Cheukting/mathqa huggingface dataset:
Question (gain): an article is sold at a certain price . by selling it at 2 / 3 of that price one loses 10 % . find the gain percent at original price ?
Options: a ) 25 % , b ) 20 % , c ) 35 % , d ) 40 % , e ) 50 %
Rationale: let the original s . p . be $ x then , new s . p . = $ 2 / 3 x loss = 10 % c . p . = 100 / 90 * 2 / 3 x = 20 x / 27 c . p . = 20 x / 27 gain = x - 20 x / 27 = 7 x / 27 gain % = 7 x / 27 * 27 / 20 x * 100 = 35 % answer is c
Answer: c
Question (other): in a sports club with 30 members , 17 play badminton and 19 play tennis and 3 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 3 = 30 39 - 2 x + x = 30 39 - x = 30 x = 9 so 9 members play both badminton and tennis . c"
Answer: c
Question (general): the local recycling plant had a contract requiring anyone who obtained recycled bottles for storage for them , to bring them back to be recycled again . the plant could make one new bottle from every 7 bottles returned . one week , on monday , they got 343 bottles to recycle . assuming that everybody brought back all the empties , how many could they eventually remake from the 343 ?
Options: a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57
Rationale: in 1 st level they will make 343 / 7 = 49 bottles . in 2 nd level they will make 49 / 7 = 7 bottles . in 3 rd level they will make 7 / 7 = 1 bottle . totally they can remake 49 + 7 + 1 = 57 bottles answer : e
Answer: e
Question (general): how many numbers between 400 and 1000 can be made with the digits 2 , 3,4 , 5,6 and 0 ?
Options: a ) 30 , b ) 60 , c ) 90 , d ) 120 , e ) 150
Rationale: "required number = 3 * 5 p 2 = 3 * 20 = 60 answer is b"
Answer: b
Question (general): the difference between the heights of two trees is 20 cm . 10 years ago , the taller one was thrice as taller as the shorter one . the present height of the taller tree is
Options: a ) 300 cm , b ) 15 cm , c ) 20 cm , d ) 10 cm , e ) 40 cm
Rationale: let their heights of x cm and ( x + 20 ) cm respectively . then , ( x + 20 ) - 10 = 3 ( x - 10 ) ⇔ x + 10 = 3 x - 30 ⇔ 2 x = 40 ∴ present height of taller tree = ( 20 + 10 ) = 30 cm . answer : 30 cm
Answer: a
Question (other): water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 108 grams of water ?
Options: a ) 16 , b ) 96 , c ) 112 , d ) 128 , e ) 142
Rationale: "solution : we are given that the ratio of hydrogen to oxygen in water , by mass , is 2 : 16 . using our ratio multiplier we can re - write this as 2 x : 16 x . we can now use these expressions to determine how much oxygen is in 108 grams of water . 2 x + 16 x = 108 18 x = 108 x = 6 since x is 6 , we know that there are 16 x 6 = 96 grams of oxygen in 108 grams of water . answer b ."
Answer: b
Question (general): in an examination , 35 % of total students failed in hindi , 45 % failed in english and 20 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 35 + 45 - 20 ) = 100 - 60 = 40 answer : d"
Answer: d
Question (general): 8 people went to a restaurant for dinner . 7 of them spent $ 10 each on their meals and the eighth spent $ 7 more than the average expenditure of all 8 people . what was the total amount of money that the 8 people spent ?
Options: a ) $ 85 , b ) $ 88 , c ) $ 91 , d ) $ 94 , e ) $ 97
Rationale: let t be the total amount of money spent . 7 * 10 + ( t / 8 + 7 ) = t 77 = 7 t / 8 t = ( 8 * 77 ) / 7 = 88 the answer is b .
Answer: b
Question (physics): a person crosses a 1080 m long street in 12 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 4.5 , c ) 4.8 , d ) 5.4 , e ) 5.5
Rationale: "speed = 1080 / ( 12 x 60 ) m / sec = 1.5 m / sec . converting m / sec to km / hr = 1.5 x ( 18 / 5 ) km / hr = 5.4 km / hr . answer : d"
Answer: d
Question (gain): there were two candidates in an election . winner candidate received 62 % of votes and won the election by 384 votes . find the number of votes casted to the winning candidate ?
