Problem stringlengths 5 628 | Rationale stringlengths 1 2.74k | options stringlengths 37 137 | correct stringclasses 5
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in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.24 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ] | "speed = 162 * ( 5 / 18 ) m / sec = 45 m / sec length of train ( distance ) = speed * time ( 45 ) * 9 = 405 meter answer : d" | a ) 150 meter , b ) 286 meter , c ) 186 meter , d ) 405 meter , e ) 265 meter | d | multiply(divide(multiply(162, const_1000), const_3600), 9) | multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)| | physics |
a train running at the speed of 162 km / hr crosses a pole in 9 seconds . find the length of the train . | "let the maximum marks be x then , 30 % of x = 150 + 30 30 x / 100 = 180 30 x = 180 * 100 = 18000 x = 600 answer is b" | a ) 750 , b ) 600 , c ) 650 , d ) 550 , e ) 500 | b | divide(add(150, 30), divide(30, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1)| | general |
a student has to obtain 30 % of the total marks to pass . he got 150 marks and failed by 30 marks . the maximum marks are ? | "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 5 = 7200 . answer : c" | a ) 5729 , b ) 5760 , c ) 7200 , d ) 2870 , e ) 2799 | c | divide(multiply(5, multiply(8, const_60)), subtract(divide(multiply(8, const_60), multiply(6, const_60)), const_1)) | multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4)| | physics |
a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ? | "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 560 . 6 ( 85 - g ) + 7 g = 560 . 510 - 6 g + 7 g = 560 . g = 560 - 510 = 50 . the answer is b ." | a ) a ) 36 , b ) b ) 50 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44 | b | subtract(560, multiply(85, 6)) | multiply(n0,n1)|subtract(n3,#0)| | general |
we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 560 . how many green hats did we buy ? | "i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 72 and that c and l 1 = 0.10 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.1 x = 20 , therefore the grand total is 200 . now we know that ... | a ) 46 , b ) 48 , c ) 56 , d ) 32 , e ) 58 | b | divide(subtract(divide(20, divide(10, const_100)), 72), 2) | divide(n3,const_100)|divide(n6,#0)|subtract(#1,n4)|divide(#2,n1)| | general |
among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 10 % of listco ' s sales staff . listco employs 72 level - 1 employees , 20 of whom ar... | "1498 - 1400 = 98 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 98 ) / ( 1400 ) = 7 % the answer is c ." | a ) 3 % , b ) 5 % , c ) 7 % , d ) 9 % , e ) 11 % | c | divide(multiply(subtract(1498, 1400), const_100), 1400) | subtract(n1,n0)|multiply(#0,const_100)|divide(#1,n0)| | gain |
the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1498 respectively . what is the rate of interest ? | "m = 9 s = 3.1 ds = 12.1 us = 5.9 x / 12.1 + x / 5.9 = 1 x = 3.97 d = 3.97 * 2 = 7.94 answer : e" | a ) 2.21 , b ) 2.48 , c ) 9.24 , d ) 7.29 , e ) 7.94 | e | multiply(divide(multiply(add(9, 3.1), subtract(9, 3.1)), add(add(9, 3.1), subtract(9, 3.1))), const_2) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|multiply(#0,#1)|divide(#3,#2)|multiply(#4,const_2)| | physics |
a man can row 9 kmph in still water . when the river is running at 3.1 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ? | "n case of stock 1 , if he invest rs . 105 , he will get a dividend of rs . 12 ( assume face value = 100 ) in case of stock 2 , if he invest rs . 88 , he will get a dividend of rs . 8 ( assume face value = 100 ) ie , if he invest rs . ( 88 * 12 ) / 8 , he will get a dividend of rs . 12 required ratio = 105 : ( 88 × 12 ... | a ) 31 : 44 , b ) 31 : 27 , c ) 16 : 15 , d ) 35 : 44 , e ) 35 : 27 | d | divide(multiply(105, const_2), multiply(88, const_3)) | multiply(n1,const_2)|multiply(n3,const_3)|divide(#0,#1)| | other |
a man invests some money partly in 12 % stock at 105 and partly in 8 % stock at 88 . to obtain equal dividends from both , he must invest the money in the ratio : | "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 15 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 15 , d = 15 b - 15 c ; every 5 minutes cyclist meets an oncoming bus : \ frac { d } { ... | a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 15 / 2 minutes | e | divide(subtract(15, divide(15, divide(add(5, 15), subtract(15, 5)))), const_1) | add(n0,n1)|subtract(n0,n1)|divide(#0,#1)|divide(n0,#2)|subtract(n0,#3)|divide(#4,const_1)| | physics |
a man cycling along the road noticed that every 15 minutes a bus overtakes him and every 5 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ? | explanation : number of questions attempted correctly = ( 70 % of 10 + 40 % of 30 + 60 % of 35 ) = 7 + 12 + 21 = 40 . questions to be answered correctly for 60 % = 60 % of total quotations = 60 % of 75 = 45 . he would have to answer 45 - 40 = 5 answer : a | a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | a | subtract(divide(multiply(75, 60), const_100), add(add(divide(multiply(10, 70), const_100), divide(multiply(30, 40), const_100)), divide(multiply(35, 60), const_100))) | multiply(n0,n6)|multiply(n1,n4)|multiply(n2,n5)|multiply(n3,n6)|divide(#0,const_100)|divide(#1,const_100)|divide(#2,const_100)|divide(#3,const_100)|add(#5,#6)|add(#8,#7)|subtract(#4,#9) | 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 ? | "sqrt ( 7 x / 3 ) to be perfect square x has to 7 / 3 ans : b" | a ) 25 / 9 , b ) 7 / 3 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25 | b | divide(7, 3) | divide(n0,n1)| | general |
a number x is multiplied by 7 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ? | "240 = 2 ^ 4 * 3 * 5 = ( 4 ) * 2 ^ 2 * 3 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 2 , 1 , and 1 . there are ( 2 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 12 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 240 . the answer is d ." | a ) 6 , b ) 8 , c ) 9 , d ) 11 , e ) 12 | d | divide(divide(divide(240, 4), const_2), const_3) | divide(n0,n1)|divide(#0,const_2)|divide(#1,const_3)| | general |
