Cheukting/mathqa huggingface dataset:
Question (general): if | 4 x + 6 | = 42 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 3 , c ) 4 , d ) - 5 , e ) 6
Rationale: "there will be two cases 4 x + 6 = 42 or 4 x + 6 = - 42 = > x = 9 or x = - 12 sum of both the values will be - 12 + 9 = - 3 answer is b"
Answer: b
Question (physics): a pipe can empty 1 / 4 th of a cistern in 12 mins . in 8 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 3 / 7 , c ) 4 / 9 , d ) 1 / 6 , e ) 4 / 7
Rationale: "1 / 4 - - - - 12 ? - - - - - 8 = = > 1 / 6 d"
Answer: d
Question (gain): 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 16 mat - weavers in 16 days ?
Options: a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 64
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 16 : : 4 : x days 4 : 16 4 * 4 * x = 16 * 16 * 4 x = ( 16 * 16 * 4 ) / ( 4 x 4 ) x = 64 . answer is e ."
Answer: e
Question (physics): suppose 8 monkeys take 8 minutes to eat 8 banana ' s . how many minutes would it take 3 monkeys to eat 3 banana ' s ?
Options: a ) 5 min , b ) 6 min , c ) 7 min , d ) 8 min , e ) 9 min
Rationale: there are equal no . of monkeys and equal no . of bananas and they take equal time and the time is 8 mint to eat a banana so each monkey take 8 mints to eat a banana ' s so 3 monkeys will take 8 mints to eat 3 banana ' s . answer : d
Answer: d
Question (general): if x + | x | + y = 4 and x + | y | - y = 3 what is x + y = ?
Options: a ) 1 , b ) - 1 , c ) 3 , d ) 5 , e ) 13
Rationale: "if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 3 hence answer should be c"
Answer: c
Question (general): there were 35 students in a hostel . if the number of students increases by 7 , the expenses of the mess increase by rs . 42 per day while the average expenditure per head diminishes by re 1 . find the original expenditure of the mess .
Options: a ) rs . 480 , b ) rs . 520 , c ) rs . 420 , d ) rs . 460 , e ) none of these
Rationale: let d be the average daily expenditure original expenditure = 35 × d new expenditure = 35 × d + 42 new average expenditure will be : ( 35 × d + 42 ) / 42 = d - 1 on solving , we get d = 12 therefore original expenditure = 35 × 12 = 420 answer : c
Answer: c
Question (other): two numbers are in the ratio of 1 : 2 . if 8 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 8 ) / ( y + 8 ) = 3 / 5 = > x = 16 and y = 32 answer : d"
Answer: d
Question (gain): if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 200 papers and 20 % discount after first 1000 papers , how much will it cost to buy 2500 sheets of xerox paper ?
Options: a ) $ 125 , b ) $ 106 , c ) $ 135 , d ) $ 90 , e ) $ 100
Rationale: "30 sec approach - solve it using approximation 2500 sheet at full price , 5 cent = 125 2500 sheet at max discount price , 4 cent = 100 your ans got to be between these two . ans b it is ."
Answer: b
Question (physics): a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 3 days . in how many days can they complete the remaining work ?
Options: a ) 6 days , b ) 2 days , c ) 8 days , d ) 4 1 / 5 days , e ) 9 days
Rationale: "work done by a in 3 days = 3 / 10 remaining work = 7 / 10 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 7 / 10 * 6 / 1 = 21 / 5 = 4 1 / 5 days . answer : d"
Answer: d
Question (general): how many integers between 265,205 and 758,805 have tens digit 1 and units digit 3 ?
Options: a ) 4,629 , b ) 4,639 , c ) 3,946 , d ) 4,926 , e ) 4,936
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 265,205 and 758,805 is 758,805 - 265,205 = 493,600 - one number per each hundred gives 133,900 / 100 = 4,936 numbers . answer : e ."
