Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
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there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle ? | let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . a... | ['a ) 6', 'b ) 5', 'c ) 8', 'd ) 6', 'e ) 3'] | c | add(divide(divide(square_edge_by_area(784), const_2), divide(add(const_3, const_4), const_3)), const_2) | add(const_3,const_4)|square_edge_by_area(n0)|divide(#1,const_2)|divide(#0,const_3)|divide(#2,#3)|add(#4,const_2) | geometry |
for any number z , z * is defined as the greatest positive even integer less than or equal to z . what is the value of 5.2 – 5.2 * ? | "since z * is defined as the greatest positive even integer less than or equal to z , then 5.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 5.2 – 5.2 * = 5.2 - 4 = 1.2 answer : b ." | a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0 | b | subtract(5.2, floor(5.2)) | floor(n0)|subtract(n0,#0)| | general |
if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 17,000 is invested at the same interest rate , what is the interest from the investment ? | "5000 * r * t / 100 = 250 rt = 5 17000 * 5 / 100 = 850 answer is d" | a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 850 , e ) $ 900 | d | divide(multiply(250, multiply(multiply(const_2, const_100), const_100)), divide(multiply(multiply(const_2, const_100), const_100), const_4)) | multiply(const_100,const_2)|multiply(#0,const_100)|divide(#1,const_4)|multiply(n1,#1)|divide(#3,#2)| | gain |
30 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ? | binders books days 30 1400 21 x 1600 20 x / 30 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 36 answer : d | a ) 87 , b ) 18 , c ) 17 , d ) 36 , e ) 10 | d | divide(divide(1600, 20), divide(1400, multiply(30, 21))) | divide(n3,n4)|multiply(n0,n2)|divide(n1,#1)|divide(#0,#2) | physics |
if the radius of a circle is decreased 30 % , what happens to the area ? | "area of square = pi * radius ^ 2 new radius = 0.7 * old radius so new area = ( 0.7 ) ^ 2 old area = > 0.49 of old area = > 49 % old area ans : a" | a ) 51 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease | a | subtract(const_100, multiply(power(divide(30, const_100), const_2), const_100)) | divide(n0,const_100)|power(#0,const_2)|multiply(#1,const_100)|subtract(const_100,#2)| | geometry |
find the amount on rs . 5000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ? | "5000 * 104 / 100 * 105 / 100 = > 5460 answer : c" | a ) 3377 , b ) 2678 , c ) 5460 , d ) 1976 , e ) 1671 | c | divide(multiply(divide(multiply(5000, add(const_100, 4)), const_100), add(const_100, 5)), const_100) | add(n3,const_100)|add(n2,const_100)|multiply(n0,#1)|divide(#2,const_100)|multiply(#0,#3)|divide(#4,const_100)| | gain |
the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 ... | "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 410 = 3690 salary of the new supervisor = 3690 â ˆ ’ 3000 = 690 answer : b" | a ) 233 , b ) 690 , c ) 287 , d ) 771 , e ) 191 | b | subtract(multiply(410, 9), subtract(multiply(430, 9), 870)) | multiply(n6,n7)|multiply(n1,n6)|subtract(#1,n5)|subtract(#0,#2)| | general |
if there are 4 peanuts in a box and mary puts 6 more peanuts inside , how many peanuts are in the box ? | 6 + 4 = 10 correct answer is c ) 10 | a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | c | add(4, 6) | add(n0,n1) | general |
how many 3 digit positive integers exist that when divided by 7 leave a remainder of 5 ? | "explanatory answer step 1 : find the first and last term of the series the smallest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 103 . the largest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 999 . the series of numbers that satisfy the condition that the... | a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129 | e | divide(subtract(subtract(multiply(const_100, const_10), const_1), add(multiply(add(const_10, const_4), 7), 5)), 7) | add(const_10,const_4)|multiply(const_10,const_100)|multiply(n1,#0)|subtract(#1,const_1)|add(n2,#2)|subtract(#3,#4)|divide(#5,n1)| | general |
if ( 10 ^ 4 * 3.456789 ) ^ 9 is written as a single term , how many digits would be to the right of the decimal place ? | "3.456789 ^ 9 has 6 * 9 = 54 decimal places . 10 ^ 36 moves the decimal place to the right 36 places . ( 10 ^ 4 * 3.456789 ) ^ 9 has 54 - 36 = 18 digits after the decimal point . the answer is c ." | a ) 6 , b ) 12 , c ) 18 , d ) 32 , e ) 48 | c | multiply(9, const_2) | multiply(n3,const_2)| | general |
if c is 30 % of a and 25 % of b , what percent of a is b ? | "answer = c 30 a / 100 = 25 b / 100 b = 30 a / 25 = 120 a / 100 = 120 %" | a ) 2.5 % , b ) 15 % , c ) 120 % , d ) 35 % , e ) 250 % | c | multiply(divide(divide(30, const_100), divide(25, const_100)), const_100) | divide(n0,const_100)|divide(n1,const_100)|divide(#0,#1)|multiply(#2,const_100)| | gain |
find the principal which yields a simple interest of rs . 20 and compound interest of rs . 24 in two years , at the same percent rate per annum ? | "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 24 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 24 – 20 ) / 20 ] * 100 = 20 % p . a . let the principal be rs . x time = t = 2 years % rate = 20 % p . a . si = ( prt / 100 ) 20 = ( x * 20 * 2 ) / 100 x = rs . 50 an... | a ) s . 50 , b ) s . 48 , c ) s . 42 , d ) s . 20 , e ) s . 60 | a | divide(multiply(subtract(24, 20), const_100), const_2) | subtract(n1,n0)|multiply(#0,const_100)|divide(#1,const_2)| | gain |
the moon revolves around the earth at a speed of approximately 0.9 kilometers per second . this approximate speed is how many kilometers per hour ? | "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 0.9 * 3600 = 3240 kilometers per hour . option c is correct" | a ) 60 , b ) 61.2 , c ) 3240 , d ) 3,600 , e ) 3,672 | c | multiply(0.9, const_3600) | multiply(n0,const_3600)| | physics |
