Cheukting/mathqa huggingface dataset:
Question (general): 3 / 4 of 1 / 2 of 2 / 5 of 5060 = ?
Options: a ) 392 , b ) 759 , c ) 753 , d ) 493 , e ) 540
Rationale: "b 759 ? = 5060 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 759"
Answer: b
Question (general): the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 18 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above
Rationale: sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 18 = 402 hence , new average = 402 ⁄ 10 = 40.2 answer a
Answer: a
Question (general): how many integers between 100 and 190 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: "the total numbers between 100 and 190 , inclusive , is 91 . 3 * 34 = 102 and 3 * 63 = 189 so the number of multiples of 3 is 30 . 5 * 20 = 100 and 5 * 38 = 190 so the number of multiples of 5 is 19 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 12 = 180 so the number of multiples of 15 is 6 . thus the total number is 91 - 30 - 19 + 6 = 48 . the answer is d ."
Answer: d
Question (general): $ 300 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 120 , e ) $ 250
Rationale: "a : ( b + c ) = 2 : 3 a ' s share = 300 * 2 / 5 = $ 120 answer is d"
Answer: d
Question (gain): what is the cp of rs 100 stock at 4 discount , with 1 / 5 % brokerage ?
Options: a ) 96.9 , b ) 96.3 , c ) 96.2 , d ) 96.7 , e ) 96.21
Rationale: explanation : use the formula , cp = 100 – discount + brokerage % cp = 100 - 4 + 1 / 5 96.2 thus the cp is rs 96.2 . answer : c
Answer: c
Question (gain): if an article is sold at 18 % profit instead of 11 % profit , then the profit would be $ 63 more . what is the cost price ?
Options: a ) $ 600 , b ) $ 900 , c ) $ 1200 , d ) $ 1500 , e ) $ 1800
Rationale: "7 % * cost price = $ 63 1 % * cost price = $ 63 / 7 = $ 9 the cost price is $ 900 . the answer is b ."
Answer: b
Question (general): how many x ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen ?
Options: a ) 3 , b ) 16 , c ) 28 , d ) 32 , e ) 56
Rationale: ways to select 3 people from 8 people ( 4 twins x 2 ) = 8 c 3 = 56 ways to select 1 twin + 1 people = 4 c 1 * 6 c 1 = 24 ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen x = 56 - 24 = 32 ans : d
Answer: d
Question (general): in the game of dubblefud , yellow chips , blue chips and green chips are each worth 2 , 4 and 5 points respectively . in a certain selection of chips , the product of the point values of the chips is 16000 . if the number of blue chips in this selection equals the number of green chips , how many yellow chips are in the selection ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: this is equivalent to : - 2 x * 4 y * 5 z = 16000 y = z ( given ) 2 x * 4 y * 5 y = 16000 2 x * y ^ 2 = 16000 / 20 2 x * y ^ 2 = 800 now from options given we will figure out which number will divide 800 and gives us a perfect square : - which gives us x = 4 as 2 * 4 * y ^ 2 = 800 y ^ 2 = 100 y = 10 number of yellow chips = 4 hence d
Answer: d
Question (physics): if a light flashes every 10 seconds , how many times will it flash in 2 / 3 of an hour ?
