Cheukting/mathqa huggingface dataset:
Question (general): find large number from below question the difference of two numbers is 1385 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1659
Rationale: "let the smaller number be x . then larger number = ( x + 1385 ) . x + 1385 = 6 x + 15 5 x = 1370 x = 274 large number = 274 + 1385 = 1659 e"
Answer: e
Question (general): the average age of 36 students in a group is 13 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 35 years , b ) 45 years , c ) 51 years , d ) 54 years , e ) 50 years
Rationale: "explanation : age of the teacher = ( 37 * 14 - 36 * 13 ) years = 50 years . answer : e"
Answer: e
Question (physics): convert 0.30 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 3 / 10 , d ) 19 / 50 , e ) none
Rationale: answer 0.30 = 30 / 100 = 3 / 10 correct option : c
Answer: c
Question (general): a certain galaxy is known to comprise approximately 5 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 8,000 , d ) 12,000 , e ) 10,000
Rationale: "total no . of stars on galaxy = 5 * 10 ^ 11 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 5 * 10 ^ 11 / 50 * 10 ^ 6 = 50 * 10 ^ 3 / 5 = 10000 therefore answer is e"
Answer: e
Question (geometry): a room is 30 m long and 24 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , the volume of the hall is :
Options: a ) 9.6 m 3
b ) 96 m 3
c ) 960 m 3
d ) 9600 m 3
e ) 96000 m 3
Rationale: let the height be h 2 ( 30 + 24 ) x h – 2 ( 30 - 24 ) h = ( 2 ( 30 x 24 ) ) / ( 2 ( 30 + 24 ) ) = ( 30 x 24 ) / 54 = 40 / 3 m volume = 30 x 24 x 40 / 3 = 9600 m 3 answer : d
Answer: d
Question (gain): if $ 120 invested at a certain rate of simple interest amounts to $ 180 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 300
Rationale: "120 amounts to 180 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 180 120 + 120 * ( r / 100 ) * ( 3 ) = 140 = > r = 50 / 3 150 in 6 years = principal + interest = 300 answer is e ."
Answer: e
Question (geometry): find the smallest number which should be multiplied with 520 to make it a perfect square
Options: a ) 337 , b ) 297 , c ) 266 , d ) 116 , e ) 130
Rationale: "explanation : 520 = 26 * 20 = 2 * 13 * 22 * 5 = 23 * 13 * 5 required smallest number = 2 * 13 * 5 = 130 130 is the smallest number which should be multiplied with 520 to make it a perfect square . answer : e"
Answer: e
Question (general): the price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980 . if its price of $ 1.20 in 1970 was 150 percent of its price in 1960 , what was its price in 1980 ?
Options: a ) $ 1.80 , b ) $ 2.00 , c ) $ 2.40 , d ) $ 2.70 , e ) $ 3.00
Rationale: the price in 1970 was 150 percent of its price in 1960 , means that the percent increase was 50 % from 1960 to 1970 ( and from 1970 to 1980 ) . therefore the price in 1980 = $ 1.2 * 1.5 = $ 1.8 . answer : a .
Answer: a
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 37 , the how old is b ?
Options: a ) 7 , b ) 9 , c ) 8 , d ) 14 , e ) 10
Rationale: explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 37 ⇒ 5 x = 35 ⇒ x = 7 . hence , b ' s age = 2 x = 14 years . answer : d
Answer: d
Question (general): if c and t are positive integers , ct + c + t can not be
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: let ct + t + c = x add 1 on both sides : ct + t + c + 1 = x + 1 t ( c + 1 ) + c + 1 = x + 1 ( c + 1 ) ( t + 1 ) = x + 1 minimum value of ( c + 1 ) = 2 minimum value of ( t + 1 ) = 2 hence x + 1 can not be prime substitute x from the given options : 6 + 1 = 7 - - > prime - - > ct + t + s can not be 6 answer : b
Answer: b
Question (geometry): the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 2 per metre approximately
Options: a ) 2972 , b ) 4567 , c ) 4235 , d ) 4547 , e ) 4675
Rationale: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 2 ) = rs . 2972 . answer : option a"
Answer: a
Question (physics): a man swims downstream 30 km and upstream 12 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 2 , e ) 4
Rationale: "30 - - - 3 ds = 10 ? - - - - 1 12 - - - - 3 us = 4 ? - - - - 1 m = ? m = ( 10 + 4 ) / 2 = 7 answer : b"
Answer: b
Question (general): a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 7 x km .
