regisss/math_qa huggingface dataset:
Problem: a and b can finish a work in 7 days and 8 days respectively . if both do work one day and leave one day . and a start the work then in how much days work will finish ?
Options: a ) 52 / 7 , b ) 8 , c ) 14 / 2 , d ) 6 , e ) 43 / 6
Rationale: ( a + b ) work in 2 days = [ 1 / 7 + 1 / 8 ] = 15 / 56 ( a + b ) work in 6 days = 45 / 56 now , the turn of a , work of a in 1 day = 1 / 7 . till now completed work = [ 45 / 56 + 1 / 7 ] = 53 / 56 , remaining work = [ 1 - 53 / 56 ] = 3 / 56 now , turn of b , 1 / 8 work b do in 1 day so , 3 / 56 part of work b do = [ 8 * 3 / 56 ] = 3 / 7 days total time taken = 6 + 1 + 3 / 7 = 52 / 7 days answer a
Answer: a
Problem: 5 pumps , working 9 hours a day , can empty a tank in 3 days . how many hours a day should 6 pumps work in order to empty the tank in 1 day ?
Options: a ) 20 hours , b ) 22.5 hours , c ) 23 hours , d ) 23.5 hours , e ) 24 hours
Rationale: "let the required hours needed be x more pumps , less hours ( indirect proportion ) more days , less hours ( indirect proportion ) hence we can write as ( pumps ) 5 : 6 } : : x : 9 ( days ) 3 : 1 = > 5 * 3 * 9 = 6 * 1 * x = > x = 45 / 2 = > 22.5 answer : b"
Answer: b
Problem: if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 79 , what is the value of a ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 36 , e ) 42
Rationale: "( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 79 a = 30 the answer is b ."
Answer: b
Problem: we run a business that rents out canoes and kayaks . a canoe rental costs $ 12 per day , and a kayak rental costs $ 18 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 504 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let x be the number of canoes . then 2 x / 3 is the number of kayaks . 12 x + ( 2 x / 3 ) * 18 = 504 12 x + 12 x = 504 24 x = 504 x = 21 ( canoes ) 2 x / 3 = 14 ( kayaks ) there were 21 - 14 = 7 more canoes rented out . the answer is c ."
Answer: c
Problem: the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 96 , b ) 106 , c ) 122 , d ) 116 , e ) 122
Rationale: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 4 = 36 runs total runs = new avg x new no . of innings = 36 * 21 = 756 runs made in the 11 th inning = 756 - 640 = 116 answer : d"
Answer: d
Problem: a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability r that a + b is prime ?
Options: a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9
Rationale: total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes r = 15 / 36 . answer : c .
Answer: c
Problem: a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 22,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,600 , e ) s . 7,500
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 22000 x 3 / 10 = rs . 6,600 . d"
Answer: d
Problem: find the value for x from below equation : x / 3 = - 6 ?
Options: a ) - 16 , b ) 11 , c ) - 12 , d ) - 18 , e ) 14
Rationale: "1 . multiply both sides by 3 : x * 3 / 3 = - 6 / 3 simplify both sides : x = - 18 d"
Answer: d
Problem: x can do a piece of work in 8 hours . y and z together can do it in 6 hours , while x and z together can do it in 4 hours . how long will y alone take to do it ?
Options: a ) 24 hours , b ) 20 hours , c ) 34 hours , d ) 12 hours , e ) 10 hours
Rationale: x ' s 1 hour work = 1 / 8 ( y + z ) ' s 1 hour work = 1 / 6 ( x + z ) ' s 1 hour work = 1 / 4 ( x + y + z ) ' s 1 hour work = ( 1 / 8 + 1 / 6 ) = 7 / 24 y ' s 1 hour ' s work = ( 7 / 24 - 1 / 4 ) = 1 / 24 y alone will take 24 hours to do the work . correct option is a
Answer: a
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 13000 after a year ?
