Cheukting/mathqa huggingface dataset:
Question (gain): the banker ' s gain on a sum due 3 years hence at 12 % per annum is rs . 360 . the banker ' s discount is :
Options: a ) rs . 1360 , b ) rs . 1000 , c ) rs . 360 , d ) rs . 640 , e ) none of these
Rationale: "explanation : bg = rs . 360 t = 3 years r = 12 % td = ( bg × 100 ) / tr = ( 360 × 100 ) / ( 3 × 12 ) = rs . 1000 bg = bd – td = > bd = bg + td = 360 + 1000 = rs . 1360 answer : option a"
Answer: a
Question (general): calculate the sum of first 19 natural numbers .
Options: a ) 190 , b ) 120 , c ) 150 , d ) 199 , e ) 110
Rationale: solution we know that ( 1 + 2 + 3 + . . . . . + 19 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 19 ) = ( 19 × 20 / 2 ) = 190 . answer a
Answer: a
Question (physics): a is twice as good a workman as b and they took 5 days together to do the work b alone can do it in ?
Options: a ) 15 days , b ) 88 days , c ) 21 days , d ) 11 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 5 x = 1 / 15 = > 15 days answer : a"
Answer: a
Question (gain): carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 5 % . what is the approximate interest he pays annually ?
Options: a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 12000
Rationale: since the options did not make sense with 5 % annual rate of interest , it is apparent that the intent was a 5 % quarterly rate . so the bank charges 5 % every quarter and compounds it in the next quarter . had it been a simple quarterly rate , we would have just found 4 * 5 % of 10,000 = $ 2000 as our answer . but since , the interest is compounded , it will be a bit more than $ 2000 . option ( c ) looks correct . answer : c
Answer: c
Question (geometry): in measuring the sides of a rectangle , one side is taken 6 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 5 % , e ) 0.7 %
Rationale: "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 106 * 95 = 10,070 , which is 0.7 % greater than the actual area . answer : e ."
Answer: e
Question (general): in a division , divident is 689 , divisior is 36 and quotient is 19 . find the remainder .
Options: a ) 4 , b ) 3 , c ) 2 , d ) 5 , e ) 6
Rationale: explanation : 689 = 36 x 19 + r 689 = 684 + r r = 689 - 684 = 5 answer : option d
Answer: d
Question (general): the product of two numbers is 120 and the sum of their squares is 289 . the sum of the number is
Options: a ) 20 , b ) 23 , c ) 27 , d ) 150 , e ) 255
Rationale: "explanation : we know ( x + y ) 2 = x 2 + y 2 + 2 xy = > ( x + y ) 2 = 289 + 2 ( 120 ) = > ( x + y ) = 529 − − − √ = 23 option b"
Answer: b
Question (other): a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 8 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
Options: a ) 2 , b ) 9 , c ) 6 , d ) 21 , e ) 30
Rationale: let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 8 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 8 ) = 0.08 t - - > 60 + 6 ( t - 8 ) = 8 t - - > t = 6 . answer : c .
Answer: c
Question (general): what is the dividend . divisor 18 , the quotient is 9 and the remainder is 3
Options: a ) a ) 145 , b ) b ) 148 , c ) c ) 165 , d ) d ) 153 , e ) e ) 158
Rationale: "d = d * q + r d = 18 * 9 + 3 d = 162 + 3 d = 165 answer : c"
Answer: c
Question (physics): the r train leaves station a moving at a constant speed , and passes by stations b and c , in this order . it takes the r train 7 hours to reach station b , and 5 additional hours to reach station c . the distance between stations a and b is m kilometers longer than the distance between stations b and c . what is the distance between stations a and c in terms of m ?
Options: a ) 1.8 m , b ) 6 m , c ) 7 m , d ) 9 m , e ) 12 m
Rationale: the reason it is failing for you is that you chose incorrect numbers . if the question says r it took 7 hrs to reach from a to b and 5 hrs to reach from b to c at a constant speed . it shows that distance ab and bc should be in ratio of 7 / 5 . if you take such numbers you can solve problem . ab = 7 , bc = 5 therefore ab - bc = 2 but from question , ab - bc = m = > m = 2 now total distance = ab + bc = 12 substitute 12 to get answer in terms of m total distance = 12 = 6 m ans b
Answer: b
Question (gain): a shirt goes on sale for 50 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 70 % , c ) 52 % , d ) 50 % , e ) 45 %
Rationale: "just assume original price is 100 . sale price = 50 then it is marked down by 10 % = 50 - 5 = 45 . hence it is 45 % od the original price . hence answer is e ."