john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 60 miles per hour , what is v in miles per hour ? | "let distance be d . we can find the total time & equate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 60 = > v = 30 answer : a" | a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70 | a | multiply(subtract(const_100, 80), subtract(divide(const_100, 60), divide(80, 80))) | divide(const_100,n2)|divide(n0,n0)|subtract(const_100,n0)|subtract(#0,#1)|multiply(#2,#3)| | physics |
the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 150 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ? | "let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 150 / ( 150 + x ) = 5 / 6 x = 30 the answer is a ." | a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90 | a | subtract(divide(multiply(divide(150, 5), 12), 2), 150) | divide(n2,n0)|multiply(n1,#0)|divide(#1,n4)|subtract(#2,n2)| | other |
divide rs . 1300 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ? | "a + b + c = 1300 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1300 = > 325 answer : e" | a ) 346 , b ) 368 , c ) 375 , d ) 337 , e ) 325 | e | divide(1300, const_3) | divide(n0,const_3)| | general |
a boy is travelling from his home to school at 4 km / hr and reached 7 min late . next day he traveled at 8 km / hr and reached 8 min early . distance between home and school ? | "let the distance be x t 1 = x / 4 hr t 2 = x / 8 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 4 - x / 8 = 1 / 4 x / 8 = 1 / 4 x = 2 km answer is a" | a ) 2 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km | a | divide(add(divide(7, const_60), divide(8, const_60)), divide(const_1, 8)) | divide(n1,const_60)|divide(n3,const_60)|divide(const_1,n2)|add(#0,#1)|divide(#3,#2)| | physics |
a , b and c , each working alone can complete a job in 2 , 4 and 6 days respectively . if all three of them work together to complete a job and earn $ 2500 , what will be c ' s share of the earnings ? | "the dollars earned will be in the same ratio as amount of work done 1 day work of c is 1 / 6 ( or 2 / 12 ) 1 day work of the combined workforce is ( 1 / 2 + 1 / 4 + 1 / 6 ) = 11 / 12 c ' s contribution is 2 / 9 of the combined effort translating effort to $ = 6 / 11 * 2500 = $ 1363.63 hence : b" | a ) $ 1206.60 , b ) $ 1363.63 , c ) $ 1263.63 , d ) $ 1463.53 , e ) $ 1163.03 | b | multiply(2500, divide(inverse(4), add(inverse(6), add(inverse(2), inverse(4))))) | inverse(n1)|inverse(n0)|inverse(n2)|add(#1,#0)|add(#3,#2)|divide(#0,#4)|multiply(n3,#5)| | physics |
according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 5 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ? | orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 5 oz can = 300 oz / 5 oz = 60 answer d , 60 cans | a ) 25 , b ) 34 , c ) 50 , d ) 60 , e ) 100 | d | divide(multiply(6, 200), divide(200, const_10)) | divide(n2,const_10)|multiply(n2,n3)|divide(#1,#0) | general |
each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes m... | if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 30 boxes , 6 are 10 - pound boxes and 24 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 16 , the ratio of 10 - pound boxes : 20 - pound boxes should be 2 : 3 . the n... | a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 21 | c | divide(subtract(add(multiply(10, divide(subtract(multiply(20, 30), multiply(30, 18)), subtract(20, 10))), multiply(20, subtract(30, divide(subtract(multiply(20, 30), multiply(30, 18)), subtract(20, 10))))), multiply(30, 16)), subtract(20, 16)) | multiply(n0,n2)|multiply(n0,n3)|multiply(n0,n4)|subtract(n2,n1)|subtract(n2,n4)|subtract(#0,#1)|divide(#5,#3)|multiply(n1,#6)|subtract(n0,#6)|multiply(n2,#8)|add(#7,#9)|subtract(#10,#2)|divide(#11,#4) | general |
two pipes can fill a tank in 18 minutes and 15 minutes . an outlet pipe can empty the tank in 54 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ? | "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 15 - 1 / 54 = ( 15 + 18 - 5 ) / 270 = 28 / 270 = 14 / 135 so , the tank becomes full in 6 minutes . answer : d" | a ) 30 minutes , b ) 17 minutes , c ) 15 minutes , d ) 6 minutes , e ) 12 minutes | d | subtract(add(divide(const_1, 18), divide(const_1, 15)), divide(const_1, 54)) | divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|subtract(#3,#2)| | physics |
how many bricks each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall 8 m x 6 m x 22.5 m | "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 25 x 11.25 x 6 ) = 6400 answer : c" | a ) 5600 , b ) 600 , c ) 6400 , d ) 7200 , e ) none of these | c | divide(multiply(multiply(8, 6), 22.5), divide(divide(multiply(multiply(25, 11.25), 6), const_100), const_100)) | multiply(n3,n4)|multiply(n0,n1)|multiply(n5,#0)|multiply(n2,#1)|divide(#3,const_100)|divide(#4,const_100)|divide(#2,#5)| | physics |
a prize of $ 500 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ? | total value of the prize = $ 500 number of people = 20 2 / 5 of 500 ( = $ 200 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 500 - 200 = $ 300 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ ... | a ) $ 160 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 360 | a | subtract(subtract(500, divide(multiply(500, 2), 5)), multiply(subtract(subtract(20, divide(multiply(20, 3), 5)), const_1), 20)) | multiply(n0,n3)|multiply(n1,n5)|divide(#0,n4)|divide(#1,n4)|subtract(n0,#2)|subtract(n1,#3)|subtract(#5,const_1)|multiply(n1,#6)|subtract(#4,#7) | general |
two trains , each 100 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ? a . 30 km / hr b . 45 km / hr | let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 8 = 3 x = > x = 25 / 3 . so , speed of the faster train = 50 / 3 = 50 / 3 * 18 / 5 = 60 km / hr . answer : c | a ) 11 , b ) 78 , c ) 60 , d ) 28 , e ) 81 | c | divide(multiply(divide(divide(add(100, 100), 8), const_3), const_2), const_0_2778) | add(n0,n0)|divide(#0,n1)|divide(#1,const_3)|multiply(#2,const_2)|divide(#3,const_0_2778) | physics |
