Cheukting/mathqa huggingface dataset:
Question (general): a bakery has 6 employees . it pays annual salaries of $ 15,000 to each of 2 employees , $ 17,000 to 1 employee , and $ 18,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 16,200 , b ) $ 16,500 , c ) $ 16,800 , d ) $ 17,000 , e ) $ 17,400
Rationale: "average = 2 ( 15000 ) + ( 17000 ) + 3 ( 18000 ) / 6 = $ 16,833 the answer is c ."
Answer: c
Question (gain): the current birth rate per certain number of people is 32 , whereas corresponding death rate is 11 per same number of people . if the net growth rate in terms of population increase is 2.1 percent , find number of persons . ( initally )
Options: a ) 1000 , b ) 10000 , c ) 100 , d ) 2000 , e ) 20000
Rationale: sol . net growth on x = ( 32 - 11 ) = 21 . net growth on 100 = ( 21 / x ã — 100 ) % = 2.1 % . then x = 1000 answer : a
Answer: a
Question (gain): if a lends rs . 4000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 112.5 , b ) 122.5 , c ) 132.5 , d ) 114.5 , e ) 180
Rationale: "( 4000 * 1.5 * 3 ) / 100 = > 180 answer : e"
Answer: e
Question (general): if x is less than y by 35 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 53.85 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 35 % ) = > 35 / ( 100 - 35 ) * 100 = 53.85 % answer : d"
Answer: d
Question (other): two numbers are in the ratio of 3 : 8 . if 24 be subtracted from each , they are in the ratio of 4 : 9 . find the numbers ?
Options: a ) 60,89 , b ) 60,88 , c ) - 27 , - 128 , d ) 60,84 , e ) - 72 , - 192
Rationale: "( 3 x - 24 ) : ( 8 x - 24 ) = 4 : 9 x = - 24 = > - 72 , - 192 answer : e"
Answer: e
Question (other): if 3 tic equals 6 tacs and 2 tacs equal 7 tocs , what is the ratio of one tic to one toc ?
Options: a ) 7 / 1 , b ) 6 / 5 , c ) 5 / 6 , d ) 3 / 10 , e ) 1 / 15
Rationale: "3 tic = 6 * tac and 2 * tac = 7 * toc ; 6 * tic = 12 * tac and 12 * tac = 42 * toc - - > 6 * tic = 42 * toc - - > tic / toc = 42 / 6 = 7 / 1 . answer : a ."
Answer: a
Question (general): in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 60 % of the total ?
Options: a ) 858 . , b ) 545 . , c ) 618 . , d ) 644 . , e ) 666 .
Rationale: "answer is a : 858 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 60 % of total is 515 , so 100 % is approx . 858 ."
Answer: a
Question (general): the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.3 kg . the weight of the new student is
Options: a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) 7 kg
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.3 weight of the new student = ( 30 * 27.3 – 29 * 28 ) = 819 - 812 = 7 answer : e"
Answer: e
Question (physics): a train 225 m long passes a man , running at 10 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 81 , b ) 90 , c ) 91 , d ) 85 , e ) 96
Rationale: "speed of the train relative to man = 225 / 10 m / sec = 45 / 2 m / sec . = 45 / 2 x 18 / 5 km / hr = 81 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 10 = 81 = 91 km / hr . answer : c"
Answer: c
Question (general): how many positive integers less than 100 are neither multiples of 4 or 5 .
Options: a ) a ) 30 , b ) b ) 60 , c ) c ) 32 , d ) d ) 33 , e ) e ) 34
Rationale: "to answer this q we require to know 1 ) multiples of 4 till 100 = 100 / 4 = 25 2 ) multiples of 5 till 100 = 100 / 5 = 20 add the two 25 + 20 = 45 ; subtract common terms that are multiple of both 4 and 5 . . lcm of 4 and 5 = 20 multiples of 20 till 100 = 100 / 20 = 5 = so total multiples of 4 and 5 = 45 - 5 = 40 ans = 100 - 40 = 60 b"
Answer: b
Question (geometry): the area of a square is equal to five times the area of a rectangle of dimensions 27 cm * 16 cm . what is the perimeter of the square ?
