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the area of a parallelogram is 72 sq m and its altitude is twice the corresponding base . then the length of the base is ? | "total time taken by jerry = ( 8 / 40 ) * 60 minutes + 14 minutes + ( 20 / 60 ) * 60 minutes = 46 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 46 / 60 ) hours = 28 * 60 / 46 = 36 miles per hour answer : option a" | a ) 36 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5 | a | divide(add(8, 20), add(add(divide(8, 40), divide(14, 60)), divide(20, 60))) | add(n0,n3)|divide(n0,n1)|divide(n2,n4)|divide(n3,n4)|add(#1,#2)|add(#4,#3)|divide(#0,#5)| | physics |
from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a black card and the second card is a king or queen ? | total surface area of cuboid = 2 ( lb + bh + lh ) = 2 ( 120 + 80 + 96 ) = 2 ( 296 ) = > 596 m ( power 2 ) answer is c . | ['a ) 576', 'b ) 566', 'c ) 596', 'd ) 556', 'e ) 586'] | c | surface_rectangular_prism(12, 10, 8) | surface_rectangular_prism(n0,n1,n2) | geometry |
when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that the merchant paid was $ 109.90 , what was the total value of the item ? | "500 84 \ / 90 / \ 6 410 3 : 205 3 - > 12 205 - > ? 820 answer : c" | a ) 620 , b ) 720 , c ) 820 , d ) 920 , e ) 1020 | c | divide(90, add(84, add(const_3, const_3))) | add(const_3,const_3)|add(n2,#0)|divide(n0,#1)| | general |
if 2 x + y = 7 and x + 2 y = 5 , then 10 xy / 3 = ? | "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( - 4 ) + ( 0.5 ) = - 3.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from - 4 to - 3.5 ) . next , the question asks for the least integer that is greater than - 3.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of - 3.5 is - 3 . final answer : a" | a ) β 3 , b ) β 1 , c ) 0 , d ) 1 , e ) 2 | a | add(0.5, negate(4)) | negate(n0)|add(n1,#0)| | general |
rakesh ' s mathematics test had 75 problems , 10 arithmetic , 30 algebra , 35 geometry problems . although he answered 70 % of arithmetic , 40 % of arithmetic and 60 % of geometry problems correctly , still he got less than 60 % problems right . how many more questions he would have to answer more to get passed ? | "explanation : given : 240 / 80 Γ’ β¬ β 60 * 40 - 10 = ? substituting the coded symbols for mathematical operations , we get , 240 * 80 / 60 + 40 / 10 = ? 240 * 1.33 + 4 = ? 319.2 + 4 = 323.2 answer : c" | a ) 355 , b ) 341 , c ) 323.2 , d ) 425.6 , e ) 225.7 | c | add(multiply(divide(60, 40), divide(240, 80)), 10) | divide(n2,n3)|divide(n0,n1)|multiply(#0,#1)|add(n4,#2)| | general |
26 : 62 : : 32 : ? | "one man can complete the work in 24 * 60 = 1440 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1440 m = 144 workers answer : a" | a ) 144 , b ) 170 , c ) 180 , d ) 190 , e ) 200 | a | divide(multiply(60, multiply(24, const_2)), 20) | multiply(n1,const_2)|multiply(n0,#0)|divide(#1,n2)| | physics |
if a mixture is 5 β 9 alcohol by volume and 4 β 9 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ? | let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 21 1 3 / 4 w = 21 w = 12 the total number of jars = 3 w = 36 answer : d | a ) 3 , b ) 6 , c ) 9 , d ) 36 , e ) 14 | d | multiply(divide(21, add(const_1, add(const_0_25, divide(const_1, const_2)))), const_3) | divide(const_1,const_2)|add(#0,const_0_25)|add(#1,const_1)|divide(n0,#2)|multiply(#3,const_3)| | general |
the average salary per month of 55 employees in a company is rs 8500 . if the managers salary is added , the average salary increases to rs 8800 , what is the salary of the manager ? | "j = 12 ; j = 3 b ; b = 12 / 3 = 4 ; twice as old so b = 4 ( now ) + ( 4 ) = 8 ; jacob is 12 + 4 = 16 answer : d" | a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17 | d | multiply(12, 3) | multiply(n0,n1)| | general |
the speed of a boat in still water in 22 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is : | "if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 12 c 2 = 12 * 11 / 2 = 66 . therefore , the answer is b ." | a ) 150 , b ) 66 , c ) 190 , d ) 210 , e ) 240 | b | add(add(add(add(add(add(add(1, 10), add(1, const_2)), add(1, const_1)), 1), 10), const_2), const_1) | add(n0,n1)|add(n1,const_2)|add(n1,const_1)|add(#0,#1)|add(#3,#2)|add(#4,n1)|add(#5,n0)|add(#6,const_2)|add(#7,const_1)| | probability |
the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 170 runs and his average excluding these two innings is 58 runs , find his highest score . | "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 β 20 = rs . 185 cp on 40 metres = 185 x 40 = rs . 7400 profit earned on 40 metres cloth = rs . 8200 β rs . 7400 = rs . 800 . answer : option a" | a ) rs . 800 , b ) rs . 1500 , c ) rs . 1000 , d ) rs . 1200 , e ) none of these | a | multiply(20, 40) | multiply(n0,n2)| | gain |
if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 4 other contributions made before john ' s , what is the size of his donation ? | sum of digits = ( 4 + 5 + 1 + x + 6 + 0 + 3 ) = 19 + x divisible by 9 clearly x = 9 answer e 9 | a ) 2 , b ) 5 , c ) 7 , d ) 8 , e ) 9 | e | log(451) | log(n0) | general |
a box contain the number of balls which is as much times greater than 15 as much times lesser than 240 . the no . of ball is ? | "required number of machines = 24 * 10 / 40 = 6 answer is b" | a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5 | b | divide(multiply(24, 10), 40) | multiply(n0,n1)|divide(#0,n2)| | physics |
students of 3 different classes appeared in common examination . pass average of 10 students of first class was 45 % , pass average of 15 students of second class was 60 % and pass average of 25 students of third class was 80 % then what will be the pass average of all students of 3 classes ? | the number of males is 170 - 110 = 60 . the number of males with advanced degrees is 60 - 25 = 35 . the number of females with advanced degrees is 80 - 35 = 45 . the answer is b . | a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60 | b | subtract(80, subtract(subtract(170, 110), 25)) | subtract(n0,n1)|subtract(#0,n3)|subtract(n2,#1) | geometry |