a car going at 40 miles per hour set out on an 90 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ? | "let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 40 m per hour = 1.5 hours distance travelled by car a = 40 * 1.5 = 60 miles since car b catches up car a at 10 : 30 , time = 90 mins = 3 / 2 hour speed of car b = 60 / ( 3 / 2 ) = 90 miles per hour answer ... | a ) 45 , b ) 50 , c ) 53 , d ) 55 , e ) 90 | e | divide(90, divide(add(multiply(subtract(10, 9), const_60), subtract(40, 10)), const_60)) | subtract(n4,n2)|subtract(n0,n4)|multiply(#0,const_60)|add(#2,#1)|divide(#3,const_60)|divide(n1,#4)| | physics |
how many bricks each measuring 30 cm x 12 cm x 10 cm , will be needed to build a wall 6 m x 4 m x 20.5 m | explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 600 x 400 x 20.5 ) / ( 30 x 12 x 10 ) = 1366 answer : b | a ) 5655 , b ) 1366 , c ) 6444 , d ) 7266 , e ) none of these | b | divide(multiply(multiply(6, 4), 20.5), divide(divide(multiply(multiply(30, 12), 10), const_100), const_100)) | multiply(n3,n4)|multiply(n0,n1)|multiply(n5,#0)|multiply(n2,#1)|divide(#3,const_100)|divide(#4,const_100)|divide(#2,#5) | physics |
a , b and c can do a work in 6 , 8 and 12 days respectively doing the work together and get a payment of rs . 1800 . what is b ’ s share ? | c 600 wc = 1 / 6 : 1 / 8 : 1 / 12 = > 4 : 3 : 2 3 / 9 * 1800 = 600 | a ) 300 , b ) 245 , c ) 600 , d ) 743 , e ) 215 | c | multiply(1800, divide(inverse(8), add(inverse(12), add(inverse(6), inverse(8))))) | inverse(n1)|inverse(n0)|inverse(n2)|add(#1,#0)|add(#3,#2)|divide(#0,#4)|multiply(n3,#5) | physics |
how many positive integers less than 50 have a reminder 01 when divided by 4 ? | "1 also gives the remainder of 1 when divided by 4 . so , there are total of 13 numbers . answer : a ." | a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17 | a | divide(factorial(subtract(add(const_4, 01), const_1)), multiply(factorial(01), 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 |
the proportion of water to alcohol in solution a is 2 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ? | "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 3 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 6 + 3 v / 10 = 14 v / 30 = 7 v / 15 . the concentration of alcohol is 7 / 15 = 46.7 % the answer is a ." | a ) 46.7 % , b ) 47.3 % , c ) 48.4 % , d ) 50.6 % , e ) 51.8 % | a | multiply(divide(add(1, 3), add(add(2, 2), add(1, 3))), const_100) | add(n1,n3)|add(n0,n2)|add(#1,#0)|divide(#0,#2)|multiply(#3,const_100)| | general |
a worker makes a toy in every 2 h . if he works for 100 h , then how many toys will he make ? | "no . of toys = 100 / 2 = 50 answer : c" | a ) 40 , b ) 54 , c ) 50 , d ) 39 , e ) none | c | divide(100, 2) | divide(n1,n0)| | physics |
a book is bought for $ 32 and sold for $ 56 . what is the profit in percentage ? | 56 / 32 = 1.75 the answer is c . | a ) 15 , b ) 35 , c ) 75 , d ) 25 , e ) 85 | c | multiply(divide(subtract(56, 32), 32), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100) | gain |
an alloy weighing 24 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ? | "in 24 ounces , gold is 24 * ( 70 / 100 ) = 16.8 ounces . now we add x ounces of pure gold to make it 90 % gold . so 16.8 + x = ( 24 + x ) * 90 / 100 = > x = 48 . answer is e ." | a ) 6 , b ) 9 , c ) 12 , d ) 24 , e ) 48 | e | divide(multiply(divide(90, const_100), 24), divide(70, const_100)) | divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|divide(#2,#1)| | gain |
the youngest of 4 children has siblings who are 3 , 5 , and 8 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 20 , what is the age of the youngest sibling ? | "x + ( x + 3 ) + ( x + 5 ) + ( x + 8 ) = 80 4 x + 16 = 80 4 x = 64 x = 16 the answer is c ." | a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18 | c | divide(subtract(multiply(4, 20), add(add(4, 5), 8)), 4) | add(n0,n2)|multiply(n0,n5)|add(n3,#0)|subtract(#1,#2)|divide(#3,n0)| | general |
on a map the distance between two mountains is 310 inches . the actual distance between the mountains is 136 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 ? | "explanation : since 310 inch = 136 km so 1 inch = 136 / 310 km so 34 inch = ( 136 ã — 34 ) / 310 = 14.91 km answer : c" | a ) 14.83 , b ) 14.81 , c ) 14.91 , d ) 14.82 , e ) 14.12 | c | divide(multiply(34, 136), 310) | multiply(n1,n2)|divide(#0,n0)| | physics |
brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 100 meters . they next meet after sally has run 100 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ? | "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 100 meters , thus second time she runs 2 * 100 = 200 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 100 meters , thu... | a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500 | b | add(multiply(const_2, 100), 100) | multiply(n0,const_2)|add(n1,#0)| | physics |
for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 3 ” 3 ? | "3 ” 3 = 9 - 3 = 6 answer : a" | a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0 | a | subtract(power(3, 2), 3) | power(n2,n0)|subtract(#0,n1)| | general |
a river 3 m deep and 32 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ? | "( 2000 * 3 * 32 ) / 60 = 3200 m 3 answer : b" | a ) 4500 , b ) 3200 , c ) 3400 , d ) 2761 , e ) 2882 | b | divide(multiply(multiply(3, 32), multiply(2, const_1000)), multiply(const_1, const_60)) | multiply(n0,n1)|multiply(n2,const_1000)|multiply(const_1,const_60)|multiply(#0,#1)|divide(#3,#2)| | physics |
a factory produces 7500 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ? | "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 7500 / 4 = 1875 toys correct answer d" | a ) 4436 toys , b ) 5487 toys , c ) 6113 toys , d ) 1875 toys , e ) 1375 toys | d | divide(7500, 5) | divide(n0,n1)| | physics |