Options: a ) 288 , b ) 744 , c ) 992 , d ) 298 , e ) 177
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 384 62 % - - - - - - - - ? = > 992 answer : c"
Answer: c
Question (other): the compound ratio of 1 : 2 , 2 : 5 and 3 : 10 ?
Options: a ) 1 : 2 , b ) 1 : 5 , c ) 3 : 5 , d ) 1 : 50 , e ) 3 : 50
Rationale: 1 / 2 * 2 / 5 * 3 / 10 = 3 / 50 3 : 50 answer : e
Answer: e
Question (general): if the product of the integers from 1 to n is divisible by 210 , what is the least possible value of n ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: "210 = 2 x 3 x 5 x 7 n must include at least up to the number 7 . the answer is a ."
Answer: a
Question (general): a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 10 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 210 , b ) 252 , c ) 280 , d ) 150 , e ) 420
Rationale: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 10 * 6 * 7 we get = 5 x 6 x 5 = 150 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( d )"
Answer: d
Question (gain): selling an kite for rs . 30 , a shop keeper gains 25 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 12.5 % , e ) 20 %
Rationale: "explanation : marked price = rs . 30 c . p . = 100 / 125 * 30 = rs . 24 sale price = 90 % of rs . 30 = rs . 27 required gain % = 3 / 24 * 100 = 12.5 % . answer : d"
Answer: d
Question (general): in a university the average age in an arts class is 21 and average age in technical class is 18 . what is the age average of university if there are 8 arts classes and 5 technical classes ?
Options: a ) 18.75 , b ) 19.85 , c ) 20.32 , d ) 20.9 , e ) 21.0
Rationale: average age of university = ( ( 8 x 21 ) + ( 5 x 18 ) ) / 13 = 19.85 answer : b
Answer: b
Question (general): a theater box office sold an average ( arithmetic mean ) of 65 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 75 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 5 : 11 , d ) 1 : 3 , e ) 13 : 15
Rationale: "deviation from the mean for the daytime staff = 75 - 65 = 10 . deviation from the mean for the evening staff = 65 - 60 = 5 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 5 : 10 = 1 : 2 . the answer is a ."
Answer: a
Question (gain): a milk man has 40 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 25 % , c ) 45 % , d ) 18 % , e ) none of these
Rationale: "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 40 liters of milk . therefore , profit percentage = 45 % . answer : c"
Answer: c
Question (general): the sum of ages of 5 children born 1 years different each is 30 years . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 16 , e ) 17
Rationale: "let the ages of children be x , ( x + 1 ) , ( x + 2 ) , ( x + 3 ) and ( x + 4 ) years . then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) = 30 5 x = 20 x = 4 . x + 4 = 4 + 4 = 8 answer : a"
Answer: a
Question (physics): in a kilometer race , if abhishek gives bharti a 40 m start , abhishek wins by 19 sec . but if abhishek gives bharti a 30 sec start , bharti wins by 40 m . find the time taken by bharti to run 5,000 m ?
Options: a ) 150 sec , b ) 750 sec , c ) 450 sec , d ) 825 sec , e ) none of these
Rationale: explanation : if abhishek takes x seconds and bharti takes y seconds to run 1 km , then : = > y = 150 sec and x = 125 sec = > x + 19 = 960 y / 1000 and = ( 960 x / 1000 ) + 30 = y = > y = 150 sec and x = 125 sec answer = ( 150 / 1000 ) × 500 = 750 sec answer : b
Answer: b
Question (general): every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 144 , how many more green disks than blue disks are in the bag ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40
Rationale: "let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 144 - - > x = 8 . g - b = 8 x - 3 x = 5 x = 40 . the answer is e ."
