Cheukting/mathqa huggingface dataset:
Question (physics): a monkey ascends a greased pole 17 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 31 st , b ) 22 nd , c ) 23 rd , d ) 24 th , e ) none of these
Rationale: "in 2 minutes , he ascends = 1 metre â ˆ ´ 15 metres , he ascends in 30 minutes . â ˆ ´ he reaches the top in 31 st minute . answer a"
Answer: a
Question (physics): a goods bullet train runs at the speed of 72 km / hr and crosses a 250 m long platform in 26 seconds . what is the length of the goods bullet train ?
Options: a ) 220 m , b ) 250 m , c ) 280 m , d ) 210 m , e ) 270 m
Rationale: e 270 m
Answer: e
Question (gain): a shopkeeper labeled the price of his articles so as to earn a profit of 40 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 26 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 140 . sp = rs . 140 - 10 % of 140 = rs . 140 - 14 = rs . 126 . gain = rs . 126 â € “ rs . 100 = rs . 26 therefore , gain / profit percent = 26 % . answer : option a"
Answer: a
Question (general): what is the tens digit of 36 ^ 5 ?
Options: a ) 1 , b ) 7 , c ) 5 , d ) 3 , e ) 9
Rationale: "36 ^ 5 = 6 ^ 7 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 7 ( dont actually calculate full values ) and answer is d : 3"
Answer: d
Question (general): evaluate : | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 40 , b ) 50 , c ) 72 , d ) 70 , e ) 80
Rationale: "according to order of operations , inner brackets first . hence | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 6 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 6 + 72 | - | 5 - 11 | = | 78 | - | - 6 | = 78 - 6 = 72 correct answer c ) 72"
Answer: c
Question (gain): find the simple interest on rs . 500 for 9 months at 6 paisa per month ?
Options: a ) 287 , b ) 270 , c ) 276 , d ) 129 , e ) 211
Rationale: "i = ( 500 * 9 * 6 ) / 100 = 270 answer : b"
Answer: b
Question (general): evaluate : 60 - 12 ÷ 4 × 2 =
Options: a ) a ) 45 , b ) b ) 54 , c ) c ) 63 , d ) d ) 72 , e ) e ) 81
Rationale: "according to order of operations , 12 ÷ 4 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 4 × 2 = 3 × 2 = 6 hence 60 - 12 ÷ 4 × 2 = 60 - 6 = 54 correct answer is b ) 54"
Answer: b
Question (physics): on a trip , a cyclist averaged 11 miles per hour for the first 22 miles and 10 miles per hour for the remaining 20 miles . if the cyclist returned immediately via the same route and took a total of 9 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?
Options: a ) 7.6 , b ) 7.8 , c ) 8 , d ) 8.2 , e ) 8.4
Rationale: the time to go 42 miles was 22 / 11 + 20 / 10 = 2 + 2 = 4 hours . the average speed for the return trip was 42 miles / 5 hours = 8.4 mph . the answer is e .
Answer: e
Question (general): on increasing the number of lines in a page by 100 , they become 240 . what is the % of increase in the no . of lines in the page ?
Options: a ) 20 % , b ) 305 , c ) 50 % , d ) 71.4 % , e ) 60 %
Rationale: "explanation : number of pages increased = 100 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 100 = 140 % increase in the number of pages in the book = 100 / 140 x 100 % = 71.4 % d"
Answer: d
Question (general): find the sum 3 / 10 + 5 / 100 + 8 / 1000 in decimal form ?
Options: a ) 0.853 , b ) 0.358 , c ) 3.58 , d ) 8.35 , e ) none
Rationale: answer 3 / 10 + 5 / 100 + 8 / 1000 = 0.3 + 0.05 + 0.008 = 0.358 correct option : b
Answer: b
Question (general): 3 distinct single digit no a , b , c are in g . p . if abs ( x ) for real x is the absolute value of x ( x if x is positive or zero , and x if x is negative ) , then the no . of different possible values of abs ( a + b - c ) is
Options: a ) 6 , b ) 4 , c ) 3 , d ) 5 , e ) 2
Rationale: if a = 1 , r = 2 then a = 1 , b = 2 , c = 4 then abs ( a + b - c ) = 1 if a = 1 , r = 3 then a = 1 , a = 3 , a = 9 then abs ( 1 + 3 - 9 ) = 5 if a = 2 , r = 2 , then a = 2 , b = 4 , c = 8 then abs ( 2 + 4 - 8 ) = 2 if a = 1 , r = - 2 then a = 1 , b = - 2 , c = 4 the abs ( 1 - 2 - 4 ) = 5 if a = 1 , r = - 3 then a = 1 , b = - 3 , c = 9 then abs ( 1 - 3 - 9 ) = 11 if a = 2 , r = - 2 then a = 2 , b = - 4 , c = - 8 then abs ( 2 - 4 - 8 ) = 10 so total 5 abs ( ) values answer : d
Answer: d
Question (general): sum of 19 odd numbers is ?