if a 7 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ? | the area a of the large cube is 7 * 7 * 6 = 294 square cm . the area of the 343 small cubes is 7 * 7 * 7 * 6 = 7 a , an increase of 600 % . the answer is d . | ['a ) 140 %', 'b ) 350 %', 'c ) 450 %', 'd ) 600 %', 'e ) 700 %'] | d | multiply(const_100, divide(multiply(surface_cube(1), surface_cube(7)), surface_cube(7))) | surface_cube(n1)|surface_cube(n0)|multiply(#0,#1)|divide(#2,#1)|multiply(#3,const_100) | geometry |
a student chose a number , multiplied it by 4 , then subtracted 142 from the result and got 110 . what was the number he chose ? | "let x be the number he chose , then 4 ⋅ x − 142 = 110 4 x = 252 x = 63 correct answer e" | a ) 58 , b ) 59 , c ) 60 , d ) 62 , e ) 63 | e | divide(add(110, 142), 4) | add(n1,n2)|divide(#0,n0)| | general |
a merchant purchased a jacket for $ 56 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 30 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this ... | "actual cost = $ 56 sp = actual cost + mark up = actual cost + 30 % sp = 56 * 100 / 70 on sale sp = 80 / 100 ( 56 * 100 / 70 ) = 64 gross profit = $ 8 answer is b" | a ) $ 0 , b ) $ 8 , c ) $ 4 , d ) $ 12 , e ) $ 15 | b | subtract(multiply(divide(56, subtract(const_1, divide(30, const_100))), subtract(const_1, divide(20, const_100))), 56) | divide(n1,const_100)|divide(n2,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|divide(n0,#2)|multiply(#4,#3)|subtract(#5,n0)| | gain |
a and b can do a piece of work in 3 days , b and c in 4 days , c and a in 6 days . how long will c take to do it ? | "2 c = ¼ + 1 / 6 – 1 / 3 = 1 / 12 c = 1 / 24 = > 24 days answer : c" | a ) 33 , b ) 77 , c ) 24 , d ) 55 , e ) 71 | c | divide(multiply(3, const_3), subtract(divide(add(divide(multiply(3, const_3), 6), add(divide(multiply(3, const_3), 3), divide(multiply(3, const_3), 4))), const_2), divide(multiply(3, const_3), 3))) | multiply(n0,const_3)|divide(#0,n0)|divide(#0,n1)|divide(#0,n2)|add(#1,#2)|add(#4,#3)|divide(#5,const_2)|subtract(#6,#1)|divide(#0,#7)| | physics |
how many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr | "explanation : relative speed = 63 - 3 = 60 km / hr = 60 * ( 5 / 18 ) = 50 / 3 m / sec time taken to pass the man will be 500 â ˆ — 3 / 50 = 30 seconds answer is c" | a ) 25 seconds , b ) 28 seconds , c ) 30 seconds , d ) 35 seconds , e ) 40 seconds | c | multiply(multiply(subtract(divide(500, multiply(subtract(63, 3), const_0_2778)), const_1), const_10), const_2) | subtract(n2,n1)|multiply(#0,const_0_2778)|divide(n0,#1)|subtract(#2,const_1)|multiply(#3,const_10)|multiply(#4,const_2)| | physics |
the current in a river is 3 mph . a boat can travel 21 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ? | "upstream speed = 21 - 3 = 18 mph downstream speed = 21 + 3 = 24 mph d / 18 + d / 24 = 10 hours solving for d we get d = 102.8 answer : d" | a ) 69 miles , b ) 88 miles , c ) 96 miles , d ) 102.8 miles , e ) 112 miles | d | divide(multiply(multiply(subtract(21, 3), add(21, 3)), 10), add(add(21, 3), subtract(21, 3))) | add(n0,n1)|subtract(n1,n0)|add(#0,#1)|multiply(#0,#1)|multiply(n2,#3)|divide(#4,#2)| | physics |
if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 180 pounds . what is leo ' s current weight ? | l + k = 180 and so k = 180 - l l + 10 = 1.5 k = 1.5 ( 180 - l ) 2.5 l = 260 l = 104 the answer is e . | a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104 | e | divide(subtract(multiply(180, divide(add(const_100, 50), const_100)), 10), add(divide(add(const_100, 50), const_100), const_1)) | add(n1,const_100)|divide(#0,const_100)|add(#1,const_1)|multiply(n2,#1)|subtract(#3,n0)|divide(#4,#2) | gain |
if the perimeter of a rectangular garden is 1200 m , its length when its breadth is 240 m is ? | "2 ( l + 240 ) = 1200 = > l = 360 m answer : e" | a ) 338 m , b ) 778 m , c ) 200 m , d ) 276 m , e ) 360 m | e | subtract(divide(1200, const_2), 240) | divide(n0,const_2)|subtract(#0,n1)| | physics |
the volumes of two cones are in the ratio 1 : 35 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ? | "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 35 = ( 1 ) 2 h 1 / ( 2 ) 2 h 2 = > h 1 / h 2 = 7 / 5 i . e . h 1 : h 2 = 7 : 5 answer : a" | a ) 7 : 5 , b ) 2 : 9 , c ) 7 : 2 , d ) 2 : 2 , e ) 2 : 8 | a | divide(divide(1, 35), power(divide(1, 2), 2)) | divide(n0,n1)|divide(n0,n3)|power(#1,n3)|divide(#0,#2)| | geometry |
a jar of 144 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ? | "144 = 16 * 9 = 18 * 8 there are 16 people in the group today . the answer is c ." | a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20 | c | divide(subtract(sqrt(add(multiply(multiply(144, 2), const_4), power(2, 2))), 2), 2) | multiply(n0,n1)|power(n1,n1)|multiply(#0,const_4)|add(#2,#1)|sqrt(#3)|subtract(#4,n1)|divide(#5,n1)| | general |
how many minutes does aditya take to cover a distance of 400 m , if he runs at a speed of 20 km / hr | "explana ɵ on : we know that , time = distancespeedspeed = 20 km / hr = 20 ∗ 518 m / sec = 509 m / sec time = ( 400 ∗ 950 ) = 72 sec = 115 min answer : op ɵ on a" | a ) 115 min , b ) 215 min , c ) 315 min , d ) 415 min , e ) none of these | a | divide(divide(400, multiply(20, const_0_2778)), const_60) | multiply(n1,const_0_2778)|divide(n0,#0)|divide(#1,const_60)| | physics |
a cyclist rides a bicycle 7 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 7 km / hr . what is the average speed for the entire trip ? | distance = 17 km time = 7 / 10 + 10 / 7 = ( 49 + 100 ) / 70 = 149 / 70 hours average speed = ( 17 * 70 ) / 149 = 7.99 km / h the answer is c . | a ) 7.59 , b ) 7.79 , c ) 7.99 , d ) 8.19 , e ) 8.39 | c | divide(add(7, 10), add(divide(7, 10), divide(10, 7))) | add(n0,n1)|divide(n0,n1)|divide(n1,n0)|add(#1,#2)|divide(#0,#3) | general |
a train 240 m long passed a pole in 24 sec . how long will it take to pass a platform 650 m long ? a . 65 | speed = 240 / 24 = 10 m / sec . required time = ( 240 + 650 ) / 10 = 89 sec . answer : b | a ) 28 sec , b ) 89 sec , c ) 85 sec , d ) 16 sec , e ) 15 sec | b | divide(add(240, 650), divide(240, 24)) | add(n0,n2)|divide(n0,n1)|divide(#0,#1) | physics |
