Cheukting/mathqa huggingface dataset:
Question (physics): two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 4 hours respectively after meeting each other . if the train a travels at 110 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 165 , c ) 120 , d ) 80 , e ) 100
Rationale: if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 9 ) = 2 / 3 this gives us that the ratio of the speed of a : speed of b as 2 : 3 . since speed of a is 110 kmph , speed of b must be 110 * ( 3 / 2 ) = 165 kmph answer b
Answer: b
Question (general): a man can row 3.9 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.3 , d ) 1.5 , e ) 1.1
Rationale: "speed of boat in still water ( b ) = 3.9 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.3 km / hr . answer : c"
Answer: c
Question (general): a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 27 , what is the total amount ?
Options: a ) 115 , b ) 116 , c ) 117 , d ) 118 , e ) 119
Rationale: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 27 39 - - - ? = > 117 answer : c"
Answer: c
Question (general): if a ( a + 4 ) = 21 and b ( b + 4 ) = 21 , where a ≠ b , then a + b =
Options: a ) − 4 , b ) − 5 , c ) 2 , d ) 46 , e ) 48
Rationale: "i . e . if a = 3 then b = - 7 or if a = - 7 then b = 3 but in each case a + b = - 7 + 3 = - 4 answer : option a"
Answer: a
Question (physics): the length of a train and that of a platform are equal . if with a speed of 90 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is :
Options: a ) 377 , b ) 267 , c ) 268 , d ) 750 , e ) 271
Rationale: speed = [ 90 * 5 / 18 ] m / sec = 25 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 25 è x = 25 * 60 / 2 = 750 . answer : d
Answer: d
Question (general): the average weight of 7 person ' s increases by 6.2 kg when a new person comes in place of one of them weighing 76 kg . what might be the weight of the new person ?
Options: a ) 160 kg , b ) 175 kg , c ) 180.7 kg , d ) 119.4 kg , e ) 190.8 kg
Rationale: "total weight increased = ( 7 x 6.2 ) kg = 43.4 kg . weight of new person = ( 76 + 43.4 ) kg = 119.4 kg option d"
Answer: d
Question (other): the cost of 3 pens and 5 pencils is rs . 100 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 150 , e ) none of these
Rationale: "explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 100 15 x + 5 x = rs . 100 x = 100 / 20 = 5 : . cost of 1 pen = 5 x = 5 x 5 = 25 : . cost of 12 pens , i . e . ( one dozen ) = 25 x 12 = rs . 300 answer : option c"
Answer: c
Question (gain): the compound interest earned on a sum for the second and the third years are $ 1200 and $ 1272 respectively . what is the rate of interest ?
Options: a ) 4 % , b ) 6 % , c ) 8 % , d ) 10 % , e ) 12 %
Rationale: "1272 - 1200 = 72 is the rate of interest on $ 1200 for one year . the rate of interest = ( 100 * 72 ) / ( 1200 ) = 6 % the answer is b ."
Answer: b
Question (general): 10 camels cost as much as 24 horses , 26 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ?
Options: a ) rs . 6184.5 , b ) rs . 4184.5 , c ) rs . 5700 , d ) rs . 4284.5 , e ) rs . 5184.5
Rationale: "cost of the camel = p 10 camels = 24 horses 26 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 170000 p = rs . [ ( 24 * 4 * 4 * 170000 ) / ( 10 * 26 * 6 * 10 ) ] p = rs . ( 65280000 / 15600 ) = > p = rs . 4184.5 answer : b"
Answer: b
Question (physics): if the perimeter of a rectangular garden is 680 m , its length when its breadth is 82 m is ?
Options: a ) 286 m , b ) 899 m , c ) 200 m , d ) 166 m , e ) 258 m
Rationale: "2 ( l + 82 ) = 680 = > l = 258 m answer : e"
Answer: e
Question (general): what is the least number . which should be added to 0.0478 to make it a perfect square ?
