Cheukting/mathqa huggingface dataset:
Question (physics): gretzky street begins at orr street and runs directly east for 5.6 kilometers until it ends when it meets howe street . gretzky street is intersected every 350 meters by a perpendicular street , and each of those streets other than orr street and howe street is given a number beginning at 1 st street ( one block east of orr street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of howe street . what is the highest - numbered street that intersects gretzky street ?
Options: a ) 12 th , b ) 13 th , c ) 14 th , d ) 15 th , e ) 16 th
Rationale: 5.6 km / 350 m = 16 . however , the street at the 5.6 - km mark is not 16 th street ; it is howe street . therefore , the highest numbered street is 15 th street . the answer is d .
Answer: d
Question (general): the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.9 kg . the weight of the new student is ?
Options: a ) 10.6 kg , b ) 10.8 kg , c ) 11 kg , d ) 13 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.9 - 19 x 15 ) kg = 13 kg . correct option : d"
Answer: d
Question (general): the difference between a two - digit number and the number obtained by interchanging the digits is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 4 , b ) 8 , c ) 16 , d ) 12 , e ) 14
Rationale: "since the number is greater than the number obtained on reversing the digits , so the ten ' s digit is greater than the unit ' s digit . let ten ' s and unit ' s digits be 2 x and x respectively . then , ( 10 x 2 x + x ) - ( 10 x + 2 x ) = 36 9 x = 36 x = 4 . required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer : b"
Answer: b
Question (general): excluding stoppages , the average speed of a bus is 80 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 30 min
Rationale: "in 1 hr , the bus covers 80 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 80 - 40 ) km i . e 40 km at 80 km / hr . stoppage time = 40 / 80 hrs = 30 min answer : e"
Answer: e
Question (general): what is the smallest integer n for which 25 ^ n > 5 ^ 12 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to solve , we want to get the bases the same . thus we need to break 25 ^ n into prime factors . 25 ^ n = ( 5 ^ 2 ) ^ n = 5 ^ ( 2 n ) ( remember that when we have a power to a power , we multiply the exponents . ) we can use the new value in the given inequality : 5 ^ ( 2 n ) > 5 ^ 12 since we have the same bases on either side of the inequality we can drop the bases and set up an equation involving just the exponents . 2 n > 12 n > 6 because n is greater than 6 , the smallest integer that satisfies the inequality 25 ^ n > 5 ^ 12 is 7 . the answer is b ."
Answer: b
Question (other): a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 4 , and the ratio of soap to salt is five times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 26 : 64 , b ) 64 : 9 , c ) 9 : 64 , d ) 9 : 60 , e ) 20 : 64
Rationale: "water : soap = 3 : 4 soap : salt = 15 : 20 = > for 15 soap , salt = 20 = > for 4 soap , salt = ( 20 / 15 ) * 4 = 80 / 15 = 16 / 3 so , water : soap : salt = 3 : 4 : 16 / 3 = 9 : 12 : 16 after open container , water : soap : salt = 2.25 : 12 : 16 so , water : salt = 2.25 : 16 = 9 : 64 answer : c"
Answer: c
Question (gain): by selling an article for $ 110 , a person gains $ 10 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 110 gain = $ 10 c . p . = 110 - 10 = 100 gain % = 10 / 100 * 100 % = 10 % answer is e"
Answer: e
Question (general): tough and tricky questions : functions . let a be a positive integer . let n # a equal n ^ ( 2 a ) if a is odd and n ^ ( 3 a ) if a is even . then ( 4 # 3 ) + ( 3 # 4 ) – ( 3 # 3 ) is equal to
Options: a ) 64 , b ) 82 , c ) 128 , d ) 512 , e ) 4096
Rationale: answer : 4 ^ 6 + 3 ^ 6 - 3 ^ 6 = 4 ^ 6 = 4096 ans e
Answer: e
Question (general): find the smallest number of 6 digits which is exactly divisible by 111 .
Options: a ) 100011 , b ) 111111 , c ) 101111 , d ) 201111 , e ) 211111
Rationale: smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 option a
Answer: a
Question (gain): a company recently conducted a survey and found that 35,000 of its customers live in rural areas . if the number of customers who live in urban areas is 140 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 78,000 , b ) 80,000 , c ) 82,000 , d ) 84,000 , e ) 86,000
Rationale: "the number of customers in urban areas is 35,000 + 1.4 * 35,000 = 84,000 . the answer is d ."
