Cheukting/mathqa huggingface dataset:
Question (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 ?
Options: a ) 5 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days
Rationale: ( 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
Answer: a
Question (gain): 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 % .
Options: a ) 237 , b ) 270 , c ) 177 , d ) 166 , e ) 111
Rationale: "explanation : cost of each share = ( 20 + 2.5 % of 20 ) = rs . 20.5 therefore , number of shares = 8200 / 20.5 = 400 answer : c"
Answer: c
Question (physics): 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 ?
Options: a ) 5.6 sec , b ) 46.67 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "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"
Answer: b
Question (general): if 1 / ( x + 2 ) + 1 / ( x - 2 ) = 1 / ( x + 2 ) , what is the value of x ?
Options: a ) - 1 , b ) 2 , c ) 1 , d ) - 2 , e ) 0
Rationale: "if we solve the question , we get x = - 2 . option : d"
Answer: d
Question (gain): find the compound interest on $ 1200 for 1 year at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 240 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 1 = 1200 * 6 / 5 = $ 1440 ci = a - p = 1440 - 1200 = $ 240 answer is c"
Answer: c
Question (geometry): find the perimeter and area of a square of side 12 cm .
Options: a ) 144 , b ) 121 , c ) 169 , d ) 196 , e ) 100
Rationale: "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"
Answer: a
Question (geometry): if the sides of a cube are in the ratio 5 : 4 . what is the ratio of their diagonals ?
Options: a ) 4 : 3 , b ) 5 : 4 , c ) 4 : 7 , d ) 3 : 4 , e ) 4 : 5
Rationale: "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"
Answer: b
Question (physics): 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 ?
Options: a ) 3 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 13 %
Rationale: bob ' s time = 640 secs . his sis ' time = 557 secs . percent increase needed = ( 640 - 557 / 640 ) * 100 = 83 / 640 * 100 = 13 % . ans ( e ) .
Answer: e
Question (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 ?
Options: a ) 7 : 00 , b ) 8 : 00 , c ) 9 : 00 , d ) 10 : 00 , e ) 11 : 00
Rationale: 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 .
Answer: c
Question (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 ? assume that jane is more efficient than jose
Options: a ) 26 days , b ) 31 days , c ) 50 days , d ) 65 days , e ) 36 days
Rationale: "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 jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 45 x + y = 90 so xy = 1350 the answer choices are : 25 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 50 days for jose and 27 days for jane . answer : c"
Answer: c
Question (general): 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 ?
Options: a ) 5 / 12 , b ) 7 / 12 , c ) 12 / 5 , d ) 7 / 5 , e ) 11 / 5
Rationale: "1 / r = 1 / x + 1 / y 1 / r = 1 / 4 + 1 / 6 = 5 / 12 r = 12 / 5 the answer is c ."
Answer: c
Question (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 .
Options: a ) 87 , b ) 27 , c ) 25 , d ) 26 , e ) 24
Rationale: "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"
Answer: c
Question (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 ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 16 = 36 - x or , 4 x = 52 or , x = 13 . answer : d"
Answer: d
Question (physics): 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 .
Options: a ) 36 kmph , b ) 40 kmph , c ) 30 kmph , d ) 42 kmph , e ) none of these
Rationale: 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
Answer: a
Question (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 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 7
Rationale: "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 ."
Answer: c
Question (general): 5 ! / ( 5 - 3 ) ! = ?
Options: a ) 36 , b ) 46 , c ) 56 , d ) 59 , e ) 60
Rationale: 5 ! / ( 5 - 3 ) ! = 5 ! / 2 ! = 5 * 4 * 3 = 60 . hence , the correct answer is e .
Answer: e
Question (gain): 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 to 12 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.99 , d ) $ 1.00 , e ) $ 1.20
Rationale: 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
Answer: c
Question (general): what is the remainder when 4 ^ 8707 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "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 hence the last digit is a 4 when 4 ^ 8707 is divided by 5 the remainder is 4 , ans = e"
Answer: e
Question (gain): 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 ?
Options: a ) 127 , b ) 1200 , c ) 1600 , d ) 1400 , e ) 1202
Rationale: "let c . p . be rs . x . then , 5 % of x = 220 - 160 = 60 x / 20 = 60 = > x = 1200 answer : b"
Answer: b
Question (general): how many integers between 100 and 170 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "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 is 5 . thus the total number is 71 - 23 - 15 + 5 = 38 . the answer is b ."
Answer: b
Question (physics): 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 ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 3 / 6 , d ) 3 / 8 , e ) 5 / 3
Rationale: "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"
Answer: d
Question (general): 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 ? ?
Options: a ) 32 , b ) 33 , c ) 34 , d ) 45 , e ) 44
Rationale: 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
Answer: c
Question (physics): 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 both work together ?
Options: a ) 8 , b ) 6 , c ) 4 , d ) 5 , e ) 9 / 2
Rationale: "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 day = 1 / 9 + 1 / 9 = 2 / 9 → no . of days to complete the work when both work together = 9 / 2 ; answer : e"
Answer: e
Question (general): find out the square of a number which when doubled exceeds its one seventh by 13 ?
Options: a ) 16 , b ) 49 , c ) 19 , d ) 26 , e ) 17
Rationale: "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"
Answer: b
Question (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 ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 244 , e ) 312
Rationale: "so 12.2 * 20 = 244 . . imo option d is correct answer . ."
Answer: d
Question (gain): 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 ?
Options: a ) 337 , b ) 400 , c ) 298 , d ) 2798 , e ) 271
Rationale: 130 14 - - - - - - - 361 - - - - - - 144 100 % - - - - - - ? = > 400 answer : b
Answer: b
Question (general): 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 ?
