Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
values |
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what is the value of ( 12 + 22 + 32 + 42 + - - - - - + 102 ) | "explanation : ( 12 + 22 + … . . + n 2 ) = ( 1 / 6 ) n ( n + 1 ) ( 2 n + 1 ) here , n = 10 therefore , ( 12 + 22 + … . . + 102 ) = ( 1 / 6 ) 10 ( 10 + 1 ) ( 2 x 10 + 1 ) = ( 1 / 6 ) x 10 x 11 x 21 = 385 answer : c" | a ) 295 , b ) 324 , c ) 385 , d ) 391 , e ) 399 | c | power(12, negate(22)) | negate(n1)|power(n0,#0)| | general |
if m and n are positive integers and m = 15 n - 1 , what is the remainder when m is divided by 5 ? | this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that m and n are positive integers and m = 15 n - 1 . we ' re asked for the remainder when m is divided by 5 . if . . . . n = 1 m = 14 14 / 5 = 2 rema... | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | e | subtract(subtract(multiply(15, const_2), 1), multiply(5, 5)) | multiply(n0,const_2)|multiply(n2,n2)|subtract(#0,n1)|subtract(#2,#1) | general |
a man has $ 10,000 to invest . he invests $ 4000 at 5 % and $ 3500 at 4 % . in order to have a yearly income of $ 500 , he must invest the remainder at : | "c 6.4 % income from $ 4000 at 5 % in one year = $ 4000 of 5 % . = $ 4000 × 5 / 100 . = $ 4000 × 0.05 . = $ 200 . income from $ 3500 at 4 % in one year = $ 3500 of 4 % . = $ 3500 × 4 / 100 . = $ 3500 × 0.04 . = $ 140 . total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340 . remaining income amount in or... | a ) 4.6 % , b ) 3.6 % , c ) 6.4 % , d ) 7.8 % , e ) 8.9 % | c | divide(subtract(subtract(500, multiply(divide(4000, const_100), 5)), multiply(divide(3500, const_100), 4)), divide(subtract(subtract(multiply(const_100, const_100), 4000), 3500), const_100)) | divide(n1,const_100)|divide(n3,const_100)|multiply(const_100,const_100)|multiply(n2,#0)|multiply(n4,#1)|subtract(#2,n1)|subtract(n5,#3)|subtract(#5,n3)|divide(#7,const_100)|subtract(#6,#4)|divide(#9,#8)| | gain |
workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.25 lacs . how many workers were they ? | "n * 50 = ( 325000 - 300000 ) = 25000 n = 25000 / 50 = 500 c" | a ) 350 , b ) 400 , c ) 500 , d ) 550 , e ) 590 | c | divide(multiply(multiply(subtract(3.25, 3), const_1000), const_100), 50) | subtract(n2,n0)|multiply(#0,const_1000)|multiply(#1,const_100)|divide(#2,n1)| | general |
in the xy - coordinate system , if ( m , n ) and ( m 1 2 , n 1 k ) are two points on the line with the equation x 5 2 y 1 5 , then k 5 | step 1 : analyze the question for any question involving the equation of a line , a good place to start is the slope - intercept form of the line , y = mx 1 b . remember that if you have two points on a line , you can derive the entire equation , and if you have an equation of the line , you can calculate any points on... | a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4 | b | multiply(2, divide(1, 2)) | divide(n0,n1)|multiply(n1,#0) | general |
if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 11 , what is the value of x ? | we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and w... | a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4 | d | divide(const_1, 4) | divide(const_1,n4) | general |
find √ ? / 13 = 4 ? | "answer let √ n / 13 = 4 then √ n = 13 x 4 = 52 ∴ n = 52 x 52 = 2704 . correct option : d" | a ) 76 , b ) 5776 , c ) 304 , d ) 2704 , e ) none | d | power(multiply(4, 13), const_2) | multiply(n0,n1)|power(#0,const_2)| | general |
an athlete runs 200 metres race in 25 seconds . what is his speed ? | "speed = distance / time = 200 / 25 = 8 m / s = 8 * 18 / 5 = 28.8 km / hr answer : e" | a ) 23 , b ) 38 , c ) 37 , d ) 30 , e ) 28.8 | e | multiply(divide(200, 25), const_3_6) | divide(n0,n1)|multiply(#0,const_3_6)| | physics |
how many odd prime numbers are there less than 125 ? | odd prime number less than 125 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 there is 29 the odd prime number answer is a | a ) 29 , b ) 34 , c ) 44 , d ) 54 , e ) 64 | a | add(subtract(125, const_100), const_4) | subtract(n0,const_100)|add(#0,const_4) | general |
the radius of a semi circle is 3.1 cm then its perimeter is ? | "36 / 7 r = 6.3 = 15.94 answer : a" | a ) 15.94 , b ) 12.41 , c ) 16.1 , d ) 32.92 , e ) 32.3 | a | add(divide(circumface(3.1), const_2), multiply(3.1, const_2)) | circumface(n0)|multiply(n0,const_2)|divide(#0,const_2)|add(#2,#1)| | physics |
a , band c can do a piece of work in 11 days , 5 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ? | ( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 5 = 16 / 55 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 55 = 6 / 55 work done in 2 day ' s = 16 / 55 + 6 / 55 = 2 / 5 2 / 5 th work done in 2 days work done = 5 / 2 * 2 = 5 days answer : a | a ) 5 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days | a | divide(55, divide(add(add(divide(55, 11), divide(55, 5)), add(divide(55, 11), divide(55, 55))), const_2)) | divide(n2,n0)|divide(n2,n1)|divide(n2,n2)|add(#0,#1)|add(#0,#2)|add(#3,#4)|divide(#5,const_2)|divide(n2,#6) | physics |
find the number of shares that can be bought for rs . 8200 if the market value is rs . 20 each with brokerage being 2.5 % . | "explanation : cost of each share = ( 20 + 2.5 % of 20 ) = rs . 20.5 therefore , number of shares = 8200 / 20.5 = 400 answer : c" | a ) 237 , b ) 270 , c ) 177 , d ) 166 , e ) 111 | c | floor(divide(8200, add(20, divide(2.5, const_100)))) | divide(n2,const_100)|add(n1,#0)|divide(n0,#1)|floor(#2)| | gain |
two trains 300 m and 400 m long run at the speed of 36 kmph and 18 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ? | "relative speed = 36 + 18 = 54 kmph * 5 / 18 = 15 m / s distance covered in crossing each other = 300 + 400 = 700 m required time = 700 * 1 / 15 = 46.67 sec answer is b" | a ) 5.6 sec , b ) 46.67 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 15 sec | b | divide(add(300, 400), multiply(add(36, 18), const_0_2778)) | add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)| | physics |
