Cheukting/mathqa huggingface dataset:
Question (gain): the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 4 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 9724 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 4 = rs 9724 answer : c"
Answer: c
Question (physics): there are 6 working days in a regular week and for each day , the working hours are 10 . a man earns rs . 2.10 per hour for regular work and rs . 4.20 per hour for overtime . if he earns rs . 525 in 4 weeks , how many hours did he work ?
Options: a ) 225 , b ) 235 , c ) 215 , d ) 255 , e ) 245
Rationale: egular working hours in 4 weeks = ( 4 × 6 × 10 ) = 240 hours amount earned by working in these regular working hours = 240 × 2.10 = rs . 504 additional amount he earned = 525 - 504 = rs . 21 hours he worked overtime = 21 / 4.2 = 210 / 42 = 5 hours total hours he worked = 240 + 5 = 245 hours answer is e .
Answer: e
Question (physics): due to construction , the speed limit along an 7 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "7 / 35 - 7 / 55 = 7 / 5 * ( 11 - 7 ) / 77 = 7 / 5 * 4 / 77 * 60 min = 7 * 12 * 4 / 77 = 336 / 77 ~ 4.3 answer - c"
Answer: c
Question (general): if the price of gasoline increases by 25 % and a driver intends to spend only 5 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 20 % , b ) 16 % , c ) 15 % , d ) 12 % , e ) 10 %
Rationale: "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.05 ( p * x ) y = ( 1.05 / 1.25 ) x = 0.84 x which is a reduction of 16 % . the answer is b ."
Answer: b
Question (geometry): the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) 4000 , b ) 345 , c ) 5673 , d ) 6530 , e ) 8154
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 * 9 = rs . 8154 answer : option e"
Answer: e
Question (geometry): d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 25 : 144 and bc = 13 cm , then find the length of de .
Options: a ) 12 , b ) 5 , c ) 14 , d ) 11 , e ) 15
Rationale: "abc and ade are similar triangles . so ( side of abc / side of ade ) ^ 2 = 169 / 25 side of abc / side of ade = 13 / 5 so the length of de = 5 answer - b"
Answer: b
Question (physics): there are 24 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 800 , b ) 820 , c ) 650 , d ) 870 , e ) 900
Rationale: "the total number of stations = 26 from 26 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 26 p 2 ways . 26 p 2 = 26 * 25 = 650 answer : c"
Answer: c
Question (gain): jaclyn buys $ 50 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 1187.5 , b ) 1234 , c ) 1289 , d ) 1345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 answer : a"
Answer: a
Question (physics): x does a work in 30 days . y does the same work in 45 days . in how many days they together will do the same work ?
Options: a ) 18 , b ) 12 , c ) 20 , d ) 30 , e ) 15
Rationale: "x ' s 1 day ' s work = 1 / 30 y ' s 1 day ' s work = 1 / 45 ( x + y ) ' s 1 day ' s work = ( 1 / 30 + 1 / 45 ) = 1 / 18 both together will finish the work in 18 days . correct option is a"
Answer: a
Question (general): how many positive integer solutions does the equation 2 x + 3 y = 100 have ?
Options: a ) 50 , b ) 33 , c ) 16 , d ) 35 , e ) 14
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 3 ) = 15.5 answer : c"
Answer: c
Question (general): if 3 : 7 : : x : 21 , then find the value of x
Options: a ) 7 , b ) 8 , c ) 11 , d ) 6 , e ) 9
Rationale: explanation : treat 3 : 7 as 3 / 7 and x : 21 as x / 21 , treat : : as = so we get 3 / 7 = x / 21 = > 7 x = 63 = > x = 9 option e
Answer: e
Question (physics): how many pieces of 0.42 meteres can be cut from a rod 36.5 meteres long
Options: a ) 30 , b ) 40 , c ) 86 , d ) 89 , e ) 95
Rationale: "explanation : we need so simple divide 36.5 / 0.42 , = ( 3650 / 42 ) = 86 option c"
Answer: c
Question (gain): if the cost price is 94 % of sp then what is the profit %
Options: a ) 5.07 % , b ) 6 % , c ) 5.7 % , d ) 6.50 % , e ) 6.25 %
Rationale: "sol . sp = rs 100 : then cp = rs 94 : profit = rs 6 . profit = { ( 6 / 94 ) * 100 } % = 6.25 % answer is e ."
