Cheukting/mathqa huggingface dataset:
Question (geometry): if the length of the longest chord of a certain circle is 20 , what is the radius of that certain circle ?
Options: a ) 2.5 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 20 = 2 * 10 so radius of the circle = 10 correct answer - c"
Answer: c
Question (gain): carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 6 % . what is the approximate interest he pays annually ?
Options: a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 12000
Rationale: "an easy way too attempt this is by approximation : for the first quarter , he pays 6 % of 10,000 which is $ 600 . so for the four quarters in the year , he will approximately play 600 * 4 = 2400 over the entire year . the compound interest will be more than 2400 . all other options are not right except d . answer : d"
Answer: d
Question (general): in a certain game of dice , the player ’ s score is determined as a sum of four throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if jim plays this game against 26 other players , what is the probability of the minimum score that will guarantee jim some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 221 , c ) 1 / 1296 , d ) 1 / 84 , e ) 1 / 42
Rationale: "toguaranteethat jim will get some monetary payoff he must score the maximum score of 6 + 6 + 6 + 6 = 24 , because if he gets even one less than that so 23 , someone can get 24 and jim will get nothing . p ( 24 ) = 1 / 6 ^ 4 = 1 / 1296 . answer : c ."
Answer: c
Question (gain): 3 candidates in an election and received 4136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?
Options: a ) 45 % , b ) 49 % , c ) 50 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 4136 + 7636 + 11628 ) = 23400 so , required percentage = 11628 / 23400 * 100 = 50 % c"
Answer: c
Question (gain): by selling a book for 200 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) a ) 215 , b ) b ) 166 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240
Rationale: sp = 120 % of cp ; : . cp = 200 × 100 / 120 = 166 option ' b '
Answer: b
Question (geometry): a piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse , leaving a smaller triangle . there was a 35 % reduction in the length of the hypotenuse of the triangle . if the area of the original triangle was 34 square inches before the cut , what is the area ( in square inches ) of the smaller triangle ?
Options: a ) 16.665
b ) 16.565
c ) 15.465
d ) 14.365
e ) 14.378
Rationale: explanation : smaller triangle and original triangle will be similar to each other . ratio of area = ( ratio of side ) 2 area of smaller triangle = area of original triangle * ( 65 / 100 ) 2 = 14.365 . answer : d
Answer: d
Question (general): in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 80 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: "x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 80 = ( 80 * 30 ) / 40 = 60 . in x game of 100 points , y gives ( 80 - 60 ) = 20 points to c . b"
Answer: b
Question (general): a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 110 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 35 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 110 = 350 m . time taken = 350 / 10 = 35 sec . answer : c"
Answer: c
Question (general): a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations f are possible ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) f = 8
Rationale: "the combinations could be f { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . . e"
Answer: e
Question (physics): by travelling at 50 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 23 kmph , b ) 24 kmph , c ) 25 kmph , d ) 26 kmph , e ) 27 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 50 * 3 x = 150 x km he covered 2 / 3 * 150 x = 100 x km in 1 / 3 * 3 x = x hours so , the remaining 50 x km , he has to cover in 2 x hours . required speed = 50 x / 2 x = 25 kmph . answer : c"
Answer: c
Question (general): what is the 29 th digit to the right of the decimal point in the decimal form of 4 / 11 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "4 / 11 = 0.363636 . . . the odd numbered positions in the decimal expansion are all 3 . the answer is c ."
Answer: c
Question (general): the average of 100 , 200300 and x is 250 and the average of 300 , 150100 , x and y is 200 . what is the value of y ?
Options: a ) 100 , b ) 150 , c ) 50 , d ) 200 , e ) 250
Rationale: we have : ( 100 + 200 + 300 + x ) / 4 = 250 600 + x = 1000 x = 400 ( 300 + 150 + 100 + x + y ) / 5 = 200 550 + 400 + y = 1000 y = 50 answer is c
Answer: c
Question (general): a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 500 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 1250 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 500 = 1250 answer : b"
Answer: b
Question (physics): a passenger train takes two hours less for a journey of 300 km if its speed is increased by 5 kmph from its normal speed . the normal speed is
Options: a ) 35 kmph , b ) 50 kmph , c ) 25 kmph , d ) 30 kmph , e ) 38 kmph
Rationale: let normal speed = x increased speed = x + 5 initial = > x = 300 / t 1 = > t 1 = 300 / x after = > ( x + 5 ) = 300 / ( t 1 - 2 ) = > ( x + 5 ) = 300 / [ ( 300 / x ) - 2 ] = > x = 25 kmph answer : c
Answer: c
Question (physics): two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 54 seconds . what is the length of each train ( in meters ) ?