Answer: e
Question (general): each child has 2 pencils and 13 skittles . if there are 8 children , how many pencils are there in total ?
Options: a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08
Rationale: 2 * 8 = 16 . answer is a .
Answer: a
Question (physics): in what time will a railway train 56 m long moving at the rate of 39 kmph pass a telegraph post on its way ?
Options: a ) 3 sec , b ) 4 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec
Rationale: "t = 56 / 39 * 18 / 5 = 5 sec answer : c"
Answer: c
Question (other): sachin is younger than rahul by 9 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 31.5 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 24.1
Rationale: "if rahul age is x , then sachin age is x - 9 , so ( x - 9 ) / x = 7 / 9 = > 9 x - 81 = 7 x = > 2 x = 81 = > x = 40.5 so sachin age is 40.5 - 9 = 31.5 answer : a"
Answer: a
Question (general): a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 245 , then how much amount should c pay as his share of rent ?
Options: a ) 35 , b ) 45 , c ) 25 , d ) 63 , e ) 55
Rationale: "a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 245 × 9 / 35 = 7 × 9 = 63 answer is d"
Answer: d
Question (probability): find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 35 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 35 , b ) 11 / 35 , c ) 8 / 35 , d ) 3 / 35 , e ) 7 / 35
Rationale: "let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 } n ( x ) = 11 , n ( s ) = 35 hence , the required probability is 11 / 35 . answer : b"
Answer: b
Question (physics): if 5 machines can produce 20 units in 10 hours , how long would it take 10 to produce 60 units ?
Options: a ) 9 , b ) 10 , c ) 15 , d ) 25 , e ) 30
Rationale: "5 machines would produce 60 units in 30 hours . increasing the amount of machines by 2 would mean dividing 30 hours by 2 . 30 / 2 = 15 answer : c"
Answer: c
Question (general): a and b started a business jointly a ' s investment was thrice the investment of b and the period of his investment was two times the period of investment of b . if b received rs . 4000 as profit , then their total profit is ?
Options: a ) 28029 , b ) 28000 , c ) 28001 , d ) 28012 , e ) 28129
Rationale: suppose b invested rs . x for y months . then , a invested rs . 3 x for 2 y months . so , a : b = ( 3 x * 2 y ) : ( x * y ) = 6 xy : xy = 6 : 1 . b ' s profit : total profit = 1 : 7 . let the total profit be rs . x then , 1 / 7 = 4000 / x or x = 28000 . answer : b
Answer: b
Question (general): the average ( arithmetic mean ) of 27 , 32 , and 64 is 6 less than the average of 29 , 42 , and x . what is x ?
Options: a ) 62 , b ) 64 , c ) 66 , d ) 68 , e ) 70
Rationale: "the average of 27 , 32 , and 64 is 41 . the average of 29 , 42 and x is 47 . then 29 + 42 + x = 141 . x = 70 . the answer is e ."
Answer: e
Question (other): in a class of 40 students , 10 did not opt for math . 15 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ?