Answer: e
Question (general): if a is a positive integer , and if the units digit of a ^ 2 is 1 and the units digit of ( a + 1 ) ^ 2 is 0 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 . , b ) 3 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: "if the units digit of a ^ 2 is 1 , then the units digit of a is either 1 or 9 . if the units digit of ( a + 1 ) ^ 2 is 0 , then the units digit of a + 1 is 0 . to satisfy both conditions , the units digit of a must be 9 . then a + 2 has the units digit of 1 , thus the units digit of ( a + 2 ) ^ 2 will be 1 . the answer is a ."
Answer: a
Question (geometry): a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 5 feet and a height of 10 feet , how far did the oil level drop in the stationary tank ?
Options: a ) 2.5 ft
b ) 1 ft
c ) 0.5 ft
d ) 0.25 ft
e ) 0.025 ft
Rationale: in order to fill up the tank , same volume is shifted from one tank to the other . pi r 1 ^ 2 h 1 = pi r 2 ^ 2 h 2 5 * 5 * 10 = 100 * 100 * h 2 h 2 = . 025 ft e is the answer
Answer: e
Question (general): a person saved $ 10 in buying an item on sale . if he spent $ 100 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 6 %
Rationale: actual price = 100 + 10 = $ 110 saving = 10 / 110 * 100 = 100 / 11 = 10 % approximately answer is b
Answer: b
Question (other): two family reunions are happening at the same hotel , the oates reunion and the yellow reunion . all 100 guests at the hotel attend at least one of the reunions . if 42 people attend the oates reunion and 65 people attend the yellow reunion , how many people attend both reunions ?
Options: a ) 2 , b ) 7 , c ) 10 , d ) 16 , e ) 22
Rationale: no of people in oates reunion = 42 no of people in yellow reunion = 65 attending both = x all guests attend at least one . therefore , 100 = 42 + 65 - ( both ) both = 7 answer b
Answer: b
Question (probability): in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 140 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Rationale: "number of newborns that can die in first month = 1 / 10 * 200 = 20 survived = 180 number of newborns that can die in second month = 1 / 10 * 180 = 18 survived = 162 number of newborns that can die in third month = 1 / 10 * 162 = 16 survived = 146 answer : b"
Answer: b
Question (geometry): the surface of a cube is 150 sq cm . find its volume ?
Options: a ) 8 cc , b ) 9 cc , c ) 125 cc , d ) 4 cc , e ) 6 cc
Rationale: "6 a 2 = 150 = 6 * 25 a = 5 = > a 3 = 125 cc answer : c"
Answer: c
Question (other): two numbers are in the ratio of 5 : 7 . if 7 is subtracted from each number , they are in the ratio of 2 : 3 . what are the two numbers ?
Options: a ) 35 , 49 , b ) 40 , 56 , c ) 45 , 63 , d ) 50 , 70 , e ) 55 , 77
Rationale: "( 5 x - 7 ) : ( 7 x - 7 ) = 2 y : 3 y 5 x - 7 = 2 y 7 x - 7 = 3 y 49 - 35 = 15 y - 14 y 14 = y 5 x - 7 = 28 x = 7 the two numbers are 5 x and 7 x which are 35 and 49 . the answer is a ."
Answer: a
Question (geometry): a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 40 - sided polygon have ?
Options: a ) 875 , b ) 740 , c ) 1425 , d ) 2025 , e ) 2500
Rationale: "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 40 . plugging it in , we get 740 diagonals ! answer ( b ) ."
Answer: b
Question (physics): in covering a distance of 24 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 4 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 7.8 kmph
Rationale: "let abhay ' s speed be x km / hr . then , 24 / x - 24 / 2 x = 3 6 x = 24 x = 4 km / hr . answer : option a"
Answer: a
Question (physics): 20 workers can finish a work in 30 days . after how many days should 5 workers leave the job so the work is completed in 35 days ?
Options: a ) 7 , b ) 6 , c ) 15 , d ) 4 , e ) 3
Rationale: work done by 15 workers in 35 days = 15 * 35 = 525 men days . now , work remaining = 600 – 525 = 75 men days and we have 5 workers . so 5 workers will work for 75 / 5 = 15 days . answer : c
Answer: c
Question (gain): a glass was filled with 10 ounces of water , and 0.02 ounce of the water evaporated each day during a 30 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.006 % , b ) 0.06 % , c ) 6 % , d ) 2 % , e ) 60 %
Rationale: "in 30 days 30 * 0.02 = 0.6 ounces of water evaporated , which is 0.6 / 10 â ˆ — 100 = 6 of the original amount of water . answer : c ."
Answer: c
Question (physics): a train 284 m in length crosses a telegraph post in 18 seconds . the speed of the train is ?