on a certain transatlantic crossing , 40 percent of a ship β s passengers held round - trip tickets and also took their cars abroad the ship . if 20 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship β s passengers held round - trip tickets ? | "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 48 are males , so remaining 90 - 36 = 54 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 54 , 100 % = 54 * 100 / 60 = 90 . . ans 40 % of 90 = 36 b" | a ) 18 , b ) 36 , c ) 42 , d ) 68 , e ) 70 | b | divide(multiply(divide(multiply(subtract(subtract(300, divide(multiply(70, 300), const_100)), 36), const_100), subtract(const_100, 40)), 40), const_100) | multiply(n0,n1)|subtract(const_100,n2)|divide(#0,const_100)|subtract(n0,#2)|subtract(#3,n3)|multiply(#4,const_100)|divide(#5,#1)|multiply(n2,#6)|divide(#7,const_100)| | gain |
a boy goes to his school from his house at a speed of 3 km / hr and return at a speed of 2 km / hr . if he takes 5 hours in going and coming , the distance between his house and school is ? | "if ab β 0 then a and b has two integer sets of pair if a = 9 then b = 8 and if a = - 9 then b = - 8 also in fraction if a = 1 / 8 then b = 1 / 9 any of the pair we check the ratio 8 a / 9 b = 1 answer : c" | a ) 64 / 81 , b ) 8 / 9 , c ) 1 , d ) 9 / 8 , e ) 81 / 64 | c | divide(multiply(8, 9), multiply(9, 8)) | multiply(n0,n1)|divide(#0,#0)| | general |
the area of a rectangular field is equal to 500 square meters . its perimeter is equal to 90 meters . find the width of this rectangle . | "the number of seats in the theater is 17 + ( 17 + 3 ) + . . . + ( 17 + 27 ) = 10 ( 17 ) + 3 ( 1 + 2 + . . . + 9 ) = 10 ( 17 ) + 3 ( 9 ) ( 10 ) / 2 = 170 + 135 = 305 the answer is e ." | a ) 265 , b ) 275 , c ) 285 , d ) 295 , e ) 305 | e | multiply(divide(add(17, 44), const_2), divide(add(subtract(44, 17), 3), 3)) | add(n0,n2)|subtract(n2,n0)|add(n1,#1)|divide(#0,const_2)|divide(#2,n1)|multiply(#3,#4)| | general |
what is the sum of the multiples of 7 from 77 to 91 , inclusive ? | "69 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 9.56 % answer : d" | a ) 9.33 % , b ) 9.44 % , c ) 9.45 % , d ) 9.56 % , e ) 9.67 % | d | multiply(divide(subtract(subtract(69, multiply(69, divide(10, const_100))), 56.16), subtract(69, multiply(69, divide(10, const_100)))), const_100) | divide(n2,const_100)|multiply(n0,#0)|subtract(n0,#1)|subtract(#2,n1)|divide(#3,#2)|multiply(#4,const_100)| | gain |
a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 60 percent of books that were loaned out are returned and there are 65 books in the special collection at that time , how many books of the special collection were loaned out during that month ? | "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 200 * 3 / 50 = 12 sec . answer : c" | a ) 26 sec , b ) 30 sec , c ) 12 sec , d ) 19 sec , e ) 12 sec | c | divide(200, multiply(subtract(63, 3), const_0_2778)) | subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
a clothing store purchased a pair of pants for $ 90 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a clothing store owner decided to decrease the selling price by 20 percent . what was the clothing store ' s gross profit on this sale ? | "cone curved surface area = Ο rl = 22 / 7 Γ 4 Γ 5 = 440 / 7 = 62 6 / 7 slant height ( l ) = β r ( power 2 ) + h ( power 2 ) = β 16 + 9 = β 25 = 5" | a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9 | c | volume_cone(4, 5) | volume_cone(n0,n1)| | geometry |
the difference between two numbers is 1365 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is | "explanation : use formula for a work members Γ£ β days = constant 8 Γ£ β 3 = 4 Γ£ β a a = 6 so answer is 6 days answer : a" | a ) 6 , b ) 8 , c ) 3 , d ) 4 , e ) 0 | a | divide(const_1, multiply(divide(const_1, multiply(const_4.0, 8)), 3)) | multiply(n0,n1)|divide(const_1,#0)|multiply(n2,#1)|divide(const_1,#2)| | physics |
34 . the side surface of a cylinder is rolled with a rectangular plate . if the perimeter of the circular base is 9 feet , and the diagonal of the rectangular plate was 15 ft . what is height of the of the cylinder ? | "diameter = 140 cm 1 / 2 * 22 / 7 * 140 + 140 = 360 answer : c" | a ) 32.8 , b ) 32.4 , c ) 360 , d ) 32.2 , e ) 32.9 | c | add(divide(circumface(70), const_2), multiply(70, const_2)) | circumface(n0)|multiply(n0,const_2)|divide(#0,const_2)|add(#2,#1)| | physics |
find the value of ( 950 + 220 / 900 ) Γ 900 | "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) Γ ( 260 - 10 ) Γ ( 130 - x ) ] = 8000 Γ 1000 = > 320 Γ 250 Γ ( 130 - x ) = 8000 Γ 1000 = > ( 130 - x ) = 8000 Γ 1000 / 320 = 100 = > x = 30 cm = 3 dm . answer : b" | a ) 90 cm , b ) 3 dm , c ) 1 m , d ) 1.1 cm , e ) none of these | b | subtract(multiply(multiply(3.3, 2.6), 1.3), divide(8000, const_1000)) | divide(n0,const_1000)|multiply(n1,n2)|multiply(n3,#1)|subtract(#2,#0)| | physics |
an electric pump can fill a tank in 4 hours . because of a leak in the tank , it took 8 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ? | "any multiple of 12 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ." | a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 % | a | divide(add(12, add(10, const_3)), const_2) | add(n1,const_3)|add(n0,#0)|divide(#1,const_2)| | general |
the ratio , by volume , of soap to alcohol to water in a certain solution is 4 : 20 : 60 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ? | i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 36 days to doing 6 w widgets . answer : b | a ) 4 , b ) 36 , c ) 8 , d ) 10 , e ) 12 | b | multiply(multiply(6, 2), 3) | multiply(n0,n4)|multiply(n3,#0) | general |
what is the units digit of 33 ^ 2 * 17 ^ 3 * 39 ^ 2 ? | "1500 - - - - 270 100 - - - - ? = > 18 % answer : a" | a ) 18 % , b ) 19 % , c ) 68 % , d ) 19 % , e ) 38 % | a | multiply(divide(subtract(1500, 1230), 1500), const_100) | subtract(n0,n1)|divide(#0,n0)|multiply(#1,const_100)| | gain |
a tank contains 6,500 gallons of a solution that is 5 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ? | clock a gains 20 seconds per minute , 1200 seconds per hour or 20 minutes per hour . the two clocks show 2 : 00 at 2 0 ' clock at 3 : 00 - clock b is at 3 : 00 clock a is at 3 : 20 ( 1 hour + gains 20 minutes ) at 4 : 00 - clock b is at 4 : 00 clock a is at 4 : 40 ( 2 hours + gains 40 minutes ) in 4 hours the clock a gains 4 * 20 = 80 minutes or 1 hour 20 minutes if clock a is at 7 : 20 the clock b is at 6 : 00 answer is b | a ) 5 : 30 , b ) 6 : 00 , c ) 5 : 45 , d ) 6 : 20 , e ) 3 : 30 | b | divide(add(add(multiply(subtract(7, 2), const_60), 20), divide(multiply(add(multiply(subtract(7, 2), const_60), 20), 20), const_60)), const_60) | subtract(n3,n1)|multiply(#0,const_60)|add(n0,#1)|multiply(n0,#2)|divide(#3,const_60)|add(#2,#4)|divide(#5,const_60) | physics |