if 1 / ( x + 2 ) + 1 / ( x - 2 ) = 1 / ( x + 2 ) , what is the value of x ? | "if we solve the question , we get x = - 2 . option : d" | a ) - 1 , b ) 2 , c ) 1 , d ) - 2 , e ) 0 | d | subtract(add(1, 1), 1) | add(n0,n0)|subtract(#0,n0)| | general |
find the compound interest on $ 1200 for 1 year at 20 % p . a . if ci is component yearly ? | "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 1 = 1200 * 6 / 5 = $ 1440 ci = a - p = 1440 - 1200 = $ 240 answer is c" | a ) $ 120 , b ) $ 150 , c ) $ 240 , d ) $ 250 , e ) $ 300 | c | subtract(multiply(1200, power(add(const_1, divide(20, const_100)), 1)), 1200) | divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|subtract(#3,n0)| | gain |
find the perimeter and area of a square of side 12 cm . | "we know that the perimeter of square = 4 ã — side side = 12 cm therefore , perimeter = 4 ã — 12 cm = 48 cm now , area of the square = ( side ã — side ) sq . units = 12 ã — 12 cm â ² = 144 cm â ² answer : a" | a ) 144 , b ) 121 , c ) 169 , d ) 196 , e ) 100 | a | square_area(12) | square_area(n0)| | geometry |
if the sides of a cube are in the ratio 5 : 4 . what is the ratio of their diagonals ? | "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 5 : 4 d 1 : d 2 = 5 : 4 where √ 3 cancelled both side answer : b" | a ) 4 : 3 , b ) 5 : 4 , c ) 4 : 7 , d ) 3 : 4 , e ) 4 : 5 | b | divide(5, 4) | divide(n0,n1)| | geometry |
bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 40 seconds and his sister ’ s time is currently 9 minutes 17 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ? | bob ' s time = 640 secs . his sis ' time = 557 secs . percent increase needed = ( 640 - 557 / 640 ) * 100 = 83 / 640 * 100 = 13 % . ans ( e ) . | a ) 3 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 13 % | e | multiply(multiply(10, 10), subtract(const_1, divide(add(multiply(9, const_60), 17), add(multiply(10, const_60), 40)))) | multiply(n0,n0)|multiply(n2,const_60)|multiply(n0,const_60)|add(n3,#1)|add(n1,#2)|divide(#3,#4)|subtract(const_1,#5)|multiply(#0,#6) | physics |
a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 10 : 30 am in the same direction at the rate of 80 km / h . at what time will the second train catch the first train ? | in one hour and thirty minutes the first train travels 105 km . the second train catches the first train at a rate of 80 km / h - 70 km / h = 10 km / h . the second train will catch the first train in 105 / 10 = 10.5 hours , so at 9 : 00 pm . the answer is c . | a ) 7 : 00 , b ) 8 : 00 , c ) 9 : 00 , d ) 10 : 00 , e ) 11 : 00 | c | divide(add(70, multiply(70, divide(const_1, const_2))), subtract(80, 70)) | divide(const_1,const_2)|subtract(n5,n2)|multiply(n2,#0)|add(n2,#2)|divide(#3,#1) | physics |
working together , jose and jane can complete an assigned task in 15 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 45 days . how long will jose take to complete the task if he worked alone ? as... | "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 15 15 ( x + y ) = xy next , we ' re told 1 job takes 45 days to complete if jose and jan... | a ) 26 days , b ) 31 days , c ) 50 days , d ) 65 days , e ) 36 days | c | multiply(const_3, 15) | multiply(n0,const_3)| | physics |
in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 4 ohms and y is 6 ohms ? | "1 / r = 1 / x + 1 / y 1 / r = 1 / 4 + 1 / 6 = 5 / 12 r = 12 / 5 the answer is c ." | a ) 5 / 12 , b ) 7 / 12 , c ) 12 / 5 , d ) 7 / 5 , e ) 11 / 5 | c | divide(multiply(6, 4), add(4, 6)) | add(n0,n1)|multiply(n0,n1)|divide(#1,#0)| | general |
the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam . | "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 40 ) = 90 ( x - 5 ) 250 = 10 x = > x = 25 answer : c" | a ) 87 , b ) 27 , c ) 25 , d ) 26 , e ) 24 | c | divide(subtract(multiply(90, 5), multiply(5, 40)), subtract(90, 80)) | multiply(n1,n3)|multiply(n1,n2)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2)| | general |
when x is multiplied by 3 , the result is 16 more than the result of subtracting x from 36 . what is the value of x ? | "the equation that can be formed is : 3 x - 16 = 36 - x or , 4 x = 52 or , x = 13 . answer : d" | a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22 | d | divide(add(36, 16), add(3, const_1)) | add(n1,n2)|add(const_1,n0)|divide(#0,#1)| | general |
a goods train leaves a station at a certain time and at a fixed speed . after 6 hours , an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph . this train catches up the goods train in 4 hours . find the speed of the goods train . | let the speed of the goods train be x kmph . distance covered by goods train in 10 hours = distance covered by express train in 4 hours . ∴ 10 x = 4 × 90 or x = 36 . so , speed of goods train = 36 kmph . answer a | a ) 36 kmph , b ) 40 kmph , c ) 30 kmph , d ) 42 kmph , e ) none of these | a | divide(multiply(4, 90), add(6, 4)) | add(n0,n2)|multiply(n1,n2)|divide(#1,#0) | physics |
if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 4 people to do 4 times of that particular work ? | "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 4 people can do 4 / 3 of the work in one day . 4 people can do 4 times the work in 3 days . the answer is c ." | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 7 | c | multiply(3, divide(4, 4)) | divide(n3,n3)|multiply(n0,#0)| | physics |
5 ! / ( 5 - 3 ) ! = ? | 5 ! / ( 5 - 3 ) ! = 5 ! / 2 ! = 5 * 4 * 3 = 60 . hence , the correct answer is e . | a ) 36 , b ) 46 , c ) 56 , d ) 59 , e ) 60 | e | divide(factorial(5), factorial(subtract(5, 3))) | factorial(n0)|subtract(n0,n2)|factorial(#1)|divide(#0,#2)| | general |
the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal ... | assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.12 * 80 90 x - 80 = 9.6 90 x = 89.6 x = 89.6 / 90 = 0.995 x is slightly under 0.9955 = 0.99 answer : c | a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.99 , d ) $ 1.00 , e ) $ 1.20 | c | multiply(add(const_1, divide(12, const_100)), divide(0.8, divide(subtract(const_100, 10), const_100))) | divide(n2,const_100)|subtract(const_100,n1)|add(#0,const_1)|divide(#1,const_100)|divide(n0,#3)|multiply(#2,#4) | gain |
