regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 17 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 x = 22 . answer d"
Answer: d
Problem: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25073 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 9 , c ) 10 ^ 8 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,073 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 79 = 80 , 48 = 50 , 25,073 = 25,000 are derived , which makes ( 79 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is c .
Answer: c
Problem: the simple form of the ratio 5 / 3 : 2 / 5 is ?
Options: a ) 10 : 6 , b ) 10 : 3 , c ) 25 : 6 , d ) 25 : 3 , e ) 30 : 3
Rationale: "5 / 3 : 2 / 5 = 25 : 6 answer : c"
Answer: c
Problem: pat , kate and mark charged a total of 180 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 100
Rationale: let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 180 - total hours charged for , x = 20 . mat charged 6 x - x or 5 x for more hours than kate , or for 100 hours . e is correct
Answer: e
Problem: one tap , working alone at its maximum constant rate , can fill a certain sink in 287 seconds . a second tap , working alone at its maximum constant rate , can fill the same sink in 283 seconds . if both taps work together at their respective maximum constant rates , the time it will take to fill the sink is closest to
Options: a ) 142 seconds , b ) 150 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds
Rationale: tap 1 : 283 secs tap 2 : 287 secs considering the average of these 2 taps : 285 secs . so 1 tap can fill the tank in 285 secs , so 2 taps can fill the tank in 285 / 2 = 142.5 secs . closest answer is a .
Answer: a
Problem: of the 85 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "neither car nor garage = total - garage - ( swim - common ) = 85 - 50 - ( 40 - 35 ) = 85 - 55 = 30 answer e"
Answer: e
Problem: a train running at the speed of 240 km / hr crosses a pole in 21 seconds . what is the length of the train ?
Options: a ) 1300 m , b ) 1350 m , c ) 1400 m , d ) 1450 m , e ) 1500 m
Rationale: "speed = ( 240 * 5 / 18 ) m / sec = ( 200 / 3 ) m / sec length of the train = ( speed x time ) = ( 200 / 3 * 21 ) m = 1400 m . answer : c"
Answer: c
Problem: the difference between the squares of two consecutive odd integers is a square < 1000 whose root equals the combined sum of the digits of the two integers . what is the sum of the digits m of the larger integer ?
Options: a ) m = 2 , b ) m = 5 , c ) m = 8 , d ) 10 , e ) 11
Rationale: really hard . but let ' s start with few concepts : 1 . square of an odd integer will be odd . 2 . difference of odd and odd will be even . 3 . any odd integer can be expressed as difference of two squares . 4 . an even integer can be expressed as difference of two squares only if that even integer is a multiple of 4 . assume two odd integers to be ( 2 x - 1 ) and ( 2 x + 1 ) . difference of their squares = ( 2 x + 1 ) ^ 2 - ( 2 x - 1 ) ^ 2 = 4 x ^ 2 + 1 + 4 x - ( 4 x ^ 2 + 1 - 4 x ) = 4 x ^ 2 + 1 + 4 x - 4 x ^ 2 - 1 + 4 x = 8 x now root of 8 x needs to be an integer such that it is equal to the sum of the digits of the two odd integers . 8 = 2 ^ 3 , so x needs to be such that itcompletesa perfect square . if we find x , we can find the value of 2 x + 1 ( larger integer ) and then sum of its digits . let ' s check the options , starting with c . for sum to be 8 , few possibilities are : 17 , 35 , 53 , 71 if we take 17 , the pair is 15 and 17 , meaning x = 8 . 8 x = 64 root of 64 = 4 but 4 is not equal to 1 + 5 + 1 + 7 . reject . if we take 35 , the pair is 33 and 35 , meaning x = 17 . 8 x = 8 * 17 reject since perfect square is not possible . if we take 53 , the pair is 51 and 53 , meaning x = 26 . 8 x = 8 * 26 reject since perfect square is not possible . if we take 71 , the pair is 69 and 71 , meaning x = 35 . 8 x = 8 * 35 reject since perfect square is not possible . i tried each option and the possibilities and then got lost . then , it occurred to me that i was only checking 2 - digit integers . what about 3 - digits ? starting with option a , only 2 - digit odd integer whose sum is 2 is 101 . if we take 101 , the pair is 99 and 101 , meaning x = 50 . 8 x = 8 * 50 = 400 root of 400 = 20 which is indeed equal to 9 + 9 + 1 + 1 . answer ( a ) .
