Cheukting/mathqa huggingface dataset:
Question (physics): two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 18 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 66 , c ) 80 , d ) 36 , e ) 96
Rationale: "a 54 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 18 mph = 54 miles"
Answer: a
Question (general): average expenditure of a person for the first 3 days of a week is rs . 360 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 390 , d ) 400 , e ) none
Rationale: "explanation : assumed mean = rs . 360 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 360 + rs . 40 = rs . 400 correct option : d"
Answer: d
Question (general): what approximate value will come in place of the question mark ( ? ) in the below question ? ( 47 % of 1442 - 36 % of 1412 ) + 63 = ?
Options: a ) 237 , b ) 278 , c ) 278 , d ) 252 , e ) 271
Rationale: explanation : since there are 5 cups of each kind , prepared with milk or tea leaves added first , are identical hence , total number of different people ways of presenting the cups to the expert is 10 ! / ( 5 ! x 5 ! ) = 252 answer : d ) 252
Answer: d
Question (general): the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 47 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 47 has the form 4 k + 3 , so the units digit of 93 ^ 47 is 7 . the units digit if powers of 5 is always 5 . 7 + 5 = 12 , so the units digit is 2 . the answer is a ."
Answer: a
Question (general): a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 400,000 ?
Options: a ) 200 , b ) 216 , c ) 300 , d ) 400 , e ) 2,500
Rationale: "first digit = last digit = 4 or 6 or 8 so three possibilities . . second = fifth = any of ten digits third = fourth = any of ten digits . . so total integers = 3 * 10 * 10 = 300 answer : c"
Answer: c
Question (general): multiplication of 2 numbers is 9375 and the quotient , when the larger one is divided by the smalleris 15 . find the sum of the numbers ?
Options: a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600
Rationale: let the numbers be x and y . then , xy = 9375 and x = 15 . y xy = 9375 ( x / y ) 15 y 2 = 625 . y = 25 . x = 15 y = ( 15 x 25 ) = 375 . sum of the numbers = x + y = 375 + 25 = 400 . c
Answer: c
Question (gain): a person distributed 20 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 40000 . find his total income ?
Options: a ) 452000 , b ) 562000 , c ) 800000 , d ) 500000 , e ) 652000
Rationale: "3 children got = 3 * 20 % = 60 % wife got = 30 % orphan house = 5 % total = 60 + 30 + 5 = 95 % remaining = 100 - 95 = 5 % 5 % = 40000 100 % = 40000 * 100 / 5 = $ 800000 answer is c"
Answer: c
Question (probability): a box contains 20 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 7 / 19 , b ) 6 / 19 , c ) 5 / 19 , d ) 4 / 19 , e ) none of these
Rationale: "explanation : please remember that maximum portability is 1 . so we can get total probability of non defective bulbs and subtract it form 1 to get total probability of defective bulbs . so here we go , total cases of non defective bulbs 16 c 2 = 16 ∗ 15 / 2 ∗ 1 = 120 total cases = 20 c 2 = 20 ∗ 19 / 2 ∗ 1 = 190 probability = 120 / 190 = 12 / 19 p of at least one defective = 1 − 12 / 19 = 7 / 19 option a"
Answer: a
Question (gain): after decreasing 24 % in the price of an article costs rs . 988 . find the actual cost of an article ?
Options: a ) 1667 , b ) 6789 , c ) 1300 , d ) 6151 , e ) 1421
Rationale: "cp * ( 76 / 100 ) = 988 cp = 13 * 100 = > cp = 1300 answer : c"
Answer: c
Question (gain): a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 846 in 4 years . the sum is ?
Options: a ) s . 738 , b ) s . 638 , c ) s . 650 , d ) s . 762 , e ) s . 735
Rationale: "s . i . for 1 year = ( 846 - 825 ) = rs . 29 s . i . for 3 years = 21 * 3 = rs . 63 principal = ( 825 - 63 ) = rs . 762 . answer : d"
Answer: d
Question (gain): of the votes cast on a certain proposal , 58 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
Options: a ) 230 , b ) 245 , c ) 260 , d ) 275 , e ) 290
Rationale: "let x be the total number of votes cast . 0.6 x = 0.4 x + 58 0.2 x = 58 x = 290 the answer is e ."
Answer: e
Question (gain): the s . i . on a certain sum of money for 3 years at 10 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 2197 , b ) 1267 , c ) 1750 , d ) 2267 , e ) 1400
Rationale: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 10 ) = rs . 1400 answer : e"
Answer: e
Question (general): for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.45 – 6.45 * ?