Options: a ) 152 , b ) 241 , c ) 345 , d ) 451 , e ) 542
Rationale: "there are 60 minutes in an hour . in 2 / 3 of an hour there are ( 60 * 2 / 3 ) minutes = 40 minutes . in 2 / 3 of an hour there are ( 60 * 40 ) seconds = 2400 seconds . light flashed for every 10 seconds . in 2400 seconds 2400 / 10 = 240 times . the count start after the first flash , the light will flashes 241 times in 2 / 3 of an hour . answer : b"
Answer: b
Question (physics): john can complete a given task in 20 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 5 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 95 / 8 , b ) 93 / 8 , c ) 90 / 8 , d ) 12 , e ) 10
Rationale: "in such questions , you need to start from the end . last 4 days john works alone and completes 5 * ( 1 / 20 ) = 1 / 4 of the work . so 3 / 4 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 20 + 1 / 12 = 8 / 60 time taken to complete 3 / 4 of the work = ( 3 / 4 ) / ( 8 / 60 ) = 45 / 8 days . so total number of days taken to complete the work = 45 / 8 + 5 = 95 / 8 days . a"
Answer: a
Question (physics): if the wheel is 18 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 18 , b ) 26 , c ) 14 , d ) 12 , e ) 9.3
Rationale: "2 * 22 / 7 * 18 * x = 1056 = > x = 9.3 answer : e"
Answer: e
Question (gain): if a large pizza has a radius that is 60 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 30 % , b ) 60 % , c ) 98 % , d ) 120 % , e ) 156 %
Rationale: "let the radius of medium pizza be r . then the radius of large pizza is 1.6 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.6 * r ) ^ 2 = 2.56 * pi * r ^ 2 , an increase of 156 % . the answer is e ."
Answer: e
Question (general): if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 25 , find the value of ab .
Options: a ) 5 , b ) 8 , c ) 4 , d ) 10 , e ) 3
Rationale: 2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 25 - 9 = 16 ab = 8 . answer is b .
Answer: b
Question (general): on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with four times the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.40 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.16 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 4 units of water was used to make 5 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 5 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 5 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 5 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.4 = 5 * x - - > x = $ 0.16 . answer : a ."
Answer: a
Question (physics): a car takes 6 hours to cover a distance of 144 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 65 kmph , d ) 16 kmph , e ) none
Rationale: "time = 6 distence = 144 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 144 / 9 = 16 kmph d )"
Answer: d
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 . 140 . find the unknown rate of two blankets ?
Options: a ) 350 , b ) 550 , c ) 490 , d ) 450 , e ) 457
Rationale: "10 * 140 = 15 = 1400 3 * 100 + 5 * 150 = 1050 1400 – 1050 = 350 answer : a"
Answer: a
Question (physics): how long will it take a train travelling at 78 kmph to pass an electric pole if the train is 110 meters in lenght ?
Options: a ) 2.07 , b ) 3.07 , c ) 5.07 , d ) 4.07 , e ) 2
Rationale: sol . speed = [ 78 x 5 / 18 ] m / sec = 21.7 m / sec . time taken = ( 110 / 21.7 ) sec = 5.07 sec . answer c
Answer: c
Question (general): find the least number which when divided by 20,25 , 35,40 leaves remainder 14,19 , 29,34 respectively .
Options: a ) 1394 , b ) 1450 , c ) 1245 , d ) 2564 , e ) 1256
Rationale: "the difference of 20 - 14 = 6 , 25 - 19 = 6 , 35 - 29 = 6 , 40 - 34 = 6 lcm of 20,25 , 35,40 = 1400 required number = 1400 - 6 = 1394 answer is a"
Answer: a
Question (general): the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 106 , c ) 100 , d ) 156 , e ) 240
Rationale: explanation : cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b
Answer: b
Question (physics): if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 54 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 40 kmh , c ) 41 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 2160 ( this number is convenient because it is divisible by 80 , 24 and 54 ) so : 2160 = 80 * t 1 = 27 hrs 2160 = 24 * t 2 = 90 hrs 2160 = 54 * t 3 = 40 hrs t = t 1 + t 2 + t 3 = 157 hrs d = rt ( 240 * 3 ) = r * 157 r = 41.27 answer : c"
Answer: c
Question (geometry): one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 22 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 7 and 10 , c ) 10 and 7 , d ) 3 and 10 , e ) 12 and 9
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 22 cm 2 more than the first area . therefore a 1 + 22 = a 2 x ( x − 3 ) + 22 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 22 = x 2 + x − 2 x − 2 2 x = 24 x = 12 . so , the sides of the rectangle are 12 cm and ( 12 − 3 ) = 9 cm long . so answer is e ."