Answer: a
Problem: if f ( x ) = 2 x + 3 , & g ( x ) = ( x - 3 ) / 2 , then what is the value of , fo ( fo ( go ( go ( fo ( fo ( go ( go . . . . . . . . . . . . . . . . ( fo ( fo ( go ( gof ( x ) ) ) ) ) . . . . . ) ) ) ) ) ) ?
Options: a ) 3 , b ) 2 , c ) 9 , d ) 7 , e ) 1
Rationale: f ( x ) = 2 x + 3 g ( x ) = ( x - 3 ) / 2 gof ( x ) = 2 x + 3 − 32 = x 2 x + 3 − 32 = x gogof ( x ) = x − 32 x − 32 fogogof ( x ) = 2 ( x − 32 ) + 32 ( x − 32 ) + 3 = 2 x − 6 + 622 x − 6 + 62 = x fofogogof ( x ) = 2 x + 3 this means , when we apply two times g ( x ) and two time f ( x ) on f ( x ) we get f ( x ) . this pattern continues , hence the answer is option ( d ) .
Answer: d
Problem: the length of the bridge , which a train 150 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 76 m , b ) 178 m , c ) 225 m , d ) 187 m , e ) 176 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 150 + x ) / 30 = 25 / 2 = > 2 ( 150 + x ) = 750 = > x = 225 m . answer : c"
Answer: c
Problem: find the number which is nearest to 3105 and is exactly divisible by 21
Options: a ) 1208 , b ) 3108 , c ) 241 , d ) 217 , e ) 3147
Rationale: "on dividing 3105 by 21 , we get 18 as remainder .  number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . answer b 3108"
Answer: b
Problem: the ratio of pens to pencils is 5 to 6 . there are 5 more pencils than pens . how many pencils are there ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 48
Rationale: "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 5 x = 5 the number of pencils is 30 . the answer is b ."
Answer: b
Problem: if length of a room is three times of its breadth and its area is 12 sq . m . what is perimeter of room ?
Options: a ) 14 m
b ) 18 m
c ) 24 m
d ) 16 m
e ) none of the above
Rationale: let breadth = x m . and length = 3 x m . x * 3 x = 12 , x ^ 2 = 4 , x = 2 . length = 6 m , breadth = 2 m . perimeter = 2 * ( 6 + 2 ) = 16 m answer d
Answer: d
Problem: p is 3 times as old as q . in 11 years , p will be twice as old as q . how old was p 3 years ago ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 30 , e ) 33
Rationale: p = 3 q so q = p / 3 p + 11 = 2 ( q + 11 ) = 2 ( p / 3 + 11 ) p / 3 = 11 p = 33 three years ago , p was 30 . the answer is d .
Answer: d
Problem: a person can row at 9 kmph and still water . he takes 8 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 32 , b ) 38 , c ) 29 , d ) 54 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 8.5 = > x / 10 + x / 8 = 17 / 2 = > ( 4 x + 5 x ) / 40 = 17 / 2 = > x = 38 km . answer : b"
Answer: b
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 50 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2250 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 50 = 30 x = 2250 km answer is d"
Answer: d
Problem: a box contains 1 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Rationale: "my complicated version of your simple approach let the 5 black balls be bbbbb and 1 red balls be r they can be arranged in 6 slots _ _ _ _ _ _ _ _ in ( 6 ! ) / ( 5 ! x 1 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 5 slots and 4 black ( bbbb ) and 1 red ( r ) they can be arranged in ( 5 ! ) / ( 4 ! x 1 ! ) hence required probability = [ ( 6 ! ) / ( 5 ! x 1 ! ) ] / [ ( 5 ! ) / ( 4 ! x 1 ! ) ] = 6 / 5 c"
Answer: c
Problem: in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 13 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the class borrowed a total of 40 * 2 = 80 books . the 27 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 13 * 2 = 38 . to maximize the number of books borrowed by 1 student , let ' s assume that 12 students borrowed 3 books and 1 student borrowed the rest . 80 - 38 - 3 * 12 = 6 the maximum number of books borrowed by any student is 6 . the answer is d ."