if the radius of a circle that centers at the origin is 5 , how many k points on the circle have integer coordinates ? | "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : k = c" | a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20 | c | subtract(subtract(multiply(5, 5), add(5, const_4)), power(const_2, const_2)) | add(n0,const_4)|multiply(n0,n0)|power(const_2,const_2)|subtract(#1,#0)|subtract(#3,#2)| | geometry |
1504 x 1504 = ? | "1504 x 1504 = ( 1504 ) 2 = ( 1500 + 4 ) 2 = ( 1500 ) 2 + ( 4 ) 2 + ( 2 x 1500 x 4 ) = 2250000 + 16 + 12000 = 2250016 + 12000 = 2262016 a" | a ) 2262016 , b ) 2250000 , c ) 12000 , d ) 2262000 , e ) 2250016 | a | multiply(divide(1504, 1504), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
marcella has 23 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ? | marcella has 23 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 23 pairs of shoes minus the 5 ' destroyed ' pairs yields 20 pa... | a ) 21 , b ) 20 , c ) 19 , d ) 18 , e ) 15 | d | subtract(23, add(floor(divide(9, const_2)), const_1)) | divide(n1,const_2)|floor(#0)|add(#1,const_1)|subtract(n0,#2) | general |
a room 3 m 21 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor . | "explanation : area of the room = ( 321 x 777 ) cm 2 . size of largest square tile = h . c . f . of 321 cm and 777 cm = 3 cm . area of 1 tile = ( 3 x 3 ) cm 2 . number of tiles required = ( 321 × 777 ) / ( 3 × 3 ) = 27713 answer : option d" | a ) 27636 , b ) 27640 , c ) 27647 , d ) 27713 , e ) 27675 | d | divide(multiply(add(multiply(3, const_100), 21), add(multiply(7, const_100), 77)), multiply(subtract(21, add(multiply(const_2, const_4), const_2)), subtract(21, add(multiply(const_2, const_4), const_2)))) | multiply(n0,const_100)|multiply(n2,const_100)|multiply(const_2,const_4)|add(n1,#0)|add(n3,#1)|add(#2,const_2)|multiply(#3,#4)|subtract(n1,#5)|multiply(#7,#7)|divide(#6,#8)| | physics |
a shopkeeper sold 15 articles at the cost price of 20 articles . then find the profit % or lost % | "here 15 articles selling price = 20 articles cost price so the difference = 20 - 15 = 5 % of profit = 5 * 100 / 15 = 33.33 % correct option is d" | a ) 30 % , b ) 31 % , c ) 20 % , d ) 33.33 % , e ) 40 % | d | multiply(divide(subtract(20, 15), 15), const_100) | subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)| | gain |
the price of 2 saris and 4 shirts is rs . 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ? | let the price of a saree and a shirt be rs . x and rs . y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - ... | a ) rs . 2400 , b ) rs . 2490 , c ) rs . 2500 , d ) rs . 2550 , e ) rs . 2600 | a | multiply(12, divide(1600, subtract(multiply(6, 2), 4))) | multiply(n0,n4)|subtract(#0,n1)|divide(n2,#1)|multiply(n5,#2) | general |
two numbers are in ratio 4 : 5 and their lcm is 180 . the smaller number is | solution : let two numbers be 4 x and 5 x ; their lcm = 180 and hcf = x ; now , 1 st number * 2 nd number = lcm * hcf or , 4 x * 5 x = 180 * x ; or , 20 x = 180 ; or , x = 9 ; then , the smaller number = 4 * 9 = 36 . answer : option c | a ) 9 , b ) 15 , c ) 36 , d ) 45 , e ) none | c | multiply(4, divide(180, multiply(5, 4))) | multiply(n0,n1)|divide(n2,#0)|multiply(n0,#1) | other |
how many cubes of 25 cm edge can be put in a cubical box of 1 m edge . | number of cubes = 100 â ˆ — 100 â ˆ — 100 / 25 â ˆ — 25 â ˆ — 25 = 64 note : 1 m = 100 cm answer : d | ['a ) 177 cm', 'b ) 100 cm', 'c ) 86 cm', 'd ) 64 cm', 'e ) 87 cm'] | d | divide(volume_cube(1), volume_cube(divide(25, const_100))) | divide(n0,const_100)|volume_cube(n1)|volume_cube(#0)|divide(#1,#2) | physics |
if an object travels at two feet per second , how many feet does it travel in one hour ? | "explanation : if an object travels at 2 feet per second it covers 2 x 60 feet in one minute , and 2 x 60 x 60 feet in one hour . answer = 7200 answer : c ) 7200" | a ) 3488 , b ) 3778 , c ) 7200 , d ) 1800 , e ) 2881 | c | multiply(multiply(const_3, const_60), const_60) | multiply(const_3,const_60)|multiply(#0,const_60)| | physics |
an apple orchard grows red and green apples . on the first day of harvest , 496 apples are collected . there are 3 times as many red apples as there are green apples . how many green apples were harvested ? | let x be the number of green apples . there were 496 total apples ; there are three times as many red apples as green apples . therefore , x + 3 x = 496 4 x = 496 x = 124 answer : d | a ) 99 , b ) 112 , c ) 118 , d ) 124 , e ) 130 | d | divide(496, add(3, const_1)) | add(n1,const_1)|divide(n0,#0) | physics |
what is the tenth digit to the right of the decimal point , in the decimal expansion of ( 1 / 5 ) ^ 10 | actually 1 / 5 = 0.2 = 2 * 10 ^ - 1 so 2 ^ 10 * 10 ^ - 10 2 has sequence 24 , 86 . hence digit will be 4 answer is c | a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8 | c | reminder(power(const_2, 10), 10) | power(const_2,n2)|reminder(#0,n2) | general |
100 liters of a mixture contains milk and water in the ratio 7 : 3 . if 10 liters of this mixture be replaced by 10 liters of milk , the ratio of milk to water in the new mixture would be ? | "quantity of milk in 100 liters if mix = 100 * 7 / 10 = 70 liters quantity of milk in 110 liters of new mix = 80 + 10 = 80 liters quantity of water in it = 110 - 80 = 30 liters ratio of milk and water in new mix = 80 : 30 = 8 : 3 answer is b" | a ) 7 : 8 , b ) 8 : 3 , c ) 3 : 8 , d ) 8 : 7 , e ) 7 : 1 | b | divide(multiply(subtract(10, const_1), 3), multiply(7, 3)) | multiply(const_2,n1)|subtract(n3,const_1)|multiply(#1,n2)|divide(#2,#0)| | other |
two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ? | "quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 4 + 7 / 2 = 19 / 4 = 4.75 litres as 6 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5 . a... | a ) 16 : 5 , b ) 14 : 5 , c ) 16 : 7 , d ) 19 : 5 , e ) none of these | d | divide(add(divide(multiply(62.5, 2), const_100), divide(multiply(87.5, 4), const_100)), add(subtract(2, divide(multiply(62.5, 2), const_100)), subtract(4, divide(multiply(87.5, 4), const_100)))) | multiply(n0,n2)|multiply(n1,n3)|divide(#0,const_100)|divide(#1,const_100)|add(#2,#3)|subtract(n2,#2)|subtract(n3,#3)|add(#5,#6)|divide(#4,#7)| | other |