Answer: e
Question (general): rice weighing 25 / 4 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
Options: a ) 22 , b ) 25 , c ) 28 , d ) 31 , e ) 34
Rationale: "25 / 4 ÷ 4 = 25 / 16 pounds in each container 25 / 16 pounds * 16 ounces / pound = 25 ounces in each container the answer is b ."
Answer: b
Question (gain): a towel , when bleached , lost 20 % of its length and 20 % of its breadth . what is the percentage decrease in area ?
Options: a ) 24 % , b ) 36 % , c ) 32 % , d ) 54 % , e ) 64 %
Rationale: "percentage change in area = ( − 20 − 20 + ( 20 × 20 ) / 100 ) % = − 36 % i . e . , area is decreased by 36 % answer : b"
Answer: b
Question (other): sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 3.6 per pound , and german chocolate cost $ 3 per pound . if the total the she spent on chocolate was $ 36 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 15 , e ) 36 / 3
Rationale: "if there were all the expensive ones , 3.6 . . . there would be 36 / 3.6 or 10 of them but since 3 $ ones are also there , answer has to be > 10 . . . . . if all were 3 $ ones , there will be 36 / 3 ans e"
Answer: e
Question (other): a business finds that their ratio of spending to income is 5 to 9 . their total profit is $ 48000 . what is their total income ?
Options: a ) $ 90000 , b ) $ 108000 , c ) $ 119000 , d ) $ 126000 , e ) $ 140000
Rationale: let x equal the amount of spending , and y equal the amount of income . we know that x = 5 / 9 y we also know that x = y - 48000 therefore we can simplify to : y - 48000 = 5 / 9 y we isolate y , and get : 4 / 9 y = 48000 and to solve for y , we get : y = 48000 answer : b
Answer: b
Question (probability): in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 300 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 219 , b ) 246 , c ) 252 , d ) 262 , e ) 270
Rationale: "number of newborns that can die in first month = 1 / 10 * 300 = 30 survived = 270 number of newborns that can die in second month = 1 / 10 * 270 = 27 survived = 243 number of newborns that can die in third month = 1 / 10 * 243 = 24 survived = 219 answer : a"
Answer: a
Question (general): what is the range of all the roots of | x ^ 2 - 6 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 5
Rationale: "we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 2 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 2 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 6 or x = 1 i guess range is 6 - 1 = 5 e"
Answer: e
Question (physics): if 6 spiders make 3 webs in 7 days , then how many days are needed for 1 spider to make 1 web ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 16
Rationale: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 6 : 1 ( webs ) 1 : 7 } : : x : 3 â ‡ ’ 6 ã — 1 ã — 7 = 1 ã — 3 ã — x â ‡ ’ x = 14 answer : option c"
Answer: c
Question (geometry): what is the perimeter , in meters , of a rectangular garden 12 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
Options: a ) 48 , b ) 56 , c ) 60 , d ) 56 , e ) 192
Rationale: "say length of garden is l meters . then ( l * 12 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 16 meters . perimeter of garden = 2 * ( 16 + 12 ) = 56 meter . answer is d"
Answer: d
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 200 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 27 sec , c ) 30 sec , d ) 24 sec , e ) 11 sec
Rationale: "explanation : d = 100 + 200 = 300 s = 36 * 5 / 18 = 10 mps t = 300 / 10 = 10 sec answer : option c"
Answer: c
Question (physics): a water tank is three - fifths full . pipe a can fill a tank in 15 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the combined rate of filling / emptying the tank = 1 / 15 - 1 / 6 = - 1 / 10 since the rate is negative , the tank will be emptied . a full tank would take 10 minutes to empty . since the tank is only three - fifths full , the time is ( 3 / 5 ) * 10 = 6 minutes the answer is c ."
Answer: c
Question (other): in a bag , there are 5 green , 6 black and 7 red pens . one pen is picked up randomly . what is the probability that it is neither red nor green ?
