Cheukting/mathqa huggingface dataset:
Question (general): at a certain high school , the senior class is 3 times the size of the junior class . if 1 / 3 of the seniors and 3 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?
Options: a ) 1 / 2 , b ) 3 / 8 , c ) 5 / 16 , d ) 1 / 4 , e ) 7 / 16
Rationale: start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 300 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 1 / 3 ) * 300 = 100 and ( 3 / 4 ) * 100 = 75 . 100 + 75 = 175 . there are a total of 400 students in the junior class and senior class combined ( 100 + 300 = 300 ) , and there are 175 total students in japanese , so 175 students in japanese / 400 total students equals 7 / 16 of the students in both classes that study japanese . answer : e
Answer: e
Question (geometry): a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 12 feet tall and 3 feet in circumference ?
Options: a ) 9 feet , b ) 12 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet
Rationale: "total circuit = 12 / 4 = 3 total feet squirrel travels = 3 * 3 = 9 feet answer : a"
Answer: a
Question (general): evaluate 2 + 22 + 222 + 2.22
Options: a ) 269.72 , b ) 268.22 , c ) 248.21 , d ) 248.22 , e ) 268.21
Rationale: "2 + 22 + 222 + 2.22 = 248.22 option d"
Answer: d
Question (general): the least number which when increased by 7 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 857 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 7 = 864 - 7 = 857 . answer a"
Answer: a
Question (geometry): what is the area of a square field whose diagonal of length 12 m ?
Options: a ) 288 , b ) 72 , c ) 200 , d ) 112 , e ) 178
Rationale: "d 2 / 2 = ( 12 * 12 ) / 2 = 72 answer : b"
Answer: b
Question (general): at a contest with 3,500 participants , 1 / 2 of the people are aged 18 to 22 . next year , the number of people aged 18 to 22 will increase by 1 / 7 . after this change , what percentage of the total 3,500 people will the 18 - to 22 - year - olds represent ?
Options: a ) 33 % , b ) 40 % , c ) 55 % , d ) 57.14 % , e ) 66.14 %
Rationale: "i just wanted to mention a couple of things here : * this is a pure ratio question ; the number 3,500 is completely irrelevant , and you can ignore it if you like . when we increase something by 1 / 7 , we are multiplying it by 1 + 1 / 7 = 8 / 7 , so the answer here must be ( 1 / 2 ) * ( 8 / 7 ) = 4 / 7 = 57.14 % . answer : d"
Answer: d
Question (general): a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes jerry can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
Answer: a
Question (gain): daniel went to a shop and bought things worth rs . 25 , out of which 30 paise went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19.7 , b ) 20 , c ) 21.3 , d ) 21.5 , e ) 22
Rationale: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 30 paise = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 25 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 5 ⇒ x = 25 − 0.3 − 5 = 19.7 a"
Answer: a
Question (general): the sum of the present age of henry and jill is 40 . what is their present ages if 11 years ago henry was twice the age of jill ?
Options: a ) and 27 , b ) and 24 , c ) and 23 , d ) and 29 , e ) of these
Rationale: "let the age of jill 11 years ago be x , age of henry be 2 x x + 11 + 2 x + 11 = 40 x = 6 present ages will be 17 and 23 answer : c"
Answer: c
Question (other): if log 2 = 0.3010 and log 3 = 0.4771 , the value of log 5 512 is :
Options: a ) 2.87 , b ) 2.965 , c ) 3.876 , d ) 3.9 , e ) 4.526
Rationale: "log 5 512 = log 512 / log 5 = log 2 ^ 9 / log ( 10 / 2 ) = 9 log 2 / log 10 - log 2 = ( 9 * 0.3010 ) / 1 - 0.3010 = 2.709 / 0.699 = 2709 / 699 = 3.876 answer c"
Answer: c
Question (physics): a is half good a work man as b and together they finish a job in 18 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 27 , d ) 36 , e ) 48
Rationale: "c 27 wc = 1 : 2 2 x + x = 1 / 18 = > x = 1 / 54 2 x = 1 / 27 = > 27 days"
Answer: c
Question (geometry): the radius and height of a right circular cone are in the ratio 3 : 4 . if its volume is 96 ∏ cm ³ , what is its slant height ?
