Cheukting/mathqa huggingface dataset:
Question (general): two students appeared at an examination . one of them secured 9 marks more than the other and his marks was 56 % of the sum of their marks . the marks obtained by them are :
Options: a ) 39,30 , b ) 41,32 , c ) 42,33 , d ) 43,34 , e ) 35,36
Rationale: let their marks be ( x + 9 ) and x . then x + 9 = 56 / 100 ( x + 9 + x ) 3 x = 99 x = 33 their marks 42 and 33 answer c
Answer: c
Question (physics): aaron will jog from home at 4 miles per hour and then walk back home by the same route at 8 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?
Options: a ) 2 , b ) 10 , c ) 12 , d ) 8 , e ) 15
Rationale: "xyt / ( x + y ) x = 4 , y = 8 t = 3 4 * 8 * 3 / 4 + 8 = 96 / 12 = 8 answer : d"
Answer: d
Question (general): if x is the product of the positive integers from 1 to 8 , inclusive , and if i , k , m , and p are positive integers such that x = 2 ^ i ∗ 3 ^ k ∗ 5 ^ m ∗ 7 ^ p , then i + k + m + p =
Options: a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "here the idea is to go expressing each factor from one to eight , decomposed into its primes : 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 1 * 2 * 3 * ( 2 * 2 ) * 5 + ( 2 * 3 ) * 7 * ( 2 * 2 * 2 ) = 2 ^ 7 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1 then i = 7 k = 2 m = 1 p = 1 i + k + m + p = 11 correct answer d"
Answer: d
Question (geometry): in right triangle abc , ac is the hypotenuse . if ac is 10 and ab + bc = 20 , what is the area of the triangle abc ?
Options: a ) 225 , b ) 450 , c ) 75 , d ) 200 , e ) 200 √ 2
Rationale: "square ab + bc = 20 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 400 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 10 ^ 2 = 100 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 100 + 2 * ab * bc = 400 . 100 + 2 * ab * bc = 400 . ab * bc = 150 . the area = 1 / 2 * ab * bc = 75 . answer : c ."
Answer: c
Question (geometry): each side of a rectangular field diminished by 40 % . by how much per cent is the area of the field diminished ?
Options: a ) 32
b ) 64
c ) 25
d ) 16
e ) none
Rationale: solution : let the original length of the rectangle be 20 unit and breadth be 10 unit . then original area = length * breadth = 20 * 10 = 200 square unit . 40 % decrease in each side , then length = ( 20 - 40 % of 20 ) = 12 unit . breadth = ( 10 - 40 % of 10 ) = 6 unit . now , area = 12 * 6 = 72 square unit . decrease in area = 200 - 72 = 128 square unit . % decrease in area = ( 128 / 200 ) * 100 = 64 % mind calculation method : let the original area be 100 square unit . 100 = = = 40 % ↓ ( decrease in length ) = = = > 60 = = = 40 % ↓ = = = ( decrease in breadth ) = = = > 36 . diminished in area = 100 - 36 = 64 % answer : option b
Answer: b
Question (general): the average of 10 numbers is calculated as 14 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) a ) 16 , b ) b ) 15 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 14 + 36 – 26 = 150 = > 150 / 10 = 15 b )"
Answer: b
Question (gain): there are two groups of students in the sixth grade . there are 20 students in group a , and 80 students in group b . if , on a particular day , 20 % of the students in group a forget their homework , and 15 % of the students in group b forget their homework , then what percentage of the sixth graders forgot their homework ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: "number of students in group a = 20 students who forget homework in group a = 20 % of 20 = 4 students number of students in group b = 80 students who forget homework in group b = 15 % of 80 = 12 students total number of students = 20 + 80 = 100 students who forgot homework = 4 + 12 = 16 students percentage of students who forget homework = 16 / 100 * 100 = 16 % answer : d"
Answer: d
Question (general): the average of 6 quantities is 8 . the average of 4 of them is 5 . what is the avg . of the remaining 2 numbers ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "sum of 8 quantities = total no of quantities x average of them = 6 x 8 = 48 sum of 4 quantities = 4 x 5 = 20 sum of 4 quantities + sum of 2 quantities = sum of 6 quantities 20 + sum of 2 quantities = 48 sum of 2 quantities = 28 average of 2 quantities = sum of 2 quantities / 2 = 28 / 2 = 14 answer : d"
Answer: d
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 . 4048 . 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 . 362 , 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 . 4048 × 1 / 11 = rs . 368 . e"
Answer: e
Question (general): a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 90 . find the number of notes of rs . 50 denomination .