Answer: d
Problem: if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of 4 m + n ?
Options: a ) 11 , b ) 18 , c ) 55 , d ) 25 , e ) 33
Rationale: "k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 4 * 10 + 15 = 55 answer : c"
Answer: c
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 3 cups of tea . last week mo drank a total of 26 cups of tea and hot chocolate together . if during that week mo drank 10 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 26 t - c = 10 - > t = 18 . c = 8 . mo drinks 3 cups of tea a day then number of days that are not rainy = 18 / 3 = 6 so number of rainy days = 7 - 6 = 1 b is the answer ."
Answer: b
Problem: the mean of 50 observations was 36 . it was found later that an observation 45 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 36.7 , b ) 36.4 , c ) 36.5 , d ) 36.9 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 45 - 23 ) = 1822 . correct mean = 1822 / 50 = 36.4 answer : b"
Answer: b
Problem: a and b are two partially filled buckets of water . if 4 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 4 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 44 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let bucket a be a and bucket b be b scenario 1 a - 4 = 1 / 3 ( b + 4 ) - - - - > 3 a - 12 = b + 4 scenario 2 b - 4 = 1 / 2 ( a + 4 ) - - - - - > 2 b - 8 = a + 4 from scenario 1 , b = 3 a - 16 substitute b with this information in stmt 2 2 ( 3 a - 16 ) - 8 = a + 4 - - - - - - > 6 a - 32 - 8 = a + 4 - - - - - - > 6 a - a = 40 + 4 - - - > 5 a = 44 a = 44 / 5 , answer choice a"
Answer: a
Problem: pipe a can fill a tank in 4 hours . due to a leak at the bottom , it takes 6 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 12 , b ) 67 , c ) 95 , d ) 36 , e ) 66
Rationale: "let the leak can empty the full tank in x hours 1 / 4 - 1 / x = 1 / 6 = > 1 / x = 1 / 4 - 1 / 6 = ( 3 - 2 ) / 12 = 1 / 12 = > x = 12 . answer : a"
Answer: a
Problem: an individual deposited 20 % of 25 % of 30 % of what he had into his account with a bank . if he deposited rs . 750 , how much was he having initially with him before depositing ?
Options: a ) rs . 500000 , b ) rs . 50000 , c ) rs . 5000 , d ) rs . 15000 , e ) rs . 6000
Rationale: let x amount he has then 20 % of 25 % of 30 % of x = 750 so x = 50000 answer : b
Answer: b
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many r cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer r = 44 . d"
Answer: d
Problem: dacid obtained 96 , 98 , 99 , 100 and 98 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 99 , c ) 88 , d ) 88 , e ) 98
Rationale: "average = ( 96 + 98 + 99 + 100 + 98 ) / 5 = 491 / 5 = 98 . answer : e"
Answer: e
Problem: if 4 x + 3 y = 8 and y − 3 x = 2 , then what is the value of x + 4 y ?
Options: a ) 10 , b ) 3 , c ) 15 , d ) 52 / 7 , e ) 60 / 7
Rationale: "4 x + 3 y = 8 − 3 x + y = 2 adding both the equations - - > x + 4 y = 10 answer : a"
Answer: a
Problem: a lemonade stand sold only small and large cups of lemonade on tuesday . 3 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 1 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 17 / 35 , e ) 1 / 10
Rationale: "let the total # of cups be 10 . # of small cups sold 3 / 5 * 10 = 6 ; # of large cups sold 10 - 6 = 4 ; let the price of small cup be $ 6 , then the price of larges cup would be 1 / 6 * 6 = $ 1 ; revenue from small cups : 6 * $ 6 = $ 36 ; revenue from large cups cups : 4 * $ 1 = $ 4 ; fraction of total revenue from large cups : 4 / ( 36 + 4 ) = 1 / 10 . answer : e ."
Answer: e
Problem: there are 10 baskets numbered from 1 to 10 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 330 , b ) 390 , c ) 450 , d ) 510 , e ) 570
Rationale: "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 10 * 11 / 2 = 55 apples . the total number of apples taken by 10 children is 10 * 55 = 550 the number of apples left in the end is 1000 - 550 = 450 apples . the answer is c ."
