Cheukting/mathqa huggingface dataset:
Question (gain): find the simple interest on rs . 300 for 9 months at 6 paisa per month ?
Options: a ) 142 , b ) 152 , c ) 162 , d ) 172 , e ) 182
Rationale: "i = ( 300 * 9 * 6 ) / 100 = 162 answer : c"
Answer: c
Question (physics): gary drove from point a to point b at 60 km / h . on his way back he took a train travelling at 110 km / h and therefore his trip back lasted 5 hours less . what is the distance ( in km ) between a and b ?
Options: a ) 600 . , b ) 630 . , c ) 660 . , d ) 690 . , e ) 720 .
Rationale: distance = speed * time d 1 = s 1 t 1 d 2 = s 2 t 2 the distance from point a to point b is the same for each trip so , d 1 = d 2 and t 2 = t 1 - 5 thus , s 1 t 1 = s 2 t 2 60 t 1 = s 2 ( t 1 - 5 ) t 1 = 11 60 * 11 = 660 answer : c
Answer: c
Question (general): when n is divided by 19 , the remainder is 7 . find thee difference between previous remainder and the remainder when 18 n is divided by 9 ?
Options: a ) 7 , b ) 5 , c ) 0 , d ) 3 , e ) 9
Rationale: let n = 7 ( leaves a remainder of 7 when divided by 19 ) 18 n = 18 ( 7 ) = 126 , which leaves a remainder of 0 when divided by 9 . difference = 7 - 0 = 7 . answer a
Answer: a
Question (gain): solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 75 percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: "75 % is 5 % - points below 80 % and 20 % - points above 55 % . so the ratio of solution p to solution q is 4 : 1 . mixture p is 4 / 5 = 80 % of the volume of mixture pq . the answer is d ."
Answer: d
Question (physics): a can complete a work in 15 days and b can do the same work in 9 days . if a after doing 5 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 4 days , c ) 6 days , d ) 7 days , e ) 10 days
Rationale: "the required answer = ( 15 - 5 ) * 9 / 15 = 40 / 10 = 6 days answer is c"
Answer: c
Question (general): the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 15 km / hr respectively . they will meet for the first time in ?
Options: a ) 50 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 15 = 35 km apart , they take 1 hour to be 1000 m apart , they take 35 * 1000 / 1000 = 35 min . answer is c"
Answer: c
Question (general): the average weight of a class of 24 students is 35 kg . if the weight of the teacher be included , the average rises by 400 g . the weight of the teacher is :
Options: a ) 45 , b ) 46 , c ) 47 , d ) 48 , e ) 49
Rationale: weight of the teacher = ( 35.4 x 25 - 35 x 24 ) kg = 45 kg . answer : a
Answer: a
Question (general): the contents of a certain box consist of 14 apples and 24 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 18 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 24 oranges , so to get to 6 oranges , we should remove 24 - 6 = 18 oranges . answer a"
Answer: a
Question (general): mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 96 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 96 ) is 96 % of juan ' s income ( 100 ) . answer : c"
Answer: c
Question (geometry): a and b are two circles . the radius of a is four times as large as the diameter of b . what is the ratio between the areas of the circles ?
Options: a ) 1 : 8 .
b ) 1 : 2 .
c ) 1 : 24 .
d ) 1 : 64 .
e ) 1 : 6 .
Rationale: given : the radius of a is 4 times as large as the diameter of b . = > r ( a ) = 4 * d ( b ) = 4 * 2 * r ( b ) = 8 r ( b ) . the radius are in ratio of 1 : 8 thus the area will be in the ratio of square of radius . 1 : 64 . hence d .
Answer: d
Question (physics): a can run 192 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 38 metre , b ) 28 metre , c ) 24 metre , d ) 15 metre , e ) 28 metre
Rationale: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 192 / 32 = 6 m / s distance covered by b in 4 seconds = speed ã — time = 6 ã — 4 = 24 metre i . e . , a beat b by 24 metre answer is c"
Answer: c
Question (other): a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 585.75 . how many boxes of plain cookies did she sell ?
Options: a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 791
Rationale: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1585.75 = > x = 791 e"
Answer: e
Question (physics): three pipes a , b and c can fill a tank from empty to full in 30 minutes , 20 minutes and 10 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution q in the liquid in the tank after 3 minutes ?