Options: a ) 15 , b ) 21 , c ) 17 , d ) 57 , e ) 77
Rationale: total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 90 - x now , 50 * x + 500 * ( 90 - x ) = 10350 50 x + 45000 - 500 x = 10350 - 450 x = - 34650 x = 77 . no . of 50 rupees note = 77 . answer : option e
Answer: e
Question (general): during 2003 , a company produced an average of 4,000 products per month . how many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 150 % over its 2003 average ?
Options: a ) 435,000 , b ) 440,000 , c ) 450,000 , d ) 480,000 , e ) 432,000
Rationale: "company produced 12 * 4000 = 48,000 products in 2003 . if company produces x products from 2004 to 2007 , then total amount of product produced in 4 years ( 2003 through 2007 ) is x + 48,000 . the gives the average of ( x + 48,000 ) / 4 . this average needs to be 300 % higher than that in 2003 . in math terms , 48,000 + 150 % ( 48,000 ) = 120,000 . so : ( x + 48,000 ) / 4 = 120,000 x + 48,000 = 480,000 x = 432,000 the answer is e ."
Answer: e
Question (general): the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . thereforedecreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 20 , e ) 22
Rationale: "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b"
Answer: b
Question (general): the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 5 ) , how many units is p from the y - axis ?
Options: a ) 2.5 , b ) 5 , c ) 7.5 , d ) 10 , e ) 12
Rationale: "the x - axis is 5 units from the point p . thus the y - axis is 10 units from the point p . the answer is d ."
Answer: d
Question (gain): two numbers are respectively 20 % and 60 % more than a third number . the percentage that is first of the second is ?
Options: a ) 34 % , b ) 68 % , c ) 51 % , d ) 75 % , e ) 83 %
Rationale: "i ii iii 120 160 100 160 - - - - - - - - - - 120 100 - - - - - - - - - - - ? = > 75 % answer : d"
Answer: d
Question (general): we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 397 . how many math books did we buy ?
Options: a ) 47 , b ) 53 , c ) 56 , d ) 61 , e ) 64
Rationale: "let m be the number of math books and let h be the number of history books . m + h = 90 . h = 90 - m . 4 m + 5 h = 397 . 4 m + 5 ( 90 - m ) = 397 . - m + 450 = 397 . m = 450 - 397 = 53 . the answer is b ."
Answer: b
Question (general): two employees a and b are paid a total of rs . 580 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?
Options: a ) s . 130 , b ) s . 140 , c ) s . 150 , d ) s . 232 , e ) s . 280
Rationale: "let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 580 but x = 150 % of y = 150 y / 100 = 15 y / 10 ∴ 15 y / 10 + y = 580 ⇒ y [ 15 / 10 + 1 ] = 580 ⇒ 25 y / 10 = 580 ⇒ 25 y = 5800 ⇒ y = 5800 / 25 = rs . 232 d )"
Answer: d
Question (general): at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 7 pencils and 11 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 7 total charts are 11 so a + 2 b = 11 add both : 3 a + 3 b = 18 so a + b = 6 total number of people = 6 a"
Answer: a
Question (general): the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number r ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = r answer : b"
Answer: b
Question (general): the average height of 35 boys in a class was calculated as 182 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 180.27 cm , b ) 180.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 182 cm . wrong total height of 35 boys = 182 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - 60 / 35 cm = 182 cm - 1.71 cm = 180.29 cm . answer : b"
Answer: b
Question (gain): the salaries of a and b together amount to $ 3000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 2250 , e ) $ 1200
Rationale: "let a ' s salary is x b ' s salary = 3000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 3000 - x ) x = $ 2250 answer is d"
Answer: d
Question (geometry): if a number is subtracted from its square we get 272 . find the number ?