what is 15 % of 2 / 3 of 0.5 ? | "500 * ( 90 / 100 ) * ( 95 / 100 ) = 427.5 answer : a" | a ) 427.5 , b ) 277 , c ) 342 , d ) 882 , e ) 212 | a | subtract(subtract(500, divide(multiply(500, 10), const_100)), divide(multiply(subtract(500, divide(multiply(500, 10), const_100)), 5), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(n2,#2)|divide(#3,const_100)|subtract(#2,#4)| | gain |
24 oz of juice p and 25 oz of juice t are mixed to make smothies x and y . the ratio of p to t in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ? | let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 350 hence , x = 250 . so , number of timeshare condos available at playa del mar = 250 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 3 / 5 x = 3 / 5 ( 250 ) = 150 the correct answer is d | a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 240 | d | add(divide(multiply(350, 2), 5), multiply(2, 5)) | multiply(n0,n2)|multiply(n0,n1)|divide(#0,n1)|add(#2,#1) | general |
if the complement of a certain angle is 7 times the measure of that certain angle , then what is the measure of that certain angle ? | "this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 8 x 12 / ( 8 + 12 ) = 96 / 20 = 4.8 days answer : a" | a ) a ) 4.8 , b ) b ) 6.333 , c ) c ) 7.333 , d ) d ) 8.5 , e ) e ) 9 | a | divide(const_1, add(divide(const_1, 8), divide(const_1, 12))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)| | physics |
what least number should be added to 1022 , so that the sum is completely divisible by 25 ? | d = 6 , r = 2 ; volume of the largest sphere = 4 / 3 Ο r 3 = 4 / 3 * Ο * 3 * 3 * 3 = 36 Ο cm 3 answer : c | ['a ) 288', 'b ) 48', 'c ) 36', 'd ) 864', 'e ) 964'] | c | multiply(divide(const_4, const_3), power(3, const_3)) | divide(const_4,const_3)|power(n3,const_3)|multiply(#0,#1) | geometry |
among the two clocks , clock a gains 20 seconds per minute . if clock a and b are set at 2 0 ' clock , when clock a is at 7 : 20 , what does clock b show ? | "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 150 / ( 36 * 5 / 18 ) , 150 / ( 54 * 5 / 18 ) } = lcm ( 15 , 10 ) = 30 sec . answer : a" | a ) 30 sec , b ) 198 sec , c ) 178 sec , d ) 665 sec , e ) 276 sec | a | divide(150, subtract(multiply(54, const_0_2778), multiply(36, const_0_2778))) | multiply(n2,const_0_2778)|multiply(n1,const_0_2778)|subtract(#0,#1)|divide(n0,#2)| | physics |
in a 100 member association consisting of men and women , exactly 10 % of men and exactly 20 % women are homeowners . what is the maximum number of members who are homeowners ? | "time taken = total distance / relative speed total distance = 50 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 50 / 10 = 5 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 5 = 30 kms . . . answer - e" | a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30 | e | multiply(4, divide(50, add(4, 6))) | add(n1,n2)|divide(n0,#0)|multiply(n1,#1)| | physics |
paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to paul and 40 % of his income to quentin , paul ' s new income would be what fraction of quentin ' s new income ? | "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 150 + 280 = 430 m . the time required = d / s = 430 / 20 = 21.5 sec . answer : d" | a ) 22 sec , b ) 77 sec , c ) 76 sec , d ) 21.5 sec , e ) 66 sec | d | divide(add(150, 280), multiply(add(42, 30), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | physics |
ele , the circus elephant , is currently 3 times older than lyn , the circus lion . in 15 years from now , lyn the circus lion will be exactly half as old as ele , the circus elephant . how old is ele today ? | we are told that : generallya cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . is it possible the cyclist to travel with maximum speed for some time ? why not , if there is right terrain for that . so , if there is long enough terrain for the maximum speed of 14 mph then the maximum distance , in miles , that the cyclist could travel in 5 hours would be 5 * 14 = 70 miles . answer : c . | a ) 42 , b ) 56 , c ) 70 , d ) 98 , e ) 140 | c | multiply(14, 5) | multiply(n1,n2) | physics |
a student committee on academic integrity has 56 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ? | "4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 5 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : b ." | a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | b | subtract(multiply(4.00, 12), 42.00) | multiply(n0,n2)|subtract(#0,n3)| | general |
two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team q . if team a ' s average speed was 5 mph greater than team q ' s , what was team q ' s average mph ? | given that the area of the square = 5929 sq . units = > side of square = Γ’ Λ Ε‘ 5929 = 77 units the radius of the circle = side of the square = 77 units length of the rectangle = 2 / 7 * 77 = 22 units given that breadth = 25 units area of the rectangle = lb = 22 * 25 = 550 sq . units answer : d | ['a ) 660 sq . units', 'b ) 440 sq . units', 'c ) 770 sq . units', 'd ) 550 sq . units', 'e ) 220 sq . units'] | d | rectangle_area(25, multiply(sqrt(5929), divide(const_2, add(const_3, const_4)))) | add(const_3,const_4)|sqrt(n0)|divide(const_2,#0)|multiply(#2,#1)|rectangle_area(n1,#3) | geometry |
in business , a and c invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by a and b was 2 : 5 , if rs 15,000 was their profit , how much amount did b receive . | ans . 12 days | a ) 12 , b ) 66 , c ) 77 , d ) 8 , e ) 6 | a | divide(multiply(20, 15), 25) | multiply(n0,n1)|divide(#0,n2)| | physics |
a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ? | "usually , you are given the annual rate of interest and it is mentioned that it is annual rate . the bank charges him a quarterly compounded annual rate of 20 % . here you find per quarter rate as ( 20 / 4 ) % = 5 % i have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5 % annual rate of interest , it is apparent that the intent was a 5 % quarterly rate . so the bank charges 5 % every quarter and compounds it in the next quarter . had it been a simple quarterly rate , we would have just found 4 * 5 % of 30,000 = $ 6000 as our answer . but since , the interest is compounded , it will be a bit more than $ 6000 . option ( d ) looks correct ." | a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 6000 , e ) $ 12000 | d | subtract(multiply(multiply(const_100, const_100), power(add(const_1, divide(5, const_100)), const_4)), multiply(const_100, const_100)) | divide(n1,const_100)|multiply(const_100,const_100)|add(#0,const_1)|power(#2,const_4)|multiply(#1,#3)|subtract(#4,#1)| | gain |