Options: a ) 56 , b ) 18 , c ) 24 , d ) 19 , e ) 12
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 7 x / ( x / 8 ) = 56 kmph answer : a"
Answer: a
Question (general): if the average of 6 digits is 16 and the average of 4 of them is 10 , calculate the average of the remaining 2 numbers ?
Options: a ) 36 , b ) 35 , c ) 28 , d ) 33 , e ) 21
Rationale: "explanation : total of the 6 digits - 6 * 16 = 96 total of the 4 digits - 4 * 10 = 40 total of the remaining 2 digits - 96 - 40 = 56 average of the remaining 2 numbers = 56 / 2 = 28 answer : c"
Answer: c
Question (gain): a company pays 20.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 66 , c ) 18 , d ) 19 , e ) 41
Rationale: "explanation : dividend on 1 share = ( 20.5 * 50 ) / 100 = rs . 10.25 rs . 25 is income on an investment of rs . 100 rs . 10.25 is income on an investment of rs . ( 10.25 * 100 ) / 25 = rs . 41 answer : e"
Answer: e
Question (general): how many diagonals does a 59 - sided convex polygon have ?
Options: a ) 1168 , b ) 1652 , c ) 2452 , d ) 3304 , e ) 4256
Rationale: a 59 - sided convex polygon has 59 vertices . if we examine a single vertex , we can see that we can connect it with 56 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 59 vertices can be connected with 56 vertices to create a diagonal then the total number of diagonals would be ( 59 ) ( 56 ) = 3304 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3304 by 2 to get 1652 . the answer is b .
Answer: b
Question (gain): a shopkeeper sold an book offering a discount of 5 % and earned a profit of 33 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 133 let marked price be $ x . then , 95 / 100 x = 133 x = 13300 / 95 = $ 140 now , s . p . = $ 140 , c . p . = $ 100 profit % = 40 % . a"
Answer: a
Question (gain): calculate how long it will take a swimmer to swim a distance of 10 km against the current of a river which flows at 3 km / hr , given that he can swim in still water at 5 km / h
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "swim in still water at = 5 speed of river = 3 us = 5 - 3 = 2 distance = 10 t = 10 / 2 = 5 answer : c"
Answer: c
Question (gain): a computer store offers employees a 30 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 900 dollars and marked up the price 30 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 30 % off retail price ) as opposed to the final retail price .
Options: a ) 352 , b ) 356 , c ) 358 , d ) 362 , e ) 365
Rationale: "cost price = 900 profit = 30 % = 30 % of 900 = 270 selling price = cp + profit sp = 1170 a discount of 30 % to employees means 30 % off on 1170 so 30 % of 1170 = 351 ans a"
Answer: a
Question (physics): the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 6360 , what is the length of the plot in metres ?
Options: a ) 70 , b ) 200 , c ) 300 , d ) 400 , e ) 140
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 6360 [ 4 l - 40 ] = 6360 / 26.50 = 240 4 l = 280 l = 280 / 4 = 70 meters . answer : a"
Answer: a
Question (other): each factor of 240 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 15 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "the # of factors 240 has is 20 ; so out of 20 factors only four are multiples of 15 : 15 , 30 , 60 , 120 and 240 , itself ; so , the probability is 5 / 20 = 1 / 4 . answer : e ."
Answer: e
Question (general): what is the least common multiple of 15 , 22 and 24 ?
Options: a ) 60 , b ) 120 , c ) 240 , d ) 1320 , e ) 1720
Rationale: "let us first write the numbers in the form of prime factors : 15 = 3 * 5 22 = 2 * 11 24 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 1320 option d"
Answer: d
Question (general): a team of 8 persons joins in a shooting competition . the best marksman scored 85 points . if he had scored 92 points , the average score for the team would have been 84 . the number of points , the team scored was :
Options: a ) 665 , b ) 376 , c ) 998 , d ) 1277 , e ) 1991
Rationale: explanation : let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a ) 665
Answer: a
Question (other): two integers are in the ratio of 1 to 3 . if 10 is added to the smaller number , the ratio becomes 2 to 1 . find the larger integer .
