Cheukting/mathqa huggingface dataset:
Question (general): carl bought 16 gumballs , lewis bought 12 gumballs , and carey bought x gumballs . the average ( arithmetic mean ) number of gumballs the 3 bought is between 19 and 25 , inclusive . what is the difference between the greatest number and the smallest number of gumballs carey could have bought ?
Options: a ) 20 , b ) 16 , c ) 22 , d ) 18 , e ) 24
Rationale: smallest gumballs = ( 19 - 16 ) + ( 19 - 12 ) + 19 = 29 largest gumballs = ( 25 - 16 ) + ( 25 - 12 ) + 25 = 47 difference = 47 - 29 = 18 d
Answer: d
Question (physics): x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 28 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 35
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 28 days whole work will be done by y in 28 * 5 / 4 = 35 days answer is e"
Answer: e
Question (general): find the principle on a certain sum of money at 7 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 939.6 , b ) 958.9 , c ) 927.78 , d ) 926.82 , e ) 902.1
Rationale: "1120 = p [ 1 + ( 7 * 12 / 5 ) / 100 ] p = 958.90 answer : b"
Answer: b
Question (gain): find the simple interest on rs . 69,600 at 16 2 / 3 % per annum for 9 months .
Options: a ) s . 8500 , b ) s . 8700 , c ) s . 7500 , d ) s . 7000 , e ) s . 6500
Rationale: "p = rs . 69600 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 69,600 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8700 answer is b ."
Answer: b
Question (physics): the lcm and hcf of two numbers are 60 and 2 respectively . find the larger of the two numbers if their sum is 22 .
Options: a ) 12 , b ) 2 , c ) 4 , d ) 54 , e ) 56
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 60 * 2 = 120 so the answer which we are looking for has to be a factor of 120 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 120 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Question (physics): excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 20 , e ) 22
Rationale: "due to stoppages , it covers 9 km less . time taken to cover 9 km = ( 9 / 54 x 60 ) min = 10 min . answer : b"
Answer: b
Question (other): the number of stamps that p and q had were in the ratio of 7 : 2 respectively . after p gave q 15 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 2 : 1 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65
Rationale: "p started with 7 k stamps and q started with 2 k stamps . ( 7 k - 15 ) / ( 2 k + 15 ) = 2 / 1 3 k = 45 k = 15 p has 7 ( 15 ) - 15 = 90 stamps and q has 2 ( 15 ) + 15 = 45 stamps . the answer is c ."
Answer: c
Question (physics): if a , b and c together can finish a piece of work in 6 days . a alone in 12 days and b in 18 days , then c alone can do it in ?
Options: a ) 1 , b ) 7 , c ) 8 , d ) 9 , e ) 36
Rationale: "c = 1 / 6 - 1 / 12 – 1 / 18 = 1 / 36 = > 36 days ' answer : e"
Answer: e
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 33 % iodine solution ?
Options: a ) 35 , b ) 49 , c ) 100 , d ) 105 , e ) 122
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 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 33 / 100 40 x + 700 = 33 x + 1155 7 x = 855 x = 122 lts correct option : e
Answer: e
Question (general): the average of 10 numbers is 23 . if each number is increased by 6 , what will the new average be ?
Options: a ) 36 , b ) 29 , c ) 72 , d ) 29 , e ) 22
Rationale: "sum of the 10 numbers = 230 if each number is increased by 6 , the total increase = 6 * 10 = 60 the new sum = 230 + 60 = 290 the new average = 290 / 10 = 29 . 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 16 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 ) 52 minutes
Rationale: "as they arrived 16 minutes earlier than usual , they saved 16 minutes on round trip from home to station ( home - station - home ) - - > 8 minutes in each direction ( home - station ) - - > wife meets husband 8 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 - 8 minutes = 52 minutes . answer : e"
Answer: e
Question (physics): on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 49 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 288.1 , d ) 296 , e ) 308
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 49 cm . : 49 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 49 / ( 3.81 ) = 308 answer will be e ."
Answer: e
Question (physics): if three painters can complete three rooms in three hours , how many painters would it take to do 27 rooms in 9 hours ?
Options: a ) 10 , b ) 8 , c ) 7 , d ) 9 , e ) 11
Rationale: explanation : three painters can complete three rooms in three hours . so 27 rooms can be painted in 9 hrs by 9 painters answer : d ) 9 painters
Answer: d
Question (general): how much is 80 % of 40 is greater than 2 / 5 of 25 ?
Options: a ) 22 , b ) 27 , c ) 18 , d ) 12 , e ) 81
Rationale: "( 80 / 100 ) * 40 â € “ ( 2 / 5 ) * 25 32 - 10 = 22 answer : a"
Answer: a
Question (general): 5000 - 4500 ÷ 10.00 = ?
