Cheukting/mathqa huggingface dataset:
Question (general): 5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?
Options: a ) 4400 , b ) 3500 , c ) 8700 , d ) 9000 , e ) 8000
Rationale: "x * ( 95 / 100 ) * ( 85 / 100 ) = 3553 x = 4400 answer a"
Answer: a
Question (gain): x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 40,000 , the amount invested by y is ?
Options: a ) 60229 , b ) 62887 , c ) 60000 , d ) 61298 , e ) 61291
Rationale: "suppose y invested rs . y . then 40000 / y = 2 / 3 or y = 60000 . answer : c"
Answer: c
Question (geometry): two cubes of their volumes in the ratio 27 : 125 . the ratio of their surface area is :
Options: a ) 1.5 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 1 : 5 , e ) 4 : 5
Rationale: "the ratio of their surface area is 27 : 125 3 : 5 answer is c ."
Answer: c
Question (gain): one night 16 percent of the female officers on a police force were on duty . if 160 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 500 , b ) 650 , c ) 800 , d ) 950 , e ) 1100
Rationale: "let x be the number of female police officers on the police force . the number of female police officers on duty was 80 . 0.16 x = 80 x = 500 the answer is a ."
Answer: a
Question (physics): steve traveled the first 2 hours of his journey at 30 mph and the remaining 3 hours of his journey at 80 mph . what is his average speed for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "distance traveled in 2 hours = 2 * 30 = 60 m distance traveled in 3 hours = 3 * 80 = 240 m total distance covered = 240 + 60 = 300 m total time = 2 + 3 = 5 h hence avg speed = total distance covered / total time taken = 300 / 5 = 60 mph answer : a"
Answer: a
Question (general): in what proportion must flour at $ 0.8 per pound be mixed with flour at $ 0.9 per pound so that the mixture costs $ 0.835 per pound ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 1 : 1 , d ) 2 : 1 , e ) 3 : 1
Rationale: "using weighted average method : let x be the proportion in which the $ 0.8 per pound flour is mixed with $ 0.9 per pound flour . thus 0.8 * x + 0.9 * ( 1 - x ) = 0.835 0.9 – 0.1 x = 0.835 x = 0.65 thus ratio of both flours is 2 : 1 d"
Answer: d
Question (general): the average of 5 numbers id 27 . if one number is excluded , the average becomes 25 . the excluded number is
Options: a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) none
Rationale: solution excluded number = ( 27 x 5 ) - ( 25 x 4 ) = 135 - 100 = 35 . answer d
Answer: d
Question (general): a batsman makes a score of 86 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 ) 38 , d ) 49 , e ) 59
Rationale: "let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 86 = 17 x therefore x = 38 answer : c"
Answer: c
Question (physics): a and b can do a piece of work in 6 days . with the help of c they finish the work in 4 days . c alone can do that piece of work in ?
Options: a ) 10 days , b ) 20 days , c ) 25 days , d ) 15 days , e ) 45 days
Rationale: "c = 1 / 5 – 1 / 6 = 1 / 30 = > 30 days answer : b"
Answer: b
Question (general): a person deposits 1 / 16 of his income as provident fund and 1 / 15 of the remaining as insurance premium . if he spends 5 / 7 of the balance on domestic needs and deposits an amount of rs . 50 in the bank , his total income would be
Options: a ) 150 , b ) 200 , c ) 250 , d ) 300 , e ) 350
Rationale: ( 1 - ( 1 / 16 ) ) ( 1 - ( 1 / 15 ) ) ( 1 - ( 5 / 7 ) ) of income = 50 hence income = 200 answer : b
Answer: b
Question (general): what is 3 / 5 of 5 / 7 of 2 / 3 ?
Options: a ) 2 / 7 , b ) 3 / 8 , c ) 9 / 16 , d ) 5 / 8 , e ) 16 / 9
Rationale: "3 / 5 * 5 / 7 * 2 / 3 = 2 / 7 answer : a"
Answer: a
Question (physics): in a survey of 350 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 7 / 12 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 41 / 70
Rationale: "- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 296 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 350 we have to find not part time and not uninsured . in other words not part time and insured = x / 350 = ( 296 - 104 + 13 ) / 350 = 41 / 70 answer is e ."
