Cheukting/mathqa huggingface dataset:
Question (general): three numbers are in the ratio 2 : 3 : 5 and their average is 50 . the largest number is :
Options: a ) 30 , b ) 75 , c ) 27 , d ) 21 , e ) 22
Rationale: "explanation : let the numbers be 2 x , 3 x and 5 x , then , ( 2 x + 3 x + 5 x ) / 3 = 50 = > 10 x = 150 = > x = 15 . largest number 5 x = 5 * 15 = 75 answer : b"
Answer: b
Question (other): in a certain school , the ratio of boys to girls is 5 to 13 . if there are 64 more girls than boys , how many boys are there ?
Options: a ) 27 , b ) 40 , c ) 45 , d ) 72 , e ) 117
Rationale: the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 64 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 64 . so 1 part corresponds to 64 / 8 = 8 and so 5 parts correspond to 5 * 8 = 40 . b
Answer: b
Question (general): a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 3 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 193
Rationale: "by the question , the equation would be 150 p - 83 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 193 . answer e for me ."
Answer: e
Question (physics): two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 630 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 15 sec , c ) 42 sec , d ) 50 sec , e ) 1 min
Rationale: "they meet every 630 / 7 + 8 = 42 sec answer is c"
Answer: c
Question (general): calculate the sum of first 60 natural numbers .
Options: a ) 1839 , b ) 2830 , c ) 1830 , d ) 1831 , e ) 1835
Rationale: "solution we know that ( 1 + 2 + 3 + . . . . . + 60 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 60 ) = ( 60 × 61 / 2 ) = 1830 . answer c"
Answer: c
Question (general): buffalo gives 4 liter milk , cow gives ( 1 / 2 ) liter milk and goat gives 1 / 4 liter milk . you have to get 20 liter milk by 20 animals . what is the number of goats ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: assume number of respective animals are x , y , z . x + y + z = 20 - - - ( 1 ) as the total number of animal has to be 20 amt of milk will be 4 x + ( 1 / 2 ) y + ( 1 / 4 ) z = 20 - - - ( 2 ) solving equation 1 and 2 we get 15 x + y = 60 - - - - ( 3 ) since buffalo gives 4 litre and total milk is 20 , x < 5 but from eq 3 , x can not be more than 4 ; further if x = 1 or 2 ; y > 20 . . . not possible , since total animal is 20 thus , x = 3 , y = 15 , z = 2 2 goats answer : b
Answer: b
Question (general): a batsman makes a score of 85 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 35
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 85 = 11 x x = 85 - 50 = 35 answer is e"
Answer: e
Question (physics): each of the three people individually can complete a certain job in 3 , 4 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?
Options: a ) 1 / 3 , b ) 9 / 20 , c ) 8 / 15 , d ) 5 / 12 , e ) 2 / 3
Rationale: the two slowest people work at rates of 1 / 4 and 1 / 6 of the job per hour . the sum of these rates is 1 / 4 + 1 / 6 = 5 / 12 of the job per hour . the answer is d .
Answer: d
Question (other): in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 80 per kg ?
Options: a ) 5 : 8 , b ) 4 : 7 , c ) 4 : 3 , d ) 9 : 5 , e ) 9 : 8
Rationale: ( 96 - 80 ) / ( 80 - 68 ) = 16 / 12 = 4 / 3 answer : c
Answer: c
Question (gain): if a man lost 4 % by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 2 , e ) 1
Rationale: "96 % - - - - 12 144 % - - - - ? 96 / 144 * 12 = 8 answer a"
Answer: a
Question (physics): the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 6 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 12 , d ) 6 , e ) 160
Rationale: "actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 6 miles / gallon . additional 6 miles / gallon is required to match the actual mileage . imo option d ."
Answer: d
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 70400 ?
Options: a ) 89100 , b ) 81028 , c ) 27772 , d ) 29889 , e ) 22312
Rationale: 70400 * 9 / 8 * 9 / 8 = 89100 . answer : a
Answer: a
Question (gain): an empty fuel tank is filled with brand z gasoline . when the tank is 1 / 4 empty , it is filled with brand y gasoline . when the tank is half empty again , it is filled with brand z gasoline . when the tank is half empty again , it is filled with brand y gasoline . at this time , what percent of the gasoline in the tank is brand z ?