Options: a ) 1 / 11 , b ) 2 / 11 , c ) 3 / 11 , d ) 4 / 11 , e ) 5 / 11
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 30 + 1 / 20 + 1 / 10 ) = 11 / 20 part filled by b in 3 minutes = 3 / 20 required ratio = 3 / 20 * 20 / 11 = 3 / 11 answer : c"
Answer: c
Question (geometry): if a 5 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
Options: a ) 100 % , b ) 200 % , c ) 300 % , d ) 400 % , e ) 500 %
Rationale: "the area a of the large cube is 5 * 5 * 6 = 150 square cm . the area of the 125 small cubes is 125 * 6 = 750 = 5 a , an increase of 400 % . the answer is d ."
Answer: d
Question (general): a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 550 ?
Options: a ) 249 , b ) 498 , c ) 676 , d ) 823 , e ) 274
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 550 y = 2 x + 2 548 = 2 x x = 274 answer : e . 274"
Answer: e
Question (physics): one copy machine can make 30 copies a minute , and a second copy machine makes 15 copies a minute . if the two copiers work together , how long would it take them to make 900 copies ?
Options: a ) 15 minutes , b ) 20 minutes , c ) 25 minutes , d ) 30 minutes , e ) 35 minutes
Rationale: "total work done by both machines in a minute = 30 + 15 = 45 copies total number of copies required = 900 time = 900 / 45 = 20 mins answer b"
Answer: b
Question (physics): two mechanics were working on your car . one can complete the given job in six hours , but the new guy takes 10 hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
Options: a ) 7 / 4 , b ) 4 / 3 , c ) 15 / 4 , d ) 56 / 15 , e ) 17 / 5
Rationale: "rate ( 1 ) = 1 / 6 rate ( 2 ) = 1 / 10 combined = 8 / 30 work done in 2 days = 8 / 15 work left = 7 / 15 rate * time = work left 1 / 8 * time = 7 / 15 time = 56 / 15 d"
Answer: d
Question (general): if xy = 4 , x / y = 16 , for positive numbers x and y , y = ?
Options: a ) 1 / 2 , b ) 2 , c ) 1 / 3 , d ) 3 , e ) 1 / 6
Rationale: "very easy question . 2 variables and 2 easy equations . xy = 4 - - - > x = 4 / y - ( i ) x / y = 16 - - - > replacing ( i ) here - - - > 4 / ( y ^ 2 ) = 16 - - - > y ^ 2 = 4 / 16 = 1 / 4 - - - > y = 1 / 2 or - 1 / 2 the question states that x and y are positive integers . therefore , y = 1 / 2 is the answer . answer a ."
Answer: a
Question (physics): if a boat is rowed downstream for 24 km in 4 hours and upstream for 48 km in 24 hours , what is the speed of the boat and the river ?
Options: a ) 4 , 3 , b ) 4 , 4 , c ) 3 , 3 , d ) 4 , 5 , e ) 4 , 2
Rationale: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 6 ; us = 2 x = ( 6 + 2 ) / 2 = 8 / 2 = 4 km / hr y = ( 6 - 2 ) / 2 = 4 / 2 = 2 km / hr answer : e"
Answer: e
Question (general): after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 50 % full . if the original contents of the reservoir totaled 280 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 45 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %
Rationale: "when the storm deposited 115 billion gallons , volume of water in the reservoir = 280 + 120 = 400 billion gallons if this is only 80 % of the capacity of the reservoir , the total capacity of the reservoir = 400 / 0.5 = 800 billion gallons therefore percentage of reservoir that was full before the storm = ( 280 / 800 ) * 100 = 35 % option c"
Answer: c
Question (physics): in a garden , there are 12 rows and 14 columns of mango trees . the distance between two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "each row contains 14 plants . leaving 2 corner plants , 12 plants in between have ( 12 x 2 ) metres & 1 metre on each side is left . length = ( 24 + 2 ) m = 26 m . answer : d"
Answer: d
Question (general): the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 86 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 86 thus m = 688 - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 688 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 16 ans : e"
Answer: e
Question (gain): a cycle is bought for rs . 800 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 20 , c ) 35 , d ) 88 , e ) 11
Rationale: "800 - - - - 180 100 - - - - ? = > 35 % answer : c"
Answer: c
Question (other): a man invests some money partly in 12 % stock at 108 and partly in 10 % stock at 60 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 3 : 4 , b ) 3 : 2 , c ) 4 : 5 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 12 % stock at 108 , investment = rs . ( 108 / 12 ) = rs . 9 . for an income of rs . 1 in 10 % stock at 60 , investment = rs . ( 60 / 10 ) = rs . 6 . ∴ ratio of investments = 9 : 6 = 3 : 2 answer b"
Answer: b
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 6 seconds . find the length of the train .