what is the remainder when 4 ^ 8707 is divided by 5 ? | "4 ^ 0 = 1 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ 5 = . . . . . 4 4 ^ 6 = . . . . . . . 6 and so on in a distinct last - digit pattern of 4,6 , 4,6 . . . after ignoring the first last - digit of 1 8707 / 2 = 4353 ( with a remainder of 1 ) so the last number is a 4 . alternatively , 8707 is an odd number and he... | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | e | subtract(divide(5, const_2), multiply(4, 4)) | divide(n2,const_2)|multiply(n0,n0)|subtract(#0,#1)| | general |
if 5 % more is gained by selling an article for rs . 220 than by selling it for rs . 160 , the cost of the article is ? | "let c . p . be rs . x . then , 5 % of x = 220 - 160 = 60 x / 20 = 60 = > x = 1200 answer : b" | a ) 127 , b ) 1200 , c ) 1600 , d ) 1400 , e ) 1202 | b | divide(subtract(220, 160), divide(5, const_100)) | divide(n0,const_100)|subtract(n1,n2)|divide(#1,#0)| | gain |
how many integers between 100 and 170 , inclusive , can not be evenly divided by 3 nor 5 ? | "the total numbers between 100 and 170 , inclusive , is 71 . 3 * 34 = 102 and 3 * 56 = 168 so the number of multiples of 3 is 23 . 5 * 20 = 100 and 5 * 34 = 170 so the number of multiples of 5 is 15 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 11 = 165 so the number of multiples of 15... | a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 44 | b | subtract(170, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2)) | add(const_3,const_4)|multiply(const_100,const_2)|multiply(#0,const_10)|add(#1,#2)|add(#3,const_2)|subtract(n1,#4)| | general |
two persons a and b can complete a piece of work in 20 days and 40 days respectively . if they work together , what part of the work will be completed in 5 days ? | "a ' s one day ' s work = 1 / 20 b ' s one day ' s work = 1 / 40 ( a + b ) ' s one day ' s work = 1 / 20 + 1 / 40 = 3 / 40 the part of the work completed in 5 days = 5 ( 3 / 40 ) = 3 / 8 . answer : d" | a ) 1 / 8 , b ) 1 / 3 , c ) 3 / 6 , d ) 3 / 8 , e ) 5 / 3 | d | multiply(5, add(divide(const_1, 20), divide(const_1, 40))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|multiply(n2,#2)| | physics |
there are x persons and y chocolates . if each person is given 1 chocolate then 1 chocolate is left , if each person is given 2 chocolates then 1 person will be left . so how many persons and chocolates are there ? ? | x person , y chocolates 1 st equation = = > ( y - 1 ) / x = 1 2 nd equation = = > y / ( x - 1 ) = 2 solving we get x = 3 , y = 4 answer : c | a ) 32 , b ) 33 , c ) 34 , d ) 45 , e ) 44 | c | subtract(multiply(const_12, const_3), 2) | multiply(const_12,const_3)|subtract(#0,n2) | general |
working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 3 days at a time . if a starts they finish the task in exactly 9 days . if b starts , they take a day more . how long does it take to complete the task if they... | "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 6 no . of days when b works = 3 → 6 x + 3 y = 1 when b starts : no . of days when a works = 4 no . of days when a works = 5 → 5 x + 4 y = 1 solving the above two equations for xy x = 1 / 9 y = 1 / 9 → total work done by ab in a da... | a ) 8 , b ) 6 , c ) 4 , d ) 5 , e ) 9 / 2 | e | inverse(add(inverse(subtract(9, const_1)), inverse(add(9, const_2.0)))) | add(const_2.0,n1)|subtract(n1,const_1)|inverse(#1)|inverse(#0)|add(#2,#3)|inverse(#4)| | physics |
find out the square of a number which when doubled exceeds its one seventh by 13 ? | "a let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 7 ) + 13 = > 14 p = p + 91 = > p = 7 p ^ 2 = 7 ^ 2 = 49 . answer : b" | a ) 16 , b ) 49 , c ) 19 , d ) 26 , e ) 17 | b | power(divide(13, subtract(const_2, divide(const_1, add(const_4, const_1)))), const_2) | add(const_1,const_4)|divide(const_1,#0)|subtract(const_2,#1)|divide(n0,#2)|power(#3,const_2)| | general |
a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 20 gallons of gasoline ? | "so 12.2 * 20 = 244 . . imo option d is correct answer . ." | a ) 190 , b ) 284.6 , c ) 300 , d ) 244 , e ) 312 | d | multiply(12.2, 20) | multiply(n0,n2)| | general |
an engineering student has to secure 36 % marks to pass . he gets 130 marks and fails by 14 marks . the maximum number of marks obtained by him is ? | 130 14 - - - - - - - 361 - - - - - - 144 100 % - - - - - - ? = > 400 answer : b | a ) 337 , b ) 400 , c ) 298 , d ) 2798 , e ) 271 | b | divide(multiply(add(130, 14), const_100), 36) | add(n1,n2)|multiply(#0,const_100)|divide(#1,n0) | gain |
united telephone charges a base rate of $ 9.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ? | lets take number of minutesx . given that , 9 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 60 minutes ans e | a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes | e | divide(subtract(12, 9), subtract(0.25, 0.2)) | subtract(n2,n0)|subtract(n1,n3)|divide(#0,#1) | general |
the cost of carpeting a room 18 m long with a carpet 75 cm wide at 45 paise per meter is rs . 81 . the breadth of the room is : | "length of the carpet = total cost / rate / m = 8100 / 45 = 180 m area of the carpet = 180 * 75 / 100 = 135 m 2 breadth of the room = ( area / length ) = 135 / 18 = 7.5 m answer : b" | a ) 7 m , b ) 7.5 m , c ) 5.5 m , d ) 6.5 m , e ) 8.5 m | b | divide(multiply(divide(81, 45), divide(75, const_100)), 18) | divide(n3,n2)|divide(n1,const_100)|multiply(#0,#1)|divide(#2,n0)| | physics |
a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 7 km ? | "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 7 / 2 = 3.5 hours . the answer is c ." | a ) 3.0 , b ) 3.25 , c ) 3.5 , d ) 3.75 , e ) 4.0 | c | divide(7, subtract(4, 2)) | subtract(n0,n1)|divide(n2,#0)| | physics |
ratio between 2 numbers is 5 : 7 and their product is 560 . what is the difference between 2 numbers ? | "explanation : x / y = 5 / 7 x × y = 560 ⇒ x = 560 / y substituting this value in first equation , we get 560 / yy = 57560 / yy = 57 ⇒ 560 y 2 = 57560 y 2 = 57 ⇒ y = 28 x = 20 so difference between the numbers could be x – y = – 8 y – x = 8 answer : c" | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 2 | c | multiply(const_3.0, divide(7, add(2, 5))) | add(const_3.0,n1)|divide(n2,#0)|multiply(n0,#1)| | general |
