Cheukting/mathqa huggingface dataset:
Question (gain): during a certain season , a team won 85 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 180 , b ) 175 , c ) 156 , d ) 150 , e ) 105
Rationale: "we are first given that a team won 85 percent of its first 100 games . this means the team won 0.85 x 100 = 85 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 85 + 0.5 t – 50 = 0.7 t 35 = 0.2 t 350 = 2 t 175 = t answer is b ."
Answer: b
Question (general): a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 8 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) 26 , b ) 30 , c ) 36 , d ) 38 , e ) 40
Rationale: "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 8 strikes , there would be 7 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 8 ' o clock , the 8 strikes and 7 intervals will take 2 * ( 8 + 7 ) = 30 secs b"
Answer: b
Question (physics): a train is running at a speed of 4040 km / hr and it crosses a post in 1818 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 150 metres
Rationale: "explanation : speed = 40 km / hr = 40 km / hr = 40 ã — 518 = 1009 m / s = 40 ã — 518 = 1009 m / s time = 18 = 18 seconds distance covered = 1009 ã — 18 = 200 m = 1009 ã — 18 = 200 m therefore , length of the train = 200 m answer is c"
Answer: c
Question (geometry): if a square mirror has a 20 - inch diagonal , what is the approximate perimeter r of the mirror , in inches ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter r must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b"
Answer: b
Question (general): if m and n are whole numbers such that mn = 121 , the value of ( m 1 ) n + 1 is :
Options: a ) 1 , b ) 10 , c ) 121 , d ) 100 , e ) 1000
Rationale: if m and n are whole numbers such that mn = 121 , the value of ( m - 1 ) n + 1 is : a . 1 b . 10 c . 121 d . 1000 sol . - we know that 112 = 121 . putting m = 11 and n = 2 , we get : ( m - 1 ) n + 1 = ( 11 - 1 ) ( 2 + 1 ) = 103 = 1000 . answer : e
Answer: e
Question (geometry): if the sides of a triangle are 28 cm , 26 cm and 10 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 130 cm 2 , e ) 886 cm 2
Rationale: "the triangle with sides 28 cm , 26 cm and 10 cm is right angled , where the hypotenuse is 28 cm . area of the triangle = 1 / 2 * 26 * 10 = 130 cm 2 answer : d"
Answer: d
Question (physics): a train is 510 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 76 seconds , b ) 18 seconds , c ) 52 seconds , d ) 19 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 510 + 140 = 650 meter time = distance / speed = 650 * ( 2 / 25 ) = 52 seconds answer : c"
Answer: c
Question (gain): how many ounces of a 60 % salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 30 , c ) 50 , d ) 60.33 , e ) 70
Rationale: "for 60 % salt solution ( x ) and 20 % salt solution ( y ) to give 40 % = ( 60 + 20 ) / 2 salt solution , we should mix equal amounts of x and y . answer : c ."
Answer: c
Question (general): a certain taxi company charges $ 3.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 16.0 , c ) 17.5 , d ) 18.7 , e ) 19.1
Rationale: "a certain taxi company charges $ 3.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 3.50 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 3.5 + $ 15.6 = $ 18.7 . answer : e ."
Answer: e
Question (other): the ratio of red balls to blue balls is 3 : 7 . 70 % of the red balls and 30 % of the blue balls are tennis balls . how many of the balls are tennis balls ?
Options: a ) 44 % , b ) 40 % , c ) 45 % , d ) 42 % , e ) 48 %
Rationale: let total no of balls 100 , red ball 30 and blue ball 70 , so tennis ball for red and blue ball respectively 30 * 70 / 100 = 21 and 70 * 30 / 100 = 21 so total 42 tennis balls out of 100 balls . . so required % is 42 % answer : d
Answer: d
Question (general): if ( c - a ) / ( c - b ) = 1 , then ( 5 b - 3 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "let ' s say c = 2 , b = 1 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 2 answer d ( hopefully ) ) )"
Answer: d
Question (general): xy = 1 then what is ( 3 ^ ( x + y ) ^ 2 ) / ( 3 ^ ( x - y ) ^ 2 )
Options: a ) 81 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 3 ^ 4 = 81 answer a"
Answer: a
Question (general): how much time does a train 125 metres long running at 60 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 7.4 s
Rationale: "explanation : 60 km / hr = 60 * 5 / 18 = 16.67 m / s speed = distance / time ; v = d / t 16.67 = 125 / t t = 7.5 s answer : c"
Answer: c
Question (general): if the number 517 * 324 is completely divisible by 7 , then the smallest whole number in the place of * will be :
Options: a ) 3 , b ) 1 , c ) 2 , d ) 4 , e ) 6
Rationale: sum of digits = ( 5 + 1 + 7 + x + 3 + 2 + 4 ) = ( 22 + x ) , which must be divisible by 7 . x = 6 . e
Answer: e
Question (general): what is the least number which when divided by 5 , 6 , 9 and 12 leaves remainder 4 in each care ?