Options: a ) 341 , b ) 351 , c ) 361 , d ) 371 , e ) 381
Rationale: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 19 odd numbers = 19 ^ 2 = 361 answer : c"
Answer: c
Question (physics): an engine moves at the speed of 90 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 9 coaches are attached speed decreases to 78 kmph . what will be the speed of train when 25 coaches are attached .
Options: a ) 90 , b ) 85 , c ) 80 , d ) 60 , e ) 70
Rationale: "1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 25 swr root = 5 decrease = 5 * 4 = 20 new speed = 90 - 20 = 70 e"
Answer: e
Question (physics): a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 188 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: "explanation : let the length of train be l m . acc . to question ( 264 + l ) / 20 = l / 8 2112 + 8 l = 20 l l = 2112 / 12 = 176 m answer b"
Answer: b
Question (general): a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 10 miles per gallon , and from town b to town c , the car averaged 12 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 11.5 , b ) 9.5 , c ) 13.5 , d ) 10.6 , e ) 14.5
Rationale: "step 1 ) took lcm of 10 and 12 . . came as 30 . just multiplied by 10 . . . ( to make easy calculation ) step 2 ) 300 distance between b to c . . . do 300 / 12 hence 25 gallons used step 3 ) twice distance . . hence 300 * 2 = 600 . . . do as above . . 600 / 10 = 60 gallons used step 4 ) total gallons . . 25 + 60 = 85 gallons step ) total miles = 300 + 600 = 900 miles hence . . average of whole journey = 900 / 85 which comes to 10.6 answer : d"
Answer: d
Question (gain): a shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee . find his net profit or loss percent ?
Options: a ) 73 1 / 3 % , b ) 13 1 / 3 % , c ) 33 1 / 3 % , d ) 23 1 / 3 % , e ) 93 1 / 3 %
Rationale: "explanation : the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 3 he selling at 3 a rupee , his sp = 4 profit = sp - cp = 4 - 3 = 1 profit percent = 1 / 3 * 100 = 33 1 / 3 % answer : c"
Answer: c
Question (physics): a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , two boggies were detached . the train now crosses a telegraph post in
Options: a ) 18 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) none of these
Rationale: "length of train = 12 × 15 = 180 m . then , speed of train = 180 ⁄ 18 = 10 m / s now , length of train = 10 × 15 = 150 m ∴ required time = 150 ⁄ 10 = 15 sec . answer c"
Answer: c
Question (general): on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 16 miles on saturday and sunday , how many miles did bill run on sunday ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 16 . . 4 x + 12 = 16 . . x = 1 . . ans = x + 4 = 1 + 4 = 5 answer a"
Answer: a
Question (general): prints a page 40 pg per min . if the printed for 2 hours except 20 min . where there was an paper jam , how many page did it print
Options: a ) 4,000 , b ) 12,880 , c ) 14,880 , d ) 8,880 , e ) 18,880
Rationale: 40 pages - - - - - - - > 1 min 2 hrs except 20 mints means = 2 * 60 = 120 - 20 = 100 mints i . e . , 100 * 40 = 4,000 pages printed . answer : a
Answer: a
Question (physics): a train 450 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 39 sec , c ) 27 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 450 m at 50 / 3 m / sec = 450 * 3 / 50 sec = 27 sec answer : c ."
Answer: c
Question (gain): during a thanksgiving weekend , a car rental company rented 6 - tenths of their vehicles , including two - fifths of the 4 wds that it had . if 40 % of the vehicles are 4 wds , then what percent of the vehicles that were not rented were not 4 wds ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: 4 / 10 of all the vehicles were not rented . ( 3 / 5 ) ( 2 / 5 ) = 6 / 25 of all the vehicles are 4 wds that were not rented . ( 6 / 25 ) / ( 4 / 10 ) = 3 / 5 is the fraction of non - rented vehicles that were 4 wds 1 - 3 / 5 = 40 % of non - rented vehicles were not 4 wds . the answer is c .