Options: a ) 0.45 , b ) 0.5 , c ) 6.45 , d ) 0.25 , e ) 6.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.45 * = 6 ( the greatest positive even integer less than or equal to 6.45 is 6 ) . hence , 6.45 – 6.45 * = 6.45 - 6 = 0.45 answer : a ."
Answer: a
Question (physics): maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 54 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the distance traveled by maxwell ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "after the 1 st hour , maxwell has travelled 4 km . and brad just left home . so the distance between them = 54 - 4 = 50 . relative speed = 4 + 6 = 10 kmph . now to cover these 50 kms , they will take 50 / 10 = 5 hrs . so in 5 hrs , maxwell walks 5 * 4 = 20 kms . so total distance travelled by maxwell = 4 + 20 = 24 . answer : d"
Answer: d
Question (general): find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2
Options: a ) 31 , b ) 22 , c ) 25 , d ) 27 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 7 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 7 x 11 ^ 2 = 2 ^ 22 x 7 ^ 7 x 11 ^ 2 total number of prime factors = ( 22 + 7 + 2 ) = 31 . answer is a ."
Answer: a
Question (general): at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 10 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 48 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 cents ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let number of apples = a number of oranges = b a + b = 10 - - - 1 . 48 = ( . 4 a + . 6 b ) / 10 = > 48 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 6 b = 4 let the number of oranges put back = c 45 * ( 10 - c ) = 40 * 6 + 60 ( 4 - c ) = > c = 2 answer b"
Answer: b
Question (geometry): a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area q covered by the two roads ?
Options: a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625
Rationale: "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads q = 1000 + 600 - 25 = 1575 answer : option c"
Answer: c
Question (general): by approximately what percent is x greater than 4 / 5 if ( 4 / 5 ) ( x ) = 1 ?
Options: a ) 73 % , b ) 56 % , c ) 41 % , d ) 37 % , e ) 29 %
Rationale: 4 / 5 = 80 % , 5 / 4 = 125 % increase by 45 percentage points 45 / 80 = 56 % , hence b
Answer: b
Question (physics): a train 120 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 22 , b ) 48.2 , c ) 99 , d ) 288 , e ) 12
Rationale: speed of the train relative to man = ( 120 / 10 ) m / sec = ( 12 ) m / sec . [ ( 12 ) * ( 18 / 5 ) ] km / hr = 43.2 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 43.2 = = > x = 48.2 km / hr . answer : b
Answer: b
Question (geometry): find the surface area of a 8 cm x 6 cm x 2 cm brick .
Options: a ) 112 cu cm , b ) 136 cu cm , c ) 164 cu cm , d ) 180 cu cm , e ) 152 cu cm
Rationale: "sol . surface area = [ 2 ( 8 x 6 + 6 x 2 + 8 x 2 ) ] = ( 2 x 76 ) = 152 cu cm answer e"
Answer: e
Question (gain): a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 15 % while buying and by 20 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 43.75 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 115 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 115 - 80 ) / 80 * 100 = ~ 43.75 % answer : d ."
Answer: d
Question (physics): a field is 90 metre long and 50 metre broad . a 25 metre long , 20 metre broad and 4 metre deep tank dug in the field and the earth taken out is spread evenly over the remaining field . how much the level of field will rise ?
Options: a ) 0.5 metre , b ) 0.3 metre , c ) 0.8 metre , d ) 0.6 metre , e ) 0.7 metre
Rationale: area of field = 90 x 50 = 4500 m 2 area of field dug out = 25 x 20 = 500 m 2 therefore , area of remaining field = 4500 m 2 - 500 m 2 = 4000 m 2 volume of the earth dug out = 25 x 20 x 4 = 2000 m 3 therefore , field will rise by 2000 / 4000 = 0.5 metre answer a
Answer: a
Question (geometry): how many odd numbers between 10 and 800 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 12 numbers . answer : a ."
Answer: a
Question (general): a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 106 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 47 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "( 9 / 106 ) / ( 3 / 20 ) = 30 / 54 = 56,6 % it means that 9 / 106 represents only 56,6 % . therefore a decrease of 47 % . answer b"
Answer: b
Question (general): the price of lunch for 15 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12 , c ) 13.8 , d ) 14 , e ) 15.87
Rationale: "x - > price without gratuity 207 = x + 0.15 x = > x = 207 / 1.15 = 180 so average price per person , excluding the gratuity = 180 / 15 = 12 the answer is b ."