Options: a ) 0.0002 , b ) 0.0004 , c ) 0.0006 , d ) 0.0008 , e ) 0.001
Rationale: "0.0478 + 0.0006 = 0.0484 ( 0.22 ) ^ 2 answer : c"
Answer: c
Question (general): the average score of a cricketer for 7 matches is 56 runs . if the average for first 4 matches is 46 , then average for last 3 matches is
Options: a ) 33.25 , b ) 32.25 , c ) 65 , d ) 67 , e ) 69
Rationale: explanation : = ( 56 × 7 ) − ( 46 × 4 ) / 3 = ( 392 − 184 ) / 3 = 69 answer : option e
Answer: e
Question (physics): if in a cricket one day match , there were no wide balls , no wides , no extras and no overthrows . what is the maximum number of runs that a batsman can score in an ideal case scenario ?
Options: a ) 2663 , b ) 1653 , c ) 3693 , d ) 4253 , e ) 2653
Rationale: b 1653 for an ideal case , the batsman will hit a six on each ball . but if he hits six on the last ball of the over , the strike will change in the next over . thus , the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over . thus the total runs that he can score in each over : 6 * 5 + 3 = 33 but this will have to go like it only till the 49 th over . in the last over , he can hit a six in the last ball as well as that will be the last ball of the match . thus runs for the last over will be 6 * 6 = 36 . hence the maximum runs = 33 * 49 + 36 = 1653
Answer: b
Question (general): how many multiples of 10 are there between 11 and 1001 ?
Options: a ) 98 , b ) 99 , c ) 100 , d ) 97 , e ) 95
Rationale: "10 * 2 = 20 10 * 100 = 1000 total multiples = ( 100 - 2 ) + 1 = 99 answer b"
Answer: b
Question (general): a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: "rom the beginning ; initially milk to water is 12 l : 8 l remove half 6 - 4 add 10 l milk 16 - 4 remove half 8 - 2 add 10 l milk 18 - 2 18 : 2 = 9 : 1 answer : b"
Answer: b
Question (physics): 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days x do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time x = 3 days to finish the task imo a"
Answer: a
Question (gain): if an investor puts $ 600 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
Options: a ) $ 661.50 , b ) $ 663.50 , c ) $ 665.50 , d ) $ 667.50 , e ) $ 669.50
Rationale: "1.05 * 1.05 * 600 = $ 661.50 the answer is a ."
Answer: a
Question (general): a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 6 is
Options: a ) 3 , b ) 7 , c ) 21 , d ) 189 , e ) 198
Rationale: in that case , the sophie prime numbers greater than 6 are 7 , 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be d
Answer: d
Question (general): the difference of two numbers is 1335 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 264
Rationale: "let the smaller number be x . then larger number = ( x + 1335 ) . x + 1335 = 6 x + 15 5 x = 1320 x = 264 smaller number = 264 . answer e"
Answer: e
Question (gain): dawson has to secure 30 % marks to clear his exam of class 8 th . he got 30 marks and failed by 36 marks . what is the maximum marks ?
Options: a ) 180 , b ) 190 , c ) 200 , d ) 210 , e ) 220
Rationale: e 220 to pass the exam ravish needs 30 + 36 = 66 marks . = > ( 66 / 30 ) * 100 = 220
Answer: e
Question (general): if the price of a book is first decreased by 15 % and then increased by 10 % , then the net change in the price will be :
Options: a ) 10 , b ) 388 , c ) 6.5 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . decreased by 15 % = 85 then increased 10 % on rs 85 = 85 + 8.5 = 93.5 net change in price = 100 - 93.5 = 6.5 answer : c"
Answer: c
Question (general): a warehouse is labeling computer inventory with 5 - digit codes . each code is to consist of 4 digits between the numbers 0 and 9 . the manager is debating whether to allow any 5 - digit codes to have leading zero ' s before a non - zero number is used . if not allowed , then numbers like 0025 cannot be used . the manager wants to measure the magnitude of the number of 5 - digit code possibilities that are lost if he disallows the use of leading zero ' s . how many such codes would be lost ?
