Cheukting/mathqa huggingface dataset:
Question (physics): after doing 3 / 5 of the biology homework on monday night , sanjay did 1 / 3 of the remaining homework on tuesday night . what fraction of the original homework would sanjay have to do on wednesday night to complete the biology assignment ?
Options: a ) 1 / 15 , b ) 2 / 15 , c ) 4 / 15 , d ) 2 / 5 , e ) none of these
Rationale: sol . ( c ) remaining homework on monday night = 1 - ( 3 / 5 ) = 2 / 5 work done on tuesday night = 1 / 3 of 2 / 5 = 2 / 15 remaining homework to complete the biology assignment = 2 / 5 - 2 / 15 = ( 6 - 2 ) / 15 = 4 / 15 answer c
Answer: c
Question (gain): difference of two numbers is 1860 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2660 , 1000 , b ) 3660 , 2000 , c ) 3000 , 4160 , d ) 2790 , 4650 , e ) 4660 , 3000
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1860 5 * y / 3 – y = 1860 2 * y / 3 = 1860 y = [ ( 1860 * 3 ) / 2 ] = 2790 . one number = 2790 , second number = 5 * y / 3 = 4650 . answer d ."
Answer: d
Question (general): a box contains 9 slips that are each labeled with one number : 1 , 2 , 3 , 5 , 8 , 13 , 21 , and 55 . two of the slips are drawn at random from the box without replacement . what is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box ?
Options: a ) 7 / 72 , b ) 1 / 6 , c ) 7 / 36 , d ) 5 / 28 , e ) 21 / 36
Rationale: probability = no : of desired outcomes / total no : of outcomes . you are picking two slips out of 8 slips . so total no : of outcomes = 8 c 2 = 28 desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box . how many such outcomes are there ? if you look at the numbers closely , you will see that the following pair of numbers will give you the desired outcome . ( 12 ) ( 23 ) ( 35 ) ( 58 ) ( 813 ) . there are 5 such pairs . if the two numbers which i pick is from any of these 5 pairs , then i get my desired outcome . so no : of desired outcomes = 5 probability = 5 / 28 answer : d
Answer: d
Question (gain): a shopkeeper sold an article offering a discount of 4 % and earned a profit of 26 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 24 , b ) 28 , c ) 31 , d ) 32 , e ) 34
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 126 let marked price be rs . x . then , 96 / 100 x = 126 x = 12600 / 96 = rs . 131.25 now , s . p . = rs . 131.25 , c . p . = rs . 100 profit % = 31 % . answer : c"
Answer: c
Question (physics): find the area of trapezium whose parallel sides are 24 cm and 14 cm long , and the distance between them is 18 cm ?
Options: a ) 288 cm 2 , b ) 277 cm 2 , c ) 345 cm 2 , d ) 276 cm 2 , e ) 342 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 24 + 14 ) * ( 18 ) = 342 cm 2 answer : e"
Answer: e
Question (physics): the reciprocal of the hcf and lcm of two are 1 / 17 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 221 , e ) 266
Rationale: "reciprocal of the hcf and lcm of two are 1 / 17 and 1 / 312 so , hcf = 17 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 17 * 312 / 24 = 221 answer : d"
Answer: d
Question (gain): a man bought 10 crates of mangoes for $ 160 total . if he lost 2 of the crates , at what price would he have to sell each of the remaining crates in order to earn a total profit of 25 percent of the total cost ?
Options: a ) $ 35 , b ) $ 25 , c ) $ 45 , d ) $ 50 , e ) $ 55
Rationale: "as given , after lost , the remaining 8 crates total cost = $ 160 so , 1 crate cost = 160 / 8 = 20 to get 25 % profit , 1 crate cost should be = 20 + 20 * 25 / 100 = $ 25 answer : b"
Answer: b
Question (physics): the speed at which a man can row a boat in still water is 6.5 kmph . if he rows downstream , where the speed of current is 2.5 kmph , what time will he take to cover 90 metres ?
Options: a ) 90 seconds , b ) 36 seconds , c ) 26 seconds , d ) 18 seconds , e ) 6.5 seconds
Rationale: "speed of the boat downstream = 6.5 + 2.5 = 9 kmph = 9 * 5 / 18 = 2.5 m / s hence time taken to cover 90 m = 90 / 2.5 = 36 seconds . answer : b"
Answer: b
Question (general): if x = 1 + √ 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 4 ?