Options: a ) 150 , b ) 278 , c ) 100 , d ) 776 , e ) 191
Rationale: ": speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 6 = 100 meter answer : c"
Answer: c
Question (general): laura took out a charge account at the general store and agreed to pay 8 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 37.8 , e ) $ 38.80
Rationale: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 8 % interest = ( 8 / 100 ) * 35 = 2.8 $ total amount that laura owes a year later = 35 + 2.8 = 37.8 $ answer d"
Answer: d
Question (general): a man purchased 3 blankets @ rs . 100 each , 4 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) a ) 600 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500
Rationale: explanation : 10 * 150 = 1500 3 * 100 + 4 * 150 = 900 1500 – 900 = 600 a
Answer: a
Question (general): rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 850 , b ) $ 840 , c ) $ 860 , d ) $ 870 , e ) $ 880
Rationale: "50 pages typed 1 x 40 pages typed 2 x ( original + one revision ) 10 pages typed 3 x ( original + two revisions ) 50 ( 6 ) + 40 ( 6 + 4 ) + 10 ( 6 + 4 + 4 ) = 300 + 400 + 140 = 840 answer - b"
Answer: b
Question (gain): a gambler has won 40 % of his 30 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 70 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: let x be the number of additional games the gambler needs to play . 0.4 ( 30 ) + 0.7 x = 0.6 ( x + 30 ) 0.1 x = 6 x = 60 the answer is e .
Answer: e
Question (gain): one night a certain hotel rented 4 / 5 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?
Options: a ) 60 % , b ) 70 % , c ) 80 % , d ) 90 % , e ) 100 %
Rationale: "the rooms which were not rented is 1 / 5 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 1 / 5 ) = 1 = 100 % the answer is e ."
Answer: e
Question (physics): a is 30 % more efficient than b . how much time they will working together take to complete a job which a alone could have done in 23 days ?
Options: a ) 25 days , b ) 13 days , c ) 14 days , d ) 20 days , e ) 15 days
Rationale: "the ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b can do work in x days then 10 : 13 : : 23 : x x = ( 23 * 13 ) / 10 x = 299 / 10 a ' s 1 day ' s work = 1 / 23 b ' s 1 day ' s work = 10 / 299 ( a + b ) ' s 1 day ' s work = 1 / 23 + 10 / 299 = 23 / 299 = 1 / 13 a and b together can do work in 13 days answer ( b )"
Answer: b
Question (general): this year , mbb consulting fired 6 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?
Options: a ) 98.5 % , b ) 100.0 % , c ) 102.8 % , d ) 103.4 % , e ) 105.0 %
Rationale: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 6 % reduction in employees lead to 94 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 94 employees is 94 * 1100 = 103400 now the new salary is more than previous salary by x % . x = ( 103400 / 100000 ) * 100 = 103.4 % so the answer is d"
Answer: d
Question (general): the average age of a group of 10 students is 20 years . if 2 more students join the group , the average age increases by 1 year . the average age of the new students is
Options: a ) 23 , b ) 21 , c ) 19.5 , d ) 20 , e ) 22.5
Rationale: "total age of 10 students = 10 * 20 = 200 and the total age of 16 students = 21 * 15 = 315 . let the average age of 2 new students be x . therefore total age of the new students = 2 x . so total age of 12 student = 200 + 5 x = 315 , x = 23 hence , the correct answer is a ."
Answer: a
Question (general): in the set of positive integers from 1 to 100 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 320 , d ) 405 , e ) 500
Rationale: "reduce 1 - 100 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 - - 85 - - 95 are valid multiples . add them - - > 500 e"
Answer: e
Question (physics): find the cost of fencing around a circular field of diameter 12 m at the rate of rs . 3.50 a meter ?
Options: a ) 131.95 , b ) 132.9 , c ) 140.33 , d ) 123.4 , e ) 190.4
Rationale: "2 * 22 / 7 * 6 = 37.7 37.7 * 3 1 / 2 = rs . 131.95 answer : a"
Answer: a
Question (general): a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 28 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 18 , d ) 17 , e ) 01
Rationale: "explanation : as there is meal for 70 adults and 28 have their meal , the meal left can be catered to 42 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 42 adults = 54 children hence , the meal can be catered to 54 children . answer : b"
Answer: b
Question (gain): a side of beef lost 25 percent of its weight in processing . if the side of beef weighed 540 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 720 , d ) 840 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 75 / 100 ) * x = 540 = > x = ( 540 * 100 ) / 75 = 720 answer c"
Answer: c
Question (general): when a random experiment is conducted , the probability that event a occurs is 1 / 3 . if the random experiment is conducted 5 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 5 / 243 , b ) 25 / 243 , c ) 64 / 243 , d ) 80 / 243 , e ) 16 / 17
Rationale: one case is : 1 / 3 * 1 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 2 ^ 3 / 3 ^ 5 we have 5 ! / 2 ! * 3 ! = 10 such cases so , 2 ^ 3 * 10 / 3 ^ 5 = 80 / 243 answer : d .
