Cheukting/mathqa huggingface dataset:
Question (gain): 70 percent of the members of a study group are women , and 40 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?
Options: a ) 0.28 , b ) 0.27 , c ) 0.25 , d ) 0.32 , e ) 0.35
Rationale: "say there are 100 people in that group , then there would be 0.7 * 0.40 * 100 = 28 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 28 / 100 . answer : a"
Answer: a
Question (general): if two integers x , y ( x > y ) are selected from - 5 to 5 ( inclusive ) , how many cases are there ?
Options: a ) 55 , b ) 60 , c ) 65 , d ) 70 , e ) 75
Rationale: "there are 11 integers from - 5 to 5 inclusive . 11 c 2 = 55 . the answer is a ."
Answer: a
Question (general): if x and y are positive integers and 5 + x + y + xy = 19 , what is the value of x + y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "try each answer choices . for a : 5 + 3 + xy = 19 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 5 + 5 + xy = 19 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 5 + 6 + xy = 19 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 5 + 8 + xy = 19 ; xy = 6 ( no combination of xy = 6 and x + y = 8 ) for e : 5 + 9 + xy = 19 ; xy = 5 ( impossible , 5 prime number . 1 + 5 does n ' t equal 9 ) therefore , answer c ."
Answer: c
Question (gain): the cost price of a radio is rs . 1500 and it was sold for rs . 1260 , find the loss % ?
Options: a ) 18 , b ) 16 , c ) 26 , d ) 17 , e ) 11
Rationale: "explanation : 1500 - - - - 240 100 - - - - ? = > 16 % answer : b"
Answer: b
Question (physics): find the area of a cuboid of length 12 cm , breadth 6 cm . and height 10 cm .
Options: a ) 400 cm cube , b ) 410 cm cube , c ) 720 cm cube , d ) 730 cm cube , e ) 480 cm cube
Rationale: "area of a cuboid = lxbxh = 12 cm x 6 cm x 10 cm = 720 cm cube answer : c"
Answer: c
Question (gain): a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1900 . the difference between the profit shares of a and c is ?
Options: a ) 288 , b ) 760 , c ) 155 , d ) 600 , e ) 441
Rationale: "ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1900 = > 5 parts out of 15 parts is rs . 1900 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1900 ) = rs . 760 answer : b"
Answer: b
Question (gain): what percent is 520 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 52 % , d ) 8 % , e ) 12 %
Rationale: "1 kg = 1000 gm 520 / 1000 ã — 100 = 52000 / 1000 = 52 % answer is c"
Answer: c
Question (physics): machine a can finish a job in 6 hours , machine в can finish the job in 12 hours , and machine с can finish the job in 8 hours . how many hours will it take for a , b , and с together to finish the job ?
Options: a ) 6 / 5 , b ) 7 / 4 , c ) 8 / 3 , d ) 9 / 2 , e ) 12 / 5
Rationale: the combined rate is 1 / 6 + 1 / 12 + 1 / 8 = 9 / 24 of the job per hour . the time to complete the job is 24 / 9 = 8 / 3 hours . the answer is c .
Answer: c
Question (general): the total marks obtained by a student in physics , chemistry and mathematics is 150 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 75 , b ) 66 , c ) 55 , d ) 44 , e ) 12
Rationale: let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : a
Answer: a
Question (gain): a man buys a cycle for rs . 1400 and sells it at a loss of 18 % . what is the selling price of the cycle ?
Options: a ) rs . 1148 , b ) rs . 1160 , c ) rs . 1190 , d ) rs . 1202 , e ) none
Rationale: "solution s . p = 82 % of rs . 1400 = rs . ( 82 / 100 × 1400 ) rs . 1148 . answer a"
Answer: a
Question (general): at a contest with 3000 participants , 1 / 2 of the people are aged 8 to 14 . next year , the number of people aged 8 to 14 will increase by 1 / 6 . after this change , what percentage of the total 3000 people will the 8 - to 14 - year - olds represent ?