Options: a ) 31.25 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 45 %
Rationale: work with fraction of brand z in the tank . 1 st step : brand z is 1 2 nd step : brand z is 1 / 4 3 rd step : brand z is ( 1 / 2 ) * ( 1 / 4 ) + 1 / 2 = 5 / 8 4 th step : brand z is ( 1 / 2 ) * ( 5 / 8 ) = 5 / 16 answer ( a )
Answer: a
Question (general): if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 29 , 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 ) = 29 - 9 = 20 ab = 10 . answer is d ."
Answer: d
Question (gain): in an election , candidate a got 55 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 261800 , b ) 355800 , c ) 356500 , d ) 356800 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 55 % therefore , the number of valid votes polled in favour of candidate a = 55 % of 476000 = 55 / 100 × 476000 = 26180000 / 100 = 261800 a )"
Answer: a
Question (physics): a 600 meter long train crosses a signal post in 30 seconds . how long will it take to cross a 3 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 3 min , e ) 5 min
Rationale: "s = 600 / 30 = 20 mps s = 3600 / 20 = 180 sec = 4 min answer : d"
Answer: d
Question (general): a certain number when divided by 39 leaves a remainder 20 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 0 , e ) 1
Rationale: "39 + 20 = 59 / 13 = 7 ( remainder ) answer : a"
Answer: a
Question (gain): a sum fetched a total simple interest of $ 4196.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8929
Rationale: "e 8929 principal = $ 100 x 4196.25 / 9 x 5 = $ 419625 / 45 = $ 8929 ."
Answer: e
Question (general): if the sum of 5 consecutive even positive integers is a , then the sum of the next 5 even consecutive integers in terms of a is :
Options: a ) a + 5 , b ) a + 10 , c ) a + 25 , d ) a + 50 , e ) 2 a + 5
Rationale: in case of consecutive integers or integers in arithmetic progression mean = median i . e . median = a / 5 = mean = third integer first integer = a / 5 - 4 second integer = a / 5 - 2 third integer = a / 5 fourth integer = a / 5 + 2 fifth integer = a / 5 + 4 i . e . sixth integer = a / 5 + 6 seventh integer = a / 5 + 8 eighth integer = a / 5 + 10 ninth integer = a / 5 + 12 tenth integer = a / 5 + 14 now mean of next 5 integers = median = a / 5 + 5 i . e . sum of next 5 integers = ( a / 5 + 10 ) * 5 = a + 50 answer : option d
Answer: d
Question (gain): an escalator moves towards the top level at the rate of 12 ft . sec and its length is 196 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 14 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec
Rationale: "time taken to cover the entire length = tot . dist / resultant speed = 196 / ( 12 + 2 ) = 14 sec answer : a"
Answer: a
Question (physics): pipe a fills a tank in 12 minutes . pipe b can fill the same tank 3 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 4 mins , b ) 6 mins , c ) 5 mins , d ) 3 mins , e ) 7 mins
Rationale: "a ' s rate is 1 / 12 and b ' s rate is 1 / 4 . the combined rate is 1 / 12 + 1 / 4 = 1 / 3 the pipes will fill the tank in 3 minutes . the answer is d ."
Answer: d
Question (gain): a sum of rs . 2730 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1629 , b ) 1680 , c ) 1677 , d ) 1698 , e ) 1679
Rationale: ( x * 8 * 3 ) / 100 = ( ( 2730 - x ) * 3 * 5 ) / 100 24 x / 100 = 40950 / 100 - 15 x / 100 39 x = 40950 = > x = 1050 second sum = 2730 â € “ 1050 = 1680 answer : b
Answer: b
Question (geometry): if the radius of a circle is decreased 60 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 84 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.4 * old radius so new area = ( 0.4 ) ^ 2 old area = > 0.16 of old area = > 16 % old area ans : d"
Answer: d
Question (physics): the speed at which a man can row a boat in still water is 22 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 80 metres ?