Options: a ) - 1 , b ) 0 , c ) 5 , d ) 2 , e ) 3
Rationale: answer x = 1 + √ 2 ∴ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 4 = x 2 ( x - 2 ) 2 + 4 = ( 1 + √ 2 ) 2 ( 1 + √ 2 - 2 ) 2 + 4 = ( √ 2 + 1 ) 2 ( √ 2 - 1 ) 2 + 4 = [ ( √ 2 ) 2 - ( 1 ) 2 ] 2 + 4 = ( 2 - 1 ) 2 = 1 + 4 = 5 correct option : c
Answer: c
Question (physics): a cube of side 1.5 meter length is cut into small cubes of side 10 cm each . how many such small cubes can be obtained ?
Options: a ) 2878 , b ) 3375 , c ) 1000 , d ) 2997 , e ) 2701
Rationale: "along one edge , the number of small cubes that can be cut = 150 / 10 = 15 along each edge 10 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 15 * 15 * 15 = 3375 answer : b"
Answer: b
Question (general): if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 70 , what is the value of c − a ?
Options: a ) 25 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 140 - - 2 subtracting 1 from 2 we have c - a = 50 ; answer : b"
Answer: b
Question (physics): the angle between the minute hand and the hour hand of a clock when the time is 8 : 30
Options: a ) 80 deg , b ) 40 deg , c ) 35 deg , d ) 75 deg , e ) 60 deg
Rationale: "angle traced hr hand 17 / 2 hrs = 300 / 12 * 17 / 2 = 255 angle by min 30 min ( 360 / 60 * 30 ) = 180 req = 255 - 180 = 75 answer d"
Answer: d
Question (physics): a large tank can filled by a and b in 30 minutes and 45 minutes respectively . how many minutes will it take to fill the tanker from empty state if b is used for half the time and a and b fill it together for the other half ?
Options: a ) 30 min , b ) 20 min , c ) 25 min , d ) 40 min , e ) 45 min
Rationale: "part filled by a + b in 1 minute = 1 / 30 + 1 / 45 = 1 / 45 suppose the tank is filled in x minutes then , x / 2 ( 1 / 45 + 1 / 45 ) = 1 x / 2 * 2 / 45 = 1 x = 45 min answer is e"
Answer: e
Question (general): the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 13 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "a + b + c = 18 b + c + d = 15 a + d = 13 a – d = 3 a + d = 13 2 d = 10 d = 5 answer : b"
Answer: b
Question (physics): if the wheel is 14 cm then the number of revolutions to cover a distance of 4136 cm is ?
Options: a ) 22 , b ) 28 , c ) 17 , d ) 12 , e ) 47
Rationale: "2 * 22 / 7 * 14 * x = 4136 = > x = 47 answer : e"
Answer: e
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 36 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 23.56 , b ) 23.59 , c ) 44.0 , d ) 23.53 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 36 + 20 ) = 112 cm parameter of the square = 112 cm i . e . 4 a = 112 a = 28 diameter of the semicircle = 28 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 28 ) = 1 / 2 ( 22 / 7 ) ( 28 ) = 44 cm to two decimal places answer : c"
Answer: c
Question (gain): on selling 15 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) s . 45 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 72
Rationale: "( c . p . of 15 balls ) - ( s . p . of 15 balls ) = ( c . p . of 5 balls ) c . p . of 10 balls = s . p . of 15 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 10 = rs . 72 . answer : option e"
Answer: e
Question (other): two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 3 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 179 : 2 , b ) 178 : 3 , c ) 179 : 1 , d ) 179 : 54 , e ) 179 : 45
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 3 = 15 / 8 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 15 / 8 + 7 / 2 = 43 / 8 = 5.375 litres as 7 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 5.375 : 1.625 = 179 : 54 . answer : d"
Answer: d
Question (general): x and y are positive integers . when x is divided by 6 , the remainder is 3 , and when x is divided by 16 , the remainder is 5 . when y is divided by 9 , the remainder is 5 , and when y is divided by 7 , the remainder is 4 . what is the least possible value of x / y ?
