Cheukting/mathqa huggingface dataset:
Question (general): in a group of cows and chickens , the number of legs was 12 more than twice the number of heads . the number of cows was :
Options: a ) 6 , b ) 7 , c ) 10 , d ) 12 , e ) 14
Rationale: "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 12 more than twice the number of heads . therefore , 2 × ( x + y ) + 14 = 4 x + 2 y . or , 2 x + 2 y + 12 = 4 x + 2 y . or , 2 x + 12 = 4 x [ subtracting 2 y from both sides ] . or , 12 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 12 = 2 x . or , x = 6 [ dividing by 2 on both sides ] . therefore , the number of cows = 6 . correct answer : a ) 6"
Answer: a
Question (general): a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 385 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 385 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 385 – 320 ) / 320 ] x 100 65 / 320 x 100 13 / 64 x 100 ≈ 13 / 65 x 100 ≈ 1 / 5 x 100 ≈ 20 % . the answer is c ."
Answer: c
Question (general): if a - b = 3 and a ^ 2 + b ^ 2 = 29 , find the value of ab .
Options: a ) 5 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 29 - 9 = 20 ab = 10 . b )"
Answer: b
Question (general): a man is 24 years older than his son . in six years , his age will be twice the age of his son . the present age of the son is
Options: a ) 14 years , b ) 28 years , c ) 20 years , d ) 22 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then â € ¹ = â € º ( x + 24 ) + 6 = 2 ( x + 6 ) â € ¹ = â € º x + 30 = 2 x + 12 x = 18 . answer e"
Answer: e
Question (general): for what value of x between − 7 and 7 , inclusive , is the value of x ^ 2 − 10 x + 16 the greatest ?
Options: a ) − 7 , b ) − 2 , c ) 0 , d ) 2 , e ) 7
Rationale: "we can see from the statement that two terms containing x , x ^ 2 will always be positive and - 10 x will be positive if x is - ive . . so the equation will have greatest value if x is - ive , and lower the value of x , greater is the equation . so - 7 will give the greatest value . . ans a"
Answer: a
Question (general): the sum of all two digit numbers divisible by 6 is
Options: a ) 910 , b ) 510 , c ) 710 , d ) 610 , e ) 810
Rationale: "required numbers are 12 , 18,24 . . . . . 96 this is an a . p . in which a = 12 , d = 6 and l = 96 . let the number of terms in it be n . then t = 96 so a + ( n - 1 ) d = 96 . 12 + ( n - 1 ) * 6 = 96 , 12 + 6 n - 6 = 96 6 + 6 n = 96 6 n = 96 - 6 n = 90 / 6 then n = 15 . required sum = n / 2 ( a + l ) = 15 / 2 ( 12 + 96 ) = 810 answer is e ."
Answer: e
Question (general): students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 182 cms . what was the ratio of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 182 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 182 m ) / ( w + m ) = 180 170 w + 182 m = 180 w + 180 m 2 m = 10 w m = 5 w m / w = 5 / 1 the ratio of men to women is 5 to 1 . b"
Answer: b
Question (general): ages of two persons differ by 14 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 13,27 , c ) 16,32 , d ) 18,34 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 14 ) = > 3 ( x - 6 ) = ( x + 14 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 8 = > x = 13 so other person age is x + 14 = 27 answer : option b"
Answer: b
Question (gain): the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 400 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 80 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 400 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 400 ) * 100 / 500 = 80 % answer : option e"
Answer: e
Question (physics): convert 2.3 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "2.3 hectares in ares 1 hectare = 100 ares therefore , 2.3 hectares = 2.3 × 100 ares = 230 ares . answer - d"
Answer: d
Question (general): jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the number ' s sum will be 13 ?
Options: a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 42 , e ) 12 / 21
Rationale: both dice addition result is 13 = ( 6 + 7 ) probability that the number on first die is 6 = 1 / 6 probability that the number on second die is 7 = 1 / 7 probability that both dice addition result is 13 = 1 / 6 * 1 / 7 = 1 / 42 d
Answer: d
Question (gain): calculate how many seconds it will take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 9 , 12 , 15 and 18 seconds ?
Options: a ) 186 , b ) 130 , c ) 180 , d ) 181 , e ) 120
Rationale: "lcm of 9 , 12 , 15 and 18 is 180 lcm = 180 answer : c"
Answer: c
Question (general): if a = 105 and a ^ 3 = 21 * 25 * 315 * b , what is the value of b ?
Options: a ) 35 , b ) 7 , c ) 45 , d ) 49 , e ) 54
Rationale: first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 315 = 3 * 3 * 5 * 7 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 3 * 5 * 7 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 ^ 3 * 7 ^ 2 b = 7 correct answer b .
Answer: b
Question (gain): boy sells a book for rs . 540 he gets a loss of 10 % , to gain 10 % , what should be the sp ?
