regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: a merchant has selected two items to be placed on sale , one of which currently sells for 35 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "expensive item = $ 100 ; cheap item = $ 65 ; we must increase $ 65 to $ 100 , so by $ 35 , which is approximately 50 % increase : ( 100 - 65 ) / 65 = ~ 0.53 . answer : c ."
Answer: c
Problem: the population of a bacteria colony doubles every day . if it was started 11 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 4096
Rationale: "2 ^ 11 ( 2 ) = 2 ^ 12 = 4096 the answer is e ."
Answer: e
Problem: the unit digit in the product 7858 * 1086 * 4582 * 9783 is ?
Options: a ) 0 , b ) 1 , c ) 8 , d ) 3 , e ) 4
Rationale: "unit digit in the given product = unit digit in 8 * 6 * 2 * 3 = 8 answer is c"
Answer: c
Problem: a train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds . its length is :
Options: a ) 200 m , b ) 400 m , c ) 500 m , d ) 700 m , e ) none of the above
Rationale: sol . let the length of the train be x metres and its speed be y m / sec . then , x / y = 20 ⇒ y = x / 20 ∴ ( x + 500 ) / 40 = x / 20 ⇔ x = 500 m . answer c
Answer: c
Problem: yesterday ' s closing prices of 1,980 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 484 , b ) 1080 , c ) 1,100 , d ) 1,320 , e ) 1,694
Rationale: lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1980 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1080 . b is my answer .
Answer: b
Problem: 20 - 8 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 54 % , e ) 75 %
Rationale: initially 72 % and 28 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 72 so , the required % is [ ( 3 / 4 ) ∗ 72 / 100 ] ∗ 100 = 54 % answer : d
Answer: d
Problem: the racing magic takes 90 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "time taken by racing magic to make one circle = 90 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 90 seconds = 90 seconds time taken for them to meet at the starting point for the second time = 2 * 90 sec = 180 seconds = 3 mins answer a"
Answer: a
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 3300 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 15 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 3300 100 r + 120 r = 3300 r = 15 % answer : e"
Answer: e
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 7.25 , c ) 7.75 , d ) 7.35 , e ) 8.25
Rationale: "runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 40 run rate needed = 25040 = 6.25 answer : a"
Answer: a
Problem: what is the unit ’ s digit of 7 ^ 6
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 7 ^ 6 = 9 answer e"
Answer: e
Problem: a can finish a work in 4 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 7 , d ) 3 / 4 , e ) none of these
Rationale: explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 4 b ' s 1 day work = 1 / 2 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 4 + 1 / 2 ) = 3 / 4 so in one day 3 / 4 work will be done answer : d
Answer: d
Problem: two pipes a and b can separately fill a tank in 16 and 10 minutes respectively . a third pipe c can drain off 60 liters of water per minute . if all the pipes are opened , the tank can be filled in 10 minutes . what is the capacity of the tank ?
Options: a ) 590 liters , b ) 960 liters , c ) 740 liters , d ) 560 liters , e ) 580 liters
Rationale: "1 / 16 + 1 / 10 - 1 / x = 1 / 10 x = 12 16 * 60 = 960 answer : b"
Answer: b
Problem: a train speeds past a pole in 15 sec and a platform 110 m long in 25 sec , its length is ?
Options: a ) 100 , b ) 150 , c ) 160 , d ) 165 , e ) 180
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 110 ) / 25 = x / 15 = > x = 165 m . answer : option d"
Answer: d
Problem: if ( t - 8 ) is a factor of t ^ 2 - kt - 47 , then k =
Options: a ) 16 , b ) 12 , c ) 2 , d ) 6 , e ) 14
Rationale: "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 6 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ) ( t + m ) d"
Answer: d
Problem: during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons . if kim purchased 15 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 100 % , c ) 116.7 % , d ) 120 % , e ) 180 %
Rationale: "kim purchased 15 gallons of gas . she paid for 10 + 0.9 * 5 = 14.5 gallons , so the overall discount she got was 0.5 / 15 = 3.33 % . isabella purchased 25 gallons of gas . she paid for 10 + 0.9 * 15 = 23.5 gallons , so the overall discount she got was 1.5 / 25 = 6 % . 6 is 6 / 3.33 * 100 = 180 % of 3.33 . answer : e ."
