Cheukting/mathqa huggingface dataset:
Question (geometry): a rectangular tiled patio is composed of 126 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 126 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5
b ) 6
c ) 9
d ) 13
e ) 28
Rationale: suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 126 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 126 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 126 ( 2 r - 4 ) * r = 126 2 r ^ 2 - 4 r - 126 = 0 r can not be negative so r = 9 and c = 14 so , answer will be c
Answer: c
Question (other): in a class of 39 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "26 + 20 - 17 = 29 39 - 29 = 10 play neither answer is c"
Answer: c
Question (geometry): a rectangular floor is covered by a rug except for a strip 2 meters wide along each of the four edge . if the floor is 10 meters by 8 meters , what is the area of the rug in square meters ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "a strip of 2 meters is covering the inner rectangular rug for all 4 sides . length of inner rug = 10 - ( 2 * 2 ) breadth of inner rug = 8 - ( 2 * 2 ) area of rug = 6 * 4 = 24 sq . mt â nswer : a"
Answer: a
Question (general): if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 18 * 12 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: "the greatest common divisor of 12 and 16 is 4 . hence 12 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 12 is 6 . hence 18 * 12 = 6 . hence ( ( 12 * 16 ) * ( 18 * 12 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ."
Answer: e
Question (physics): if 24 men take 15 days to to complete a job , in how many days can 18 men finish that work ?
Options: a ) 20 , b ) 19 , c ) 18 , d ) 17 , e ) 16
Rationale: ans . 20 days
Answer: a
Question (physics): the circumference of the front wheel of a cart is 40 ft long and that of the back wheel is 48 ft long . what is the distance travelled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 1200 ft , b ) 800 ft , c ) 900 ft , d ) 1000 ft , e ) 1500 ft
Rationale: "total distance - x x / 40 - x / 48 = 5 x = 1200 ft answer a"
Answer: a
Question (physics): a train requires 10 seconds to pass a pole while it requires 30 seconds to cross a stationary train which is 600 mtrs long . find the speed of the train .
Options: a ) 110 kmph , b ) 120 kmph , c ) 108 kmph , d ) 100 kmph , e ) 98 kmph
Rationale: "in 10 s the train crosses the pole and in 30 sec the train crosses one more stationary train in 20 sec the train travels a distance of 600 mtrs speed = 600 / 20 = 30 m / s = 30 ( 3600 / 1000 ) = 30 * 18 / 5 = 108 kmph answer : c"
Answer: c
Question (general): the average of runs of a cricket player of 10 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 76 , b ) 80 , c ) 85 , d ) 87 , e ) 89
Rationale: "explanation : average = total runs / no . of innings = 36 so , total = average x no . of innings = 36 x 10 = 360 . now increase in avg = 4 runs . so , new avg = 36 + 4 = 40 runs total runs = new avg x new no . of innings = 40 x 11 = 440 runs made in the 11 th inning = 440 - 360 = 80 answer : b"
Answer: b
Question (gain): john had a stock of 800 books in his bookshop . he sold 62 on monday , 62 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ?
Options: a ) 78 % , b ) 66 % , c ) 62 % , d ) 64 % , e ) 60 %
Rationale: "let n be the total number of books sold . hence n = 62 + 62 + 60 + 48 + 40 = 272 let m be the books not sold m = 800 - n = 1400 - 272 = 528 percentage books not sold / total number of books = 528 / 800 = 0.66 = 66 % correct answer b"
Answer: b
Question (general): a certain city with a population of 180,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 10,900 , d ) d ) 15,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 180 k x = 15,000 answer : d"
Answer: d
Question (general): a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 100 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "given that p is smallest integer greater than 200 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 c"
Answer: c
Question (physics): circular gears l and r start to rotate at the same time at the same rate . gear l makes 20 complete revolutions per minute and gear r makes 40 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 6 more revolutions than gear l ?