how many of the positive divisors of 240 are also multiples of 4 not including 240 ? | connie has a 1 6 chance of winning 6 dollars her first turn . she has a 5 / 6 1 / 6 chance of winning 1 dollar her second turn . next , she has a 25 36 1 / 6 chance of winning 1 / 6 dollars her third turn . generalizing , connie ' s expected earnings form a geometric series with initial term 1 / 6 * 6 = 1 and common ra... | a ) 32 / 31 , b ) 33 / 31 , c ) 34 / 31 , d ) 36 / 31 , e ) 0 / 31 | d | divide(const_1, subtract(const_1, divide(divide(subtract(6, 1), 6), 6))) | subtract(n0,n4)|divide(#0,n0)|divide(#1,n0)|subtract(const_1,#2)|divide(const_1,#3) | general |
one day , connie plays a game with a fair 6 - sided die . connie rolls the die until she rolls a 6 , at which point the game ends . if she rolls a 6 on her first turn , connie wins 6 dollars . for each subsequent turn , connie wins 1 6 of the amount she would have won the previous turn . what is connie ' s expected ear... | "0.06 * 0.05 = 0.003 = 0.3 % the answer is b ." | a ) 0.125 % , b ) 0.3 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 % | b | multiply(6, divide(5, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | gain |
in the manufacture of a certain product , 6 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ? | "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 26 = > 2 x = 26 = > x = 13 c" | a ) 11 , b ) 12 , c ) 13 , d ) 16 , e ) 18 | c | divide(26, const_2) | divide(n0,const_2)| | general |
in a group of ducks and cows , the total number of legs are 26 more than twice the no . of heads . find the total no . of buffaloes . | at 3 / 4 th of speed he is late by ' 2 hrs ' x - 3 / 4 ( x ) = 2 x = 8 so 8 - 2 = 6 hrs ( since 2 hrs late ) answer : c | a ) 5 hours , b ) 3 hours , c ) 6 hours , d ) 12 hours , e ) 15 hours | c | divide(multiply(multiply(multiply(divide(3, 4), 2), divide(3, 4)), 2), subtract(multiply(divide(3, 4), 2), multiply(multiply(divide(3, 4), 2), divide(3, 4)))) | divide(n0,n1)|multiply(n2,#0)|multiply(#0,#1)|multiply(n2,#2)|subtract(#1,#2)|divide(#3,#4) | physics |
a man walking at 3 / 4 th of the speed , reaches his office late by 2 hours . what is the usual time ? | because a + b = 1 , 2 a + 2 b = 2 ( a + b ) = 2 × 1 = 2 . correct answer d | a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 1 | d | subtract(add(add(2, 1), 2), add(2, 1)) | add(n0,n1)|add(n1,#0)|subtract(#1,#0) | general |
given a + b = 1 , find the value of 2 a + 2 b . two solutions are presented below . only one is correct , even though both yield the correct answer . | "let the sums be p . now , 45 % of p = 4016.25 or , p = 8925 answer a" | a ) 8925 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these | a | divide(multiply(const_100, 4016.25), multiply(9, 5)) | multiply(n0,const_100)|multiply(n1,n2)|divide(#0,#1)| | gain |
a sum fetched total simple interest of 4016.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ? | "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 333 ) + 2 ( 555 ) = 2220 the answer is b ." | a ) 2210 , b ) 2220 , c ) 2230 , d ) 2240 , e ) 2250 | b | multiply(add(add(multiply(add(add(5, 3), 2), const_100), multiply(add(add(const_4.0, 3), 2), const_10)), add(add(5, 3), 2)), 3) | add(n2,n3)|add(n1,#0)|multiply(#1,const_100)|multiply(#1,const_10)|add(#2,#3)|add(#4,#1)|multiply(#5,const_2)| | general |
what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 3 , and 5 if each digit can be used only once in each number ? | "let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 25 % are male i . e 25 / 100 * 20 = 5 geese ( males ) and now we know out of the total 20 geese , 5 are male , then 15 have t... | a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 9 / 7 | e | divide(divide(divide(25, const_100), divide(30, const_100)), divide(divide(multiply(multiply(const_2, const_4), const_10), const_100), divide(30, const_100))) | divide(n1,const_100)|divide(n0,const_100)|multiply(const_2,const_4)|divide(#0,#1)|multiply(#2,const_10)|divide(#4,const_100)|divide(#5,#1)|divide(#3,#6)| | general |
a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 25 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a c... | "other number = ( 11 * 7700 ) / 275 = 308 . answer : c" | a ) 288 , b ) 277 , c ) 308 , d ) 988 , e ) 112 | c | multiply(11, 275) | multiply(n0,n2)| | physics |
the h . c . f of two numbers is 11 and their l . c . m is 7700 . if one of the numbers is 275 , then the other is ? | "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 7 = 21 the answer is b ." | a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27 | b | add(add(11, divide(subtract(11, 5), 2)), 7) | subtract(n4,n0)|divide(#0,n1)|add(n4,#1)|add(n2,#2)| | physics |
a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 7 , ab = 5 and ac = 11 , what is the length of ae ? | "between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 4 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 4 + 4 = 30 meter answer is e ." | a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30 | e | add(add(multiply(subtract(12, const_1), 2), divide(10, 2)), divide(10, 2)) | divide(n0,n2)|subtract(n1,const_1)|multiply(n2,#1)|add(#0,#2)|add(#3,#0)| | physics |
in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of four metre is left from all sides of the boundary of the garden . what is the length of the garden ? | "out of the 17 integers : 9 are odd and 8 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 9 odd numbers first 2 . 10 th ... | a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 3 | d | add(divide(17, const_2), 1) | divide(n1,const_2)|add(n0,#0)| | general |
each of the integers from 1 to 17 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ? | sum of last 4 matches = ( ( 10 × 45 ) – ( 6 × 48 ) = 162 average = 162 / 4 = 40.5 answer : d | a ) 43.25 , b ) 43 , c ) 38 , d ) 40.5 , e ) 36 | d | divide(subtract(multiply(45, 10), multiply(6, 48)), 4) | multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4) | general |
