Cheukting/mathqa huggingface dataset:
Question (gain): rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage w .
Options: a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %
Rationale: "given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % w = ( 97 / 556 ) * 100 = 17.4 % answer : b"
Answer: b
Question (general): cereal a is 9 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 5 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
Rationale: "( 9 / 100 ) a + ( 2 / 100 ) b = ( 4 / 100 ) ( a + b ) 5 a = 2 b = > a / b = 2 / 5 answer is b ."
Answer: b
Question (physics): how long does a train 180 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?
Options: a ) 33 , b ) 56 , c ) 55 , d ) 82 , e ) 62
Rationale: "explanation : t = ( 660 + 180 ) / 54 * 18 / 5 t = 56 answer : option b"
Answer: b
Question (general): a profit of rs . 500 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) rs . 200 , b ) rs . 100 , c ) rs . 300 , d ) rs . 50 , e ) rs . 90
Rationale: "a profit of rs . 500 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 300 and 200 . difference in profit share = 300 - 200 = 100 answer : b"
Answer: b
Question (gain): a man buys rs . 56 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 42
Rationale: "dividend on rs . 56 = rs . 9 / 100 x 56 = rs . 5.04 . rs . 12 is an income on rs . 100 . rs . 5.04 is an income on rs . 100 / 12 x 5.04 = rs . 42 . answer : option e"
Answer: e
Question (gain): of 440 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 55
Rationale: "say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 440 = 1.25 b + b - 0.25 b - - > b = 220 , a = 1.25 b = 275 and { both } = 0.25 b = 55 . the number of students who read only book a is { a } - { both } = 125 - 25 = 100 ; the number of students who read only book b is { b } - { both } = 275 - 55 - 220 ; the difference is 220 - 55 = 165 . answer : e ."
Answer: e
Question (gain): on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 30 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 14.3 % , d ) 22 % , e ) 30 %
Rationale: "suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 30 % of y exceeded the speed limit but did n ' t received the ticket , i . e . 3 y / 10 . it means 7 y / 10 received the ticket . hence , 7 y / 10 = x / 10 or y / x = 1 / 7 or y / x * 100 = 1 / 7 * 100 = 14.3 % c"
Answer: c
Question (physics): ajay can ride 50 km in 1 hour . in how many hours he can ride 750 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 750 km in = 750 / 50 * 1 = 15 hours answer is b"
Answer: b
Question (general): a number of 47 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 17
Rationale: "to maximize # of boxes we should minimize marbles per box : 14 * 3 + 1 * 5 = 47 - - > 14 + 1 = 15 . answer : c ."
Answer: c
Question (gain): 12 is subtracted from 95 % of a number , the result is 178 . find the number ?
Options: a ) 200 , b ) 240 , c ) 198 , d ) 190 , e ) 322
Rationale: "( 95 / 100 ) * x â € “ 12 = 178 9.5 x = 1900 x = 200 answer : a"
Answer: a
Question (gain): a man invests rs . 8000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 4000 , e ) none of these
Rationale: explanation : interest on rs . 8000 at 5 % per annum = ( 8000 × 5 × 1 ) / 100 = rs . 400 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 8000 + x ) × 6 × 1 / 100 . = > 400 + 2 x / 25 = ( 8000 + x ) × 6 × 1 / 100 . = > 40000 + 8 x = ( 8000 + x ) × 6 . = > 40000 + 8 x = 48000 + 6 x . = > 2 x = 8000 . = > x = 4000 . answer : d
Answer: d
Question (general): the cost per unit of electricity during a 4 year period is as follows : year 1 , $ 3 per unit ; year 2 , $ 4 per unit ; year 3 , $ 5 per unit ; year 4 , $ 6 per unit . if a factory spent equal dollars on electricity each year , what was the average cost of a unit of electricity during the 4 year period ?
Options: a ) $ 4.31 , b ) $ 4.51 , c ) $ 4.21 , d ) $ 5.21 , e ) $ 5.61
Rationale: let money spent each year = $ 60 units bought first year = 20 units bought second year = 15 units bought third year = 12 units bought fourth year = 10 total number of units = 57 total money spent = 60 * 4 = 240 average = 240 / 57 = 4.21 answer : c
Answer: c
Question (physics): in what time will a train 45 m long cross an electric pole , it its speed be 108 km / hr ?