x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 6 . if x invested rs . 5000 . the amount invested by y is | "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.2 t had round trip tickets and took their cars . 0.5 x had round trip tickets and took their cars . 0.5 x = 0.2 t x = 0.4 t the answer is b ." | a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 65 % | b | divide(20, subtract(const_1, divide(50, const_100))) | divide(n1,const_100)|subtract(const_1,#0)|divide(n0,#1)| | gain |
if 20 liters of chemical x are added to 80 liters of a mixture that is 15 % chemical x and 85 % chemical y , then what percentage of the resulting mixture is chemical x ? | "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 7 = 35 km imo , correct answer is ` ` b . ' '" | a ) 20 km , b ) 35 km , c ) 40 km , d ) 50 km , e ) 60 km | b | multiply(60, divide(multiply(5, 7), 60)) | multiply(n1,n2)|divide(#0,n0)|multiply(n0,#1)| | physics |
if 40 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ? | "answer is e . since prime factor of 95 is 5 x 19 . 19 is a prime number and not part of the first 18 positive integers . a ) 9 x 11 b ) 12 x 7 c ) 12 x 6 d ) 13 x 5 e ) 3 x 19" | a ) 99 , b ) 84 , c ) 72 , d ) 65 , e ) 95 | e | multiply(add(18, const_3), const_3) | add(n0,const_3)|multiply(#0,const_3)| | general |
if ' a ' completes a piece of work in 3 days , which ' b ' completes it in 5 days and ' c ' takes 10 days to complete the same work . how long will they take to complete the work , if they work together ? | x / 5 + 22 = 3 x / 4 = > x = 40 litres answer : d | a ) 25 litres , b ) 35 litres , c ) 30 litres , d ) 40 litres , e ) none of these | d | divide(22, subtract(divide(3, 4), divide(1, 5))) | divide(n3,n4)|divide(n0,n1)|subtract(#0,#1)|divide(n2,#2) | general |
cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost q is what percent of the original cost ? | 3 x = 450 x = 150 therefore , the salesman sold 150 kg in the morning and 2 β
150 = 300 kg in the afternoon . so answer is c . | a ) 120 , b ) 180 , c ) 300 , d ) 280 , e ) 320 | c | multiply(divide(450, const_3), const_2) | divide(n0,const_3)|multiply(#0,const_2) | other |
walking with 4 / 5 of my usual speed , i miss the bus by 7 minutes . what is my usual time ? | "explanation : ( a + b ) one day work = 1 / 10 now a does half of the work in 6 days so a can complete the whole work in 12 days a β s one day work = 1 / 12 b β s one day work = 1 / 10 - 1 / 12 = 2 / 120 = 1 / 60 b alone can complete the work in 60 days so half of the work in 30 days answer : option e" | a ) 4 , b ) 8 , c ) 5 , d ) 6 , e ) 30 | e | multiply(10, divide(6, 10)) | divide(n1,n0)|multiply(n0,#0)| | physics |
renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 5 days . in what time suma can do it alone ? | "a = { 4 , 5,6 , 7,8 , 9,10 , 11,12 , . . . 16 } b = { 6 , 7,8 , 9,10 , 11,12 . . . } thus we see that there are 11 distinct integers that are common to both . e is the correct answer ." | a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 11 | e | add(6, 4) | add(n0,n2)| | other |
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 ? | "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 30 5 x = 1335 x = 267 large number = 267 + 1365 = 1632 d" | a ) 1235 , b ) 1456 , c ) 1567 , d ) 1632 , e ) 1635 | d | add(multiply(divide(subtract(1365, 30), subtract(6, const_1)), 6), 30) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)|add(n2,#3)| | general |
a salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100 . if the sale price of each machine was $ 10,000 and the salesperson received a $ 32,000 commission , how many machines did she sell ? | "let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 = > x = 4 . age of youngest child = x = 4 years . answer : a" | a ) 4 years , b ) 8 years , c ) 10 years , d ) 12 years , e ) none of these | a | divide(subtract(divide(50, divide(5, 3)), multiply(subtract(5, const_1), 3)), 3) | divide(n0,n1)|subtract(n0,const_1)|divide(n2,#0)|multiply(n1,#1)|subtract(#2,#3)|divide(#4,n1)| | general |
a , b and c can do a piece of work in 7 days , 14 days and 28 days respectively . how long will they take to finish the work , if all the three work together ? | his pay check was $ 1320 . out of this , $ 150 was his fixed salary so the total commission he earned was $ 1320 - $ 150 = $ 1170 he earns 10 % on the sales of first $ 10,000 which gives a commission of $ 1000 . he earns 5 % on every subsequent dollar . since he earns another $ 170 , he must have had sales of another 170 * ( 100 / 5 ) = 3400 so his total sales must have been $ 10,000 + $ 3400 = $ 13,400 a | a ) 13,400 , b ) 14,800 , c ) 16,400 , d ) 15,800 , e ) 19,600 | a | divide(add(multiply(150, divide(const_100, 5)), multiply(const_100, const_100)), multiply(10, const_100)) | divide(const_100,n5)|multiply(const_100,const_100)|multiply(n1,const_100)|multiply(n0,#0)|add(#3,#1)|divide(#4,#2) | general |
simplify : 256 x 256 - 144 x 144 | then the area is : 8 ' ' x 30 ' ' = 240 square inches , or 240 square units hence a | ['a ) 240 square units', 'b ) 180 square units', 'c ) 100 square units', 'd ) 150 square units', 'e ) 160 square units'] | a | rectangle_area(sqrt(subtract(power(30, const_2), power(8, const_2))), 8) | power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|sqrt(#2)|rectangle_area(n0,#3) | geometry |
three unbiased coins are tossed . what is the probability of getting 3 heads and 1 tail ? | "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 5 miles per hour . the time to catch up is 60 / 5 = 12 hours . in 12 hours , train a travels another 30 * 12 = 360 miles for a total of 420 miles . the answer is a ." | a ) 420 , b ) 450 , c ) 480 , d ) 510 , e ) 540 | a | multiply(divide(multiply(30, const_2), subtract(35, 30)), 35) | multiply(n0,const_2)|subtract(n1,n0)|divide(#0,#1)|multiply(n1,#2)| | physics |
what is the smallest positive integer x , such that 1,152 x is a perfect cube ? | "solution p ( none is defective ) = 21 c 2 / 25 c 2 = 7 / 10 p ( at least one is defective ) = ( 1 - 7 / 10 ) = 3 / 10 . answer a" | a ) 3 / 10 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 95 , e ) none | a | subtract(const_1, divide(choose(subtract(25, 4), const_2), choose(25, const_2))) | choose(n0,const_2)|subtract(n0,n1)|choose(#1,const_2)|divide(#2,#0)|subtract(const_1,#3)| | probability |