Options: a ) 140 , b ) 240 , c ) 340 , d ) 144 , e ) 122
Rationale: "area of the square = s * s = 3 ( 27 * 16 ) = > s = 9 * 4 = 36 cm perimeter of the square = 4 * 36 = 144 cm . answer : d"
Answer: d
Question (other): the present ratio of students to teachers at a certain school is 30 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 ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "lets say t = 10 - - - > s = 300 - - - > 350 / 15 = a bit less than 25 ( a and b will only make this ratio lesser , eliminate a and b ) go for t = 12 - - > s = 30 * 12 = 360 - - - > 360 + 50 / 12 + 5 = less than 25 . either you can now go further with t = 15 or mark e as the answer . check : t = 15 - - - > s = 30 * 15 = 450 - - - > 450 + 50 / 20 = 25 . answer : e"
Answer: e
Question (physics): a train is 360 meter long is running at a speed of 60 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 27 seconds , b ) 29 seconds , c ) 40 seconds , d ) 30 seconds , e ) 12 seconds
Rationale: "speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 3 / 50 ) = 30 seconds answer : d"
Answer: d
Question (general): a reduction of 40 % in the price of bananas would enable a man to obtain 64 more for rs . 40 . what is the reduced price / dozen ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "sol . lie purchases 6 a bananas mere for 4096 of rs 40 or , rs 16 . reduced price per do 3 a"
Answer: a
Question (general): a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.4 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
Options: a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 240 , e ) e . 200
Rationale: "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.4 = 240 answer : d"
Answer: d
Question (physics): excluding stoppages , the speed of a bus is 48 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 5 , b ) 4.15 , c ) 4.25 , d ) 5.5 , e ) none of these
Rationale: "due to stoppages , it covers 314 km less . time taken to cover 3 km = ( ( 3 / 48 ) ã — 60 ) = 4.15 min . option ( b ) is correct"
Answer: b
Question (other): in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 60 people were made to stand in a column , how many columns could be formed ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "16 * 30 = 60 * n n = 8 the answer is b ."
Answer: b
Question (geometry): carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 2 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 65 , b ) 63 , c ) 52 , d ) 60 , e ) 68
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 2 w = 120 = > w = 60 answer d"
Answer: d
Question (gain): a man took loan from a bank at the rate of 12 % p . a . s . i . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 15002 , b ) 15001 , c ) 15000 , d ) 15007 , e ) 15009
Rationale: principal = ( 100 * 5400 ) / ( 12 * 3 ) = rs . 15000 . answer : c
Answer: c
Question (general): a certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 130,000 and variables costs averaging $ 8 per item . if the manufacturer ’ s selling price per item is $ 12 , how many items the manufacturer produce and sell to earn an annual profit of $ 140,000 ?
Options: a ) 2,858 , b ) 8,667 , c ) 21,429 , d ) 35,000 , e ) 67,500
Rationale: "let the items manufactured or sold bex 130000 + 8 x = 12 x - 140000 4 x = 270000 x = 67500 ans : e"
Answer: e
Question (general): how many numbers between 100 and 714 are divisible by 2 , 3 , and 7 together ?
Options: a ) 112 , b ) 77 , c ) 267 , d ) 15 , e ) 99
Rationale: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 714 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 714 : 714 / 42 = 17 hence , 42 * 14 = 714 is the last number divisible by 42 within 714 hence , total numbers divisible by 2 , 3 , 7 together are ( 17 â € “ 2 ) = 15 answer : d"
Answer: d
Question (physics): how many paying stones , each measuring 3 m * 2 m are required to pave a rectangular court yard 60 m long and 14 m board ?
Options: a ) 99 , b ) 140 , c ) 26 , d ) 17 , e ) 12
Rationale: "60 * 14 = 3 * 2 * x = > x = 140 answer : b"
Answer: b
Question (physics): if a light flashes every 6 seconds , how many times will it flash in 1 / 2 of an hour ?
Options: a ) 301 times , b ) 351 times , c ) 401 times , d ) 451 times , e ) 481 times
Rationale: "in 1 / 2 of an hour there are 30 * 60 = 1800 seconds the number of 6 - second intervals = 1800 / 6 = 300 after the first flash , there will be 300 more flashes for a total of 301 . the answer is a ."
Answer: a
Question (general): the average runs scored by a batsman in 30 matches is 40 . in the next 10 matches the batsman scored an average of 13 runs . find his average in all the 30 matches ?
Options: a ) 24.3 , b ) 25.3 , c ) 26.3 , d ) 28.3 , e ) 34.5
Rationale: "total score of the batsman in 30 matches = 600 . total score of the batsman in the next 10 matches = 130 . total score of the batsman in the 30 matches = 730 . average score of the batsman = 730 / 30 = 24.3 . answer : a"
Answer: a
Question (general): a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 36 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: let x be the wholesale price . then 1.8 x = 36 and x = 36 / 1.8 = 20 . to achieve a 100 % markup , the price needs to be $ 40 . the retailer needs to increase the price by $ 4 more . the answer is b .