Options: a ) 13 , b ) 15 , c ) 7 , d ) 17 , e ) 18
Rationale: 40 students total 10 did not opt for math 15 did not opt for science 2 did not opt for either total of 30 students in math and 13 did not opt for sci but did for math 30 - 13 = 7 7 students of the class opted for both math and science answer : c . 7
Answer: c
Question (physics): a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 15 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 22 , e ) 40
Rationale: "i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 15 ) x solve for r , r = 55 55 - 15 = 40 mpg e"
Answer: e
Question (gain): sahil purchased a machine at rs 14000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22000 , b ) rs . 24000 , c ) rs . 26000 , d ) rs . 30000 , e ) none of these
Rationale: "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 14000 + 5000 + 1000 = 20000 150 % of 20000 = 150 / 100 * 20000 = 30000 option d"
Answer: d
Question (gain): the salary of a person was reduced by 50 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 75 % , e ) 100 %
Rationale: "let the original salary be $ 100 new salary = $ 50 increase on 50 = 50 increase on 100 = 50 / 50 * 100 = 100 % ( approximately ) answer is e"
Answer: e
Question (general): the average of first seven multiples of 3 is :
Options: a ) 9 , b ) 16 , c ) 12 , d ) 8 , e ) 10
Rationale: "explanation : ( 3 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 3 x 28 / 7 = 12 answer : c"
Answer: c
Question (physics): there are 25 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 156 , b ) 167 , c ) 157 , d ) 352 , e ) 702
Rationale: "the total number of stations = 27 from 27 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in ² ⁰ p ₂ ways . ² ⁰ p ₂ = 27 * 26 = 702 . answer : e"
Answer: e
Question (general): look carefully for the pattern , and then choose which pair of numbers comes next . 28 25 5 21 18 5 14
Options: a ) 11 5 , b ) 10 7 , c ) 11 8 , d ) 5 10 , e ) 10 5
Rationale: explanation : this is an alternating subtraction series with the interpolation of a random number , 5 , as every third number . in the subtraction series , 3 is subtracted , then 4 , then 3 , and so on . answer : option a
Answer: a
Question (physics): if in a cricket one day match , there were no wide balls , no wides , no extras and no overthrows . what is the maximum number of runs that a batsman can score in 35 overs in an ideal case scenario ?
Options: a ) 1158 , b ) 1651 , c ) 1653 , d ) 1654 , e ) none
Rationale: solution : 1158 explanation : for an ideal case , the batsman will hit a six on each ball . but if he hits six on the last ball of the over , the strike will change in the next over . thus , the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over . thus the total runs that he can score in each over : 6 * 5 + 3 = 33 but this will have to go like it only till the 34 th over . in the 35 th over , he can hit a six in the last ball as well as that will be the last ball of his destination . thus runs for the 35 th over will be 6 * 6 = 36 . hence the maximum runs = 33 * 34 + 36 = 1158 answer a
Answer: a
Question (general): there is a total of 90 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 3 and the probability that it will be green is 1 / 5 . what is the probability that the marble will be either red or blue ?
Options: a ) 1 / 3 , b ) 3 / 5 , c ) 7 / 15 , d ) 11 / 30 , e ) 17 / 30
Rationale: "p ( red or blue ) = 1 - p ( white ) - p ( green ) = 15 / 15 - 5 / 15 - 3 / 15 = 7 / 15 the answer is c ."
Answer: c
Question (general): 10 , 15 , 22.5 , 33.75 , 50.62 , ( . . . )
Options: a ) 60 , b ) 60.75 , c ) 75.93 , d ) 76.33 , e ) 70.1
Rationale: "10 ( 10 ã — 3 ) ã · 2 = 15 ( 15 ã — 3 ) ã · 2 = 22.5 ( 22.5 ã — 3 ) ã · 2 = 33.75 ( 33.75 ã — 3 ) ã · 2 = 50.62 ( 50.62 ã — 3 ) ã · 2 = 75.93 answer is c"
Answer: c
Question (probability): a coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed . if 8 possible outcomes are equally likely . find the probability that the die shows a number greater than 4 , if it is known that the first throw of the coin results in a tail
Options: a ) 2 / 4 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 6 , e ) 1 / 4
Rationale: sample space s = { hh , ht , t 1 , t 2 , t 3 , t 4 , t 5 , t 6 } let a be the event that the die shows a number greater than 4 and b be the event that the first throw of the coin results in a tail then , a = { t 5 , t 6 } b = { t 1 , t 2 , t 3 , t 4 , t 5 , t 6 } required probability = ( 2 / 8 ) / ( 6 / 8 ) = 1 / 3 answer : b
Answer: b
Question (gain): john purchased a grinder and a mobile for rs . 15000 & rs . 10000 respectively . he sold the grinder at a loss of 4 % and the mobile phone at a profit of 10 % . overall how much he make a profit .