Options: a ) 8 cm
b ) 10 cm
c ) 12 cm
d ) 14 cm
e ) none
Rationale: sol . let the radius and the height of the cone be 3 x and 4 x respectively . then , 1 / 3 * ∏ * ( 3 x ) ² * 4 x = 96 ∏ ⇔ 36 x ³ = ( 96 * 3 ) ⇔ x ³ = [ 96 * 3 / 36 ] = 8 ⇔ x = 2 & ther 4 ; radius = 6 cm , height = 8 cm . slant height = √ 6 ² + 8 ² cm = √ 100 cm = 10 cm . answer b
Answer: b
Question (gain): rs . 1500 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 . 84 . how much was lent at 5 % ?
Options: a ) 299 , b ) 466 , c ) 578 , d ) 600 , e ) 677
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 84 5 x / 100 + 90 – 6 x / 100 = 84 x / 100 = 6 = > x = 600 answer : d"
Answer: d
Question (physics): an engine moves at the speed of 60 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 4 coaches are attached speed decreases to 48 kmph . what will be the speed of train when 36 coaches are attached .
Options: a ) 24 , b ) 28 , c ) 20 , d ) 32 , e ) 40
Rationale: "1 . no . of coaches = 4 sqr root = 2 speed decreases by 12 12 = k * 2 k = 6 no . of coaches = 36 swr root = 6 decrease = 6 * 6 = 36 new speed = 60 - 36 = 24 a"
Answer: a
Question (general): you and your friend spent a total of $ 15 for lunch . your friend spent $ 5 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 6 , e ) $ 10
Rationale: "my lunch = l , my friends lunch = l + 5 ( l ) + ( l + 5 ) = 15 l + l + 5 - 5 = 15 - 5 2 l = 10 l = 5 my friends lunch l + 5 = 5 + 5 = $ 10 , the answer is e"
Answer: e
Question (physics): the rear – most end of a 66 foot truck exits a 330 foot tunnel exactly 6 seconds after the front – most end of the truck entered the tunnel . if the truck traveled the entire tunnel at a uniform speed , what is the speed of the truck in miles per hour ( 1 mile = 5,280 feet ) ?
Options: a ) 225 , b ) 90 , c ) 45 , d ) 37.5 , e ) 27
Rationale: total length will be 330 + 66 = 396 time = 6 secs speed = 396 / 6 = 66 feet / sec conversion to miles per hour = 66 * 3600 / 5280 = 45 . answer c
Answer: c
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 800 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 15550 , c ) rs . 15600 , d ) rs . 16500 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 800 × 20.625 ) = 16500 . answer d"
Answer: d
Question (general): 2 men and 2 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )
Options: a ) 4 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: the list should be wmwmw . hence , from women 2 ! and men 2 ! , we get ( 2 ! ) ( 2 ! ) = 4 . therefore , the correct answer is a .
Answer: a
Question (physics): a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts six hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 12 , e ) e ) 5
Rationale: "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 6 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 6 + t ) = 40 * t t = 18 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 18 / 60 = 12 hrs time taken by a = 6 + t = 6 + 18 = 24 hrs time taken by k = 12 hrs so k starts 24 - 12 = 12 hrs after a . ( answer d )"
Answer: d
Question (general): how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 70 m long and 16 1 / 2 m board ?
Options: a ) 99 , b ) 18 , c ) 16 , d ) 10 , e ) 231
Rationale: "70 * 33 / 2 = 5 / 2 * 2 * x = > x = 231 answer : e"
Answer: e
Question (gain): what is the rate percent when the simple interest on rs . 1200 amount to rs . 160 in 4 years ?
Options: a ) 3.3 % , b ) 7 % , c ) 9 % , d ) 2 % , e ) 4 %
Rationale: "160 = ( 1200 * 4 * r ) / 100 r = 3.3 % answer : a"
Answer: a
Question (other): the simple form of the ratio 2 / 3 : 2 / 5 is ?