Options: a ) 2.5 , b ) 3 , c ) 2 , d ) 1.3 , e ) 1.5
Rationale: "when x is divided by 6 , the remainder is 3 : so , the possible values of x are : 3 , 9 , 15 , 21 , etc . when x is divided by 16 , the remainder is 5 : so , the possible values of x are : 5,21 . . . stop . since both lists include 21 , the smallest possible value of x is 21 . when y is divided by 9 , the remainder is 5 : so , the possible values of y are : 5 , 14 , 23,32 etc . when y is divided by 7 , the remainder is 4 : so , the possible values of y are : 6 , 14 , . . . stop . since both lists include 14 , the smallest possible value of y is 14 since the smallest possible values of x and y are 21 and 14 respectively , the smallest possible value of x / y is 1.5 . so , e is the correct answer to the original question ."
Answer: e
Question (physics): in what time will a train 600 meters long cross an electric pole , if its speed is 144 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 15 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 144 * ( 5 / 18 ) = 40 m / sec time = distance / speed = 600 / 40 = 15 seconds answer : d"
Answer: d
Question (general): a certain class of students is being divided into teams . the class can either be divided into 10 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 6 , b ) 36 , c ) 120 , d ) 60 , e ) 72
Rationale: "let total no of students in the class be n so , we are told that n is divisible by both 10 24 so , lets find the least common multiple of 10 24 , ie 120 so our answer is ( c ) 120"
Answer: c
Question (gain): a man took a loan from a bank at the rate of 12 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 2000 , b ) rs . 10,000 , c ) rs . 15,000 , d ) rs . 20,000 , e ) none
Rationale: "solution principal = rs . ( 100 x 5400 / 12 x 3 ) = rs . 15000 . answer c"
Answer: c
Question (other): the ratio of the present age of sandy to that of molly is 7 : 2 . twelve years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 39 , b ) 45 , c ) 51 , d ) 57 , e ) 63
Rationale: "let the present age of sandy be 7 x years and that of molly be 2 x years . ( 7 x + 12 ) / ( 2 x + 12 ) = 5 / 2 4 x = 36 x = 9 six years ago , sandy ' s age was 7 ( 9 ) - 6 = 57 the answer is d ."
Answer: d
Question (physics): the sides of a triangle are in the ratio 3 : 5 : 7 . if the pereimeter is 60 cms , the longest side is
Options: a ) 7 , b ) 30 , c ) 28 , d ) 25 , e ) 16
Rationale: "3 x + 5 x + 7 x = 60 15 x = 60 x = 4 longest side = 7 * 4 = 28 answer : c"
Answer: c
Question (other): how many positive integers between 5 and 5000 ( both are inclusive ) are there such that they are multiples of 5 ?
Options: a ) 1500 , b ) 1000 , c ) 999 , d ) 1001 , e ) 1005
Rationale: "multiples of 5 = 5 , 10,15 - - - - - , 5000 number of multiples of 5 = > 5000 - 5 / 5 + 1 = 1000 answer is b"
Answer: b
Question (gain): the sale price sarees listed for rs . 528 after successive discount is 20 % and 10 % is ?
Options: a ) 288 , b ) 277 , c ) 380 , d ) 290 , e ) 262
Rationale: "528 * ( 80 / 100 ) * ( 90 / 100 ) = 380 answer : c"
Answer: c
Question (physics): a train covers a distance of 9 km in 6 min . if it takes 5 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 100 , b ) 105 , c ) 110 , d ) 120 , e ) 125
Rationale: "speed = ( 9 / 6 * 60 ) km / hr = ( 90 * 5 / 18 ) m / sec = 25 m / sec . length of the train = 25 * 5 = 125 m . answer : option e"
Answer: e
Question (other): the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 52 black cars in the lot , how many red cars are there in the lot ?
Options: a ) 11 , b ) 20 , c ) 24 , d ) 27 , e ) 32
Rationale: "b is correct r / b = 3 / 8 and b = 52 r = 52 * 3 / 8 = 20"
Answer: b
Question (other): in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 5 : 9 . if the shop carries 204 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 51 , b ) 66 , c ) 98 , d ) 112 , e ) 154
Rationale: let us assume the number of dogs , cats and bunnies to be 3 x , 5 x and 9 x total dogs and bunnies = 12 x . and we are given that 12 x = 204 . hence x = 17 . dogs = 3 x = 3 * 17 = 51 ( option a )
Answer: a
Question (general): a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 900 . how many workers were part of the latter production run ?