Answer: d
Question (gain): a reduction of 30 % in the price of oil enables a house wife to obtain 6 kgs more for rs . 940 , what is the reduced price for kg ?
Options: a ) 72 , b ) 47 , c ) 40 , d ) 28 , e ) 20
Rationale: "940 * ( 30 / 100 ) = 282 - - - - 6 ? - - - - 1 = > rs . 47 answer : b"
Answer: b
Question (other): the compound ratio of 5 : 6 , 3 : 2 and 6 : 5 ?
Options: a ) 1 : 1 , b ) 1 : 87 , c ) 1 : 6 , d ) 3 : 2 , e ) 1 : 2
Rationale: "5 / 6 * 3 / 2 * 6 / 5 = 3 / 2 3 : 2 answer : d"
Answer: d
Question (gain): a certain company reported that the revenue on sales increased 30 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 39 %
Rationale: assume the revenue in 2000 to be 100 . then in 2003 it would be 130 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 130 ) / 130 = 50 / 130 = 39 % answer : e .
Answer: e
Question (gain): if a man lost 5 % by selling oranges at the rate of 8 a rupee at how many a rupee must he sell them to gain 52 % ?
Options: a ) 5 , b ) 8 , c ) 7 , d ) 4 , e ) 2
Rationale: "95 % - - - - 8 152 % - - - - ? 95 / 152 * 8 = 5 answer : a"
Answer: a
Question (physics): there are 32 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 1800 , b ) 1820 , c ) 1150 , d ) 1122 , e ) 1900
Rationale: the total number of stations = 34 from 34 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 34 p 2 ways . 34 p 2 = 34 * 33 = 1122 answer : d
Answer: d
Question (physics): a and b together can do a work in 4 days . a alone can do it in 12 days . what time b will take to do the work alone ?
Options: a ) 6 days , b ) 8 days , c ) 12 days , d ) 10 days , e ) 5 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 4 a alone can do 1 day ' s work = 1 / 12 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 4 ) - ( 1 / 12 ) = 6 days answer : option a"
Answer: a
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 1.9 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 99 , b ) 72 , c ) 48 , d ) 96 , e ) 22
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 1.9 = 3 km = 3000 m . required time = 3000 * 3 / 125 = 72 sec . answer : b"
Answer: b
Question (physics): a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 5 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 5 = 19 the answer is a ."
Answer: a
Question (physics): a can run 288 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 38 metre , b ) 28 metre , c ) 23 metre , d ) 15 metre , e ) 36 metre
Rationale: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 288 / 32 = 9 m / s distance covered by b in 4 seconds = speed ã — time = 9 ã — 4 = 36 metre i . e . , a beat b by 36 metre answer is e"
Answer: e
Question (general): 417 x 417 + 383 x 383 = ?
Options: a ) 320578 , b ) 80578 , c ) 80698 , d ) 81268 , e ) none of them
Rationale: "= ( 417 ) ^ 2 + ( 383 ) ^ 2 = ( 400 + 17 ) ^ 2 + ( 400 - 17 ) ^ 2 = 2 [ ( 400 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 160000 + 289 ] = 2 x 160289 = 320578 answer is a"
Answer: a
Question (general): if x / y = 7 / 4 , then ( x + y ) / ( x - y ) = ?
Options: a ) 5 , b ) 11 / 3 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 5
Rationale: "any x and y satisfying x / y = 7 / 4 should give the same value for ( x + y ) / ( x - y ) . say x = 7 and y = 4 , then ( x + y ) / ( x - y ) = ( 7 + 4 ) / ( 7 - 4 ) = 11 / 3 . answer : b ."
Answer: b
Question (general): if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.50 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 8.00
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.5 ) = $ 7 ( as the charge is 0.5 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 7 = 8 answer is e ."
Answer: e
Question (general): if 1.5 x = 0.04 y , then the value of ( y - x ) ( y + x ) is :
Options: a ) 1405.25 , b ) 1305.25 , c ) 1205.25 , d ) 1505.25 , e ) 1605.25
Rationale: "let us assume x = 1 and y = 37.5 then 1.5 ( x ) = 0.04 ( y ) that is 1.5 ( 1 ) = 0.04 ( 37.5 ) = 1.5 = 1.5 therfore from given equation ( 37.5 - 1 ) ( 37.5 + 1 ) = ( 36.5 ) ( 38.5 ) = 1405.25 answer : a"
Answer: a