Cheukting/mathqa huggingface dataset:
Question (physics): a motorcyclist goes from bombay to pune , a distance of 256 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 5 , c ) 1 : 4 , d ) 1 : 1 , e ) 5 : 8
Rationale: "t = 256 / 32 = 8 h t = 8 - 3 = 5 time ratio = 8 : 5 speed ratio = 5 : 8 answer : e"
Answer: e
Question (general): the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years x in which the population would be doubled assuming there is no emigration or immigration is
Options: a ) 20 , b ) x = 25 , c ) x = 30 , d ) x = 35 , e ) 40
Rationale: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."
Answer: d
Question (general): when the positive integer y is divided by 9 , the remainder is 5 . what is the remainder when 3 y is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 6
Rationale: lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y = 9 k + 5 multiplying by 3 will give 3 y = 27 k + 15 we can also write 3 y = 27 k + 9 + 6 now 27 k and 9 are divisible by 9 leaving the remainder as 6 hence e is the answer .
Answer: e
Question (general): let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 70 th number in this set ?
Options: a ) 557 , b ) 608 , c ) 613 , d ) 616 , e ) 621
Rationale: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 70 th number = 8 * ( 70 - 1 ) + 5 = 557 answer = a"
Answer: a
Question (general): find the minimum value of 5 cosa + 12 sina + 12
Options: a ) - 1 , b ) 1 , c ) 2 , d ) 3 , e ) none of these
Rationale: "solution : 5 cosa + 12 sina + 12 = 13 ( 5 / 13 cosa + 12 / 13 sina ) + 12 now , for any values of b we can get sinb = 5 / 13 and we can replace cosb = 12 / 13 . we see that our assumption is right because we satisfy the condition sin ^ 2 b + cos ^ 2 b = 1 so we get 13 ( sinbcosa + cosbsina ) + 12 = 13 ( sin ( a + b ) ) + 12 . therefore we know that minimum value of sinx = - 1 and greatest is 1 so the least value of the expression becomes when sin ( a + b ) = - 1 then the value of the whole term becomes 13 . ( - 1 ) + 12 = - 13 + 12 = - 1 answer a"
Answer: a
Question (gain): julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 122 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 720 , c ) 1080 , d ) 2200 , e ) 3600
Rationale: "$ 120 for 2 years = $ 60 per year . extra $ 2 yearned with the compound interest is the percent yearned on percent . so , $ 2 is yearned on $ 60 , which means that the interest = 30 % . this on the other hand means that half of the savings = 60 * 30 = $ 1800 . twice of that = $ 3,600 . answer : e ."
Answer: e
Question (general): when positive integer n is divided by 7 , the remainder is 1 . when n is divided by 11 , the remainder is 5 . what is the smallest positive integer k such that k + n is a multiple of 77 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "n = 7 p + 1 = 11 q + 5 n + 6 = 7 p + 7 = 11 q + 11 n + 6 is a multiple of 7 and 11 , so it is a multiple of 77 . the answer is c ."
Answer: c
Question (physics): a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 29 m * 2 m * 0.75 m ?
Options: a ) 29000 , b ) 27908 , c ) 78902 , d ) 25000 , e ) 27991
Rationale: "29 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 29 = 1 / 100 * x = > x = 29000 answer : a"
Answer: a
Question (physics): on a map , 1 inch represents 28 miles . how many b inches would be necessary to represent a distance of 383.6 miles ?
Options: a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7
Rationale: b inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c
Answer: c
Question (gain): a worker is paid a regular rate of rs . 30 for completing a survey . the worker completes 100 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 20 % higher than her regular rate . if she completed 50 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 2200 , b ) 1100 , c ) 2500 , d ) 2800 , e ) 3300
Rationale: "amount earned using her cell phone = 50 * 36 = 1800 earned for remaining surveys = 50 * 30 = 1500 total earning = 3300 answer : e"
Answer: e
Question (physics): a man goes from a to b at a speed of 20 kmph and comes back to a at a speed of 30 kmph . find his average speed for the entire journey ?