Answer: b
Question (general): in the city of san durango , 60 people own cats , dogs , or rabbits . if 30 people owned cats , 40 owned dogs , 16 owned rabbits , and 12 owned exactly two of the 3 types of pet , how many people owned all 3 ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 7 , e ) 32
Rationale: you are considering a case when cat dogs and rabbit are not exactly equal to 12 . the solution shall be 60 = 30 + 40 + 16 - 12 - 2 x and hence x shall be 7 . answer d
Answer: d
Question (gain): a certain company ’ s profit in 1996 was 17 percent greater than its profit in 1995 , and its profit in 1997 was 25 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 33 % , d ) 35 % , e ) 46.25 %
Rationale: "profit in 1995 - 100 profit in 1996 - 117 % increae profit in 1997 in comparison to 1995 = 17 + 117 * 25 % = 46.25 correct option : e"
Answer: e
Question (physics): a can give b 80 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 130.12 , b ) 130.43 , c ) 130.22 , d ) 111.0 , e ) 111.12
Rationale: a runs 1000 m while b runs 920 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 920 = 869.56 m b can give c = 1000 - 869.56 = 130.43 m . answer : b
Answer: b
Question (general): what is the smallest no . that should be added to 45454 to make it exactly divisible by 9 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 4 + 5 + 4 + 5 + 4 = 22 , the next multiple of 9 is 27 . 5 must be added to 45454 to make it divisible by 9 c"
Answer: c
Question (geometry): 30 square stone slabs of equal size were needed to cover a floor area of 58.8 sq . m . find the length of each stone slab ?
Options: a ) 140 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 58.8 / 30 m 2 = 1.96 m 2 length of each slab √ 1.96 = 1.4 m = 140 cm"
Answer: a
Question (physics): nhai employs 100 men to build a highway of 2 km in 50 days working 8 hours a day . if in 25 days they completed 1 / 3 part of work . than how many more emploies should nhai hire to finish it in time working 10 hours a day
Options: a ) 60 , b ) 70 , c ) 80 , d ) 50 , e ) 40
Rationale: "( m 1 * d 1 * h 1 ) / w 1 = ( m 2 * d 2 * h 2 ) / w 2 ( 100 * 25 * 8 ) / ( 1 / 3 ) = ( ( 100 + a ) * 25 * 10 ) ) / ( 2 / 3 ) 160 = 100 + a a = 60 answer : a"
Answer: a
Question (general): the average of first four prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "23 + 29 + 31 + 37 = 120 / 4 = 30 answer : c"
Answer: c
Question (general): jar x is 1 / 4 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 / 2 , e ) 2 / 3
Rationale: "let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 4 + p / 4 = p / 2 the answer is d ."
Answer: d
Question (physics): the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 40 kms . what was the total distance traveled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 612 kms , d ) 752 kms , e ) 152 kms
Rationale: "explanation : total distance travelled in 12 hours = ( 40 + 42 + 44 + . . . . . upto 12 terms ) this is an a . p with first term , a = 40 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 40 + { 12 - 1 ) x 2 ] = 6 ( 102 ) = 612 kms . answer : c"
Answer: c
Question (general): in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 60 per square m ?
Options: a ) rs . 50000 , b ) rs . 52000 , c ) rs . 57000 , d ) rs . 60000 , e ) rs . 67000
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 60 * 950 = rs . 57000 c"
Answer: c
Question (geometry): in the coordinate plane , a circle centered on point ( - 3 , - 3 ) passes through point ( 1 , 1 ) . what is the area of the circle ?
Options: a ) 9 π , b ) 32 π , c ) 25 π , d ) 37 π , e ) 41 π
Rationale: "r ^ 2 = ( - 3 - 1 ) ^ 2 + ( - 3 - 1 ) ^ 2 = 16 + 16 = 32 area of circle = π r ^ 2 = 32 π answer : b"
Answer: b
Question (other): a small island country of 5000 people has an emigration and immigration statistic per 500 persons of 50.4 and 15.4 respectively . how long will it take for the population to be half of its current number .
Options: a ) 6.8 , b ) 8.5 , c ) 6.1 , d ) 9.1 , e ) 7.14
Rationale: annual decrease is ( 500 + 15.4 - 50.4 ) * 10 = 4650 hence every year there is a decrease of 350 for the population to become half 2500 must emigrate therefore 2500 / 350 = 133.3 correct option is e ) 7.14
Answer: e
Question (general): the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 66 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.85 kgs , c ) 58.9 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 66 ) = 1178 kgs actual average weight is 1178 / 20 = 58.9 kgs c"
Answer: c
Question (gain): in a certain store , the profit is 320 % of the cost . if the cost increases by 40 % but the selling price remains constant , approximately what percentage of the selling price is the profit
Options: a ) 67 % , b ) 80 % , c ) 90 % , d ) 100 % , e ) none of above
Rationale: explanation : let c . p . = rs . 100 . then , profit = rs . 320 , s . p . = rs . 420 . new c . p . = 140 % of rs . 100 = rs . 140 new s . p . = rs . 420 . profit = rs . ( 420 - 140 ) = rs . 280 required percentage = ( 280 / 420 ) * 100 = 66.67 % ( approx ) = 67 % answer : a
Answer: a
Question (physics): if the perimeter of a rectangular garden is 480 m , its length when its breadth is 100 m is ?
