Cheukting/mathqa huggingface dataset:
Question (gain): in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 174 votes . find the total number of valid votes ?
Options: a ) 435 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 174 = > 4 x / 10 = 174 = > 4 x = 1740 = > x = 435 . answer : a"
Answer: a
Question (physics): if the wheel is 14 cm then the number of revolutions to cover a distance of 1320 cm is ?
Options: a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11
Rationale: "2 * 22 / 7 * 14 * x = 1320 = > x = 15 answer : a"
Answer: a
Question (physics): a train 125 m long passes a man , running at 8 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 37 km / hr , b ) 53 km / hr , c ) 36 km / hr , d ) 26 km / hr , e ) 87 km / hr
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 8 = 45 = > x = 53 km / hr . answer : b"
Answer: b
Question (other): two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 4 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 3 : 1 , d ) 1 : 5 , e ) 1 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 4 = 5 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 2 + 7 / 2 = 6 litres as 8 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 6 : 2 = 3 : 1 . answer : c"
Answer: c
Question (physics): the cross - section of a water channel is a trapezium in shape . if the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 880 square meters , what is the depth of the channel ( in meters ) ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "1 / 2 * d * ( 14 + 8 ) = 880 d = 80 the answer is d ."
Answer: d
Question (general): 1 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.02775 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 1 / 36 = . 02 something answer ( b )
Answer: b
Question (physics): in what time will a train 100 m long cross an electric pole , it its speed be 162 km / hr ?
Options: a ) 2.5 , b ) 2.9 , c ) 2.4 , d ) 2.8 , e ) 2.22
Rationale: "speed = 162 * 5 / 18 = 45 m / sec time taken = 100 / 45 = 2.22 sec . answer : e"
Answer: e
Question (general): which number need to add to 956734 to get a number exactly divisible by 412 ?
Options: a ) 345 , b ) 342 , c ) 343 , d ) 342 , e ) 341
Rationale: "956734 / 412 = 2322 and reminder = 70 . 412 - 70 = 342 so , the next number divisible by 412 is 342 places in front of 956734 which means 342 + 956734 = 957076 342 should be added to 956734 b"
Answer: b
Question (gain): a man walking at a rate of 15 km / hr crosses a bridge in 40 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1110 m , c ) 2000 m , d ) 1000 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 40 minutes = 15 / 18 * 40 * 60 = 2000 m answer is c"
Answer: c
Question (physics): a circular wheel radius is 1.75 m . for covering 11 k . m how much time it revolve ?
Options: a ) 10
b ) 100
c ) 1000
d ) 10000
e ) 50
Rationale: distance traveled in 1 round = perimeter = { 2 * 22 / 7 * 175 / 100 } m = 11 m total no . of revolution in covering 11 km = 11000 / 11 = 1000 answer c
Answer: c
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 2 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 2 . so , x = 32.5 ounces . water = ( 60 / 65 ) * ( 65 / 2 ) = = 30 ounces . ans b"
Answer: b
Question (general): 0.0006688 / 0.0000150 x 19.85 = ?
Options: a ) 850 , b ) 900 , c ) 950 , d ) 1000 , e ) 2000
Rationale: "explanation : ? = 6688 / 150 x 19.85 = 45 x 20 = 900 answer : option b"
Answer: b
Question (general): find the highest value of ' a ' so that 365 a 24 is divisible by 8 .
Options: a ) 9 , b ) 8 , c ) 0 , d ) 2 , e ) 1
Rationale: "explanation : given , number is divisible by 8 only if ' a 24 ' is divisible by 8 . . : highest value of a is ' 8 ' . answer : option b"
Answer: b
Question (general): in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 70 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 40 , e ) 25
Rationale: "12 * 70 = 840 840 % 21 = 40 answer : d"
Answer: d
Question (gain): last year a certain bond price with a face value of 5000 yielded 6 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4615 , b ) 5325 , c ) 5351 , d ) 6000 , e ) 6154
Rationale: interest = 0.06 * 5000 = 0.065 * selling price - - > selling price = 0.06 * 5000 / 0.065 - - > selling price = ~ 4,615 answer : a .
