 th of the tank in a minute and pipe b empties 1 / 90 th of the tank ( 1 / 30 ) - ( 1 / 90 ) = ( 1 / x ) 2 / 90 = 1 / x = > x = 45 answer : d | a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50 | d | divide(const_1, subtract(divide(const_1, 30), divide(const_1, 90))) | divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2) | physics |