the averge score of a cricketer for 10 matches is 45 runs . if the average for the first 6 matches is 48 . then find the average for the last 4 matches ? | "explanation : let the cost price = rs 100 then , marked price = rs 140 required gain = 8 % , so selling price = rs 108 discount = 140 - 108 = 32 discount % = ( 32 / 140 ) * 100 = 22.85 % option b" | a ) 23.85 % , b ) 22.85 % , c ) 21.85 % , d ) 20.85 % , e ) none of these | b | subtract(const_100, multiply(divide(add(8, const_100), add(40, const_100)), const_100)) | add(n1,const_100)|add(n0,const_100)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)| | gain |
a shopkeeper fixes the marked price of an item 40 % above its cost price . the percentage of discount allowed to gain 8 % is | "b 16.8 sec d = 60 + 80 = 140 m s = 60 * 5 / 18 = 50 / 3 t = 140 * 3 / 50 = 8.4 sec answer is b" | a ) 5.8 sec , b ) 8.4 sec , c ) 12.4 sec , d ) 6.8 sec , e ) 1.8 sec | b | divide(add(60, 80), multiply(60, const_0_2778)) | add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)| | physics |
how long does a train 60 m long travelling at 60 kmph takes to cross a bridge of 80 m in length ? | "the percent of the budget for transportation is 100 - ( 55 + 9 + 5 + 4 + 2 ) = 25 % 100 % of the circle is 360 degrees . then ( 25 % / 100 % ) * 360 = 90 degrees the answer is e ." | a ) 18 ° , b ) 36 ° , c ) 54 ° , d ) 72 ° , e ) 90 ° | e | divide(multiply(const_360, subtract(const_100, add(add(add(add(55, 9), 5), 4), 2))), const_100) | add(n0,n1)|add(n2,#0)|add(n3,#1)|add(n4,#2)|subtract(const_100,#3)|multiply(#4,const_360)|divide(#5,const_100)| | geometry |
a circle graph shows how the budget of a certain company was spent : 55 percent for salaries , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the perce... | "96 / 7 = 13 . xx we are not concerned about the exact value of 96 / 7 as we just need the integers . since the values are small , we can write down the integers . the different integers between 5 and 96 / 7 would be 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12,13 total number of integers = 9 option b" | a ) 7 , b ) 9 , c ) 10 , d ) 12 , e ) 15 | b | add(subtract(divide(96, 7), 5), const_1) | divide(n1,n2)|subtract(#0,n0)|add(#1,const_1)| | general |
how many integers are between 5 and 96 / 7 , inclusive ? | "( 256 ) ^ 2 - ( 144 ) ^ 2 = ( 256 + 144 ) ( 256 - 144 ) = 400 x 112 = 44800 answer is b" | a ) 761200 , b ) 44800 , c ) 761800 , d ) 761500 , e ) none of them | b | add(multiply(256, 256), multiply(144, 144)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | general |
simplify : 256 x 256 - 144 x 144 | "perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 20 ( p ^ 2 ) / 16 = 2 p + 20 p ^ 2 = 32 p + 320 p ^ 2 - 32 p - 320 = 0 p ^ 2 - 40 p + 8 p - 320 = 0 p ( p - 40 ) + 8 ( p + 40 ) = 0 ( p - 40 ) ( p + 8 ) = 0 p = 40 or - 8 discarding negative value , p = 40 answer is... | a ) 28 , b ) 36 , c ) 40 , d ) 56 , e ) 64 | c | subtract(subtract(add(const_10, multiply(20, 2)), const_0_25), const_0_25) | multiply(n0,n1)|add(#0,const_10)|subtract(#1,const_0_25)|subtract(#2,const_0_25)| | geometry |
the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 20 , what is the perimeter of the garden , in feet ? | first we need to figure out what numbers are exactly divisible by 7 , 12,10 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,10 ) = 42 * 10 = 420 the numbers which will leave remainder 4 will be { 420 + 4 , 420 x 2 + 4 , , . . . } the largest such number less than or equal to 1856 is 420 * 4 + 4 or... | a ) 168 , b ) 172 , c ) 182 , d ) 140 , e ) 160 | b | subtract(1856, add(4, multiply(gcd(1856, lcm(lcm(7, 12), 10)), lcm(lcm(7, 12), 10)))) | lcm(n1,n2)|lcm(n3,#0)|gcd(n0,#1)|multiply(#2,#1)|add(n4,#3)|subtract(n0,#4) | general |
which is the least number that must be subtracted from 1856 so that the remainder when divided by 7 , 12 , 10 is 4 ? | "average = ( 5 + 10 + 15 ) / 3 = 10 answer is a" | a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 21 | a | divide(add(add(add(3, const_1), add(add(3, const_1), const_2)), add(subtract(5, 3), subtract(5, const_2))), 3) | add(n0,const_1)|subtract(n1,n0)|subtract(n1,const_2)|add(#0,const_2)|add(#1,#2)|add(#0,#3)|add(#5,#4)|divide(#6,n0)| | general |
find the average of first 3 multiples of 5 ? | "explanation : increase in 10 years = ( 242500 - 134800 ) = 107700 increase % = ( 107700 / 134800 x 100 ) % = 79 % . required average = ( 79 / 10 ) % = 7.9 % . answer : option b" | a ) 4.37 % , b ) 7.9 % , c ) 6.8 % , d ) 8.75 % , e ) none | b | add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(2, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(2, const_3)), const_1000)), 1), const_10), const_100), const_4) | add(n2,const_3)|add(const_3,const_4)|multiply(const_10,const_1000)|multiply(#2,const_10)|multiply(#0,const_100)|multiply(#1,const_10)|add(#0,#5)|subtract(#3,const_1000)|multiply(#6,const_1000)|subtract(#7,const_1000)|subtract(#9,#4)|divide(#10,#8)|subtract(#11,n0)|divide(#12,const_10)|multiply(#13,const_100)|add(#14,co... | general |
the population of a town increased from 1 , 34,800 to 2 , 42,500 in a decade . the average percent increase of population per year is : | "to solve this type of question , simply divide the volume of wall with the volume of brick to get the numbers of required bricks so lets solve this number of bricks = volume of wall / volume of 1 brick = 800 ∗ 600 ∗ 22.5 / 25 ∗ 11.25 ∗ 6 = 6400 answer : a" | a ) 6400 , b ) 3777 , c ) 2679 , d ) 2667 , e ) 1997 | a | divide(multiply(multiply(multiply(8, const_100), multiply(6, const_100)), 22.5), multiply(multiply(25, 11.25), 6)) | multiply(n3,const_100)|multiply(n4,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(n2,#2)|multiply(n5,#3)|divide(#5,#4)| | physics |
how many bricks , each measuring 25 cm * 11.25 cm * 6 cm , will be needed to build a wall 8 m * 6 m * 22.5 m | "65 % of 160 = x 0.65 * 160 = x 104 = x answer : c" | a ) 84 , b ) 94 , c ) 104 , d ) 114 , e ) 124 | c | divide(multiply(65, 160), const_100) | multiply(n0,n1)|divide(#0,const_100)| | gain |
a soccer team played 160 games and won 65 percent of them . how many games did it win ? | "explanation : 80 + 25 = 105 / 15 = 7 ( remainder ) d" | a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 9 | d | subtract(subtract(subtract(80, 25), const_4), const_2) | subtract(n0,n1)|subtract(#0,const_4)|subtract(#1,const_2)| | general |
