Cheukting/mathqa huggingface dataset:
Question (general): a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 270 kilos of plankton , how many kilos did he consume on the sixth hour ?
Options: a ) 33 , b ) 47 , c ) 50 , d ) 53 , e ) 62
Rationale: "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 270 / 9 = 30 , so the median is also 30 , and that is the amount eaten in the 5 th hour . we need to add 3 to find the total eaten in the next hour , so the answer is 33 . option a"
Answer: a
Question (physics): in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 8 days , working 5 hours a day , the number of men required is :
Options: a ) 24 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 5 : 8 : : 12 : x = > 8 x 5 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 5 ) = > x = 24 answer : a"
Answer: a
Question (other): if the radii of umbra and penumbra cast by an object on a wall are of the ratio 2 : 6 , what is the area of the penumbra ring around the umbra of the latter ’ s radius is 40 cms ?
Options: a ) 40288.57 cm ^ 2
b ) 40388.57 cm ^ 2
c ) 40488.57 cm ^ 2
d ) 40588.57 cm ^ 2
e ) 40688.57 cm ^ 2
Rationale: et the radius of umbra and penumbra are 2 k and 6 k . then as given radius of umbra = 40 cm so 2 k = 40 k = 20 radius of penumbra = 20 * 6 = 120 area of penumbra ring around the umbra = area of penumbra - area of umbra 22 / 7 * [ ( 120 ) ^ 2 - ( 40 ) ^ 2 ] = 40288.57 cm ^ 2 answer : a
Answer: a
Question (physics): if in a box of dimensions 6 m * 5 m * 4 m smaller boxes of dimensions 60 cm * 50 cm * 40 cm are kept in it , then what will be the maximum number of the small boxes that can be kept in it ?
Options: a ) 1098 , b ) 1000 , c ) 1628 , d ) 1098 , e ) 1094
Rationale: 6 * 5 * 4 = 60 / 100 * 50 / 100 * 40 / 100 * x 1 = 1 / 10 * 1 / 10 * 1 / 10 * x = > x = 1000 answer : b
Answer: b
Question (geometry): the area of a square field is 64816 sq m . how long will a lady take to cross the field diagonally at the rate of 7.2 km / hr ?
Options: a ) 2 min , b ) 4 min , c ) 5 min , d ) 3 min , e ) 3.5 min
Rationale: "area of a square field = 64816 sq m let the side of square = a a ^ 2 = 64816 = > a = 254.59 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 254.59 = 360 speed of lady = 7.2 km / hour = 7200 m / hour = 120 m / min time taken by lady to cross the field diagonally = 360 / 120 = 3 min answer d"
Answer: d
Question (general): the ratio 15 : 25 expressed as percent equals to
Options: a ) 70 % , b ) 60 % , c ) 30 % , d ) 75 % , e ) none of above
Rationale: "explanation : actually it means 15 is what percent of 25 , which can be calculated as , ( 15 / 25 ) * 100 = 15 * 4 = 60 answer : option b"
Answer: b
Question (other): the ratio between the number of sheep and the number of horses at the stewar farm is 2 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 18 , b ) 16 , c ) 32 , d ) 56 , e ) 58
Rationale: "et no of sheep and horses are 2 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 2 * 8 ) = 16 answer : b"
Answer: b
Question (other): the ratio of the arithmetic mean of two numbers to one of the numbers is 4 : 6 . what is the ratio of the smaller number to the larger number ?
Options: a ) 1 : 5 , b ) 1 : 4 , c ) 1 : 3 , d ) 1 : 2 , e ) 2 : 3
Rationale: for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 4 : 6 , thus the smaller number must have a ratio of 2 . the ratio of the smaller number to the larger number is 2 : 6 = 1 : 3 . the answer is c .
Answer: c
Question (physics): the speed of a boat in still water in 22 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 10.6 , b ) 10.2 , c ) 10.8 , d ) 10.4 , e ) 10.0
Rationale: "speed downstream = ( 22 + 4 ) = 26 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 26 = 10.4 km answer is d ."