Options: a ) 5 : 0 , b ) 5 : 3 , c ) 5 : 1 , d ) 5 : 2 , e ) 5 : 7
Rationale: "2 / 3 : 2 / 5 = 10 : 6 = 5 : 3 answer : d"
Answer: d
Question (physics): on a map , 1 inch represents 28 miles . how many inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: "28 miles represented by 1 inch 1 mile represented by ( 1 / 28 ) inch 383.6 miles represented by ( 1 / 28 ) * 383.6 approximately = 14 we should use estimation here as the answer options are not close . ( 28 * 10 = 280 and 28 * 20 = 560 , hence we select the only option between 10 and 20 ) answer c"
Answer: c
Question (general): the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.5 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 2 : 5
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.5 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.5 ) < = > k = 0.3 / 0.6 = 1 / 2 . required ratio = 1 / 2 : 1 = 1 : 2 . answer : a"
Answer: a
Question (physics): a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 3 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 8 , b ) 16 , c ) 21 , d ) 22 , e ) 27
Rationale: i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 3 ) x solve for r , r = 11 11 - 3 = 8 mpg a
Answer: a
Question (general): how many multiples of 5 are less than 5000 , and also multiples of 50 ?
Options: a ) 100 , b ) 208 , c ) 625 , d ) 832 , e ) 833
Rationale: the lcm of 5 and 50 is 50 . divide 5000 / 50 = 100 . xxx . so a is your answer .
Answer: a
Question (general): solution for 3.15 + . 014 + . 458
Options: a ) 3.622 , b ) 3.911 , c ) 4.938 , d ) 2.986 , e ) 2.999
Rationale: "3.15 + . 014 + . 458 = 0 0 = 0 - 3.15 - 0.014 - 0.458 0 = - 3.622 answer : a"
Answer: a
Question (gain): a , b and c are entered into a partnership . a invested rs . 6500 for 6 months , b invested rs . 8400 for 5 months and c invested for rs . 10000 for 3 months . a is a working partner and gets 5 % of the total profit for the same . find the share of c in a total profit of rs . 7400 .
Options: a ) 2997 , b ) 1900 , c ) 2887 , d ) 2898 , e ) 27912
Rationale: "65 * 6 : 84 * 5 : 100 * 3 26 : 28 : 20 c share = 74000 * 95 / 100 = 7030 * 20 / 74 = > 1900 . answer : b"
Answer: b
Question (general): 3 , 7,12 , 18,25 . . . . . . . . . . . . . . 9 th terms
Options: a ) 43 , b ) 53 , c ) 63 , d ) 65 , e ) 78
Rationale: "3 + 4 = 7 7 + 5 = 12 12 + 6 = 18 18 + 7 = 25 25 + 8 = 33 33 + 9 = 42 42 + 10 = 52 52 + 11 = 63 answer : c"
Answer: c
Question (general): if 60 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
Options: a ) 33 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "60 % of ( x - y ) = 30 % of ( x + y ) ( 60 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 6 ( x - y ) = 3 ( x + y ) 3 x = 9 y x = 3 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 3 y ) x 100 ) = 33 % answer is a ."
Answer: a
Question (physics): working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exactly 10 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ?
Options: a ) 5 , b ) 4.5 , c ) 6 , d ) 7 , e ) 8
Rationale: work done by a & b in a day = x & y respectively . when a starts : no . of days when a works = 6 no . of days when b works = 4 → 6 x + 4 y = 1 when b starts : no . of days when b works = 5 no . of days when a works = 5 → 5 x + 5 y = 1 solving the above two equations for xy x = 1 / 10 y = 1 / 10 → total work done by ab in a day = 1 / 10 + 1 / 10 = 2 / 10 = 1 / 5 → no . of days to complete the work when both work together = 5 answer : a
Answer: a
Question (general): a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many q ways can the test be completed if every question is unanswered ?
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Rationale: 5 choices for each of the 4 questions , thus total q of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c .