a certain no . when divided by 80 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ? | "sp of 1 m of cloth = 9000 / 80 = rs . 112.5 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 112.5 - rs . 23.5 = rs . 89 . answer : b" | a ) 22 , b ) 89 , c ) 90 , d ) 78 , e ) 80 | b | subtract(divide(9000, 80), 23.5) | divide(n1,n0)|subtract(#0,n2)| | physics |
a trader sells 80 meters of cloth for rs . 9000 at the profit of rs . 23.5 per metre of cloth . what is the cost price of one metre of cloth ? | chicken - ch cows - c sheep - s ch + c = 6 s c > ch and c > s each cow has 4 legs and 1 head each chicken has 2 legs and 1 head so 5 c + 3 ch = 100 ( sum of legs and head ) there are 2 possible solutions to this equation c = 11 and ch = 9 or c = 14 and ch = 10 since from first equation where ch + c = 6 s the sum of ch ... | a ) 5 , b ) 8 , c ) 10 , d ) 4 , e ) 17 | d | subtract(6, const_2) | subtract(n0,const_2) | general |
a farm has chickens , cows and sheep . there are 6 times the number of chickens and cows than sheep . if there are more cows than chickens or sheep , and together , cows and chickens have a total of 100 feet and heads , how many sheep live at the farm ? | "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.75 = 45 democrats are expected to vote for candidate a ; 40 * 0.25 = 10 republicans are expected to vote for candidate a . thus total of 45 + 10 = 55 registered voters are expected to vote for candidate a ... | a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 % | d | add(multiply(60, divide(75, const_100)), multiply(subtract(const_100, 60), divide(25, const_100))) | divide(n1,const_100)|divide(n2,const_100)|subtract(const_100,n0)|multiply(n0,#0)|multiply(#1,#2)|add(#3,#4)| | gain |
in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 75 percent of the registered voters who are democrats and 25 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are e... | "let x be the distance to big rock . time = x / 3 + x / 7 = 1 x = 21 / 10 = 2.1 km the answer is c ." | a ) 1.5 , b ) 1.8 , c ) 2.1 , d ) 2.4 , e ) 2.7 | c | multiply(divide(subtract(5, 2), add(add(5, 2), subtract(5, 2))), add(5, 2)) | add(n0,n1)|subtract(n0,n1)|add(#0,#1)|divide(#1,#2)|multiply(#0,#3)| | physics |
a rower can row 5 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ? | "24 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 24 = 1 / 100 * x = > x = 24000 answer : c" | a ) 29798 , b ) 27908 , c ) 24000 , d ) 25000 , e ) 27991 | c | divide(divide(divide(multiply(multiply(multiply(24, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5) | multiply(n3,const_100)|multiply(n4,const_100)|multiply(n5,const_100)|multiply(#0,#1)|multiply(#3,#2)|divide(#4,n0)|divide(#5,n1)|divide(#6,n2)| | physics |
a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m ? | "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 65 + 26 = 91 members have not passed the test , thus 0.7 * total = 91 - - > total = 130 . answer : d ." | a ) 60 , b ) 80 , c ) 100 , d ) 130 , e ) 140 | d | divide(add(26, 65), divide(subtract(const_100, 65), const_100)) | add(n0,n1)|subtract(const_100,n1)|divide(#1,const_100)|divide(#0,#2)| | gain |
thirty percent of the members of a swim club have passed the lifesaving test . among the members who have not passed the test , 26 have taken the preparatory course and 65 have not taken the course . how many members are there in the swim club ? | "12 x = 16 y = 28 z 3 x = 4 y = 7 z 3 ( 4 * 7 ) = 4 ( 3 * 7 ) = 7 ( 3 * 4 ) addition = 28 + 21 + 12 = 61 answer would be multiple of 61 which is 122 answer : c" | a ) 52 , b ) 58 , c ) 122 , d ) 84 , e ) 168 | c | divide(multiply(multiply(16, 28), 12), const_4) | multiply(n1,n2)|multiply(n0,#0)|divide(#1,const_4)| | general |
if 12 x = 16 y = 28 z , then what is a possible sum of positive integers x , y , and z ? | "first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 34000 - 30000 = 4000 so 10 more machines . . total = 110 machines imo b . ." | a ) 90 , b ) 110 , c ) 105 , d ) 115 , e ) 120 | b | add(100, divide(subtract(multiply(multiply(multiply(add(4, 3), multiply(3, const_2)), 100), multiply(add(4, const_1), const_2)), multiply(multiply(multiply(100, 100), divide(3, 100)), 100)), multiply(multiply(100, 100), divide(4, 100)))) | add(n0,n2)|add(const_1,n2)|divide(n0,n1)|divide(n2,n1)|multiply(const_2,n0)|multiply(n1,n1)|multiply(#0,#4)|multiply(#1,const_2)|multiply(#2,#5)|multiply(#3,#5)|multiply(#6,n1)|multiply(n1,#8)|multiply(#10,#7)|subtract(#12,#11)|divide(#13,#9)|add(n1,#14)| | gain |
a 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 d... | "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 28 = > 2 x = 28 = > x = 14 c" | a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | c | divide(28, const_2) | divide(n0,const_2)| | general |
in a group of ducks and cows , the total number of legs are 28 more than twice the no . of heads . find the total no . of buffaloes . | "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 26 ) = rs . 208 . profit = 208 - 150 = 58 so , profit % = ( 58 / 150 ) * 100 = 39 % option b" | a ) 12 % , b ) 39 % , c ) 14 % , d ) 15 % , e ) 16 % | b | divide(multiply(subtract(multiply(26, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20))) | add(n2,n3)|multiply(n0,n2)|multiply(n1,n3)|add(#1,#2)|multiply(n4,#0)|subtract(#4,#3)|multiply(#5,const_100)|divide(#6,#3)| | gain |
a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 26 per kg , then his gain percent is | abel in the 2 days that he worked completed 1 / 5 of the job = 4 / 5 remains then if ben had to leave 4 days before the completion , this means that carla had to work alone for these 4 days in which she completed 1 / 4 of the job . now together , ben and carla completed the job in ( 1 / 12 + 1 / 15 ) ( t ) = 11 / 20 3 ... | a ) 6 , b ) 7 , c ) 7 2 / 3 , d ) 9 , e ) 10 | c | multiply(add(2, 4), 4) | add(n3,n4)|multiply(n4,#0) | physics |
abel can complete a work in 10 days , ben in 12 days and carla in 16 days . all of them began the work together , but abel had to leave after 2 days and ben 4 days before the completion of the work . how long did the work last ? | "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 4 ) * 270 = 67 gallons total paint used = 157 gallons . option b" | a ) 18 , b ) 157 , c ) 175 , d ) 216 , e ) 250 | b | add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 4)) | divide(n0,n2)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n4)|add(#3,#1)| | physics |
joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 4 of the remaining paint . how many gallons of paint has joe used ? | "0 = 1 * 1 - 1 2 = 2 * 2 - 2 6 = 3 * 3 - 3 12 = 4 * 4 - 4 20 = 5 * 5 - 5 30 = 6 * 6 - 6 42 = 7 * 7 - 7 similarly 8 * 8 - 8 = 56 answer : e" | a ) 55 , b ) 85 , c ) 59 , d ) 63 , e ) 56 | e | subtract(negate(20), multiply(subtract(6, 12), divide(subtract(6, 12), subtract(0,2, 6)))) | negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)| | general |
0,2 , 6 , 12 , 20 , 30 , 42 , ___ | "distance covered in 1 min = ( 66 * 1000 ) / 60 = 1100 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 1100 / 4.4 = 250 answer : e" | a ) 210 , b ) 220 , c ) 230 , d ) 240 , e ) 250 | e | divide(divide(multiply(66, const_1000), const_60), multiply(multiply(divide(add(66, const_2), add(const_4, const_3)), const_2), divide(divide(140, const_100), const_2))) | add(n1,const_2)|add(const_3,const_4)|divide(n0,const_100)|multiply(n1,const_1000)|divide(#3,const_60)|divide(#2,const_2)|divide(#0,#1)|multiply(#6,const_2)|multiply(#5,#7)|divide(#4,#8)| | physics |
the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 66 kmph ? | "explanation : let the number of hens be x and the number of cows be y . then , x + y = 50 . . . . ( i ) and 2 x + 4 y = 160 x + 2 y = 80 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 30 the required answer = 20 . answer : d" | a ) 22 , b ) 23 , c ) 24 , d ) 20 , e ) 28 | d | divide(subtract(multiply(50, const_4), 160), const_2) | multiply(n0,const_4)|subtract(#0,n1)|divide(#1,const_2)| | general |
a man has some hens and cows . if the number of heads be 50 and the number of feet equals 160 , then the number of hens will be : | "we ' re told that the number of women in a town is equal to 50 % of the number of men in that town . men = 10 women = 5 we ' re asked for the number of men , as a percentage of the number of women . m / w % = 10 / 5 = 200 % answer is c" | a ) 100 % , b ) 120 % , c ) 200 % , d ) 150 % , e ) 180 % | c | multiply(divide(const_100, 50), const_100) | divide(const_100,n0)|multiply(#0,const_100)| | gain |
if a population of women in a town is 50 % of men . what is the population of men as a percentage of population of women ? | "650 = 10 * 65 1300 = 20 * 65 the even multiples are 65 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ." | a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11 | b | add(divide(subtract(1301, 649), multiply(65, const_2)), const_1) | multiply(n0,const_2)|subtract(n2,n1)|divide(#1,#0)|add(#2,const_1)| | general |
how many even multiples of 65 are there between 649 and 1301 ? | "explanation : relative speed = 70 + 90 = 160 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 160 hr = 1 / 80 hr = 3600 / 80 seconds = = 45 seconds answer : option b" | a ) 56 , b ) 45 , c ) 47 , d ) 26 , e ) 25 | b | multiply(divide(add(1.10, 0.9), add(70, 90)), const_3600) | add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(#2,const_3600)| | physics |
two trains are moving in opposite directions with speed of 70 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds | "0,08 r = x / 100 * 0.1 r answer a" | a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 % | a | multiply(divide(multiply(subtract(const_1, divide(20, const_100)), divide(10, const_100)), divide(10, const_100)), const_100) | divide(n4,const_100)|divide(n3,const_100)|divide(n1,const_100)|subtract(const_1,#1)|multiply(#0,#3)|divide(#4,#2)|multiply(#5,const_100)| | gain |
in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 10 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ? | "one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 26 * 2 = 52 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one clas... | a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 9 , e ) 2 and 8 | c | divide(subtract(multiply(26, 2), 32), 2) | multiply(n0,n1)|subtract(#0,n2)|divide(#1,n0)| | general |
a certain experimental mathematics program was tried out in 2 classes in each of 26 elementary schools and involved 32 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and... | "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 5 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 5 hence x = 7 . answer is a" | a ) 7 , b ) 11 , c ) 13 , d ) 15 , e ) 17 | a | add(5, 2) | add(n0,n5)| | general |
if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 5 ) , what is the value of x ? | "1.8 hectares in ares 1 hectare = 100 ares therefore , 1.8 hectares = 1.8 × 100 ares = 180 ares . answer - c" | a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares . | c | divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 1.8), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2))) | add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2)| | physics |
convert 1.8 hectares in ares | explanation : number of students appeared from school ' p ' = 100 , say number of students qualified from school ' p ' = 70 and number of students appeared from school ' q ' = 130 number of students qualified from school ' q ' = 50 % more than those qualified from school ' p ' . = 70 + 35 = 105 % of students qualified ... | a ) 80.78 % , b ) 80.76 % , c ) 80.72 % , d ) 80.79 % , e ) 80.74 % | b | multiply(divide(multiply(divide(add(50, const_100), const_100), divide(70, const_100)), divide(add(30, const_100), const_100)), const_100) | add(n2,const_100)|add(n1,const_100)|divide(n0,const_100)|divide(#0,const_100)|divide(#1,const_100)|multiply(#3,#2)|divide(#5,#4)|multiply(#6,const_100) | general |
in an examination , the percentage of students qualified to the students appeared from school ' p ' is 70 % . in school ' q ' , the number of students appeared is 30 % more than the students appeared from school ' p ' and the number of students qualified from school ' q ' is 50 % more than the students qualified from s... | let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 75 ) = 300 x = 71 and the fourth person has a height of 71 + 10 = 81 inches the answer is e . | a ) 73 , b ) 75 , c ) 77 , d ) 79 , e ) 81 | e | add(divide(subtract(multiply(75, 4), add(6, add(4, 6))), 4), add(4, 6)) | add(n0,n2)|multiply(n0,n3)|add(n2,#0)|subtract(#1,#2)|divide(#3,n0)|add(#0,#4) | general |