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: "one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 3 , then 3 x = y , where x is the smaller integer . if adding 10 to the smaller integer makes the ratio 2 to 1 , then x + 10 = 2 y . substituting y = 3 x into the second equation yields x + 10 = 6 x . so , x = 2 ( smaller integer ) and , y = 3 x = 6 ( larger integer ) so a is the correct answer . another option is to test the answer choices . a ) the larger number is 6 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 2 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 2 ) , we get 12 . so , the new ratio is 12 to 6 which is the same as 2 to 1 . therefore choice a is correct . b ) the larger number is 9 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 3 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 3 ) , we get 13 so , the new ratio is 13 to 9 . no good . we want a resulting ratio of 2 to 1 eliminate b c ) the larger number is 10 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 3.33 ( which is not an integer ) since both numbers are integers , the larger number can not be 10 . eliminate c d ) the larger number is 12 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 4 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 4 ) , we get 14 so , the new ratio is 14 to 12 which is 7 to 6 . no good . we want a resulting ratio of 2 to 1 eliminate d e ) the larger number is 15 given : the two integers are in the ratio of 1 to 3 so , the smaller number must be 5 if 10 is added to the smaller number , the ratio becomes 2 to 1 if we add 10 to the smaller number ( 5 ) , we get 15 so , the new ratio is 15 to 15 . this is the same as the ratio of 1 to 1 eliminate e therefore a is the only correct choice ."
Answer: a
Question (physics): at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 20 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 76 , c ) 44 , d ) 66 , e ) 11
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 20 / 5 = 4 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 4 = 44 secs . answer : c"
Answer: c
Question (gain): the price of a t . v . set worth rs . 30000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 22678 , b ) 26699 , c ) 29000 , d ) 19000 , e ) 26711
Rationale: "money paid in cash = rs . 1000 balance payment = ( 30000 - 1000 ) = rs . 29000 answer : c"
Answer: c
Question (physics): 55 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 84 m , b ) 88 m , c ) 120 m , d ) 70 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 55 ⇔ = [ 55 * 20 * 20 * 7 / 22 ] = 7000 cm = 70 m . answer d"
Answer: d
Question (geometry): a metallic sheet is of rectangular shape with dimensions 48 m x 34 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :
Options: a ) 4830 , b ) 5120 , c ) 4608 , d ) 7500 , e ) 8960
Rationale: "l = ( 48 - 16 ) m = 32 m , b = ( 34 - 16 ) m = 18 m , h = 8 m . volume of the box = ( 32 x 18 x 8 ) m 3 = 4608 m 3 . answer : option c"
Answer: c
Question (physics): a train speeds past a pole in 15 seconds and a platform 120 meters long in 25 seconds . what is the length of the train ( in meters ) ?
Options: a ) 100 m , b ) 140 m , c ) 130 m , d ) 180 m , e ) 170 m
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 120 = 25 * ( x / 15 ) 10 x = 1800 x = 180 meters the answer is d ."
Answer: d
Question (other): a certain fruit stand sold apples for $ 0.70 each and guava for $ 0.50 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.30 , what total number of apples and bananas did the customer purchase ?
Options: a ) 12 , b ) 13 , c ) 11 , d ) 14 , e ) 5
Rationale: some multiple of 7 + some multiple of 5 should yield 63 . to get to a some multiple of 5 , we should ensure that a 3 or 8 ( 5 + 3 ) should be a multiple of 7 . 63 is a direct multiple of 7 , however in this case there wo n ' t be any guava . hence the next option is to look for a multiple of 7 that has 8 as the unit digit . 28 satisfies this hence no . of apples is 4 and no of bananas is 7 . c
Answer: c
Question (other): if 25 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 500 , b ) 600 , c ) 620 , d ) 640 , e ) 660
Rationale: "we know 25 % people study biology , therefore the no of people not studying = 100 - 25 = 75 % > therefore the people not studying biology out of a total 880 people are = 75 % of 880 > ( 75 / 100 ) * 880 = 660 people e"
Answer: e
Question (general): find large number from below question the difference of two numbers is 1380 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1245 , b ) 1345 , c ) 1455 , d ) 1577 , e ) 1653
Rationale: "let the smaller number be x . then larger number = ( x + 1380 ) . x + 1380 = 6 x + 15 5 x = 1365 x = 273 large number = 273 + 1380 = 1653 e"
Answer: e
Question (probability): 4 dice are thrown simultaneously on the board . find the probability which show the same face ?