Answer: c
Problem: the positive numbers w , x , y , and z are such that x is 30 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 20 - answer c"
Answer: c
Problem: an exam consists of 7 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 70 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16
Rationale: if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 219 / 256 . d
Answer: d
Problem: what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 7
Options: a ) 2 / 15 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these
Rationale: explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 7 = . 71 so biggest is 4 / 5 and smallest is 2 / 3 their difference is 4 / 5 - 2 / 3 = 2 / 15 option a
Answer: a
Problem: last year department store x had a sales total for december that was 5 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 1 / 4 , b ) 4 / 15 , c ) 1 / 3 , d ) 5 / 16 , e ) 4 / 5
Rationale: "let avg for 11 mos . = 10 therefore , dec = 50 year total = 11 * 10 + 50 = 160 answer = 50 / 160 = 5 / 16 = d"
Answer: d
Problem: if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 6.2 ] + [ - 3.4 ] + [ 12.7 ] ?
Options: a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "you are asked what the closest lesser integer value to [ x ] is . [ - 6.2 ] = - 7.0 [ - 3.4 ] = - 4.0 [ 12.7 ] = 12.0 therefore , answer is : - 7.0 - 4.0 + 12.0 = - 1.0 option a ."
Answer: a
Problem: a towel , when bleached , was found to have lost 20 % of its length and 10 % of its breadth . the percentage of decrease in area is :
Options: a ) 13 % , b ) 14 % , c ) 18 % , d ) 20 % , e ) 28 %
Rationale: let original length = x and original breadth = y . decrease in area = xy - ( 80 / 100 * x * 90 / 100 * y ) = ( xy - 18 / 25 * xy ) = 7 / 25 * xy . decrease % = ( 7 / 25 * xy * 1 / xy * 100 ) % = 28 % . answer is e
Answer: e
Problem: at what rate percent per annum will the simple interest on a sum of money be 2 / 5 of the amount in 10 years ?
Options: a ) 4 % , b ) 74 % , c ) 64 % , d ) 74 % , e ) 94 %
Rationale: let sum = x . then , s . i . = 2 x / 5 , time = 10 years . rate = ( 100 * 2 x ) / ( x * 5 * 10 ) = 4 % answer : a
Answer: a
Problem: a cycle is bought for rs . 900 and sold for rs . 1125 , find the gain percent ?
Options: a ) 27 % , b ) 20 % , c ) 80 % , d ) 30 % , e ) 25 %
Rationale: "900 - - - - 225 100 - - - - ? = > 25 % answer : e"
Answer: e
Problem: the vertex of a rectangle are ( 1 , 0 ) , ( 5 , 0 ) , ( 1 , 2 ) and ( 5 , 2 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?
Options: a ) 3 , b ) 6 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 6
Rationale: "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 3 , 1 ) . the slope of a line passing through ( 0,0 ) and ( 3 , 1 ) is 1 / 3 . the answer is c ."
Answer: c
Problem: a 140 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 41.1 sec , b ) 20.2 sec , c ) 31.8 sec , d ) 43.2 sec , e ) none of the above
Rationale: speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 140 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 660 m time = distance / speed = 660 x 18 / ( 5 x 55 ) = 43.2 sec ans is : d
Answer: d
Problem: how long will a boy take to run round a square field of side 50 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 80 sec , b ) 45 sec , c ) 1 min , d ) 32 sec , e ) 25 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 50 * 4 = 200 m time taken = 200 * 2 / 5 = 80 sec answer is a"
Answer: a
Problem: if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 28 , what is the common ratio of the g . p ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 , d ) 9 , e ) 1 / 9
Rationale: "28 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 28 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 28 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 27 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 27 = r ^ 3 r = 3 a"
Answer: a
Problem: 19 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 38 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 19 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 19 * 21 * 8 = 14 * x * 6 x = 38 answer : c"
Answer: c
Problem: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,056 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 400 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1056 / 1000 ) - 1 = 0.053 = 5.3 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.056 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.056 - 0.01 x = - 0.004 x = - 0.004 / - 0.01 = 4 / 10 = 40 % so x = 40 % of the 1000 which is 400 answer : b"
Answer: b
Problem: the length of the bridge , which a train 135 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 235 , b ) 240 , c ) 245 , d ) 250 , e ) 255
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 135 + x ) / 30 = 25 / 2 x = 240 m . answer : option b"
Answer: b
Problem: there are two inlets and one outlet to a cistern . one of the inlets takes 4 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern . both of the inlets are turned on at 8 : 30 am with the cistern completely empty , and at 10 : 30 am , the outlet is turned on and it takes 1 more hour to fill the cistern completely . how much time does the outlet working alone takes to empty the cistern when the cistern is full ?