Answer: e
Problem: a man can row downstream at the rate of 16 km / hr and upstream at 6 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 11,5 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 16 + 6 ) = 11 km / hr rate of current = 1 / 2 ( 16 - 6 ) = 5 km / hr answer : option b"
Answer: b
Problem: a rectangular lawn of dimensions 100 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) a ) 3820 , b ) b ) 930 , c ) c ) 9309 , d ) d ) 4500 , e ) e ) 8302
Rationale: "explanation : area = ( l + b – d ) d ( 100 + 60 – 10 ) 10 = > 1500 m 2 1500 * 3 = rs . 4500 answer : option d"
Answer: d
Problem: find avrg speed if a man travels at speed of 18 km / hr up and 24 km / hr dawn at an altitude of 300 m .
Options: a ) 25.8 , b ) 26.8 , c ) 27.8 , d ) 20.5 , e ) 21.8
Rationale: "avg speed = 2 * x * y / ( x + y ) = 2 * 18 * 24 / ( 18 + 24 ) = 20.5 answer : d"
Answer: d
Problem: nitin ranks 27 th in a class of 89 students . what is rank from the last ?
Options: a ) 63 , b ) 65 , c ) 67 , d ) 87 , e ) 89
Rationale: "explanation : number students behind the nitin in rank = ( 89 - 27 ) = 62 nitin is 63 th from the last answer : a ) 63"
Answer: a
Problem: set a consists of the integers from 3 to 12 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "a = { 3,4 , 5,6 , 7,8 , 9,10 , 11,12 } b = { 6 , 7,8 , 9,10 , 11,12 . . . } thus we see that there are 7 distinct integers that are common to both . b is the correct answer ."
Answer: b
Problem: what is the units digit of the expression 14 ^ 7 − 20 ^ 4 ?
Options: a ) 8 , b ) 3 , c ) 4 , d ) 6 , e ) 0
Rationale: i think answer on this one should be a too . since we know that 14 ^ 7 > 20 ^ 4 , as will said one should always check if the number is positive .
Answer: a
Problem: the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 424 different signs . if the company used 422 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 424 signs ?
Options: a ) 246 , b ) 248 , c ) 1692 , d ) 15,128 , e ) 30,256
Rationale: "# of 2 - letter codes possible from 424 different signs = 424 * 424 . # of 2 - letter codes possible from 422 different signs = 422 * 422 . the difference = 424 ^ 2 - 422 ^ 2 = ( 424 - 422 ) ( 424 + 422 ) = 1692 . answer : c ."
Answer: c
Problem: thin rectangular slab of potato was cut into two pieces for an osmosis lab . one piece is 50 mm greater than the other . if the original uncut slab is 600 mm , what is the length of the other piece of the potato after it is cut .
Options: a ) 550
b ) 275
c ) 50
d ) 300
e ) 250
Rationale: piece one as p 1 , and piece two as p 2 . p 2 + 50 = p 1 as eq . a p 1 + p 2 = 600 as eq . b substitute eq . a into eq . b , resulting in ( p 2 + 50 ) + p 2 = 600 mm . group like terms , p 2 + p 2 = 600 - 50 ( 2 * p 2 / 2 ) = 550 / 2 solves to p 2 = 275 . ansewr is b .
Answer: b
Problem: a alone can complete a work in 16 days and b alone can do in 12 days . star ɵ ng with a , they work on alternate days . the total work will be completed in
Options: a ) 1314 , b ) 1312 , c ) 1334 , d ) 1344 , e ) none of these
Rationale: explana ɵ on : a ' s 1 day work = 1 / 16 b ' s 1 day work = 1 / 12 as they are working on alternate day ' s so their 2 days work = ( 1 / 16 ) + ( 1 / 12 ) = 7 / 48 [ here is a small technique , total work done will be 1 , right , then mul ɵ ply numerator ɵ ll denominator , as 7 * 6 = 42 , 7 * 7 = 49 , as 7 * 7 is more than 48 , so we will consider 7 * 6 , means 6 pairs ] work done in 6 pairs = 6 * ( 7 / 48 ) = 7 / 8 remaining work = 1 - 7 / 8 = 1 / 8 on 13 th day it will a turn , then remaining work = ( 1 / 8 ) - ( 1 / 16 ) = 1 / 16 on 14 th day it is b turn , 1 / 12 work done by b in 1 day 1 / 16 work will be done in ( 12 * 1 / 16 ) = 3 / 4 day so total days = 1334 answer : c
Answer: c
Problem: a cistern which could be filled in 6 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 15 hrs , d ) 90 hrs , e ) 11 hrs
Rationale: "1 / 6 - 1 / x = 1 / 10 = > 15 hrs answer : c"
Answer: c
Problem: george is 8 years more than christopher and ford is 2 years younger than christopher . the sum of their ages is 60 . find the ages of ford .