Answer: e
Question (general): the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 60 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) a ) 12.5 % , b ) b ) 13 % , c ) c ) 13.15 % , d ) d ) 14 % , e ) e ) 15 %
Rationale: "quantity x rate = price 1 x 1 = 1 0.6 x 1.25 = 0.755 decrease in price = ( 0.125 / 1 ) × 100 = 12.5 % a )"
Answer: a
Question (general): a batsman scored 160 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 64 % , b ) 66 % , c ) 60 % , d ) 68 % , e ) 70 %
Rationale: "explanation : number of runs made by running = 160 - ( 3 x 4 + 8 x 6 ) = 160 - ( 60 ) = 100 now , we need to calculate 100 is what percent of 160 . = > 100 / 160 * 100 = 68 option d"
Answer: d
Question (physics): a train covers a distance of 6 km in 10 min . if it takes 12 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 120 m , b ) 180 m , c ) 240 m , d ) 220 m , e ) 280 m
Rationale: "speed = ( 6 / 10 * 60 ) km / hr = ( 36 * 5 / 18 ) m / sec = 10 m / sec . length of the train = 10 * 12 = 120 m . answer : a"
Answer: a
Question (gain): 60 % of the employees of a company are men . 60 % of the men in the company speak french and 50 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
Options: a ) 4 % , b ) 10 % , c ) 96 % , d ) 90 % , e ) 65 %
Rationale: "no of employees = 100 ( say ) men = 60 women = 40 men speaking french = 0.6 * 60 = 36 employees speaking french = 0.5 * 100 = 50 therefore women speaking french = 50 - 36 = 14 and women not speaking french = 40 - 14 = 26 % of women not speaking french = 26 / 40 * 100 = 65 % answer e"
Answer: e
Question (geometry): an error 2 % in excess is made while measuring the side ofa square . the % of error in the calculated area of the square is ?
Options: a ) 4 %
b ) 4.04 %
c ) 4.23 %
d ) 4.56 %
e ) 5 %
Rationale: 100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b
Answer: b
Question (general): in a group of donkeys and pigs , the numbers of legs are 16 more than twice the number of heads . the number of donkeys is
Options: a ) 6 , b ) 8 , c ) 11 , d ) 12 , e ) 13
Rationale: let the number of donkeys be x and the number of pigs be y . then , 4 x + 2 y = 2 ( x + y ) = 16 or 2 x + ( 2 x + 2 y ) = ( 2 x + 2 y ) + 16 or 2 x = 16 or x = 8 . answer : b
Answer: b
Question (gain): a furniture dealer purchased a desk for $ 240 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) $ 40 , b ) $ 60 , c ) $ 160 , d ) $ 90 , e ) $ 100
Rationale: "purchase price = 240 selling price = x 240 + 0.4 * x = x 0.6 * x = 240 x = 400 profit = 400 - 240 = 160 answer : c"
Answer: c
Question (gain): a , b and c enter into a partnership . a invests 3 times as much as b invests and 2 / 3 of what c invests . at the end of the year , the profit earned is rs . 12375 . what is the share of c ?
Options: a ) rs . 2250 , b ) rs . 3375 , c ) rs . 6750 , d ) rs . 5625 , e ) none of these
Rationale: "explanation : let the investment of c be rs . x . the inverstment of b = rs . ( 2 x / 3 ) the inverstment of a = rs . ( 3 × ( 2 / 3 ) x ) = rs . ( 2 x ) ratio of capitals of a , b and c = 2 x : 2 x / 3 : x = 6 : 2 : 3 c ' s share = rs . [ ( 3 / 11 ) × 12375 ] = rs . 3375 answer : option b"
Answer: b
Question (gain): a shopkeeper has 280 kg of apples . he sells 40 % of these at 20 % profit and remaining 60 % at 20 % profit . find his % profit on total .