Options: a ) 53.33 % , b ) 50 % , c ) 58.33 % , d ) 55.33 % , e ) 68 %
Rationale: "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 3000 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 6 , we are multiplying it by 1 + 1 / 6 = 7 / 6 , so the answer here must be ( 1 / 2 ) * ( 7 / 6 ) = 7 / 12 = 58.33 % . answer : c"
Answer: c
Question (general): if henry were to add 7 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
Options: a ) 25 , b ) 40 , c ) 64 , d ) 80 , e ) 56
Rationale: "7 / 8 x - 3 / 4 x = 7 galls 1 / 8 * x = 7 gallons x = 56 gallons answer e"
Answer: e
Question (general): the average weight of 16 boys in a class is 50.25 kgs and that of the remaining 8 boys is 45.15 kgs . find the average weight of all the boys in the class .
Options: a ) 47.55 kgs , b ) 48 kgs , c ) 48.55 kgs , d ) 49.25 kgs , e ) none of these
Rationale: "solution required average = ( 50.25 x 16 + 45.15 x 8 / 16 + 8 ) = ( 804 + 361.20 / 24 ) = 1165.20 / 24 = 48.55 answer c"
Answer: c
Question (general): of the 150 employees at company x , 50 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "150 employees 50 are full - time 100 have worked at company x for at least a year 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 150 - 50 = 100 employees not full time 100 - 20 = 80 employees not full time who worked over a year 100 employees have worked at company x for at least a year - 80 employees not full time who worked over a year = 20 full - time employees of company x have worked at the company for at least a year ans a"
Answer: a
Question (gain): solution x is 40 % chemical a and 60 % chemical b by volume . solution y is 50 % chemical a and 50 % chemical b by volume . if a mixture of x and y is 47 % chemical a , what percent of the mixture is solution x ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "the volume of the mixture be x + y . 0.4 x + 0.5 y = 0.47 ( x + y ) x = 3 y / 7 x / ( x + y ) = ( 3 y / 7 ) / ( 10 y / 7 ) = 3 / 10 = 30 % . the answer is d ."
Answer: d
Question (gain): a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 30.00 ?
Options: a ) $ 10.00 , b ) $ 11.20 , c ) $ 14.40 , d ) $ 16.80 , e ) $ 18.00
Rationale: "for retail price = $ 30 first maximum discounted price = 30 - 30 % of 30 = 30 - 9 = 21 price after additional discount of 20 % = 21 - 20 % of 21 = 21 - 4.2 = 16.8 answer : option d"
Answer: d
Question (general): the simple interest on a sum of money will be rs . 500 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 2261 , b ) 2888 , c ) 1200 , d ) 2699 , e ) 900
Rationale: "p - - - 10 - - - - 500 p - - - 5 - - - - - 250 3 p - - - 5 - - - - - 750 - - - - - - = > 900 answer : e"
Answer: e
Question (geometry): 16 meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?
Options: a ) 2 √ 2 , b ) 4 , c ) 5 , d ) 4 √ 2 , e ) none of these
Rationale: "area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 16 = > x / 360 * 2 * pi * r + 2 r = 16 = > 2 a / r + 2 r = 16 = > a = ( r 16 - 2 r ^ 2 ) / 2 = r 8 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 8 - 2 r = 0 r = 4 b"
Answer: b
Question (physics): amar takes as much time in running 21 meters as a car takes in covering 54 meters . what will be the distance covered by amar during the time the car covers 1.8 km ?
Options: a ) 700 m , b ) 500 m , c ) 670 m , d ) 700 m , e ) 640 m
Rationale: "distance covered by amar = 21 / 54 ( 1.8 km ) = 7 / 18 ( 1800 ) = 700 m answer : d"
Answer: d
Question (gain): an alloy weighing 16 ounces is 50 % gold . how many ounces of pure gold must be added to create an alloy that is 80 % gold ?