there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 75 . ... | sum of interior angles of a polygon = ( n - 2 ) × 180 ° where n = number of sides there will be n angles which are in a . p . therefore , since we need to find maximum value of n , put minimum value for a and d . i . e . , take a = 20 and d = 20 then sum of the angles = n / 2 [ 2 × 20 + ( n − 1 ) 20 ] therefore , 10 n ... | a ) 12 , b ) 14 , c ) 21 , d ) 25 , e ) cant determine | b | divide(add(sqrt(subtract(power(subtract(20, const_3), const_2), multiply(const_4, multiply(divide(add(multiply(const_10, multiply(const_4, const_2)), const_100), const_10), const_2)))), subtract(20, const_3)), const_2) | multiply(const_2,const_4)|subtract(n0,const_3)|multiply(#0,const_10)|power(#1,const_2)|add(#2,const_100)|divide(#4,const_10)|multiply(#5,const_2)|multiply(#6,const_4)|subtract(#3,#7)|sqrt(#8)|add(#9,#1)|divide(#10,const_2) | general |
if the angles of an n sided polygon are in a . p and a > = 20 and d > = 20 then wat is the maximum possible value of n ? | "sum of the 9 numbers = 207 if each number is increased by 4 , the total increase = 4 * 9 = 36 the new sum = 207 + 36 = 243 the new average = 243 / 9 = 27 . answer : c" | a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29 | c | multiply(23, 4) | multiply(n1,n2)| | general |
the average of 9 numbers is 23 . if each number is increased by 4 , what will the new average be ? | "shopkeeper sells 800 g instead of 1000 g . so , his gain = 1000 - 800 = 200 g . thus , % gain = 200 * 100 ) / 800 = 25 % . answer : option b" | a ) 10 % , b ) 25 % , c ) 11.11 % , d ) 12 % , e ) none of these | b | multiply(divide(add(multiply(const_2, const_100), divide(const_100, const_2)), 800), const_100) | divide(const_100,const_2)|multiply(const_100,const_2)|add(#0,#1)|divide(#2,n0)|multiply(#3,const_100)| | gain |
a shopkeeper forced to sell at cost price , uses a 800 grams weight for a kilogram . what is his gain percent ? | "say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 54 . now , plug options for x . only b and e give an integer value for y . but only for b x > y as needed . answer : b ." | a ) 6 , b ) 10 , c ) 8 , d ) 9 , e ) 12 | b | add(const_4, add(floor(divide(58, add(const_4, const_3))), const_1)) | add(const_3,const_4)|divide(n0,#0)|floor(#1)|add(#2,const_1)|add(#3,const_4)| | general |
company z has 58 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday . | "four wheeler = 20 * 4 = 80 ( max ) 2 wheel = 1 so no of 4 wheeler = 20 answer : d" | a ) 11 , b ) 12 , c ) 13 , d ) 20 , e ) 25 | d | divide(subtract(82, 2), 4) | subtract(n3,n0)|divide(#0,n1)| | general |
if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 82 ? | "50 % of x = x / 2 ; 25 % of 2500 = 25 / 100 * 2500 = 625 given that , x / 2 = 625 - 25 = > x / 2 = 600 = > x = 1200 . answer : c" | a ) 1880 , b ) 2160 , c ) 1200 , d ) 8400 , e ) 1210 | c | divide(subtract(multiply(2500, divide(25, const_100)), 25), divide(50, const_100)) | divide(n2,const_100)|divide(n0,const_100)|multiply(n3,#0)|subtract(#2,n1)|divide(#3,#1)| | general |
if 50 % of x is 25 less than 25 % of 2500 , then x is ? | "30 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 30 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 30 × 25 × 0.6 / 25 × 0.4 = 45 men answerc" | a ) 25 , b ) 30 , c ) 45 , d ) 20 , e ) none of these | c | divide(multiply(30, divide(subtract(const_100, 40), const_100)), divide(const_4, const_10)) | divide(const_4,const_10)|subtract(const_100,n3)|divide(#1,const_100)|multiply(n1,#2)|divide(#3,#0)| | physics |
a contractor undertakes to built a walls in 50 days . he employs 30 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ? | "pass percentage = 100 - ( 30 + 35 - 35 ) = 100 - 30 = 70 answer : d" | a ) 10 % , b ) 20 % , c ) 30 % , d ) 70 % , e ) 50 % | d | subtract(const_100, subtract(add(30, 35), 35)) | add(n0,n1)|subtract(#0,n2)|subtract(const_100,#1)| | general |
in an examination , 30 % of total students failed in hindi , 35 % failed in english and 35 % in both . the percentage of these who passed in both the subjects is : | let the cp = 100 profit = ( 320 / 100 ) × 100 = 320 sp = cp + profit = 100 + 320 = 420 if the cost increases by 25 % , new cp = ( 125 / 100 ) × 100 = 125 selling price is constant , hence new sp = 420 profit = sp – cp = 420 – 125 = 295 required percentage = ( 295 / 420 ) × 100 = 2950 / 42 = 1475 / 21 ≈ 70 answer : e | a ) 180 % , b ) 120 % , c ) 90 % , d ) 80 % , e ) 70 % | e | multiply(divide(subtract(add(320, const_100), add(25, const_100)), add(320, const_100)), const_100) | add(n0,const_100)|add(n1,const_100)|subtract(#0,#1)|divide(#2,#0)|multiply(#3,const_100) | gain |
in a shop , the profit is 320 % of the cost . if the cost increases by 25 % but the selling price remains constant , find out approximately what percentage of the selling price is the profit ? | total expenditure = 40 + 25 + 15 + 10 = 90 % saving = ( 100 - 90 ) = 10 % 10 / 100 × salary = 1200 , salary = 12000 rs . answer : a | a ) 12000 , b ) 6000 , c ) 8000 , d ) 10000 , e ) none of these | a | divide(multiply(1200, const_100), 10) | multiply(n4,const_100)|divide(#0,n3) | gain |
a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 10 % on conveyance . if his savings at the end of the month is rs . 1200 , then his salary per month in rupees is : | "explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 7 ) + 6000 ( v - 7 ) < = > 2000 v = 42000 < = > v = 21 . answer : b" | a ) 76 , b ) 21 , c ) 26 , d ) 28 , e ) 11 | b | add(7, divide(multiply(7, subtract(12000, 8000)), subtract(8000, 6000))) | subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)| | general |
the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ? | "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 108 x = 123 answer : a" | a ) 123 , b ) 267 , c ) 277 , d ) 267 , e ) 120 | a | divide(add(108, 138), 2) | add(n1,n2)|divide(#0,n0)| | general |