Options: a ) 3630 , b ) 3900 , c ) 8828 , d ) 2387 , e ) 2813
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 13000 = 3900 answer : b"
Answer: b
Problem: if two students starting from same point , walking in the opposite directions with 6 km / hr and 9 km / hr as average speeds respectively . then the distance between them after 4 hours is ?
Options: a ) 65 km , b ) 55 km , c ) 15 km , d ) 60 km , e ) 75 km
Rationale: explanation : total distance = distance traveled by person a + distance traveled by person b = ( 6 × 4 ) + ( 9 × 4 ) = 24 + 36 = 60 km answer : d
Answer: d
Problem: dacid obtained 51 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 29 , b ) 38 , c ) 39 , d ) 70 , e ) 75
Rationale: "average = ( 51 + 65 + 82 + 67 + 85 ) / 5 = 70 answer : d"
Answer: d
Problem: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 23 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 9 / 8 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 23 ) = 36 / 32 = 9 / 8 . answer : a ."
Answer: a
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 20 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 25 % , e ) 27.5 %
Rationale: "since 20 % of the customers who sample the candyare notcaught , then 80 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.80 = 0.22 ; { % of customers who sample candy } = 0.275 answer : e ."
Answer: e
Problem: if the selling price of 50 articles is equal to the cost price of 40 articles , then the loss or gain percent is ?
Options: a ) 20 % , b ) 80 % , c ) 90 % , d ) 22 % , e ) 24 %
Rationale: "let c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 40 . loss % = 10 / 50 * 100 = 20 % . answer : a"
Answer: a
Problem: 3 students appear at an examination of mathematics . the probability of their success are 1 / 2 , 1 / 4 , 1 / 5 respectively . find the probability of success of at least two .
Options: a ) 1 / 60 , b ) 2 / 50 , c ) 9 / 40 , d ) 3 / 40 , e ) 4 / 50
Rationale: the probability of success of at least two students will involve the following possibilities . the first two students are successful , the last two students are successful , the first and third students are successful and all the three students are successful . therefore , the required probability = 1 / 2 x 1 / 4 x 4 / 5 + 1 / 4 x 1 / 5 x 1 / 2 + 1 / 2 x 1 / 5 x 3 / 4 + 1 / 2 x 1 / 4 x 1 / 5 = 9 / 40 answer : c
Answer: c
Problem: if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 2 , then what is the value of abc / def ?
Options: a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 8 , e ) 1 / 4
Rationale: "say a = 3 . then : a / b = 1 / 3 - - > b = 9 ; b / c = 2 - - > c = 9 / 2 ; c / d = 1 / 2 - - > d = 9 ; d / e = 3 - - > e = 3 ; e / f = 1 / 2 - - > f = 6 . abc / def = ( 3 * 9 * 9 / 2 ) / ( 9 * 3 * 6 ) = 3 / 4 . answer : c ."
Answer: c
Problem: a train leaves delhi at 9 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 42 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 229 , b ) 288 , c ) 787.5 , d ) 888 , e ) 121
Rationale: "d = 30 * 5 = 150 rs = 42 – 30 = 8 t = 150 / 8 = 18.75 d = 42 * 18.75 = 787.5 km answer : c"
Answer: c
Problem: a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 2 km on foot . his total journey is
Options: a ) 16 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 25 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 2 = x 5 x + 12 = 6 x x = 12 km answer : option c"
Answer: c
Problem: the average of 7 consecutive numbers is 33 . the highest of these numbers is :
Options: a ) 28 , b ) 30 , c ) 33 , d ) 36 , e ) 28
Rationale: "the average of 7 consecutive numbers will be the 4 th number which is given to be = 33 5 th number = 34 , 6 th number = 35 , 7 th number = 36 answer : d ."
Answer: d
Problem: 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 / 6 . 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 ) 116 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Rationale: "the probability of survival for each of the first 3 months of life is 1 - 1 / 6 = 5 / 6 , so of 200 newborn 200 * 5 / 6 * 5 / 6 * 5 / 6 = ~ 116 is expected to survive . answer : a ."
Answer: a
Problem: find the circumference of radius 7 cm .