Options: a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 12 , e ) e ) 15
Rationale: gear l - - 20 rotations per 60 seconds - - 2 rotation per 6 seconds . gear r - - 40 rotations per 60 seconds - - 4 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 2 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 2 units . required net difference should be 6 rotations = > 3 ( 6 seconds later ) = = > 18 seconds . answer : a
Answer: a
Question (physics): two pipes a and b can fill a tank in 4 and 12 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 12 , b ) 3 , c ) 6 , d ) 9 , e ) 10
Rationale: "part filled by a in 1 min . = 14 part filled by b in 1 min . = 1 / 12 part filled by ( a + b ) in 1 min . = 1 / 4 + 1 / 12 = 1 / 3 . both the pipes can fill the tank in 3 minutes . answer : b"
Answer: b
Question (general): a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1206 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138
Rationale: "let the required number be x . then , 43 x – 34 x = 1206 or 9 x = 1206 or x = 134 . required number = 134 . answer : c"
Answer: c
Question (gain): a company pays 18.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 66 , c ) 18 , d ) 37 , e ) 01
Rationale: "explanation : dividend on 1 share = ( 18.5 * 50 ) / 100 = rs . 9.25 rs . 25 is income on an investment of rs . 100 rs . 9.25 is income on an investment of rs . ( 9.25 * 100 ) / 25 = rs . 37 answer : d"
Answer: d
Question (physics): 1000 men have provisions for 20 days . if 650 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.5 , c ) 12.6 , d ) 12.2 , e ) 12.1
Rationale: "1000 * 20 = 1650 * x x = 12.1 answer : e"
Answer: e
Question (gain): david ' s bank ' s saving amount is decreased 10 % due to loan payment and current balance is rs . 90000 . find the actual balance before deduction ?
Options: a ) 8000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 100000
Rationale: 10 % decreased 90 % balance = 90000 100 % = 90000 / 90 * 100 = 100000 answer : e
Answer: e
Question (other): the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 2200 , then what is the income of p 1 ?
Options: a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 5500 , e ) s . 4200
Rationale: "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 2200 … ( i ) and 4 x – 2 y = 2200 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 2200 - > x = 1100 p 1 ’ s income = rs 5 * 1100 = rs . 5500 answer : d"
Answer: d
Question (general): 3 math classes : x , y , and z , take an algebra test . the average score in class x is 83 . the average score in class y is 76 . the average score in class z is 85 . the average score of all students in classes x and y together is 79 . the average score of all students in classes y and z together is 81 . what is the average score for all the 3 classes , taken together ?
Options: a ) 81 , b ) 81.5 , c ) 82 , d ) 84.5 , e ) none of these
Rationale: explanation : let the number of students in classes x , y and z be a , b and c respectively . then total of x = 83 a total of y = 76 b total of z = 85 c and , ( 83 a + 76 b ) / ( a + b ) = 79 . i . e 4 a = 3 b . also , ( 76 b + 85 c ) / ( b + c ) = 81 . i . e 4 c = 5 b . hence , b = ( 4 / 3 ) a , c = ( 5 / 4 ) b = ( 5 / 4 ) x ( 4 / 3 ) a = ( 5 / 3 ) a . average of x , y and z = ( 83 a + 76 b + 85 c ) / ( a + b + c ) . = > 83 a + 76 ∗ ( 4 / 3 ) a + 85 ∗ ( 5 / 3 ) a / a + ( 4 / 3 ) a + ( 5 / 3 ) a . = > 978 / 12 = > 81.5 answer : b
Answer: b
Question (physics): a can finish a piece of work in 4 days . b can do it in 14 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "2 / 4 + ( 2 + x ) / 14 = 1 = > x = 5 days answer : b"
Answer: b
Question (general): the population of a town increased from 1 , 34,000 to 2 , 32,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 7.3 % , c ) 7.6 % , d ) 8.75 % , e ) none
Rationale: "explanation : increase in 10 years = ( 232500 - 134000 ) = 98500 . increase % = ( 98500 / 134000 x 100 ) % = 73 % . required average = ( 73 / 10 ) % = 7.3 % . answer : option b"
Answer: b
Question (general): if r is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of r ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: answer is c . numbers in format of 3 ^ k in the series from 1 to 30 inclusive r are : 3 * 1 , 3 * 2 , 3 * 3 , 3 * 4 , 3 * 5 , 3 * 3 * 2 , 3 * 7 , 3 * 8 , 3 * 3 * 3 , 3 * 10 . total number of 3 = 13 . so k = 14 .
Answer: c
Question (general): rs . 460 was divided among 41 boys and girls such that each boy rs . 12 and each girl got rs . 8 . what is the number of boys ?