Options: a ) 11 , b ) 24 , c ) 55 , d ) 66 , e ) 71
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 20 ) + ( d / 30 ) ] = ( 2 d ) / [ 5 d / 60 ) = > 24 kmph . answer : b"
Answer: b
Question (general): find the maximum value of the function f ( x ) = x − 5 if x is a number between - 5 and 13 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) none
Rationale: solution : since f ( x ) is a linear function whose slope is 1 , a positive number , it is strictly increasing for all x . therefore its maximal value is reached for the largest value of x , x = 13 and f ( x ) = 13 - 5 = 8 . answer c
Answer: c
Question (gain): a shopkeeper sold 30 articles at the cost price of 35 articles . then find the profit % or lost %
Options: a ) 12 % , b ) 15 % , c ) 16.67 % , d ) 18 % , e ) 22 %
Rationale: "here 30 articles selling price = 35 articles cost price so the difference = 35 - 30 = 5 % of profit = 5 * 100 / 30 = 16.67 % correct option is c"
Answer: c
Question (gain): a cycle is bought for rs . 900 and sold for rs . 1140 , find the gain percent ?
Options: a ) 11 , b ) 27 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 240 100 - - - - ? = > 27 % answer : b"
Answer: b
Question (general): the average of 5 quantities is 12 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 24 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: "answer : a ( 5 x 12 - 3 x 4 ) / 2 = 24"
Answer: a
Question (general): a trained covered x km at 30 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 22.5 , b ) 99 , c ) 24 , d ) 66 , e ) 887
Rationale: "total time taken = x / 30 + 2 x / 20 hours = 2 x / 15 hours average speed = 3 x / ( 2 x / 15 ) = 22.5 kmph answer : a"
Answer: a
Question (gain): the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 28,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 877888 , d ) 124000 , e ) 188871
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 28,000 is made = 96,000 + 28,000 = rs . 1 , 24,000 answer : d"
Answer: d
Question (general): if | 20 x - 10 | = 130 , then find the product of the values of x ?
Options: a ) - 45 , b ) 50 , c ) - 42 , d ) 35 , e ) - 30
Rationale: "| 20 x - 10 | = 130 20 x - 10 = 130 or 20 x - 10 = - 130 20 x = 140 or 20 x = - 120 x = 7 or x = - 6 product = - 6 * 7 = - 42 answer is c"
Answer: c
Question (general): gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 60 and the turban . find the price of the turban .
Options: a ) 27 , b ) 30 , c ) 29 , d ) 10 , e ) 11
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 60 . thus , 3434 ( 90 + x ) = 60 + x or 270 + 3 x = 240 + 4 x or x = 30 answer : b"
Answer: b
Question (general): find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1450 ?
Options: a ) rs . 1000 , b ) rs . 1250 , c ) rs . 1010 , d ) rs . 10000 , e ) none of these
Rationale: "explanation : 1450 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1250 answer : option b"
Answer: b
Question (physics): how many seconds will a 600 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 25 , b ) 36 , c ) 40 , d ) 45 , e ) 50
Rationale: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 600 * 3 / 50 = 36 sec answer : b"
Answer: b
Question (physics): a ship 450 m long is running at a speed of 24 km / hr . in what time will it pass a bridge 900 m long ?
Options: a ) 202.5 sec , b ) 205.5 sec , c ) 200 sec , d ) 1350 sec , e ) 900 sec
Rationale: total length = 450 + 900 = 1350 speed = 24 km / h = ( 24 * 5 ) / 18 = 20 / 3 m / s time = ( 1350 * 3 ) / 20 = 202.5 sec . answer : a
Answer: a
Question (general): at company x , senior sales representatives visit the home office once every 12 days , and junior sales representatives visit the home office once every 8 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: "each 24 - day period , senior representatives visit the home office 2 times while junior representatives visit 3 times , thus 50 % more . the answer is d ."