Options: a ) s . 400 , b ) s . 120 , c ) s . 420 , d ) s . 450 , e ) s . 290
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 10000 ( 1 + 10 / 100 ) = 10000 + 1000 total sp - total cp = r + m - ( 15000 + 10000 ) = - 600 + 1000 = rs . 400 as this is positive , an overall profit of rs . 400 was made . a"
Answer: a
Question (general): a boat crossed a lake from north to east at the speed of 10 km / h , entered a river and covered twice as much distance going upstream at 9 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.8 km / h that day , what was its approximate downstream speed ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 11
Rationale: one way of solving this is : speed of boat on still water ( lake ) = 10 kmph speed upstream = 9 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 10 + 1 = 11 kmph ans is e
Answer: e
Question (physics): a train covers a distance of 20 km in 20 min . if it takes 9 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 150 m , b ) 200 m , c ) 120 m , d ) 225 m , e ) 160 m
Rationale: "speed = ( 20 / 20 * 60 ) km / hr = ( 60 * 5 / 18 ) m / sec = 50 / 3 m / sec . length of the train = 50 / 3 * 9 = 150 m . answer : a"
Answer: a
Question (physics): a 180 m long train is running at 72 kmph . if it crossed the platform in 20 sec . then find the platform length ?
Options: a ) 220 m , b ) 110 m , c ) 230 m , d ) 100 m , e ) 90 m
Rationale: length = speed * time length = 72 km / hr * time length = [ 72 * ( 5 / 18 ) ] * 20 { ( ie ) ( x ) km / hr ) } = x * ( 5 / 18 ) = 20 * 20 length = 400 m length of platform = length - length of the train length of platform = 400 - 180 length of platform = 220 m option a
Answer: a
Question (physics): two cars start at the same time from opposite ends of a highway that is 333 miles long . one car is riding at 54 mph and the second car is riding at 57 mph . how long after they begin will they meet ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "as cars are moving in opposite directions their speeds will be added . so their relative speeds : 57 + 54 = 111 mph total distance to be covered = 333 miles . time taken would be : 333 miles / 111 mph = 3 hours c is the answer ."
Answer: c
Question (physics): it takes joey the postman 1 hours to run a 1 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 5 mile / hour , what is the speed with which joey returns ?
Options: a ) 1.67 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 3 miles an hour let the other half be x miles an hour now , avg speed = 5 mile an hour 2 * 1 * x / 1 + x = 5 2 x = 5 x + 5 = > 3 x = 5 = 5 / 3 = 1.67 a"
Answer: a
Question (general): the average weight of a class is x pounds . when a new student weighing 70 pounds joins the class , the average decreases by 1 pound . in a few months the student ’ s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds . none of the other students ’ weights changed . what is the value of x ?
Options: a ) 26 , b ) 86 , c ) 88 , d ) 90 , e ) 92
Rationale: "when the student weighs 80 pounds the average weight is x - 1 pounds ; when the student weighs 110 pounds the average weight is x + 4 pounds . so , the increase in total weight of 110 - 70 = 40 pounds corresponds to the increase in average weight of ( x + 4 ) - ( x - 1 ) = 5 pounds , which means that there are 40 / 5 = 8 students ( including the new one ) . so , initially there were 5 student . total weight = 5 x + 70 = 8 ( x - 1 ) - - > x = 26 pounds . answer : a ."
Answer: a
Question (gain): the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 6500 , brokerage being 1 / 4 % , is :
Options: a ) 90.03 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 6500 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 6500 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 90.27 . = market value of rs . 100 stock = rs . 90.27 - re . 0.25 . = market value of rs . 100 stock = rs . 90.03 . answer : a"
Answer: a
Question (physics): a factory produces 5500 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 1100 toys , b ) 5487 toys , c ) 6113 toys , d ) 2354 toys , e ) 1375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 5500 / 5 = 1100 toys correct 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 of all the even integers between 1 and 100 ?
Options: a ) 1250 , b ) 1530 , c ) 2120 , d ) 2540 , e ) 2550
Rationale: "average of the set : ( largest + smallest ) / 2 = ( 100 + 2 ) / 2 = 51 ; # of terms : ( largest - smallest ) / 2 + 1 = ( 100 - 2 ) / 2 + 1 = 50 the sum = 51 * 50 = 2550 answer : e"
Answer: e
Question (general): the average weight of a , b , c is 45 kg . the avg wgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .
Options: a ) 36 kg , b ) 84 kg , c ) 31 kg , d ) 45 kg , e ) 12 kg
Rationale: "sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . ans : b"
Answer: b
Question (geometry): what is the area of a circle with the circumference of 88 cms ?
Options: a ) 618 sq cms , b ) 516 sq cms , c ) 600 sq cms , d ) 615 sq cms , e ) none of these
Rationale: "circum = 2 * pi * r 88 = 2 * pi * r r = 44 / pi area of circle = pi * r 2 a = pi * ( 44 / pi ) 2 a = 616 answer : e"
Answer: e
Question (general): how many different positive integers exist between 10 ^ 2 and 10 ^ 3 , the sum of whose digits is equal to 2 ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "101 110 200 total no . is 3 a"
Answer: a
Question (gain): how many litres of pure acid are there in 8 litres of a 20 % solution
Options: a ) 1.5 , b ) 1.6 , c ) 1.7 , d ) 1.8 , e ) 1.9
Rationale: "explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 8 * 20 / 100 = 1.6 answer : option b"
Answer: b
Question (general): evaluate : 1024 x 237 + 976 x 237
Options: a ) 486000 , b ) 568000 , c ) 378000 , d ) 474000 , e ) none of them
Rationale: "1024 x 237 + 976 x 237 = 237 x ( 1024 + 976 ) = 237 x 2000 = 474000 . answer is d ."
Answer: d
Question (physics): gary ’ s gas station serves an average of 16 cars per hour on saturdays , 10 cars per hour on sundays , and 9 cars per hour on all other days of the week . if the station is open from 6 a . m . to 10 p . m . every day , how many cars does gary ’ s station serve over the course of a typical week ?
Options: a ) 1,136 , b ) 1,200 , c ) 1,240 , d ) 1,280 , e ) 1,320
Rationale: "6 a . m . to 10 p . m . = 16 hours number of cars serviced on weekdays = ( 16 * 9 * 5 ) number of cars serviced on saturday = ( 16 * 16 ) number of cars serviced on sunday = ( 16 * 10 ) number of cars served in a week = 16 ( 45 + 16 + 10 ) = 16 * 71 = 1136 answer : a"
Answer: a
Question (general): what is the remainder when 81 + 82 + 83 … … + 815 is divided by 6
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "thus odd powers will have remainder 2 ; and even powers will have remainder 4 now , 81 + 82 + 83 … … + 81581 + 82 + 83 … … + 815 will have the following powers - odd = 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 ( 8 odd powers ) ; sum of remainder = 16 even powers = 2 , 4 , 6 , 8 , 10 , 12 , 14 ( 7 even powers ) ; sum of remainder = 28 total sum of remainder = 44 44 / 6 = remainder 2 hence correct answer will be ( c ) 2 . . . ."
Answer: c
Question (general): the avg weight of a , b & c is 50 kg . if d joins the group , the avg weight of the group becomes 53 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 51 kg . what is the weight of a ?
Options: a ) 56 , b ) 65 , c ) 73 , d ) 89 , e ) 90
Rationale: "a + b + c = 3 * 50 = 150 a + b + c + d = 4 * 53 = 212 - - - - ( i ) so , d = 62 & e = 62 + 3 = 65 b + c + d + e = 51 * 4 = 204 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 212 – 204 = 8 a = e + 8 = 65 + 8 = 73 answer : c"
Answer: c
Question (gain): in an election between two candidates , the winner has a margin of 20 % of the votes polled . if 3000 people change their mind and vote for the loser , the loser would have won by a margin of 20 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 15000 , b ) 20000 , c ) 30000 , d ) 60000 , e ) 45000
Rationale: "winner - looser 60 % - 40 % if 3000 people change their mind and vote for the loser : winner - looser 40 % - 60 % thus 3,000 people compose 20 % of all voters , which means that the total number of votes is 15,000 . answer : a"
Answer: a
Question (general): p , q and r have $ 5000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2400 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 2000
Rationale: "e 2000 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 5000 - r ) = > 3 r = 10000 - 2 r = > 5 r = 10000 = > r = 2000 ."
Answer: e