a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 108 . what was the number he chose ? | "let the third number is x . then first number = ( 100 - 30 ) % of x = 70 % of x = 7 x / 10 second number is ( 63 x / 100 ) difference = 7 x / 10 - 63 x / 100 = 7 x / 10 so required percentage is , difference is what percent of first number ( 7 x / 100 * 10 / 7 x * 100 ) % = 10 % answer : b" | a ) 8 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 12 % | b | subtract(multiply(divide(subtract(37, 30), subtract(const_100, 30)), const_100), const_10) | subtract(n1,n0)|subtract(const_100,n0)|divide(#0,#1)|multiply(#2,const_100)|subtract(#3,const_10)| | gain |
two numbers are less than third number by 30 % and 37 % respectively . how much percent is the second number less than by the first | "30 * 18 / 5 = 108 kmph answer : b" | a ) 122 , b ) 108 , c ) 110 , d ) 150 , e ) 100 | b | multiply(divide(30, const_1000), const_3600) | divide(n0,const_1000)|multiply(#0,const_3600)| | physics |
express 30 mps in kmph ? | "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 8 = > 2 x = 8 = > x = 4 b" | a ) 5 , b ) 4 , c ) 6 , d ) 3 , e ) 2 | b | divide(8, const_2) | divide(n0,const_2)| | general |
in a group of ducks and cows , the total number of legs are 8 more than twice the no . of heads . find the total no . of buffaloes . | "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 1500 = $ 2790 the total price is $ 4000 + $ 2850 + $ 2790 = $ 9640 the answer is e... | a ) $ 8280 , b ) $ 8520 , c ) $ 8710 , d ) $ 8930 , e ) $ 9640 | e | multiply(multiply(2, const_3), const_100) | multiply(n4,const_3)|multiply(#0,const_100)| | gain |
a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 5,000 meters of fabric ? | "log 8 x + log 8 ( 1 / 6 ) = 1 / 3 = > ( log x / log 8 ) + ( log 1 / 6 / log 8 ) = log ( 81 / 3 ) = log 2 = > log x = log 2 – log 1 / 6 = log ( 2 * 6 / 1 ) = log 12 answer : a" | a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26 | a | multiply(power(8, divide(1, 3)), 6) | divide(n2,n5)|power(n0,#0)|multiply(n3,#1)| | general |
if log 8 x + log 8 1 / 6 = 1 / 3 , then the value of x is : | "sol . let the numbers be x and y . then , ( x + y ) = 12 and x 2 + y 2 = 124 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 12 ) 2 - 124 = 144 - 124 = 20 xy = 10 . answer a" | a ) 10 , b ) 44 , c ) 80 , d ) 88 , e ) 90 | a | divide(subtract(power(12, const_2), 124), const_2) | power(n0,const_2)|subtract(#0,n1)|divide(#1,const_2)| | general |
if the sum of two numbers is 12 and the sum of their squares is 124 , then the product of the numbers is | "c . p . = rs . 5 x and s . p . = rs . 8 x . then , gain = rs . 3 x required ratio = 3 x : 5 x = 3 : 5 d" | a ) 23 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 25 | d | divide(subtract(8, 5), 5) | subtract(n0,n1)|divide(#0,n1)| | other |
the ratio between the sale price and the cost price of an article is 8 : 5 . what is the ratio between the profit and the cost price of that article ? | "b 90 sum = ( n x n ) + n hence , 9 x 9 = 81 + 9 = 90" | a ) 80 , b ) 90 , c ) 30 , d ) 70 , e ) 60 | b | multiply(add(9, const_1), 9) | add(n0,const_1)|multiply(n0,#0)| | physics |
tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 9 even numbers . his mother immediately worked out the answer . how much had he scored in math ? | "line k passes through the origin and has slope 1 / 7 means that its equation is y = 1 / 7 * x . thus : ( x , 1 ) = ( 7 , 1 ) and ( 7 , y ) = ( 7,1 ) - - > x - y = 7 - 1 = 6 . answer : a" | a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 3 | a | multiply(multiply(7, 7), divide(1, 7)) | divide(n0,n3)|multiply(n1,n3)|multiply(#0,#1)| | general |
in the coordinate plane , points ( x , 1 ) and ( 7 , y ) are on line k . if line k passes through the origin and has slope 1 / 7 , then x - y = | "length = 15 cm , breadth = 13 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 15 + 13 ) cm = 2 × 28 cm = 56 cm we know that the area of rectangle = length × breadth = ( 15 × 13 ) cm 22 = 195 cm 2 answer : d" | a ) 71 cm 2 , b ) 121 cm 2 , c ) 141 cm 2 , d ) 195 cm 2 , e ) 221 cm 2 | d | square_area(15) | square_area(n0)| | geometry |
find the perimeter and area of the rectangle of length 15 cm and breadth 13 cm . | "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 400 - 50 = 350 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 350 = 150 . answer is b" | a ) 120 , b ) 150 , c ) 100 , d ) 180 , e ) 220 | b | subtract(add(175, 325), subtract(400, 50)) | add(n1,n2)|subtract(n0,n3)|subtract(#0,#1)| | other |
out of 400 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ? | "sum of first 20 multiples of 12 are = ( 12 × 1 ) + ( 12 × 2 ) + ( 12 × 3 ) + . . . . . . + ( 12 × 19 ) + ( 12 × 20 ) . = 12 ( 1 + 2 + 3 + . . . . . + 20 ) use the formula : n ( n + 1 ) 2 ⇒ 12 × ( 20 × 21 ) 2 = 2520 . answer : a" | a ) 2520 , b ) 3878 , c ) 2778 , d ) 27 , e ) 911 | a | add(divide(divide(20, divide(divide(divide(divide(divide(20, const_2), const_2), const_2), const_2), const_2)), const_2), add(const_1, sqrt(divide(divide(20, divide(divide(divide(divide(divide(20, const_2), const_2), const_2), const_2), const_2)), const_2)))) | divide(n0,const_2)|divide(#0,const_2)|divide(#1,const_2)|divide(#2,const_2)|divide(#3,const_2)|divide(n0,#4)|divide(#5,const_2)|sqrt(#6)|add(#7,const_1)|add(#8,#6)| | general |
find the sum of first 20 multiples of 12 . | total no . of handshakes = 49 + 48 + 47 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 1225 or , if there are n persons then no . of shakehands = nc 2 = 50 c 2 = 1225 answer : c | a ) 190 , b ) 200 , c ) 1225 , d ) 220 , e ) 230 | c | multiply(subtract(50, const_1), divide(50, const_2)) | divide(n0,const_2)|subtract(n0,const_1)|multiply(#0,#1) | general |
50 men shake hands with each other . maximum no of handshakes without cyclic handshakes . | "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 10 minutes the population increases by 10 x 4 = 40 people . answer . a ." | a ) 40 , b ) 100 , c ) 150 , d ) 240 , e ) 300 | a | multiply(divide(const_60, 15), 10) | divide(const_60,n0)|multiply(n1,#0)| | physics |