Answer: d
Question (probability): find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 40 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 40 , b ) 12 / 40 , c ) 8 / 40 , d ) 3 / 40 , e ) 7 / 40
Rationale: "let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23,29 , 31,37 } n ( x ) = 12 , n ( s ) = 40 hence , the required probability is 12 / 40 . answer : b"
Answer: b
Question (physics): john can complete a given task in 10 days . jane will take only 20 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 4 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 8 , b ) 9 , c ) 8.5 , d ) 9.5 , e ) 10.5
Rationale: "in such questions , you need to start from the end . last 4 days john works alone and completes 4 * ( 1 / 10 ) = 2 / 5 of the work . so 3 / 5 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 20 + 1 / 12 = 8 / 60 time taken to complete 4 / 5 of the work = ( 3 / 5 ) / ( 8 / 60 ) = 9 / 2 days . so total number of days taken to complete the work = 9 / 2 + 4 = 8.5 days . c"
Answer: c
Question (general): find the sum the difference between the compound and s . i . on a certain sum of money for 5 years at 20 % per annum is rs . 75 of money ?
Options: a ) 1489 , b ) 6845 , c ) 2598 , d ) 1875 , e ) 2600
Rationale: "p = 75 ( 100 / 20 ) 5 = > p = 1875 answer : d"
Answer: d
Question (general): p has $ 32 more than what q and r together would have had if both b and c had 1 / 6 of what p has . how much does p have ?
Options: a ) $ 44 , b ) $ 48 , c ) $ 52 , d ) $ 56 , e ) $ 60
Rationale: "p = ( 2 / 6 ) * p + 32 ( 4 / 6 ) * p = 32 p = 48 the answer is b ."
Answer: b
Question (general): a salt manufacturing company produced a total of 2000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 80 , b ) 85 , c ) 83 , d ) 95 , e ) 00
Rationale: "total production of salt by the company in that year = 2000 + 2100 + 2200 + . . . . + 3100 = 30600 . average monthly production of salt for that year = 30600 / 365 â ‰ ˆ 84 answer : c"
Answer: c
Question (other): how many terminating zeroes e does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Question (general): the average age of a group of n people is 14 years old . one more person aged 32 joins the group and the new average is 16 years old . what is the value of n ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "14 n + 32 = 16 ( n + 1 ) 2 n = 16 n = 8 the answer is d ."
Answer: d
Question (gain): a 75 - liter solution of cool - drink is made from 8 % jasmine water . if 3 liters of jasmine and 12 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 10.3 % , b ) 11.5 % . , c ) 10 % . , d ) 12.2 % , e ) 12 % .
Rationale: "denominator 75 + 3 + 12 90 numerator 75 * 0.08 = 6 - - - > jasmine water 6 + 3 = 9 - - - > new content of jasmine water in new solution ratio 9 / 90 answer : c"
Answer: c
Question (gain): the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 216 . find the principal ?
Options: a ) 2277 , b ) 2667 , c ) 5400 , d ) 2766 , e ) 1811
Rationale: "p = 216 ( 100 / 5 ) ^ 2 = > p = 5400 answer : c"
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 15 sec . what is the length of the train ?
Options: a ) 287 , b ) 699 , c ) 250 , d ) 168 , e ) 150
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 12 = 250 m answer : c"
Answer: c
Question (general): rewrite ( 10 ^ 38 ) – 85 as a base 10 integer , what is the sum of the digits in that integer ?
Options: a ) 354 , b ) 357 , c ) 330 , d ) 370 , e ) 360
Rationale: we know that ( 10 ^ 38 ) is ending 00 , so ( 10 ^ 38 ) – 85 = 9 . . . . 9915 total number of digits in ( 10 ^ 38 ) – 85 is 38 , or 36 digits of 9 and two digits 1 and 5 . answer choice is 36 * 9 + 6 = 330 answer is c 330
Answer: c
Question (general): he average of 10 numbers is 23 . if each number is increased by 4 , what will the new average be ?
