Cheukting/mathqa huggingface dataset:
Question (general): in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 100 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 18 , b ) 16 , c ) 17 , d ) 15 , e ) 19
Rationale: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 100 5 x - 10 = 100 5 x = 90 x = 18 answer : a"
Answer: a
Question (gain): how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 3 - percent solution ?
Options: a ) 35 , b ) 33 1 / 3 , c ) 27 , d ) 16 2 / 3 , e ) 19.5
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 3 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 3 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 3 x = 4.5 since you need a 15 l solution , you must evaporate 19.5 of the original 50 l solution to get a 3 % solution . answer is e ."
Answer: e
Question (general): average age of 7 members of a family is 29 years . if present age of the youngest member is 5 year , find average age of the remaining members at the time of birth of the youngest member .
Options: a ) 28 , b ) 37 , c ) 29 , d ) 237 , e ) 212
Rationale: average age ( present ) of 7 members = 29 years 5 years ago , average age of 7 members was 29 - 5 = 24 years . since , the youngest member was not born 5 years ago . therefore , average age of remaining 6 members is increased by 246246 = 4 years . therefore , 5 years ago , average age of 6 members was 24 + 4 = 28 years . answer : a
Answer: a
Question (probability): there is a 50 % chance jen will visit chile this year , while there is a 25 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ? [ / b ]
Options: a ) 25 % , b ) 50 % , c ) 62.5 % , d ) 63.5 % , e ) 75 %
Rationale: "the thing to note in the question is she would not be visiting both . thus p ( chile ) * ( 1 - p ( madagascar ) ) + p ( madagascar ) * ( 1 - p ( chile ) ) which is ( 1 / 2 * 3 / 4 ) + ( 1 / 4 * 1 / 2 ) , 3 / 8 * 1 / 8 = 1 / 2 = 50 % answer : b"
Answer: b
Question (general): thabo owns exactly 200 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 20 , c ) 35 , d ) 45 , e ) 50
Rationale: "i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 200 3 x + 60 + x = 200 x = 35 answer ( c . )"
Answer: c
Question (general): on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 4 cups of tea . last week mo drank a total of 26 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 26 t - c = 14 - > t = 20 . c = 6 . mo drinks 4 cups of tea a day then number of days that are not rainy = 20 / 4 = 5 so number of rainy days = 7 - 5 = 2 a is the answer ."
Answer: a
Question (gain): the market value of a certain machine decreased by 25 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 4,000 , e ) $ 800
Rationale: "d . market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 25 / 100 ) = 8000 - 2000 = $ 6000 market value in 1984 = market value in 1983 - ( 25 % of $ 8000 ) = 6000 - 2000 = $ 4000"
Answer: d
Question (general): if n is a prime number greater than 3 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 3 , square it and see what would be the remainder upon division of it by 12 . n = 5 - - > n ^ 2 = 25 - - > remainder upon division 25 by 12 is 1 . answer : b"
Answer: b
Question (gain): in the manufacture of a certain product , 10 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.25 % , b ) 0.5 % , c ) 0.75 % , d ) 1.25 % , e ) 2.5 %
Rationale: "0.1 * 0.05 = 0.005 = 0.5 % the answer is b ."
Answer: b
Question (physics): convert 300 inches into centimeter ?
Options: a ) 762 cm , b ) 750 cm , c ) 650 cm , d ) 710 cm , e ) 754 cm
Rationale: "1 inch = 2.54 cm 300 inches = 300 * 2.54 = 762 cm answer is e"
Answer: e
Question (physics): a boat goes 130 km downstream in 10 hours , and 75 km upstream in 15 hours . the speed of the stream is ?
Options: a ) 3.5 , b ) 3 , c ) 5 , d ) 4 , e ) 8
Rationale: "125 - - - 10 ds = 130 ? - - - - 1 75 - - - - 15 us = 5 ? - - - - - 1 s = ( 13 - 5 ) / 2 = 4 kmph . answer : d"
Answer: d
Question (general): pat , kate , and mark charged a total of 135 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 18 , b ) 36 , c ) 75 , d ) 90 , e ) 108
Rationale: 75 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 135 = > x = 15 30 : 15 : 90 90 - 15 = 75 answer c
Answer: c
Question (general): sum of the squares of 3 no . is 52 and the sum of their products taken two at a time is 72 . find the sum ?