Answer: a
Question (general): if 5 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 8 , b ) 6 , c ) 7 , d ) 10 , e ) 9
Rationale: "5 ( log 2 ^ 2 * 5 ^ 2 ) = x 5 log ( 5 * 2 ) ^ 2 = x 5 * 2 log ( 5 * 2 ) = x 10 log 10 = x log 10 base 10 = 1 so 10 * 1 = x x = 10 answer : d"
Answer: d
Question (gain): there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 58 %
Options: a ) 18.75 , b ) 19.75 , c ) 26.89 , d ) 21.75 , e ) 22.75
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 58 / 100 = 50.40 so x = 26.89 answer : c"
Answer: c
Question (gain): the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 14 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 19 , b ) 14 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 14 x = 14 answer : b"
Answer: b
Question (gain): the population of a town is 7500 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9300 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7500 ã — 100 / 90 ã — 100 / 90 = 9259 a )"
Answer: a
Question (geometry): a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 7 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 880 , b ) $ 1050 , c ) $ 1280 , d ) $ 1460 , e ) $ 1640
Rationale: "the total surface area is 2 ( 2 * 3 + 3 * 7 + 2 * 7 ) = 82 square feet the total cost is 82 * $ 20 = $ 1640 the answer is e ."
Answer: e
Question (other): how many of the positive factors of 24 , 16 and how many common factors are there in numbers ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "factors of 24 - 1 , 2 , 3 , 4 , 8 , 12 and 24 factors of 16 - 1 , 2 , 4 , 8 and 16 comparing both , we have three common factors of 45,16 - 4 answer d"
Answer: d
Question (gain): a company pays 12.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 66 , c ) 18 , d ) 19 , e ) 01
Rationale: "explanation : dividend on 1 share = ( 12.5 * 50 ) / 100 = rs . 6.25 rs . 25 is income on an investment of rs . 100 rs . 6.25 is income on an investment of rs . ( 6.25 * 100 ) / 25 = rs . 25 answer : a"
Answer: a
Question (general): a box contains 10 tablets of medicine a and 13 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "the worst case scenario will be if we remove all 13 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 13 + 2 = 15 tablets . answer : b ."
Answer: b
Question (general): what is the smallest number which , when increased by 7 , is divisible by 7 , 8 , and 24 ?
Options: a ) 154 , b ) 161 , c ) 168 , d ) 175 , e ) 182
Rationale: "lcm ( 7 , 8,24 ) = 24 x 7 = 168 so the least divisible number is 168 , and the number we are looking for is 168 - 7 = 161 . the answer is b ."
Answer: b
Question (gain): find the simple interest on rs . 73,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 8125 , d ) 9125 , e ) none of them
Rationale: "p = rs . 73000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 73,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 9125 answer is d ."
Answer: d
Question (general): find large number from below question the difference of 2 no . ' s is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ?
Options: a ) 1245 , b ) 1430 , c ) 1540 , d ) 1600 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Question (physics): calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes at 13 km / hr downstream and 4 km / hr upstream .
Options: a ) 4.5 kmph , b ) 9.5 kmph , c ) 7.5 kmph , d ) 8.5 kmph , e ) 5.5 kmph
Rationale: "speed in still water = ( 13 + 4 ) 1 / 2 kmph = 8.5 kmph . answer : d"
Answer: d
Question (physics): two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 7 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
Options: a ) 7 / 4 , b ) 4 / 3 , c ) 15 / 4 , d ) 10 / 3 , e ) 64 / 21
Rationale: rate ( 1 ) = 1 / 6 rate ( 2 ) = 1 / 7 combined = 13 / 42 work done in 2 days = 13 / 21 work left = 8 / 21 rate * time = work left 1 / 8 * time = 8 / 21 time = 64 / 21 e
Answer: e
Question (general): car dealership x , the total profit from sales increased by 10 percent over the previous years , while the number of cars sold decreased by 10 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 18 % , b ) 20 % , c ) 22 % , d ) 23 % , e ) 25 %
Rationale: "let profit be x and cars sold be y originally profit / car = x / y now it is 1.1 x / 0.9 y = 11 / 9 ( x / y ) increase in profit per car = ( ( 2 / 9 ) ( x / y ) ) / ( x / y ) * 100 = 22.22 % answer = c"
Answer: c
Question (general): of 70 players on a football team , 28 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 56 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: "total = 70 thrower = 28 rest = 70 - 28 = 42 left handed = 42 / 3 = 14 right handed = 28 if all thrower are right handed then total right handed is 28 + 28 = 56 so a . 56 is the right answer"
Answer: a
Question (gain): on a certain day , tim invested $ 500 at 10 percent annual interest , compounded annually , and lana invested 900 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5 , b ) $ 12.75 , c ) $ 51.75 , d ) $ 100.75 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 500 ( 1.10 ) ^ 2 = 500 ( 1.21 ) = 605 and lana would have 900 ( 1.05 ) ^ 2 = 900 ( 1.1025 ) = 992.25 thus , tim earned 105 dollars , while lana earned 92.25 dollars the difference is $ 12.75 and the answer is b ."