area of four walls of a room is 99 m 2 . the length and breadth of the room are 7.5 m and 3.5 m respectively . the height of the room is : | "28 / 3 = 9 . xxx 86 / 6 = 14 . xxx so we need to find prime numbers between 9 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b" | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | floor(const_2) | floor(const_2)| | general |
a number when divided by a certain divisor left remainder 251 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ? | "44 + 28 + 10 = 82 % 100 β 82 = 18 % 800 * 18 / 100 = 144 the answer is c ." | a ) 120 , b ) 132 , c ) 144 , d ) 156 , e ) 168 | c | subtract(800, add(add(multiply(divide(44, const_100), 800), multiply(divide(28, const_100), 800)), multiply(divide(10, const_100), 800))) | divide(n1,const_100)|divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#0)|multiply(n0,#1)|multiply(n0,#2)|add(#3,#4)|add(#6,#5)|subtract(n0,#7)| | gain |
a fruit seller had some oranges . he sells 10 % oranges and still has 360 oranges . how many oranges he had originally ? | "m = 6.0 s = 1.5 ds = 7.5 us = 4.5 as = ( 2 * 7.5 * 4.5 ) / 12 = 5.6 answer : b" | a ) 7 , b ) 5.6 , c ) 6 , d ) 9 , e ) 3 | b | divide(add(6, subtract(6, 1.5)), const_2) | subtract(n0,n1)|add(n0,#0)|divide(#1,const_2)| | general |
the population of a town is 10000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ? | "( 20 - 12 ) / ( 25 - 20 = 8 / 5 = 8 : 5 answer : a" | a ) 8 : 5 , b ) 5 : 8 , c ) 20 : 25 , d ) 12 : 20 , e ) 25 : 12 | a | divide(divide(subtract(20, 12), subtract(25, 12)), subtract(const_1, divide(subtract(20, 12), subtract(25, 12)))) | subtract(n2,n1)|subtract(n0,n1)|divide(#0,#1)|subtract(const_1,#2)|divide(#2,#3)| | other |
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 | "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 4 15 women ' s 1 day work = ( 1 / 4 - 10 / 100 ) = 3 / 20 1 woman ' s 1 day work = 1 / 100 1 woman alone can complete the work in 100 days . answer : a" | a ) 100 days , b ) 667 days , c ) 177 days , d ) 187 days , e ) 225 days | a | multiply(divide(multiply(const_1, 100), subtract(multiply(const_1, 100), multiply(10, 4))), multiply(15, 4)) | multiply(n3,const_1)|multiply(n0,n2)|multiply(n1,n2)|subtract(#0,#1)|divide(#0,#3)|multiply(#4,#2)| | physics |
a 240 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train . | cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 4 people . so $ 100 . but , he also has to put in the average for himself ( the fiveth person ) , so add $ 75 . so $ 175 is your answer . answer b | a ) $ 100 , b ) $ 175 , c ) $ 200 , d ) $ 250 , e ) $ 450 | b | add(subtract(multiply(add(4, const_1), 75), multiply(add(4, const_1), 50)), 50) | add(n2,const_1)|multiply(n1,#0)|multiply(n0,#0)|subtract(#1,#2)|add(n0,#3) | general |
34.94 + 240.016 + 23.98 = ? | "( x * 5 ) = ( 0.5 * 8 ) x = 4 / 5 x = 0.8 answer = e" | a ) a ) 1.12 , b ) b ) 1.2 , c ) c ) 1.25 , d ) d ) 0.9 , e ) e ) 0.8 | e | divide(multiply(0.5, 8), 5) | multiply(n0,n2)|divide(#0,n1)| | general |
two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days . the number of days required by 1 man to complete the work is | "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 75 + 20 ) kg = 95 kg the answer is c ." | a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg | c | add(multiply(2.5, 8), 75) | multiply(n0,n1)|add(n2,#0)| | general |
what is the smallest positive integer k such that the product of 2205 x k is a perfect square ? | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 200 resolutions . = 200 * 2 * 22 / 7 * 12.6 = 15825.6 cm = 158.256 m answer : d" | a ) 158.210 m , b ) 704 m , c ) 153.256 m , d ) 158.256 m , e ) 204 m | d | divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 12.6), const_2), 200), const_100) | add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)| | physics |
the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is : | "( 250 ) ^ 2 - ( 100 ) ^ 2 = ( 250 + 100 ) ( 250 - 100 ) = 350 x 150 = 52500 . answer is c ." | a ) 761200 , b ) 761400 , c ) 52500 , d ) 761500 , e ) none of them | c | add(multiply(250, 250), multiply(100, 100)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | general |
a certain industrial loom weaves 0.13 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ? | "let the previous year ' s height be x . 1.1 x = 143 x = 130 the answer is c ." | a ) 140 cm , b ) 136 cm , c ) 130 cm , d ) 127 cm , e ) 125 cm | c | subtract(143, divide(multiply(143, 10), const_100)) | multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)| | physics |
a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 1 , - 4 ) . what is the smallest possible area of that circle ? | "c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 35 . loss % = 15 / 50 * 100 = 30 % answer c" | a ) 45 % , b ) 23 % , c ) 30 % , d ) 60 % , e ) 56 % | c | subtract(50, 35) | subtract(n0,n1)| | gain |
two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every fourth , starting with the fourth , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ? | explanation : Γ’ Λ Ε‘ 3 / 4 a 2 = 4 Γ’ Λ Ε‘ 3 - > a = 4 answer is d | ['a ) 4 / 3 cm', 'b ) 3 / 4 cm', 'c ) 3 cm', 'd ) 4 cm', 'e ) 5 cm'] | d | sqrt(divide(multiply(4, sqrt(3)), multiply(multiply(divide(const_1, 2), divide(const_1, 2)), sqrt(3)))) | divide(const_1,n2)|sqrt(n1)|multiply(n0,#1)|multiply(#0,#0)|multiply(#3,#1)|divide(#2,#4)|sqrt(#5) | geometry |
a truck covers a distance of 288 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 90 km more than that travelled by the truck ? | "if sides are a and b , after increase sides would be 1.25 a and 1.25 b . percentage increase in area = ( 1.25 a * 1.25 b - ab ) * 100 / ab = 56.25 % answer : b" | a ) 54.25 % , b ) 56.25 $ , c ) 53.25 % , d ) 55.25 % , e ) 58.25 % | b | multiply(subtract(power(add(divide(25, const_100), const_1), const_2), const_1), const_100) | divide(n0,const_100)|add(#0,const_1)|power(#1,const_2)|subtract(#2,const_1)|multiply(#3,const_100)| | geometry |
how much is 80 % of 40 is greater than 4 / 5 of 30 ? | "let rate in r = 100 x then p = 70 x g = 100 y p = 90 y thus 70 x = 90 y or x = 1.28 y ans r = 128 y so increase = 28 % answer : a" | a ) 28 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 150 % | a | multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 30), subtract(const_100, 10)), const_100)), multiply(divide(subtract(const_100, 30), subtract(const_100, 10)), const_100)), const_100) | subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)|divide(#4,#3)|multiply(#5,const_100)| | gain |
