Cheukting/mathqa huggingface dataset:
Question (gain): a 14 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 175 , b ) rs . 92 , c ) rs . 112.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 14 , investment = rs . ( 100 / 8 x 14 ) = rs . 175 ∴ market value of rs . 100 stock = rs . 175 answer a"
Answer: a
Question (other): in the third grade of windblown school there are 84 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: "total = 84 failed in math = 84 / 3 = 28 failed in literature = 84 / 6 = 14 the least failed in both can be 0 while max can be 14 answer a"
Answer: a
Question (geometry): the diameters of two spheres are in the ratio 1 : 2 what is the ratio of their volumes ?
Options: a ) 1 : 9 , b ) 1 : 2 , c ) 1 : 8 , d ) 1 : 1 , e ) 1 : 6
Rationale: "1 : 8 answer : c"
Answer: c
Question (gain): find the number of shares that can be bought for rs . 8200 if the market value is rs . 25 each with brokerage being 2.5 % .
Options: a ) 237 , b ) 320 , c ) 177 , d ) 166 , e ) 111
Rationale: "explanation : cost of each share = ( 25 + 2.5 % of 25 ) = rs . 25.625 therefore , number of shares = 8200 / 25.625 = 320 answer : b"
Answer: b
Question (physics): find the distance covered by a man walking for 30 min at a speed of 10 km / hr ?
Options: a ) 1 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "distance = 10 * 20 / 60 = 5 km answer is d"
Answer: d
Question (general): a certain ball team has an equal number of right - and left - handed players . on a certain day , two - thirds of the players were absent from practice . of the players at practice that day , one - third were right handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of left handed players who were not at practice ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 7 / 5 , d ) 5 / 7 , e ) 3 / 2
Rationale: "say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 12 absent and 6 present . of the players at practice that day , one - third were right - handed - - > 6 * 1 / 3 = 2 were right - handed and 4 left - handed . the number of right - handed players who were not at practice that day is 9 - 2 = 7 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 7 / 5 . answer : c ."
Answer: c
Question (other): a container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 4 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 5 : 11 , e ) 7 : 3
Rationale: "container 1 has 12 ounces in the ratio 1 : 2 or , x + 2 x = 12 gives x ( alcohol ) = 4 and remaining water = 8 container 2 has 4 ounces in the ratio 1 : 3 or , x + 3 x = 4 gives x ( alcohol ) = 1 and remaining water = 3 mixing both we have alcohol = 4 + 1 and water = 8 + 3 ratio thus alcohol / water = 5 / 11 answer d"
Answer: d
Question (gain): the number which exceeds 16 % of it by 84 is :
Options: a ) 100 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 84 x - 16 / 100 x = 84 x - 4 / 25 x = 84 21 / 25 x = 84 x = ( 84 x 25 / 21 ) = 100 answer a"
Answer: a
Question (gain): find the principal which yields a simple interest of rs . 20 and compound interest of rs . 21 in two years , at the same percent rate per annum ?
Options: a ) rs . 520 , b ) rs . 480 , c ) rs . 420 , d ) rs . 200 , e ) rs . 600
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 21 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 21 – 20 ) / 20 ] * 100 = 5 % p . a . let the principal be rs . x time = t = 2 years % rate = 5 % p . a . si = ( prt / 100 ) 20 = ( x * 5 * 2 ) / 100 x = rs . 200 answer : d"
Answer: d
Question (other): ratio between rahul and deepak is 4 : 3 , after 4 years rahul age will be 32 years . what is deepak present age .
Options: a ) 14 , b ) 15 , c ) 20 , d ) 21 , e ) 24
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 4 = 32 = > x = 7 so deepak age is = 3 ( 7 ) = 21 option d"
Answer: d
Question (physics): a train 850 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 510 , b ) 450 , c ) 500 , d ) 520 , e ) 589
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 850 + x ) / 60 = 65 / 3 x = 450 m . answer : option b"
Answer: b
Question (gain): in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 140 of the workers of that company are men , how many of the workers are women ?