the edges of three metal cubes are 1 cm , 2 cm , and 3 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ? | "the total volume is 1 ^ 3 + 2 ^ 3 + 3 ^ 3 = 36 the edge of the new cube is the cube root of 36 which is about 3.3 cm . the answer is a ." | a ) 3.3 , b ) 3.5 , c ) 3.7 , d ) 3.9 , e ) 4.1 | a | power(add(power(3, 2), add(1, power(2, 2))), const_0_33) | power(n1,n1)|power(n2,n1)|add(n0,#0)|add(#2,#1)|power(#3,const_0_33)| | physics |
a scale 6 ft . 8 inches long is divided into 2 equal parts . find the length of each part . | explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 2 parts = 80 / 2 = 40 inches answer : e | a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 40 inches | e | divide(add(multiply(6, const_12), 8), 2) | multiply(n0,const_12)|add(n1,#0)|divide(#1,n2) | general |
right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 11 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 20 % , then al would have exactly $ 22 more than eliot in his accou... | "lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 11 * ( a + e ) = = > 10 a = 12 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 ... | a ) $ 110 , b ) $ 120 , c ) $ 183.3 , d ) $ 220 , e ) $ 260 | c | divide(multiply(22, const_100), subtract(multiply(add(11, 1), 10), add(const_100, 20))) | add(n0,n1)|add(n3,const_100)|multiply(n4,const_100)|multiply(#0,n2)|subtract(#3,#1)|divide(#2,#4)| | general |
if 11 oranges bought 10 r and 10 oranges sold 11 r . what is the profit | suppose he bought 110 apples . cp = rs 100 sp = rs 121 % profit = 100 * ( 121 - 100 ) / 100 = 21 % answer : d | a ) 11 % , b ) 20 % , c ) 22 % , d ) 21 % , e ) 23 % | d | multiply(divide(subtract(divide(11, 10), divide(10, 11)), divide(10, 11)), const_100) | divide(n0,n1)|divide(n1,n0)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100) | gain |
the speed at which a man can row a boat in still water is 15 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 110 meters ? | "the speed of the boat downstream = 15 + 3 = 18 km / hr 18 km / hr * 5 / 18 = 5 m / s the time taken to cover 110 meters = 110 / 5 = 22 seconds . the answer is b ." | a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 28 | b | divide(110, multiply(add(15, const_3.0), const_0_2778)) | add(n0,n1)|multiply(#0,const_0_2778)|divide(const_100.0,#1)| | physics |
find the simple interest on rs . 567 for 7 months at 9 paisa per month ? | "explanation : i = ( 567 * 7 * 9 ) / 100 = 357.21 answer : option a" | a ) s . 357.21 , b ) s . 322.12 , c ) s . 400 , d ) s . 278.9 , e ) s . 300 | a | multiply(567, divide(7, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | gain |
the least number which when divided by 4 , 6 , 7 and 8 leaves a remainder 6 , but when divided by 9 leaves no remainder , is | "explanation : l . c . m of 4 , 6 , 7 , 8 = 168 therefore required number is of the form 168 k + 6 . least value of k for which ( 168 k + 6 ) is divisible by 9 is k = 2 therefore required number = ( 168 x 2 + 6 ) = 342 . answer : b" | a ) 340 , b ) 342 , c ) 523 , d ) 363 , e ) none of these | b | multiply(lcm(lcm(lcm(4, 6), 7), 8), const_2) | lcm(n0,n1)|lcm(n2,#0)|lcm(n3,#1)|multiply(#2,const_2)| | general |
if 0.6 : 1.4 : : 2 : 4 : x , then x = ? | "explanation : 0.6 × x = 2.4 × 1.4 x = ( 2.4 × 1.4 ) / 0.6 = 24 / 10 × 17 / 10 × 1 / ( 6 / 10 ) 24 / 10 × 14 / 10 × 10 / 6 2 / 5 × 14 = 28 / 5 = 5.6 answer : option b" | a ) 56 , b ) 5.6 , c ) 0.56 , d ) 0.056 , e ) none of these | b | divide(add(multiply(1.4, const_3.0), 1.4), 2) | multiply(const_3.0,n1)|add(n1,#0)|divide(#1,n2)| | general |
the tax on a commodity is diminished by 10 % and its consumption increases by 10 % . find the effects on revenue ? | "since tax consumption = revenue . therefore , net % change in revenue = ( x + y + xy / 100 ) % = [ - 10 + 10 + ( - 10 x 10 ) / 100 ] % or - 1 % . therefore , revenue decreased by 1 % . answer : a" | a ) 1 % decrease , b ) 2 % increase , c ) 3 % decrease , d ) 4 % decrease , e ) none of these | a | subtract(const_100, multiply(multiply(add(const_1, divide(10, const_100)), subtract(const_1, divide(10, const_100))), const_100)) | divide(n1,const_100)|divide(n0,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|multiply(#4,const_100)|subtract(const_100,#5)| | general |
at 15 : 00 there were 20 students in the computer lab . at 15 : 03 and every three minutes after that , 4 students entered the lab . if at 15 : 10 and every ten minutes after that 8 students left the lab , how many students were in the computer lab at 15 : 44 ? | "initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 27 d" | a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30 | d | add(subtract(add(multiply(floor(divide(44, 03)), const_3.0), 20), multiply(floor(divide(44, 8)), 8)), 03) | divide(n10,n5)|divide(n10,n8)|floor(#0)|floor(#1)|multiply(n5,#2)|multiply(n8,#3)|add(n2,#4)|subtract(#6,#5)|add(n4,#7)| | physics |
' a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the difference between the maximum and minimum possible values of ' a + b ' ? | a = 4 , b = 5 as they have to co - primes ( hcf being 1 and lcm = 20 ) so a + b = 9 is their max and min value hence difference = 0 answer - a | a ) 0 , b ) 12 , c ) 13 , d ) 9 , e ) 11 | a | subtract(add(divide(20, const_4), const_4), add(divide(20, const_4), const_4)) | divide(n0,const_4)|add(#0,const_4)|subtract(#1,#1) | general |
if a , b and c together can finish a piece of work in 4 days . a alone in 6 days and b in 18 days , then c alone can do it in ? | "c = 1 / 4 - 1 / 6 – 1 / 18 = 1 / 36 = > 36 days ' answer : e" | a ) 1 , b ) 7 , c ) 8 , d ) 9 , e ) 36 | e | divide(const_1, subtract(subtract(const_0_25, divide(const_1, 6)), divide(const_1, 18))) | divide(const_1,n1)|divide(const_1,n2)|subtract(const_0_25,#0)|subtract(#2,#1)|divide(const_1,#3)| | physics |