Options: a ) 44 , b ) 55 , c ) 66 , d ) 77 , e ) 88
Rationale: "circumference of circle = 2 π r = 2 × 22 / 7 × 7 = 44 cm answer : a"
Answer: a
Problem: in what time will a train 50 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 1.25 sec , b ) 2.75 sec , c ) 3.5 sec , d ) 2.39 sec , e ) 9.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 50 / 40 = 1.25 sec . answer : a"
Answer: a
Problem: a square carpet with an area 169 m 2 must have 2 metres cut - off one of its edges in order to be a perfect fit for a rectangular room . what is the area of rectangular room ?
Options: a ) 180 m 2
b ) 164 m 2
c ) 152 m 2
d ) 143 m 2
e ) none of these
Rationale: side of square carpet = √ area = √ 169 = 13 m after cutting of one side , measure of one side = 13 – 2 = 11 m and other side = 13 m ( remain same ) ∴ area of rectangular room = 13 × 11 = 143 m 2 answer d
Answer: d
Problem: a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 3 is
Options: a ) 3 , b ) 189 , c ) 221 , d ) 227 , e ) 230
Rationale: "in that case , the sophie prime numbers greater than 5 are 7 , 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be b ."
Answer: b
Problem: a number x is multiplied by 5 , and this product is then divided by 7 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?
Options: a ) 25 / 9 , b ) 9 / 5 , c ) 5 / 7 , d ) 3 / 5 , e ) 9 / 25
Rationale: "sqrt ( 5 x / 7 ) to be perfect square x has to 5 / 7 ans : c"
Answer: c
Problem: the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > 0 or y > x ?
Options: a ) 5 / 8 , b ) 1 / 6 , c ) 3 / 8 , d ) 1 / 2 , e ) 3 / 4
Rationale: "the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points above the x - axis satisfy the condition that y > 0 . the union of these two areas is 5 / 8 of the circle . the answer is a ."
Answer: a
Problem: in a kilometer race , a beats b by 25 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 167 sec , b ) 190 sec , c ) 390 sec , d ) 716 sec , e ) 123 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 25 = 400 sec . time taken by a = 400 - 10 = 390 sec . answer : c"
Answer: c
Problem: one week , a certain truck rental lot had a total of 26 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 14 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 18 , b ) 16 , c ) 12 , d ) 24 , e ) 4
Rationale: "n - not rented trucks ; r - rented trucks n + r = 26 n + r / 2 = 14 r = 24 d"
Answer: d
Problem: each week , harry is paid x dollars per hour for the first 15 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 33 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: 42 x = 15 x + 1.5 x ( h - 15 ) = = > 42 = 15 + 1.5 ( h - 15 ) = = > h - 15 = 27 / 1.5 = 18 = = > h = 33 answer is a
Answer: a
Problem: shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 200 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 245 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 4000 , b ) 3500 , c ) 2500 , d ) 3000 , e ) 2000
Rationale: "so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 100 , thus 0.2 x = $ 100 - - > x = $ 1,000 . since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,000 = $ 2,000 answer e"
Answer: e
Problem: how many seconds will a train 100 meters long take to cross a bridge 160 meters long if the speed of the train is 36 kmph ?
Options: a ) 26 , b ) 72 , c ) 25 , d ) 82 , e ) 27
Rationale: "explanation : d = 100 + 160 = 260 s = 36 * 5 / 18 = 10 mps t = 260 / 10 = 26 sec answer : option a"
Answer: a
Problem: at a bank , the service charges for transactions were us dollar 1 for every 5 transactions . the bank recently revised the charges to us dollar 0.75 for every 3 transactions . by approximately what percent did the ratio of price to transactions increase from the previous charge ?
Options: a ) 28 , b ) 24 , c ) 23 , d ) 22 , e ) 25
Rationale: initial charge / transaction ratio = 1 / 5 = 3 / 15 revised charge / transaction ratio = . 75 / 3 = 3.75 / 15 answer : e
Answer: e
Problem: convert 800 miles into meters ?