Answer: d
Question (other): the present ratio of students to teachers at a certain school is 45 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 4 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "we are given that the ratio of students to teacher is 45 to 1 . we can rewrite this using variable multipliers . students : teachers = 45 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers  25 / 1 = ( 45 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 45 x + 50 25 x + 125 = 45 x + 50 3.75 = x x ~ 4 since x is the present number of teachers , currently there are 4 teachers . answer a ."
Answer: a
Question (other): the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 10 of her stamps , the ration of the number of kaye had to the number of alberto had was 3 : 2 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 80
Rationale: "c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 10 a 2 = 3 x + 10 k 2 / a 2 = 3 / 2 ( 5 x - 10 ) / ( 3 x + 10 ) = 3 / 2 2 * ( 5 x - 10 ) = 3 * ( 3 x + 10 ) 10 x - 20 = 9 x + 30 x = 50 k 2 = 5 * 50 - 10 = 240 a 2 = 3 * 50 + 10 = 160 k 2 - a 2 = 80 answer : e"
Answer: e
Question (physics): a certain bacteria colony doubles in size every day for 16 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 10 , d ) 15 , e ) 19
Rationale: if there is one bacteria colony , then it will reach the limit of its habitat in 16 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 15 times . answer : d . similar questions to practice : hope it helps .
Answer: d
Question (geometry): find the area of the quadrilateral of one of its diagonals is 15 cm and its off sets 6 cm and 4 cm ?
Options: a ) 50 cm 2 , b ) 60 cm 2 , c ) 75 cm 2 , d ) 90 cm 2 , e ) 150 cm 2
Rationale: "1 / 2 * 15 ( 6 + 4 ) = 75 cm 2 answer : c"
Answer: c
Question (general): the average of 10 numbers is 23 . if each number is increased by 1 , what will the new average be ?
Options: a ) 36 , b ) 24 , c ) 72 , d ) 29 , e ) 22
Rationale: "sum of the 10 numbers = 230 if each number is increased by 1 , the total increase = 1 * 10 = 10 the new sum = 230 + 10 = 240 the new average = 240 / 10 = 24 . answer : b"
Answer: b
Question (physics): sakshi can do a piece of work in 15 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 15 , b ) 16 , c ) 18 , d ) 12 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 15 : x ⇒ x = ( 15 x 4 / 5 ) ⇒ x = 12 days . hence , tanya takes 16 days is complete the work . answer d"
Answer: d
Question (physics): an electric pump can fill a tank in 5 hours . because of a leak in the tank , it took 10 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?
Options: a ) 10 hours , b ) 12 hours , c ) 8 hours , d ) 5 hours , e ) 15 hours
Rationale: "work done by the leak in 1 hour = 1 / 5 - 1 / 10 = 1 / 10 the leak will empty the tank in 10 hours answer is a"
Answer: a
Question (general): 4 , 6 , 12 , 14 , 28 , 30 , . . ?
Options: a ) 20 , b ) 40 , c ) no = 60 , d ) 80 , e ) 100
Rationale: "c 60 the given sequence is a combination of two series 4 , 12 , 28 , . . . . and 6 , 14 , 30 , . . . . the pattern is + 8 , + 16 , + 32 . so , the missing number = ( 28 + 32 ) = 60"
Answer: c
Question (geometry): a cubical block of metal weighs 6 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48 , b ) 99 , c ) 266 , d ) 28 , e ) 17
Rationale: "explanation : if you double the sides of a cube , the ratio of the surface areas of the old and new cubes will be 1 : 4 . the ratio of the volumes of the old and new cubes will be 1 : 8 . weight is proportional to volume . so , if the first weighs 6 pounds , the second weighs 6 x 8 pounds = 48 . answer : a ) 48"
Answer: a
Question (gain): working together at their respective constant rates , machine a and machine b can produce 1,600 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1,600 unit total would it produce ?
Options: a ) 25 , b ) 33 , c ) 50 , d ) 67 , e ) 75
Rationale: 1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 1600 units in 24 hrs , so it can produce 1600 * 8 / 24 = 533.33 units is 8 hrs . 533.33 is 33.33 % of 1600 . b is the answer
Answer: b
Question (general): find the value for x from below equation : x / 3 = - 4 ?