wo passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ? | 1 h - - - - - 5 ? - - - - - - 60 12 h rs = 16 + 21 = 37 t = 12 d = 37 * 12 = 444 answer : b | a ) 227 , b ) 444 , c ) 277 , d ) 298 , e ) 212 | b | multiply(divide(60, subtract(21, 16)), add(16, 21)) | add(n0,n1)|subtract(n1,n0)|divide(n2,#1)|multiply(#0,#2) | physics |
the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 3135 . what was his original salary ? | "x * ( 110 / 100 ) * ( 95 / 100 ) = 3135 x * ( 11 / 10 ) * ( 1 / 100 ) = 33 x = 3000 answer : d" | a ) 2277 , b ) 2999 , c ) 1000 , d ) 3000 , e ) 1971 | d | divide(3135, multiply(add(const_1, divide(10, const_100)), subtract(const_1, divide(5, const_100)))) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|subtract(const_1,#1)|multiply(#2,#3)|divide(n2,#4)| | gain |
a train speeds past a pole in 15 sec and a platform 130 m long in 25 sec , its length is ? | "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 130 ) / 25 = x / 15 = > x = 195 m . answer : option a" | a ) 195 , b ) 150 , c ) 160 , d ) 170 , e ) 180 | a | multiply(130, subtract(const_2, const_1)) | subtract(const_2,const_1)|multiply(n1,#0)| | physics |
city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 4 : 35 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ? | "train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 4 : 35 pm + 2 hrs = 6 : 35 pm answer : d . 6 : 35" | a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 35 , e ) 7 : 00 | d | divide(add(4, const_2), 35) | add(n4,const_2)|divide(#0,n5)| | physics |
if - 11 a and - 8 b are negative integers , then ( - 11 a ) * ( - 8 b ) + ab is | answer : c | a ) 88 ab , b ) - 89 ab , c ) 89 ab , d ) - 88 a , e ) - 88 b | c | add(multiply(11, 8), const_1) | multiply(n0,n1)|add(#0,const_1) | general |
what is the thousandths digit in the decimal equivalent of 43 / 5000 ? | "43 / 5000 = 43 / ( 5 * 10 ^ 3 ) = ( 43 / 5 ) * 10 ^ - 3 = 8.6 * 10 ^ - 3 = . 0086 thousandths digit = 8 answer e" | a ) 0 , b ) 1 , c ) 3 , d ) 5 , e ) 8 | e | floor(multiply(const_100, divide(43, 5000))) | divide(n0,n1)|multiply(#0,const_100)|floor(#1)| | general |
what is the difference between the largest number and the least number written with the digits 5 , 3 , 1 , 4 ? | explanation : 1345 5431 - - - - - - - - - - - - 4086 answer : c | a ) 6084 , b ) 3788 , c ) 4086 , d ) 2721 , e ) 1812 | c | subtract(add(add(add(multiply(multiply(5, const_100), const_10), multiply(4, const_100)), multiply(3, const_10)), 1), add(add(add(const_1000, multiply(3, const_100)), multiply(4, const_10)), 5)) | multiply(n0,const_100)|multiply(n3,const_100)|multiply(n1,const_10)|multiply(n1,const_100)|multiply(n3,const_10)|add(#3,const_1000)|multiply(#0,const_10)|add(#6,#1)|add(#5,#4)|add(#7,#2)|add(n0,#8)|add(n2,#9)|subtract(#11,#10) | general |
if ( a – b ) is 9 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is : | ( a – b ) – ( c + d ) = 9 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 9 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 9 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 9 = ( c – a ) – 3 = > 2 ( a – c ) = 6 = > ( a – c ) = 3 answer : c | a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | divide(9, 3) | divide(n0,n1) | general |
the population of a town increased from 1 , 75,000 to 2 , 10,000 in a decade . the average percent increase of population per year is | "solution increase in 10 years = ( 210000 - 175000 ) = 35000 . increase % = ( 35000 / 175000 ã — 100 ) % = 20 % . required average = ( 20 / 10 ) % = 2 % . answer a" | a ) 2 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none | a | 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 |
there are 408 boys and 240 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed . | "explanation : hcf ( 408 , 240 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 240 / 24 = 17 + 10 = 27 answer : a" | a ) 27 , b ) 32 , c ) 35 , d ) 30 , e ) 45 | a | divide(add(408, 240), multiply(multiply(multiply(const_2, const_2), const_2), const_3)) | add(n0,n1)|multiply(const_2,const_2)|multiply(#1,const_2)|multiply(#2,const_3)|divide(#0,#3)| | general |
an alloy weighing 20 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 20 * ( 70 / 100 ) = 14 ounces . now we add x ounces of pure gold to make it 90 % gold . so 14 + x = ( 24 + x ) * 90 / 100 = > x = 76 . answer is d ." | a ) 6 , b ) 9 , c ) 12 , d ) 76 , e ) 48 | d | divide(multiply(divide(90, const_100), 20), divide(70, const_100)) | divide(n2,const_100)|divide(n1,const_100)|multiply(n0,#0)|divide(#2,#1)| | gain |
the cost of the paint is rs . 20 per kg . if 1 kg of paint covers 15 sq . ft , how much will it cost to paint outside of a cube having 5 feet each side | explanation : surface area of a cube = 6 x 5 ^ 2 = 150 sq . ft quantity of paint required = ( 150 / 15 ) = 10 kg cost of painting = 20 x 10 = rs . 200 answer : a | ['a ) rs . 200', 'b ) rs . 672', 'c ) rs . 546', 'd ) rs . 876', 'e ) none of these'] | a | multiply(divide(surface_cube(5), 15), 20) | surface_cube(n3)|divide(#0,n2)|multiply(n0,#1) | geometry |
a student committee on academic integrity has 30 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ? | "xc 1 * ( x - 1 ) c 1 = 30 x ^ 2 - x - 30 = 0 ( x - 6 ) ( x + 5 ) = 0 x = 6 , - 5 - 5 ca n ' t possible . d" | a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 11 | d | divide(add(const_1, sqrt(add(multiply(const_4, 30), power(negate(const_1), const_2)))), const_2) | multiply(n0,const_4)|negate(const_1)|power(#1,const_2)|add(#0,#2)|sqrt(#3)|add(#4,const_1)|divide(#5,const_2)| | other |
what is the difference between the largest number and the least number written with the digits 9 , 3 , 5 , 7 ? | "explanation : 3579 9753 - - - - - - - - - - - - 6174 answer : e" | a ) 6084 , b ) 3788 , c ) 2077 , d ) 2721 , e ) 6174 | e | subtract(add(add(add(multiply(multiply(9, const_100), const_10), multiply(7, const_100)), multiply(3, const_10)), 5), add(add(add(const_1000, multiply(3, const_100)), multiply(7, const_10)), 9)) | multiply(n0,const_100)|multiply(n3,const_100)|multiply(n1,const_10)|multiply(n1,const_100)|multiply(n3,const_10)|add(#3,const_1000)|multiply(#0,const_10)|add(#6,#1)|add(#5,#4)|add(#7,#2)|add(n0,#8)|add(n2,#9)|subtract(#11,#10)| | general |