Options: a ) 18 , b ) 21 , c ) 13 , d ) 16 , e ) 14
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 52 + 2 * 72 a + b + c = â ˆ š 196 = 14 answer e"
Answer: e
Question (probability): a bag contains 3 red , 2 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 3 + 2 + 4 = 9 n ( s ) = 9 c 3 = 84 n ( e ) = 3 c 1 * 2 c 1 * 4 c 1 = 3 * 2 * 4 = 24 probability = 24 / 84 = 2 / 7 answer is a"
Answer: a
Question (physics): how many seconds will a 650 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 48 km / hr ?
Options: a ) 25 , b ) 45 , c ) 54 , d ) 44 , e ) 48
Rationale: "speed of train relative to man = 48 - 3 = 45 km / hr . = 45 * 5 / 18 = 25 / 2 m / sec . time taken to pass the man = 650 * 2 / 25 = 54 sec . answer : c"
Answer: c
Question (general): when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 7 , the remainder is 6 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 6 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 6 . . d"
Answer: d
Question (general): what is the unit digit in [ ( 6273 ) ^ 1793 x ( 625 ) ^ 317 x ( 341 ) ^ 491 ] ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 5 , e ) none of them
Rationale: unit digit in ( 6374 ) ^ 1793 = unit digit in ( 4 ) ^ 1793 = unit digit in [ ( 4 ^ 2 ) ^ 896 x 4 ] = unit digit in ( 6 x 4 ) = 4 unit digit in ( 625 ) ^ 317 = unit digit in ( 5 ) ^ 317 = 5 unit digit in ( 341 ) ^ 491 = unit digit in ( 1 ) ^ 491 = 1 required digit = unit digit in ( 4 x 5 x 1 ) = 0 answer is 0
Answer: a
Question (gain): what is the rate percent when the simple interest on rs . 780 amount to rs . 130 in 4 years ?
Options: a ) 4.16 , b ) 5.16 , c ) 6.16 , d ) 7.16 , e ) 8.16
Rationale: "130 = ( 780 * 4 * r ) / 100 r = 4.16 % answer : a"
Answer: a
Question (physics): the cross - section of a river bank is a trapezium in shape . if the river bank is 12 m wide at the top and 8 m wide at the bottom and the area of cross - section is 500 sq m , the depth of river bank is ?
Options: a ) 20 m , b ) 60 m , c ) 40 m , d ) 50 m , e ) 90 m
Rationale: 1 / 2 * d ( 12 + 8 ) = 500 d = 50 answer : d
Answer: d
Question (general): what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 19 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 2 : 1 , d ) 13 : 11 , e ) 14 : 8
Rationale: correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 6 : 3 = 2 : 1
Answer: c
Question (physics): x can do a piece of work in 20 days . he works at it for 10 days and then y finished it in 12 days . how long will y take to complete the work ?
Options: a ) 10 , b ) 12 , c ) 24 , d ) 29 , e ) 30
Rationale: "work done by x in 10 days = 10 * 1 / 20 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 1 / 2 work is done by y in 12 days whole work will be done by y in 12 * 2 = 24 days answer is c"
Answer: c
Question (physics): a man can row upstream at 27 kmph and downstream at 35 kmph , and then find the speed of the man in still water ?
Options: a ) 31 , b ) 92 , c ) 30 , d ) 32 , e ) 23
Rationale: "us = 27 ds = 35 m = ( 35 + 27 ) / 2 = 31 answer : a"
Answer: a
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum m of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum m = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Question (general): by how much does the larger root of the equation 2 a ^ 2 + 5 a = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: for 2 a ^ 2 + 5 a = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) .
Answer: e
Question (general): if x + 1 / x = 2 then find x 2 + 1 / x 2
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: if x + 1 / x = p = = > x ^ 2 + 1 / x ^ 2 = p ^ 2 - 2 ans = 2 ^ 2 - 2 = 2 answer : b
Answer: b
Question (geometry): the faces of a triangular prism are to be painted by 5 different colors . in how many ways can be this be done ?
Options: a ) a . 720
b ) b . 256
c ) c . 1
d ) d . 120
e ) e . 36
Rationale: if i have to paint 5 sides with 5 different colour . . . first face can have 5 c 1 options , 2 nd would have 4 c 1 , and subsequent ones would have 3 c 1 , 2 c 1 and 1 options respectively . total options = 5 c 1 x 4 c 1 x 3 c 1 x 2 c 1 x 1 = 120 distinct ways correct answer - d
Answer: d
Question (geometry): three interviewers , a , b , and c are interviewing 30 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer a admitted 10 applicants , b admitted 12 applicants , and c admitted 15 applicants , at least how many applicants get the admission ?
Options: a ) 6 , b ) 2 , c ) 0 , d ) 8 , e ) 12
Rationale: "if a admitted 10 are overlapping with b admission of 12 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : c"
Answer: c
Question (gain): during a sale of 30 % on everything in a store , a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies . the store still makes a profit of 12 % on this sale . what is the mark up percentage on each candy ?