Options: a ) 430 , b ) 450 , c ) 550 , d ) 590 , e ) 660
Rationale: "cost price = 540 / 90 x 100 = 600 to gain 10 % = 600 x 10 / 100 = 60 sp = cp + gain = 600 + 60 = 660 answer : e"
Answer: e
Question (general): xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 1 / 16 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: "p ( xavier will solve ) = 1 / 3 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 3 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 16 . ans . a ."
Answer: a
Question (general): a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 723 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 22200 , b ) 21897 , c ) 28799 , d ) 30000 , e ) 32782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 723 p = 30000 answer : d"
Answer: d
Question (other): if 0.2 of a number is equal to 0.08 of another number , the ratio of the numbers i
Options: a ) 2 : 3 , b ) 2 : 5 , c ) 3 : 20 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.2 a = 0.08 b â ‡ ” a / b = 0.08 / 0.20 = 8 / 20 = 2 / 5 â ˆ ´ a : b = 2 : 5 . answer b"
Answer: b
Question (other): a person want to give his money of $ 1800 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 700 , b ) $ 600 , c ) $ 900 , d ) $ 500 , e ) $ 400
Rationale: "b ' s share = 1800 * 3 / 9 = $ 600 answer is b"
Answer: b
Question (physics): in what time will a train 240 metres long cross an electric pole , if its speed be 126 km / hr ?
Options: a ) 6.75 sec , b ) 6.85 sec , c ) 6.55 sec , d ) 6.44 sec , e ) 7.85 sec
Rationale: "solution speed = ( 126 x 5 / 18 ) m / sec = 35 m / sec time taken = ( 240 / 35 ) sec = 6.85 sec . answer b"
Answer: b
Question (general): a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 7 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?
Options: a ) $ 54.00 , b ) $ 78.40 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80
Rationale: correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.07 ( $ 1120 ) = $ 78.40 . the correct answer is b .
Answer: b
Question (physics): how long does a train 110 m long travelling at 60 kmph takes to cross a bridge of 200 m in length ?
Options: a ) 18.6 sec , b ) 14.9 sec , c ) 12.4 sec , d ) 16.8 sec , e ) 11.8 sec
Rationale: "a 18.6 sec d = 110 + 200 = 310 m s = 60 * 5 / 18 = 50 / 3 t = 310 * 3 / 50 = 18.6 sec answer is a"
Answer: a
Question (general): excepting ‘ seldom ’ which means – rarely , infrequently and not often , is the antonym .
Options: a ) 22 , b ) 278 , c ) 267 , d ) 176 , e ) 971
Rationale: answer : d
Answer: d
Question (geometry): if y is the smallest positive integer such that 7350 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: "i just tried plugging in the numbers and found out that 6 * 7350 = 44 , 100 , which is a square of 210 c"
Answer: c
Question (general): simplify : 0.6 * 0.6 + 0.6 * 0.6
Options: a ) 0.52 , b ) 0.42 , c ) 0.48 , d ) 0.64 , e ) 0.46
Rationale: "given exp . = 0.6 * 0.6 + ( 0.6 * 6 ) = 0.36 + 0.1 = 0.46 answer is e ."
Answer: e
Question (physics): two pipes a and b can fill a tank in 24 minutes and 32 minutes respectively . if both the pipes are opened simultaneously , after how much time should b be closed so that the tank is full in 18 minutes ?
Options: a ) 7 minute , b ) 9 minute , c ) 10 minute , d ) 8 minute , e ) 11 minute
Rationale: pipe a will work for 18 minutes . suppose pipe b is closed after x minutes than we have 18 / 24 + x / 32 = 1 x = 8 minute . answer : d
Answer: d
Question (general): the average height of 35 boys in a class was calculated as 181 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 179.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 181 cm . wrong total height of 35 boys = 181 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - 60 / 35 cm = 181 cm - 1.71 cm = 179.29 cm . answer : b"
Answer: b
Question (gain): in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 280 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 700 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 280 ( 40 * 7 = 280 ) 100 % - - - - - > 700 ( 100 * 7 = 700 ) answer : option b"
Answer: b
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 990 grams per kg , what is his percent ?
Options: a ) 1.01 % , b ) 25 % , c ) 22 % , d ) 29 % , e ) 45 %
Rationale: "990 - - - 10 100 - - - ? = > 1.01 % answer : a"
Answer: a
Question (general): a factory that employs 1000 assembly line workers pays each of these workers $ 5 per hour for the first 40 hours worked during a week and 1 ½ times that rate for hours worked in excess of 40 . what was the total payroll for the assembly - line workers for a week in which 30 percent of them worked 30 hours , 50 percent worked 40 hours , and the rest worked 50 hours ?