Options: a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 54 seconds , the relative difference in distance traveled is 54 * 25 / 9 = 150 meters this distance is twice the length of each train . the length of each train is 150 / 2 = 75 meters the answer is d ."
Answer: d
Question (general): the jogging track in a sports complex is 660 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 5.28 min , c ) 5.08 min , d ) 4.8 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 660 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 660 m apart , they take ( 100 / 825 * 660 / 1000 ) hrs = ( 660 / 8250 * 60 ) min = 4.8 min . answer : d"
Answer: d
Question (general): in a room with 9 people , 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 1
Rationale: "( 6 / 9 ) ( 7 / 8 ) + ( 5 / 9 ) ( 6 / 8 ) if you choose one of the 6 with one other friend , then you have a 7 / 8 chance of not picking their friend 2 nd . if you choose one of the 5 with 2 friends , you have a 6 / 8 chance of not picking one of their friends second . add them up . 42 / 72 + 30 / 72 72 / 72 = 1 e . 1"
Answer: e
Question (physics): find the area of trapezium whose parallel sides are 24 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 227 , b ) 299 , c ) 315 , d ) 161 , e ) 212
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 24 + 18 ) * ( 15 ) = 315 cm 2 answer : c"
Answer: c
Question (general): the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 20 , 60 , and what number ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 80 = 25 a"
Answer: a
Question (gain): a and b started a business investing rs . 92,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 9 : 2 , b ) 3 : 2 , c ) 23 : 5 , d ) 18 : 4 , e ) 17 : 4
Rationale: a : b = 92000 : 20000 = 92 : 20 = 46 : 10 = 23 : 5 answer : c
Answer: c
Question (gain): the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 15 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 13 % , e ) 150 %
Rationale: "let rate in r = 100 x then p = 75 x g = 100 y p = 85 y thus 75 x = 85 y or x = 1.13 y ans r = 113 y so increase = 13 % answer : d"
Answer: d
Question (gain): if a large pizza has a radius that is 20 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 20 % , b ) 36 % , c ) 44 % , d ) 50 % , e ) 64 %
Rationale: "let the radius of medium pizza be r . then the radius of large pizza is 1.2 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.2 * r ) ^ 2 = 1.44 * pi * r ^ 2 , an increase of 44 % . the answer is c ."
Answer: c
Question (probability): how many cubes of 5 cm edge can be cut out of a cube of 15 cm edge
Options: a ) 36 , b ) 232 , c ) 27 , d ) 48 , e ) none of these
Rationale: "explanation : number of cubes = ( 15 x 15 x 15 ) / ( 5 x 5 x 5 ) = 27 answer : c"
Answer: c
Question (gain): 160 is what percent of 50 ?
Options: a ) 5 % , b ) 20 % , c ) 320 % , d ) 200 % , e ) 500 %
Rationale: "50 * x = 160 - - > x = 3.2 - - > 3.2 expressed as percent is 320 % . answer : c ."
Answer: c
Question (other): a precious stone weighing 35 grams worth rs . 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5 . if the price varies as the square of the weight then find the loss incurred .
Options: a ) rs . 5750 , b ) rs . 6000 , c ) rs . 5500 , d ) rs . 5000 , e ) rs . 7000
Rationale: the price varies as the square of the weight , p = k x w 2 12250 = k x 352 k = 10 thus , p = 10 w 2 when the two pieces are in the ratio 2 : 5 ( weight wise ) then we know that their weights must be 10 g and 25 g respectively . their values should be : 10 g piece : 10 x 102 = rs . 1000 ; 25 g piece : 10 x 252 = rs . 6250 . total value of stone now , = 1000 + 6250 = rs . 7250 loss incurred = 12250 - 7250 = rs . 5000 answer : d
Answer: d
Question (general): what is the decimal equivalent of ( 1 / 4 ) ^ 1 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 4 ) = 0.25 answer : d"
Answer: d
Question (general): find the least number must be subtracted from 5474827 so that remaining no . is divisible by 12 ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 7 , e ) 2
Rationale: "on dividing 5474827 by 12 we get the remainder 7 , so 7 should be subtracted d"
Answer: d
Question (other): how many even integers from 1 to 200 ( both inclusive ) have even number of factors ?