Answer: d
Question (general): in plutarch enterprises , 60 % of the employees are marketers , 20 % are engineers , and the rest are managers . marketers make an average salary of $ 50,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 290,000 , e ) $ 340,000
Rationale: "for sake of ease , let ' s say there are 10 employees : 6 marketers , 2 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 6 * $ 50,000 ) and the engineers ( 2 * $ 80,000 ) > > > $ 800,000 - $ 300,000 - $ 160,000 = $ 340,000 . the correct answer is e ."
Answer: e
Question (physics): two stations a and b are 20 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: "suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 20 45 x = 45 x = 1 . so , they meet at 8 a . m . answer : option e"
Answer: e
Question (probability): a bag contains 6 red , 3 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 6 + 3 + 4 = 13 n ( s ) = 13 c 3 = 286 n ( e ) = 6 c 1 * 3 c 1 * 4 c 1 = 72 probability = 72 / 286 = 1 / 4 answer is d"
Answer: d
Question (geometry): a crate measures 2 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 2 for the surface 8 * 12 face . volume = 8 pi answer a"
Answer: a
Question (other): if 0.3 of a number is equal to 0.06 of another number , the ratio of the numbers i
Options: a ) 3 : 15 , b ) 1 : 2 , c ) 3 : 20 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.3 a = 0.06 b â ‡ ” a / b = 0.06 / 0.30 = 6 / 30 = 3 / 15 . â ˆ ´ a : b = 3 : 15 . answer a"
Answer: a
Question (general): if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 93 , what is the value of x ?
Options: a ) 95 , b ) 91 , c ) 102 , d ) 101 , e ) 85
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 93 x = 91 answer : b"
Answer: b
Question (physics): a person crosses a 1800 m long street in 12 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 4.5 , c ) 4.8 , d ) 5.4 , e ) 9
Rationale: "speed = 1800 / ( 12 x 60 ) m / sec = 2.5 m / sec . converting m / sec to km / hr = 2.5 x ( 18 / 5 ) km / hr = 9 km / hr . answer : e"
Answer: e
Question (gain): calculate the amount that an investor needs to be invest to earn $ 1023 in interest in 24 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 12 % compounded semi - annually ?
Options: a ) 3980 , b ) 3600 , c ) 3700 , d ) 3800 , e ) 3900
Rationale: "the approach is substitution , our interest requirement is $ 1023 after 24 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields $ 1023 in 24 months 3900 yielded $ 1023 using the formula a = p ( 1 + r / n ) nt hence answer is e"
Answer: e
Question (physics): a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates c apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: "number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates c / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c"
Answer: c
Question (physics): a person can row at 9 kmph and still water . he takes 4 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 33 , b ) 77 , c ) 26 , d ) 28 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 4.5 = > x / 10 + x / 8 = 9 / 2 = > ( 4 x + 5 x ) / 40 = 9 / 2 = > x = 20 km . answer : e"
Answer: e
Question (physics): the distance from steve ' s house to work is 35 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 17.5
Rationale: time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 35 km = > speed = 17.5 kmph e
Answer: e
Question (geometry): the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the 4 walls of the room at rs . 3 per square feet if there is one door of dimensions 6 feet * 3 feet and 3 windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4528 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 2718
Rationale: area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 3 = rs . 2718 answer : e
Answer: e
Question (general): the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively , is :
Options: a ) 123 , b ) 127 , c ) 235 , d ) 305 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1657 - 6 ) and ( 2037 - 5 ) = h . c . f . of 1651 and 2032 = 127 . answer : b"
Answer: b
Question (general): in an examination , 300 students appeared . out of these students ; 28 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 33 , b ) 37 , c ) 54 , d ) 99 , e ) 01
Rationale: "the number of students with first division = 28 % of 300 = 28 / 100 × 300 = 8400 / 100 = 84 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 84 + 162 ) = 54 answer : c"
Answer: c
Question (general): the average of first 13 even numbers is ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "sum of 13 even numbers = 13 * 14 = 110 average = 182 / 13 = 14 answer : e"
Answer: e
Question (physics): a 250 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 41.1 sec , b ) 20.2 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 250 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 770 m time = distance / speed = 770 x 18 / ( 5 x 55 ) = 50.4 sec ans is : d"
Answer: d
Question (gain): what is 15 percent of 54 ?