Answer: b
Question (geometry): a cube of sides 9 is first painted red and then cut into smaller cubes of side 3 . how many of the smaller cube have painted on exactly 2 sides ?
Options: a ) 30
b ) 24
c ) 12
d ) 8
e ) 9
Rationale: n = side of big cube / side of small cube and no . of smaller cubes with two surfaces painted is ( n - 2 ) * 12 ( 3 - 2 ) * 12 = 12 ans answer : c
Answer: c
Question (gain): sam invested rs . 5000 @ 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 ?
Options: a ) 500.2 , b ) 320.0 , c ) 220.5 , d ) 100.1 , e ) 230.2
Rationale: "p = rs . 5000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 5000 * ( 1 + 5 / 100 ) 2 ] = ( 5000 * 21 / 20 * 21 / 20 ) = rs . 220.50 answer : c"
Answer: c
Question (gain): a person incurs 20 % loss by selling a watch for $ 1000 . at what price should the watch be sold to earn 20 % profit ?
Options: a ) $ 1000 , b ) $ 950 , c ) $ 1500 , d ) $ 1150 , e ) $ 1250
Rationale: "let the new selling price be $ x ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 20 ) / 1000 = ( 100 + 20 ) / x x = 120 * 1000 / 80 = 1500 answer is c"
Answer: c
Question (physics): a , b and c can complete a piece of work in 24 , 6 and 12 days respectively . working together , they will complete the same work in :
Options: a ) 33 / 7 , b ) 43 / 7 , c ) 24 / 7 , d ) 19 / 7 , e ) none
Rationale: if a can do a piece of work in n days , then a ' s 1 day ' s work = 1 / n ( a + b + c ) ' s 1 day ' s work = 1 / 24 + 1 / 6 + 1 / 12 = 7 / 24 so , all the three together will complete the job in = 24 / 7 days answer : c
Answer: c
Question (physics): a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is :
Options: a ) 35 , b ) 36 , c ) 37 , d ) 40 , e ) 45
Rationale: "according to given condition vt = ( v + 3 ) ( t - 2 / 3 ) vt = ( v - 2 ) ( t + 2 / 3 ) here v is velocity in kmph , t is time in hours and 2 / 3 is value of 40 min in hour on solving we will get t = 10 / 3 and and v = 12 so distance = ( 10 / 3 ) * 12 = 40 kms answer : d"
Answer: d
Question (physics): two pipes a and b can fill a cistern in 20 and 30 minutes respectively , and a third pipe c can empty it in 60 minutes . how long will it take to fill the cistern if all the three are opened at the same time ?
Options: a ) 15 min , b ) 15 1 / 7 min , c ) 17 1 / 7 min , d ) 7 1 / 7 min , e ) 7 2 / 7 min
Rationale: "1 / 20 + 1 / 30 - 1 / 60 = 4 / 60 60 / 4 = 15 answer : a"
Answer: a
Question (gain): a shoe merchant has declared a 10 % rebate in prices . how much rebate would one get if he purchases 5 pairs of shoes at rs . 28 each ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: explanation : 5 shirts * rs . 28 = rs . 140 rebate = 10 % * 140 = 14 correct option : d
Answer: d
Question (general): if the average of 8 digits is 20 and the average of 5 of them is 12 , calculate the average of the remaining 3 numbers ?