Options: a ) 13 , b ) 14 , c ) 5 , d ) 6 , e ) 7
Rationale: "integers having even number of factors will be perfect squares . even numbers will have even perfect squares . thus , the possible values for the perfect squares are : 4 , 16,36 , 64,100 , 144,196 and the corresponding integers are 2 , 4,6 , 8,10 , 12,14 ( more than 6 ) . thus e is the correct answer ."
Answer: e
Question (physics): working alone , pump a can empty a pool in 6 hours . working alone , pump b can empty the same pool in 9 hours . working together , how many minutes will it take pump a and pump b to empty the pool ?
Options: a ) 192 , b ) 200 , c ) 208 , d ) 216 , e ) 224
Rationale: "pump a can empty ( 1 / 6 ) of the pool per hour . pump b can empty ( 1 / 9 ) of the pool per hour . together the pumps can empty 1 / 6 + 1 / 9 = 5 / 18 of the pool per hour . 1 pool / ( 5 / 18 ) pool per hour = 18 / 5 hours = 216 minutes . the answer is d ."
Answer: d
Question (general): a bakery has 6 employees . it pays annual salaries of $ 18,000 to each of 2 employees , $ 20,000 to 1 employee , and $ 21,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 19,200 , b ) $ 19,500 , c ) $ 19,800 , d ) $ 20,000 , e ) $ 20,400
Rationale: "average = 2 ( 18000 ) + ( 20000 ) + 3 ( 21000 ) / 6 = $ 19,833 the answer is c ."
Answer: c
Question (other): a box contains 4 black , 3 red and 6 green marbles . 3 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?
Options: a ) 24 / 286 , b ) 25 / 709 , c ) 25 / 286 , d ) 24 / 268 , e ) 24 / 226
Rationale: "explanation : total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 3 marbles are drawn from 13 marbles at random . therefore , n ( s ) = 13 c 3 = 286 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 4 c 3 + 3 c 3 + 6 c 3 = 4 + 1 + 20 = 25 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 25 / 286 answer : c"
Answer: c
Question (geometry): how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 19 inches than that of a rectangular sheet of paper measuring 9.5 inches by 11 inches ?
Options: a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %
Rationale: "let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 19 is twice 9.5 then the area will be double which means 100 % greater . the answer is c ."
Answer: c
Question (physics): annika hikes at a constant rate of 10 minutes per kilometer . she has hiked 2.5 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes . if annika continues east , then turns around and retraces her path to reach the start of the trail in exactly 45 minutes , for how many kilometers total did she hike east ?
Options: a ) 3.625 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "set up two r x t = d cases . 1 . 1 / 10 km / min x t = 2.5 from which t = 25 mins . we know total journey time now is 45 + 25 = 70 the rate is the same ie 1 / 10 km / min . set up second r x t = d case . 1 / 10 km / min x 70 = 7 km now the total journey would be halved as distance would be same in each direction . 7 / 2 = 3.5 b ."
Answer: b
Question (general): find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 18 of money ?
Options: a ) 1800 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789
Rationale: "p = 18 ( 100 / 10 ) 2 = > p = 1800 answer : a"
Answer: a
Question (general): 544 , 509 , 474 , 439 , . . . ?
Options: a ) 404 , b ) 302 , c ) 108 , d ) 115 , e ) 210
Rationale: "each number is 35 less than the previous number . 544 544 - 35 = 509 509 - 35 = 474 474 - 35 = 439 439 - 35 = 404 answer : a"
Answer: a
Question (geometry): if the sum of a number and its square is 182 , what is the number ?