Options: a ) 24 % , b ) 20 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 40 x 20 % + 60 x 20 % = 20 this profit will remain same for any total quantity unless the % of products remains the same . hence ' b ' is the answer"
Answer: b
Question (other): how many positive integers less than 30 have no common prime factor with 30 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "30 = 2 * 3 * 5 . so , the number must be less than 30 and not have primes 2 , 3 , or 5 . this means that the number could be : 1 , 7 , 11 , 13 , 17 , 19 , 23 , or 29 . total of 8 numbers . answer : d ."
Answer: d
Question (physics): a 300 m long train crosses a platform in 38 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 288 , b ) 350 , c ) 889 , d ) 276 , e ) 333
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 38 = 50 / 3 3 x + 900 = 1900 = > x = 333 m . answer : e"
Answer: e
Question (physics): two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 36 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 18.4 sec , b ) 77 sec , c ) 76 sec , d ) 20 sec , e ) 66 sec
Rationale: "relative speed = ( 42 + 36 ) * 5 / 18 = 21.7 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 21.7 = 18.4 sec . answer : a"
Answer: a
Question (general): tough and tricky questions : mixture problems . a drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 35 ounces of an alcoholic drink that is 1 part rum to 3 parts coke . what is the ratio of rum to coke in the resulting mixture ?
Options: a ) 2 : 5 , b ) 5 : 15 , c ) 3 : 5 , d ) 4 : 7 , e ) 14 : 5
Rationale: answer = b ) 5 : 15 . . . . . . . . . . . . . . . . . . . . . . . . rum . . . . . . . . . . . . . . . . . . . . . coke . . . . . . . . . . . . . . . . . total first drink . . . . . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . . . . . . . . 6 ( ratio 1 : 2 ) second drink . . . . . . . 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 . . . . . . . . . . . . . . . . . . . 32 ( ratio 1 : 3 ) total . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 . . . . . . . . . . . . . . . . . . . . 38 ratio = 10 : 30 = 5 : 15 b
Answer: b
Question (physics): excluding stoppages , the speed of a bus is 70 km / hr and including stoppages , it is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 118 min , b ) 10 min , c ) 18 min , d ) 16 min , e ) 25 min
Rationale: "due to stoppages , it covers 30 km less . time taken to cover 30 km = 30 / 70 * 60 = 25 min . answer : e"
Answer: e
Question (general): 49 x 49 x 49 x 49 = 7 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 16 , e ) 20
Rationale: "solution 49 * 49 * 49 * 49 = ( 72 * 72 * 72 * 72 ) = 7 ( 2 + 2 + 2 + 2 ) = 78 so , the correct answer is 8 answer c"
Answer: c
Question (general): calculate 12351 ÷ ? = 69
Options: a ) 179 , b ) 119 , c ) 129 , d ) 173 , e ) 156
Rationale: "answer let 12351 ÷ ? = 69 then x = 12351 / 69 = 179 . option : a"
Answer: a
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 minutes , then the area of the park ( in sq . m ) is ?
Options: a ) 153600 , b ) 153629 , c ) 151299 , d ) 153129 , e ) 152109
Rationale: "let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m ^ 2 = 153600 m ^ 2 . answer : a"
Answer: a
Question (physics): if 9 engines consume 24 metric tonnes of coal , when each is working 8 hoursa day , how much coal will be required for 8 engines , each running 13 hours a day , it is being given that 3 engines of former type consume as much as 4 engines of latter type ?
Options: a ) 23 , b ) 25 , c ) 26 , d ) 28 , e ) 30
Rationale: explanation : let 3 engines of former type consume 1 unit in 1 hour . then , 4 engines of latter type consume 1 unit in 1 hour . therefore 1 engine of former type consumes ( 1 / 3 ) unit in 1 hour . 1 engine of latter type consumes ( 1 / 4 ) unit in 1 hour . let the required consumption of coal be x units . less engines , less coal consumed ( direct proportion ) more working hours , more coal consumed ( direct proportion ) less rate of consumption , less coal consumed ( direct proportion ) number of engines 9 : 8 working hours 8 : 13 } : : 24 : x rate of consumption ( 1 / 3 ) : ( 1 / 4 ) ( 9 * 8 * ( 1 / 3 ) * x ) = ( 8 * 13 * ( 1 / 4 ) * 24 ) < = > 24 x = 624 < = > x = 26 . answer : c
Answer: c
Question (physics): it takes 40 identical printing presses 15 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 21 , e ) 24
Rationale: 40 printing presses can do 1 / 15 of the job each hour . 30 printing presses can do 3 / 4 * 1 / 15 = 1 / 20 of the job each hour . the answer is c .