Options: a ) 13.3 , b ) 38.3 , c ) 35.3 , d ) 31.3 , e ) 33.3
Rationale: "explanation : total of the 8 digits - 8 * 20 = 160 total of the 5 digits - 5 * 12 = 60 total of the remaining 3 digits - 160 - 60 = 100 average of the remaining 3 numbers = 100 / 3 = 33.3 answer : e"
Answer: e
Question (gain): in a restaurant , the profit is 120 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 49 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: "explanation : let c . p . = rs . 100 . then , profit = rs . 120 , s . p . = rs . 220 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 220 . profit = rs . ( 220 - 112 ) = rs . 108 . required percentage = ( 108 / 220 * 100 ) % = 49 % appox answer : b"
Answer: b
Question (general): a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 278 , b ) 277 , c ) 278 , d ) 450 , e ) 272
Rationale: "10 * 150 = 1500 3 * 100 + 5 * 150 = 1050 1500 – 1050 = 450 answer : d"
Answer: d
Question (gain): a shop owner sells 30 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 30 m cloth ) – ( c . p . of 30 m cloth ) selling price of 20 m cloth = selling price of 30 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 20 m cloth = rs . 2000 and s . p . of 20 m cloth = rs . rs . 3000 profit % = 10 × 100 = 50 % 20 profit of 50 % was made by the merchant . c"
Answer: c
Question (gain): a certain dark blue paint contains 40 percent blue pigment and 60 percent red pigment by weight . a certain green paint contains 40 percent blue pigment and 60 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 3.5 , b ) 4 , c ) 4.5 , d ) 3 , e ) 5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 6 = 3 grams of red pigment
Answer: d
Question (general): in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds x in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out x : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b"
Answer: b
Question (general): if ( a – b ) is 13 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 ) = 13 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 13 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 13 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 13 = ( c – a ) – 3 = > 2 ( a – c ) = 10 = > ( a – c ) = 5 answer : e"
Answer: e
Question (general): how many integers between 1 and 1,400 are divisible by 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "lcm of the given numbers = 175 therefore , number of integers = 1400 / 175 = 8 answer is option e"
Answer: e
Question (physics): rahul can done a work in 5 days and meena can done a work in 10 days . in how many days that both are work together ?
Options: a ) 3 / 10 , b ) 10 / 3 , c ) 1 / 3 , d ) 5 , e ) 6 / 3
Rationale: a ' s one day work = 1 / 5 b ' s one day work = 1 / 10 a + b = 1 / 5 + 1 / 10 = 10 + 5 / 50 = 10 / 3 days ans : option b
Answer: b
Question (physics): a bicycle wheel has a diameter of 0.75 m . how many complete revolutions does it make in 1 km ?
Options: a ) 424 , b ) 448 , c ) 1408 , d ) 710 , e ) 223
Rationale: "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.75 m ) = 424.6 . hence 424 complete revolutions . answer a"
Answer: a
Question (general): country x taxes each of its citizens an amount equal to 15 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b .
Answer: b
Question (general): if a ^ 2 + b ^ 2 = 10 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 70
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 10 - 20 = - 10 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 10 + 20 = 30 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 30 - 10 = 20 b"
Answer: b
Question (physics): a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 8 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "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 + 8 = 22 the answer is c ."
Answer: c
Question (probability): on a windy day , out of every 3 sand dunes formed , only 1 remains . out of 5 blown - out sand - dunes , 1 has treasure and only 2 out of 3 sand dunes formed have lucky coupons . find the probability that the blown - out sand dune will contain both the things .
Options: a ) 2 / 25 , b ) 4 / 75 , c ) 7 / 75 , d ) 3 / 5 , e ) 4 / 45
Rationale: probability of sand dune blown out = 2 / 3 probability that it has treasure = 1 / 5 probability that it has lucky coupon = 2 / 3 total probability = 2 / 3 * 1 / 5 * 2 / 3 = 4 / 45 answer : e
Answer: e
Question (general): in the faculty of reverse - engineering , 250 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 674 . , e ) 666 .
Rationale: "answer is d : 674 solution : total number of students studying both are 423 + 250 - 134 = 539 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 539 , so 100 % is approx . 674 ."
Answer: d