Options: a ) 33 , b ) 30 , c ) 36 , d ) 28 , e ) 26
Rationale: explanation : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - assume that the number of boys = b and number of girls is g number of boys + number of girls = 41 = > b + g = 41 - - - - - - - - - - - - ( equation 1 ) given that each boy got rs . 12 and each girl got rs . 8 and total amount = rs . 460 = > 12 b + 8 g = 460 - - - - - - - - ( equation 2 ) now we need solve equation 1 and equation 2 to get b and g ( equation 1 ) × 8 = > 8 b + 8 g = 8 × 41 = 328 − − − − − − − − ( equation 3 ) ( equation 2 ) - ( equation 3 ) = 4 b = 460 - 328 = 132 = > b = 1324 = 33 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - given that amount received by a boy = rs . 12 and amount received by a girl = rs . 8 total amount = 460 given that number of boys + number of girls = 41 hence mean amount = 460 / 41 by the rule of alligation , we have amount received by a boy amount received by a girl 12 8 mean amount 460 / 41 460 / 41 - 8 = 132 / 41 12 - 460 / 41 = 32 / 41 number of boys : number of girls = 132 / 41 : 32 / 41 = 132 : 32 = 66 : 16 = 33 : 8 given that number of boys + number of girls = 41 hence number of boys = 41 × 3341 = 33 answer : option a
Answer: a
Question (gain): a shopkeeper sells 200 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) 12 , b ) 27 , c ) 29 , d ) 55 , e ) 95
Rationale: sp per metre = 18000 / 200 = rs . 90 loss per metre = rs . 5 cp per metre = 90 + 5 = rs . 95 . answer : e
Answer: e
Question (general): find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 .
Options: a ) 29 , b ) 27 , c ) 28 , d ) 24 , e ) 21
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 2 = 2 ^ 22 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer is a ."
Answer: a
Question (general): 1235 1253 1325 . . . . . . . . . + 5321 the addition problem above shows 4 of the 24 different integers that can be formed by using each of the digits 12 , 35 exactly once in each integer . what is the sum of these 24 integers ?
Options: a ) 73,326 , b ) 78,524 , c ) 84,820 , d ) 89,918 , e ) 95,560
Rationale: in each of the units , tens , hundreds , and thousands place , each digit will appear 6 times . then the sum equals 6 ( 1111 ) + 6 ( 2222 ) + 6 ( 3333 ) + 6 ( 5555 ) = 73,326 the answer is a .
Answer: a
Question (physics): a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution . if 45 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ?
Options: a ) 3.0 , b ) 5.0 , c ) 5.5 , d ) 6.5 , e ) 6.75
Rationale: "construct an equation : 15 / 100 = x / 45 - > x = 6.75 answer : e ."
Answer: e
Question (physics): two trains of equal lengths take 5 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 22 , b ) 12 , c ) 7.5 , d ) 99 , e ) 21
Rationale: "speed of the first train = 120 / 5 = 24 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 24 + 8 = 32 m / sec . required time = ( 120 + 120 ) / 32 = 7.5 sec . answer : c"
Answer: c
Question (gain): machine a and machine b are each used to manufacture 880 sprockets . it takes machine a 10 hours longer to produce 880 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 6 , b ) 6.6 , c ) 8.8 , d ) 100 , e ) 110
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 880 qt = 800 for a : ( t + 10 ) ( q ) = 880 qt + 10 q = 880 800 + 10 q = 880 q = 8 so a can produce 8 / hour . then b can produce = 8 ( 1.1 ) = 8.8 / hour . c"
Answer: c
Question (gain): an empty fuel tank with a capacity of 204 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 66 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 204 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 204 - a gallons of fuel b is 0.16 ( 204 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 204 - a ) = 30 - - > a = 66 . answer : d ."
Answer: d
Question (general): what is the largest 4 digit number exactly divisible by 50 ?
Options: a ) 4676 , b ) 4678 , c ) 9950 , d ) 9504 , e ) 9936
Rationale: "largest 4 digit number = 9999 9999 ÷ 50 = 199 , remainder = 49 hence largest 4 digit number exactly divisible by 50 = 9999 - 49 = 9950 answer : c"
Answer: c
Question (physics): if teena is driving at 55 miles per hour and is currently 7.5 miles behind poe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of poe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . poe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena can cover 7.5 miles in 30 mins teena will cover 15 miles in 60 mins so answer 30 + 60 = 90 mins = d"
Answer: d
Question (gain): the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1512 respectively . what is the rate of interest ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "1512 - 1400 = 112 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 112 ) / ( 1400 ) = 8 % the answer is d ."