Options: a ) 0.5 , b ) 1.25 , c ) 1.5 , d ) 2.5 , e ) 3.5
Rationale: "speed = 108 * 5 / 18 = 30 m / sec time taken = 45 / 30 = 1.5 sec . answer : c"
Answer: c
Question (other): in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 10 of the housing units , including 1 / 4 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 3 / 4 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15
Rationale: 1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 4 ( equiped with cable tv ) i . e . 1 / 4 ( 1 / 5 ) = 1 / 20 therefore only video cassette recorder = 1 / 10 - 1 / 20 = 1 / 20 total = 1 / 5 + 1 / 20 + neither cable tv nor videocassette recorders 1 = 1 / 4 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 1 / 4 = 3 / 4 hence a .
Answer: a
Question (general): two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 45 sec . the length of each train is ?
Options: a ) 50 , b ) 26 , c ) 27 , d ) 62.5 , e ) 21
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 45 = 25 / 9 = > x = 65.5 . answer : d"
Answer: d
Question (general): a batsman makes a score of 87 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options: a ) 19 , b ) 29 , c ) 39 , d ) 49 , e ) 59
Rationale: "solution let the average after 17 th inning = x . then , average after 16 th inning = ( x - 3 ) average = 16 ( x - 3 ) + 87 = 17 x or x = ( 87 - 48 ) = 39 . answer c"
Answer: c
Question (physics): in what time will a train 100 meters long cross an electric pole , if its speed is 360 km / hr
Options: a ) 1 second , b ) 4.5 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 360 * ( 5 / 18 ) = 100 m / sec time = distance / speed = 100 / 100 = 1 second answer : a"
Answer: a
Question (gain): a 340 - liter solution of kola is made from 64 % water , 9 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 8 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 26.5 % .
Rationale: "denominator : 340 + 8 + 3.2 + 6.8 = 358 numerator : 340 ( 1 - . 64 - . 09 ) + 3.2 340 ( 0.27 ) + 3.2 91.8 + 3.2 95 ratio : 95 / 358 = 0.265 answer : e"
Answer: e
Question (general): if ( 5 ^ 11 ) ( 9 ^ 6 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 11 ) ( 9 ^ 6 ) = 3 ( 15 ^ x ) = > 5 ^ 11 * 3 ^ 12 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 11 * 3 ^ 12 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 11 answer c"
Answer: c
Question (general): find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5
Options: a ) 26 , b ) 32 , c ) 25 , d ) 27 , e ) 29
Rationale: "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 5 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 5 = 2 ^ 22 x 7 ^ 5 x 11 ^ 5 total number of prime factors = ( 22 + 5 + 5 ) = 32 . answer is b ."
Answer: b
Question (geometry): a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 5 inches wide on each side , the total area would have been ( m + 180 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 21 , b ) 36 , c ) 38 , d ) 40 , e ) 42
Rationale: "let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 2 ) ( b + 2 ) = m - - - - ( 2 ) and ( l + 10 ) ( b + 10 ) = m + 180 - - - - - - - - - > ( l + 10 ) ( b + 10 ) - 180 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 2 ) ( b + 2 ) = ( l + 10 ) ( b + 10 ) - 180 lb + 2 l + 2 b + 4 = lb + 10 l + 10 b + 100 - 180 simplify 8 l + 8 b = 84 - - - - - - > 2 ( l + b ) = 21 ( check eq ( 1 ) ) answer is a"
Answer: a
Question (general): a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 50 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 77.27 , e ) 97.2
Rationale: "let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 50 * 5 = 250 student ' s average = ( 600 + 250 ) / 11 = 77.27 answer d"
Answer: d
Question (general): jim ’ s taxi service charges an initial fee of $ 2.35 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.5 , e ) $ 5.40
Rationale: "let the fixed charge of jim ’ s taxi service = 2.35 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.35 + ( 3.6 / . 4 ) * . 35 = 2.35 + 9 * . 35 = 5.5 $ answer d"
Answer: d
Question (general): a miniature roulette wheel is divided into 9 equal sectors , each bearing a distinct integer from 1 to 9 , inclusive . each time the wheel is spun , a ball randomly determines the winning sector by settling in that sector . if the wheel is spun three times , approximately what is the probability that the product of the three winning sectors ’ integers will be even ?
Options: a ) 50 % , b ) 67 % , c ) 83 % , d ) 90 % , e ) 96 %
Rationale: "the only way to have an odd product is if all 3 integers are odd . p ( odd product ) = 5 / 9 * 5 / 9 * 5 / 9 = 125 / 729 p ( even product ) = 1 - 125 / 729 = 604 / 729 which is about 83 % the answer is c ."