Options: a ) 7
b ) 21
c ) 19
d ) 15
e ) 17
Rationale: x ^ 2 â € “ x = 272 = > x = 17 answer e
Answer: e
Question (physics): a train 120 m long crosses a platform 220 m long in 20 sec ; find the speed of the train ?
Options: a ) 87 kmph , b ) 65 kmph , c ) 54 kmph , d ) 61 kmph , e ) 18 kmph
Rationale: "d = 120 + 220 = 340 t = 20 s = 340 / 20 * 18 / 5 = 61 kmph answer : d"
Answer: d
Question (general): for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 88 θ 33 ) θ 17 ) - ( 90 θ ( 33 θ 17 ) ) ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "( ( 88 θ 33 ) θ 17 ) the remainder of 88 divided by 33 is 22 ; the remainder of 22 divided by 17 is 5 ; ( 98 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 98 divided by 16 is 2 . 5 - 2 = 3 . answer : d ."
Answer: d
Question (general): if solomon distributes his toys in the ratio of 1 / 4 : 1 / 6 : 1 / 10 : 1 / 9 between his 4 friends a , b , c and d , then find the total number of toys solomon should have ?
Options: a ) 111.7 , b ) 118.7 , c ) 113.7 , d ) 218.7 , e ) 418.7
Rationale: here , a : b : c : d = 1 / 4 : 1 / 6 : 1 / 10 : 1 / 9 1 ) l . c . m of 4 : 6 : 10 : 9 is 180 2 ) find the number of pens each friend received - - - - - - - - - ( to find no . of pens each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 4 ) x 180 = 45 b = ( 1 / 6 ) x 180 = 30 c = ( 1 / 10 ) x 180 = 18 d = ( 1 / 7 ) x 180 = 25.7 3 ) total number of toys = ( 45 x + 30 x + 18 x + 25.7 x ) = 118.7 x minimum number of pens ( x ) = 1 therefore , total number of pens = 118.7 pens . correct option : b
Answer: b
Question (geometry): the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.40 per metre .
Options: a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 2888
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.40 ) = rs . 5808 . answer : d ) 5808"
Answer: d
Question (gain): an article is bought for rs . 675 and sold for rs . 1000 , find the gain percent ?
Options: a ) 34 % , b ) 44 % , c ) 48 % , d ) 32 % , e ) 46 %
Rationale: "675 - - - - 325 100 - - - - ? = > = 48 % answer : c"
Answer: c
Question (gain): a 13 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 72 , b ) rs . 92 , c ) rs . 162.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 13 , investment = rs . ( 100 / 8 x 13 ) = rs . 162.50 ∴ market value of rs . 100 stock = rs . 162.50 answer c"
Answer: c
Question (other): from a container , 6 liters milk was drawn out and was replaced by water . again 6 liters of mixture was drawn out and was replaced by the water . thus the quantity of milk and water in the container after these two operations is 9 : 16 . the quantity of mixture is :
Options: a ) 15 , b ) 26 , c ) 22 , d ) 27 , e ) 11
Rationale: explanation : let quantity of mixture be x liters . suppose a container contains x units of liquid from which y units are taken out and replaced by water . after operations , the quantity of pure liquid = units , where n = no of operations . so , quantity of milk = given that , milk : water = 9 : 16 milk : ( milk + water ) = 9 : ( 9 + 16 ) milk : mixture = 9 : 25 answer : a ) 15
Answer: a
Question (physics): a train travels from new york to chicago , a distance of approximately 480 miles , at an average rate of 60 miles per hour and arrives in chicago at 5 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time )
Options: a ) 10 : 00 , b ) 4 : 00 , c ) 5 : 00 , d ) 6 : 00 , e ) 7 : 00
Rationale: 5 : 00 in evening in chicago = 6 : 00 in evening in new york . so , the train was in chicago 6 : 00 in the evening , new york time . the trip took t = d / r = 480 / 60 = 8 hours . therefore , the train depart from new york at 6 : 00 - 8 hours = 10 : 00 in the morning , new york time . answer : a .