Options: a ) 24 , b ) 18 , c ) 9 , d ) 27 , e ) 18
Rationale: "an alloy of 16 oz which is 50 % gold means there is 8 oz of gold . to get to an alloy that is 80 % gold , let ' s use this expression : ( 8 + x ) / ( 16 + x ) = 0.8 with x representing the amount of pure gold that must be added to get to 80 % . the expression we are using represents the new total weight of pure gold over the new total new weight of the alloy and this fraction should represent 80 % or 0.8 . you will see that 24 is the correct answer , as 32 / 40 = 0.8 choose a"
Answer: a
Question (gain): what percent of 12.4 kg is 20 gms ?
Options: a ) 25 , b ) 16 , c ) 18 , d ) 19 , e ) 17
Rationale: "explanation : required percentage = ( 20 / 12400 * 100 ) % = 4 / 25 % = 0.16 % answer : b ) . 16 %"
Answer: b
Question (gain): what percent of the year 2017 is 219 days ?
Options: a ) 56 % , b ) 72 % , c ) 64,5 % , d ) 51 % , e ) 60 %
Rationale: "explanation : total days in the year 2017 = 365 required percentage = ( 219 / 365 ) ã — 100 = 60 % answer : option d"
Answer: d
Question (general): from 4 officers and 8 jawans in how many can 6 be chosen to include exactly one officer ?
Options: a ) 150 , b ) 164 , c ) 259 , d ) 311 , e ) 224
Rationale: required number of ways = 4 c 1 * 8 c 5 = 224 answer is e
Answer: e
Question (geometry): if each side of a rectangle is increased by 100 % , by what % the area increases ?
Options: a ) 100 %
b ) 200 %
c ) 250 %
d ) 300 %
e ) 400 %
Rationale: if length is l and width is b then area = l * b now new l and b is 2 l and 2 b respectively . so new area is = 4 * l * b % increase = 300 % answer : d
Answer: d
Question (physics): a train 560 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 56 , c ) 41 , d ) 42 , e ) 34
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 560 + 140 = 700 m required time = 700 * 2 / 25 = 40 sec answer : option b"
Answer: b
Question (physics): a boat sails 15 km of a river towards upstream in 5 hours . how long will it take to cover the same distance downstream , if the speed of current is one - fourth the speed of the boat in still water ?
Options: a ) 7 h , b ) 3 h , c ) 4 h , d ) 2 h , e ) 9 h
Rationale: explanation : upstream speed = b - s downstream speed = b + s b - s = 15 / 5 = 3 km / h again b = 4 s therefore b - s = 3 = 3 s = > s = 1 and b = 4 km / h therefore b + s = 5 km / h therefore , time during downstream = 15 / 5 = 3 h answer : b
Answer: b
Question (general): the tax on a commodity is diminished by 22 % and its consumption increased by 11 % . the effect on revenue is ?
Options: a ) 8 , b ) 6 , c ) 5 , d ) 4 , e ) 2
Rationale: "100 * 100 = 10000 88 * 111 = 9768 - - - - - - - - - - - 10000 - - - - - - - - - - - 232 100 - - - - - - - - - - - ? = > 2 % decrease answer : e"
Answer: e
Question (general): if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 16 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 9 / 16 , e ) 3 / 4
Rationale: "i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 16 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 16 = not integer we can not forget multiples of 16 from 1 to 96 we have 6 numbers that are multiple of 16 therefore , 48 / 96 + 6 / 96 = 54 / 96 = 9 / 16 answer : d"
Answer: d
Question (physics): there was two trains from calcutta to kanyakumari one train is fast service travels with a speed 75 km per hour another travels with a speed of 44 km per hour the time taken to reach from calcutta to kanyakumari is 4 hours less than the first train . . . find the distance b / w calcatta to kanyakumari
Options: a ) 415.8 km , b ) 425.8 km , c ) 435.8 km , d ) 445.8 km , e ) 455.8 km
Rationale: let distance b / w calcutta to kanyakumari is = x km then eqn is x / 44 - x / 75 = 4 = > x * ( 75 - 44 ) = 4 * 75 * 44 = > x = 425.8 km answer : b
Answer: b
Question (other): in a group of 10 doctors , 3 doctors are only pediatricians ; the others are surgeons or general practitioners - but not both . a team of 3 doctors is to be chosen which must have at least 1 pediatrician , how many different teams can be chosen ?