a bag contains 4 red , 3 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ? | "p ( both are red ) , = 4 c 29 c 2 = 4 c 29 c 2 = 6 / 36 = 1 / 6 c" | a ) 1 / 13 , b ) 2 / 23 , c ) 1 / 6 , d ) 4 / 27 , e ) 3 / 23 | c | divide(choose(4, 2), choose(add(add(4, 3), 2), 2)) | add(n0,n1)|choose(n0,n3)|add(n2,#0)|choose(#2,n3)|divide(#1,#3)| | other |
what is the value of 8 1 / 3 % of 600 + 37 ½ of 400 | "25 * 600 / 300 + 75 * 400 / 200 = 50 + 150 = 200 answer : d" | a ) 100 , b ) 300 , c ) 150 , d ) 200 , e ) 250 | d | subtract(multiply(divide(divide(subtract(power(8, 1), power(3, 600)), const_1000), const_1000), 8), divide(divide(subtract(power(8, 1), power(3, 600)), const_1000), const_1000)) | power(n0,n1)|power(n2,n3)|subtract(#0,#1)|divide(#2,const_1000)|divide(#3,const_1000)|multiply(n0,#4)|subtract(#5,#4)| | general |
there is a 30 % chance jen will visit chile this year , while there is a 50 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ? | p ( chile and not madagascar ) = 0.3 * 0.5 = 0.15 p ( madagascar and not chile ) = 0.5 * 0.7 = 0.35 total probability = 0.15 + 0.35 = 0.5 = 50 % the answer is c . | a ) 25.0 % , b ) 37.5 % , c ) 50.0 % , d ) 62.5 % , e ) 75 % | c | multiply(add(multiply(divide(subtract(power(multiply(const_2, const_5), const_2), 30), power(multiply(const_2, const_5), const_2)), divide(50, power(multiply(const_2, const_5), const_2))), multiply(divide(30, power(multiply(const_2, const_5), const_2)), divide(50, power(multiply(const_2, const_5), const_2)))), power(mu... | multiply(const_2,const_5)|power(#0,const_2)|divide(n1,#1)|divide(n0,#1)|subtract(#1,n0)|divide(#4,#1)|multiply(#3,#2)|multiply(#5,#2)|add(#7,#6)|multiply(#8,#1) | probability |
how much 45 % of 60 is greater than 35 % of 40 ? | "( 45 / 100 ) * 60 – ( 35 / 100 ) * 40 27 - 14 = 13 answer : b" | a ) 18 , b ) 13 , c ) 15 , d ) 17 , e ) 71 | b | subtract(divide(multiply(45, 60), const_100), divide(multiply(35, 40), const_100)) | multiply(n0,n1)|multiply(n2,n3)|divide(#0,const_100)|divide(#1,const_100)|subtract(#2,#3)| | gain |
three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 180 . what is their h . c . f . ? | "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 180 x = 15 hcf of 2 x , 3 x and 4 x = x = 15 the answer is a ." | a ) 15 , b ) 20 , c ) 40 , d ) 60 , e ) 70 | a | multiply(2, 4) | multiply(n0,n2)| | other |
the length of minute hand of a clock is 5.4 cm . what is the area covered by this in 5 minutes | "area of circle is pi * r ^ 2 but in 5 minutes area covered is ( 5 / 60 ) * 360 = 30 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.4 ^ 2 ) * ( 30 / 360 ) = 7.63 cm ^ 2 answer : e" | a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 7.27 , e ) 7.63 | e | multiply(divide(add(multiply(const_2, 5), const_2), add(const_3, const_4)), multiply(multiply(5.4, 5.4), divide(multiply(const_1, const_60), multiply(const_100, const_3_6)))) | add(const_3,const_4)|multiply(n1,const_2)|multiply(const_1,const_60)|multiply(const_100,const_3_6)|multiply(n0,n0)|add(#1,const_2)|divide(#2,#3)|divide(#5,#0)|multiply(#6,#4)|multiply(#7,#8)| | physics |
donovan and michael are racing around a circular 600 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ? | one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 600 / 45 = > 40 / 3 2 . speed / rate of michael = distance / time = > 600 / 40 = > 15 relative speed between them = 15 - 40 / 3 = > 5 / 3 ( we subtract the rates if moving in the same direction and add the... | a ) 8 , b ) 7 , c ) 9 , d ) 6 , e ) 5 | c | divide(divide(600, subtract(divide(600, 40), divide(600, 45))), 40) | divide(n0,n2)|divide(n0,n1)|subtract(#0,#1)|divide(n0,#2)|divide(#3,n2) | physics |
if the function q is defined by the formula q = 5 w / ( 4 m ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , m is doubled , and z is tripled ? | we just need to find the factor thats all , w - > quadrupled - > 4 w m - > doubled - > 2 m z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and m * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b | a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27 | b | divide(4, multiply(2, power(const_3, 2))) | power(const_3,n2)|multiply(n2,#0)|divide(n1,#1) | general |
carol spends 1 / 4 of her savings on a stereo and 2 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ? | total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 2 / 3 ) ( 1 / 4 ) s = ( 1 / 3 ) * ( 1 / 4 ) * s = ( 1 / 12 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 12 ) / s = 1 / 4 answer : a | a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 1 / 2 , e ) 7 / 12 | a | divide(1, 4) | divide(n0,n1) | general |
one week , a certain truck rental lot had a total of 18 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 12 trucks on the lot that saturday morning , what is ... | "n - not rented trucks ; r - rented trucks n + r = 18 n + r / 2 = 12 r = 12 c" | a ) 18 , b ) 16 , c ) 12 , d ) 8 , e ) 4 | c | add(12, multiply(18, divide(50, const_100))) | divide(n1,const_100)|multiply(n0,#0)|add(n2,#1)| | general |
a grocer has 400 pounds of coffee in stock , 25 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ? | 1 . 25 % of 400 = 100 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 160 pounds of decaffeinated out of 500 pounds , that means 160 / 500 * 100 % = 32 % . the correct answer is c . | a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 40 % | c | multiply(divide(add(multiply(divide(25, const_100), 400), multiply(100, divide(60, const_100))), add(400, 100)), const_100) | add(n0,n2)|divide(n1,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(n2,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100) | gain |