if $ 910 are divided between worker a and worker b in the ratio 5 : 9 , what is the share that worker b will get ? | "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . β΄ discount % = [ 11 / 111 * 100 ] % = 9.9 % answer c" | a ) 10 % , b ) 10.5 % , c ) 9.9 % , d ) 12.5 % , e ) none | c | multiply(const_100, divide(add(multiply(add(const_2, const_3), const_2), 1), add(const_100, 11))) | add(const_2,const_3)|add(n0,const_100)|multiply(#0,const_2)|add(#2,n1)|divide(#3,#1)|multiply(#4,const_100)| | gain |
a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is | cost per capsule in r is 5.25 / 250 = 0.525 / 25 = 0.021 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.002 the answer is e | a ) $ 0.25 , b ) $ 0.12 , c ) $ 0.05 , d ) $ 0.03 , e ) $ 0.002 | e | subtract(divide(2.99, 130), divide(5.25, 250)) | divide(n3,n2)|divide(n1,n0)|subtract(#0,#1) | general |
what least number must be added to 9879 , so that the sum is completely divisible by 10 ? | "s : e = 1 : 3 e : m = 4 : 5 - - - - - - - - - - - - s : e : m = 4 : 12 : 15 4 / 31 * 162 = 20.9 answer : b" | a ) 10.9 , b ) 20.9 , c ) 30.9 , d ) 35 , e ) 45 | b | add(add(add(multiply(4, const_3), 4), multiply(multiply(4, const_3), add(multiply(4, const_3), 4))), 4) | multiply(n1,const_3)|add(n1,#0)|multiply(#1,#0)|add(#1,#2)|add(n1,#3)| | general |
the speed of a bus increases by 2 kmph after every one hour . if the distance travelled in the first one hour was 35 km , what was the total distance travelled in 12 hours ? | "e 1 21 ( x + y ) + 5 = 21 ( - x + y ) + 47 21 x + 21 y + 5 = - 21 x + 21 y + 47 21 x + 5 = - 21 x + 47 42 x = 42 = > x = 1" | a ) - 2 , b ) - 1 , c ) 0 , d ) 2 , e ) 1 | e | divide(add(5, 47), add(21, 21)) | add(n1,n3)|add(n0,n0)|divide(#0,#1)| | general |
3 men and 7 women can complete a work in 10 days . but 4 men and 6 women need 8 days to complete the same work . in how many days will 10 women complete the same work ? | 2 ( 7.5 + 3.5 ) Γ h = 99 2 ( 11 ) h = 99 22 h = 99 h = 99 / 22 = 9 / 2 = 4.5 m answer is d . | ['a ) 2.5 m', 'b ) 3.5 m', 'c ) 1.5 m', 'd ) 4.5 m', 'e ) 5.5 m'] | d | divide(99, add(multiply(7.5, const_2), multiply(3.5, const_2))) | multiply(n2,const_2)|multiply(n3,const_2)|add(#0,#1)|divide(n0,#2) | physics |
convert 40 miles into yards ? | "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 300 n = 22.13 or n = 22 answer : - b" | a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25 | b | subtract(add(multiply(reminder(7, 300), 3), reminder(3, 300)), reminder(1, 300)) | reminder(n1,n0)|reminder(n3,n0)|reminder(n2,n0)|multiply(n3,#0)|add(#3,#1)|subtract(#4,#2)| | general |
a taxi leaves point a 2 hours after a bus left the same spot . the bus is traveling 20 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in two hours . | "total cases : 12 ( student one has 4 options and student two has three options , 4 x 3 = 12 ) non - favourable cases : 6 ( when two students sit together . students in desk 1 and desk 2 , in desk 2 and desk 3 , in desk 3 and desk 4 ) for each of these cases there are two possibilities because the positions can be interchanged . hence 2 x 3 = 6 . so favourable cases : 12 - 6 = 6 . answer : d" | a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12 | d | permutation(subtract(4, const_1), 2) | subtract(n1,const_1)|permutation(#0,n0)| | probability |
salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 20 % vinegar , dressing p comprises what percentage of the new dressing ? | "let each side of the square be a , then area = a x a new side = 125 a / 100 = 5 a / 4 new area = ( 5 a x 5 a ) / ( 4 x 4 ) = ( 25 a Β² / 16 ) increased area = = ( 25 a Β² / 16 ) - a Β² increase % = [ ( 9 a Β² / 16 ) x ( 1 / a Β² ) x 100 ] % = 56.25 % answer : b" | a ) 56.29 % , b ) 56.25 % , c ) 56.95 % , d ) 53.25 % , e ) 36.25 % | b | square_area(add(const_1, divide(25, const_100))) | divide(n0,const_100)|add(#0,const_1)|square_area(#1)| | gain |
usc invited each south carolina high school to send up to 39 students to watch a football game . a section which has 199 seats in each row is reserved for those students . what is the least number of rows needed to guarantee that if 2006 students show up , then all students from the same high school can be seated in the same row ? | "explanation : 720 - - - 280 100 - - - ? = > 38.9 % answer : c" | a ) 15 % , b ) 25 % , c ) 38.9 % , d ) 45 % , e ) 35 % | c | subtract(multiply(divide(const_100, 720), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100) | add(const_2,const_3)|divide(const_100,n0)|multiply(#0,const_2)|multiply(#2,const_100)|multiply(#1,#3)|subtract(#4,const_100)| | gain |
one - third of 600 is what percent of 120 ? | "the mean of numbers 28 , x , 42 , 78 and 104 is 62 : 28 + x + 42 + 78 + 82 + 104 = 62 * 6 - - > x = 38 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 511 + 1023 + 38 ) / 5 = 391 . answer : c ." | a ) 395 , b ) 275 , c ) 391 , d ) 415 , e ) 365 | c | divide(add(add(add(add(subtract(multiply(104, add(const_4, const_1)), add(add(add(28, 42), 78), 82)), 62), 128), 255), 511), add(const_4, const_1)) | add(const_1,const_4)|add(n0,n1)|add(n2,#1)|multiply(n4,#0)|add(n3,#2)|subtract(#3,#4)|add(n5,#5)|add(n6,#6)|add(n7,#7)|add(n8,#8)|divide(#9,#0)| | general |
what is the average of xx , 2 x 2 x , and 66 ? | machine b produces 100 part in 80 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 80 / 2 = 40 minutes . now , machine a produces 100 parts in 40 minutes which is 100 / 40 = 10 / 4 parts / minute . 10 / 4 parts x a total of 20 minutes = 10 / 4 * 20 = 50 e | a ) 60 , b ) 80 , c ) 70 , d ) 40 , e ) 50 | e | multiply(multiply(divide(100, 80), const_2), 20) | divide(n0,n2)|multiply(#0,const_2)|multiply(n3,#1) | gain |