Options: a ) 85 , b ) 140 , c ) 60 , d ) 80 , e ) 75
Rationale: the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 10 r = 3 so , total teams is 10 c 3 = 10 ! / ( 3 ! ( 10 - 3 ) ! ) = 120 , and n = 10 - 3 = 7 r = 3 for teams without a pediatrician is 7 c 3 = 7 ! / ( 3 ! ( 7 - 3 ) ! ) = 35 , so , teams with at least 1 pediatrician = 120 - 35 = 85 answer : a
Answer: a
Question (geometry): if the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm , a square with the same area as the original rectangle would result . find the perimeter of the original rectangle ?
Options: a ) 76 , b ) 27 , c ) 19 , d ) 50 , e ) 11
Rationale: "let x and y be the length and breadth of the rectangle respectively . then , x - 4 = y + 3 or x - y = 7 - - - - ( i ) area of the rectangle = xy ; area of the square = ( x - 4 ) ( y + 3 ) ( x - 4 ) ( y + 3 ) = xy < = > 3 x - 4 y = 12 - - - - ( ii ) solving ( i ) and ( ii ) , we get x = 16 and y = 9 . perimeter of the rectangle = 2 ( x + y ) = [ 2 ( 16 + 9 ) ] cm = 50 cm . answer : d"
Answer: d
Question (general): a football player scores 4 goals in his fifth match thus increasing his average goals score by 0.2 . the total number of goals in his 5 matches would be
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 16
Rationale: "while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer e = 16 goals if . . . . total goals = 16 goals 5 th game = 4 goals 1 st 4 games = 12 goals avg . for 1 st 4 games = 12 / 4 = 3 goal / game avg . for all 5 games = 6 / 5 = 3.2 goals / game this is an exact match for what we ' re told in the prompt , so answer e must be the answer ."
Answer: e
Question (general): the unit digit in the product 784 * 618 * 917 * 463 is ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 5 , e ) 6
Rationale: "unit digit in the given product = unit digit in 4 * 8 * 7 * 3 = 2 answer is b"
Answer: b
Question (gain): how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 35 % iodine solution ?
Options: a ) 35 , b ) 49 , c ) 100 , d ) 105 , e ) 140
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % iodine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 35 / 100 40 x + 700 = 35 x + 1225 5 x = 525 x = 105 lts correct option : d"
Answer: d
Question (physics): if 8 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 32 days , c ) 42 days , d ) 48 days , e ) 44 days
Rationale: "8 * 80 = 20 * x x = 32 days answer : b"
Answer: b
Question (gain): in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 18 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 144 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,18 = 18 / 100 x = 80 * 18 / 100 x = 14.4 14.4 / 10 = 1,44 = 144 % , answer d"
Answer: d
Question (physics): a courtyard is 30 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 24000 , c ) 20000 , d ) 27999 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 3000 × 1600 / 20 × 10 ) = 24000 answer : b"
Answer: b
Question (general): what is the smallest positive integer that leaves a remainder of 1 when divided by 2 , remainder of 2 when divided by 3 , a remainder of 3 when divided by 4 , and a remainder of 9 when divided by 10 ?