Options: a ) 12.59 , b ) 11.53 , c ) 15.69 , d ) 14.56 , e ) 18.98
Rationale: speed of the boat downstream = 22 + 3 = 25 kmph = 25 * 5 / 18 = 6.94 m / s hence time taken to cover 80 m = 80 / 6.94 = 11.53 seconds . answer : 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 twice 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 $ 0.70 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.46
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 2 units of water was used to make 3 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 3 . 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 3 . 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 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.7 = 3 * x - - > x = $ 0.46 . answer : e ."
Answer: e
Question (general): if one - third of one - fourth of a number is 18 , then 3 - tenth of that number is : a . 35
Options: a ) 23 , b ) 87 , c ) 26 , d ) 64.8 , e ) 01
Rationale: explanation : the number is 1 / 3 of 1 / 4 is = 15 then 1 / 3 ã — 1 / 4 = 18 number is 216 then 216 ã — 3 / 10 = 64.8 answer : d
Answer: d
Question (gain): during a certain season , a team won 75 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 180 , b ) 170 , c ) 156 , d ) 150 , e ) 125
Rationale: we are first given that a team won 75 percent of its first 100 games . this means the team won 0.75 x 100 = 75 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 75 + 0.5 t – 50 = 0.7 t 25 = 0.2 t 250 = 2 t 125 = t answer is e .
Answer: e
Question (general): if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability e that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."
Answer: d
Question (physics): p , q and r together earn rs . 1890 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ?
Options: a ) s . 40 , b ) s . 70 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: "explanation : amount earned by p , q and r in 1 day = 1890 / 9 = 210 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 210 = 40 = > amount earned by r in 1 day = 40 answer : option a"
Answer: a
Question (general): the greatest number that divides 690 and 875 leaving remainders 10 and 25 respectively is :
Options: a ) 170 , b ) 130 , c ) 150 , d ) 120 , e ) 180
Rationale: "explanation : 690 - 10 = 680 , 875 – 25 = 850 highest number that can divide 680 and 850 exactly is hcm of the numbers . hcf of 680 and 850 = 170 answer : a"
Answer: a
Question (gain): a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 25 speak english well , while 65 of them do not speak english . if 55 % of students do not speak french , how many students were surveyed ?
Options: a ) 190 , b ) 175 , c ) 225 , d ) 200 , e ) 250
Rationale: number of students who speak french are 65 + 25 = 90 of total students , the percentage of students who do not speak french was 55 % - - > percentage of who do is 45 % 90 - - - - - - - 45 % x - - - - - - - 100 % x = 90 * 100 / 45 = 200 = number of all students answer is d
Answer: d
Question (other): a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 510 kilograms of pears that day , how many kilograms did he sell in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 340 , d ) 280 , e ) 320
Rationale: "3 x = 510 x = 170 therefore , the salesman sold 170 kg in the morning and 2 ⋅ 170 = 340 kg in the afternoon . so answer is c ."
Answer: c
Question (general): find the sum of all 3 digit natural numbers , which are divisible by 8 .
Options: a ) 61376 , b ) 54411 , c ) 612314 , d ) 64170 , e ) 64171
Rationale: the three digit natural numbers divisible by 8 are 104 , 112 , 120 , … . 992 . let sndenote their sum . that is , sn = 104 112 120 128 , 992 g + + + + + . now , the sequence 104 , 112 , 120 , g , 992 forms an a . p . a = 104 , d = 8 , l = 992 n = l - a / d n = 112 s 112 = n / 2 ( a + l ) = 61376 option a
Answer: a
Question (general): each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.65 % , what fraction of the products was checked by worker y ?
Options: a ) 1 / 5 , b ) 1 / 2 , c ) 2 / 3 , d ) 1 / 4 , e ) 2 / 5
Rationale: "x : 0.5 % is 0.15 % - points from 0.65 % . y : 0.8 % is 0.15 % - points from 0.65 % . therefore the ratio of products checked by y : x is 1 : 1 . thus , worker y checked 1 / 2 of the products . the answer is b ."
Answer: b
Question (geometry): the radius of the two circular fields is in the ratio 4 : 10 the area of the second field is what percent greater than the area of the first ?
