Cheukting/mathqa huggingface dataset:
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 55 ?
Options: a ) s . 3944 , b ) s . 3948 , c ) s . 3942 , d ) s . 3965 , e ) s . 3740
Rationale: "let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 55 = rs . 3740 . answer : e"
Answer: e
Question (general): in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 9 years older than b , the present age of b is
Options: a ) 16 years , b ) 88 years , c ) 39 years , d ) 66 years , e ) 77 years
Rationale: "let b ' s age = x years . then , as age = ( x + 9 ) years . ( x + 9 + 10 ) = 2 ( x — 10 ) hence x = 39 . present age of b = 39 years answer : c"
Answer: c
Question (physics): how many times hour hand covers full circle in a day ?
Options: a ) 3 times , b ) 2 times , c ) 4 times , d ) 5 times , e ) once
Rationale: 2 times answer : b
Answer: b
Question (general): if x ^ 2 + ( 1 / x ^ 2 ) = 3 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 7 , b ) 11 , c ) 12 , d ) 14 , e ) 15
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 3 ^ 2 - 2 = 7 . thus , the answer is a ."
Answer: a
Question (general): how many integers between 400 and 1000 are there such that their unit digit is odd ?
Options: a ) 250 , b ) 150 , c ) 300 , d ) 400 , e ) 450
Rationale: there are 600 numbers from 401 to 1000 ( inclusive ) . half of the numbers are odd , so there are 300 odd numbers . the answer is c .
Answer: c
Question (general): how many 4 - digit numbers contain no . 2 ?
Options: a ) 22 , b ) 98 , c ) 28 , d ) 29 , e ) 22
Rationale: answer : b
Answer: b
Question (gain): a company pays 15.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 25 , b ) 31 , c ) 18 , d ) 19 , e ) 01
Rationale: "explanation : dividend on 1 share = ( 15.5 * 50 ) / 100 = rs . 7.75 rs . 25 is income on an investment of rs . 100 rs . 7.75 is income on an investment of rs . ( 7.75 * 100 ) / 25 = rs . 31 answer : b"
Answer: b
Question (general): the average of first 6 prime numbers is ?
Options: a ) 10.11 , b ) 11.11 , c ) 12.11 , d ) 6.83 , e ) 14.11
Rationale: "sum of 6 prime no . = 41 average = 41 / 6 = 6.83 answer : d"
Answer: d
Question (other): jaya ranks 5 th in a class of 53 . what is her rank from the bottom in the class ?
Options: a ) 49 th , b ) 48 th , c ) 47 th , d ) 50 th , e ) none of these
Rationale: there are 4 students above her . when takan from bottom there are 4 students below her rank . so her rank wud be 53 - 4 i . e . 49 th . answer : a
Answer: a
Question (physics): if the weight of 10 meters long rod is 23.4 kg . what is the weight of 6 meters long rod ?
Options: a ) 7.2 kg . , b ) 10.8 kg . , c ) 14.04 kg . , d ) 18.0 kg , e ) none
Rationale: "answer ∵ weight of 10 m long rod = 23.4 kg ∴ weight of 1 m long rod = 23.4 / 10 kg ∴ weight of 6 m long rod = 23.4 x 6 / 10 = 14.04 kg option : c"
Answer: c
Question (general): a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 30000 rs , what is the value of buzness ?
Options: a ) 75000 , b ) 160000 , c ) 170000 , d ) 60000 , e ) 70000
Rationale: if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 30000 - > x = 60000 answer : d
Answer: d
Question (physics): 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 > x or x < 0 ?
Options: a ) 5 / 8 , b ) 4 / 5 , 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 to the left of the y - axis satisfy the condition that x < 0 . the union of these two areas is 5 / 8 of the circle . the answer is a ."
Answer: a
Question (general): at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 15 . if the price per share of stock k was $ 16 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?