Options: a ) 981 , b ) 1000 , c ) 1011 , d ) 10000 , e ) 1110
Rationale: the number of codes possible if leading zero is allowed = 10 * 10 * 10 * 10 * 10 = 10 ^ 5 the number of codes possible if leading zero is not allowed = 9 * 10 * 10 * 10 * 10 = 9 * 10 ^ 4 the difference = 10 ^ 5 - 9 * 10 ^ 4 = 10 ^ 4 ( 10 - 9 ) = 10 ^ 4 . answer : d . similar questions to practice : hope it helps .
Answer: d
Question (physics): tim and é lan are 90 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 30 miles . , b ) 35 miles . , c ) 45 miles . , d ) 60 miles . , e ) 65 miles .
Rationale: "in 1 st hour : relative speed of the two will be 10 + 5 = 15 miles / hour . as they move towards each other , the distance between them reduces by 15 miles . distance left between them : 90 - 15 = 75 miles . in 2 nd hour : speed of tim : 20 mph , that of elan : 10 mph . relative speed of the two will be 20 + 10 = 30 miles / hour . as they move towards each other , the distance between them reduces by 30 miles . distance left between them : 75 - 30 = 45 miles . in 3 rd hour : speed of tim : 40 mph , that of elan : 20 mph . relative speed of the two will be 40 + 20 = 60 miles / hour . now in order to cover the remaining distance of 45 miles . they will take : ( 45 / 60 ) hrs . = ( 3 / 4 ) hour . distance travelled by tim ? in first hour : 1 hour * ( 10 miles per hour ) = 10 miles in second hour : 1 hour * ( 20 miles per hour ) = 20 miles in third hour : ( 3 / 4 ) hour * ( 40 miles per hour ) = 30 miles total distance travelled : 10 + 20 + 30 = 60 miles . d is the answer"
Answer: d
Question (general): every year an amount increases by 1 / 9 th of itself . how much will it be after two years if its present value is rs . 64000 ?
Options: a ) 81000 , b ) 81007 , c ) 81008 , d ) 79012.3 , e ) 81022
Rationale: "64000 * 10 / 9 * 10 / 9 = 79012.3 answer : d"
Answer: d
Question (gain): if c is 20 % of a and 10 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 200 %
Rationale: answer = e 20 a / 100 = 10 b / 100 b = 20 a / 10 = 200 a / 100 = 200 %
Answer: e
Question (general): an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 3600 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 4500 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: "4 - - - 3600 5 - - - ? = > 4500 answer : b"
Answer: b
Question (geometry): the area of a triangle will be when a = 1 m , b = 2 m , c = 5 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 1
Rationale: s = ( 1 + 2 + 5 ) / 2 = 4 answer : c
Answer: c
Question (physics): a and b can do a work in 25 days and 10 days respectively . a starts the work and b joins him after 2 days . in how many days can they complete the remaining work ?
Options: a ) 4.28 days , b ) 4.38 days , c ) 5.28 days , d ) 6.28 days , e ) 2.28 days
Rationale: "work done by a in 2 days = 2 / 5 remaining work = 3 / 5 work done by both a and b in one day = 1 / 25 + 1 / 10 = 7 / 50 remaining work = 3 / 5 * 50 / 7 = 4.28 days . answer : a"
Answer: a
Question (gain): a grocery store priced a gallon of milk at 25 % above the wholesale price of $ 4 . if a customer comes in with a coupon for 5 % off milk , how much does that customer pay ?
Options: a ) $ 4.95 , b ) $ 4.75 , c ) $ 5.05 , d ) $ 4.50 , e ) $ 5.25
Rationale: wholesale cost of milk = $ 4 milk was priced at 25 % above $ 4 = $ 5 % discount given by coupon = 5 % customer paid = . 95 * 5 = $ 4.75 answer b
Answer: b
Question (general): a number is doubled and 9 is added . if resultant is trebled , it becomes 81 . what is that number
Options: a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 81 = > 2 x + 9 = 27 = > x = 9 answer : option a"
Answer: a
Question (general): what is the average of odd numbers from 1 to 79 ?