a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 36 / 49 . how many marbles are in the bag ? | ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probabi... | a ) 24 , b ) 48 , c ) 84 , d ) 72 , e ) 80 | c | divide(12, subtract(const_1, sqrt(divide(36, 49)))) | divide(n2,n3)|sqrt(#0)|subtract(const_1,#1)|divide(n0,#2) | other |
288 ã · ? ã — 15 + 270 = 405 | "explanation : 288 ã · ? ã — 15 = 405 - 270 = 135 ( 288 ã — 15 ) / ? = 135 ? = ( 288 ã — 15 ) / 135 = 32 answer : option c" | a ) 24 , b ) 25 , c ) 32 , d ) 39 , e ) 43 | c | add(add(divide(multiply(add(subtract(405, 270), 15), const_2), const_10), divide(divide(multiply(add(subtract(405, 270), 15), const_2), const_10), const_10)), const_1) | subtract(n3,n2)|add(n1,#0)|multiply(#1,const_2)|divide(#2,const_10)|divide(#3,const_10)|add(#3,#4)|add(#5,const_1)| | general |
how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 7 , and the digit 2 can be used only once ? | "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 7 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 2 = 160 numbers with two 2 - s , 2 x 2 x 1 * 5 ... | a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320 | b | subtract(multiply(multiply(add(4, const_1), add(4, const_1)), multiply(4, 4)), multiply(multiply(add(4, const_1), add(4, const_1)), 4)) | add(n0,const_1)|multiply(n0,n0)|multiply(#0,#0)|multiply(#2,#1)|multiply(#2,n0)|subtract(#3,#4)| | physics |
a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 8 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ? | "correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.08 ( $ 1120 ) = $ 89.60 . the correct answer is b ." | a ) $ 54.00 , b ) $ 89.60 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80 | b | divide(multiply(subtract(1720, 600), 8), const_100) | subtract(n3,n0)|multiply(n1,#0)|divide(#1,const_100)| | general |
what is the remainder of g = 3 ^ 19 when divided by 10 ? | "i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 ... | a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9 | d | reminder(power(3, reminder(19, const_4)), 10) | reminder(n1,const_4)|power(n0,#0)|reminder(#1,n2)| | general |
what is the value of ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) . . . ( log 63 64 ) ? | using the identity ( loga b ) ( logb c ) = loga c repeatedly , we obtain ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) . . . ( log 63 64 ) = log 2 64 = 6 correct answer d | a ) 1 / 6 , b ) 2 , c ) 5 / 2 , d ) 6 , e ) 32 | d | multiply(add(5, const_1), divide(log(2), log(2))) | add(n5,const_1)|log(n0)|divide(#1,#1)|multiply(#0,#2) | other |
how many 2 x 2 x 2 cubes could fit in a box of 7 x 9 x 4 ? | the answer is a ) 31 . a 2 x 2 x 2 cube has an area of 8 . a 7 x 9 x 4 box has an area of 252 . if you divide 252 by 8 , you get 31.5 . since that means you can only fit 31 entire cubes in the box , the answer is 31 . | a ) 31 , b ) 32 , c ) 30 , d ) 33 , e ) 29 | a | volume_rectangular_prism(7, 9, 4) | volume_rectangular_prism(n3,n4,n5)| | geometry |
by selling a book for 300 , 20 % profit was earned . what is the cost price of the book ? | "sp = 120 % of cp ; : . cp = 300 × 100 / 120 = 250 option ' b '" | a ) a ) 215 , b ) b ) 250 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240 | b | original_price_before_gain(20, 300) | original_price_before_gain(n1,n0)| | gain |
the h . c . f . of two numbers is 15 and their l . c . m . is 420 . if one of the numbers is 375 , then the other is : | "other number = ( 15 x 420 ) / 375 = 16.8 . answer : c" | a ) 12.21 , b ) 283 , c ) 16.8 , d ) 318 , e ) 32.4 | c | multiply(15, 375) | multiply(n0,n2)| | physics |
what is the sum of all the multiples of 10 between 0 and 85 ? | "the multiples of 10 between 0 and 85 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 . if these are all added together , the result is 360 . final answer : d" | a ) 500 , b ) 620 , c ) 450 , d ) 360 , e ) 440 | 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)), 10), 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 |
find large number from below question the difference of two no . ' s is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ? | "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e" | a ) 1456 , b ) 1563 , c ) 1546 , d ) 1643 , e ) 1635 | e | multiply(divide(subtract(1365, 15), subtract(6, const_1)), 6) | subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|multiply(n1,#2)| | general |
if | x + 2 | = 10 , what is the sum of all the possible values of x ? | "there will be two cases x + 2 = 10 or x + 2 = - 10 = > x = 8 or x = - 12 sum of both the values will be - 12 + 8 = - 4 answer : c" | a ) - 16 , b ) - 13 , c ) - 4 , d ) - 2 , e ) 12 | c | add(2, 10) | add(n0,n1)| | general |
in a group of cows and chickens , the number of legs was 18 more than twice the number of heads . the number of cows was : | "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 18 more than twice the number of heads . therefore , 2 × ( x + y ) + 18 = 4 x + 2 y . or , 2 x + 2 y + 18 = 4 x + 2 y . or... | a ) 5 , b ) 7 , c ) 9 , d ) 12 , e ) 14 | c | divide(18, subtract(const_4, const_2)) | subtract(const_4,const_2)|divide(n0,#0)| | general |
before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 3.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ? | pete covered 3.5 * 60 = 210 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 210 = 1 / 42 . answer : c . | a ) 1 / 3 , b ) 1 / 30 , c ) 1 / 42 , d ) 2 , e ) 30 | c | divide(const_1, multiply(divide(3.5, 5), const_60)) | divide(n1,n0)|multiply(#0,const_60)|divide(const_1,#1) | physics |