Options: a ) $ 180,000 , b ) $ 185,000 , c ) $ 190,000 , d ) $ 200,000 , e ) $ 205,000
Rationale: "30 % of 1000 = 300 worked for 30 hours payment @ 5 / hr total payment = 300 * 30 * 5 = 45000 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 45000 + 100000 + 40000 + 15000 = 200000 hence , answer is d"
Answer: d
Question (general): 50 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 350 , e ) 660
Rationale: "5 x / 10 - x / 3 = 110 1 x / 6 = 110 x = 660 answer : e"
Answer: e
Question (geometry): the bases of a hemisphere and a cone are equal . if their heights are also equal then ratio between their curved surface area is —
Options: a ) 1 : √ 2
b ) √ 2 ∶ 1
c ) 1 : 2
d ) 2 : 1
e ) none of these
Rationale: both having same radius and the heights are same . so height of cone is same as the radius . 2 π r ^ 2 / π rl 2 r / √ ( r ^ 2 + h ^ 2 ) , where π r gets cancelled on both sides and l ^ 2 = r ^ 2 + h ^ 2 2 r / √ ( 2 r ^ 2 ) , r = h 2 / √ 2 √ 2 / 1 answer : b
Answer: b
Question (general): the average age of a , b and c is 26 years . if the average age of a and c is 29 years , what is the age of b in years ?
Options: a ) 19 , b ) 35 , c ) 20 , d ) 32 , e ) 21
Rationale: "c 20 age of b = age of ( a + b + c ) – age of ( a + c ) = 26 × 3 – 29 × 2 = 78 – 58 = 20 years"
Answer: c
Question (gain): a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 25 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: "let the total solution is 150 l with 80 l water 70 l syrup . to make 25 % syrup solution , the result solution must have 112.5 l syrup and 37.5 l syrup . therefore we are taking 32.5 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 32.5 l syrup in 69.6 l solution we started by multiplying 10 now to get to the result we need to divide by 32.5 = > amount of solution to be replaced with water = ( 69.6 / 32.5 ) = 2.14 . correct option : c"
Answer: c
Question (physics): in what time will a train 175 m long cross an electric pole , it its speed be 180 km / hr ?
Options: a ) 7.5 , b ) 6.5 , c ) 5.5 , d ) 4.5 , e ) 3.5
Rationale: "speed = 180 * 5 / 18 = 50 m / sec time taken = 175 / 50 = 3.5 sec . answer : e"
Answer: e
Question (general): 80 % of the population of a village is 64000 . the total population of the village is ?
Options: a ) 26799 , b ) 24000 , c ) 80000 , d ) 29973 , e ) 12312
Rationale: "x * ( 80 / 100 ) = 64000 x = 800 * 100 x = 80000 answer : c"
Answer: c
Question (physics): the sum of 33 consecutive integers is 3333 . what is the greatest integer in the set ?
Options: a ) 113 , b ) 115 , c ) 117 , d ) 119 , e ) 121
Rationale: "let x be the first integer in the set , then x + 32 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 32 ) = 33 x + 32 * 33 / 2 = 33 ( x + 16 ) then x + 16 = 101 x = 85 the largest integer in the set is 85 + 32 = 117 the answer is c ."
Answer: c
Question (geometry): the perimeter of a triangle is 42 cm and the inradius of the triangle is 5.0 cm . what is the area of the triangle ?
Options: a ) 128 cm 2 , b ) 36.0 cm 2 , c ) 105 cm 2 , d ) 25 cm 2 , e ) 135 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 5.0 * 42 / 2 = 105 cm 2 answer : c"
Answer: c
Question (other): find the probability that the number drawn is a factor of 50 .
Options: a ) 1 / 25 , b ) 1 / 50 , c ) 3 / 25 , d ) 3 / 50 , e ) 7 / 50
Rationale: "the factors of 50 are 1 , 2 , 5 , 10 , 25 , 50 therefore , required probability = 6 / 100 = 3 / 50 . answer : d"
Answer: d
Question (general): company c sells a line of 20 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 12000 , b ) 11000 , c ) 10000 , d ) 13000 , e ) 15000
Rationale: the average price of 20 products is $ 1,200 means that the total price of 20 products is 20 * 1,200 = $ 24,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 9 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 9 items is $ 1,000 . thus the minimum possible value of 19 products is 10 * 400 + 9 * 1,000 = $ 13,000 . therefore , the greatest possible selling price of the most expensive product is $ 24,000 - $ 13,000 = $ 11,000 . answer : b .