Answer: c
Question (other): two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 3 : 2 . the first number is :
Options: a ) a ) 3 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 3 : 2 x = 1 = > 3 x = 3 answer : a"
Answer: a
Question (physics): at a speed of 60 miles per hour , a certain car uses 1 gallon of gasoline every 30 miles . if the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 60 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 11 / 36 , c ) 7 / 12 , d ) 2 / 3 , e ) 5 / 6
Rationale: "gas used = ( 5 hours ) * ( 60 miles / hour ) * ( 1 gallon / 30 miles ) = 10 gallons portion used = ( 10 ) / 12 = 5 / 6 ans e"
Answer: e
Question (physics): on a map , 2 inches represent 30 miles . how many miles approximately is the distance if you measured 38 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 226 , b ) 228 , c ) 230 , d ) 224 , e ) 232
Rationale: "1 inch = 2.54 cm 2 inch = 2.54 * 2 cm 5.08 cm = 30 miles 38 cms = 30 / 5.08 * 38 = 224 miles answer : d"
Answer: d
Question (general): a is an integer greater than 49 but less than 61 , b is an integer greater than 59 but less than 71 , what is the range of a / b ?
Options: a ) 2 / 7 , b ) 1 / 2 , c ) 3 / 4 , d ) 1 , e ) 5 / 4
Rationale: "min value of a / b will be when b is highest and a is lowest - - - > a = 50 and b = 70 so , a / b = 5 / 7 max value of a / b will be when b is lowest and a is highest - - - > a = 60 and b = 60 so , a / b = 1 range is 1 - ( 5 / 7 ) = 2 / 7 . answer should be a ."
Answer: a
Question (general): find the value of x , y by solving the below equations x + y = 15 x - y = 5
Options: a ) 10 , 5 , b ) 8 , 7 , c ) 9 , 6 , d ) 11 , 4 , e ) 12 , 3
Rationale: x + y = 15 - - - ( i ) x - y = 5 - - - - - ( ii ) by adding ( i ) and ( ii ) - - - - - - - - - - - - 2 x = 20 = = > x = 20 / 2 = 10 by replacing the value of x in ( i ) we get 10 + y = 15 = = > y = 15 - 10 = 5 . so , x = 10 , y = 5 answer a ) 10 , 5
Answer: a
Question (general): in a urban village of india named ` ` owlna ' ' , 90 % people have refrigerator , 86 % people have television , 80 % people got computers and 80 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 23 % , b ) 36 % , c ) 30 % , d ) 34 % , e ) 42 %
Rationale: "b 10 % 100 - [ ( 100 - 90 ) + ( 100 - 86 ) + ( 100 - 80 ) + ( 100 - 80 ) ] = 100 - ( 10 + 14 + 20 + 20 ) = 100 - 64"
Answer: b
Question (gain): the annual interest rate earned by an investment increased by 8 percent from last year to this year . if the annual interest rate earned by the investment this year was 27 percent , what was the annual interest rate last year ?
Options: a ) 22 % , b ) 20 % , c ) 25 % , d ) 23 % , e ) 21 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.08 i ( last year ) = 1.08 i ( last year ) 27 = 1.08 x i ( last year ) i ( last year ) = 27 / 1.08 = 2700 / 108 = 25 % answer : c"
Answer: c
Question (general): if a and b are positive numbers , and a ^ 3 + b ^ 3 = 140 , then the greatest possible value of a is between :
Options: a ) 0 and 2 , b ) 2 and 3 , c ) 3 and 4 , d ) 4 and 5 , e ) 5 and 8
Rationale: if a = 5.1 and b is a bit less than 2 , then a ^ 3 + b ^ 3 can equal 140 . if a > 8 , then a ^ 3 + b ^ 3 > 140 . the answer is e .
Answer: e
Question (physics): a train 160 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 sec , b ) 50 sec , c ) 44 sec , d ) 24 sec , e ) 60 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 160 + 140 = 300 m required time = 300 * 2 / 25 = 24 sec answer : d"
Answer: d
Question (general): the proportion of water to alcohol in solution a is 4 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 39 % , b ) 40 % , c ) 41 % , d ) 42 % , e ) 43 %
Rationale: let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 5 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 10 + 3 v / 10 = 4 v / 10 = 2 v / 5 . the concentration of alcohol is 2 / 5 = 40 % the answer is b .
Answer: b
Question (gain): at what rate percent on simple interest will rs . 750 amount to rs . 900 in 4 years ?
Options: a ) 6 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 3 %
Rationale: "150 = ( 750 * 4 * r ) / 100 r = 5 % answer : d"
Answer: d
Question (general): if m is not equal to zero , and m + 1 / m = 1 , then what is the value of m ^ 4 + ( 1 / m ) ^ 4 ?