Options: a ) 100 % , b ) 80 % , c ) 75 % , d ) 66 + 2 / 3 % , e ) 55 %
Rationale: "hi akhil , i can share the way i solved it . . let ' s say marked price = m so , there ' s a discount of 20 % on m so , new s . p . = 80 % of m now , the child convinces the owner to sell 20 candies for the price of 14 candies . let ' s say each candy after discount is 1 $ . so , s . p . of 20 candies = 20 $ . the child bought it for 14 $ so , he got a discount of 6 / 20 * 100 = 30 % so , the latest s . p . = 70 % of 80 % of m = 0.7 * 0.8 m now , we are given that the shopkeeper still makes a profit of 12 % . so we have , 0.7 * 0.8 * m = 1.12 c . p so , we get , m = 2 c . p . i . e . marked price was kept 100 % above c . p . b"
Answer: b
Question (geometry): there are two cubes with ratio between volume is 125 : 64 . then what is the value of length of each cube ?
Options: a ) 25 : 16
b ) 16 : 25
c ) 4 : 5
d ) 5 : 4
e ) 150 : 96
Rationale: given 6 a 12 : a 22 = 150 : 96 then a 12 : a 22 = 25 : 16 a 1 : a 2 = 5 : 4 so the answer is d
Answer: d
Question (general): how many positive integers less than 247 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 41 , c ) 42 , d ) 53 , e ) 64
Rationale: from here , it might be easier to go up in bounds of 60 , so we know that 61 - 120 gives 10 more numbers . 121 - 180 and 181 - 240 as well . this brings us up to 240 with 40 numbers . a cursory glance at the answer choices should confirm that it must be 41 , as all the other choices are very far away . the numbers 244 will come and complete the list that ’ s ( naughty or nice ) under 250 . answer choice b is correct here .
Answer: b
Question (physics): ram , who is half as efficient as krish , will take 36 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 8 days , d ) 6 days , e ) 18 days
Rationale: "number of days taken by ram to complete task = 36 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 36 days is 36 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 36 w / 3 w = 12 days answer b"
Answer: b
Question (general): the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 24 different signs . if the company used 22 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 24 signs ?
Options: a ) 246 , b ) 248 , c ) 92 , d ) 15,128 , e ) 30,256
Rationale: "# of 2 - letter codes possible from 24 different signs = 24 * 24 . # of 2 - letter codes possible from 22 different signs = 22 * 22 . the difference = 24 ^ 2 - 22 ^ 2 = ( 24 - 22 ) ( 24 + 22 ) = 92 . answer : c ."
Answer: c
Question (general): find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 5 as remainder
Options: a ) 1637 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1635
Rationale: let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 5 5 x = 1360 x = 272 large number = 272 + 1365 = 1637 a
Answer: a
Question (general): the sum of ages of 10 children born at the intervals of 1 years each is 105 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 5 , c ) 2 , d ) 7 , e ) 6
Rationale: "let the ages of children be x , ( x + 1 ) , ( x + 2 , ( x + 3 ) , ( x + 4 ) , ( x + 5 ) , ( x + 6 ) , ( x + 7 ) , ( x + 8 ) , and ( x + 9 ) years . then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + ( x + 5 ) + ( x + 6 ) + ( x + 7 ) + ( x + 8 ) + ( x + 9 ) = 105 10 x = 60 x = 6 age of the youngest child = x = 6 years . answer : e"
Answer: e
Question (physics): a pipe can fill a cistern in 33 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 10 min
Rationale: "full cistern filled in = 33 minutes 1 / 11 part filled in = 33 * 1 / 11 = 3 minutes answer is c"
Answer: c
Question (geometry): a wooden cube whose edge length is 8 inches is composed of smaller cubes with edge lengths of one inch . the outside surface of the large cube is painted red and then it is split up into its smaller cubes . if one cube is randomly selected from the small cubes , what is the probability that the cube will have at least one red face ?
Options: a ) 46.3 % , b ) 50.4 % , c ) 54.2 % , d ) 57.8 % , e ) 61.3 %
Rationale: "there are a total of 8 * 8 * 8 = 512 cubes . all the exterior cubes will have at least one face painted red . the interior is formed by 6 * 6 * 6 = 216 cubes . the number of cubes with at least one side painted red is 512 - 216 = 296 cubes the probability that a cube has at least one side painted red is 296 / 512 which is about 57.8 % the answer is d ."