Answer: b
Question (general): the total age of a and b is 12 year more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 24 , c ) data inadequate , d ) none of these , e ) 34
Rationale: "solution ( a + b ) - ( b + c ) = 12 ⇔ a - c = 12 . answer a"
Answer: a
Question (geometry): the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 867 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 19 m
b ) 17 m
c ) 10 m
d ) 12 m
e ) 18 m
Rationale: answer : option b explanation : let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 867 3 b 2 = 867 b 2 = 289 = 172 ( b > 0 ) b = 17 m . answer : option b
Answer: b
Question (general): in a fuel station the service costs $ 1.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 293.85 $ , e ) 312.12 $
Rationale: "service cost of 3 van and 2 truck = 1.05 * ( 3 + 2 ) = 5.25 fuel in 3 van = 3 * 65 = 195 litre fuel in 2 trucks = 2 * 65 ( 1 + 120 / 100 ) = 286 total fuel ( van + truck ) = 481 litre total fuel cost = 481 * 0.6 = 288.6 total cost = fuel + service = 288.6 + 5.25 = 293.85 answer is d"
Answer: d
Question (gain): how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 34 % iodine solution ?
Options: a ) 35 , b ) 49 , c ) 100 , d ) 105 , e ) 136
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 34 / 100 40 x + 700 = 34 x + 1220 6 x = 820 x = 136 lts correct option : e"
Answer: e
Question (physics): a car runs 375 km in 3 hours . what ' s the car ' s speed ?
Options: a ) 124 , b ) 125 , c ) 126 , d ) 127 , e ) none
Rationale: solution : 375 ÷ 3 = 125 answer b
Answer: b
Question (physics): two men a and b working together complete a piece of work which it would have taken them respectively 12 and 18 days to complete if they worked separately . they received rs . 149.25 as their payment . find the share of a in the amount they received ?
Options: a ) rs . 89.55 , b ) rs . 59.70 , c ) rs . 85.56 , d ) rs . 88.56 , e ) none of these
Rationale: lcm of 12 and 18 is 36 no of untits of a is 3 units no of units of b is 2 units then 5 - - > 149.25 3 - - - > ? ( 3 * 149.25 ) / 5 = 89.55 answer : a
Answer: a
Question (other): a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 1 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 4 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 1 - - > e : l = 3 : 1 = 12 : 4 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 12 : 9 . thus , l : s = 4 : 9 . answer : b ."
Answer: b
Question (other): the compound ratio of 7 : 6 , 3 : 2 and 4 : 5 ?
Options: a ) 7 : 5 , b ) 1 : 87 , c ) 1 : 6 , d ) 1 : 9 , e ) 1 : 2
Rationale: 7 / 6 * 3 / 2 * 4 / 5 = 7 / 5 7 : 5 answer : a
Answer: a
Question (general): how many times digit 5 is used while writing numbers from 1 to 500 ?
Options: a ) 103 , b ) 98 , c ) 94 , d ) 105 , e ) 100
Rationale: "in 1 to 100 there are 20 in 100 to 200 there are 20 in 200 to 300 there are 20 in 300 to 400 there are 20 in 400 to 500 there are 20 so total is 100 correct option : e"
Answer: e
Question (gain): there are 50 students in a class . if 14 % are absent on a particular day , find the number of students present in the class .
Options: a ) 43 , b ) 36 , c ) 28 , d ) 129 , e ) 11
Rationale: "number of students absent on a particular day = 14 % of 50 i . e . , 14 / 100 × 50 = 7 therefore , the number of students present = 50 - 7 = 43 students . answer : a"
Answer: a
Question (physics): excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 31 kmph . of how many minutes does the train stop per hour ?
Options: a ) 18.6 , b ) 27 , c ) 12 , d ) 121 , e ) 28
Rationale: "explanation : t = 14 / 45 * 60 = 18.6 answer : option a"
Answer: a
Question (physics): audrey 4 hours to complete a certain job . ferris can do the same job in 3 hours . audrey and ferris decided to collaborate on the job , working at their respective rates . while audrey worked continuously , ferris took 2 breaks of equal length . if the two completed the job together in 2 hours , how many minutes long was each of ferris ’ breaks ?
Options: a ) 5 , b ) 15 , c ) 17 , d ) 20 , e ) 25
Rationale: "audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 2 breaks = . 3 / 2 = . 15 hrs = 15 m so answer is b ) 15 mins"
Answer: b
Question (general): 5358 x 71 = ?
Options: a ) 273762 , b ) 283758 , c ) 383298 , d ) 273258 , e ) 380418
Rationale: "e 5358 x 71 = 5358 x ( 70 + 1 ) = 5358 x 50 + 5358 x 1 = 375060 + 5358 = 380418"
Answer: e
Question (physics): a swimmer can swim in still water at 4 km / h . if the speed of the water current is 1 km / h , how many hours will the swimmer take to swim against the current for 6 km ?
Options: a ) 1.2 , b ) 1.4 , c ) 1.6 , d ) 1.8 , e ) 2
Rationale: the swimmer can swim against the current at a speed of 4 - 1 = 3 km / h . the time it will take is 6 / 3 = 2 hours . the answer is e .
Answer: e