Options: a ) 1287472 , b ) 845796 , c ) 804670 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 800 mile = 800 * 1609.34 = 1287472 meters answer is a"
Answer: a
Problem: nil and ethan are brothers . they left their home at the same time and drove to the same beach . nil drove at a speed of 80 miles per hour . ethan drove at a speed of 20 miles per hour . nil arrived at the beach 0.5 hour earlier than ethan . what is the distance between their home and the beach ?
Options: a ) 70 miles , b ) 80 miles , c ) 90 miles , d ) 100 miles , e ) 110 miles
Rationale: every hour , nil gets ahead of ethan 80 - 20 = 60 miles . when nil arrived at the beach , ethan is only 20 × 0.5 = 10 miles behind . that tells us they only drove 1 hour when nil arrived at the beach . the distance between their home and the beach is nil ’ s speed × nil ’ s time = 80 × 1 = 80 miles . correct answer b
Answer: b
Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 19 !
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: solution - consider multiples of 25 ! = > 3,6 , 9,12 , 15,18 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 - - - - count 3 ' s = 8 so answer is 8 answer : a
Answer: a
Problem: a reduction of 15 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 1200 , what is the reduced price for kg ?
Options: a ) 43 , b ) 55 , c ) 35 , d ) 45 , e ) 40
Rationale: "1200 * ( 15 / 100 ) = 180 - - - - 4 ? - - - - 1 = > rs . 45 answer : d"
Answer: d
Problem: x , y , and z are different prime numbers . the product x ^ 2 * y ^ 2 * z is divisible by how many different positive numbers ?
Options: a ) 6 , b ) 8 , c ) 12 , d ) 18 , e ) 24
Rationale: "the exponents of x ^ 2 * y ^ 2 * z are 2 , 2 , and 1 . the number of factors is ( 2 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 18 the answer is d ."
Answer: d
Problem: a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 48 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 72 , b ) 75 , c ) 80 , d ) 84 , e ) 90
Rationale: "let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 96 + ( d / 2 ) / v 8 d / 480 - 5 d / 480 = ( d / 2 ) / v d / 160 = d / 2 v and so v = 80 km / hr the answer is c ."
Answer: c
Problem: a soccer store typically sells replica jerseys at a discount of 60 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 50 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , e is the answer"
Answer: e
Problem: how many real solutions does the equation x 5 + 2 x 3 + 8 x 2 + 16 = 0 have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: note that x 5 + 2 x 3 + 8 x 2 + 16 = ( x 3 + 8 ) ( x 2 + 2 ) = ( x + 2 ) ( x 2 - 2 x + 4 ) ( x 2 + 2 ) . since the quadratic equations x 2 - 2 x + 4 = 0 and x 2 + 2 = 0 have no real solutions , the original equation has just one real solution , x = - 2 . correct answer b
Answer: b
Problem: a man is 20 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 18 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 20 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 20 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 18 answer : e"
Answer: e
Problem: a man can row downstream at the rate of 10 km / hr and upstream at 6 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 8,2 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 10 + 6 ) = 8 km / hr rate of current = 1 / 2 ( 10 - 6 ) = 2 km / hr answer : option b"
Answer: b
Problem: in a can , there is a mixture of milk and water in the ratio 8 : 5 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 12 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 18.4 , c ) 48 , d ) 50 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 8 / 13 ( t - 8 ) after adding milk , quantity of milk in the mixture = 12 / 17 t . 12 t / 17 - 8 = 8 / 13 ( t - 8 ) 20 t = 1456 - 1088 = > t = 18.4 . answer : b"
Answer: b
Problem: matt and peter can do together a piece of work in 20 days . after they have worked together for 12 days matt stops and peter completes the remaining work in 8 days . in how many days peter complete the work separately .
Options: a ) 21 , b ) 24 , c ) 20 , d ) 25 , e ) 30
Rationale: "together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 8 days which means that the whole job ( 1 ) can be completed in x days . x = 8 / ( 8 / 20 ) = 20 c"
Answer: c
Problem: if 40 % of a number exceeds 25 % of it by 18 , then find the number ?