Options: a ) a ) 6 , b ) b ) 10 , c ) c ) 11 , d ) d ) 15 , e ) e ) 34
Rationale: "the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 900 . . thus for the current period = 900 - 500 = 400 ( 5 n + 45 ) k = 400 k = 400 / 5 n + 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 equate 1 and 2 500 / 5 n + 20 = 400 / 5 n + 45 500 ( 5 n + 45 ) = 400 ( 5 n + 20 ) 25 n + 225 = 20 n + 80 5 n = 145 n = 29 thus n + 5 = 34 hence e"
Answer: e
Question (general): there are 5 guys who have equal number of bullets . all of them shoot 4 bullets . the remaining bullets are equal to the total number of bullets remaining is equal to the bullets each had after division . what was the original number of bullets each one had ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 25
Rationale: let initially each was having x bullets they shot 4 bullets so 5 x - 20 = x x = 5 so each was having 5 bullets . total was 25 . answer : e
Answer: e
Question (gain): the cost price of an article is 55 % of the marked price . calculate the gain percent after allowing a discount of 15 % .
Options: a ) 40.5 % , b ) 48.7 % , c ) 54.5 % , d ) 55.6 % % , e ) none
Rationale: sol . let marked price = rs . 100 . then , c . p . = rs . 55 . s . p = rs . 85 . â ˆ ´ gain % = [ 30 / 55 * 100 ] % = 54.5 % . answer c
Answer: c
Question (geometry): a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 4 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?
Options: a ) 1.6 , b ) 1 , c ) 0.4 , d ) 0.16 , e ) 0.016
Rationale: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 16 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 160 / 10,000 = 16 / 1000 = 0.016 ft the answer is e ."
Answer: e
Question (general): peter and tom shared the driving on a certain trip . if peter and tom both drove for the same amount of time , but peter only drove 2 / 5 of the total distance , what was the ratio of tom ' s average speed to peter ' s average speed ?
Options: a ) 1 : 5 , b ) 2 : 5 , c ) 1 : 2 , d ) 3 : 2 , e ) 2 : 3
Rationale: the answer is suppose to be d . 3 : 2 . it ' s from the gmatprep option d is answer
Answer: d
Question (general): a grocery shop has a sale of rs . 6735 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 4691 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6735 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6735 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34309 + x = 39000 = > x = 39000 − 34309 = 4691 answer : d"
Answer: d
Question (physics): a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 6
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 12 t = 12 / 2 = 6 answer : e"
Answer: e
Question (general): 1 / 4 of all the juniors and 2 / 3 of all the seniors are going on a trip . if there are 2 / 3 as many juniors as seniors , what fraction of the students are not going on the trip ?
Options: a ) 4 / 9 , b ) 1 / 2 , c ) 2 / 3 , d ) 1 / 3 , e ) 5 / 6
Rationale: j be the number of juniors and s be the number of seniors . there are 2 / 3 as many juniors as seniors 23 ∗ s = j j / s = 23 going on trip = j 4 + 23 ∗ s fraction = ( j 4 + 23 s ) / ( j + s ) = ( 2 / 3 * 1 / 4 + 2 / 3 ) / ( 2 / 3 + 1 ) = 1 / 2 fraction not on trip = 1 / 2 answer : b
Answer: b
Question (gain): sonika deposited rs . 4500 which amounted to rs . 8400 after 2 years at simple interest . had the interest been 4 % more . she would get how much ?
Options: a ) 9680 , b ) 8790 , c ) 8760 , d ) 9020 , e ) 5000
Rationale: "( 4500 * 2 * 4 ) / 100 = 360 8400 - - - - - - - - 8760 answer : c"
Answer: c
Question (general): a grocer has a sale of rs . 4000 , rs . 6524 , rs . 5689 , rs . 7230 and rs . 6000 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7000 ?