Answer: c
Question (other): local kennel has cats and dogs in the ratio of 2 : 3 . if there are 6 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 24 , b ) 18 , c ) 30 , d ) 15 , e ) 12
Rationale: lets work with the data given to us . we know that there ratio of cats to dogs is 2 : 3 or cats 2 dogs 3 we can write number of cats as 2 x and number of dogs as 3 x and we know that 3 x - 2 x = 6 ( therefore x = 6 ) then # of dogs = 3 x 6 = 18 answer is b
Answer: b
Question (general): in the coordinate plane a slope of the line k is 3 / 2 times the y - intercept of the line k . what is the x - intercept of the line k ?
Options: a ) - 2 , b ) 2 / 3 , c ) - 2 / 3 , d ) 1 / 4 , e ) 3 / 2
Rationale: as y = 3 / 2 mx + m , from 0 = 3 / 2 mx + m we get x = 2 / 3 . hence , the correct answer choice is b .
Answer: b
Question (general): 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 140000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 6800 , e ) s . 5600
Rationale: cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 140000 p = rs . [ ( 24 * 4 * 4 * 140000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 53760000 / 9600 ) = > p = rs . 5600 answer : e
Answer: e
Question (gain): a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) s . 933.33 , b ) s . 1009 , c ) s . 1007 , d ) s . 1006 , e ) s . 1002
Rationale: "explanation : 90 % 105 % - - - - - - - - 15 % - - - - 140 100 % - - - - ? = > rs . 933.33 answer : a"
Answer: a
Question (general): how many positive integers less than 15 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 14 , b ) 13 , c ) 12 , d ) 8 , e ) 10
Rationale: the number = 2 a + 3 b < 20 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 - > the number = 5 , 8 , 11 - - > 3 numbers when a = 2 , b = 1 , 2,3 - > . . . . - - > 3 numbers when a = 3 , b = 1,2 , 3,4 - - > . . . . - - > 2 numbers total number is already 8 . look at the answer there is no number greater than 8 - - > we dont need to try any more answer must be d
Answer: d
Question (physics): the sum of all consecutive odd integers from − 31 to 41 , inclusive , is
Options: a ) 110 , b ) 135 , c ) 150 , d ) 165 , e ) 185
Rationale: "the sum of the odd numbers from - 31 to + 31 is 0 . let ' s add the remaining numbers . 33 + 35 + 37 + 39 + 41 = 5 ( 37 ) = 185 the answer is e ."
Answer: e
Question (other): find the compound ratio of ( 2 : 5 ) , ( 6 : 11 ) and ( 11 : 2 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 6 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 5 * 6 / 11 * 11 / 2 = 2 / 1 = 6 : 5 answer is d"
Answer: d
Question (gain): if a man lost 4 % by selling oranges at the rate of 24 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 16 , b ) 8 , c ) 9 , d ) 4 , e ) 3
Rationale: "96 % - - - - 24 144 % - - - - ? 96 / 144 * 24 = 16 answer : a"
Answer: a
Question (other): the ratio of the number of females to males at a party was 1 : 2 but when 6 females and 6 males left , the ratio became 1 : 3 . how many people were at the party originally ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "the total number of people are x females + 2 x males . 3 * ( x - 6 ) = 2 x - 6 x = 12 there were 3 x = 36 people at the party originally . the answer is d ."
Answer: d
Question (physics): one robot builds a robot in 1 hour , another one builds a robot in 2 hours . the 2 robots work together and when a new robot is complete , it joins the others , working at a constant rate of one robot in 2 hours . how much time will it take until there are 6 robots altogether , if the robots build only one robot at a time ?