Options: a ) 130 , b ) 140 , c ) 156 , d ) 184 , e ) 196
Rationale: explanation : lcm of 5 , 6 , 9 and 12 is 180 required number = 180 + 4 = 184 answer : option d
Answer: d
Question (physics): sakshi can do a piece of work in 25 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 15 , b ) 20 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 25 : x ⇒ x = ( 25 x 4 / 5 ) ⇒ x = 20 days . hence , tanya takes 16 days is complete the work . answer b"
Answer: b
Question (gain): at what price must an article costing rs . 47.50 be marked in order that after deducting 8 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 64.54 , b ) 62.6 , c ) 62.1 , d ) 62.7 , e ) 62.2
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 92 / 100 ) = 59.375 mp = 64.54 answer : a"
Answer: a
Question (general): in a bag , there are two 6 - sided dice ( numbered 1 to 6 ) , 3 12 - sided dice ( numbered 1 to 12 ) , and two 20 - sided dice ( numbered 1 to 20 ) . if 4 of these dice are selected at random from the bag , and then the 4 are rolled and we find the sum of numbers showing on the 4 dice , how many different possible totals are there for this sum ?
Options: a ) 60 , b ) 50 , c ) 42 , d ) 84 , e ) 61
Rationale: as ' complex - looking ' as this question might appear , it ' s actually rather simple . pay careful attention to what the specific questions asks for - the number of different possible sums from 4 dice . since we ' re dealing with some ' special ' dice ( some 12 - sided and 20 - sided dice ) , we have to adjust out math accordingly , but the possibilities are rather limited : 1 ) the minimum number on any given die is 1 2 ) the maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each . with 4 dice , we could end up with any sum between : 4 ( if we rolled 1 s on all 4 dice ) to 64 ( if we rolled two 20 s on the 20 - sided dice and two 12 s on the 12 - sided dice ) . thus , there are only 61 possible sums . e
Answer: e
Question (physics): convert 50 miles into yards ?
Options: a ) 25630 yards , b ) 35200 yards , c ) 88000 yards , d ) 42560 yards , e ) 41520 yards
Rationale: "1 mile = 1760 yards 50 miles = 50 * 1760 = 88000 yards answer is c"
Answer: c
Question (physics): a bus covers a distance of 12 km in 5 min . if it takes 5 sec to pass a telegraph post , then the length of the bus is ?
Options: a ) 120 m , b ) 180 m , c ) 240 m , d ) 200 m , e ) 280 m
Rationale: speed = ( 12 / 5 * 60 ) km / hr = ( 144 * 5 / 18 ) m / sec = 40 m / sec . length of the bus = 40 * 5 = 200 m . answer : d
Answer: d
Question (general): a number is doubled and 9 is added . if the resultant is trebled , it becomes 69 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 69 2 x = 14 = > x = 7 answer : d"
Answer: d
Question (physics): x can finish a work in 18 days . y can finish the same work in 15 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 5 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "work done by x in 1 day = 1 / 18 work done by y in 1 day = 1 / 15 work done by y in 10 days = 10 / 15 = 2 / 3 remaining work = 1 – 2 / 3 = 1 / 3 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 18 ) = 6 c"
Answer: c
Question (general): n ^ ( n / 2 ) = 8 is true when n = 8 in the same way what is the value of n if n ^ ( n / 2 ) = 20 ?
Options: a ) 8 , b ) 14 , c ) 10 , d ) 20 , e ) 40
Rationale: n ^ ( n / 2 ) = 20 apply log n / 2 logn = log 20 nlogn = 2 log 20 = log 20 ^ 2 = log 400 logn = log 400 now apply antilog n = 400 / n now n = 20 . answer : d
Answer: d
Question (physics): amar takes as much time in running 12 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.6 km ?
Options: a ) 600 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m
Rationale: "d 400 m distance covered by amar = 12 / 4.8 ( 1.6 km ) = 2.5 ( 1600 ) = 400 m answer is d"
Answer: d
Question (general): find the unit ’ s digit in the product ( 76 ^ 41 ) * ( 41 ^ 14 ) * ( 14 ^ 87 ) * ( 87 ^ 76 )
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: units digit of 87 ^ 76 = 1 because 87 ^ 3 n + 1 has units place as 1 units digit of 14 ^ 87 = 4 because 14 ^ ( some odd no . ) has units place as 4 units digit of 41 ^ 14 = 1 because 41 ^ ( some even no . ) has units place as 1 units digit of 76 ^ 41 = 6 because 76 ^ ( any positive no . ) has units place as 6 so , units digit of the product is = ` ` 4 ` ` ( units digit of 1 * 4 * 1 * 6 ) answer : d
Answer: d
Question (geometry): what is the area of an equilateral triangle whose one side length is 40 ?