Answer: a
Question (physics): the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 7 seconds than it was moving after 2 seconds ?
Options: a ) 4 , b ) 55 , c ) 15 , d ) 48 , e ) 63
Rationale: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 2 ) = 2 ^ 2 + 2 * 2 = 8 z ( 7 ) = 7 ^ 2 + 2 * 7 = 63 therefore z ( 7 ) - z ( 3 ) = 63 - 8 = 55 km / hr option b"
Answer: b
Question (geometry): the diagonals of a rhombus are 11 cm and 16 cm . find its area ?
Options: a ) 277 , b ) 266 , c ) 150 , d ) 88 , e ) 212
Rationale: "1 / 2 * 11 * 16 = 88 answer : d"
Answer: d
Question (general): in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.6 times as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 1990
Rationale: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 1950 ro = 10 , ri = 40 1990 ro = 50 , ri = 80 = 1.6 times thus ans : e"
Answer: e
Question (general): a room is 8 meters 16 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 107 , b ) 153 , c ) 178 , d ) 198 , e ) 165
Rationale: "let us calculate both the length and width of the room in centimeters . length = 8 meters and 16 centimeters = 816 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 816 and 432 = 48 thus , the number of square tiles required = ( 816 x 432 ) / ( 48 x 48 ) = 17 x 9 = 153 answer : b"
Answer: b
Question (other): there are 8 executives , including the ceo and cfo , that are asked to form a small team of 5 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 34 , b ) 35 , c ) 36 , d ) 37 , e ) 38
Rationale: "the total number of ways to form a team of 5 is 8 c 5 = 56 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 6 c 3 = 20 . the number of ways to form an acceptable team is 56 - 20 = 36 . the answer is c ."
Answer: c
Question (gain): victor gets 92 % marks in examinations . if these are 460 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 376 , d ) 288 , e ) 271
Rationale: "let the maximum marks be m then 92 % of m = 460 ⇒ 92 / 100 × m = 460 ⇒ m = ( 460 × 100 ) / 92 ⇒ m = 46000 / 92 ⇒ m = 500 therefore , maximum marks in the examinations are 500 . answer : b"
Answer: b
Question (general): max planned to buy bike , sales man advised him to buy within this month , if he purchase next month means state tax will be increasing 10 % than its cost and it would be 82500 . what is the bike ' s selling price in this month
Options: a ) 70000 , b ) 73000 , c ) 75000 , d ) 77000 , e ) 79000
Rationale: sp * ( 110 / 100 ) = 82500 sp = 750 * 100 = > sp = 75000 answer : c
Answer: c
Question (physics): a boy goes to his school from his house at a speed of 3 km / hr and returns at a speed of 2 km / hr . if he takes 5 hours in going and coming . the distance between his house and school is ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 5 , e ) 7
Rationale: "average speed = ( 2 * 3 * 2 ) / ( 3 + 2 ) = 12 / 5 km / hr . distance traveled = 12 / 5 * 5 = 12 km . distance between house and school = 12 / 2 = 6 km . answer : c"
Answer: c
Question (geometry): find the perimeter of a triangle with sides measuring 7 centimeters , 10 centimeters and 15 centimeters .
Options: a ) 10 cm
b ) 15 cm
c ) 32 cm
d ) 35 cm
e ) 20 cm
Rationale: perimeter of triangle = a + b + c perimeter = 7 cm + 10 cm + 15 cm = 32 cm answer : c .