Options: a ) 7.3 , b ) 8.1 , c ) 9.5 , d ) 10.2 , e ) 11.6
Rationale: "( 15 / 100 ) * 54 = 8.1 the answer is b ."
Answer: b
Question (gain): a sum of money at simple interest amount to rs 720 after 2 years and to rs 1020 after a further period of 5 years . the sum is :
Options: a ) 600 , b ) 450 , c ) 650 , d ) 500 , e ) 550
Rationale: simple interest for 5 year = rs . ( 1020 - 720 ) = rs . 300 . simple interest for 2 year = rs . ( 300 / 5 × 2 ) = rs . 120 . principal = rs . ( 720 - 120 ) = rs . 600 . answer : a
Answer: a
Question (gain): an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 2 / 3 % , then the amount invested in each share was ?
Options: a ) 23777 , b ) 35000 , c ) 29977 , d ) 26777 , e ) 19871
Rationale: let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 29 / 3 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) / 100 = 29000 / 3 = 9700 ( 9 x + 1100000 - 11 x ) = 970000 x = 65000 sum invested at 9 % = rs . 65000 sum invested at 11 % = rs . ( 100000 - 65000 ) = rs . 35000 . answer : b
Answer: b
Question (gain): a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 100 more . what was the sum ?
Options: a ) s . 350 , b ) s . 700 , c ) s . 200 , d ) s . 600 , e ) s . 500
Rationale: "at 5 % more rate , the increase in s . i for 10 years = rs . 100 ( given ) so , at 5 % more rate , the increase in si for 1 year = 100 / 10 = rs . 10 / - i . e . rs . 10 is 5 % of the invested sum so , 1 % of the invested sum = 10 / 5 therefore , the invested sum = 10 × 100 / 5 = rs . 200 answer : c"
Answer: c
Question (gain): a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 6,000 meters of fabric ?
Options: a ) $ 9,300 , b ) $ 10,400 , c ) $ 11,500 , d ) $ 12,600 , e ) $ 13,700
Rationale: "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 2500 = $ 4650 the total price is $ 4000 + $ 2850 + $ 4650 = $ 11,500 the answer is c ."
Answer: c
Question (probability): there are 6 red balls and 4 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that all 3 balls selected are blue balls ?
Options: a ) 1 / 18 , b ) 1 / 24 , c ) 1 / 30 , d ) 1 / 36 , e ) 1 / 48
Rationale: the number of ways of choosing 3 balls from the jar is 10 c 3 = 120 . the number of ways of choosing 3 blue balls is 4 c 3 = 4 . p ( 3 blue balls ) = 4 / 120 = 1 / 30 . the answer is c .
Answer: c
Question (general): in plutarch enterprises , 70 % of the employees are marketers , 10 % are engineers , and the rest are managers . marketers make an average salary of $ 50,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 370,000 , e ) $ 320,000
Rationale: for sake of ease , let ' s say there are 10 employees : 7 marketers , 1 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 50,000 ) and the engineers ( $ 80,000 ) > > > $ 800,000 - $ 350,000 - $ 80,000 = $ 370,000 . the correct answer is d .
Answer: d
Question (physics): working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel eight times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 8 and w = 8 s then we have 1 / ( 8 * s ) + 1 / s = 1 / 8 < = > 9 / ( 8 * s ) = 1 / 8 < = > s = 9 ans : d
Answer: d
Question (physics): a boat running up stram takes 6 hours to cover a certain distance , while it takes 7 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
Options: a ) 2 : 3 , b ) 5 : 6 , c ) 4 : 5 , d ) 13 : 1 , e ) 8 : 1
Rationale: "explanation : let speed of boat is x km / h and speed stream is y km / hr 6 ( x + y ) = 7 ( x - y ) 6 x + 6 y = 7 x - 7 y 13 y = x 13 y = x x / y = 13 / 1 13 : 1 answer : option d"
Answer: d
Question (general): company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.6 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.6 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 32 hours . total hours = 72 then the fraction would be 32 / 72 = 4 / 9 . therefore answer e
Answer: e
Question (physics): a car traveled 75 % of the way from town a to town b at an average speed of 50 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 60 miles per hour . what is s ?