Answer: c
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 400 sq . ft , how many feet of fencing will be required ?
Options: a ) 60 feet , b ) 50 feet , c ) 40 feet , d ) 30 feet , e ) 5 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 400 = > breadth = 20 feet area to be fenced = 2 b + l = 2 * 20 + 20 = 60 feet answer : option a"
Answer: a
Question (gain): one night 20 percent of the female officers on a police force were on duty . if 100 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 250 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 100 number of female officers on duty on that night = 100 / 2 = 50 ( 20 / 100 ) * f = 50 = > f = 250 answer c"
Answer: c
Question (physics): if a certain number of people can dig earth 100 m deep , 25 m long , and 30 m broad in 12 days , then find the number of days the same number of people will require to dig earth 75 m deep , 20 m long and 50 m broad .
Options: a ) 12 , b ) 18 , c ) 6 , d ) 1 , e ) 17
Rationale: explanation : more number of days means – more length , more depth and more width . hence , it ’ s a direct proportion . ( 100 * 25 * 30 ) : ( 75 * 20 * 50 ) : : 12 : x 75000 : 75000 : : 12 : x x = 12 answer a
Answer: a
Question (general): a mixture of 125 gallons of wine and water contains 20 % water . how much water must be added to the mixture in order to increase the percentage of water to 25 % of the new mixture ?
Options: a ) 10 glas , b ) 8.5 gals , c ) 8 gals , d ) 6.66 gals , e ) 8.33 gals
Rationale: "in 125 gallons of the solution there are 0.2 ∗ 125 = 250 gallons of water . we want to add ww gallons of water to 125 gallons of solution so that 25 + w gallons of water to be 25 % of new solution : 25 + w = 0.25 ( 125 + w ) - - > w = 25 / 3 ≈ 8.33 answer : e ."
Answer: e
Question (general): the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 61.5 . when one student dropped the class , the average of the remaining scores increased to 64.0 . what is the quiz score of the student who dropped the class ?
Options: a ) a ) 10 , b ) b ) 24 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70
Rationale: "total score of 16 students is 16 * 61.50 = 984 total score of 15 students is 15 * 64 = 960 so , the score of the person who left is 24 ( 984 - 960 ) answer will be ( b )"
Answer: b
Question (geometry): the ratio , by volume , of soap to alcohol to water in a certain solution is 4 : 40 : 90 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 200 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 1300
b ) 1500
c ) 1600
d ) 1700
e ) 1800
Rationale: soap : alcohol initial ratio soap : alcohol : water - - > 4 : 40 : 90 initial soap : alcohol = 4 / 40 = 4 : 40 after doubled soap : alcohol = 2 * 4 / 40 = 8 : 40 initial soap : water = 4 / 90 = 4 : 90 after halved soap : water : 1 / 2 * 4 / 90 = 2 / 90 = 2 : 90 after soap : alcohol : water - - > 8 : 40 : 360 - - > 1 : 5 : 45 given alcohol 200 cubic centimeter . ratio is 40 : 200 : 1800 ( 1 : 5 : 45 ) for 200 cubic centimeter of alcohol - - - 1800 cubic cm water is required . answer - e
Answer: e
Question (physics): there is enough provisions for 2400 women in an army camp for 100 days . if there were 1200 men less , how long will the provision last ?