Options: a ) 4550 , b ) 5000 , c ) 0.5 , d ) 4000 , e ) none
Rationale: "answer given expression = 5000 - 4500 ÷ 10.00 = 5000 - 450 = 4550 correct option : a"
Answer: a
Question (general): the average age of applicants for a new job is 30 , with a standard deviation of 7 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 14 , c ) 15 , d ) 18 , e ) 30
Rationale: "within one standard deviation of the average age means 31 + / - 7 23 - - 30 - - 37 number of dif . ages - 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 total = 15 c"
Answer: c
Question (physics): a worker can load one truck in 5 hours . a second worker can load the same truck in 4 hours . if both workers load one truck simultaneously while maintaining their constant rates , approximately how long , in hours , will it take them to fill one truck ?
Options: a ) 1.8 , b ) 2.0 , c ) 2.2 , d ) 2.4 , e ) 2.6
Rationale: "the workers fill the truck at a rate of 1 / 5 + 1 / 4 = 9 / 20 of the truck per hour . then the time to fill one truck is 20 / 9 which is about 2.2 hours . the answer is c ."
Answer: c
Question (general): find the largest 4 digit number which isexactly divisible by 88 ?
Options: a ) 8765 , b ) 8907 , c ) 9944 , d ) 9954 , e ) 9990
Rationale: "largest 4 digit number is 9999 after doing 9999 ÷ 88 we get remainder 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 c"
Answer: c
Question (general): how many of the positive divisors of 600 are also multiples of 4 not including 600 ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 11 , e ) 12
Rationale: "600 = 2 ^ 6 * 3 * 5 = ( 4 ) * 2 * 3 * 5 ^ 2 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 1 , 1 , and 2 . there are ( 1 + 1 ) ( 1 + 1 ) ( 2 + 1 ) = 12 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 600 . the answer is d ."
Answer: d
Question (general): little john had $ 8.50 . he spent $ 1.25 on sweets and gave to his two friends $ 1.20 each . how much money was left ?
Options: a ) $ 3.85 , b ) $ 4.85 , c ) $ 5.85 , d ) $ 2.85 , e ) $ 1.85
Rationale: "john spent and gave to his two friends a total of 1.25 + 1.20 + 1.20 = $ 3.65 money left 8.50 - 3.65 = $ 4.85 correct answer is b ) $ 4.85"
Answer: b
Question (other): the ratio of buses to cars on river road is 1 to 17 . if there are 80 fewer buses than cars on river road , how many cars are on river road ?
Options: a ) 40 , b ) 85 , c ) 60 , d ) 30 , e ) 20
Rationale: b / c = 1 / 17 c - b = 80 . . . . . . . . . > b = c - 80 ( c - 80 ) / c = 1 / 17 testing answers . clearly eliminate acde put c = 85 . . . . . . . . . > ( 85 - 80 ) / 85 = 5 / 85 = 1 / 17 answer : b
Answer: b
Question (general): a car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour . the average speed for the entire trip was 60 mph . how many hours long is the trip ?
Options: a ) 6 , b ) 8 , c ) 11 , d ) 12 , e ) 14
Rationale: "in 4 hr journey = 55 * 4 = 220 mph let in the next additional hour journey = 70 * x = 70 x mph so , ( 220 + 70 x ) / ( 4 + x ) = 60 = > 220 + 70 x = 240 + 60 x = > 10 x = 20 = > x = 2 h so the trip is ( 4 + x ) = > 6 hours long answer : a"
Answer: a
Question (general): arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 11 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 11 0 = a + d - 10 a + d = 10 a = d ( as they are twin brothers ) a = d = 5 c is the answer"
Answer: c
Question (physics): one men and three women working 7 hours a day finish a work in 5 days . four men and four women working 3 hours a day complete the work in 7 days . the number of days in which only 7 men working 4 hours a day will finish the work is ?
Options: a ) 4 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "1 m + 3 w - - - - - 35 h 4 m + 4 w - - - - - - - 21 h 7 m - - - - - - - ? d 35 m + 105 w = 84 m + 84 m 21 w = 49 m 4 * 35 = 7 * x = > x = 20 hours 20 / 4 = 5 days answer : b"
Answer: b
Question (gain): fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 40 kg of fresh grapes ?
Options: a ) 5 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 10 kg , e ) none of these
Rationale: "the weight of non - water in 20 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 40 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 5 answer : a"
Answer: a
Question (general): a man engaged a servant on the condition that he would pay him rs . 500 and a uniform after one year service . he served only for 9 months and received uniform and rs . 250 , find the price of the uniform ?