Options: a ) 5 / 18 , b ) 7 / 18 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 5
Rationale: explanation : neither red nor green means the pen drawn is black . total number of outcomes = ( 5 + 6 + 7 ) = 18 . number of favourable outcomes = 6 = number of black pens . hence , probability of the event = 6 / 18 = 1 / 3 . answer : c
Answer: c
Question (general): if ( c - a ) / ( c - b ) = 1 , then ( 5 b + 5 a ) / ( c - a ) =
Options: a ) 10 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "let ' s say c = 2 , b = 1 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 10 answer a ( hopefully ) ) )"
Answer: a
Question (other): the marks obtained by polly and sandy are in the ratio 5 : 6 and those obtained by sandy and willy are in the ratio of 9 : 7 . the marks obtained by polly and willy are in the ratio of . . . ?
Options: a ) 9 : 8 , b ) 11 : 10 , c ) 13 : 12 , d ) 15 : 14 , e ) 17 : 16
Rationale: polly : sandy = 5 : 6 = 15 : 18 sandy : willy = 9 : 7 = 18 : 14 polly : sandy : willy = 15 : 18 : 14 polly : willy = 15 : 14 the answer is d .
Answer: d
Question (physics): x can finish a work in 36 days . y can finish the same work in 24 days . y worked for 12 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 12 , b ) 13 , c ) 16 , d ) 17 , e ) 18
Rationale: "work done by x in 1 day = 1 / 36 work done by y in 1 day = 1 / 24 work done by y in 12 days = 12 / 24 = 1 / 2 remaining work = 1 – 1 / 2 = 1 / 2 number of days in which x can finish the remaining work = ( 1 / 2 ) / ( 1 / 36 ) = 18 e"
Answer: e
Question (general): a ( 4 , w ^ 2 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 9 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: "y = x ^ 2 + 9 w ^ 2 = 4 ^ 2 + 9 w ^ 2 = 25 w = 5 answer c"
Answer: c
Question (physics): two cars started at the same time , from the same point , driving along the same road . the rate of the first car is 50 mph and the rate of the second car is 60 mph . how long will it take for the distance between the two cars to be 30 miles ?
Options: a ) 1 hrs , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: car 1 50 50 50 total = 150 car 2 60 60 60 total = 180 differece = 30 miles after 3 hrs . answer : c
Answer: c
Question (physics): a train 240 m long passes a pole in 24 seconds . how long will it take to pass a platform 650 m long ?
Options: a ) 65 , b ) 80 , c ) 85 , d ) 82 , e ) 89
Rationale: speed = ( 240 / 24 ) m / sec = 10 m / sec . therefore , required time = ( 240 + 650 ) / 10 sec = 89 sec . answer is e .
Answer: e
Question (gain): a feed store sells two varieties of birdseed : brand a , which is 40 % millet and 60 % sunflower , and brand b , which is 65 % millet and 35 % safflower . if a customer purchases a mix of the two types of birdseed that is 50 % millet , what percent of the mix is brand a ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 55 %
Rationale: "another method to solve this question using equations : 1 kg of brand a will have 400 g millet and 600 g sunflower . 1 kg of brand b will gave 650 g millet and 350 g sunflower . suppose , x kg of brand a and y kg of brand b are in the mixture . then total weight of millet = 400 x + 650 y g total weight of mixture = 1000 x + 1000 y g given that millet is 500 % hence ( 400 x + 650 y ) / ( 1000 x + 1000 y ) = 1 / 2 or , 800 x + 1300 y = 1000 x + 1000 y or 300 y = 200 x or , x / y = 3 / 2 % of brand a = ( 3 / ( 3 + 2 ) ) * 100 = 60 % hence answer is d"
Answer: d
Question (physics): a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 360 in all . for how many days was he absent ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 19
Rationale: "30 * 25 = 750 360 - - - - - - - - - - - 380 25 + 7.50 = 32.5 390 / 32.5 = 12 b"
Answer: b
Question (general): when a number is divided by 13 , the remainder is 11 . when the same number is divided by 17 , then remainder is 9 . what is the number ?