Options: a ) 1.4 % , b ) 5.9 % , c ) 11.1 % , d ) 6.67 % , e ) 23.6 %
Rationale: "opening = 15 closing = 16 rise in price = 1 so , percent increase = 1 / 15 * 100 = 6.67 answer : d"
Answer: d
Question (other): of the 70 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "neither car nor garage = total - garage - ( swim - common ) = 70 - 50 - ( 40 - 35 ) = 70 - 55 = 15 answer b"
Answer: b
Question (gain): john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 57000 and ingrid makes $ 72000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 %
Rationale: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 129000 = 24 / 43 . 24 / 43 is a little above 24 / 48 = 1 / 2 . thus , our answer is just a little above 35 . answer : d"
Answer: d
Question (general): if a - b = 3 and a 2 + b 2 = 29 , then find the value of ab
Options: a ) 7 , b ) 8.5 , c ) 10 , d ) 12 , e ) 14
Rationale: explanation : 2 ab = ( a 2 + b 2 ) − ( a − b ) 2 = > 2 ab = 29 - 9 = 20 = > ab = 10 option c
Answer: c
Question (general): when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 1.30 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 255 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 663
Rationale: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 1.30 = $ 663 answer e"
Answer: e
Question (gain): a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 50 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 4 hours ?
Options: a ) 40 % , b ) 35 % , c ) 30 % , d ) 25 % , e ) 20 %
Rationale: "the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.5 ( 6 ) = 3 gallons at the start , the amount of water is 0.5 ( 6 ) = 3 gallons after 4 hours , the amount of water is 3 - 0.5 ( 4 ) = 1 gallon the concentration of water is 1 / ( 3 + 1 ) = 1 / 4 = 25 % the answer is d ."
Answer: d
Question (other): he ratio between the sale price and the cost price of an article is 4 : 7 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 6 , b ) 3 : 7 , c ) 3 : 8 , d ) 2 : 1 , e ) 8 : 3
Rationale: "let c . p . = rs . 7 x and s . p . = rs . 4 x . then , gain = rs . 3 x required ratio = 3 x : 7 x = 3 : 7 . answer : b"
Answer: b
Question (physics): a man covers a certain distance on bike . had he moved 4 kmph faster , he would have taken 72 minutes less . if he moves slow by 4 kmph , he will take hours more to cover the distance . what is the distance travelled by him ?
Options: a ) 48 km , b ) 56 km , c ) 64 km , d ) 96 km , e ) 106 km
Rationale: explanation : let the distance be ' d ' and the speed be ' x ' kmph . d / x + 4 = d / x - 72 / 60 d / x - d / ( x - y ) = 6 / 5 = d ( x + 4 - x ) / x ( x - 4 ) = 6 / 5 ∴ d / x ( x + 4 ) = 3 / 10 . . . . . . ( i ) d / x - 4 - d / x = 2 ∴ dx - dx + 4 d / x ( x - 4 ) = 2 ∴ d / x ( x - 4 ) = 1 / 2 . . . . . ( ii ) from equation ( i ) and ( ii ) : 3 / 10 x ( x + 4 ) = 1 / 2 x ( x - 4 ) ∴ 3 ( x + 4 ) = 5 ( x - 4 ) = 3 x + 12 = 5 x - 20 2 x = 32 ∴ x = 16 kmn - 1 ∴ d = x ( x - 4 ) / 2 = 16 x 12 / 2 = 16 x 6 = 96 km answer : option d
Answer: d
Question (general): if 0.6 : x : : 5 : 8 , then x is equal to :
Options: a ) a ) 0.96 , b ) b ) 1.2 , c ) c ) 1.25 , d ) d ) 1.3 , e ) e ) 0.8
Rationale: "( x * 5 ) = ( 0.6 * 8 ) x = 4.8 / 5 x = 0.96 answer = a"
Answer: a
Question (physics): excluding stoppages , the speed of a bus is 50 km / hr and including stoppages , it is 36 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 118 min , b ) 10 min , c ) 18 min , d ) 16 min , e ) 15 min
Rationale: "due to stoppages , it covers 14 km less . time taken to cover 14 km = 14 / 50 * 60 = 16 min . answer : d"
Answer: d
Question (general): 7 x + y = 19 , and x + 3 y = 1 . find the value of 2 x + y
Options: a ) 20 , b ) 18 , c ) 11 , d ) 5 , e ) 50
Rationale: add these two equations 8 x + 4 y = 20 divide by 2 ( to get 2 x + y ) answer will be d . 10
Answer: d
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 12 and 16 ?