Options: a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 500 , e ) s . 120
Rationale: "9 / 12 = 3 / 4 * 500 = 375 250 - - - - - - - - - - - - - 125 1 / 4 - - - - - - - - 125 1 - - - - - - - - - ? = > rs . 500 answer : d"
Answer: d
Question (physics): shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 60 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 40 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 46
Rationale: we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 40 hence answer is d
Answer: d
Question (physics): a and b undertake to do a piece of work for rs . 1200 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of c .
Options: a ) 150 , b ) 450 , c ) 750 , d ) 800 , e ) none of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 1200 * 4 / 8 ) = rs . 600 , b ' s share = rs . ( 1200 * 3 / 8 ) = rs . 450 c ' s share = rs . [ 1200 - ( 300 + 225 » ) = rs . 150 . answer is a"
Answer: a
Question (general): a big container is 30 % full with water . if 27 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 60 liters
Rationale: "a big container is 30 % full with water and after 27 liters of water is added , the container becomes 75 % full . hence these 27 liters account for 45 % of the container , which means that the capacity of it is 27 / 0.45 = 60 liters . or : if the capacity of the container is x liters then : 0.3 x + 27 = 0.75 x - - > x = 60 liters . answer : e ."
Answer: e
Question (general): in a group of cows and hens , the number of legs are 14 more than twice the number of heads . the number of cows is
Options: a ) 22 , b ) 7 , c ) 8 , d ) 6 , e ) 51
Rationale: "let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 14 4 x + 2 y = 2 x + 2 y + 14 2 x = 14 x = 7 . answer : b"
Answer: b
Question (gain): a computer store offers employees a 15 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 500 dollars and marked up the price 15 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 15 % off retail price ) as opposed to the final retail price .
Options: a ) 52.5 , b ) 54.5 , c ) 55.5 , d ) 57.5 , e ) 59.5
Rationale: cost price = 500 profit = 15 % = 15 % of 500 = 75 selling price = cp + profit sp = 575 a discount of 10 % to employees means 10 % off on 575 so 10 % of 575 = 57.5 ans d
Answer: d
Question (physics): find the area of trapezium whose parallel sides are 30 cm and 12 cm long , and the distance between them is 16 cm ?
Options: a ) 288 cm 2 , b ) 277 cm 2 , c ) 285 cm 2 , d ) 336 cm 2 , e ) 340 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 30 + 12 ) * ( 16 ) = 336 cm 2 answer : d"
Answer: d
Question (physics): working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 3 pages a minute more than printer a ?
Options: a ) 600 , b ) 800 , c ) 1000 , d ) 360 , e ) 1500
Rationale: answer : d .
Answer: d
Question (general): a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 964 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 22200 , b ) 31897 , c ) 38799 , d ) 40000 , e ) 42782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 964 p = 40000 answer : d"
Answer: d
Question (general): a box contains 9 slips that are each labeled with one number : 1 , 3 , 5 , 8 , 13 , 21 , 34 and 55 . two of the slips are drawn at random from the box without replacement . what is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box ?
Options: a ) 7 / 72 , b ) 1 / 6 , c ) 5 / 28 , d ) 15 / 36 , e ) 21 / 36
Rationale: probability = no : of desired outcomes / total no : of outcomes . you are picking two slips out of 8 slips . so total no : of outcomes = 8 c 2 = 28 desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box . how many such outcomes are there ? if you look at the numbers closely , you will see that the following pair of numbers will give you the desired outcome . ( 3,5 ) ( 5,8 ) ( 8,13 ) ( 13,21 ) ( 21,34 ) . there are 7 such pairs . if the two numbers which i pick is from any of these 5 pairs , then i get my desired outcome . so no : of desired outcomes = 5 probability = 5 / 28 answer : c
Answer: c
Question (general): the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if x 9 = 160 , what is the value of x ?
Options: a ) 18 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "ab = ( a - 1 ) ( b - 1 ) x 9 = ( x - 1 ) ( 9 - 1 ) = 160 - - > x - 1 = 20 - - > x = 21 answer : e"
Answer: e
Question (gain): what percent is 3 gm of 1 kg ?
Options: a ) 1.5 % , b ) 0.3 % , c ) 2.5 % , d ) 3.5 % , e ) 4 %
Rationale: "1 kg = 1000 gm 3 / 1000 × 100 = 300 / 1000 = 3 / 10 = 0.3 % b )"
Answer: b
Question (physics): john began driving from home on a trip averaging 30 miles per hour . how many miles per hour must carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after john ?