Answer: c
Question (general): if x < y < z and y - x > 7 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 6 , b ) 7 , c ) 11 , d ) 8 , e ) 10
Rationale: "we have : 1 ) x < y < z 2 ) y - x > 5 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 7 the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 11 ( y - 2 = 9 , y = 11 ) 2 < 11 < z , since z is odd , the least possible value for z is 13 z - x = 13 - 2 = 11 answer c"
Answer: c
Question (general): a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 100000 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: "a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 100000 n = 1000 satisfies this . e"
Answer: e
Question (physics): jim drove 1096 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 104 miles , b ) 432 miles , c ) 456 miles , d ) 887 miles , e ) 767 miles
Rationale: "the number of miles to drive to finish his journey is given by 1200 - 1096 = 104 miles correct answer a"
Answer: a
Question (physics): ram , who is half as efficient as krish , will take 18 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 8 days , d ) 6 days , e ) 18 days
Rationale: "number of days taken by ram to complete task = 18 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 18 days is 18 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 18 w / 3 w = 6 days answer d"
Answer: d
Question (general): a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm ^ 3 , then the weight of the pipe is :
Options: a ) 3.6 kg , b ) 3.696 kg , c ) 36 kg , d ) 36.9 kg , e ) 3.06 kg
Rationale: "external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 x [ ( 4 ) ^ 2 - ( 3 ) ^ 2 ] x 21 ) cm ^ 3 ( 22 / 7 x 7 x 1 x 21 ) cm ^ 3 462 cm ^ 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b"
Answer: b
Question (general): the average weight of 7 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 76 kg , b ) 77 kg , c ) 75.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 7 × 1.5 = 10.5 kg so the weight of new person = 65 + 10.5 = 75.5 kg answer c"
Answer: c
Question (gain): mr . jones gave 40 % of the money he had to his wife . he also gave 20 % of the remaining amount to his 3 sons . and half of the amount now left was spent on miscellaneous items and the remaining amount of rs . 12000 was deposited in the bank . how much money did mr . jones have initially ?
Options: a ) 40000 , b ) 45000 , c ) 50000 , d ) 62000 , e ) none of these
Rationale: explanation : let the initial amount be x , amount given to his wife = ( 40 / 100 ) x = 2 x / 5 balance = ( x - ( 2 x / 5 ) ) = 3 x / 5 amount given to his wife = ( 20 / 100 ) * ( 3 x / 5 ) = 3 x / 25 balance = 3 x / 5 - 3 x / 25 = 12 x / 25 amountt spent on miscellaneous items = ( 1 / 2 ) * ( 12 x / 25 ) = 6 x / 25 which is equal to 12000 hence , = > 6 x / 25 = 12000 = > x = 50000 answer : c
Answer: c
Question (general): he total marks obtained by a student in physics , chemistry and mathematics is 170 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 65 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 170 + p c + m = 170 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 170 / 2 = 85 . answer : d"
Answer: d
Question (gain): find the compound interest on rs . 10000 at 12 % rate of interest for 1 year , compounded half - yearly
Options: a ) rs . 1036 , b ) rs . 1236 , c ) rs . 1186 , d ) rs . 1206 , e ) rs . 1226
Rationale: "amount with ci = 10000 [ 1 + ( 12 / 2 * 100 ) ] 2 = rs . 11236 therefore , ci = 11236 – 10000 = rs . 1236 answer : b"
Answer: b
Question (general): 25 onions on a scale weigh 5.12 kg . when 3 onions are removed from the scale , the average weight of the 22 onions is 200 grams . what is the average weight ( in grams ) of the 3 onions which were removed ?
Options: a ) 200 , b ) 220 , c ) 240 , d ) 260 , e ) 280
Rationale: 22 * 200 = 4400 . the other 3 onions weigh a total of 720 grams . the average weight is 720 / 3 = 240 grams . the answer is c .
Answer: c
Question (general): a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) s . 220 , b ) s . 120 , c ) s . 320 , d ) s . 50 , e ) s . 90
Rationale: "a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 360 and 240 . difference in profit share = 360 - 240 = 120 answer : b"
Answer: b
Question (geometry): a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 5 inches wide on each side , the total area would have been ( m + 144 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 10 ) ( y + 10 ) = m and so ( 2 ) xy + 10 x + 10 y + 100 = m + 144 let ' s subtract equation ( 1 ) from equation ( 2 ) . 8 x + 8 y + 96 = 144 2 x + 2 y = 12 , which is the perimeter of the photograph . the answer is b ."
Answer: b
Question (general): 3 candidates contested an election and received 1000 , 2000 and 4000 votes respectively . what percentage of the total votes did the winning candidate got ?