Options: a ) 15 , b ) 26 , c ) 28 , d ) 91 , e ) none of these
Rationale: "let the number be x . then , x + x 2 = 182 ( x + 14 ) ( x - 13 ) = 0 x = 13 answer : e"
Answer: e
Question (general): the difference between compound and simple interest on a certain sum of money for 3 years at 6 2 / 3 % p . a is rs . 184 . find the sum ?
Options: a ) 33772 , b ) 26782 , c ) 26788 , d ) 13500 , e ) 27761
Rationale: p = ( 184 * 106 ) / [ 6 2 / 3 * 6 2 / 3 * ( 300 * 6 2 / 3 ) ] p = 13500 answer : d
Answer: d
Question (geometry): a block of wood has dimensions 10 cm x 10 cm x 80 cm . the block is painted red and then cut evenly at the 40 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 5.6 %
b ) 8.4 %
c ) 11.2 %
d ) 14.8 %
e ) 17.5 %
Rationale: the area of each half is 100 + 4 ( 400 ) + 100 = 1800 the area that is not painted is 100 . the fraction that is not painted is 100 / 1800 = 1 / 18 = 5.6 % the answer is a .
Answer: a
Question (physics): the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 3200 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 3200 x = ( 2 ^ 7 * 25 ) / 2 ^ 9 = 25 / 4 the answer is b ."
Answer: b
Question (general): a vessel of capacity 2 litre has 30 % of alcohol and another vessel of capacity 6 litre had 45 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 33 % . , e ) 51 % .
Rationale: "30 % of 2 litres = 0.6 litres 45 % of 6 litres = 2.7 litres therefore , total quantity of alcohol is 3.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 33 % d"
Answer: d
Question (gain): company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 60 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 89 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 60 % more than company a ' s assets which is 160 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 80 a + b = 180 kw = 160 kw / ( a + b ) * 100 = 160 / 180 * 100 = 88.88 % or 89 % c"
Answer: c
Question (geometry): a certain rectangular window is ( 2 / 5 ) times as long as it is wide . if its perimeter is 28 feet , what are its dimensions in terms of length by width ?
Options: a ) 12 by 2 , b ) 11 by 3 , c ) 10.5 by 3.5 , d ) 10 by 4 , e ) 9 by 3
Rationale: "2 x + 2 y = 28 x + y = 14 x + ( 2 / 5 ) x = 14 1.4 x = 14 x = 10 answer d"
Answer: d
Question (physics): a person travels equal distances with speeds of 5 km / hr , 6 km / hr and 7 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 5 km , b ) 3 km , c ) 7 km , d ) 9 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 5 + x / 6 + x / 7 = 27 / 53 27 x / 53 = 47 / 60 = > x = 1.54 total distance = 3 * 1.54 = 4.61 km . answer : a"
Answer: a
Question (gain): if the a radio is sold for rs 490 and sold for rs 465.50 . find loss value .
Options: a ) 24.5 , b ) 12.5 , c ) 17.25 , d ) 6.5 , e ) 13.62
Rationale: "cp = rs 490 , sp = 465.50 . loss = rs ( 490 - 465.50 ) = rs 24.50 . ans : a"
Answer: a
Question (general): set s consists of integers { 4 , 7 , 10 , 14 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 50 % . what is the value of integer n ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "the average of the numbers in set s is 10 . if we increase the mean by 50 % , the new mean is 15 . thus , on average , 5 numbers increase by 5 . therefore n = 15 + 25 = 40 the answer is d ."
Answer: d
Question (general): a ’ s speed is 51 / 44 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 51 , b ) 4 / 51 , c ) 7 / 51 , d ) 3 / 44 , e ) 7 / 44
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 51 meters , b covers 44 meters in that time . so if the race is 51 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 51 meters ) would be the same as the time required by b ( to cover 44 meters ) to reach the finish line . so b should get a head start of 7 / 51 th of the race . answer ( c )"
Answer: c
Question (general): john and mike enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if john received $ 800 more than mike did , what was the profit made by their business in that year ?
Options: a ) 46457 , b ) 465745 , c ) 3000 , d ) 3456 , e ) 35346
Rationale: say the profit was $ x . john share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.7 mike ' s share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.3 thus ( x - x / 3 ) * 0.7 - ( x - x / 3 ) * 0.3 = 800 - - > x = 3000 . answer is c
Answer: c