calculate how much time could be saved if the train would run at its usual speed , given that it ran at 6 / 8 of its own speed and got to its destination in 11 hours ? | new speed = 6 / 8 of usual speed new time = 6 / 8 of usual time 6 / 8 of usual time = 10 hrs usual time = 10 * 6 / 8 = 7.5 hrs time saved = 10 - 7.5 = 2.5 hrs answer is a | a ) 2.5 hrs , b ) 2.9 hrs , c ) 4.5 hrs , d ) 3.5 hrs , e ) 1.5 hrs | a | add(divide(reminder(subtract(multiply(11, const_60), multiply(multiply(11, divide(6, 8)), const_60)), const_60), const_100), floor(divide(subtract(multiply(11, const_60), multiply(multiply(11, divide(6, 8)), const_60)), const_60))) | divide(n0,n1)|multiply(n2,const_60)|multiply(n2,#0)|multiply(#2,const_60)|subtract(#1,#3)|divide(#4,const_60)|reminder(#4,const_60)|divide(#6,const_100)|floor(#5)|add(#7,#8) | physics |
a person spent rs . 7,540 from his salary on food and 5,690 on house rent . after that he was left with 60 % of his monthly salary . what is his monthly salary ? | "total money spent on food and house rent = 7,540 + 5,690 = 13,230 which is 100 - 60 = 40 % of his monthly salary ∴ his salary = 13230 x 100 / 40 = 33075 answer : d" | a ) 73,075 , b ) 34,075 , c ) 23,075 , d ) 33,075 , e ) 32,075 | d | divide(add(multiply(add(const_4, const_1), const_100), 60), sqrt(const_100)) | add(const_1,const_4)|sqrt(const_100)|multiply(#0,const_100)|add(n2,#2)|divide(#3,#1)| | gain |
a survey was sent to 80 customers , 9 of whom responded . then the survey was redesigned and sent to another 63 customers , 12 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ? | "rate of first survey = 9 / 80 rate of second survey = 12 / 63 % response rate increase ( 12 / 63 - 9 / 80 ) / ( 9 / 80 ) = 69 % answer is e = 69 %" | a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 69 % | e | floor(multiply(subtract(divide(12, 63), divide(9, 80)), const_100)) | divide(n3,n2)|divide(n1,n0)|subtract(#0,#1)|multiply(#2,const_100)|floor(#3)| | gain |
the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 12 minutes is | "b = 15 km / hr , s = 3 km / hr , downstream b + s = 15 + 3 = 18 km / hr down stream time t = 12 min , we have to change it to hours so t = 12 / 60 = 1 / 5 hrs . distance = speed * time = 18 * 1 / 5 = 3.6 km . answer : d" | a ) 1.2 km , b ) 1.8 km , c ) 2.4 km , d ) 3.6 km , e ) 1.6 km | d | multiply(divide(12, const_60), add(15, 3)) | add(n0,n1)|divide(n2,const_60)|multiply(#0,#1)| | physics |
a sum of rs . 395 was divided among a , b , and c in such a way that b gets 25 % more than a and 20 % more than c . what is the share of a ? | let each one ’ s share is a , b and c respectively , then b = 125 a / 100 = 120 c / 100 a = 100 b / 125 = 4 / 5 b , c = 100 b / 120 = 5 / 6 b 4 / 5 b + b + 5 / 6 b = 395 , 79 b / 30 = 395 , b = 395 * 30 / 79 = 150 a = 4 * 150 / 5 = 120 answer : d | a ) rs . 195 , b ) rs . 180 , c ) rs . 98 , d ) rs . 120 , e ) rs . 130 | d | multiply(divide(subtract(const_100, 25), const_100), divide(395, add(add(divide(subtract(const_100, 25), const_100), divide(subtract(const_100, 20), const_100)), const_1))) | subtract(const_100,n1)|subtract(const_100,n2)|divide(#0,const_100)|divide(#1,const_100)|add(#2,#3)|add(#4,const_1)|divide(n0,#5)|multiply(#2,#6) | general |
the ratio 5 : 4 expressed as a percent equals | "solution 5 : 4 = 5 / 4 = ( 5 / 4 x 100 ) % . = 125 % . answer d" | a ) 12.5 % , b ) 40 % , c ) 80 % , d ) 125 % , e ) none | d | multiply(divide(5, 4), const_100) | divide(n0,n1)|multiply(#0,const_100)| | general |
the current birth rate per certain number of people is 52 , whereas corresponding death rate is 16 per same number of people . if the net growth rate in terms of population increase is 1.2 percent , find number of persons . ( initally ) | "sol . net growth on x = ( 52 - 16 ) = 36 . net growth on 100 = ( 36 / x ã — 100 ) % = 1.2 % . then x = 3000 answer : c" | a ) 4000 , b ) 2000 , c ) 3000 , d ) 5000 , e ) 1000 | c | multiply(const_100, divide(subtract(52, 16), 1.2)) | subtract(n0,n1)|divide(#0,n2)|multiply(#1,const_100)| | gain |
14 , 28 , 20 , 40 , 32 , 64 , . . . ? | "first , multiply by 2 and then subtract 8 . 14 14 * 2 = 28 28 - 8 = 20 20 * 2 = 40 40 - 8 = 32 32 * 2 = 64 64 - 8 = 56 answer : c" | a ) 10 , b ) 25 , c ) 56 , d ) 21 , e ) 36 | c | subtract(negate(40), multiply(subtract(28, 20), divide(subtract(28, 20), subtract(14, 28)))) | negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)| | general |
the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 6 ? | "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 6 = 38 runs total runs = new avg x new no . of innings = 38 * 21 = 798 runs made in the 11 th inning = 798 - 640 = 158 answer : c" | a ) 96 , b ) 106 , c ) 158 , d ) 116 , e ) 122 | c | subtract(multiply(add(20, const_1), add(6, 32)), multiply(20, 32)) | add(n0,const_1)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)| | general |
a is half good a work man as b and together they finish a job in 26 days . in how many days working alone b finish the job ? | "wc = 1 : 2 2 x + x = 1 / 26 = > x = 1 / 78 2 x = 1 / 78 = > 39 days answer : d" | a ) 98 days , b ) 21 days , c ) 17 days , d ) 39 days , e ) 19 days | d | multiply(26, divide(const_3, const_2)) | divide(const_3,const_2)|multiply(n0,#0)| | physics |
jane and ashley take 20 days and 10 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s wor... | "let us assume that the work is laying 40 bricks . jane = 2 bricks per day ashley = 4 brick per day together = 6 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 32 last 4 days jane works alone , no . of bricks = 8 remaining bricks = 40 - 40 = 0 so together , they would take 0 / 6 = 0 total n... | a ) 12 days , b ) 15 days , c ) 16 days , d ) 18 days , e ) 20 days | a | add(add(divide(subtract(subtract(const_1, multiply(const_4, divide(const_1, 20))), multiply(add(const_4, const_4), divide(const_1, 10))), add(divide(const_1, 20), divide(const_1, 10))), add(const_4, const_4)), const_4) | add(const_4,const_4)|divide(const_1,n0)|divide(const_1,n1)|add(#1,#2)|multiply(#1,const_4)|multiply(#0,#2)|subtract(const_1,#4)|subtract(#6,#5)|divide(#7,#3)|add(#0,#8)|add(#9,const_4)| | physics |
if john runs in the speed of 9 km / hr from his house , in what time will he reach the park which is 300 m long from his house ? | speed = 9 * 5 / 18 = 2.5 m / sec time taken = 300 / 2.5 = 120 sec ie . 2 mins . answer : a | a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 6 | a | multiply(divide(300, multiply(9, const_1000)), const_60) | multiply(n0,const_1000)|divide(n1,#0)|multiply(#1,const_60) | physics |