if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is ? | "how to deal with inequalities involving absolute values ? first example shows us the so callednumber case in this case we have | y + 3 | β€ 3 which is generalized | something | β€ some number . first we solve as if there were no absolute value brackets : y + 3 β€ 3 y β€ 0 so y is 0 or negative second scenario - remove the absolute value brackets . put a negative sign around the other side of the inequality , andflip the sign : y + 3 > = - 3 y > = - 6 therefore we have a possible range for y : - 6 = < y < = 0 ok , so far so good , we ' re half way through . what about x ? here ' s the formula : 2 y β 3 x + 6 = 0 , rewrite it as 2 y + 6 = 3 x . you can say that 2 y + 6 is a multiple of 3 ( = 3 x ) . so all values which must be integer must also satisfy this constraint . i ' m just saying that , so it ' s easier to evaluate all the possible numbers ( - 6 , - 3 , 0 ) . if you plug in y = 0 , x will be 2 and xy = 0 as the lowest possible value t . hence , answer choice c is the one to go ." | a ) - 12 , b ) - 3 , c ) 0 , d ) 2 , e ) none of the above | c | multiply(divide(add(6, multiply(negate(add(3, 3)), 2)), 3), negate(add(3, 3))) | add(n0,n0)|negate(#0)|multiply(n2,#1)|add(n4,#2)|divide(#3,n0)|multiply(#4,#1)| | general |
when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.12 , what is the value of y ? | "this is easiest to solve with a bell - curve histogram . m here is equal to Β΅ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 66 % is one st . dev , then on either side of m we have 66 / 2 = 33 % . so , 33 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 33 = 83 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 83 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it c" | a ) 16 % , b ) 32 % , c ) 83 % , d ) 84 % , e ) 92 % | c | subtract(const_100, divide(subtract(const_100, 66), const_2)) | subtract(const_100,n0)|divide(#0,const_2)|subtract(const_100,#1)| | general |
the sum of two numbers is 528 and their h . c . f is 33 . the number of pairs of numbers satisfying the above condition is | "total = english + german - both + neither - - > 54 = english + 22 - 12 + 0 - - > english = 44 - - > only english = english - both = 44 - 12 = 32 . answer : e ." | a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32 | e | subtract(subtract(add(54, 12), 22), 12) | add(n0,n1)|subtract(#0,n2)|subtract(#1,n1)| | other |
there is enough provisions for 600 men in an army camp for 25 days . if there were 300 men less , how long will the provision last ? | the answer is 12 rows . if 59 schools send 34 students each , then we can sit at most 5 groups of students in the same row , so we will need 12 rows . next , 12 rows are sufficient . assume that this is not the case . suppose the groups of students are seated like this : first the largest group , then the second largest group , then the third largest group , etc . suppose we run out of space - there are not enough seats in any row to seat together the next group . suppose the first group that can not be seated together is the kth group and it consists of n students . then k 61 since any row fits at least 5 groups . also , n 2006 / k 2006 / 61 < 33 ( all groups already seated are no smaller than the kth group ) . so , n 32 . since there is not enough space in any of the 12 rows to seat the kth group , then there must be at least 168 students seated in each of the 12 rows . now , 12 Γ 168 = 2016 > 2006 a contradiction . so , 12 rows are sufficient . correct answer b | a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15 | b | add(divide(2006, 199), const_2) | divide(n2,n1)|add(#0,const_2) | physics |
a no . when divided by 221 gives a remainder 43 , what remainder will beobtained by dividing the same number 19 ? | let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 6 ) ( y + 6 ) = m and so ( 2 ) xy + 6 x + 6 y + 36 = m + 64 let ' s subtract equation ( 1 ) from equation ( 2 ) . 4 x + 4 y + 32 = 64 2 x + 2 y = 16 , which is the perimeter of the photograph . the answer is a . | ['a ) 16', 'b ) 24', 'c ) 32', 'd ) 40', 'e ) 48'] | a | divide(subtract(64, subtract(power(multiply(3, const_2), const_2), power(multiply(1, const_2), const_2))), const_2) | multiply(n1,const_2)|multiply(n0,const_2)|power(#0,const_2)|power(#1,const_2)|subtract(#2,#3)|subtract(n2,#4)|divide(#5,const_2) | geometry |
the speed of a boat in still water in 22 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is : | "the first digit and last digit are the same so the 3 possibilities are 4 , 6 , or 8 . the second and third digits can be any digit from 0 to 9 . the total number of palindromic integers is 3 * 10 * 10 = 300 the answer is c ." | a ) 200 , b ) 216 , c ) 300 , d ) 400 , e ) 2,500 | c | multiply(multiply(subtract(6, const_4), const_10), const_10) | subtract(n2,const_4)|multiply(#0,const_10)|multiply(#1,const_10)| | general |
if 5 machines can produce 20 units in 10 hours , how long would it take 25 to produce 100 units ? | unit digit in the given product = unit digit in 6 * 2 * 1 * 4 = 8 answer is a | a ) 8 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | subtract(multiply(multiply(multiply(4556, 3432), 4581), 2784), subtract(multiply(multiply(multiply(4556, 3432), 4581), 2784), add(const_4, const_4))) | add(const_4,const_4)|multiply(n0,n1)|multiply(n2,#1)|multiply(n3,#2)|subtract(#3,#0)|subtract(#3,#4) | general |
a train is 410 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length | "k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . c" | a ) 0 , b ) 1 , c ) 0 , d ) 54 , e ) can not be determined | c | 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 |
what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 450 ? | "explanation : let the length of train be l m . acc . to question ( 276 + l ) / 20 = l / 8 2208 + 8 l = 20 l l = 2208 / 12 = 184 m answer a" | a ) 184 , b ) 176 , c ) 175 , d ) 96 , e ) none of these | a | multiply(divide(276, subtract(20, 8)), 8) | subtract(n2,n0)|divide(n1,#0)|multiply(n0,#1)| | physics |
what quantity of water should be added to reduce 20 liters of 80 % acidic liquid to 20 % acidic liquid ? | "total movies submitted are 760 . as per question we need to take 1 / 4 of 760 to be considered for top 10 movies = 190 approximate the value we 190 . imo option b is the correct answer . . ." | a ) 191 , b ) 190 , c ) 193 , d ) 212 , e ) 213 | b | divide(760, 4) | divide(n3,n1)| | general |
2 cow β s and 5 goats are brought for rs . 1050 . if the average price of a goat be rs . 90 . what is the average price of a cow . | 4 * 9 = 36 . answer is d . | a ) 22 , b ) 65 , c ) 12 , d ) 36 , e ) 10 | d | multiply(9, 4) | multiply(n0,n2) | general |