Answer: e
Question (gain): a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 4 , e ) 1 : 2
Rationale: "he needs to make a profit of 20 % , which means he needs to sell the milk + water combination for 39.6 ( 20 % of 33 + 33 ) now , he plans to sell 1 liter of this solution of milk and water for 36 . which means he needs to sell 1.1 liters of this solution to earn 39.6 . ( 36 for 1 liter and so 39.6 for 1.1 liters ) hence the water added would be . 1 liter . therefore the ratio of water to milk is . 1 / 1 = 1 / 10 answer : b"
Answer: b
Question (physics): a train covers a distance of 12 km in 10 min . if it takes 10 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 200 , b ) 288 , c ) 120 , d ) 776 , e ) 991
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 10 = 200 m . answer : a"
Answer: a
Question (general): two employees a and b are paid a total of rs . 550 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 ) 130 , b ) 140 , c ) 150 , d ) 220 , e ) 280
Rationale: let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 550 but x = 150 % of y = 150 y / 100 = 15 y / 10 ∴ 15 y / 10 + y = 550 ⇒ y [ 15 / 10 + 1 ] = 550 ⇒ 25 y / 10 = 550 ⇒ 25 y = 5500 ⇒ y = 5500 / 25 = rs . 220 d )
Answer: d
Question (general): of the families in city x in 1991 , 60 percent owned a personal computer . the number of families in city x owning a computer in 1993 was 20 percent greater than it was in 1991 , and the total number of families in city x was 9 percent greater in 1993 than it was in 1991 . what percent of the families in city x owned a personal computer in 1993 ?
Options: a ) 59 % , b ) 55 % , c ) 63 % , d ) 66 % , e ) 68 %
Rationale: "say a 100 families existed in 1991 then the number of families owning a computer in 1991 - 60 number of families owning computer in 1993 = 60 * 120 / 100 = 72 number of families in 1993 = 109 the percentage = 72 / 109 * 100 = 66 % . answer : d"
Answer: d
Question (gain): at a local appliance manufacturing facility , the workers received a 10 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 83 % , b ) 80 % , c ) 20 % , d ) 17 % , e ) 9 %
Rationale: let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 110 = 1100 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 110 = 9.09 so he can reduce his work by 0.91 hours . which is > 9 % . answer e
Answer: e
Question (general): determine the value of ( 25 / 32 + 50 / 64 ) * 2
Options: a ) 25 / 8 , b ) 25 / 4 , c ) 25 / 6 , d ) 3 , e ) none
Rationale: "solution : both fractions should be reduced before performing arithmetic operations . we get ( 25 / 32 + 2.25 / 2.32 ) * 2 = ( 25 / 32 + 25 / 32 ) * 2 = 2 * ( 25 / 32 ) * 2 = 4 ( 25 / 32 ) = 25 / 8 answer a"
Answer: a
Question (physics): a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 10 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 4800 , b ) 1200 , c ) 1680 , d ) 1100 , e ) 1300
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 10 = 1200 answer : b"
Answer: b
Question (general): a school has received 40 % of the amount it needs for a new building by receiving a donation of $ 600 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 300 , c ) $ 100 , d ) $ 400 , e ) $ 250
Rationale: "let us suppose there are 100 people . 40 % of them donated $ 16000 ( 400 * 40 ) $ 16000 is 40 % of total amount . so total amount = 16000 * 100 / 40 remaining amount is 60 % of total amount . 60 % of total amount = 16000 * ( 100 / 40 ) * ( 60 / 100 ) = 24000 this amount has to be divided by 60 ( remaining people are 60 ) so per head amount is 24000 / 60 = $ 400 answer : d"
Answer: d
Question (general): in township k each property is taxed at 10 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 28,000 , by how much will the property tax increase ?
Options: a ) $ 800 , b ) $ 1000 , c ) $ 600 , d ) $ 400 , e ) $ 500
Rationale: increase in house value = $ 28,000 - $ 20,000 = $ 8000 so , tax increase = 10 % of $ 8000 = $ 800 answer : a
Answer: a
Question (general): george is 8 years more than christopher and ford is 2 years younger than christopher . the sum of their ages is 60 . find the ages of george .