Options: a ) 299 m , b ) 140 m , c ) 200 m , d ) 167 m , e ) 128 m
Rationale: "2 ( l + 100 ) = 480 = > l = 140 m answer : b"
Answer: b
Question (general): a family pays $ 800 per year for an insurance plan that pays 60 percent of the first $ 1000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,600 , e ) $ 2,000
Rationale: assuming the medical expenses are $ 1000 or more , the family pays $ 800 + $ 400 = $ 1200 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 600 when the medical expenses are $ 1600 . the answer is d .
Answer: d
Question (other): the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 10 and 15 . the larger of the two numbers is :
Options: a ) 350 , b ) 250 , c ) 450 , d ) 500 , e ) 620
Rationale: "explanation : clearly , the numbers are ( 30 x 10 ) and ( 30 x 15 ) . { \ color { blue } \ therefore } larger number = ( 30 x 15 ) = 450 . answer : c ) 450"
Answer: c
Question (general): in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 10 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 55 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 10 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 10 = 4 / 9 ( t - 10 ) 10 t = 990 - 440 = > t = 55 . answer : d"
Answer: d
Question (gain): in a particular state , 70 % of the counties received some rain on monday , and 50 % of the counties received some rain on tuesday . no rain fell either day in 20 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "70 + 50 + 20 = 140 % the number is 40 % above 100 % because 40 % of the counties were counted twice . the answer is b ."
Answer: b
Question (physics): a train passes a platform in 16 seconds . the same train passes a man standing on the platform in 10 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 40 , b ) 50 , c ) 90 , d ) 30 , e ) 20
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 10 = 150 m let the length of the platform = l time taken to cross the platform = ( 150 + l ) / 15 = > ( 150 + l ) / 15 = 16 = > 150 + l = 15 × 16 = 240 = > l = 240 - 150 = 90 meter answer is c"
Answer: c
Question (other): a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 10 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 ) 42 , b ) 70 , c ) 140 , d ) 180 , e ) 315
Rationale: "1 of 7 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more thn one deparments . we can choose any of the 4 candidates for the math dep . , which gives as 4 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 4 * 45 = 180 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans d"
Answer: d
Question (general): sum of two numbers is 25 . first exceeds by 5 from the other . then the numbers will be ?
Options: a ) 20 , 5 , b ) 10 , 15 , c ) 15 , 10 , d ) 5 , 20 , e ) 12 , 13
Rationale: "explanation : x + y = 25 x - y = 5 x = 15 y = 10 answer : c"
Answer: c
Question (other): if 35 % of the 840 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 546 , b ) 550 , c ) 555 , d ) 532 , e ) 515
Rationale: "we know 35 % people study biology , therefore the no of people not studying = 100 - 35 = 65 % > therefore the people not studying biology out of a total 840 people are = 65 % of 840 > ( 65 / 100 ) * 840 = 546 people a"
Answer: a
Question (physics): a train is 410 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 76 seconds , b ) 18 seconds , c ) 40 seconds , d ) 19 seconds , e ) 44 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 410 + 140 = 550 meter time = distance / speed = 550 * ( 2 / 25 ) = 44 seconds answer : e"
Answer: e
Question (physics): if a is thrice as fast as b and together can do a work in 30 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 42 , c ) 28 , d ) 54 , e ) 40
Rationale: a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 30 = 3 + 1 / 3 x = 4 / 3 x = 1 / 30 x = 30 * 4 / 3 = 40 answer : e
Answer: e
Question (physics): angelina walked 200 meters from her home to the grocery at a constant speed . she then walked 300 meters to the gym at double the speed . she spent 50 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 200 / x . . the speed to gym = 2 x . . so time taken = 300 / 2 x = 150 / x . . its given 200 / x - 150 / x = 50 . . 50 / x = 50 . . x = 1 m / secs . . so grocery to gym = 2 * 1 = 2 m / s . . . answer : a"
Answer: a
Question (general): the sum of the ages of 5 children born at the intervals of 3 year each is 40 year . what is the age of the eldest child ?
Options: a ) 14 year , b ) 8 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 40 â ‡ ” 5 x = 10 â ‡ ” x = 2 . â ˆ ´ age of the youngest child = x + 12 = 2 + 12 = 14 years . answer a"
Answer: a