Options: a ) 35 , b ) 55 , c ) 39 , d ) 40 , e ) 60
Rationale: carla starts 30 minutes later and it takes 3 hr for carla to meet john so john total time travelled = 3 hr + 30 minutes john distance = 30 * ( 3 1 / 2 ) = 105 so carla need to travle 105 to meet john in 3 hrs speed of carla = 105 / 3 = 35 miles per hour answer is a
Answer: a
Question (other): two brother x and y appeared for an exam . let a be the event that x is selected and b is the event that y is selected . the probability of a is 17 and that of b is 29 . find the probability that both of them are selected .
Options: a ) 2 / 63 , b ) 2 / 67 , c ) 2 , d ) 3 / 31 , e ) 4
Rationale: given , a be the event that x is selected and b is the event that y is selected . p ( a ) = 17 , p ( b ) = 29 . let c be the event that both are selected . p ( c ) = p ( a ) × p ( b ) as a and b are independent events : = ( 17 ) × ( 29 ) = 2 / 63 answer is a
Answer: a
Question (other): sandy is younger than molly by 12 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 12 x = 6 sandy is 42 years old . the answer is a .
Answer: a
Question (general): the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 302 to 400 inclusive ?
Options: a ) 11,550 , b ) 14,550 , c ) 17,550 , d ) 20,550 , e ) 23,550
Rationale: "2 + 4 + 6 + 8 + . . . + 100 = 2550 302 + 304 + . . . + 400 = 50 ( 300 ) + ( 2 + 4 + . . . + 100 ) = 15,000 + 2550 = 17,550 the answer is c ."
Answer: c
Question (physics): walking at the rate of 8 kmph a man cover certain distance in 3 hrs . . running at a speed of 16 kmph the man will cover the same distance in .
Options: a ) 1.2 hr , b ) 2.5 hr , c ) 1.5 hr , d ) 48 min , e ) 58 min
Rationale: distance = speed * time 8 * 3 = 24 km new speed = 16 kmph therefore time = d / s = 24 / 16 = 1.5 hr . answer : c .
Answer: c
Question (general): a man can row 3.3 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1
Rationale: speed of boat in still water ( b ) = 3.3 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.1 km / hr . answer : e
Answer: e
Question (physics): two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer q between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) q = 12 , b ) q = 15 , c ) q = 17 , d ) q . 18 , e ) q = 20
Rationale: "since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ."
Answer: d
Question (other): if three numbers in the ratio 3 : 2 : 5 be such that the sum of their squares is 1862 , the middle number will be
Options: a ) 10
b ) 14
c ) 18
d ) 22
e ) 24
Rationale: explanation : let the numbers be 3 x , 2 x and 5 x . then , 9 x + 4 x + 25 x = 1862 ⇒ 38 x = 1862 ⇒ x = 49 ⇒ x = 7 . middle number = 2 x = 14 option b
Answer: b
Question (physics): factory x ' s bulbs work for over 5000 hours in 79 % of cases , whereas factory y ' s bulbs work for over 5000 hours in 85 % of cases . it is known that factory x supplies 80 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 5000 hours ?
Options: a ) 80.2 % , b ) 88 % , c ) 87.4 % , d ) 85 % , e ) 83.9 %
Rationale: for x , 80 % of 79 % will work . for y , 20 % of 85 % will work . * 20 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.80 ( 0.79 ) = . 632 0.20 ( 0.85 ) = 0.17 the combined probability then is 63.2 + 17 = 80.2 % ans a
Answer: a
Question (physics): a train 150 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 13 km / hr , b ) 59 km / hr , c ) 17 km / hr , d ) 18 km / hr , e ) 12 km / hr
Rationale: "speed of the train relative to man = ( 150 / 10 ) m / sec = ( 15 ) m / sec . [ 15 ) * ( 18 / 5 ) ] km / hr = 54 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 54 = = > x = 59 km / hr . answer : b"
Answer: b
Question (other): each factor of 210 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 40 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "210 = 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 / 16 . answer : a"
Answer: a
Question (physics): if the population of a certain country increases at the rate of 10 person every 60 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 100 , b ) 200 , c ) 600 , d ) 800 , e ) 1000
Rationale: "answer = 10 * 60 ( 1 hour = 60 minutes ) = 600 answer = c"
Answer: c
Question (general): the units digit of ( 10 ) ^ ( 87 ) + ( 5 ) ^ ( 46 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "any power of anything ending in 5 always has a units digit of 5 . so the first term has a units digit of 5 . done . the second term anything power to 10 unit digit will be zero then 5 + 0 = 5 , e"
Answer: e
Question (gain): double of quarter of 4 percent written as a decimal is :
Options: a ) 0.003 , b ) 0.0005 , c ) 0.25 , d ) 0.02 , e ) none of these
Rationale: explanation : solution : ( 2 ) * ( 1 / 4 ) * 4 % = 2 * ( 1 / 4 * 1 / 100 ) = 0.02 . answer : d
Answer: d