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "christopher age = x george age , y = x + 8 - - - - - - - - - - > ( 1 ) ford age , z = x - 2 - - - - - - - - - - - - > ( 2 ) sum of their ages , x + y + z = 60 - - - - > ( 3 ) substitute z and y values in equation ( 3 ) therefore , x + ( x + 8 ) + ( x - 2 ) = 60 = > 3 x + 8 - 2 = 60 = > 3 x = 60 - 6 = > 3 x = 54 = > x = 54 / 3 x = 18 ( christopher ' s age ) substitute x value in equation 1 & 2 y = x + 8 y = 18 + 8 y = 26 answer : b"
Answer: b
Question (general): if 0.25 : x : : 2 : 6 , then x is equal to
Options: a ) 0.65 , b ) 0.25 , c ) 0.75 , d ) 0.85 , e ) none
Rationale: "sol . ( x × 2 ) = ( 0.25 × 6 ) ⇒ x = 1.5 / 2 = 0.75 . answer c"
Answer: c
Question (gain): a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 10 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: "let the total solution is 150 l with 80 l water 70 l syrup . to make 10 % syrup solution , the result solution must have 135 l syrup and 15 l syrup . therefore we are taking 55 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 55 l syrup in 117.9 l solution we started by multiplying 10 now to get to the result we need to divide by 55 = > amount of solution to be replaced with water = ( 117.9 / 55 ) = 2.14 . correct option : c"
Answer: c
Question (general): 287 x 287 + 269 x 269 - 2 x 287 x 269 = ?
Options: a ) 534 , b ) 446 , c ) 354 , d ) 324 , e ) none of them
Rationale: = a ^ 2 + b ^ 2 - 2 ab where a = 287 and b = 269 = ( a - b ) ^ 2 = ( 287 - 269 ) ^ 2 = ( 18 ) ^ 2 = 324 answer is d
Answer: d
Question (physics): worker a takes 12 hours to do a job . worker b takes 15 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 40 days , b ) 40 / 9 days , c ) 39 / 9 days , d ) 30 / 9 days , e ) 20 / 3 days
Rationale: "a ' s one hour work = 1 / 12 . b ' s one hour work = 1 / 15 . ( a + b ) ' s one hour work = 1 / 12 + 1 / 15 = 9 / 60 = 3 / 20 . both a & b can finish the work in 20 / 3 days e"
Answer: e
Question (physics): jamal had a bag of marbles . he had 12 yellow , 10 blue , 5 green and 1 black marbles . he decided to randomly select a ball from the bag . what is the proabilitly that he will draw a black marble ?
Options: a ) 10 / 28 , b ) 1 / 28 , c ) 12 / 28 , d ) 28 / 1 , e ) 582 / 695
Rationale: b
Answer: b
Question (general): the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 100 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?
Options: a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 400
Rationale: "if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 100 group # 2 = ( likeunderstood ) = 3 / 4 ( 1 / 4 ) n = 100 n = 400 answer = ( e )"
Answer: e
Question (gain): find the compound interest on rs . 10,000 in 2 years at 4 % per annum , the interest being compounded half - yearly .
Options: a ) rs 824.32 , b ) rs 822.32 , c ) rs 700 , d ) rs 900 , e ) rs 624.00
Rationale: "principal = rs . 10000 ; rate = 2 % per half - year ; time = 2 years = 4 half - years . amount = rs [ 10000 * ( 1 + ( 2 / 100 ) ) 4 ] = rs ( 10000 * ( 51 / 50 ) * ( 51 / 50 ) * ( 51 / 50 ) * ( 51 / 50 ) ) = rs . 10824.32 . : . c . i . = rs . ( 10824.32 - 10000 ) = rs . 824.32 . answer a rs 824.32"
Answer: a
Question (gain): in an acoustics class , 120 students are male and 100 students are female . 25 % of the male students and 20 % of the female students are engineering students . 20 % of the male engineering students and 25 % of the female engineering students passed the final exam . what percentage of engineering students passed the exam ?
Options: a ) 5 % , b ) 10 % , c ) 16 % , d ) 22 % , e ) none of these
Rationale: explanation : the number of female engineering students in the class is ( 20 / 100 ) × 100 = 20 . now , 25 % of the female engineering students passed the final exam : 25 . hence , the number of female engineering students who passed is 5 . there are 120 male students in the class . and 25 % of them are engineering students . hence , the number of male engineering students is ( 1 / 4 ) × 120 = 30 . now , 20 % of the male engineering students passed the final exam : - 20 . hence , the number of male engineering students who passed is 6 . hence , the total number of engineering students who passed is : ( female engineering students who passed ) + ( male engineering students who passed ) = > 5 + 6 = 11 . the total number of engineering students in the class is : ( number of female engineering students ) + ( number of male engineering students ) = = > 30 + 20 = 50 hence , the percentage of engineering students who passed is : - = > ( total number of engineering students passed / total number of engineering students ) × 100 . = > ( 11 / 50 ) × 100 . = > 22 % . answer : d
Answer: d
Question (other): the probability that a computer company will get a computer hardware contract is 2 / 3 and the probability that it will not get a software contract is 5 / 9 . if the probability of getting at least one contract is 4 / 5 , what is the probability that it will get both the contracts ?