Answer: b
Question (general): a soft drink company had 6000 small and 15000 big bottles in storage . if 11 % of small 12 % of big bottles have been sold , then the total bottles remaining in storage is
Options: a ) 15360 , b ) 16010 , c ) 15060 , d ) 14930 , e ) 18540
Rationale: "6000 + 15000 - ( 0.11 * 6000 + 0.12 * 15000 ) = 18540 . answer : e ."
Answer: e
Question (general): solve the equation for x : 6 x - 27 + 3 x = 4 + 9 - x ?
Options: a ) 4 , b ) 5 , c ) 3 , d ) 9 , e ) 6
Rationale: "9 x + x = 13 + 27 10 x = 40 = > x = 4 answer : a"
Answer: a
Question (gain): a sum of money at simple interest amounts to rs . 840 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 798 , c ) 654 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 840 ) = rs . 14 . s . i . for 3 years = rs . ( 14 x 3 ) = rs . 42 . principal = rs . ( 840 - 42 ) = rs . 798 . answer : b"
Answer: b
Question (geometry): the dimensions of a rectangular solid are 4 inches , 6 inches , and 8 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 10 : 17 , b ) 2 : 5 , c ) 5 : 16 , d ) 25 : 7 , e ) 2 : 3
Rationale: answer : e .
Answer: e
Question (physics): annika hikes at a constant rate of 12 minutes per kilometer . she has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes . if annika continues east , then turns around and retraces her path to reach the start of the trail in exactly 51 minutes , for how many kilometers total did she hike east ?
Options: a ) 3.625 , b ) 3 , c ) 4.5 , d ) 4 , e ) 3.5
Rationale: "set up two r x t = d cases . 1 . 1 / 12 km / min x t = 2.75 from which t = 33 mins . we know total journey time now is 51 + 33 = 84 . the rate is the same ie 1 / 12 km / min . set up second r x t = d case . 1 / 12 km / min x 84 = 7 km now the total journey would be halved as distance would be same in each direction . 7 / 2 = 3.5 e ."
Answer: e
Question (geometry): if y is the smallest positive integer such that 1,260 multiplied by y is the square of an integer , then y must be
Options: a ) 23 , b ) 51 , c ) 38 , d ) 35 , e ) 37
Rationale: "1260 = 2 * 2 * 3 * 3 * 7 * 5 , so we need one 7 and one 5 to make it a square of a number . so 7 * 5 = 35 ans : d"
Answer: d
Question (general): if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 25 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 375
Rationale: "( 348 / 116 ) 125 = 375 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 125 = 375 ( 300 + 75 ) answer e"
Answer: e
Question (geometry): how many books each of volume 250 meter cube can be packed into a crate of volume 4500 meter cube
Options: a ) 25 , b ) can not be determined , c ) 10 , d ) 15 , e ) 20
Rationale: "gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 4500 m 3 can be 450 * 10 or 45 * 100 or just 4500 * 1 we do n ' t know , so we cant calculate answer : b"
Answer: b
Question (physics): how long does a train 90 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 90 + 170 = 260 m s = 60 * 5 / 18 = 50 / 3 t = 260 * 3 / 50 = 15.6 sec answer : d"
Answer: d
Question (physics): a certain hospital has a policy that for every 50 patients there should be 2 doctors . if the number of patients visiting the hospital every day is 400 , how many doctors are there in the hospital ?
Options: a ) 4 , b ) 16 , c ) 5 , d ) 14 , e ) 11
Rationale: 2 / 50 = x / 400 x = 16 answer is b
Answer: b
Question (gain): what will be the compound interest on rs . 30000 after 3 years at the rate of 12 % per annum
Options: a ) rs 10123.20 , b ) rs 12147.84 , c ) rs 10123.40 , d ) rs 10123.50 , e ) none of these
Rationale: "explanation : ( 30000 × ( 1 + 12 / 100 ) 3 ) = > 30000 × 28 / 25 × 28 / 25 × 28 / 25 = > 42147.84 so compound interest will be 42147.84 - 30000 = rs 12147.84 option b"
Answer: b
Question (general): 5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 2553 , how much was it in the beginning ?