Options: a ) 30 % , b ) 50 % , c ) 57 % , d ) 62 % , e ) 75 %
Rationale: total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 required percentage = 4000 / 7000 * 100 = 57 % ( approximately ) answer : option c
Answer: c
Question (geometry): the area of a triangle will be when a = 3 m , b = 5 m , c = 10 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 1
Rationale: s = ( 3 + 5 + 10 ) / 2 = 9 answer : d
Answer: d
Question (probability): what is the sum of all 5 digit numbers which can be formed with the digits 0 , 1,2 , 3,4 without repetation ?
Options: a ) 2599980 , b ) 235500 , c ) 923580 , d ) 765432 , e ) 765434
Rationale: "10 ( 11111 ) * 4 ! - 10 ( 1111 ) 3 ! = 2599980 answer : a"
Answer: a
Question (general): an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 64 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 64 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 64 ( x - y ) - - > x + y = 64 . answer : d ."
Answer: d
Question (gain): 20 litres of mixture contains 40 % alcohol and the rest water . if 8 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 26.32 % , b ) 35.14 % , c ) 28.57 % , d ) 25 % , e ) 31.14 %
Rationale: "alcohol in the 20 litres of mix . = 40 % of 20 litres = ( 40 * 20 / 100 ) = 8 litres water in it = 20 - 8 = 12 litres new quantity of mix . = 20 + 8 = 28 litres quantity of alcohol in it = 8 litres percentage of alcohol in new mix . = 8 * 100 / 28 = 50 / 3 = 28.57 % answer is c"
Answer: c
Question (physics): jane makes toy bears . when she works with an assistant , she makes 90 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 200 %
Rationale: "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional values the productivity in 1 st case is 0.5 bears / hour and in the 2 nd case it is 1 bear / hour hence the productivity is double with the assistant i . e . the increase in productivity is 120 % d"
Answer: d
Question (general): 12.036 divided by 0.04 gives :
Options: a ) 30.09 , b ) 300.9 , c ) 30.06 , d ) 100.9 , e ) 300.6
Rationale: "= 12.036 / 0.04 = 1203.6 / 4 = 300.9 answer is b ."
Answer: b
Question (general): if 20 liters of chemical x are added to 80 liters of a mixture that is 5 % chemical x and 95 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 24 % , b ) 26 % , c ) 28 % , d ) 30 % , e ) 32 %
Rationale: "the amount of chemical x in the solution is 20 + 0.05 ( 80 ) = 24 liters . 24 liters / 100 liters = 24 % the answer is a ."
Answer: a
Question (general): the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 4.4 miles in the sixth 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 35 , b ) 40 , c ) 48 , d ) 51 , e ) 54
Rationale: "( 4.4 miles / 8 minutes ) * 60 minutes / hour = 33 mph let x be the original speed . x - 5 ( 3 ) = 33 x = 48 mph the answer is c ."
Answer: c
Question (general): for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score r for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean r = 74 . answer : a ."
Answer: a
Question (physics): a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 240 meter length ?
Options: a ) 65 seconds , b ) 46 seconds , c ) 40 seconds , d ) 97 seconds , e ) 48 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 240 = 600 meter time = distance / speed = 600 * ( 2 / 25 ) = 48 seconds answer : e"
Answer: e
Question (general): in one year , the population , of a village increased by 10 % and in the next year , it decreased by 10 % . if at the end of 2 nd year , the population was 7920 , what was it in the beginning ?
Options: a ) 8008 , b ) 8000 , c ) 8022 , d ) 8021 , e ) 8022
Rationale: "x * 110 / 100 * 90 / 100 = 7920 x * 0.99 = 7920 x = 7920 / 0.99 = > 8000 answer : b"
Answer: b
Question (gain): the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 35 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 960 , d ) $ 864 , e ) $ 660
Rationale: "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 135 % of $ 640 = $ 864 d"
Answer: d
Question (general): if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 3720 , r will receive
Options: a ) 720 , b ) 700 , c ) 800 , d ) 900 , e ) none of these
Rationale: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 3720 * ( 6 / 31 ) = 120 * 6 = 720 . answer : option a"
Answer: a
Question (physics): it costs $ 2 for the first 15 minutes to use the bumper cars at a fair ground . after the first 15 minutes it costs $ 6 per hour . if a certain customer uses the bumper cars for 3 hours and 25 minutes , how much will it cost him ?
Options: a ) $ 22 , b ) $ 3 , c ) $ 15 , d ) $ 21 , e ) $ 30
Rationale: 3 hrs 25 min = 205 min first 15 min - - - - - - > $ 2 time left is 190 min . . . now , 60 min costs $ 6 1 min costs $ 6 / 60 190 min costs $ 6 / 60 * 190 = > $ 19 so , total cost will be $ 19 + $ 2 = > $ 21 the answer will be ( d ) $ 21
Answer: d