a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 40 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ? | first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 40 % increase over cost . here , we need to think about percentage increa... | a ) 1 : 20 , b ) 1 : 10 , c ) 17 : 8 , d ) 17 : 4 , e ) 17 : 60 | e | divide(subtract(33, divide(36, divide(add(const_100, 40), const_100))), divide(36, divide(add(const_100, 40), const_100))) | add(n1,const_100)|divide(#0,const_100)|divide(n2,#1)|subtract(n0,#2)|divide(#3,#2) | gain |
if the sides of a triangle are 26 cm , 18 cm and 10 cm , what is its area ? | the triangle with sides 26 cm , 18 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 18 * 10 = 90 cm 2 answer : option a | ['a ) 90', 'b ) 110', 'c ) 130', 'd ) 140', 'e ) 150'] | a | divide(multiply(18, 10), const_2) | multiply(n1,n2)|divide(#0,const_2) | geometry |
if x is the sum of first 100 positive even integers and y is the sum of first 100 positive odd integers , what is the value of x - y ? please try to explain your answers | first even minus first odd = 2 - 1 = 1 ; the sum of first 2 even integers minus the sum of first 2 odd integers = ( 2 + 4 ) - ( 1 + 3 ) = 2 ; the sum of first 3 even integers minus the sum of first 3 odd integers = ( 2 + 4 + 6 ) - ( 1 + 3 + 5 ) = 3 ; we can see the patterns here , so the sum of first 100 positive even ... | a ) 0 , b ) 25 , c ) 50 , d ) 75 , e ) 100 | e | multiply(100, const_1) | multiply(n0,const_1) | general |
the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 30 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ? | "3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 30 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 30 ) = $ 180 . the answer is c ." | a ) $ 120 , b ) $ 150 , c ) $ 180 , d ) $ 210 , e ) $ 240 | c | divide(30, subtract(divide(5, 3), divide(3, 2))) | divide(n3,n4)|divide(n0,n1)|subtract(#0,#1)|divide(n2,#2)| | general |
if x - y - z = 03 x + 4 y + 3 z = 45 x + 2 y + 7 z = 22 , what is the value of z ? | explanation : 4 x + 2 y - 5 z = - 21 â € “ - - - - - - - i 2 x - 2 y + z = 7 â € “ - - - - - - ii 4 x + 3 y - z = - 1 - - - - - - - - iii solve the first equation for x . x - y - z = 0 x = y + z substitute the solution for x into the second and third equations . ii - - - > 3 * ( y + z ) + 4 y + 3 z = 4 3 y + 3 z + 4 y ... | a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 1 | a | divide(divide(multiply(divide(add(multiply(add(const_1, const_4), add(22, multiply(const_4, 22))), add(22, multiply(const_2, 22))), add(add(45, 2), multiply(add(const_1, const_4), 7))), 7), 22), add(const_1, const_4)) | add(const_1,const_4)|add(n3,n4)|multiply(n6,const_2)|multiply(n6,const_4)|add(n6,#2)|add(n6,#3)|multiply(n5,#0)|add(#1,#6)|multiply(#0,#5)|add(#4,#8)|divide(#9,#7)|multiply(n5,#10)|divide(#11,n6)|divide(#12,#0) | general |
a call center has two teams . each member of team a was able to process 1 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ? | "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 1 calls , so total calls for team a = 5 fraction for team b = 40 / ( 40 + 5 ) = 8 / 9 = answer = c" | a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 9 , d ) 1 / 2 , e ) 1 / 5 | c | divide(multiply(8, 5), add(multiply(8, 5), multiply(5, 1))) | multiply(n1,n3)|multiply(n0,n1)|add(#0,#1)|divide(#0,#2)| | general |
how much space , in cubic units , is left vacant when maximum number of 3 x 3 x 3 cubes are fitted in a rectangular box measuring 6 x 9 x 11 ? | "no of cubes that can be accommodated in box = ( 6 * 9 * 11 ) / ( 3 * 3 * 3 ) 6 * 9 in numerator can be perfectly divided by 3 * 3 in denominator . side with length 11 ca n ' t be perfectly divided by 3 and hence is the limiting factor . closet multiple of 3 less that 11 is 9 . so vacant area in cube = = 6 * 9 * ( 11 -... | a ) 112 , b ) 111 , c ) 110 , d ) 109 , e ) 108 | e | multiply(subtract(6, multiply(3, const_2)), multiply(9, 11)) | multiply(n4,n5)|multiply(n0,const_2)|subtract(n3,#1)|multiply(#0,#2)| | geometry |
the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 17 km / hr respectively . they will meet for the first time in ? | "clearly , the two will meet when they are 1000 m apart to be 20 + 17 = 37 km apart , they take 1 hour to be 1000 m apart , they take 37 * 1000 / 1000 = 37 min . answer is d" | a ) 50 min , b ) 40 min , c ) 35 min , d ) 37 min , e ) 20 min | d | add(20, 17) | add(n1,n2)| | general |
if the sum of two numbers is 18 and the sum of their squares is 180 , then the product of the numbers is | "according to the given conditions x + y = 18 and x ^ 2 + y ^ 2 = 180 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 18 ^ 2 = 180 + 2 xy so xy = 144 / 2 = 72 answer : a" | a ) 72 , b ) 44 , c ) 80 , d ) 88 , e ) 48 | a | divide(subtract(power(18, const_2), 180), const_2) | power(n0,const_2)|subtract(#0,n1)|divide(#1,const_2)| | general |
sam invested rs . 15000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ? | "p = rs . 15000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 15000 * ( 1 + 5 / 100 ) 2 ] = ( 15000 * 21 / 20 * 21 / 20 ) = rs . 16537.50 answer : c" | a ) rs . 16,500 , b ) rs . 16 , 525.50 , c ) rs . 16 , 537.50 , d ) rs . 18,150 , e ) rs . 19,150 | c | multiply(power(add(divide(divide(10, const_2), const_100), const_1), const_2), 15000) | divide(n1,const_2)|divide(#0,const_100)|add(#1,const_1)|power(#2,const_2)|multiply(n0,#3)| | gain |
if the area of a square with sides of length 3 centimeters is equal to the area of a rectangle with a width of 3 centimeters , what is the length of the rectangle , in centimeters ? | "let length of rectangle = l 3 ^ 2 = l * 3 = > l = 9 / 3 = 3 answer a" | a ) 3 , b ) 8 , c ) 12 , d ) 16 , e ) 18 | a | divide(power(3, const_2), 3) | power(n0,const_2)|divide(#0,n1)| | geometry |
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