Options: a ) - 5 , b ) - 4 , c ) - 3 , d ) - 2 , e ) - 1
Rationale: m + 1 / m = 1 we square both sides so we have m ^ 2 + 1 / m ^ 2 + 2 = 1 or m ^ 2 + 1 / m ^ 2 = - 1 squaring again we have m ^ 4 + 1 / m ^ 4 + 2 = 1 or m ^ 4 + 1 / m ^ 4 = - 1 answer = - 1 ( e )
Answer: e
Question (other): the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 539 , krishan has ?
Options: a ) s . 2890 , b ) s . 2330 , c ) s . 1190 , d ) s . 1620 , e ) s . 3179
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 539 : n & there n = 289 x 539 / 49 = rs . 3179 answer : e"
Answer: e
Question (general): the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 20 per cent . the two reductions together are equal to a single reduction of
Options: a ) 33 , b ) 40 , c ) 99 , d ) 28 , e ) 72
Rationale: "explanation : let the original price of the cycle be 100 . after the first reduction the price will be 75 . this new price is then reduced by 20 % = 0.8 x 75 = 60 60 represents a reduction of 40 percent on the original . answer : b ) 40 %"
Answer: b
Question (gain): suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3960 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 360 , e ) s . 368
Rationale: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3960 × 1 / 11 = rs . 360 . d"
Answer: d
Question (other): in a ratio which is equal to 7 : 9 , if the antecedent is 56 , then the consequent is ?
Options: a ) 72 , b ) 85 , c ) 64 , d ) 51 , e ) 45
Rationale: "we have 7 / 9 = 56 / x 7 x = 56 * 9 x = 72 consequent = 72 answer is a"
Answer: a
Question (gain): if 20 % of a certain number is 60 , then what is 80 % of that number ?
Options: a ) 220 , b ) 210 , c ) 240 , d ) 250 , e ) 260
Rationale: "explanation : 20 % = 20 * 3 = 60 80 % = 80 * 3 = 240 answer : option c"
Answer: c
Question (physics): if 2 men or 3 women can reap a field in 5 days how long will 5 men and 6 women take to reap it ?
Options: a ) 2 / 24 , b ) 6 / 18 , c ) 2 / 22 , d ) 5 / 12 , e ) 9 / 10
Rationale: "explanation : 2 men reap 2 / 5 field in 1 day 1 man reap 1 / ( 2 x 5 ) 3 women reap 1 / 43 field in 1 day 1 woman reap 1 / ( 5 x 3 ) 5 men and 6 women reap ( 5 / ( 2 x 5 ) + 6 / ( 3 x 5 ) ) = 9 / 10 in 1 day 5 men and 6 women will reap the field in 9 / 10 days answer : option e"
Answer: e
Question (gain): a customer went to a shop and paid a total of $ 30 , out of which $ 1.28 was for sales tax on taxable purchases . if the tax rate was 8 % , then what was the cost of the tax free items ?
Options: a ) $ 9.84 , b ) $ 10.68 , c ) $ 11.26 , d ) $ 12.72 , e ) $ 13.54
Rationale: the total cost was $ 30 . the tax was $ 1.28 let the original price of the taxable items = x given that tax rate = 8 % 0.08 x = 1.28 x = $ 16 the cost of the tax free items was $ 30 - $ 16 - $ 1.28 = $ 12.72 the answer is d .
Answer: d
Question (general): 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 11
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 16 , d ) 2 ^ 12 , e ) 2 ^ 37
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 so you can notice the pattern . . . in the end you will have 2 ^ 11 + 2 ^ 11 , which will give you 2 ^ 12 answer d"
Answer: d
Question (general): if a number p is prime , and 2 p + 5 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: 1 / 7 = 014285 . . . ( a repeating pattern one digit long ) a
Answer: a
Question (physics): walking at 25 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 8 , b ) 16 , c ) 42 , d ) 48 , e ) 54
Rationale: "speed is inversly proprtional to time walking at 25 % of speed meand 1 / 4 s takes 4 t . it takes 24 minutes extra to cover the distance . then 4 t = t + 24 3 t = 24 t = 8 . option a is correct"
Answer: a