Options: a ) 120 , b ) 150 , c ) 200 , d ) 64 , e ) 100
Rationale: "use the elimination method to find the correct option . of all the options only 120 fits 40 % of 120 = 48 25 % of 120 = 30 48 - 30 = 18 required number is 180 . answer : a"
Answer: a
Problem: jack rode his bicycle at an average speed of 5 mph for some time and then at an average speed of 15 mph for the rest of the journey . if he made no stops during the trip , and his average speed for the entire journey was 10 miles per hour , for what fraction of the total time did he ride at 15 mph ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 3 , d ) 2 / 5 , e ) 1 / 2
Rationale: we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . the average speed for the entire journey is 10 mph ; so , he rode at 5 mph and 15 mph for an equal duration of time . difference is 5 and 5 , respectively . 5 - - - - 10 - - - - 15 this shows that you can divide the entire journey into 2 equal parts . thus , 1 / 2 of the journey he rode at 10 mph , and 1 / 2 of the journey he rode at 15 mph . answer : e
Answer: e
Problem: of the female students at barkely university , 1 / 6 are on the honor roll . of the male students , 2 / 5 are on the honor roll . if 3 / 5 of the students are female , what is ratio of male to female students on honor roll ?
Options: a ) 8 / 5 , b ) 3 / 15 , c ) 23 / 30 , d ) 43 / 60 , e ) 53 / 90
Rationale: "let the total students be 100 given 3 / 5 of the students are females = 60 then males = 2 / 5 = 40 1 / 6 of the females are on honor roll = 10 males on the honor roll = 2 / 5 = 16 ratio of m : f students on honor roll = 16 / 10 = 8 / 5 a"
Answer: a
Problem: if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 7
Rationale: "( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 7 = e"
Answer: e
Problem: the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 85 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 105 kg
Rationale: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 85 + 20 ) kg = 105 kg the answer is e ."
Answer: e
Problem: if it takes a tub 6 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ?
Options: a ) 48 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 50 seconds , d ) 2 minutes , 24 seconds , e ) 4 minutes , 12 seconds
Rationale: if 5 / 7 of tub ' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 6 minutes to drain 5 / 7 th of tub it takes 6 * ( 7 / 5 ) minutes to drain the entire tub and 6 * ( 7 / 5 ) * ( 2 / 7 ) min to drain 2 / 7 th of the tub which is 2.4 minutes or 12 / 5 minutes or 2 minute 24 seconds so answer is d
Answer: d
Problem: the compound ratio of 5 : 6 , 5 : 2 and 4 : 5 ?
Options: a ) 1 : 1 , b ) 5 : 3 , c ) 1 : 6 , d ) 1 : 9 , e ) 1 : 2
Rationale: "5 / 6 * 5 / 2 * 4 / 5 = 5 / 3 5 : 3 answer : b"
Answer: b
Problem: the average of 10 numbers is 60 . out of 10 numbers the average of first 6 no . is 68 , and last 6 numbers is 75 then find 7 th number ?
Options: a ) a ) 78 , b ) b ) 65 , c ) c ) 258 , d ) d ) 62 , e ) e ) 48
Rationale: "7 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 68 + 6 * 75 - 10 * 60 = 258 answer is c"
Answer: c
Problem: for a certain exam , a score of 42 was 5 standard deviations below mean and a score of 67 was 2.5 standard deviations above mean . what was the mean score for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 58.67 , e ) 82.2
Rationale: "mean - 5 sd = 42 mean + 2.5 sd = 67 by solving above equations we get , sd ( absolute value ) = 3.33 mean = 58.67 ans . d"
Answer: d
Problem: how many integers between 1 and 1,050 are divisible by 10 , 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 3
Rationale: "prime factorization of given numbers 10 = 2 * 5 25 = 5 ^ 2 35 = 5 * 7 lcm of the given numbers = 2 * 5 ^ 2 * 7 = 50 * 7 = 350 therefore , number of integers = 1050 / 350 = 3 answer : option e"
Answer: e