Options: a ) 77 kmph , b ) 55 kmph , c ) 57 kmph , d ) 58 kmph , e ) 76 kmph
Rationale: "s = 284 / 18 * 18 / 5 = 57 kmph answer : c"
Answer: c
Question (general): roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be 3 times as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 72 , b ) 84 , c ) 88 , d ) 96 , e ) 108
Rationale: r = j + 8 = k + 4 r + 2 = 3 ( j + 2 ) ( j + 8 ) + 2 = 3 j + 6 j = 2 r = 10 k = 6 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 8 = 96 the answer is d .
Answer: d
Question (general): a mixture of 120 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 2 liters , b ) 3 liters , c ) 8 liters , d ) 5 liters , e ) 7 liters
Rationale: number of liters of water in 120 liters of the mixture = 20 % of 120 = 20 / 100 * 120 = 24 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 24 + p ) and total volume of mixture is ( 120 + p ) . ( 24 + p ) = 25 / 100 * ( 120 + p ) 96 + 4 p = 120 + p p = 8 liters . answer : c
Answer: c
Question (general): 5 friends visited a fruit stall , and everyone decided to contribute equally to the total bill of $ 100 . if one of the friends had a coupon for 6 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?
Options: a ) 18 , b ) 18.8 , c ) 19 , d ) 17.8 , e ) 17.9
Rationale: at the non - discounted price , each friend would pay $ 20 , as $ 100 divided by 5 friends is $ 20 per friend . but if the bill is 6 % off , then each friend would pay 6 % less . 6 % of $ 20 is $ 1.2 , so each friend saves $ 1.2 and pays the remaining 18.8 correct option : option b
Answer: b
Question (general): a certain country is divided into 5 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 15 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 15 the total number of traditionalists is 5 p / 15 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ."
Answer: e
Question (general): an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 22050 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 25 %
Rationale: "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 22050 / - - 17640 / - = rs . 4410 / - rate of interest = ( 4410 / 17640 ) × ( 100 / 1 ) = > 25 % answer : option e"
Answer: e
Question (general): which number can we add to 859722 to get a number exactly divisible by 456 ?
Options: a ) 294 , b ) 306 , c ) 318 , d ) 338 , e ) 362
Rationale: "859722 / 456 = 1885 with a remainder of 162 . we need to add 456 - 162 = 294 the answer is a ."
Answer: a
Question (physics): find the l . c . m of 12 , 25 , 24 and 20 .
Options: a ) 240 , b ) 600 , c ) 320 , d ) 150 , e ) 250
Rationale: "explanation : 6 x 2 x 2 x 5 x 5 = 600 answer : option b"
Answer: b
Question (physics): walking with 4 / 5 of my usual speed , i miss the bus by 3 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 34 min , d ) 20 min , e ) 12 min
Rationale: speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 3 4 - - - - - - - - - ? è 12 answer : e
Answer: e
Question (probability): what is the probability of getting a sum 9 from two throws of a dice ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 12 , e ) none of these
Rationale: "in two throws of a dice , n ( s ) = ( 6 x 6 ) = 36 . let e = event of getting a sum = { ( 3 , 6 ) , ( 4 , 5 ) , ( 5 , 4 ) , ( 6 , 3 ) } . p ( e ) = n ( e ) / n ( s ) = 4 / 36 = 1 / 9 . answer : c"
Answer: c
Question (general): in the hillside summer camp there are 100 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 150 . , b ) 145 . , c ) 100 . , d ) 30 . , e ) 25 .
Rationale: "given there are 100 students , 90 % of 50 = 90 boys and remaining 10 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 1000 to existing 90 then the count will be 190 and the girls number will be 10 as it . now boys are 95 % and girls are 5 % . ( out of 200 students = 190 boys + 10 girls ) . imo option c is correct ."
Answer: c
Question (general): what is the sum of the integers from - 185 to 195 inclusive ?
Options: a ) 0 , b ) 5 , c ) 375 , d ) 1905 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = - 185 + 195 / 2 = 5 number of items ( n ) = b - a + 1 = 195 - ( - 185 ) + 1 = 195 + 186 = 381 . sum = average * n = 5 * 381 = 1905 . answer is d"
Answer: d
Question (probability): a jar contains only red , yellow , and orange marbles . if there are 3 red , 5 yellow , and 4 orange marbles , and 2 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 6 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 6 possible orderings the probabbility is the same . so , it should be ( 1 / 22 ) * ( 6 ) , which indeed is 6 / 22 . e"
Answer: e
Question (general): 10 years ago , the average age of a family of 4 members was 24 years . two children having been born ( with age diference of 2 years ) , the present average age of the family is the same . the present age of the youngest child is ?