Options: a ) 2988 , b ) 2776 , c ) 4400 , d ) 2871 , e ) 3162
Rationale: "x * ( 95 / 100 ) * ( 85 / 100 ) = 2553 x = 3162 answer : e"
Answer: e
Question (geometry): a rectangular block 6 cm by 12 cm by 15 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 50 , e ) 35
Rationale: "volume of the block = 6 * 12 * 15 = 1080 cm ^ 3 side of the largest cube = h . c . f of 6 , 12,15 = 3 cm volume of the cube = 3 * 3 * 3 = 27 cm ^ 3 number of cubes = 1080 / 27 = 40 answer is c"
Answer: c
Question (physics): a cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 52 m 2 , d ) 62 m 2 , e ) 55 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 8 x 1.25 + 4 x 1.25 ) + 8 x 4 ] m 2 = 62 m 2 . answer : d"
Answer: d
Question (geometry): in measuring the sides of a rectangle , one side is taken 12 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 6.4 % , c ) 3 % , d ) 5 % , e ) 2.6 %
Rationale: "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 112 * 95 = 10,640 , which is 6.4 % greater than the actual area . answer : b ."
Answer: b
Question (general): in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 7720 votes were polled , then how many valid votes did b get ?
Options: a ) 1888 , b ) 2999 , c ) 2834 , d ) 2509 , e ) 2991
Rationale: let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 7720 32.5 k = 32.5 k / 100 k * 7720 = 2509 the number of valid votes polled in favour of b is 2834 . answer : d
Answer: d
Question (physics): a 180 meter long train crosses a man standing on the platform in 9 sec . what is the speed of the train ?
Options: a ) 72 , b ) 108 , c ) 1266 , d ) 188 , e ) 211
Rationale: "s = 180 / 9 * 18 / 5 = 72 kmph answer : a"
Answer: a
Question (gain): 3 candidates in an election and received 3000 , 5000 and 15000 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 65.21 % , b ) 50.16 % , c ) 57 % , d ) 60 % , e ) 65.24 %
Rationale: "total number of votes polled = ( 3000 + 5000 + 15000 ) = 23000 so , required percentage = 15000 / 23000 * 100 = 65.21 % a"
Answer: a
Question (general): lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 16 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "l = r l = 3 c r = c + 16 3 c = c + 16 c = 8 the answer is b ."
Answer: b
Question (gain): in the fifth grade at parkway elementary school there are 420 students . 296 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 ) 89
Rationale: "total students = 420 boys = 296 , girls = 124 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 = 124 - 35 = 89 . correct option : e"
Answer: e
Question (geometry): the percentage increase in the area of a rectangle , if each of its sides is increased by 20 %
Options: a ) 33 , b ) 37 , c ) 44 , d ) 99 , e ) 277
Rationale: "explanation : let original length = x metres and original breadth = y metres . original area = xy increased length = and increased breadth = new area = the difference between the original area and new area is : increase % = = 44 % ] answer : c ) 44 %"
Answer: c
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 . 69 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 = 69 1 percent for 1 year = 23 = > 100 percent = 2300 answer : d"
Answer: d
Question (general): if 5 x = 6 y = z , what is x + y , in terms of z ?
Options: a ) z / 2 , b ) 2 z , c ) z / 3 , d ) 11 z / 30 , e ) z / 9
Rationale: "5 x = 6 y = z x = z / 5 and y = z / 6 x + y = z / 5 + z / 6 = 11 z / 30 answer is d"
Answer: d
Question (general): if the mean of numbers 38 , x , 70 , 88 and 110 is 69 , what is the mean of 50 , 72 , 97 , 125,147 and x ?
Options: a ) 73.5 , b ) 77.86 , c ) 86.67 , d ) 66.69 , e ) 70.56
Rationale: "mean = ( sum of all no . in series ) / ( no . in series ) m 1 = 69 = ( x + 38 + 70 + 88 + 110 ) / ( 5 ) 69 x 5 = 290 + x x = 39 therefore mean of 2 nd series m 2 = ( x + 50 + 62 + 97 + 125 + 147 ) / 6 m 2 = 86.67 answer = c"
Answer: c
Question (physics): a train 200 m long running at 54 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 175 , b ) 266 , c ) 350 , d ) 277 , e ) 232
Rationale: length of the platform = 54 * 5 / 18 * 25 = 375 – 200 = 175 answer : a
Answer: a
Question (physics): liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 60 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )
Options: a ) 50 mph , b ) 45 mph , c ) 48 mph , d ) 52 mph , e ) 70 mph
Rationale: "let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 60 where s is the speed and 30 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 60 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 70 mph therefore answer is e"
Answer: e
Question (physics): a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 5.4 hours , then the distance covered at 40 kmph is
Options: a ) 130 km , b ) 120 km , c ) 100 km , d ) 140 km , e ) 148
Rationale: let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 5.4 or , x / 40 + ( 250 - x ) / 60 = 5.4 or , ( 3 x + 500 - 2 x ) / / 120 = 5.4 or 500 + x = 648 x = 148 answer : e
Answer: e