Answer: e
Question (general): if the sum of two numbers is 22 and the sum of their squares is 404 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 48
Rationale: "according to the given conditions x + y = 22 and x ^ 2 + y ^ 2 = 404 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 22 ^ 2 = 404 + 2 xy so xy = 80 / 2 = 40 answer : a"
Answer: a
Question (general): there are 200 female managers in a certain company . find the total number w of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 300 , b ) w = 400 , c ) w = 500 , d ) w = 600 , e ) none of these
Rationale: "{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."
Answer: c
Question (gain): a store reduced the price of all items in the store by 10 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
Options: a ) 80.0 , b ) 80.9 , c ) 81.0 , d ) 81.1 , e ) 81.9
Rationale: "consider price of the all items as $ 100 after a initial reduction of 10 % price becomes = 0.9 * 100 = $ 90 after the final reduction of 10 % price becomes = 0.9 * 90 = $ 81 price of all items on second day is 81 % of price on first day correct answer option c"
Answer: c
Question (gain): on the first of the year , james invested x dollars at proudstar bank in an account that yields 0.5 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?
Options: a ) 2.04 % , b ) 4.12 % , c ) 5 % , d ) 8.25 % , e ) 10 %
Rationale: per quarter , interest = 0.5 % so for a year , interest = 2 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 2 % answer = 2.04 % = answer : a
Answer: a
Question (probability): the chance of rain on any given day in tel - aviv is 50 % . what is the probability w that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days w = 15 / 64 ans a it is .
Answer: a
Question (general): the sum of two numbers is 77 . 5 times one number is equal to 6 times the other . the bigger of the two numbers is
Options: a ) 10 , b ) 42 , c ) 14 , d ) 15 , e ) 60
Rationale: a : b 5 : 6 a + b = 77 5 x + 6 x = 77 x = 7 then two numbers are 35,42 . the bigger number is 42 answer : b
Answer: b
Question (other): income and expenditure of a person are in the ratio 7 : 6 . if the income of the person is rs . 14000 , then find his savings ?
Options: a ) 500 , b ) 1000 , c ) 1500 , d ) 2000 , e ) 2500
Rationale: "let the income and the expenditure of the person be rs . 7 x and rs . 6 x respectively . income , 7 x = 14000 = > x = 2000 savings = income - expenditure = 7 x - 6 x = x so , savings = rs . 2000 . answer : d"
Answer: d
Question (general): 3 people took gmat practice tests in which the minimum and maximum possible scores are 200 and 800 , respectively . they each took a test 3 times , and no one scored below 400 or over 700 . if the individual ranges of the 3 people ' s scores in those 3 practice tests were 40 , 70 and 100 , what is the difference between the maximum and minimum possible ranges of all their scores put together .
Options: a ) 70 , b ) 80 , c ) 100 , d ) 140 , e ) 200
Rationale: according to the information in the question the maximum range would be between 400 and 700 ( 300 ) . the minimum range would be the greatest range for any one individual , which is listed in the problem as 100 . so the difference between these would be 300 - 100 or 200 . answer : e
Answer: e
Question (general): if p / q = 3 / 11 , then 2 p + q = ?
Options: a ) 12 , b ) 14 , c ) 17 , d ) 15 , e ) 16
Rationale: let p = 3 , q = 11 then 2 * 3 + 11 = 17 so 2 p + q = 17 . answer : c
Answer: c
Question (general): what is the probability of rolling a total of 5 with a single roll of two fair 6 - sided dice , each with the distinct numbers 1 through 6 on each side ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 2 / 7 , d ) 1 / 3 , e ) 1 / 9
Rationale: totalsample spacefrom two fair six - sided dice is 36 . there are six possible ways to be 5 i . e . ( 1 + 4 ) , ( 2 + 3 ) , ( 3 + 2 ) , ( 4 + 1 ) so , total probability is 4 / 36 or 1 / 9 . answer is e .
Answer: e
Question (gain): if the simple interest on a certain sum of money for 6 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 3.3 % , b ) 7.2 % , c ) 6.1 % , d ) 5.0 % , e ) 3.1 %
Rationale: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 6 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 6 ) = 20 / 6 = 3.3 % answer : option a"
Answer: a
Question (general): the population of a city is 415600 . it increased by 25 % in the first year and decreased by 30 % in the second year . what is the population of the city at the end of second year ?