Options: a ) 1 , b ) 7 , c ) 3 , d ) 9 , e ) 2
Rationale: total age of 4 members , 10 years ago = ( 24 x 4 ) years = 96 years . total age of 4 members now = [ 96 + ( 10 x 4 ) ] years = 136 years . total age of 6 members now = ( 24 x 6 ) years = 144 years . sum of the ages of 2 children = ( 144 - 136 ) years = 8 years . let the age of the younger child be years . then , age of the elder child = years . so , age of younger child = 3 years . answer : c
Answer: c
Question (other): a certain quantity of 70 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 7 / 9
Rationale: let ' s say that the total original mixture a is 100 ml the original mixture a thus has 70 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 70 ml and 25 ml is 45 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 45 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 35 % . therefore , 35 out of 45 is 7 / 9 and e is the answer .
Answer: e
Question (general): f 1 ( x ) f 1 ( x ) = 2 x - 1 and fn ( x ) = f 1 ( fn − 1 ( x ) ) fn ( x ) = f 1 ( fn − 1 ( x ) ) for n ≥ ≥ 2 . find f 5 ( 2 )
Options: a ) 7 , b ) 6 , c ) 78 , d ) 9 , e ) 1
Rationale: answer : a
Answer: a
Question (other): of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 22 boys and 38 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 22 boys . so 22 - 6 - 6 = 10 boys must be neither happy nor sad . answer ( e )"
Answer: e
Question (general): real - estate salesman z is selling a house at a 10 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 10 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 10 percent discount . salesman y ' s final price is what fraction of salesman x ' s final price ?
Options: a ) 38 / 6 , b ) 38 / 5 , c ) 77 / 81 , d ) 38 / 7 , e ) 38 / 10
Rationale: "let the retail price be = x selling price of z = 0.90 x selling price of x = 0.90 * 0.90 x = 0.81 x selling price of y = ( ( 0.90 x + 0.81 x ) / 2 ) * 0.90 = 0.86 x * 0.90 = 0.77 x 0.77 x = k * 0.81 x k = 0.77 / 0.81 = 77 / 81 answer : c"
Answer: c
Question (physics): find the distance covered by a man walking for 42 min at a speed of 10 km / hr ?
Options: a ) 7 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "distance = 10 * 42 / 60 = 7 km answer is a"
Answer: a
Question (general): the output of a factory was increased by 15 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 20 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 27 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: the original output increases by 15 % and then 20 % . total % change = a + b + ab / 100 total % change = 15 + 20 + 15 * 20 / 100 = 38 % now , you want to change it to 0 , so , 0 = 38 + x + 38 x / 100 x = - 38 ( 100 ) / 138 = 27 % approximately answer is b
Answer: b
Question (general): in a sample of associates at a law firm , 30 percent are second - year associates , and 60 percent are not first - year associates . what percentage of the associates at the law firm have been there for more than two years ?
Options: a ) 10 , b ) 20 , c ) 30 % , d ) 40 , e ) 50
Rationale: let the sample be 100 . given 60 % are not first year i . e . there could be second year ( x ) and more than 2 years ( y ) possibility . 60 % = ( x ) + y given 30 % = second year ( x ) club both , we get y = 30 % . answer : option c is correct answer .
Answer: c
Question (geometry): in a company of 160 employees , 90 are females . a total of 80 employees have advanced degrees and the rest have a college degree only . if 40 employees are males with college degree only , how many employees are females with advanced degrees ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "the number of males is 160 - 90 = 70 . the number of males with advanced degrees is 70 - 40 = 30 . the number of females with advanced degrees is 80 - 30 = 50 . the answer is c ."
Answer: c
Question (gain): in business , a and c invested amounts in the ratio 3 : 2 , whereas the ratio between amounts invested by a and b was 3 : 1 , if rs 60000 was their profit , how much amount did c receive .
Options: a ) 10000 , b ) 20000 , c ) 15000 , d ) 61000 , e ) 26000
Rationale: "explanation : a : b = 3 : 1 = 3 : 1 = > a : c = 3 : 2 = 3 : 2 = > a : b : c = 3 : 1 : 2 c share = ( 2 / 6 ) * 60000 = 20000 option b"
Answer: b
Question (general): the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 50 , and what number ?
Options: a ) 40 , b ) 45 , c ) 55 , d ) 45 , e ) 50
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 60 = 45 d"
Answer: d
Question (general): an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 49 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 49 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 49 ( x - y ) - - > x + y = 49 . answer : d ."
Answer: d
Question (general): how many times will the digit 4 be written when listing the integers from 1 to 1000 ?
Options: a ) 512 , b ) 300 , c ) 294 , d ) 264 , e ) 385
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 4 ) 3000 / 10 = 300 times . answer : b ."
Answer: b