Options: a ) 70 min , b ) 94 min , c ) 109 min , d ) 114 min , e ) 120 min
Rationale: "first the 2 robots work at the rate of 1 + 1 / 2 = 3 / 2 so they complete one robot in 2 / 3 rd of an hour = 40 minutes - ( 1 ) now the 3 robots work together at the rate of 1 + 1 / 2 + 1 / 2 = 4 / 2 = 2 / 1 so they complete one robot in 1 / 2 an hour , i . e 30 minutes - ( 2 ) now the 4 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 = 5 / 2 so they complete one robot in 2 / 5 th of an hour , i . e . 24 minutes - ( 3 ) now the 4 robots work together at the rate of 1 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 = 3 so they complete one robot in 1 / 3 th of an hour , i . e . 20 minutes - ( 4 ) and now we have 5 robots so total = ( 1 ) + ( 2 ) + ( 3 ) + ( 4 ) = 114 minutes answer - d"
Answer: d
Question (gain): john had a stock of 1200 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 23.8 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
Rationale: let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1200 - n = 1200 - 402 = 798 percentage books not sold / total number of books = 798 / 1200 = 0.665 = 66.5 % correct answer c
Answer: c
Question (general): if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 16 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 16 . then 4 n < 16 and n < 4 . the largest possible integer is n = 3 . the answer is c ."
Answer: c
Question (general): find the average of all numbers between 2 and 63 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 32.5 , e ) 35
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 ) / 12 = 390 / 12 = 32.5 answer : option d"
Answer: d
Question (general): a mixture contains alcohol and water in the ratio 4 : 3 . if 7 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 14 litres , c ) 30 litres , d ) 22 litres , e ) 8 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 7 ) = 4 / 5 20 x = 4 ( 3 x + 7 ) 8 x = 28 x = 3.5 quantity of alcohol = ( 4 x 3.5 ) litres = 14 litres . answer is b ."
Answer: b
Question (gain): a sum fetched total simple interest of 4016.25 at the rate of 12 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 6693.75 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 60 % of p = 4016.25 or , p = 6693.75 answer a"
Answer: a
Question (gain): a man buys 50 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 5.3 % , b ) 7.6 % , c ) 10.6 % , d ) 12 % , e ) none of these
Rationale: "explanation : let marked price be re . 1 each c . p . of 50 pens = rs . 46 s . p . of 50 pens = 99 % of rs . 50 = rs . 49.50 profit % = ( profit / c . p . ) x 100 profit % = ( 3.50 / 46 ) x 100 = 7.6 % answer b"
Answer: b
Question (general): a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord w , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . w = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d"
Answer: d
Question (general): what is the least value of x , so that 2 x 5475 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 4 , d ) 3 , e ) 2
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 5 + 4 + 7 + 5 = 23 + x least value of x may be ' 4 ' , so that the total 23 + 4 = 27 is divisible by 9 . answer : option c"
Answer: c
Question (general): in the rectangular coordinate system , if the line x = 5 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 3 / 7
Rationale: "x = 5 y + 5 , and thus y = x / 5 - 1 the slope is 1 / 5 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 5 and thus p = 2 / 5 the answer is d ."
Answer: d
Question (general): in digging a pond 20 m * 15 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 3387 , b ) 1000 , c ) 2866 , d ) 1500 , e ) 1121
Rationale: "20 * 15 * 5 = 1500 answer : d"
Answer: d
Question (physics): a train overtakes two persons who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . the length of the train is :
Options: a ) 10 , b ) 100 , c ) 50 , d ) 200 , e ) 300
Rationale: 2 kmph = ( 2 x 5 / 18 ) m / sec = 5 / 9 m / sec . 4 kmph = ( 4 x 5 / 18 ) m / sec = 10 / 9 m / sec . let the length of the train be x metres and its speed by y m / sec . then , ( x / y - 5 / 9 ) = 9 and ( x / y - 10 / 9 ) = 10 . 9 y - 5 = x and 10 ( 9 y - 10 ) = 9 x = > 9 y - x = 5 and 90 y - 9 x = 100 . on solving , we get : x = 50 . therefore length of the train is 50 m . answer : c
Answer: c
Question (general): the sum of the present ages of two persons a and b is 45 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 55 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "a + b = 45 , a = 2 b 2 b + b = 45 = > b = 15 then a = 30 . 5 years , their ages will be 35 and 20 . sum of their ages = 35 + 20 = 55 . answer : a"
Answer: a
Question (geometry): the length of a rectangle is two third of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 4761 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 13 units ?
Options: a ) 598 sq . units
b ) 556 sq . units
c ) 589 sq . units
d ) 958 sq . units
e ) 985 sq . units
Rationale: given that the area of the square = 4761 sq . units = > side of square = â ˆ š 4761 = 69 units the radius of the circle = side of the square = 69 units length of the rectangle = 2 / 3 * 69 = 46 units given that breadth = 13 units area of the rectangle = lb = 46 * 13 = 598 sq . units answer : a
Answer: a