Options: a ) 30 , b ) 25 , c ) 35 , d ) 40 , e ) 45
Rationale: "sum of n odd natural number is given by , sum of n odd natural numbers = n * n average of n odd natural numbers is given by , = ( n * n ) / n = n . here , n = number of terms = ( 79 + 1 ) / 2 = 40 . so , required average = 40 . answer : d"
Answer: d
Question (general): 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 120000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 4800 , e ) s . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 120000 p = rs . [ ( 24 * 4 * 4 * 120000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 46080000 / 9600 ) = > p = rs . 4800 answer : d"
Answer: d
Question (gain): in an exam ashley secured 332 marks . if she secured 83 % makes , find the maximum marks
Options: a ) 133 , b ) 376 , c ) 377 , d ) 400 , e ) 377
Rationale: let the maximum marks be m . ashley ’ s marks = 83 % of m ashley secured 332 marks therefore , 83 % of m = 332 ⇒ 83 / 100 × m = 332 ⇒ m = ( 332 × 100 ) / 83 ⇒ m = 33200 / 83 ⇒ m = 400 therefore , ashley got 332 marks out of 400 marks . answer : d
Answer: d
Question (general): a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is
Options: a ) 20 years , b ) 21 years , c ) 22 years , d ) 24 years , e ) none of these
Rationale: "explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years = > ( x + 24 ) + 2 = 2 ( x + 2 ) = > x + 26 = 2 x + 4 so , x = 22 option c"
Answer: c
Question (general): a number when divided by 100 leaves 11 as a remainder . what will be the remainder if the number is divided by 11 ?
Options: a ) 11 , b ) 1 , c ) 2 , d ) 3 , e ) 21
Rationale: "let 100 + 11 = 111 111 divided evenly by eleven leaves a remainder of one . correct answer is b ."
Answer: b
Question (general): if 3 x = 8 y = z , what is x + y , in terms of z ?
Options: a ) z / 2 , b ) 2 z , c ) 11 z / 24 , d ) 3 z / 5 , e ) z / 9
Rationale: "3 x = 8 y = z x = z / 3 and y = z / 8 x + y = z / 3 + z / 8 = 11 z / 24 answer is c"
Answer: c
Question (physics): a train requires 10 seconds to pass a pole while it requires 35 seconds to cross a stationary train which is 500 mtrs long . find the speed of the train .
Options: a ) 68 kmph , b ) 70 kmph , c ) 72 kmph , d ) 60 kmph , e ) 50 kmph
Rationale: "in 10 s the train crosses the pole and in 35 sec the train crosses one more stationary train in 25 sec the train travels a distance of 500 mtrs speed = 500 / 25 = 20 m / s = 20 ( 3600 / 1000 ) = 20 * 18 / 5 = 72 kmph answer : c"
Answer: c
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 12000 x 7 ) + 6000 ( x - 7 ) 2000 x = 42000 x = 21 . answer b"
Answer: b
Question (physics): the radius of a wheel is 22.6 cm . what is the distance covered by the wheel in making 750 resolutions ?
Options: a ) 754 m , b ) 704 m , c ) 1055.04 m , d ) 1058.04 m , e ) 204 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 750 resolutions . = 750 * 2 * 22 / 7 * 22.6 = 105504 cm = 1055.04 m answer : c"
Answer: c
Question (gain): car z travels 45 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
Options: a ) 320 , b ) 360 , c ) 400 , d ) 408.3 , e ) 440
Rationale: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 45 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 36 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 36 miles / gallon * 10 gallons = 360 miles . answer b ."
Answer: b
Question (other): evaluate : log 3 27
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "solution log 3 27 = n = 3 n = 27 = 33 n ‹ = › 3 . answer a"
Answer: a
Question (physics): how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 140 m length ?
Options: a ) 82.1 sec . , b ) 12.5 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 140 = 250 m . required time = 250 / 20 = 12.5 sec . answer : b"
Answer: b
Question (general): the average of 12 result is 55 . average of the first 6 of them is 42 and that of the last 6 is 48 . find the 8 th result ?