Options: a ) 367300 , b ) 363580 , c ) 363650 , d ) 373650 , e ) 386750
Rationale: as per given data , p = 415600 , r 1 = 25 % incresed , r 2 = 30 % decreased population of the city at the end of the second year = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) = 415600 ( 1 + 25 / 100 ) ( 1 - 30 / 100 ) = 363650 answer : c
Answer: c
Question (general): what is the least value of x , so that 2 x 5472 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 9 , 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 + 2 = 20 + x least value of x may be ' 7 ' , so that the total 20 + 7 = 27 is divisible by 9 . answer : option a"
Answer: a
Question (physics): a thief is spotted by a policeman from a distance of 150 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 200 m , c ) 400 m , d ) 600 m , e ) none of them
Rationale: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 150 m / 1000 ) x 1 / 2 hr = 3 / 40 hr . in 3 / 40 hrs , the thief covers a distance of 8 x 3 / 40 km = 3 / 5 km = 600 m answer is d"
Answer: d
Question (physics): car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 70 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 15 , b ) 20 , c ) 40 , d ) 42 , e ) 68
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 70 t t = 1.2 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 1.2 = 42 miles answer : - d"
Answer: d
Question (general): a fruit juice company earns $ 150 per 100 gallons of apple juice sold , $ 170 per 100 gallons of guava juice sold , $ 130 per 100 gallons of grape juice sold , $ 100 per 100 gallons of orange juice . if the company manages to sell 230 gallons of apple , 210 gallons of guava , 310 gallons of grape , 270 gallons of orange on a particular day . what is the average earning of the company per 100 gallon of the juice sold ?
Options: a ) 134.8 , b ) 141.2 , c ) 147.2 , d ) 152.3 , e ) 160.1
Rationale: earning of the company from apple = 150 / 100 x 230 = 345 earning of the company from guava = 170 / 100 x 210 = 357 earning of the company from grape = 130 / 100 x 310 = 403 earning of the company from orange = 100 / 100 x 270 = 270 total earning of the company = 345 + 357 + 403 + 270 = 1375 total juice sold = 1020 average earning per 100 gallon of juice sold = ( 1375 / 1020 ) x 100 = $ 134.8 answer : a
Answer: a
Question (general): if a mixture is 1 ⁄ 7 alcohol by volume and 2 ⁄ 7 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?
Options: a ) 4 / 2 , b ) 3 / 2 , c ) 1 / 2 , d ) 5 / 2 , e ) 7 / 2
Rationale: "should be a sub - 600 level q . . volume = { 1 / 7 } / { 2 / 7 } = 1 / 2 c"
Answer: c
Question (physics): a man sitting in a train which is travelling at 50 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 72 kmph . , d ) 80 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 50 ) kmph = 62 kmph . answer b"
Answer: b
Question (general): the average of 10 numbers is 7 . if each number is multiplied by 12 , then the average of new set of numbers is
Options: a ) 28 , b ) 236 , c ) 288 , d ) 84 , e ) 26
Rationale: explanation : if each number is multiplied by k , then the new average increases by k times . so new average = 84 answer : d
Answer: d
Question (physics): a train 500 m long can cross an electric pole in 50 sec and then find the speed of the train ?
Options: a ) 76 kmph , b ) 54 kmph , c ) 72 kmph , d ) 34 kmph , e ) 36 kmph
Rationale: "length = speed * time speed = l / t s = 500 / 50 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : e"
Answer: e
Question (geometry): the length of a rectangle is increased by 40 % while its width is halved . what is the % change in area ?
Options: a ) 25 %
b ) 30 %
c ) 50 %
d ) 65 %
e ) 70 %
Rationale: the original area is l * w the new area is 1.4 l * 0.5 w = 0.7 * l * w = l * w - 0.3 * l * w the area decreased by 30 % . the answer is b .