Answer: c
Question (physics): in a 500 m race , ravi beats ramesh by 5 seconds or 100 m . they decide to run another race and this time ravi gives ramesh a head tart of 200 m . if ravi ’ s speed is twice his previous speed and ramesh ’ s speed is one and half times his previous speed , how far from the starting point should the winning post be so that they finish at the same time ?
Options: a ) 500 m , b ) 1000 m , c ) 1500 m , d ) 2000 m , e ) 2500 m
Rationale: ravi beats ramesh by 5 sec or 100 mtr . . . . means ramesh cover 100 mtr in 5 sec . . . . by this we can get ramesh speed in 20 m / sec 20 . . . . . . . . . . . . . in 1 sec 500 . . . . . . . . in 500 / 20 = 25 sec ( ramesh ' s time ) so ravi take 20 sec to cover 500 mtr . . . . . . by this we can get that ravis speed is 25 m / sec now assume x be the distance from staring line where we need to put the winning post . according to question ravi ’ s speed will be 25 * 2 = 50 m / sec & ramesh ’ s speed will be 20 * 1.5 = 30 m / sec now assume x be the distance from staring line where we need to put the winning post . they will take same time to reach the wining post . as ravi gives ramesh a 200 m ahead start so he has to accede x meter and ramesh has to accede ( x - 200 ) meter hence we may write , x / 50 = ( x - 200 ) / 30 x = 500 meter answer : a
Answer: a
Question (general): a store owner estimates that the average price of type a products will increase by 25 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.25 * 4500 = 5625 cost of type b products next year = 1.1 * 8300 = 9130 total 5625 + 9130 = 14755 answer : a"
Answer: a
Question (geometry): two isosceles triangles have equal vertical angles and their areas are in the ratio 25 : 49 . find the ratio of their corresponding heights .
Options: a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 5 / 7 , e ) 2 / 3
Rationale: "we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 25 / 49 - - > height / height = 5 / 7 . answer : d ."
Answer: d
Question (general): a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 280 , then how much amount should c pay as his share of rent ?
Options: a ) 35 , b ) 45 , c ) 25 , d ) 72 , e ) 55
Rationale: a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 280 × 9 / 35 = 8 × 9 = 72 answer is d
Answer: d
Question (gain): exactly 30 % of the reporters for a certain wire service cover local politics in country x . if 25 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 60 % , d ) 80 % , e ) 84 %
Rationale: let ' s assume there are 100 reporters - - > 30 reporters cover local politics . now , as 25 % of the reporters who cover all politics do not cover local politics then the rest 75 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 75 % of them equal to 30 ( # of reporters who cover local politics ) : 0.75 x = 30 - - > x = 40 , hence 40 reporters cover politics and the rest 100 - 40 = 60 reporters do not cover politics at all . answer : c .
Answer: c
Question (general): positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 16 . what is the value of x ?
Options: a ) 20 , b ) 40 , c ) 80 , d ) 160 , e ) 320
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 16 ( y / 100 ) * x = 16 ( x / 400 ) * x = 16 x ^ 2 = 16 * 400 x = 80 the answer is c ."
Answer: c
Question (physics): excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 17 , c ) 15 , d ) 18 , e ) 12
Rationale: "t = 12 / 48 * 60 = 15 answer : c"
Answer: c
Question (geometry): difference between the length & breadth of a rectangle is 26 m . if its perimeter is 208 m , then the ratio of area and perimeter is ? ? we have : ( l - b ) = 26 and 2 ( l + b ) = 208 or ( l + b ) = 104 ?
Options: a ) 315 : 26 , b ) 315 : 25 , c ) 315 : 30 , d ) 415 : 35 , e ) 425 : 35
Rationale: "solving the two equations , we get : l = 63 and b = 40 . area = ( l x b ) = ( 63 x 40 ) m 2 = 2520 m ^ 2 the required ratio is 2520 : 208 = 315 : 26 a"
Answer: a