Options: a ) 35 , b ) 564 , c ) 526 , d ) 48 , e ) 50
Rationale: "sum of all the 12 results = 12 * 55 = 660 sum of the first 6 of them = 6 * 42 = 252 sum of the last 6 of them = 6 * 48 = 288 so , the 8 th number = 600 + 252 - 288 = 564 . b"
Answer: b
Question (gain): 15 % of 75 is the same as vx % of 450 . find x .
Options: a ) 1 , b ) 2.5 , c ) 3 , d ) 4 , e ) 5
Rationale: 15 % of 75 = 11.25 450 * x / 100 = 11.25 x = 2.5 answer : b
Answer: b
Question (physics): a fill pipe can fill 1 / 2 of cistern in 25 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 10 min , b ) 15 min , c ) 20 min , d ) 25 min , e ) 30 min
Rationale: "required time = 25 * 2 * 1 / 2 = 25 minutes answer is d"
Answer: d
Question (general): a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 520 ?
Options: a ) 259 , b ) 498 , c ) 676 , d ) 823 , e ) 1,002
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 520 y = 2 x + 2 518 = 2 x x = 259 answer : a . 259"
Answer: a
Question (gain): if 15 % of 40 is greater than 25 % of a number by 2 , the number is
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "explanation : 15 / 100 * 40 - 25 / 100 * x = 2 or x / 4 = 4 so x = 16 option b"
Answer: b
Question (general): john purchased 1325 large bottles at $ 1.89 per bottle and 750 small bottles at $ 1.38 per bottle . what was the approximate average price paid per bottle ?
Options: a ) $ 1.63 , b ) $ 1.71 , c ) $ 1.68 , d ) $ 1.72 , e ) $ 1.76
Rationale: "( 1325 * 1.89 + 750 * 1.38 ) / ( 1325 + 750 ) = ~ 1.71 option ( b )"
Answer: b
Question (general): find the smallest number of six digits exactly divisible by 25 , 35,45 and 15 .
Options: a ) 100555 , b ) 100775 , c ) 100885 , d ) 100995 , e ) 100665
Rationale: "smallest number of six digits is 100000 . required number must be divisible by l . c . m . of 25,35 , 45,15 i . e 1575 , on dividing 100000 by 1575 , we get 800 as remainder . therefore , required number = 100000 + ( 1575 â € “ 800 ) = 100775 . answer is b ."
Answer: b
Question (physics): the moon revolves around the earth at a speed of approximately 1.05 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 62.5 , d ) 3,780 , e ) 3,672
Rationale: moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.05 * 3600 = 3780 kilometers per hour . option d is correct
Answer: d
Question (physics): the speed of a car is 100 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 80 , d ) 54 , e ) 15
Rationale: "s = ( 100 + 60 ) / 2 = 80 kmph answer : c"
Answer: c
Question (general): a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 1446 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 32200 , b ) 41897 , c ) 58799 , d ) 60000 , e ) 62782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 1446 p = 60000 answer : d"
Answer: d
Question (gain): a man buys a cycle for rs . 2000 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) 1800 , b ) 1420 , c ) 1430 , d ) 1440 , e ) 1540
Rationale: "s . p . = 90 % of rs . 2000 = 90 / 100 x 2000 = rs . 1800 answer : a"
Answer: a
Question (physics): a runs twice as fast as b and gives b a start of 71 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 80 m . , c ) 150 m . , d ) 142 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 71 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 71 m is 71 / 1 = 71 m so the total time taken by a and b to reach = 2 * 71 = 142 m answer : d"
Answer: d
Question (gain): a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of b .
Options: a ) 240 , b ) 288 , c ) 277 , d ) 390 , e ) 361
Rationale: "( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 13 / 21 * 630 = 390 answer : d"
Answer: d
Question (gain): a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 500 , find the original price per kg ?
Options: a ) s . 12.7 , b ) s . 12.4 , c ) s . 12.5 , d ) s . 12.1 , e ) s . 12.9
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 500 - - - 80 ? - - - 2 = > rs . 12.5 answer : c"
Answer: c
Question (general): evaluate : 59 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 51 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 59 - 12 * 3 * 2 = 59 - 8 = 51 correct answer b"
Answer: b