Answer: b
Question (general): if 5 x = 3 y and xy ≠ 0 , what is the ratio of 1 / 5 * x to 1 / 6 * y ?
Options: a ) 25 / 6 , b ) 36 / 25 , c ) 18 / 25 , d ) 5 / 6 , e ) 25 / 36
Rationale: "5 x = 3 y = > x / y = 3 / 5 1 / 5 * x to 1 / 6 * y = x / y * 6 / 5 = ( 3 / 5 ) * ( 6 / 5 ) = 18 / 25 ans : c"
Answer: c
Question (general): a family pays $ 800 per year for an insurance plan that pays 70 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "assuming the medical expenses are $ 1000 or more , the family pays $ 800 + $ 300 = $ 1100 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 700 . the insurance will pay another $ 400 when the medical expenses are $ 1400 . the answer is c ."
Answer: c
Question (general): for every integer n ≥ 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 101 ) – g ( 99 ) ?
Options: a ) 0 , b ) 98 , c ) 99 , d ) 100 , e ) 90
Rationale: "g ( 101 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 g ( 101 ) - g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 - 1 * 3 * 5 * 7 * 9 * . . . * 99 = 1 * 3 * 5 * 7 * 9 * . . . * 99 * ( 101 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 100 hence : d"
Answer: d
Question (general): two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 72 seconds . the length of each train is :
Options: a ) 82 m , b ) 50 m , c ) 72 m , d ) 100 m , e ) none of these
Rationale: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 72 secs the total distance traveled is 72 x 25 / 9 = 200 m . therefore the length of each train is = 200 / 2 = 100 m . answer d"
Answer: d
Question (gain): a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 30 % ?
Options: a ) 1 / 2 , b ) 2 / 6 , c ) 3 / 6 , d ) 9 / 6 , e ) 15 / 2
Rationale: c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 180 % of re . 1 = rs . 9 / 5 for rs . 9 / 5 , toffees sold = 6 . for re . 1 , toffees sold = 9 x 5 / 6 = 15 / 2 . answer e
Answer: e
Question (physics): how many seconds will a train 140 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 28 sec , b ) 29 sec , c ) 24 sec , d ) 25 sec , e ) 26 sec
Rationale: "d = 140 + 150 = 290 s = 36 * 5 / 18 = 10 mps t = 290 / 10 = 29 sec b"
Answer: b
Question (physics): a man swims downstream 96 km and upstream 64 km taking 4 hours each time ; what is the speed of the current ?
Options: a ) 6 , b ) 4 , c ) 2 , d ) 8 , e ) 5
Rationale: "96 - - - 4 ds = 24 ? - - - - 1 64 - - - - 4 us = 16 ? - - - - 1 s = ? s = ( 24 - 16 ) / 2 = 4 answer : b"
Answer: b
Question (general): sophia finished 2323 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?
Options: a ) 140 , b ) 320 , c ) 745 , d ) 270 , e ) 350
Rationale: let x be the total number of pages in the book , then she finished 23 ⋅ x pages . then she has x − 23 ⋅ x = 13 ⋅ xpages left . 23 ⋅ x − 13 ⋅ x = 90 13 ⋅ x = 90 x = 270 so the book is 270 pages long . correct answer is d ) 270
Answer: d
Question (physics): on her annual road trip to visit her family in seal beach , california , traci stopped to rest after she traveled 1 ⁄ 3 of the total distance and again after she traveled 1 ⁄ 4 of the distance remaining between her first stop and her destination . she then drove the remaining 300 miles and arrived safely at her destination . what was the total distance , in miles , from traci ’ s starting point to seal beach ?
Options: a ) 600 , b ) 300 , c ) 350 , d ) 400 , e ) 550
Rationale: let d = total distance traci traveled 1 / 3 = d / 3 i . e . remaining distance = 2 d / 3 she traveled 1 / 4 th of 2 d / 3 = d / 6 thus : d = ( d / 3 ) + ( d / 6 ) + 300 d = 600 answer : a
Answer: a