Options: a ) - 12 , b ) 1 , c ) - 2 , d ) - 3 , e ) 4
Rationale: "1 . multiply both sides by 3 : x * 3 / 3 = - 4 / 3 . simplify both sides : x = - 12 a"
Answer: a
Question (general): a sum of money is sufficient to pay x ' s wages for 36 days and y ' s wages for 45 days . the same money is sufficient to pay the wages of both for ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: let the total money be $ x x ' s 1 day work = $ x / 36 y ' s 1 day work = $ x / 45 x + y 1 day work = $ x / 20 money is sufficient to pay the wages of both for 20 days answer is e
Answer: e
Question (physics): length of a rectangular plot is 16 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 58 m , b ) 60 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let breadth = x metres . then , length = ( x + 16 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 16 ) + x ] = 200 2 x + 16 = 100 2 x = 84 x = 42 . hence , length = x + 16 = 58 m a"
Answer: a
Question (gain): at what price must an article costing rs . 75 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 62.0 , c ) 62.6 , d ) 62.1 , e ) 98.68
Rationale: "cp = 75 sp = 75 * ( 125 / 100 ) = 93.75 mp * ( 95 / 100 ) = 93.75 mp = 98.68 answer : e"
Answer: e
Question (physics): two stations a and b are 155 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: "suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 155 45 x = 180 x = 4 . so , they meet at 11 a . m . answer : option c"
Answer: c
Question (general): each week , harry is paid x dollars per hour for the first 12 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 32 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "42 x = 12 x + 1.5 x ( h - 12 ) = = > 42 = 12 + 1.5 ( h - 12 ) = = > h - 12 = 30 / 1.5 = 20 = = > h = 32 answer is a"
Answer: a
Question (geometry): if the volume of two cubes are in the ratio 64 : 1 , the ratio of their edges is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 5 , d ) 4 : 1 , e ) none of these
Rationale: "explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 64 / 1 = > ( a / b ) 3 = ( 4 / 1 ) 3 a / b = 4 / 1 = > a : b = 4 : 1 option d"
Answer: d
Question (general): a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 5 : 3 and b : c = 5 : 2 . if the total runs scored by all of them are 60 , the runs scored by b are ?
Options: a ) 20.23 , b ) 20.13 , c ) 30.93 , d ) 19.56 , e ) 10.93
Rationale: "a : b = 5 : 3 b : c = 5 : 2 a : b : c = 25 : 15 : 6 15 / 46 * 60 = 19.56 answer : d"
Answer: d
Question (physics): a van takes 6 hours to cover a distance of 180 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 70 kmph , d ) 80 kmph , e ) 20 kmph
Rationale: "time = 6 distence = 180 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 180 / 9 = 20 kmph e"
Answer: e
Question (gain): find the principal which yields a simple interest of rs . 20 and compound interest of rs . 30 in two years , at the same percent rate per annum ?
Options: a ) s . 20 , b ) s . 48 , c ) s . 42 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 30 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 30 – 20 ) / 20 ] * 100 = 50 % p . a . let the principal be rs . x time = t = 2 years % rate = 50 % p . a . si = ( prt / 100 ) 20 = ( x * 50 * 2 ) / 100 x = rs . 20 answer : a"
Answer: a
Question (physics): a can do a work in 40 days , b in 60 days . a alone start the work after 10 days he left work . in how many days b can finish the work ?
Options: a ) 20 days , b ) 15 days , c ) 30 days , d ) 45 days , e ) 50 days
Rationale: 10 days work of a = 10 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 b can finish 3 / 4 work = 60 * 3 / 4 = 45 days answer is d
Answer: d
Question (other): a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 81 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: 1 c 4 * 2 c 7 = 4 * 21 = 84 the answer is ( c )
Answer: c
Question (other): each factor of 150 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 / 3
Rationale: "the # of factors 150 has is 12 so out of 12 factors only four are multiples of 15 : 15 , 30,75 and 150 , itself ; so , the probability is 4 / 12 = 1 / 3 . answer : c ."
Answer: c
Question (general): 15.03 ã — 0.01 = ?