Options: a ) 170 , b ) 180 , c ) 190 , d ) 200 , e ) 210
Rationale: "we have , m 1 d 1 = m 2 d 2 2400 * 100 = 1200 * d 2 d 2 = 2400 * 100 / 1200 = 200 days . answer : d"
Answer: d
Question (physics): a thief steals a car at 2.30 pm and drives it at 60 kmph . the theft is discovered at 3 pm and the owner sets off in another car at 75 kmph when will he overtake the thief
Options: a ) 3.3 pm , b ) 5.5 pm , c ) 4.9 pm , d ) 5 pm , e ) 5.2 pm
Rationale: let the thief is overtaken x hrs after 2.30 pm distance covered by the thief in x hrs = distance covered by the owner in x - 1 / 2 hr 60 x = 75 ( x - ½ ) x = 5 / 2 hr thief is overtaken at 2.30 pm + 2 ½ hr = 5 pm answer is d .
Answer: d
Question (physics): two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 100 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ?
Options: a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 1 hour 40 minutes , e ) 2 hours 40 minutes
Rationale: "both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 100 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where 2 / 3 represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 100 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 100 + 60 ) = 160 minutes on the road . e . 2 hours 40 minutes"
Answer: e
Question (general): if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 56 km , c ) 60 km , d ) 40 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 15 15 x = 10 x + 200 5 x = 200 x = 40 km . answer : d"
Answer: d
Question (general): nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1.5 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40
Rationale: "d its is . let price = x ( x - 1.5 ) 8 = 6 x x = 6 hence total money = 6 * 6 = 36"
Answer: d
Question (general): there are 40 doors marked with numbers 1 to 40 . there are 40 individuals marked 1 to 40 . an operation on a door is defined as changing the status of the door from open to closed or vice versa . all the doors are closed to start with . one at a time , one randomly chosen individual goes and operates the doors . the individual however operates only those doors which are a multiple of the number he / she is carrying . for example , the individual marked with number 5 operates the doors marked with 5 , 10 , 15 , 20 , 25 , 30 , 35 , and 40 . if every individual in the group gets one turn , then how many doors are open at the end ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: if a door is closed at the start , it requires an odd number of people to operate to be open at the end . only the perfect squares have an odd number of factors . the doors which are open at the end are : 1 , 4 , 9 , 16 , 25 , 36 for a total of 6 doors . the answer is d .
Answer: d
Question (general): for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 7.2 – 7.2 * ?
Options: a ) 1.2 , b ) 0.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: since y * is defined as the greatest positive even integer less than or equal to y , then 7.2 * = 6 ( the greatest positive even integer less than or equal to 7.2 is 6 ) . hence , 7.2 – 7.2 * = 7.2 - 6 = 1.2 answer : a .
Answer: a
Question (gain): p and q started a business investing rs 85000 and rs 10000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 17 : 5 , b ) 17 : 3 , c ) 17 : 6 , d ) 17 : 2 , e ) 17 : 8
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 85000 : 10000 = 85 : 10 = 17 : 2 option d"
Answer: d
Question (probability): a bag contains 5 white marbles and 5 black marbles . if each of 5 girls and 5 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 126 , b ) 1 / 120 , c ) 1 / 24 , d ) 4 / 25 , e ) 1 / 2
Rationale: "consider a case when all girls select black marbles . . . so girl 1 will chose 1 black marble out of 10 . . and black marble will be chosen from 5 black marbles girl 1 will have a probability of picking black marble 5 / 10 girl 2 will have to pick a black marble out of 4 and total remaining no . of marbles 9 = 4 / 9 so we have probability of all girls selecting black marbles as 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 * 1 / 6 = 1 / 252 since girls can also select white marbles so we will have 2 cases so probability of girls selecting all same colour marbles is 2 * 1 / 252 or 1 / 126 ans is a"
Answer: a
Question (physics): if the radius of a circle that centers at the origin is 5 , how many m points on the circle have integer coordinates ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20
Rationale: "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : m = c"
Answer: c