Options: a ) 150 , b ) 200 , c ) 250 , d ) 300 , e ) 237.5
Rationale: "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 50 = 1.5 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 60 = 1.5 + t » 100 / 60 = 1.5 + t » 2.5 = 1.5 + t » t = 0.1667 back to 2 nd part of the trip formula : 25 / s = 0.1667 » s = 150 ans a"
Answer: a
Question (general): when positive integer n is divided by positive integer j , the remainder is 12 . if n / j = 134.02 , what is value of j ?
Options: a ) 300 , b ) 600 , c ) 500 , d ) 112 , e ) 620
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.02 , the decimal part of the decimal quotient , must equal the remainder , 12 , divided by the divisor j . 0.02 = 12 / j 0.02 * j = 12 j = 12 / 0.02 = 1200 / 2 = 600 / 1 = 600 so j = 600 , answer = b ."
Answer: b
Question (physics): joshua and jose work at an auto repair center with 5 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 21 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 7 probability of chosing jose second = 1 / 6 total = 1 / 42 probability of chosing jose first = 1 / 7 probability of chosing josh second = 1 / 6 total = 1 / 42 final = 1 / 42 + 1 / 42 = 1 / 21 a"
Answer: a
Question (general): in the coordinate plane , points ( x , 2 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 2 ) = ( 4 , 2 ) and ( 10 , y ) = ( 10,5 ) - - > 4 + 5 = 2 + 5 = 9 . answer : c ."
Answer: c
Question (general): the average score of a cricketer in 2 matches is 20 and in other 3 matches is 30 . then find the average score in all the 5 matches ?
Options: a ) 26 , b ) 27 , c ) 30 , d ) 35 , e ) 42
Rationale: "average in 5 matches = ( 2 * 20 + 3 * 30 ) / 2 + 3 = 40 + 90 / 5 = 130 / 5 = 26 answer is a"
Answer: a
Question (gain): 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 10 mat - weavers in 10 days ?
Options: a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 16
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 10 : : 4 : x days 4 : 10 4 * 4 * x = 10 * 10 * 4 x = ( 10 * 10 * 4 ) / ( 4 x 4 ) x = 25 . answer is a ."
Answer: a
Question (general): rahul played weel in this season . his current batting averagge is 51 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: "51 x + 78 = 54 ( x + 1 ) = > 3 x = 24 = > x = 8 answer : a"
Answer: a
Question (gain): in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 14 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 112 % , e ) 138 %
Rationale: "0,112 r = x / 100 * 0.1 r answer d"
Answer: d
Question (other): a garrison of 400 men had a provision for 31 days . after 25 days 320 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 30 days , c ) 10 days , d ) 16 days , e ) 18 days
Rationale: "400 - - - 31 400 - - - 6 80 - - - ? 400 * 6 = 80 * x = > x = 30 days . answer : b"
Answer: b
Question (physics): a jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . the train is running at 45 kmph in the same direction . how much time does it take for the train to pass the jogger ?
Options: a ) 46 , b ) 36 , c ) 18 , d ) 22 , e ) 23
Rationale: explanation : distance to be covered = 240 + 120 = 360 m relative speed = 36 km / hr = 36 × 10 / 36 = 10 m / s time = distance / speed = 360 / 10 = 36 seconds answer : option b
Answer: b
Question (other): the dimensions of a field are 10 m by 10 m . a pit 5 m long , 5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?
Options: a ) 2 m , b ) 2.5 m , c ) 1.5 m , d ) 1.25 m , e ) 1 m
Rationale: "the volume of the earth removed is 5 * 5 * 3 = 75 m ^ 3 . the remaining area of the field is 10 * 10 - 5 * 5 = 75 m ^ 2 . 75 m ^ 3 of the earth evenly spread over the area of 75 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 75 / 75 = 1 m . answer : e"
Answer: e