Answer: d
Question (physics): x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 36 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 36 days whole work will be done by y in 36 * 5 / 4 = 45 days answer is a
Answer: a
Question (general): mr . hanson has a pool of money from which to give out christmas bonuses to his 5 employees . he wants all his employees to have identical bonuses , but when he divides them out , he finds he has 2 dollars left over , as the payroll system will only accept whole dollar amounts . the next christmas , mr . hanson discovers the pool for the bonuses is 3 times the size . this time , how much money will be left over ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: set x = to amount of money for bonuses , and y to be the amount of each individual bonus . x = 5 * y + 2 . 3 x = 15 * y + 6 3 x = 3 * 5 * y + 6 3 x = 5 ( 3 ( y + 1 ) ) + 1 remainder is then 1 , so option b .
Answer: b
Question (general): calculate 469138 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4690910862 , d ) 4586870843 , e ) none
Rationale: "answer 469138 x 9999 = 469138 x ( 10000 - 1 ) = 4691380000 - 469138 = 4690910862 . option : c"
Answer: c
Question (gain): the cash difference between the selling prices of an book at a profit of 8 % and 16 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 55 : 23 , b ) 52 : 33 , c ) 52 : 53 , d ) 27 : 29 , e ) 51 : 34
Rationale: "let c . p . of the book be $ x . then , required ratio = 108 % of x / 116 % of x = 108 / 116 = 27 / 29 = 27 : 29 d"
Answer: d
Question (geometry): if a rectangular billboard has an area of 117 square feet and a perimeter of 44 feet , what is the length of each of the shorter sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 9 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 117 and a perimeter of 44 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 117 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 117 , so the correct answer is let ' s test answer d : 9 if . . . the shorter side = 9 . . . the area = 117 . . . . 117 / 9 = 13 = the longer side perimeter = 9 + 9 + 13 + 13 = 44 d"
Answer: d
Question (physics): bird is flying 120 km / hr between b to r . two trains at b to r at 60 kmph . the distance traveled by the bird before it is killed ?
Options: a ) 90 kms . , b ) 100 kms . , c ) 110 kms . , d ) 120 kms . , e ) 130 kms .
Rationale: it will depend on the distance between b and r . if distance between b and r is 120 kms , time taken by trains before collision = 120 / ( 60 + 60 ) = 1 hr distance traveled by bird in 1 hr = 120 kms . so the distance traveled by the bird before it is killed = 120 kms . answer : d
Answer: d
Question (general): a = 5 ^ 15 - 125 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get none different values and answer is a . . . ."
Answer: a
Question (physics): in a 600 m race , the ratio of the speeds of two contestants a and b is 5 : 4 . a has a start of 100 m . then , a wins by :
Options: a ) 200 m , b ) 20 m , c ) 403 m , d ) 20 m , e ) 23 m
Rationale: to reach the winning post a will have to cover a distance of ( 600 - 100 ) m , i . e . , 500 m . while a covers 5 m , b covers 4 m . while a covers 500 m , b covers 4 x 500 / 5 m = 400 m . thus , when a reaches the winning post , b covers 400 m and therefore remains 200 m behind . a wins by 200 m . answer : a
Answer: a
Question (other): at present the ratio between the ages of arun and deepak is 2 : 3 . after 5 years , arun ' s age will be 25 years . what is the age of deepak at present ?
Options: a ) 20 years , b ) 30 years , c ) 15 years , d ) 25 years , e ) 28 years
Rationale: "let the present ages of arun and deepak be 2 x years and 3 x years respectively 2 x + 5 = 25 2 x = 20 x = 10 deepak ' s age = 3 x = 30 years answer is b"
Answer: b
Question (physics): the length of the bridge is 200 m , which a 100 m long train cross in 60 sec . then what is the speed of train ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 10 , e ) 8
Rationale: speed = length / time length = ( 200 + 100 ) = 300 m time = 60 sec speed = 300 / 60 = 5 m / sec answer b
Answer: b
Question (general): if a = 105 and a ^ 3 = 21 × 25 × 45 × e , what is the value of e ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × e = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x e = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x e = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x e e = 7 ^ 2 = 49 answer d"
Answer: d
Question (gain): if i earn a profit 50 $ in a day and i have 9 employees . after keeping 10 percent profit for me , and distribute remianing money equally among my employees then how much each employee would get ?
Options: a ) $ 3 , b ) $ 7 , c ) $ 1 , d ) $ 5 , e ) $ 9
Rationale: since i earned $ 50 sp 10 percent would be 5 $ and 45 $ would remain . dividing 45 by 9 , each employee would get 5 $ each and hince option d is correct .
Answer: d