Options: a ) 85 , b ) 95 , c ) 105 , d ) 120 , e ) 210
Rationale: "20 % of the workerswithoutretirement plan are women , this means 80 % of the workerswithoutretirement plan are men right ? makes 100 % = no retirement plan . then 40 % of those wo have a retirement plan are men , which means 60 % of those who have a retirement plan are women . these percentages are always refering to the subgroupsretirement plan = yesandno retirement plan . make the total workers equal x and work from there and it should be fine > x / 3 have no retirement plan at all . i struggled with the question a lot , it was hard for me although usually i have no problems with sets questions like this . i believe it must be a 700 + question . yes , you are right . i read the question incorrectly ! i glazed overnotfor some reason . if 20 % of the workers who do not have a retirement plan are women , 80 % who do not have retirement plan are men . also 40 % who do have retirement plan are men . since 1 / 3 do not have retirement plan and 2 / 3 do have , it becomes a simple weighted average question . cavg = ( 80 * 1 + 40 * 2 ) / 3 = 160 / 3 % are men total = 120 * 300 / 160 = 225 no . of women = 225 - 140 = 85 a"
Answer: a
Question (general): if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a ∪ b ) = 6 / 15 find p ( a | b )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 4 / 7
Rationale: "p ( a | b ) = p ( a ∪ b ) / p ( b ) p ( a | b ) = ( 6 / 15 ) / ( 4 / 15 ) = 3 / 2 . c"
Answer: c
Question (physics): worker a takes 8 hours to do a job . worker b takes 6 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 20 / 9 , b ) 40 / 9 , c ) 50 / 9 , d ) 24 / 7 , e ) 80 / 9
Rationale: "one day work of a = 1 / 8 one day work of b = 1 / 6 so one day work of a and b together = 1 / 8 + 1 / 6 = 7 / 24 so total days required = 24 / 7 answer : d"
Answer: d
Question (geometry): the length of the rectangular field is double its width . inside the field there is square shaped pond 7 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 54 , b ) 32 , c ) 75 , d ) 28 , e ) 11
Rationale: "a / 8 = 7 * 7 = > a = 7 * 7 * 8 x * 2 x = 7 * 7 * 8 x = 14 = > 2 x = 28 answer : d"
Answer: d
Question (general): how many numbers from 32 to 97 are exactly divisible by 9 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "option ' b ' 32 / 9 = 3 and 97 / 9 = 10 = = > 10 - 3 = 7 numbers"
Answer: b
Question (general): the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 4 ) , how many units is p from the y - axis ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: "the x - axis is 4 units from the point p . thus the y - axis is 8 units from the point p . the answer is c ."
Answer: c
Question (physics): if 20 men can build a wall 66 metres long in 4 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 278.4 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 567.6 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 4 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 4 * 20 ) = 567.6 mtrs answer : e"
Answer: e
Question (gain): the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 250 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 50 % , d ) 25 % , e ) 30 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 250 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 250 ) * 100 / 500 = 50 % answer : option c"
Answer: c
Question (physics): a train , 800 meter long is running with a speed of 78 km / hr . it crosses a tunnel in 1 minute . what is the length of the tunnel ( in meters ) ?
Options: a ) 440 m , b ) 500 m , c ) 260 m , d ) 430 m , e ) 450 m
Rationale: "explanation : distance = 800 + x meter where x is the length of the tunnel time = 1 minute = 60 seconds speed = 78 km / hr = 78 × 10 / 36 m / s = 130 / 6 = 65 / 3 m / s distance / time = speed ( 800 + x ) / 60 = 65 / 3 = > 800 + x = 20 × 65 = 1300 = > x = 1300 - 800 = 500 meter answer : option b"
Answer: b
Question (general): a library has an average of 150 visitors on sundays and 120 on other days . the avearge number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 50 , b ) 75 , c ) 150 , d ) 125 , e ) 100
Rationale: "since the month begin with sunday , so there will be five sundays in the month required average = ( 150 * 5 + 120 * 25 ) / 30 = 3750 / 30 = 125 answer is d"
Answer: d
Question (geometry): find the smallest number which should be multiplied with 520 to make it a perfect square .
Options: a ) 30 , b ) 120 , c ) 55 , d ) 35 , e ) none of these
Rationale: "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 (geometry): in a company of 200 employees , 120 are females . a total of 100 employees have advanced degrees and the rest have a college degree only . if 40 employees are males with a college degree only , how many employees are females with advanced degrees ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "the number of males is 200 - 120 = 80 . the number of males with advanced degrees is 80 - 40 = 40 . the number of females with advanced degrees is 100 - 40 = 60 . the answer is a ."
Answer: a
Question (other): in what ratio should a variety of rice costing rs . 4.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 5 / 12
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 4.5 ) = 5 / 12 answer : e"
Answer: e
Question (gain): in a certain pond , 60 fish were caught , tagged , and returned to the pond . a few days later , 60 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1818 , d ) 2500 , e ) 10 000
Rationale: "the percent of tagged fish in the second catch is 2 / 60 * 100 = 3.33 % . we are told that 3.33 % approximates the percent of tagged fish in the pond . since there are 60 tagged fish , then we have 0.033 x = 60 - - > x = 1,818 . answer : c ."
Answer: c
Question (gain): a man walking at a rate of 15 km / hr crosses a bridge in 10 minutes . the length of the bridge is ?