Options: a ) 19 , b ) 22 , c ) 52 , d ) 36 , e ) 38
Rationale: "prime factorization of the given numbers 12 = 2 ^ 2 * 3 48 = 2 ^ 4 * 3 greatest common factor = 4 lowest common multiple = 48 sum = 4 + 48 = 52 answer c"
Answer: c
Question (general): the least number which must be subtracted from 909 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 0 , d ) d ) 5 , e ) e ) 6
Rationale: "on dividing 909 by 9 , we get remainder = 0 therefore , required number to be subtracted = 0 answer : c"
Answer: c
Question (other): a person want to give his money of $ 3600 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 2000 , b ) $ 1200 , c ) $ 2500 , d ) $ 1800 , e ) $ 1600
Rationale: "b ' s share = 3600 * 3 / 9 = $ 1200 answer is b"
Answer: b
Question (general): each week , harry is paid x dollars per hour for the first 24 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 ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "42 x = 24 x + 1.5 x ( h - 24 ) = = > 42 = 24 + 1.5 ( h - 24 ) = = > h - 24 = 18 / 1.5 = 12 = > h = 36 answer is b"
Answer: b
Question (gain): rs . 1600 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 85 . how much was lent at 5.00001 % ?
Options: a ) 1100 , b ) 1200 , c ) 1300 , d ) 1400 , e ) 1700
Rationale: ( x * 5 * 1 ) / 100 + [ ( 1600 - x ) * 6 * 1 ] / 100 = 85 5 x / 100 + ( 9600 – 6 x ) / 100 = 85 = > x = 1100 answer : a
Answer: a
Question (general): a box contains 10 tablets of medicine a and 16 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 18 , e ) 21
Rationale: "the worst case scenario will be if we remove all 16 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 16 + 2 = 18 tablets . answer : d ."
Answer: d
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 171 ?
Options: a ) 2820 , b ) 3440 , c ) 4860 , d ) 5560 , e ) 6720
Rationale: "100 + 102 + . . . + 170 = 100 * 36 + ( 2 + 4 + . . . + 70 ) = 100 * 36 + 2 * ( 1 + 2 + . . . + 35 ) = 100 * 36 + 2 ( 35 ) ( 36 ) / 2 = 100 * 36 + 35 * 36 = 135 ( 36 ) = 4860 the answer is c ."
Answer: c
Question (physics): a train 3000 m long can cross an electric pole in 120 sec and then find the speed of the train ?
Options: a ) 90 , b ) 95 , c ) 100 , d ) 105 , e ) 110
Rationale: "length = speed * time speed = l / t s = 3000 / 120 s = 25 m / sec speed = 25 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 90 kmph answer : a"
Answer: a
Question (general): at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 500 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ?
Options: a ) 1,108 , b ) 4,100 , c ) 2,108 , d ) 2,124 , e ) 2,256
Rationale: "we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 500 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . e . a total of 500 x 8 = 4000 hot dogs . we are left with ~ $ 16 . similarly , let ' s use $ 3 for calculation . we can buy 5 20 - pack hot dogs ( 3 x 5 ) , a total of 20 x 5 = 100 hot dogs . so we have 4100 hot dogs . 2108 looks far - fetched ( since we are not likely to be left with > $ 1.55 ) . hence , ( b ) 4100 ( answer b )"
Answer: b
Question (physics): a can give b 60 meters start and c 120 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 63.83 , b ) 111.67 , c ) 111.64 , d ) 111.11 , e ) 101.12
Rationale: "a runs 1000 m while b runs 940 m and c runs 880 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 880 ) / 940 = 936.17 m . b can give c = 1000 - 936.17 = 63.83 m . answer : a"
Answer: a
Question (geometry): you have 59 cubic blocks . what is the minimum number that needs to be taken away in order to construct a solid cube with none left over ?
Options: a ) 27
b ) 43
c ) 11
d ) 32
e ) 45
Rationale: d 32 the next cube number below 64 ( 4 × 4 × 4 ) is 27 ( 3 × 3 × 3 ) . in order to construct a solid cube , therefore , with none left over , 59 – 27 = 32 blocks need to be taken away .
Answer: d
Question (physics): from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 8 kilometers per hour , while ferry q takes a route that is three times longer . if ferry p is slower than ferry q by 1 kilometer per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 12
Rationale: "the distance traveled by ferry p is 24 km . then the distance traveled by ferry q is 72 km . ferry q travels at a speed of 9 kph . the time of the journey for ferry q is 72 / 9 = 8 hours , which is 5 hours more than ferry p . the answer is a ."