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "christopher age = x george age , y = x + 8 - - - - - - - - - - > ( 1 ) ford age , z = x - 2 - - - - - - - - - - - - > ( 2 ) sum of their ages , x + y + z = 60 - - - - > ( 3 ) substitute z and y values in equation ( 3 ) therefore , x + ( x + 8 ) + ( x - 2 ) = 60 = > 3 x + 8 - 2 = 60 = > 3 x = 60 - 6 = > 3 x = 54 = > x = 54 / 3 x = 18 ( christopher ' s age ) substitute x value in equation 1 & 2 y = x + 8 y = 18 + 8 y = 26 ( george ' s age ) z = x - 2 z = 18 - 2 z = 16 ( ford ' s age ) answer : c"
Answer: c
Problem: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 28 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 28 . . 4 x + 12 = 28 . . x = 4 . . ans = x + 4 = 4 + 4 = 8 aswer d"
Answer: d
Problem: bhanu spends 30 % of his income on petrol on scooter 14 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 98 , b ) 140 , c ) 62 , d ) 797 , e ) 123
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 14 % ( 700 ) = rs . 98 answer : a"
Answer: a
Problem: a man covered a certain distance at some speed . if he had moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . what is the distance in km ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 45
Rationale: explanation : speed = 2 v 1 v 2 / v 1 − v 2 = 2 × 3 × 23 − 2 = 12 km / h = hr distance = vt 1 ( 1 + v / v 1 ) = 12 × 40 / 60 ( 1 + 12 / 3 ) = 40 km answer is c
Answer: c
Problem: if x * y = xy – 2 ( x + y ) for all integers x and y , then 2 * ( – 3 ) =
Options: a ) – 16 , b ) – 11 , c ) – 4 , d ) 4 , e ) 16
Rationale: "the quickest ( rather only ) way is to apply the given formula : 2 * ( - 3 ) = 2 * ( - 3 ) - 2 ( 2 + ( - 3 ) ) = - 6 + 2 = - 4 option ( c )"
Answer: c
Problem: a man is 18 years older than his son . in eight years , his age will be twice the age of his son . the present age of this son is
Options: a ) 5 years , b ) 10 years , c ) 15 years , d ) 20 years , e ) 25 years
Rationale: "explanation : let ' s son age is x , then father age is x + 18 . = > 2 ( x + 8 ) = ( x + 18 + 8 ) = > 2 x + 16 = x + 26 = > x = 10 years answer : option b"
Answer: b
Problem: 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 ) + 5 , 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 ) + 5 = 10 / 2 + 5 = 10 . the correct answer is c ."
Answer: c
Problem: a student got 72 % in math and 84 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 65 % , b ) 67 % , c ) 69 % , d ) 71 % , e ) 73 %
Rationale: "72 + 84 + x = 3 * 75 x = 69 the answer is c ."
Answer: c
Problem: if f ( x ) = ax ^ 2 – 6 x + ax + 1 , then f ( b ) – f ( - b ) will equal :
Options: a ) 0 , b ) - 12 b + 2 ab , c ) 2 ab ^ 4 – 8 b ^ 2 – 6 , d ) - 2 ab ^ 4 + 8 b ^ 2 + 6 , e ) 2 ab ^ 4 – 8 b ^ 2 + 2 ab – 6
Rationale: f ( x ) = ax ^ 2 – 6 x + ax + 1 f ( b ) = ab ^ 2 – 6 b + ab + 1 f ( - b ) = ab ^ 2 + 6 b - ab + 1 f ( b ) - f ( - b ) = ab ^ 2 – 6 b + ab + 1 - ab ^ 2 - 6 b + ab - 1 = - 12 b + 2 ab answer b
Answer: b
Problem: a 100 meter long train crosses a man standing on the platform in 5 sec . what is the speed of the train ?