Options: a ) 2 hours , b ) 2.5 hours , c ) 3 hours , d ) 3.5 hours , e ) 8 hours
Rationale: "the combined inflow rate of the two inlets is 1 / 4 + 1 / 8 = 3 / 8 cistern / hour . thus , working together , it takes 8 / 3 hours ( time is reciprocal of rate ) to fill the cistern . from 8 : 30 am to 10 : 30 am , so in 2 hours , the inlet pipes will fill ( time ) * ( rate ) = 2 * 3 / 8 = 3 / 4 th of the cistern . then the outlet is turned on and the remaining 1 / 4 th of the cistern is filled in 1 hour . letting x to be the rate of the outlet , we would have : 3 / 8 - x = 1 / 4 - - > x = 1 / 8 cistern / hour , which means that it takes 8 hours the outlet working alone to empty the cistern . answer : e ."
Answer: e
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 80 , how much more remains to be paid ?
Options: a ) $ 640 , b ) $ 680 , c ) $ 720 , d ) $ 760 , e ) $ 800
Rationale: "90 % remains to be paid so the remaining amount is 9 * 80 = $ 720 . the answer is c ."
Answer: c
Problem: mike needs 30 % to pass . if he scored 212 marks and falls short by 22 marks , what was the maximum marks he could have got ?
Options: a ) 343 , b ) 777 , c ) 780 , d ) 867 , e ) 232
Rationale: "if mike had scored 22 marks more , he could have scored 30 % therefore , mike required 212 + 22 = 234 marks let the maximum marks be m . then 30 % of m = 234 ( 30 / 100 ) × m = 234 m = ( 234 × 100 ) / 30 m = 23400 / 30 m = 780 answer : c"
Answer: c
Problem: if shares of two persons in profits are rs . 400 and rs . 500 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 4 : 5 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "profit = time * capital so 400 : 500 = 4 : 5 answer : b"
Answer: b
Problem: in the xy - plane , the point ( 2 , 1 ) is the center of a circle . the point ( - 2 , 1 ) lies inside the circle and the point ( 2 , - 5 ) lies outside the circle . if the radius r of the circle is an integer , then r =
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: an easy way to solve this question will be just to mark the points on the coordinate plane . you ' ll see that the distance between the center ( 2 , 1 ) and the point inside the circle ( - 2 , 1 ) is 4 units ( both points are on y = 1 line so the distance will simply be 2 - ( - 2 ) = 4 ) so the radius must be more than 4 units . the distance between the center ( 2,1 ) and the point outside the circle ( 2 , - 5 ) is 6 units ( both points are on x = 2 line so the distance will simply be 1 - ( - 5 ) = 6 ) so the radius must be less than 6 units , which implies 4 < r < 6 , thus as r is an integer then r = 5 . answer : b .
Answer: b
Problem: the sum of three consecutive integers is 102 . find the lowest of the three ?
Options: a ) 15 , b ) 33 , c ) 56 , d ) 96 , e ) 88
Rationale: "explanation : three consecutive numbers can be taken as ( p - 1 ) , p , ( p + 1 ) . so , ( p - 1 ) + p + ( p + 1 ) = 102 3 p = 102 = > p = 34 . the lowest of the three = ( p - 1 ) = 34 - 1 = 33 . answer b"
Answer: b
Problem: in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 21,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 125 % , c ) 147 % , d ) 150 % , e ) 225 %
Rationale: "the percent increase is ( 21947 - 8902 ) / 8902 = 13045 / 8902 = 1.47 so the approximate answer is c"
Answer: c