Options: a ) 0.1503 , b ) 0.001503 , c ) 1.503 , d ) 0.001503 , e ) none of these
Rationale: "15.03 ã — 0.01 = ? or , ? = 0.1503 answer a"
Answer: a
Question (physics): 12 men can complete a piece of work in 4 days , while 15 women can complete the same work in 4 days . 6 men start working on the job and after working for 2 days , all of them stopped working . how many women should be put on the job to complete the remaining work , if it is to be completed in 3 days .
Options: a ) 15 , b ) 18 , c ) 22 , d ) 25 , e ) 26
Rationale: one man ’ s one day ’ s work = 1 / 48 one woman ’ s one day ’ s work = 1 / 60 6 men ’ s 2 day ’ s work = ( ( 6 / 48 ) x 2 ) = 1 / 4 remaining work = 3 / 4 now , 1 / 60 work s done in 1 day by 1 woman . thus , 3 / 4 work will be done in 3 days by ( 60 x ( 3 / 4 ) x ( 1 / 3 ) ) = 15 women . answer : a
Answer: a
Question (general): mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 20 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 27 % , e ) 37 %
Rationale: "lets assume that candidate got 20 % votes and total votes is 100 . candidate won = 20 remaining = 80 to get 50 % , candidate requires 30 votes from 100 which is 30 % and 30 votes from 80 . 30 / 80 = 37.5 % which is approx 37 % . hence the answer is e"
Answer: e
Question (general): in a mixture 60 litres , the ratio of milk and water 2 : 1 . if this ratio is to be 1 : 2 , then the quanity of water to be further added is :
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: quantity of milk = ( 60 x 2 / 3 ) litres = 40 litres . quantity of water in it = ( 60 - 40 ) litres = 20 litres . new ratio = 1 : 2 let quantity of water to be added further be x litres . then , milk : water = ( 40 / ( 20 + x ) ) now , ( 40 / ( 20 + x ) ) = 1 / 2 = 20 + x = 80 = x = 60 . therefore , quantity of water to be added = 60 litres . answer is e .
Answer: e
Question (physics): a tap can fill a tank in 16 hours . after half the tank is filled , 3 more similar taps are opened . what is the total time taken to fill the tank completely ?
Options: a ) 2 hrs , b ) 1 hrs , c ) 10 hrs , d ) 5 hrs , e ) 4 hrs
Rationale: explanation : a tap can fill a tank in 16 hours . therefore the tap can fill half the tank in 8 hours . one tap take time to fill half of the tank = 8 hrs 4 taps take time to fill half of the tank = 8 / 4 hrs = 2 hrs total time taken to fill the tank = 8 hr + 2 hr = 10 hrs answer : c
Answer: c
Question (gain): the sale price sarees listed for rs . 600 after successive discount is 20 % and 5 % is ?
Options: a ) 227 , b ) 358 , c ) 456 , d ) 787 , e ) 191
Rationale: "600 * ( 80 / 100 ) * ( 95 / 100 ) = 456 answer : c"
Answer: c
Question (gain): a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 700 , what is the reduced price for kg ?
Options: a ) 35 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 700 * ( 25 / 100 ) = 175 - - - - 5 ? - - - - 1 = > rs . 35"
Answer: a
Question (physics): robert is travelling on his cycle and has calculated to reach point a at 2 p . m . if he travels at 10 kmph , he will reach there at 12 noon if he travels at 15 kmph . at what speed must he travel to reach a at 1 p . m . ?
Options: a ) 8 , b ) 12 , c ) 11 , d ) 16 , e ) 18
Rationale: "explanation : let the distance travelled by x km . then , = > ( x / 10 ) - ( x / 15 ) = 2 = > 3 x - 2 x = 60 = > x = 60 = > time taken to travel 60 km at 10 km / hr = 60 / 10 = 6 hours . = > so , robert started 6 hours before 2 p . m . i . e . , at 8 a . m . therefore , speed required = ( 60 / 5 ) km / hr = 12 km / hr answer : b"
Answer: b
Question (general): the average of 10 consecutive integers is 16 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is c .
Answer: c
Question (general): after 2 games , team b had an average of 61.5 points per game . if it got only 47 points in game 3 , how many more points does it need to score to get its total above 500 ?