what least number should be subtracted from 642 so that the remainder when divided by 5 , 7 , and 9 will leave in each case the same remainder 4 ? | "the lcm of 5 , 7 , and 9 is 315 . the next multiple is 2 * 315 = 630 . 630 + { remainder } = 630 + 4 = 634 , which is 8 less than 642 . answer : c ." | a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10 | c | subtract(642, add(multiply(multiply(multiply(5, 7), 9), const_2), 4)) | multiply(n1,n2)|multiply(n3,#0)|multiply(#1,const_2)|add(n4,#2)|subtract(n0,#3)| | general |
9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 6 miles per hour faster than the first runner ' s rate . how far apart , to the neares... | "if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 14 m / h - - > 7 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 7 ^ 2 d ^ 2 = 65 = ~ 8 answer option c" | a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14 | c | sqrt(add(power(multiply(8, divide(1, const_2.0)), 2), power(multiply(subtract(8, 2), divide(1, 6)), 6))) | divide(n3,n4)|subtract(n1,n4)|multiply(n1,#0)|multiply(#0,#1)|power(#2,n2)|power(#3,n4)|add(#4,#5)|sqrt(#6)| | physics |
a train 250 m long running at 72 kmph crosses a platform in 20 sec . what is the length of the platform ? | "d = 72 * 5 / 18 = 20 = 400 â € “ 250 = 150 m answer : a" | a ) 150 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m | a | subtract(multiply(20, multiply(72, const_0_2778)), 250) | multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)| | physics |
raman ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percent does he loss . | explanation : let the origianl salary = rs . 100 it will be 150 % of ( 50 % of 100 ) = ( 150 / 100 ) * ( 50 / 100 ) * 100 = 75 so new salary is 75 , it means his loss is 25 % option d | a ) 75 , b ) 65 , c ) 45 , d ) 25 , e ) 85 | d | divide(subtract(multiply(const_100, const_100), multiply(subtract(const_100, 50), add(const_100, 50))), const_100) | add(n0,const_100)|multiply(const_100,const_100)|subtract(const_100,n0)|multiply(#0,#2)|subtract(#1,#3)|divide(#4,const_100) | gain |
if 80 % of a number is equal to four - third of another number , what is the ratio of first number to the second number ? | "let 80 % of a = 4 / 3 b then 80 a / 100 = 4 b / 3 4 a / 5 = 4 b / 3 a / b = 5 / 3 a : b = 5 : 3 answer is a" | a ) 5 : 3 , b ) 1 : 4 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3 | a | divide(divide(const_1, const_4), divide(80, const_100)) | divide(const_1,const_4)|divide(n0,const_100)|divide(#0,#1)| | general |
two pipes can fill a tank in 18 minutes and 15 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ? | "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 15 - 1 / 45 = ( 5 + 6 - 2 ) / 90 = 9 / 90 = 1 / 10 so , the tank becomes full in 10 minutes . answer : d :" | a ) 11 minutes , b ) 17 minutes , c ) 18 minutes , d ) 10 minutes , e ) 16 minutes | d | subtract(add(divide(const_1, 18), divide(const_1, 15)), divide(const_1, 45)) | divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|subtract(#3,#2)| | physics |
223.124 x 11.98 ã · 6.001 + 11.11 = ? | "explanation : ? = 223.124 x 11.98 ã · 6.001 + 11.11 â ‰ ˆ ( 223.124 x 12 / 6 ) + 11.11 â ‰ ˆ 446.248 + 11.11 â ‰ ˆ 457.358 answer : option e" | a ) 983.578 , b ) 459.121 , c ) 781.189 , d ) 656.112 , e ) 457.358 | e | multiply(223.124, power(11.98, 6.001)) | power(n1,n2)|multiply(n0,#0)| | general |
pipe p can fill a tank in 6 hours , pipe q in 12 hours and pipe r in 24 hours . if all the pipes are open , in how many hours will the tank be filled ? | "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 6 + 1 / 12 + 1 / 24 ) = 7 / 24 all the three pipes together will fill the tank = 24 / 7 = 3.4 hours answer d" | a ) 2 hours , b ) 2.4 hours , c ) 3 hours , d ) 3.4 hours , e ) 4.5 hours | d | inverse(add(divide(const_1, 24), add(divide(const_1, 6), divide(const_1, 12)))) | divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|add(#3,#2)|inverse(#4)| | physics |
4 friends , peter , john , quincy , and andrew , are pooling their money to buy a $ 1200 item . peter has twice as much money as john . quincy has $ 20 more than peter . andrew has 15 % more than quincy . if they put all their money together and spend the $ 1200 , they will have $ 11 left . how much money does peter ha... | p = 2 j ; q = p + 20 ; a = 1.15 ( q ) p + j + q + r - 1200 = 11 p + 0.5 p + p + 20 + 1.15 ( p + 20 ) = 1211 p + 0.5 p + p + 20 + 1.15 p + 23 = 1211 p + 0.5 p + p + 1.15 p + 43 = 1211 p + 0.5 p + p + 1.15 p = 1168 3.65 p = 1168 p = 320 answer : a | a ) $ 320 , b ) $ 160 , c ) $ 200 , d ) $ 410 , e ) $ 325 | a | divide(subtract(subtract(add(1200, 11), 20), multiply(divide(add(const_100, 15), const_100), 20)), add(add(add(const_1, divide(const_1, const_2)), const_1), divide(add(const_100, 15), const_100))) | add(n1,n5)|add(n3,const_100)|divide(const_1,const_2)|add(#2,const_1)|divide(#1,const_100)|subtract(#0,n2)|add(#3,const_1)|multiply(n2,#4)|add(#6,#4)|subtract(#5,#7)|divide(#9,#8) | general |
a man travelled from the village to the post - office at the rate of 25 kmph and walked back at the rate of 4 kmph . if the whole journey took 5 hours 48 minutes , find the distance of the post - office from the village | explanation : average speed = ( 2 × a × b ) / ( a + b ) here a = 25 b = 4 average speed = 2 × 25 × 4 / ( 25 + 4 ) = 200 / 29 kmph . distance covered in 5 hours 48 minutes = speed × time distance = ( 200 / 29 ) × ( 29 / 5 ) = 40 kms distance covered in 5 hours 48 minutes = 40 kms distance of the post office from the vil... | a ) 20 , b ) 87 , c ) 276 , d ) 198 , e ) 171 | a | divide(multiply(divide(add(25, 4), 5), divide(multiply(multiply(25, 4), const_2), add(25, 4))), const_2) | add(n0,n1)|multiply(n0,n1)|divide(#0,n2)|multiply(#1,const_2)|divide(#3,#0)|multiply(#2,#4)|divide(#5,const_2) | physics |
893.7 – 573.07 – 95.007 = ? | "solution given expression = 893.7 - ( 573.07 + 95.007 ) = 893.7 - 668.077 = 225.623 . answer a" | a ) 225.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these | a | subtract(893.7, divide(573.07, 95.007)) | divide(n1,n2)|subtract(n0,#0)| | general |