Answer: a
Question (general): n a certain flower shop , which stocks 4 types of flowers , there are 1 / 3 as many violets as carnations , and 1 / 4 as many tulips as violets . if there are equal numbers of roses and tulips , what percent of the flowers in the shop are carnations ?
Options: a ) 62 , b ) 63 , c ) 64 , d ) 66.66 , e ) 65
Rationale: given : - violets - c / 3 carnations - c tulip - c / 12 rose - c / 12 total flowers in terms of c = c / 3 + c + c / 12 + c / 12 = 18 c / 12 percentage of carnations = c / 3 c / 2 * 100 = 66.66 % answer d
Answer: d
Question (general): at a contest with 500 participants , 1 / 2 of the people are aged 28 to 32 . next year , the number of people aged 28 to 32 will increase by 1 / 8 . after this change , what percentage of the total 500 people will the 28 - to 32 - year - olds represent ?
Options: a ) 33.25 % , b ) 40.25 % , c ) 50.25 % , d ) 55.25 % , e ) 56.25 %
Rationale: "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 8 , we are multiplying it by 1 + 1 / 8 = 9 / 8 , so the answer here must be ( 1 / 2 ) * ( 9 / 8 ) = 9 / 16 = 56.25 % . answer is e"
Answer: e
Question (gain): on a purchase of $ 130 , a store offered a payment plan consisting of a $ 30 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ?
Options: a ) 23.5 % , b ) 24.5 % , c ) 23.1 % , d ) 25.5 % , e ) 26.5 %
Rationale: 12 * 10 + 30 = 150 . ( 30 / 130 ) * 100 = 23.1 answer : c
Answer: c
Question (general): the largest 4 digit number exactly divisible by 66 is ?
Options: a ) 9935 , b ) 9939 , c ) 9944 , d ) 9966 , e ) 9960
Rationale: "largest 4 - digit number = 9999 66 ) 9999 ( 151 9966 largest number : 9966 answer : d"
Answer: d
Question (general): ashok secured average of 77 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 38 , b ) 27 , c ) 92 , d ) 17 , e ) 80
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 77 therefore total marks in 6 subjects = 77 * 6 = 462 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 462 – 370 = 92 answer : c"
Answer: c
Question (general): roses can be purchased individually for $ 7.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 316 , d ) 324 , e ) 325
Rationale: "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 7.3 = ~ 4 roses for that amount . total = 312 + 4 = 316 . answer : c ."
Answer: c
Question (geometry): what is the equation of a circle of radius 5 units centered at ( 3 , 2 ) ?
Options: a ) x ^ 2 + y ^ 2 + 6 x – 4 y = 23
b ) x ^ 2 + y ^ 2 - 6 x + 4 y = 23
c ) x ^ 2 + y ^ 2 + 6 x + 4 y = 23
d ) x ^ 2 + y ^ 2 - 6 x – 4 y = - 12
e ) x ^ 2 + y ^ 2 - 6 x – 4 y = 12
Rationale: the equation of a circle with center at ( a , b ) and radius r is ( x - a ) ^ 2 + ( y - b ) ^ 2 = r ^ 2 = > answer = ( x - 3 ) ^ 2 + ( y - 2 ) ^ 2 = 5 ^ 2 solving , , we get the equation in answer choice e .
Answer: e
Question (geometry): if the diameter of circle r is 20 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 14 % , e ) 4 %
Rationale: "let diameter of circle r , dr = 20 and diameter of circle s , ds = 100 radius of circle r , rr = 10 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 10 / 50 ) ^ 2 = ( 2 / 10 ) ^ 2 = 4 % answer : e"
Answer: e
Question (physics): walking with 4 / 5 of my usual speed , i arrive at the bus stop 9 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "let t = usual time = distance / usual speed t + 9 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 36 the answer is d ."
Answer: d
Question (physics): what will be the length of the mini - train , if it crosses a pole in 3 sec while travelling at a speed of 75 kmph ?