Options: a ) 72 kmph , b ) 108 kmph , c ) 176 kmph , d ) 134 kmph , e ) 161 kmph
Rationale: "s = 100 / 5 * 18 / 5 = 72 kmph answer : a"
Answer: a
Problem: what is the sum r of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 3 ?
Options: a ) 897 , b ) 164850 , c ) 164749 , d ) 149700 , e ) 156720
Rationale: the series is = > 101 + . . . 998 number of terms = > 300 sum = > 300 / 2 * [ 101 + 998 ] hence sum r = > 164850 i . e . option b
Answer: b
Problem: find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of rs . 12 per square metre .
Options: a ) 1824 , b ) 1854 , c ) 1872 , d ) 1888 , e ) 1999
Rationale: explanation : area of the carpet = area of the room = ( 13 × 9 ) m 2 = 117 m 2 . length of the carpet = ( area / width ) = 117 × ( 4 / 3 ) m = 156 m . therefore cost of carpeting = ( 156 × 12 ) = rs . 1872 answer : option c
Answer: c
Problem: each week a restaurant serving mexican food uses the same volume of chili paste , which comes in either 25 - ounce cans or 15 - ounce cans of chili paste . if the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs , then how many larger cans are required to fulfill its weekly needs ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 100 , e ) 45
Rationale: let x be the number of 25 ounce cans . therefore ( x + 30 ) is the number of 15 ounce cans . total volume is same , therefore 25 x = 15 ( x + 30 ) 10 x = 450 x = 45 ans - e
Answer: e
Problem: a boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream , it takes 5 hours . what is the speed of the boat in still water ?
Options: a ) 2.75 , b ) 5.95 , c ) 7.95 , d ) 3.25 , e ) 4.95
Rationale: "speed downstream = 22 / 4 = 5.5 kmph speed upstream = 22 / 5 = 4.4 kmph speed of the boat in still water = ( 5.5 + 4.4 ) / 2 = 4.95 kmph answer : e"
Answer: e
Problem: express a speed of 54 kmph in meters per second ?
Options: a ) 10 mps , b ) 76 mps , c ) 15 mps , d ) 97 mps , e ) 16 mps
Rationale: "54 * 5 / 18 = 15 mps answer : c"
Answer: c
Problem: the cash difference between the selling prices of an article at a profit of 8 % and 6 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 52 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 53 , e ) none of these
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 108 % of x ) / ( 106 % of x ) = 108 / 106 = 54 / 53 = 54 : 53 . answer : d"
Answer: d
Problem: the tax on a commodity is diminished by 16 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 3.8 % , c ) 3.4 % , d ) 3.6 % , e ) 1 %
Rationale: 100 * 100 = 10000 84 * 115 = 9660 - - - - - - - - - - - 10000 - - - - - - - - - - - 340 100 - - - - - - - - - - - ? = > 3.4 % decrease answer : c
Answer: c
Problem: the maximum number of student amoung them 2010 pens and 1050 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 90 , b ) 60 , c ) 30 , d ) 1911 , e ) none of these
Rationale: "solution required number of student = h . c . f of 2010 and 1050 = 30 . answer c"
Answer: c
Problem: two quarts containing 2 ⁄ 3 water and 1 ⁄ 3 formula are mixed with 3 quarts containing 3 ⁄ 8 water and 5 ⁄ 8 formula . approximately what percent of the combined 5 - quart mixture is water ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: since we are asking of water in the end , lets concentrate on water only . . a solution has 2 quarts with fraction of water = 2 / 3 , almost 67 % . . b solution has 3 quarts with fraction of water = 3 / 8 almost 37 % . . so the ratio a : b = 2 : 3 . . . the average will therefore be closer to b % and will be 2 / ( 2 + 3 ) of { 67 - 37 } away from b . . 2 / ( 2 + 3 ) of { 67 - 37 } = 2 / 5 * 30 = 12 . . so 37 + 12 = 49 nearly 50 % answer : c
Answer: c
Problem: two numbers are in the ratio 3 : 4 . if their l . c . m . is 48 . what is sum of the numbers ?