one man traveled a distance of 61 km in 9 hrs . he traveled partly on footat 4 km / hr and partly on bicycle ta 9 km / hr . the distance traveled on foot is ? | let the distance travelled on foot be x km . then , distance travelled on bicycle = ( 61 - x ) km . so , x + ( 61 - x ) = 9 4 9 9 x + 4 ( 61 - x ) = 9 x 36 5 x = 80 x = 16 km . c | a ) 11 km , b ) 13 km , c ) 16 km , d ) 18 km , e ) 19 km | c | add(subtract(add(9, 9), 4), const_2) | add(n1,n1)|subtract(#0,n2)|add(#1,const_2) | physics |
ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 64500 . what is his profit percent ? | "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 64500 profit ( % ) = ( 64500 - 55000 ) / 55000 * 100 = 17.3 % answer : c" | a ) 22 , b ) 77 , c ) 17.3 , d ) 99 , e ) 88 | c | multiply(divide(subtract(64500, add(42000, 13000)), add(42000, 13000)), const_100) | add(n0,n1)|subtract(n2,#0)|divide(#1,#0)|multiply(#2,const_100)| | gain |
in the coordinate plane , points ( x , 3 ) and ( 5 , y ) are on line k . if line k passes through the origin and has slope 3 / 5 , then x + y = | "line k passes through the origin and has slope 3 / 5 means that its equation is y = 3 / 5 * x . thus : ( x , 3 ) = ( 3 , 5 ) and ( 5 , y ) = ( 3 , 5 ) - - > x + y = 3 + 5 = 8 . answer : b" | a ) 9 , b ) 8 , c ) 7 , d ) 5 , e ) 6 | b | multiply(multiply(5, 5), divide(3, 5)) | divide(n0,n3)|multiply(n1,n3)|multiply(#0,#1)| | general |
on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 30 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ? | "0.1 m = 0.70 e = > e / m = 1 / 7 * 100 = 14.28 % so answer is e . m - # of motorists e - # of motorists exceeding speed" | a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 14.28 % | e | divide(const_100, multiply(multiply(divide(10, const_100), divide(30, const_100)), const_100)) | divide(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)|multiply(#2,const_100)|divide(const_100,#3)| | gain |
a question paper has 2 parts , a & b , each containing 6 questions . if a student has to choose 4 from part a & 3 from part b , in how many ways can he choose the questions ? | "there 6 questions in part a out of which 4 question can be chosen as = 6 c 4 . similarly , 3 questions can be chosen from 6 questions of part b as = 6 c 3 . hence , total number of ways , = 6 c 4 * 6 c 3 = [ 6 ! / ( 2 ! 4 ! ) ] * [ 6 ! / ( 3 ! * 3 ! ) ] = { 15 } * { 6 * 5 * 4 * 3 / ( 3 * 2 * 1 ) } = 300 . d" | a ) 100 , b ) 200 , c ) 350 , d ) 150 , e ) 140 | d | divide(multiply(choose(6, 4), choose(6, 3)), 6) | choose(n1,n2)|choose(n1,n3)|multiply(#0,#1)|divide(#2,n1)| | probability |
a man invests some money partly in 12 % stock at 132 and partly in 10 % stock at 80 . to obtain equal dividends from both , he must invest the money in the ratio : | "solution for an income of rs . 1 in 12 % stock at 132 , investment = rs . ( 132 / 12 ) = rs . 11 . for an income of rs . 1 in 10 % stock at 80 , investment = rs . ( 80 / 10 ) = rs . 8 . ∴ ratio of investments = 11 : 8 = 11 : 8 answer c" | a ) 3 : 4 , b ) 3 : 5 , c ) 11 : 8 , d ) 16 : 15 , e ) none | c | divide(multiply(132, const_2), multiply(80, const_3)) | multiply(n1,const_2)|multiply(n3,const_3)|divide(#0,#1)| | other |
george baked a total of 150 pizzas for 7 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ? | "3 / 5 of the 150 pizzas cooked on saturday = 90 pizzas 3 / 5 of the remaining pizzas on sunday = 36 pizzas we ' re left with ( 150 - 90 - 36 ) = 24 pizzas for the remaining 5 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w th f 8 7 6 2 1 ... | a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 2 | b | divide(subtract(subtract(subtract(150, multiply(150, divide(3, 7))), multiply(subtract(150, multiply(150, divide(3, 7))), divide(3, 7))), 3), subtract(subtract(subtract(150, multiply(150, divide(3, 7))), multiply(subtract(150, multiply(150, divide(3, 7))), divide(3, 7))), 3)) | divide(n2,n1)|multiply(n0,#0)|subtract(n0,#1)|multiply(#0,#2)|subtract(#2,#3)|subtract(#4,n2)|divide(#5,#5)| | general |
a train 200 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ? | "answer : c . speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 200 m at 50 / 3 m / sec = 200 * 3 / 50 sec = 12 sec" | a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec | c | divide(200, multiply(subtract(68, 8), const_0_2778)) | subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
at veridux corporation , there are 200 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ? | "well , first let â € ™ s take care of the â € œ totals â € . the numbers in the â € œ totals â € row must add up . if 90 are females , the other 200 â € “ 90 = 110 must be males . similarly , the numbers in the â € œ totals â € column must add up . if 40 are managers , then the other 200 â € “ 40 = 160 must be a... | a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 65 | e | multiply(40, const_1) | multiply(n2,const_1)| | general |
find the value of ( √ 1.21 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) is | "( √ 1.21 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) 11 / 9 + 12 / 7 = > ( 77 + 108 ) / 63 = > 185 / 63 answer is e ." | a ) 195 / 63 , b ) 145 / 63 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63 | e | add(divide(sqrt(1.21), sqrt(0.81)), divide(sqrt(1.44), sqrt(0.49))) | sqrt(n0)|sqrt(n1)|sqrt(n2)|sqrt(n3)|divide(#0,#1)|divide(#2,#3)|add(#4,#5)| | general |
the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 49 ) is : | "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 49 has the form 4 k + 1 , so the units digit of 93 ^ 49 is 3 . the units digit of powers of 5 is always 5 . 3 + 5 = 8 , so the units digit is 8 . the answer is d ." | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0 | d | add(reminder(multiply(reminder(49, const_4), 93), const_10), reminder(35, const_10)) | reminder(n3,const_4)|reminder(n0,const_10)|multiply(n2,#0)|reminder(#2,const_10)|add(#3,#1)| | general |
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