Options: a ) 72 %
b ) 96 %
c ) 94 %
d ) 84 %
e ) 82 %
Rationale: r = 4 ï € r 2 = 16 r = 10 ï € r 2 = 100 100 ï € â € “ 84 ï € 100 - - - - ? = > 84 % . answer : d
Answer: d
Question (physics): a river 2 m deep and 45 m wide is flowing at the rate of 5 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 m 3 , b ) 4580 m 3 , c ) 7500 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 5000 * 2 * 45 ) / 60 = 7500 m 3 answer : option c"
Answer: c
Question (general): if the range q of the 6 numbers 4 , 314 , 710 and x is 12 , what is the difference between the greatest possible value of x and least possible value of x ?
Options: a ) 0 , b ) 2 , c ) 12 , d ) 13 , e ) 15
Rationale: the range q of a set is the difference between the largest and smallest elements of a set . without x , the difference between the largest and smallest elements of a set is 14 - 3 = 11 < 12 , which means that in order 12 to be the range of the set x must be either the smallest element so that 14 - x = 12 - - - > x = 2 or x must the largest element so that x - 3 = 12 - - > x = 15 . the the difference between the greatest possible value of x and least possible value of x is 15 - 2 = 13 . answer : d .
Answer: d
Question (physics): a person is traveling at 60 km / hr and reached his destiny in 4 hr . 30 m then find the distance ?
Options: a ) 150 km , b ) 270 km , c ) 246 km , d ) 196 km , e ) 205 km
Rationale: "t = 4 hr 30 m = 9 / 2 hr d = t * s = 60 * 9 / 2 = 270 km answer is b"
Answer: b
Question (other): if 80 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 55 %
Rationale: "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 80 - x ) + x + ( 55 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 135 x = 55 ans : e"
Answer: e
Question (physics): a train 300 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 72 , b ) 67 , c ) 54 , d ) 26 , e ) 27
Rationale: "length = speed * time speed = l / t s = 300 / 20 s = 15 m / sec speed = 15 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 54 kmph answer : c"
Answer: c
Question (physics): a train is 385 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 42 seconds , b ) 30 seconds , c ) 40 seconds , d ) 50 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 385 + 140 = 525 meter time = distance / speed = 525 ∗ 2 / 25 = 42 seconds option a"
Answer: a
Question (general): ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of a * b ?
Options: a ) 10000 , b ) 11000 , c ) 19000 , d ) 20000 , e ) 21000
Rationale: "yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 a * b = 110 * 100 = 11000 ans : b"
Answer: b
Question (physics): the distance between two cities a and b is 330 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 10 a . m , b ) 10.30 a . m , c ) 11 a . m , d ) 11.30 a . m , e ) none of these
Rationale: explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 330 . therefore , 60 x + 75 ( x - 1 ) = 330 . = > x = 3 . so , they meet at ( 8 + 3 ) i . e , 11 a . m . answer : c
Answer: c
Question (physics): in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 m and a distance of one meter is left from all sides of the boundary of the length of the garden is :
Options: a ) 450 sq mtrs , b ) 460 sq mtrs , c ) 480 sq mtrs , d ) 490 sq mtrs , e ) 470 sq mtrs
Rationale: "length of garden = 1 + 2 * 11 + 1 = 24 m breadth of garden = 1 + 9 * 2 + 1 = 20 m area = 24 * 20 = 480 sq mtrs answer : c"
Answer: c
Question (physics): there are 10 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 156 , b ) 167 , c ) 132 , d ) 352 , e ) 380
Rationale: "the total number of stations = 12 from 12 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 12 p ₂ ways . ² ⁰ p ₂ = 12 * 11 = 132 . answer : c"
Answer: c
Question (general): total dinning bill of 9 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 21.84 , b ) 12.84 , c ) 16.98 , d ) 24.84 , e ) 15.84
Rationale: "dinner bill of 9 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 9 = $ 16.98 answer : c"
Answer: c
Question (physics): find the length of the longest pole that can be placed in a room 12 m long 8 m broad and 9 m high .
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "length of longest pole = length of the diagonal of the room = sqrt ( 12 ^ 2 + 8 ^ 2 + 9 ^ 2 = sqrt ( 289 ) = 17 m . answer is e ."
Answer: e
Question (general): find the average of first 4 multiples of 8 ?
Options: a ) 20 , b ) 12.6 , c ) 22.5 , d ) 31.3 , e ) 40.8
Rationale: "average = ( 8 + 16 + 24 + 32 ) / 4 = 20 answer is a"
Answer: a