Options: a ) 500 m , b ) 1110 m , c ) 950 m , d ) 1000 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 10 minutes = 15 / 18 * 10 * 60 = 500 m answer is a"
Answer: a
Question (general): 12 + 13 + 14 + . . . 61 + 62 + 63 = ?
Options: a ) 1361 , b ) 1362 , c ) 1950 , d ) 1364 , e ) 1365
Rationale: "sum = 12 + 13 + 14 + . . . 61 + 62 + 63 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 63 positive integers = 63 * 64 / 2 sum of first 11 positive integers = 11 * 12 / 2 sum = 12 + 13 + 14 + . . . 61 + 62 + 63 = 63 * 64 / 2 - 11 * 12 / 2 = 1950 answer : c"
Answer: c
Question (general): tickets numbered from 1 to 21 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 ] p ( e ) = n ( e ) / n ( s ) = 7 / 21 = 1 / 3 the answer is a ."
Answer: a
Question (gain): a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 63 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: "1 percent for 3 years = 63 1 percent for 1 year = 21 = > 100 percent = 2100 answer : b"
Answer: b
Question (general): ( 128.5 x 64 ) + ( 13.8 x 465 ) = ? x 25
Options: a ) 524.48 , b ) 556.02 , c ) 574.36 , d ) 585.64 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 64 ) + ( 13.8 x 465 ) / 25 = 8224 + 6417 / 25 = 585.64 answer : option d"
Answer: d
Question (gain): 128 students represent x percent of the boys at a school . if the boys at the school make up 50 % of the total school population of x students , what is x ?
Options: a ) 160 , b ) 190 , c ) 225 , d ) 250 , e ) 500
Rationale: let b be the number of boys in the school . 128 = xb / 100 b = 0.5 x 12800 = 0.5 x ^ 2 x ^ 2 = 25600 x = 160 the answer is a .
Answer: a
Question (general): a basket contains 5 apples , of which 1 is spoiled and the rest are good . if henry is to select 2 apples from the basket simultaneously and at random , what is the possibility that the 2 apples selected will include the spoiled apple ?
Options: a ) 1 / 5 , b ) 3 / 10 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5
Rationale: "p ( both apples are not spoiled ) = 4 c 2 / 5 c 2 = 4 * 3 / 5 * 4 = 3 / 5 p ( one of the apple spoiled ) = 1 - 3 / 5 = 2 / 5 answer is c ."
Answer: c
Question (general): the difference in compound interest earned on a deposit ( compounded annually ) in year 1 and year 2 is $ 40 . had the interest rate been 3 times its present value , the difference w would have been how much ?
Options: a ) 40 / 3 , b ) 40 , c ) 120 , d ) 360 , e ) 420
Rationale: case 1 : deposit = $ x ; rate of increase = r . interest yearned in 1 year = xr . deposit in 1 year = x + xr . interest yearned in 2 year = ( x + xr ) r . the difference w = ( x + xr ) r - xr = xr ^ 2 = 40 . case 2 : deposit = $ x ; rate of increase = 3 r . interest yearned in 1 year = x ( 3 r ) . deposit in 1 year = x + 3 xr . interest yearned in 2 year = ( x + 3 xr ) 3 r . the difference = ( x + 3 xr ) 3 r - 3 xr = 9 xr ^ 2 . since from case 1 we know that xr ^ 2 = 40 , then 9 xr ^ 2 = 9 * 40 = 360 . answer : d .
Answer: d
Question (physics): the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 7500 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 87.50 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 7500 ⇔ 12 x 2 = 7500 ⇔ x 2 = 625 ⇔ x = 25 . so , length = 75 m and breadth = 100 m . perimeter = [ 2 ( 75 + 100 ) ] m = 350 m . ∴ cost of fencing = rs . ( 0.25 × 350 ) = rs . 87.50 . answer d"
Answer: d
Question (geometry): the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is
Options: a ) 38 % , b ) 40 % , c ) 44 % , d ) 48 % , e ) 50 %
Rationale: let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . 25 xy c )
Answer: c
Question (general): what is the value of ( p + q ) / ( p - q ) if p / q is 5 ?
Options: a ) 4 / 3 , b ) 3 / 2 , c ) 2 / 6 , d ) 7 / 8 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 5 + 1 ) / ( 5 - 1 ) = 6 / 4 = 3 / 2 answer : b"
Answer: b
Question (geometry): find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 8 cm and 2 cm ?