Options: a ) 2 / 113 , b ) 3 / 117 , c ) 1 / 216 , d ) 3 / 111 , e ) 4 / 121
Rationale: "the total number of elementary events associated to the random experiments of throwing four dice simultaneously is : = 6 × 6 × 6 × 6 = 64 = 6 × 6 × 6 × 6 = 64 n ( s ) = 64 n ( s ) = 64 let xx be the event that all dice show the same face . x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) = 6 hence required probability , = n ( x ) n ( s ) = 664 = n ( x ) n ( s ) = 664 = 1 / 216 c"
Answer: c
Question (general): tough and tricky questions : word problems . operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 8 , when a # b = 100 ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 13 , e ) 17
Rationale: official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 8 = 10 / 2 + 8 = 13 . the correct answer is d
Answer: d
Question (general): if an integer n is to be chosen at random from the integers 1 to 88 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 33 / 44
Rationale: "n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 88 , there are 44 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 44 + 12 ) / 88 = 66 / 88 = 33 / 44 ans is e"
Answer: e
Question (general): according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 240 6 ounces servings of orange juice ?
Options: a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 30
Rationale: "its e . total juice rquired = 240 * 6 = 1440 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1440 / 48 = 30 . answer e"
Answer: e
Question (general): mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 38400 , how much amount per month would he have spent on clothes and transport ?
Options: a ) 4038 , b ) 8076 , c ) 3200 , d ) 4845.6 , e ) none of these
Rationale: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 38400 ⁄ 12 = 3200 answer c"
Answer: c
Question (gain): daniel went to a shop and bought things worth rs . 50 , out of which 90 paise went on sales tax on taxable purchases . if the tax rate was 15 % , then what was the cost of the tax free items ?
Options: a ) a ) 19.7 , b ) b ) 20 , c ) c ) 43.1 , d ) d ) 21.5 , e ) e ) 22
Rationale: total cost of the items he purchased = rs . 50 given that out of this rs . 50 , 90 paise is given as tax = > total tax incurred = 90 paise = rs . 90 / 100 let the cost of the tax free items = x given that tax rate = 15 % ∴ ( 50 − 90 / 100 − x ) 15 / 100 = 90 / 100 ⇒ 15 ( 50 − 0.9 − x ) = 90 ⇒ ( 50 − 0.9 − x ) = 6 ⇒ x = 50 − 0.9 − 6 = 43.1 c
Answer: c
Question (general): ( 7 + 7 + 7 ÷ 7 ) / ( 5 + 5 + 5 ÷ 5 ) = ?
Options: a ) 1 , b ) 1 / 5 , c ) 15 / 11 , d ) 3 / 11 , e ) none
Rationale: "answer given expression = ( 7 + 7 + 7 ÷ 7 ) / ( 5 + 5 + 5 ÷ 5 ) = ( 14 + 1 ) / ( 10 + 1 ) = 15 / 11 option : c"
Answer: c
Question (general): if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 3410 , r will receive
Options: a ) 660 , b ) 700 , c ) 800 , d ) 900 , e ) none of these
Rationale: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 3410 * ( 6 / 31 ) = 110 * 6 = 660 . answer : option a"
Answer: a
Question (general): running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 1 w widgets ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 1 * 6 = 6 days to produce 1 w widgets . answer : b
Answer: b
Question (general): a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 175 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 30 coins , c ) 50 coins , d ) 100 coins , e ) none of these
Rationale: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 175 ⇒ 1.75 x = 175 ⇒ x = 100 coins answer d"
Answer: d
Question (gain): x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 6 . if x invested rs . 5000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 15,000 , e ) none
Rationale: solution suppose y invested rs . y then , 5000 / y = 2 / 6 â € ¹ = â € º y = ( 5000 ã — 6 / 2 ) . â € ¹ = â € º y = 15000 . answer d
Answer: d
Question (general): if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 9 a - 11 b ?
Options: a ) - 4 , b ) 70 , c ) 0 , d ) 2 , e ) 4
Rationale: "this implies 9 a - b = 10 b + 70 , 9 a - b = - 12 b - 2 a , 10 b + 70 = - 12 b - 2 a manipulating the second equation gives us 9 a - b = 10 b + 70 = = > 9 a - 11 b = 70 answer is b"
Answer: b
Question (general): the largest number of six digits
Options: a ) 100000 , b ) 222222 , c ) 333333 , d ) 888888 , e ) 999999
Rationale: answer : option e
Answer: e
Question (physics): a 600 meter long train crosses a signal post in 40 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 ) 9 min , e ) 3 min
Rationale: "s = 600 / 40 = 15 mps s = 3600 / 15 = 240 sec = 4 min . answer : a"
Answer: a