Answer: d
Question (general): in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is
Options: a ) 86 , b ) 90 , c ) 92 , d ) 94 , e ) 96
Rationale: "divisor = ( 6 * 3 ) + 2 = 20 5 * quotient = 20 quotient = 4 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 4 ) + 6 = 86 . a"
Answer: a
Question (general): a number when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 31
Options: a ) 5 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "explanation : p ÷ 44 = 432 = > p = 432 * 44 = 19008 p / 31 = 19008 / 31 = 613 , remainder = 5 option a"
Answer: a
Question (gain): if $ 120 invested at a certain rate of simple interest amounts to $ 160 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 250
Rationale: "120 amounts to 160 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 160 120 + 120 * ( r / 100 ) * ( 3 ) = 160 = > r = 100 / 9 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) 250 answer is e ."
Answer: e
Question (general): the population of a town increased from 1 , 33,400 to 1 , 93,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.5 % , b ) 5.5 % , c ) 6.5 % , d ) 8.75 % , e ) none
Rationale: "explanation : increase in 10 years = ( 193500 - 133400 ) = 60100 . increase % = ( 60100 / 133400 x 100 ) % = 45 % . required average = ( 45 / 10 ) % = 4.5 % . answer : option a"
Answer: a
Question (gain): a person distributed 20 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 60000 . find his total income ?
Options: a ) a ) 1200000 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 500000 , e ) e ) 652000
Rationale: "3 children got = 3 * 20 % = 60 % wife got = 30 % orphan house = 5 % total = 60 + 30 + 5 = 95 % remaining = 100 - 95 = 5 % 5 % = 60000 100 % = 60000 * 100 / 5 = $ 1200000 answer is a"
Answer: a
Question (general): a = 5 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "a = 5 ^ 15 - 625 ^ 3 = > 5 ^ 15 - ( 5 ^ 4 ) ^ 3 = > 5 ^ 15 - 5 ^ 12 = 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 * 124 124 = 31 * 4 a / x is integer for condition of 2 < p < x only 5 and 31 satisfies this hence answer is c"
Answer: c
Question (physics): a car takes 6 hours to cover a distance of 360 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 70 , e ) 65
Rationale: "time = 6 distance = 360 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 360 / 9 = 40 kmph answer c ."
Answer: c
Question (probability): if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84
Rationale: "if we are to select 4 people from 7 couples without any restriction , how many ways can we make the selection ? 14 ! / 4 ! 10 ! = 1001 if we are to select 4 people from 7 couples with restriction that no married couple can both make it to the group , only a representative ? 7 ! / 4 ! 3 ! = 35 but we know that to select a person from each couple , take 2 possibilities 35 * 2 * 2 * 2 * 2 = 560 probability = desired / all possibilities = 560 / 1001 = 47 / 84 answer : e"
Answer: e
Question (gain): a shopkeeper has 100 kg of apples . he sells 50 % of these at 25 % profit and remaining 50 % at 30 % profit . find his % profit on total .
Options: a ) 27.5 % , b ) 25.6 % , c ) 31.5 % , d ) 35.9 % , e ) 29.5 %
Rationale: "total number of apples = 100 let the cost price be x selling price at 25 % profit = 1.25 x selling price at 30 % profit = 1.3 x profit % = ( ( sp - cp ) / cp ) * 100 profit % = ( ( 1 / 2 ) * 100 * 1.25 x + ( 1 / 2 ) * 100 * 1.3 x - 100 x ) / 100 x * 100 = ( 255 - 200 ) / 2 = 27.5 % answer is a"
Answer: a
Question (general): a card game called “ high - low ” divides a deck of 52 playing cards into 2 types , “ high ” cards and “ low ” cards . there are an equal number of “ high ” cards and “ low ” cards in the deck and “ high ” cards are worth 2 points , while “ low ” cards are worth 1 point . if you draw cards one at a time , how many ways can you draw “ high ” and “ low ” cards to earn 6 points if you must draw exactly 4 “ low ” cards ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "great question ravih . this is a permutations problem ( order matters ) with repeating elements . given thatlowcards are worth 1 pt andhigh cards 2 pts , and you must draw 3 low cards , we know that you must also draw 1 high card . the formula for permutations problems with repeating elements isn ! / a ! b ! . . . where n represents the number of elements in the group and a , b , etc . represent the number of times that repeating elements are repeated . here there are 4 elements and thelowcard is repeated 3 times . as a result , the formula is : 5 ! / 4 ! which represents ( 5 * 4 * 3 * 2 * 1 ) / ( 4 * 3 * 2 * 1 ) which simplifies to just 5 , giving you answer e ."
Answer: e
Question (gain): a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 970 gm . for a kg . his gain is … % .
Options: a ) 3.09 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 7.26 %
Rationale: "his percentage gain is 100 * 30 / 970 as he is gaining 30 units for his purchase of 970 units . so 3.09 % . answer : a"
Answer: a