Options: a ) 140 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 182 cm 2 , e ) 200 cm 2
Rationale: "1 / 2 * 28 ( 8 + 2 ) = 140 cm 2 answer : a"
Answer: a
Question (general): 3 machines operating independently , simultaneously , and at the same constant rate can fill a certain production order in 44 hours . if one additional machine were used under the same operating conditions , in how manyfewerhours of simultaneous operation could the production order be fulfilled ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 11 , e ) 48
Rationale: if 3 machines can do the work in 44 hr then 4 machines can do the work in 3 / 4 * 44 = 33 hrs . hence time saved will be 11 hr option d is the correct answer
Answer: d
Question (gain): in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are accounting majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17
Rationale: pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are accounting majors is p = 3 . the answer is a .
Answer: a
Question (physics): a train 250 m long is running at a speed of 58 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
Rationale: "answer : d . speed of the train relative to man = ( 58 - 8 ) kmph = ( 50 * 5 / 18 ) m / sec = ( 125 / 9 ) m / sec time taken by the train to cross the man = time taken by it to cover 250 m at 125 / 9 m / sec = 250 * 9 / 125 sec = 18 sec"
Answer: d
Question (general): line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 10 ) . what is the slope of line m ?
Options: a ) - 3 , b ) 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : b solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 10 ) . midpoint is ( 4 , - 3 ) as we can see that the y axis of intercept point is ( 0 , - 2 ) means line m is parallel to x axis slope m = 1 ans : b"
Answer: b
Question (gain): on a certain transatlantic crossing , 20 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 66.6 %
Rationale: "0.20 p = rt + c 0.5 ( rt ) = no c = > 0.50 ( rt ) had c 0.20 p = 0.50 ( rt ) rt / p = 40 % answer - b"
Answer: b
Question (gain): in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 , d ) 91 , e ) 108
Rationale: total students = 420 boys = 312 , girls = 108 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 108 - 35 = 73 . correct option : b
Answer: b
Question (physics): a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 60 percent .
Options: a ) 145 , b ) 150 , c ) 175 , d ) 180 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 60 percent 180 min . answer : d
Answer: d
Question (general): if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 14 . what is the value of f ( 6 ) ?
Options: a ) 3 , b ) 0 , c ) 1 , d ) 2 , e ) 4
Rationale: "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 14 then f ( 5 ) = 14 - 5 = 9 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 9 - 6 = 3 . answer : a . questions on funtions to practice :"
Answer: a
Question (gain): the banker â € ™ s discount of a certain sum of money is rs . 80 and the true discount on the same sum for the same time is rs . 70 . the sum due is
Options: a ) 210 , b ) 280 , c ) 560 , d ) 450 , e ) none
Rationale: "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 80 * 70 / 80 - 70 ] = rs . [ 80 * 70 / 10 ] = rs . 560 answer c"
Answer: c
Question (physics): in what time will a train 150 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 1.9 sec , c ) 3.8 sec , d ) 6.9 sec , e ) 2.9 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 150 / 40 = 3.8 sec . answer : c"
Answer: c
Question (other): from a container having pure milk , 10 % is replaced by water and the process is repeated twice . at the end of the second operation , the milk is ?
Options: a ) 50 % , b ) 60 % , c ) 55 % , d ) 75 % , e ) 81 %
Rationale: "let the total quantity of original milk = 1000 gm milk after 1 st operation = 90 % of 1000 = 900 gm milk after second operation = 90 % of 900 = 810 gm strength of final mixture = 81 % answer is e"
Answer: e
Question (general): what is the smallest number which , when increased by 9 , is divisible by 8 , 11 , and 24 ?
Options: a ) 237 , b ) 246 , c ) 255 , d ) 264 , e ) 273
Rationale: lcm ( 8 , 11,24 ) = 24 x 11 = 264 so the least divisible number is 264 , and the number we are looking for is 264 - 9 = 255 . the answer is c .
Answer: c
Question (general): on an order of 19 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 0.05 % , b ) 0.5 % , c ) 1 % , d ) 5 % , e ) 10 %
Rationale: "clearly , the retailer gets 1 dozen out of 20 dozens free . equivalent discount = 1 / 20 * 100 = 5 % . answer d ) 5 %"
Answer: d
Question (gain): a glass was filled with 10 ounces of water , and 0.02 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.02 % , c ) 0.2 % , d ) 4 % , e ) 40 %
Rationale: we are given that 0.02 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.02 by 20 . this gives us : 0.02 x 20 = 0.4 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 0.4 / 10 ) x 100 % ( 4 / 100 ) x 100 % = 4 % answer d
Answer: d
Question (gain): i sold a book at a profit of 10 % . had i sold it for $ 140 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 2800 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 140 5 % of cost = $ 140 cost = 140 * 100 / 5 = $ 2800 answer is d"
Answer: d