Options: a ) 28 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 48 = > 12 x = 48 = > x = 48 / 12 = 4 sum of the numbers = 3 x + 4 x = 7 x = 7 x 4 = 28 answer : option a"
Answer: a
Problem: a cricketer scored 134 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 55.22 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 134 - ( 12 x 4 + 2 x 6 ) = 134 - ( 60 ) = 74 now , we need to calculate 72 is what percent of 134 . = > 74 / 134 * 100 = 55.22 % answer : a"
Answer: a
Problem: a worker makes a toy in every 2 h . if he works for 80 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 45 , d ) 39 , e ) none
Rationale: "answer let number of toys be n . more hours , more toys ( direct proportion ) 2 : 80 : : 1 : n ⇒ n = 80 / 2 = 40 toys correct option : a"
Answer: a
Problem: bhavan travelled for 20 hours . he covered the first half of the distance at 50 kmph and remaining half of the distance at 40 kmph . find the distance travelled by bhavan ?
Options: a ) 888.89 , b ) 788.89 , c ) 899.89 , d ) 688.89 , e ) 899.99
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 50 + ( x / 2 ) / 40 = 20 = > x / 100 + x / 80 = 20 = > ( 4 x + 5 x ) / 400 = 20 = > x = 888.89 km answer : a
Answer: a
Problem: what is the tens digit of 7 ^ 957 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 957 = 4 * 239 + 1 the ten ' s digit will be 0 . answer d"
Answer: d
Problem: ? x 40 = 173 x 240
Options: a ) 545 , b ) 685 , c ) 1038 , d ) 495 , e ) 534
Rationale: "let y x 40 = 173 x 240 then y = ( 173 x 240 ) / 40 = 1038 answer : c"
Answer: c
Problem: rose made a part payment of $ 300 toward buying a brand new car , which represents 5 % of the total cost of the car , how much remains to be paid ?
Options: a ) $ 5700 , b ) $ 5500 , c ) $ 5800 , d ) $ 5200 , e ) $ 5880
Rationale: explanation : let ' s start with what the total price of the car would be . if 5 % is equal to $ 300 then 100 % equals $ x . we just have to multiply $ 300 by 20 to get total amount = $ 6000 . out of this amount we then need to deduct the amount already paid which was $ 300 so we have $ 6000 - $ 300 = $ 5700 answer : option a
Answer: a
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 x 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in
Options: a ) 5 hours , b ) 7 hours , c ) 8 hours , d ) 14 hours , e ) 18 hours
Rationale: "work done by the leak in 1 hour = 1 / 2 - 3 / 7 = 1 / 14 . leak will empty the tank in 14 hrs . answer : d"
Answer: d
Problem: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 12 , 0 ) , ( 0 , - 3.5 ) , ( - 12 , 0 ) ?
Options: a ) 84 , b ) 88 , c ) 112 , d ) 116 , e ) 120
Rationale: "area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 12 + 12 = 24 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 24 * 7 = 84 a is the answer"
Answer: a
Problem: rs . 6000 is lent out in two parts . one part is lent at 7 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 480 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 2 : 1 , b ) 5 : 6 , c ) 5 : 2 , d ) 5 : 8 , e ) 5 : 2
Rationale: "let the amount lent at 7 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 480 = > x = 5000 amount lent at 10 % = 2000 required ratio = 2000 : 1000 = 2 : 1 answer : a"
Answer: a
Problem: the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 7.2 . the true discount is
Options: a ) rs . 72 , b ) rs . 36 , c ) rs . 54 , d ) rs . 60 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 7.2 x 100 / 12 x 1 ) = rs . 60 . answer d"
Answer: d
Problem: n is the greatest number which divides 1305 , 4665 and 6905 and gives the same remainder in each case . what is the sum of the digits in n ?
Options: a ) 23 , b ) 28 , c ) 4 , d ) 1 , e ) 25
Rationale: if the remainder is same in each case and remainder is not given , hcf of the differences of the numbers is the required greatest number 6905 - 1305 = 5600 6905 - 4665 = 2240 4665 - 1305 = 3360 hence , the greatest number which divides 1305 , 4665 and 6905 and gives the same remainder , n = hcf of 5600 , 2240 , 3360 = 1120 sum of digits in n = sum of digits in 1120 = 1 + 1 + 2 + 0 = 4 answer is c
Answer: c
Problem: john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 2 % and the mobile phone at a profit of 10 % . overall how much he make a profit .
Options: a ) s . 90 , b ) s . 120 , c ) s . 200 , d ) s . 250 , e ) s . 500
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 2 / 100 ) = 15000 - 300 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 300 + 800 = rs . 500 as this is positive , an overall profit of rs . 200 was made . e"
Answer: e