Options: a ) 100 √ 3 , b ) 200 √ 3 , c ) 300 √ 3 , d ) 350 √ 3 , e ) 400 √ 3
Rationale: "- > - > the area of an equilateral triangle with one side length of a is √ 3 a 2 / 4 . thus , √ 3 ( 40 ^ 2 ) / 4 = 400 √ 3 and the answer is e . correct option : e"
Answer: e
Question (physics): a man ate 100 bananas in 5 days , each day eating 6 more than the previous day . how many bananas did he eat on the first day ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: let the number of bannanas in first day be x for consecutive five days it will be like x , x + 6 , x + 12 , x + 18 , x + 24 the sum of those are 100 , 5 x + 60 = 100 so , x = 8 answer : c
Answer: c
Question (general): what is the least value of x . so that 1894 x is divisible by 3 ?
Options: a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7
Rationale: the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 1 + 8 + 9 + 4 + x = 22 + x least value of x may be 2 therefore 22 + 2 = 24 is divisible by 3 . a
Answer: a
Question (physics): if takes 25.5 minutes to download a file using modem a . modem b work at 17 % of the speed of modem a . how long does it take to download a file using a modem b ?
Options: a ) 130 minutes , b ) 140 minutes , c ) 150 minutes , d ) 160 minutes , e ) 170 minutes
Rationale: let speed of modem a be k so speed of modem b is 17 / 100 * k time taken by modem a = 25.5 minutes let time taken by modem b = x k * 25.5 = 17 / 100 * k * x 0.17 * x = 25.5 x = 25.5 / 0.17 = 150 minutes answer : c
Answer: c
Question (gain): the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 9 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 9 , b ) 17 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 9 x = 9 answer : a"
Answer: a
Question (general): on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent w of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before w = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b"
Answer: b
Question (gain): what annual installment will discharge a debt of $ 100 due in 3 years at 10 % simple interest ?
Options: a ) 25.6 , b ) 50.2 , c ) 30.3 , d ) 45 , e ) 56
Rationale: let each installment be x [ x + ( x * 10 * 1 / 100 ) ] + [ x + ( x * 10 * 2 / 100 ) ] + x = 100 11 x / 10 + 12 x / 10 + x = 100 x = 30.3 answer is c
Answer: c
Question (physics): a boat can travel with aspeed of 20 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 125 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: speed downstream = ( 20 + 5 ) km / hr = 25 km / hr . time taken to travel 125 km downstream = 125 / 25 hrs = 5 hrs . answer : e
Answer: e
Question (physics): john bought 9.25 m of cloth for $ 397.75 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 58 , d ) 56 , e ) 43
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 397.75 cost per metre = 397.75 ÷ 9.25 the cost of the cloth per metre = $ 43 answers : e"
Answer: e
Question (gain): a sum fetched total simple interest of 4016.25 at the rate of 13 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 6178.85 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 65 % of p = 4016.25 or , p = 6178.85 answer a"
Answer: a
Question (general): what could be the range of a set consisting of odd multiples of 3 ?
Options: a ) 21 , b ) 24 , c ) 35 , d ) 62 , e ) 70
Rationale: "range = the difference between the greatest and the smallest numbers in the sequence . our sequence is odd and is a multiple of 7 . every number in that sequence can be represented like this : 3 * ( 2 n + 1 ) where n is any positive integer . range = 3 * ( 2 m + 1 ) - 3 * ( 2 n + 1 ) = 3 * 2 * ( m - n ) = 6 * ( m - n ) . m , n - any positive integers the answer must be divisible by 6 , which is only 24 . the correct answer is b"
Answer: b
Question (physics): i walk a certain distance and ride back taking a total time of 37 minutes . i could walk both ways in 55 minutes . how long would it take me to ride both ways ?