Options: a ) 805 , b ) 740 , c ) 670 , d ) 530 , e ) 330
Rationale: ( 2 * 61.5 ) + 47 + x > 500 123 + 47 + x > 500 170 + x > 500 = > x > 330 option e
Answer: e
Question (physics): calculate the number of bricks , each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10 % of its volume is occupied by mortar ?
Options: a ) 3388 , b ) 27678 , c ) 6000 , d ) 2977 , e ) 27681
Rationale: 10 * 4 / 100 * 5 * 90 / 100 = 25 / 100 * 15 / 100 * 8 / 100 * x 10 * 20 * 90 = 15 * 2 * x = > x = 6000 answer : c
Answer: c
Question (other): a class has a ratio of 3 : 6 : 7 of children with red hair , blonde hair and black hair respectively . if the class has 9 kids with red hair , how many kids are in the class ?
Options: a ) 99 , b ) 48 , c ) 16 , d ) 22 , e ) 60
Rationale: since there are 9 children with red hair , and the class exists in a 3 : 6 : 7 ratio , there are 3 times more children than the unit ratio . therefore 9 red - haired children 3 * ( 6 ) blonde - haired children 3 * ( 7 ) black - haired children 9 + 18 + 21 = 48 alternatively , a part - to - whole ratio can be set up . since the whole is 3 + 6 + 7 = 16 , 9 / 3 = x / 16 3 * 16 = 48 answer : b )
Answer: b
Question (probability): a certain club has 10 members , including parry . one of the 10 members is chosen at random to be the president , one of the remaining 9 members is to be chosen at random to be the secretary , and one of the remaining 8 members is to be chosen at random to be the treasurer . what is the probability that parry will be either the member chose to be secretary or the member chose to be treasurer ?
Options: a ) 1 / 720 , b ) 1 / 80 , c ) 1 / 10 , d ) 1 / 9 , e ) 1 / 5
Rationale: in order to become a secretary the person can not be chosen as a president . this can be done in 9 / 10 ways . then to become a secretary this person ' s probability is 1 / 9 probability to become a secretary = ( 9 / 10 * 1 / 9 ) = 1 / 10 similar concept for treasurer . probability of not president = 9 / 10 , probability of not secretary = 8 / 9 , probability of treasurer 1 / 8 probability to become a treasurer = ( 9 / 10 * 8 / 9 * 1 / 8 ) = 1 / 10 since , the problem is saying parry secretary or treasurer it is addition : 1 / 10 + 1 / 10 = 1 / 5 = e
Answer: e
Question (general): a millionaire bought a job lot of hats 1 / 4 of which were brown . the millionaire sold 2 / 3 of the hats including 4 / 5 of the brown hats . what fraction of the unsold hats were brown .
Options: a ) 1 / 60 , b ) 1 / 15 , c ) 3 / 20 , d ) 3 / 5 , e ) 3 / 4
Rationale: if initially he had x hats . x / 4 were brown . sold x * 2 / 3 hats . left with x / 3 hats . sold ( x / 4 ) * ( ( 4 / 5 ) = x / 5 brown hats and left with x / 4 - x / 5 = x / 20 brown hats . fraction of brown hats in total remaining hats = ( x / 20 ) / ( x / 3 ) = 3 / 20 hats answer : c
Answer: c
Question (physics): if three machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 36 , b ) 60 , c ) 75 , d ) 80 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 3 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 2 = 10 / 3 * x x = 3 / 5 hour so 36 minutes answer : a"
Answer: a
Question (general): { ( 481 + 426 ) 2 - 4 x 481 x 426 } = ?
Options: a ) 3025 , b ) 4200 , c ) 3060 , d ) 3210 , e ) none of these
Rationale: "explanation : here , the given statement is like ( a + b ) 2 - 4 ab where a = 481 and b = 426 ( a + b ) 2 - 4 ab = ( a 2 + 2 ab + b 2 ) - 4 ab = a 2 - 2 ab + b 2 = ( a - b ) 2 hence { ( 481 + 426 ) 2 - 4 x 481 x 426 } = ( 481 - 426 ) 2 = 552 = 3025 . answer : option a"
Answer: a