if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 10 minutes ? | "let the retail price be = x selling price of z = 0.75 x selling price of x = 0.95 * 0.75 x = 0.71 x selling price of y = ( ( 0.75 x + 0.71 x ) / 2 ) * 0.70 = 0.73 x * 0.75 = 0.55 x 0.55 x = k * 0.71 x k = 0.55 / 0.71 = 55 / 71 answer : b" | a ) 21 / 34 , b ) 55 / 71 , c ) 25 / 34 , d ) 26 / 34 , e ) 27 / 34 | b | multiply(divide(divide(multiply(divide(add(subtract(const_100, 25), multiply(subtract(const_100, 25), divide(subtract(const_100, 5), const_100))), const_2), subtract(const_100, 30)), const_100), multiply(subtract(const_100, 25), divide(subtract(const_100, 5), const_100))), const_10) | subtract(const_100,n1)|subtract(const_100,n0)|subtract(const_100,n2)|divide(#0,const_100)|multiply(#3,#1)|add(#4,#1)|divide(#5,const_2)|multiply(#6,#2)|divide(#7,const_100)|divide(#8,#4)|multiply(#9,const_10)| | general |
real - estate salesman z is selling a house at a 25 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 5 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 30 percent discount . ... | "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 3 / 5 . 2 / 5 p ( a n b ) = 6 / 25 . a" | a ) 6 / 25 , b ) 3 / 25 , c ) 8 / 25 , d ) 2 / 13 , e ) 3 / 17 | a | multiply(divide(3, 5), divide(2, 5)) | divide(n0,n1)|divide(n2,n3)|multiply(#0,#1)| | general |
if p ( a ) = 3 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events . | "on the first three flips , you must get heads . whats the probability of getting heads ? its 1 / 2 so for the first three flips , your probability is ( 1 / 2 ) ^ 3 = 1 / 8 now for the last two , you want to get tails only . whats the prob of getting tails ? well , its the same as prob of getting a heads , namely , 1 /... | a ) 3 / 5 , b ) 1 / 2 , c ) 1 / 5 , d ) 1 / 8 , e ) 1 / 32 | e | power(divide(1, 2), 5) | divide(n0,n1)|power(#0,n2)| | probability |
if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips ? | "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + o... | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | d | add(add(5, const_2), const_2) | add(n0,const_2)|add(#0,const_2)| | general |
if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value q of z - x ? | originally let there be x men . less men , more days ( indirect ) : . ( x - 10 ) : x : : 100 : 110 or x - 10 / x = 100 / 110 or 11 x - 110 = 10 x or x = 110 so , originally there were 110 men . answer : d | a ) 75 , b ) 82 , c ) 100 , d ) 110 , e ) 120 | d | divide(multiply(divide(add(100, 10), 10), 10), subtract(divide(add(100, 10), 10), 10)) | add(n0,n1)|divide(#0,n1)|multiply(n1,#1)|subtract(#1,n1)|divide(#2,#3) | physics |
a piece of work can finish by a certain number of men in 100 days . if however , there were 10 men less , it would take 10 days more for the work to be finished . how many men were there originally ? | d = 150 + 200 = 350 s = 54 * 5 / 18 = 15 mps t = 350 / 15 = 23.3 sec c ) 23.3 sec | a ) 17 sec , b ) 21 sec , c ) 23.3 sec , d ) 27.5 sec , e ) 29 sec | c | divide(add(200, 150), multiply(54, const_0_2778)) | add(n0,n1)|multiply(n2,const_0_2778)|divide(#0,#1) | physics |
how many seconds will a train 150 meters long take to cross a bridge 200 meters long if the speed of the train is 54 kmph ? | "percentage error in calculated area = ( 6 + 6 + ( 6 ã — 6 ) / 100 ) % = 12.36 % answer : e" | a ) 14.05 % , b ) 14.02 % , c ) 14 % , d ) 13 % , e ) 12.36 % | e | divide(multiply(subtract(square_area(add(const_100, 6)), square_area(const_100)), const_100), square_area(const_100)) | add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)| | gain |
an error 6 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ? | distance is same s 1 t 1 = s 2 t 2 40 t = 50 ( t - 1 ) t = 5 distance = speed * time 40 * 5 = 200 answer : b | a ) 150 , b ) 200 , c ) 450 , d ) 500 , e ) 600 | b | multiply(divide(50, subtract(50, 40)), 40) | subtract(n1,n0)|divide(n1,#0)|multiply(n0,#1) | physics |
liz drove from point a to point b at 40 km / h . on her way back she drove at 50 km / h and therefore her way back lasted one hour less . what is the distance ( in km ) between a and b ? | "first , you must find the total weight of the mixture given that 80 % of it will be dough . 80 % * total = 36 = > ( 8 / 10 ) total = 36 = > total = 360 / 8 = > total = 45 oz , from there , you must find 10 % of the total 40 oz of the mixture . 20 % * total = > ( 2 / 10 ) ( 45 ) = 9 oz choclate used , not forgetting th... | a ) 2 , b ) 4 , c ) 6 , d ) 3 , e ) 1 | e | multiply(divide(20, const_100), 20) | divide(n2,const_100)|multiply(n2,#0)| | gain |
uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 10 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ? | "a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 7 / 4 ) * 4 = 2 / 7 the answer is e ." | a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 2 / 7 | e | multiply(divide(subtract(const_100, 60), add(const_100, 75)), divide(5, 4)) | add(n2,const_100)|divide(n1,n0)|subtract(const_100,n3)|divide(#2,#0)|multiply(#3,#1)| | general |
the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 75 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ? | ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a | a ) 25 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) 45 % | a | divide(multiply(700, const_100), add(add(multiply(const_2, const_1000), const_100), 700)) | multiply(n0,const_100)|multiply(const_1000,const_2)|add(#1,const_100)|add(n0,#2)|divide(#0,#3) | general |
in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the b... | "actual miles / gallon is = 480 / 4 = 12 miles / gallon . current engine miles / gallon is 8 miles / gallon . additional 4 miles / gallon is required to match the actual mileage . answer : b" | a ) 2 , b ) 4 , c ) 12 , d ) 40 , e ) 160 | b | subtract(divide(480, 40), 8) | divide(n1,n0)|subtract(#0,n2)| | physics |
the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 8 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flig... | "age of the teacher = ( 23 * 13 - 22 * 12 ) = 35 years . answer : c" | a ) 31 , b ) 36 , c ) 35 , d ) 53 , e ) 57 | c | add(22, const_1) | add(n0,const_1)| | general |
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