Options: a ) 14 / 45 , b ) 4 / 9 , c ) 4 / 5 , d ) 4 / 6 , e ) none of these
Rationale: "explanation : let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 2 / 3 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 5 / 9 ) = 4 / 9 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 4 / 5 = ( 2 / 3 ) + ( 4 / 9 ) - p ( ab ) . = > p ( ab ) = 14 / 45 . hence , the required probability is 14 / 45 . answer : a"
Answer: a
Question (general): | 8 - 3 | - | 4 - 6 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 8 - 3 | - | 4 - 6 | = | 5 | - | - 2 | = 5 - 2 = 3 correct answer a"
Answer: a
Question (general): if x is an integer and 2.134 × 10 ^ x is less than 240,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "x is an integer and 2.134 × 10 x is less than 240,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 240,000 to remain true , the greatest number is 213,400 , which makes x = 5 c . 5"
Answer: c
Question (physics): two trains of length 90 m and 100 m are 200 m apart . they start moving towards each other on parallel tracks , at speeds 71 kmph and 89 kmph . after how much time will the trains meet ?
Options: a ) 47 / 10 , b ) 46 / 10 , c ) 45 / 10 , d ) 42 / 10 , e ) 43 / 10
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 71 + 89 ) * 5 / 18 = 44.4 mps . the time required = d / s = 200 / 44.4 = 45 / 10 sec . answer : c"
Answer: c
Question (general): in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 13 , e ) 15
Rationale: "total # of students = 40 avg # of books per student = 2 total # of books = 40 * 2 = 80 # of student borrowed at least 3 books = 40 - 2 - 12 - 10 = 16 # of books borrowed by above 16 students = 80 - ( 12 * 1 ) - ( 10 * 2 ) = 48 considering that 15 out of above 16 students borrowed only 3 books , # of books borrowed = 15 * 3 = 45 so maximum # of books borrowed by any single student = 48 - 45 = 3 option a"
Answer: a
Question (general): of the 20210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 49.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . e
Answer: e
Question (general): find the total number of prime factors in the expression ( 4 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2
Options: a ) 26 , b ) 22 , c ) 25 , d ) 27 , e ) 33
Rationale: ( 4 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 13 x 2 ^ 13 x 7 ^ 5 x 11 ^ 2 = 2 ^ 26 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 26 + 5 + 2 ) = 33 . answer is e .
Answer: e
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 650 resolutions ?
Options: a ) 724 m , b ) 704 m , c ) 915.2 m , d ) 278 m , e ) 927 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 650 resolutions . = 650 * 2 * 22 / 7 * 22.4 = 91520 cm = 915.2 m answer : c"
Answer: c
Question (general): a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 20 , b ) 25 , c ) 27 , d ) 22 , e ) 91
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 22 ) years . ( x + 22 ) + 2 = 2 ( x + 2 ) x + 24 = 2 x + 4 = > x = 20 . answer : a"
Answer: a
Question (physics): a can run 2 km distance in 2 min . , while b can run this distance in 2 min 40 sec . by how much distance can a beat b ?
Options: a ) 150 m , b ) 100 m , c ) 500 m , d ) 180 m , e ) 190 m
Rationale: a takes time 2 minutes = 120 sec b takes time 2.40 minutes = 160 sec diffrence = 160 - 120 = 40 sec now we are to find distance covered in 40 sec by b 160 sec = 2000 m 1 sec = 25 / 2 m 40 sec = 40 x 25 / 2 = 500 m answer : c
Answer: c
Question (physics): stacy and heather are 20 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 2 mile per hour faster than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ?
Options: a ) 5 miles , b ) 7 miles , c ) 9 miles , d ) 10 miles , e ) 12 miles
Rationale: "original distance between s and h = 20 miles . speed of s = 5 + 2 = 7 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 24 / 60 = t + 2 / 5 hours . now , the total distances traveled by s and h = 20 miles - - - > 7 * ( t + 2 / 5 ) + 5 * t = 20 - - - > t = 86 / 60 hours . thus h has traveled for 86 / 60 hours giving you a total distance for h = 5 * 86 / 60 = 7 miles . b is thus the correct answer . p . s . : based on the wording of the question , you should calculatehow far from theoriginal destination has heather walkedwhen the two meet . ' original destination ' for h does not make any sense . original destination for h was situated at a distance of 20 miles ."
Answer: b