Options: a ) 58 , b ) 59 , c ) 60 , d ) 61 , e ) 62
Rationale: remainder of 1 when divided by 2 : ( 2 - 1 = 1 ) remainder of 2 when divided by 3 : ( 3 - 2 = 1 ) remainder of 3 when divided by 4 : ( 4 - 3 = 1 ) remainder of 9 when divided by 10 : ( 2 - 1 = 1 ) so n + 1 should be divisible by 23 , 410 ( where n is desired number ) l . c . m . of 23 , 410 = 60 ( = n + 1 ) n = 59 answer : b
Answer: b
Question (physics): tim ' s garden is shaped like a square whose side is 28 meters . what ' s the length of the fence which surrounds the garden ?
Options: a ) 110 meters
b ) 111 meters
c ) 112 meters
d ) 113 meters
e ) 114 meters
Rationale: solution : all sides of the square are equal . the length of the fence is 4 times the side . p = 4 × 28 = 112 meters answer c
Answer: c
Question (other): find the fraction which has the same ratio to 2 / 6 that 3 / 4 has to 1 / 2
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 6 / 8 , d ) 9 / 4 , e ) 7 / 5
Rationale: "p : 2 / 6 = 3 / 4 : 1 / 2 as the product of the means is equal to the product of the extremes . p * 1 / 2 = 2 / 6 * 3 / 4 p * 1 / 2 = 6 / 24 p = 1 / 2 = > p = 1 / 2 answer : a"
Answer: a
Question (physics): if 13 lions can kill 13 deers in 13 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 13 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 13 ( lions ) * 13 ( min ) / 13 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 13 answer : b"
Answer: b
Question (general): if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 66 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80
Rationale: "let the price of one shirt be ss and of jeans be j : 3 j + 2 s = 69 2 j + 3 s = 66 subtracting the second from the first gives : j − s = 3 or j = s + 3 plug j in either of the equations and solve for s , which is $ 12 answer : b ."
Answer: b
Question (physics): each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 30 minutes earlier than usual . how much time did the man spend walking ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 40 minutes , d ) 55 minutes , e ) 35 minutes
Rationale: "as they arrived 30 minutes earlier than usual , they saved 30 minutes on round trip from home to station ( home - station - home ) - - > 15 minutes in each direction ( home - station ) - - > wife meets husband 15 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 15 minutes = 45 minutes . answer : a"
Answer: a
Question (physics): the speed of a car is 145 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 89 kmph , b ) 92 kmph , c ) 75 kmph , d ) 102.5 kmph , e ) 77 kmph
Rationale: "s = ( 145 + 60 ) / 2 = 102.5 kmph d"
Answer: d
Question (general): the greatest number which on dividing 1657 and 2037 leaves remainders 10 and 7 respectively , is :
Options: a ) 123 , b ) 1 , c ) 235 , d ) 305 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1657 - 10 ) and ( 2037 - 7 ) = h . c . f . of 1647 and 2030 = 1 . answer : b"
Answer: b
Question (gain): a grocer has 400 pounds of coffee in stock , 40 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 44 %
Rationale: "1 . 40 % of 400 = 160 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 220 pounds of decaffeinated out of 500 pounds , that means 220 / 500 * 100 % = 44 % . the correct answer is e ."
Answer: e
Question (general): if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 21 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 21 . then 4 n < 21 and n < 5.25 . the largest possible integer is n = 5 . the answer is e ."
Answer: e
Question (other): each factor of 290 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 16 , d ) 3 / 16 , e ) 1 / 4
Rationale: "290 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 6 answer : c ."
Answer: c
Question (general): the average runs of a cricket player of 13 innings was 22 . how many runs must he make in his next innings so as to increase his average of runs by 5 ?
Options: a ) 92 , b ) 42 , c ) 64 , d ) 76 , e ) 84
Rationale: explanation : average after 14 innings = 27 required number of runs = ( 27 * 14 ) – ( 22 * 13 ) = 378 – 286 = 92 answer a
Answer: a
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling alongthe boundary ofthe park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 13400 m , b ) 147600 m , c ) 153600 m , d ) 187500 m , e ) 196700 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m c"
Answer: c