Options: a ) 349 , b ) 300 , c ) 500 , d ) 450 , e ) 250
Rationale: x = 13 p + 11 and x = 17 q + 9 13 p + 11 = 17 q + 9 17 q - 13 p = 2 q = 2 + 13 p / 17 least value of p which q = 2 + 13 p / 17 = > 26 x = ( 13 * 26 + 11 ) = 349 answer a
Answer: a
Question (general): a football player scores 3 goals in his fifth match thus increasing his average goals score by 0.2 . the total number of goals in his 5 matches would be
Options: a ) 4 , b ) 6 , c ) 8 , d ) 11 , e ) 12
Rationale: while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should go higher or lower with your next test . here , i ' ll start with answer d = 11 goals if . . . . total goals = 11 goals 5 th game = 3 goals 1 st 4 games = 8 goals avg . for 4 games = 8 / 4 = 2 goals / game avg . for all 5 games = 6 / 5 = 2.2 goals / game 2.2 * 5 = 11 so answer d
Answer: d
Question (physics): 350 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 17
Rationale: "26 trees have 25 gaps between them , required distance ( 350 / 25 ) = 14 c"
Answer: c
Question (gain): the population of a town is 8000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 4500 , c ) 5120 , d ) 5230 , e ) 5366
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 × 80 / 100 × 80 / 100 = 5120 c"
Answer: c
Question (gain): a pair of articles was bought for $ 900 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 300 , b ) $ 500 , c ) $ 350 , d ) $ 400 , e ) $ 600
Rationale: "s . p . of each of the article = 900 / 2 = $ 450 let m . p = $ x 90 % of x = 450 x = 450 * 100 / 90 = $ 500 answer is b"
Answer: b
Question (gain): what will be the fraction of 10 %
Options: a ) 1 / 10 , b ) 1 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these
Rationale: "explanation : 10 * 1 / 100 = 1 / 10 option a"
Answer: a
Question (gain): a man buys an item at rs . 600 and sells it at the loss of 20 percent . then what is the selling price of that item
Options: a ) rs . 480 , b ) rs . 760 , c ) rs . 860 , d ) rs . 960 , e ) none of these
Rationale: "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 600 = 80 / 100 * 600 = 480 option a"
Answer: a
Question (gain): last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.8 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.8 ( x ) + 0.5 ( 1 - x ) = 0.75 0.3 x = 0.75 - 0.5 x = 0.25 / 0.3 x = 5 / 6 therefore the answer is d : 5 / 6 ."
Answer: d
Question (general): if k is an integer and 0.00010101 x 10 ^ k is greater than 10 , what is the least possible value of k ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "0.00010101 * 10 ^ k > 10 we need to move the decimal point to the right 5 places to get 10.101 this is equivalent to multiplying by 10 ^ 5 . the answer is c ."
Answer: c
Question (general): what least number must be subtracted from 42398 so that remaining no . is divisible by 15
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : on dividing 42398 by 15 we get the remainder 8 , so 8 should be subtracted option d"
Answer: d
Question (gain): what is 35 % of 4 / 13 of 650 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "this problem can be solved easily if we just use approximation : 35 % is a little over 1 / 3 , while 4 / 13 is a little less than 4 / 12 , which is 1 / 3 . thus , the answer is about 1 / 3 of 1 / 3 of 650 , or 1 / 9 of 650 . since the first 1 / 3 is a slight underestimate and the second 1 / 3 is a slight overestimate , the errors will partially cancel each other out . our estimate will be relatively accurate . the number 650 is a bit more than 630 , so ( 1 / 9 ) * 630 will be about 70 . keeping track not only of your current estimate , but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently . the answer is c ."
Answer: c