Options: a ) 12 mins , b ) 10 mins , c ) 19 mins , d ) 15 mins , e ) 20 mins
Rationale: let the distance be x km . then , ( time taken to walk x km ) + ( time taken to ride x km ) = 37 min . ( time taken to walk 2 x km ) + ( time taken to ride 2 x km ) = 74 min . but , the time taken to walk 2 x km = 55 min . time taken to ride 2 x km = ( 74 - 55 ) min = 19 min . ans : c
Answer: c
Question (general): a store owner estimates that the average price of type a products will increase by 35 % next year and that the price of type b products will increase by 15 % next year . this year , the total amount paid for type a products was $ 4000 and the total price paid for type b products was $ 5300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 11,495 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: cost of type a products next year = 1.35 * 4000 = 5400 cost of type b products next year = 1.15 * 5300 = 6095 total 5400 + 6095 = 11495 answer : b
Answer: b
Question (geometry): the area of a parallelogram is 242 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 11 , e ) 2
Rationale: "2 x * x = 242 = > x = 11 answer : d"
Answer: d
Question (general): a part - time employee whose hourly wage was increased by 10 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 9.09 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.1 x now we need to find number of hours worked so that x * y = 1.1 x * z i . e z = x * y / 1.1 x = 1 / 1.1 y % decrease = ( y - 1 / 1.1 y ) / y * 100 = 1 - 1 / 1.1 * 100 = 9.09 % thus my answer is a .
Answer: a
Question (general): a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 150,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 50,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 5 a * 1 + a * 5 ) / 6 = 10 a / 6 = 50000 answer is c . $ 50,000"
Answer: c
Question (geometry): the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 2304 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40
b ) b . 100
c ) c . 400
d ) d . 1,800
e ) e . 10,000
Rationale: the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 2304 pi r = 12 so area = 4 . pi . r ^ 2 = 576 . pi = 576 x 3.14 = 1800 ( approx ) d
Answer: d
Question (general): in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 35 , what is the greatest possible value of b x a ?
Options: a ) 0 , b ) 10 , c ) 20 , d ) 30 , e ) 35
Rationale: "i also was confused when i was looking forabove number : d as far as i understood , 35 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 35 x 1 ( a = 3 , b = 5 respectively we have = 15 ) . but we do n ' t have this number in answer choices , move on . ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 35 x 3 = 105 ( a = 0 b = 5 respectively . hey ! that ' s 0 now . 35 x 5 = 175 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) . this is the greatest possible value of b x a . imo e ."
Answer: e
Question (general): if 2 x - y = 4 then 6 x - 3 y = ?
Options: a ) 15 , b ) 12 , c ) 18 , d ) 10 , e ) 14
Rationale: 6 x - 3 y = 3 * ( 2 x - y ) = 3 * 4 = 12 answer : b
Answer: b
Question (general): find 3486 / 189
Options: a ) 18.44 , b ) 18.48 , c ) 18.42 , d ) 18.49 , e ) 18.41
Rationale: first we make the denominator 200 . i . e . , we are introducing an error of 11 which is 11189 = 11711189 = 117 th of the denominator . now 3486200 = 17.433486200 = 17.43 but this answer is less than actual answer . so we have to increase it by 1 / 17 th part of it . 117 × 17.43 ≃ 1117 × 17.43 ≃ 1 so final answer = 17.43 + 1 = 18.43 actual answer = 18.44 answer : a
Answer: a
Question (general): mary and mike enter into a partnership by investing $ 600 and $ 400 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 mary received $ 1000 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 8500 , b ) $ 9500 , c ) $ 7000 , d ) $ 7500 , e ) $ 6500
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 6 : 4 . i . e . , 60 % of 2 x would go to mary and 40 % of 2 x would go to mike . hence , mary would get ( 60 - 40 ) % of 2 x more than mike or 20 % of 2 x = $ 1000 i . e . , ( 20 / 100 ) * 2 x = 1000 or 2 x = 5000 . hence , the profit made by the company during the year $ 3 x = $ 7500 . answer : d"
Answer: d
Question (gain): a bookstore has a shelf that contains biographies which normally sell for $ 20 each and mysteries that normally sell for $ 12 each . during a sale , the biographies and mysteries are discounted at different rates so that a customer saves a total of $ 19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries . if the sum of the discount rates for the two types of books is 27 percent , what is the discount rate on mysteries ?
Options: a ) 10 % , b ) 11 % , c ) 12.5 % , d ) 13 % , e ) 14 %
Rationale: "let b be the discount on biographies and m be the discount on mysteries so . , b + m = 0.27 - - - - - ( 1 ) and ( 20 * 5 + 12 * 3 ) - ( 20 * 5 * ( 1 - b ) + 12 * 3 * ( 1 - m ) ) = 19 - - > 100 ( 1 - ( 1 - b ) ) + 36 ( 1 - ( 1 - m ) = 19 100 b + 36 m = 19 - - - - - - ( 2 ) solving 12 . , we get m = 0.125 = 12.5 % c"
Answer: c