Options: a ) 60 m , b ) 65 m , c ) 63.5 m , d ) 64 m , e ) 62.5 m
Rationale: explanation : d = 75 * 5 / 18 * 3 = 62.5 m answer : option e
Answer: e
Question (general): if 4 x = 8 y = 12 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 52 , b ) 58 , c ) 84 , d ) 122 , e ) 180
Rationale: "4 x = 8 y = 12 z x = 2 y = 3 z 3 ( 2 * 3 ) = 2 ( 3 * 1 ) = 3 ( 1 * 2 ) addition = 18 + 6 + 6 = 30 answer would be multiple of 30 which is 180 answer : e"
Answer: e
Question (general): find a two digit number , given that the sum of the digits is 12 and the difference of the digits is 6 . ?
Options: a ) 41 , b ) 46 , c ) 42 , d ) 46 , e ) 47
Rationale: "using elimination method find which of the options fit the description of the number . . . from the option only 41 meets this description sum of digits - - - 4 + 1 = 5 difference of digits - - - 4 - 1 = 3 answer a ."
Answer: a
Question (physics): it takes joey the postman 1 hours to run a 3 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 6 mile / hour , what is the speed with which joey returns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 18
Rationale: "let his speed for one half of the journey be 3 miles an hour let the other half be x miles an hour now , avg speed = 6 mile an hour 2 * 3 * x / 3 + x = 6 6 x = 6 x + 18 = > x = 18 e"
Answer: e
Question (general): 2056 x 987 = ?
Options: a ) 1936372 , b ) 2029272 , c ) 1896172 , d ) 1923472 , e ) none of them
Rationale: "= 2056 x 987 = 2056 x ( 1000 - 13 ) = 2056 x 1000 - 2056 x 13 = 2056000 - 26728 = 2029272 answer is b"
Answer: b
Question (geometry): a rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn . the area of the lawn is 2109 sq . m . what is the width of the road ?
Options: a ) 5 m , b ) 4 m , c ) 2 m , d ) 3 m , e ) 6 m
Rationale: "area of the park = 60 * 40 = 2400 m ^ 2 given area of the lawn = 2109 m ^ 2 total area of the cross roads = 2400 - 2109 = 291 m ^ 2 assume that the width of the cross road = x = area of road 1 + road 2 - common area cross road = 60 x + 40 x - x ^ 2 total area of cross road = 60 x + 40 x - x ^ 2 = 291 m ^ 2 ( x - 97 ) ( x - 3 ) = 0 x = 3 answer d"
Answer: d
Question (physics): a train is moving at 6 / 7 of its usual speed . the train is 30 minutes too late . what is the usual time for the train to complete the journey ?
Options: a ) 1 hour , b ) 30 minutes , c ) 3 hours , d ) 2 hours 30 min , e ) 2 hours
Rationale: "new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 30 minutes represents 1 / 6 of the usual time . the usual time is 3 hours . the answer is c ."
Answer: c
Question (general): we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 530 . how many green hats did we buy ?
Options: a ) a ) 36 , b ) b ) 20 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
Rationale: let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 530 . 6 ( 85 - g ) + 7 g = 530 . 510 - 6 g + 7 g = 530 . g = 530 - 510 = 20 . the answer is b .
Answer: b
Question (general): a volunteer organization is recruiting new members . in the fall they manage to increase their number by 5 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.15 % , c ) 14.95 % , d ) 13.33 % , e ) 12.52 %
Rationale: "( 100 % + 5 % ) * ( 100 % - 19 % ) = 1.05 * . 81 = 0.8505 . 1 - 0.8505 = 14.95 % lost = - 14.95 % the answer is c the organization has lost 14.95 % of its total volunteers from fall to spring ."
Answer: c
Question (physics): two cars are driving toward each other . the first car is traveling at a speed of 90 km / h , which is 50 % faster than the second car ' s speed . if the distance between the cars is 975 km , how many hours will it take until the two cars meet ?
Options: a ) 6 , b ) 6.5 , c ) 7 , d ) 7.5 , e ) 8
Rationale: "the speed of the first car is 90 km / h . the speed of the second car is 90 / 1.5 = 60 km / h . the two cars complete a total of 150 km each hour . the time it takes the cars to meet is 975 / 150 = 6.5 hours . the answer is b ."
Answer: b
Question (gain): find the annual income derived by investing $ 6800 in 40 % stock at 136 .
Options: a ) 550 , b ) 2000 , c ) 250 , d ) 3000 , e ) 400
Rationale: "by investing $ 136 , income obtained = $ 40 . by investing $ 6800 , income obtained = $ [ ( 40 / 136 ) * 6800 ] = $ 2000 . answer b ."
Answer: b