Options: a ) s . 12557 , b ) s . 14993 , c ) s . 15560 , d ) s . 12589 , e ) s . 12500
Rationale: "total sale for 5 months = rs . ( 4000 + 6524 + 5689 + 7230 + 6000 ) = rs . 29443 required sale = rs . [ ( 7000 x 6 ) - 29443 ] = rs . ( 42000 - 29443 ) = rs . 12557 . option a"
Answer: a
Question (physics): in one hour , a boat goes 14 km / hr along the stream and 8 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 14 km / hr , b ) 13 km / hr , c ) 12 km / hr , d ) 11 km / hr , e ) 10 km / hr
Rationale: "let speed of the boat in still water = a and speed of the stream = b then a + b = 14 a - b = 8 adding these two equations , we get 2 a = 22 = > a = 11 ie , speed of boat in still water = 11 km / hr answer : d"
Answer: d
Question (general): at a contest with 2000 participants , 1 / 2 of the people are aged 16 to 18 . next year , the number of people aged 16 to 18 will increase by 1 / 4 . after this change , what percentage of the total 2000 people will the 16 - to 18 - year - olds represent ?
Options: a ) 62.50 % , b ) 60 % , c ) 70 % , d ) 65 % , e ) 66 / 3 %
Rationale: i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 2000 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 4 , we are multiplying it by 1 + 1 / 4 = 5 / 4 , so the answer here must be ( 1 / 2 ) * ( 5 / 4 ) = 5 / 8 = 62.50 % . answer : a
Answer: a
Question (physics): two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively . in what time will they cross each other completely ?
Options: a ) 26 sec , b ) 28 sec , c ) 12 sec , d ) 77 sec , e ) 66 sec
Rationale: "d = 250 m + 250 m = 500 m rs = 80 + 70 = 150 * 5 / 18 = 125 / 3 t = 500 * 3 / 125 = 12 sec answer : c"
Answer: c
Question (general): the closest approximation of f ( 69.28 × 0.004 ) / 0.03 is
Options: a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920
Rationale: f ( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c
Answer: c
Question (other): there are 9 executives , including the ceo and cfo , that are asked to form a small team of 4 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 97 , b ) 99 , c ) 101 , d ) 103 , e ) 105
Rationale: the total number of ways to form a team of 4 is 9 c 4 = 126 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 7 c 2 = 21 . the number of ways to form an acceptable team is 126 - 21 = 105 . the answer is e .
Answer: e
Question (general): the average of first 11 prime numbers is ?
Options: a ) 14.55 , b ) 11.11 , c ) 12.11 , d ) 13.11 , e ) 14.11
Rationale: "sum of 11 prime no . = 160 average = 160 / 11 = 14.55 answer : a"
Answer: a
Question (physics): if 12 men or 20 women can do a piece of work in 108 days , then in how many days can 9 men and 12 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "d 80 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 108 days . so , 27 women can do it in ( 20 * 108 ) / 27 = 80 days ."
Answer: d
Question (gain): the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 7500 , brokerage being 1 / 4 % , is :
Options: a ) 103.92 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 7500 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 7500 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 104.17 = market value of rs . 100 stock = rs . 104.17 - re . 0.25 . = market value of rs . 100 stock = rs . 103.92 . answer : a"
Answer: a
Question (probability): a bag contains 6 black and 5 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 5 / 11 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 5 ) = 11 . number of white balls = 5 p ( drawing a white ball ) = 5 / 11 option b ."
Answer: b
Question (other): in what ratio water be mixed with milk costing rs . 12 per liter to obtain a mixture worth of rs . 8 per litre ?
Options: a ) 2 : 7 , b ) 1 : 2 , c ) 2 : 9 , d ) 2 : 2 , e ) 2 : 6
Rationale: answer with explanation : by the rule of allegation , i . c . p of 1 liter of water = 0 ii . c . p of 1 liter of milk = 12 iii . mean price ( p ) = 8 iv . d – m = 12 - 8 = 4 v . m – c = 8 - 0 = 8  ratio of water and milk = 4 : 8 = 1 : 2 answer : b
Answer: b
Question (general): find the largest number of 4 digits which is exactly divisible by 2718 , 1615
Options: a ) 8600 , b ) 8610 , c ) 8620 , d ) 8630 , e ) 8640
Rationale: explanation : lcm of 27 - 18 - 16 - 15 is 2160 . after dividing 9999 by 2160 we get 1359 remainder . so answer will be 9999 - 1359 = 8640 option e
Answer: e