the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 432 . find the principal ? | perimeter = distance covered in 8 min = ( 12000 / 60 * 8 ) m = 1600 m let , length = 3 x meters and breadth = 2 x meters then , 2 ( 3 x + 2 x ) = 1600 or x = 160 therefore , length = 480 m and breadth = 320 m therefore , area = ( 480 * 320 ) m 2 = 153600 m 2 answer : c | ['a ) 1536 m 2', 'b ) 15360 m 2', 'c ) 153600 m 2', 'd ) 163600 m 2', 'e ) none of these'] | c | multiply(multiply(divide(multiply(8, divide(multiply(12, const_1000), multiply(multiply(const_3, const_2), const_10))), const_10), 2), multiply(divide(multiply(8, divide(multiply(12, const_1000), multiply(multiply(const_3, const_2), const_10))), const_10), 3)) | multiply(n0,const_1000)|multiply(const_2,const_3)|multiply(#1,const_10)|divide(#0,#2)|multiply(n1,#3)|divide(#4,const_10)|multiply(n3,#5)|multiply(n2,#5)|multiply(#6,#7) | physics |
the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee β s report , what is the probability that the two members selected will both be social teachers ? | "12519 x 9999 = 12519 x ( 10000 - 1 ) = 12519 x 10000 - 12519 x 1 = 125190000 - 12519 = 125177481 a" | a ) 125177481 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 477899932 | a | multiply(subtract(9999, const_4), 12519) | subtract(n1,const_4)|multiply(#0,n0)| | general |
simplify : 250 x 250 - 100 x 100 | "wc = 2 : 1 2 x + x = 1 / 9 x = 1 / 27 = > 27 days answer : e" | a ) 17 days , b ) 12 days , c ) 29 days , d ) 25 days , e ) 27 days | e | multiply(divide(multiply(9, add(const_2, const_1)), const_2), const_2) | add(const_1,const_2)|multiply(n0,#0)|divide(#1,const_2)|multiply(#2,const_2)| | physics |
a certain company β s profit in 1996 was 25 percent greater than its profit in 1995 , and its profit in 1997 was 30 percent greater than its profit in 1996 . the company β s profit in 1997 was what percent greater than its profit in 1995 ? | "( 875 233 / 899 ) Γ 899 ( 786625 + 233 ) / 899 Γ 899 786858 / 899 Γ 899 786858 c" | a ) 786845 , b ) 786857 , c ) 786858 , d ) 786859 , e ) 786860 | c | multiply(add(divide(233, 899), 875), 899) | divide(n1,n2)|add(n0,#0)|multiply(#1,n2)| | general |
the total cost of 100 paper plates and 200 paper cups is $ 8.00 at the same rates what is the total cost of 20 of the plates and 40 of the cups ? | "answer : aalgebraically , the question looks like this : 2.5 = 0.35 x + 0.25 ythere are six possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 4 pens : $ 1.40 5 pens : $ 1.75 and 1 pencils for $ 0.25 each . that ' s 5 pens and 1 pencils for a total of 6 pens and pencils . choice ( a ) is correct ." | a ) 6 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | a | multiply(divide(2.00, add(0.35, 0.25)), const_2) | add(n0,n1)|divide(n2,#0)|multiply(#1,const_2)| | other |
in a renowned city , the average birth rate is 9 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day . | "speed = [ 108 x 5 / 18 ] m / sec = 30 m / sec time = 10 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 10 = > 130 + x = 300 = > x = 170 m . answer : d" | a ) 200 m , b ) 225 m , c ) 245 m , d ) 170 m , e ) 240 m | d | subtract(multiply(divide(multiply(108, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 130) | speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)| | physics |
15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 4 hrs . each would it take for 21 women if 3 women do as much work as 2 men ? | "lcm ( 7 , 8,24 ) = 24 x 7 = 168 so the least divisible number is 168 , and the number we are looking for is 168 - 9 = 159 . the answer is c ." | a ) 143 , b ) 150 , c ) 159 , d ) 168 , e ) 177 | c | subtract(lcm(24, 8), 9) | lcm(n2,n3)|subtract(#0,n0)| | general |
if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 990 , what is the least possible value of n ? | "required sum = ( 53 + 59 + 61 + 67 ) = 240 note : 1 is not a prime number answer d" | a ) 249 , b ) 248 , c ) 246 , d ) 240 , e ) 241 | d | add(add(add(add(add(add(const_12, const_2), const_1), add(add(const_12, const_2), add(add(add(add(add(const_2, const_4), const_4), subtract(const_10, const_1)), add(add(const_2, const_4), const_4)), add(const_10, const_2)))), add(add(add(const_12, const_2), const_1), const_1)), 50), add(const_2, const_4)) | add(const_12,const_2)|add(const_2,const_4)|add(const_10,const_2)|subtract(const_10,const_1)|add(#0,const_1)|add(#1,const_4)|add(#5,#3)|add(#4,const_1)|add(#6,#5)|add(#8,#2)|add(#0,#9)|add(#4,#10)|add(#11,#7)|add(n0,#12)|add(#13,#1)| | general |
the present population of a town is 60,000 . the population increases annually at 10 % . find the population after 3 years . | "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 150 / 2 = 75 sq m l b = 75 i . e . , l * l / 3 = 75 l 2 = 225 = > l = 15 answer : b" | a ) 65 , b ) 15 , c ) 18 , d ) 16 , e ) 14 | b | multiply(sqrt(divide(divide(150, 2), const_3)), const_3) | divide(n1,n2)|divide(#0,const_3)|sqrt(#1)|multiply(#2,const_3)| | gain |
a pyramid has a square base of 6 cm , and the four lateral faces are four congruent equilateral triangles . what is the total surface area of the pyramid in square cm ? | "let the time taken be = x one way distance = 66 x total distance traveled = 2 * 66 x = 132 x total time taken = x + 2 x = 3 x average speed = 132 x / 3 x = 44 answer : e" | a ) 24 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 . | e | inverse(add(inverse(66), divide(inverse(66), const_2))) | inverse(n0)|divide(#0,const_2)|add(#1,#0)|inverse(#2)| | physics |
if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 690 , what is the least possible value of n ? | "along one edge , the number of small cubes that can be cut = 550 / 110 = 5 along each edge 5 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 5 * 5 * 5 = 125 answer : a" | a ) 125 , b ) 127 , c ) 152 , d ) 140 , e ) 190 | a | divide(power(power(5.5, const_2), const_3), power(5.5, const_3)) | power(n0,const_2)|power(n0,const_3)|power(#0,const_3)|divide(#2,#1)| | physics |
a block of wood has dimensions 10 cm x 10 cm x 90 cm . the block is painted red and then cut evenly at the 45 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ? | "for 100 - 40 - 10 = 50 pages only cost is 5 $ per page for the first time page is typed - 50 * 5 = 250 $ ; for 40 pages the cost is : first time 5 $ + 2 $ of the first revision - 40 * ( 5 + 2 ) = 280 $ ; for 10 pages the cost is : first time 5 $ + 2 $ of the first revision + 2 $ of the second revision - 10 ( 5 + 2 + 2 ) = 90 $ ; total : 250 + 280 + 90 = 620 $ . answer : b ." | a ) $ 430 , b ) $ 620 , c ) $ 650 , d ) $ 680 , e ) $ 770 | b | add(add(multiply(100, 5), multiply(40, 2)), multiply(multiply(10, 2), const_2)) | multiply(n0,n2)|multiply(n1,n3)|multiply(n1,n4)|add(#0,#1)|multiply(#2,const_2)|add(#3,#4)| | general |