Options: a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes
Rationale: lets take number of minutesx . given that , 9 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 60 minutes ans e
Answer: e
Question (physics): 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 :
Options: a ) 7 m , b ) 7.5 m , c ) 5.5 m , d ) 6.5 m , e ) 8.5 m
Rationale: "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"
Answer: b
Question (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 ?
Options: a ) 3.0 , b ) 3.25 , c ) 3.5 , d ) 3.75 , e ) 4.0
Rationale: "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 ."
Answer: c
Question (general): ratio between 2 numbers is 5 : 7 and their product is 560 . what is the difference between 2 numbers ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 2
Rationale: "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"
Answer: c
Question (physics): 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 ) ?
Options: a ) 3.3 , b ) 3.5 , c ) 3.7 , d ) 3.9 , e ) 4.1
Rationale: "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 ."
Answer: a
Question (general): a scale 6 ft . 8 inches long is divided into 2 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 40 inches
Rationale: 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
Answer: e
Question (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 account . how much money does eliot have in his account right now ?
Options: a ) $ 110 , b ) $ 120 , c ) $ 183.3 , d ) $ 220 , e ) $ 260
Rationale: "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 = 22 + 1.2 e = = > 11 a = 220 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 11 a = 220 + 10 a = = > a = 220 ; e = 183.3 c"
Answer: c
Question (gain): if 11 oranges bought 10 r and 10 oranges sold 11 r . what is the profit
Options: a ) 11 % , b ) 20 % , c ) 22 % , d ) 21 % , e ) 23 %
Rationale: suppose he bought 110 apples . cp = rs 100 sp = rs 121 % profit = 100 * ( 121 - 100 ) / 100 = 21 % answer : d
Answer: d
Question (physics): 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 ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 28
Rationale: "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 ."
Answer: b
Question (gain): find the simple interest on rs . 567 for 7 months at 9 paisa per month ?
Options: a ) s . 357.21 , b ) s . 322.12 , c ) s . 400 , d ) s . 278.9 , e ) s . 300
Rationale: "explanation : i = ( 567 * 7 * 9 ) / 100 = 357.21 answer : option a"
Answer: a
Question (general): 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
Options: a ) 340 , b ) 342 , c ) 523 , d ) 363 , e ) none of these
Rationale: "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"
Answer: b
Question (general): if 0.6 : 1.4 : : 2 : 4 : x , then x = ?
Options: a ) 56 , b ) 5.6 , c ) 0.56 , d ) 0.056 , e ) none of these
Rationale: "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"
Answer: b
Question (general): the tax on a commodity is diminished by 10 % and its consumption increases by 10 % . find the effects on revenue ?
Options: a ) 1 % decrease , b ) 2 % increase , c ) 3 % decrease , d ) 4 % decrease , e ) none of these
Rationale: "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"
Answer: a
Question (physics): 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 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30
Rationale: "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"
Answer: d
Question (general): ' 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 ' ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 9 , e ) 11
Rationale: 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
Answer: a
Question (physics): 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 ?
Options: a ) 1 , b ) 7 , c ) 8 , d ) 9 , e ) 36
Rationale: "c = 1 / 4 - 1 / 6 – 1 / 18 = 1 / 36 = > 36 days ' answer : e"
Answer: e
Question (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 ?
Options: a ) 227 , b ) 444 , c ) 277 , d ) 298 , e ) 212
Rationale: 1 h - - - - - 5 ? - - - - - - 60 12 h rs = 16 + 21 = 37 t = 12 d = 37 * 12 = 444 answer : b
Answer: b
Question (gain): 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 ?
Options: a ) 2277 , b ) 2999 , c ) 1000 , d ) 3000 , e ) 1971
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 3135 x * ( 11 / 10 ) * ( 1 / 100 ) = 33 x = 3000 answer : d"
Answer: d
Question (physics): a train speeds past a pole in 15 sec and a platform 130 m long in 25 sec , its length is ?
Options: a ) 195 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "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"
Answer: a
Question (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 ?
Options: a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 35 , e ) 7 : 00
Rationale: "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"
Answer: d
Question (general): if - 11 a and - 8 b are negative integers , then ( - 11 a ) * ( - 8 b ) + ab is
Options: a ) 88 ab , b ) - 89 ab , c ) 89 ab , d ) - 88 a , e ) - 88 b
Rationale: answer : c
Answer: c
Question (general): what is the thousandths digit in the decimal equivalent of 43 / 5000 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 5 , e ) 8
Rationale: "43 / 5000 = 43 / ( 5 * 10 ^ 3 ) = ( 43 / 5 ) * 10 ^ - 3 = 8.6 * 10 ^ - 3 = . 0086 thousandths digit = 8 answer e"
Answer: e
Question (general): what is the difference between the largest number and the least number written with the digits 5 , 3 , 1 , 4 ?
Options: a ) 6084 , b ) 3788 , c ) 4086 , d ) 2721 , e ) 1812
Rationale: explanation : 1345 5431 - - - - - - - - - - - - 4086 answer : c
Answer: c
Question (general): if ( a – b ) is 9 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: ( 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
Answer: c
Question (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
Options: a ) 2 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 210000 - 175000 ) = 35000 . increase % = ( 35000 / 175000 ã — 100 ) % = 20 % . required average = ( 20 / 10 ) % = 2 % . answer a"
Answer: a
Question (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 .
Options: a ) 27 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "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"
Answer: a
Question (gain): 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 ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 76 , e ) 48
Rationale: "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 ."
Answer: d
Question (geometry): 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
Options: a ) rs . 200
b ) rs . 672
c ) rs . 546
d ) rs . 876
e ) none of these
Rationale: 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
Answer: a