Options: a ) 26 , b ) 27 , c ) 88 , d ) 99 , e ) 12
Rationale: sum of the 10 numbers = 230 if each number is increased by 4 , the total increase = 4 * 10 = 40 the new sum = 230 + 40 = 270 the new average = 270 / 10 = 27 . answer : b
Answer: b
Question (gain): a man buy a book in rs 50 & sale it rs 70 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 40 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 70 profit = 70 - 50 = 20 % = 20 / 50 * 100 = 40 % answer : b"
Answer: b
Question (physics): a tank is filled by 3 pipes a , b , c in 6 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 42 hr , c ) 40 hr , d ) 20 hr , e ) 50 hr
Rationale: suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 6 7 / x = 1 / 6 x = 42 hours answer is b
Answer: b
Question (general): first column specifies the no of days prior to departure information . second column specifies the percentage discount offered . 0 - 6 days = = > 0 % 7 - 13 days = = > 10 % 14 - 29 days = = > 25 % 30 days or more = = > 40 % the table above shows the discount structure for advanced purchase of tickets at a particular airline . a passenger bought a ticket at this airline for $ 1050 . the ticket agent informed her that , had she purchased the ticket one day later , she would have paid $ 210 more . how many days before her departure did she purchase her ticket .
Options: a ) 6 , b ) 7 , c ) 13 , d ) 14 , e ) 29
Rationale: first i figured out the percentage change from the immediate previous amount for each of the period . thus it comes - 0 - 6 days = = > 0 % 7 - 13 days = = > 10 % ( 90 % of the price ) 14 - 29 days = = > 17 % ( approx ) ( went from 90 % to 75 % ) 30 days or more = = > 20 % ( went from 75 % to 60 % ) if the passenger had to pay the extra amount , she had to pay = ( 210 + 1050 ) = 1260 now 210 is somehow between 10 % and 20 % of 1260 . so 17 % is the choice here . correct ans : 14 days answer : d
Answer: d
Question (general): a no . when divided by 158 gives a remainder 50 , what remainder will be obtainedby dividingthe same no . 16 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "158 + 50 = 208 / 16 = 13 ( remainder ) d"
Answer: d
Question (physics): a man can row a distance of 6 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 20 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 6 : 41 , e ) 5
Rationale: "explanation : he covered 6 km in 1 hour , so he might cover 20 km in 3 hours 19 minutes . but he took 10 hours . he would have saved 10 â € “ 3 hours 19 minutes = 6 hours 41 minutes . answer : d"
Answer: d
Question (general): 1395 x 1395
Options: a ) 1946025 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these
Rationale: "1395 x 1395 = ( 1398 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 5 ) 2 - ( 5 x 1400 x 5 ) = 1946025 . answer : option a"
Answer: a
Question (general): the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 20 positive perfect squares ?
Options: a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 2,316 , e ) 2,870
Rationale: "first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 20 and c = 1 / 2 into the equation and simplify to get the answer 2870 . option e ."
Answer: e
Question (general): a mixture of 70 litres of milk and water contains 10 % water . how many litres of water should be added to the mixture so that the mixture contains 12 1 / 2 % water ?
Options: a ) 2 , b ) 8 , c ) 6 , d ) 3 , e ) 4
Rationale: "a 2 quantity of milk in the mixture = 90 / 100 ( 70 ) = 63 litres . after adding water , milk would form 87 1 / 2 % of the mixture . hence , if quantity of mixture after adding x liters of water , ( 87 1 / 2 ) / 100 x = 63 = > x = 72 hence 72 - 70 = 2 litres of water must be added ."
Answer: a
Question (general): if a = 2 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 ) ?
Options: a ) - 14 , b ) - 60 , c ) 0 , d ) 4 , e ) 14
Rationale: "if a = - 1 , then putting values in equation = - [ ( 2 ) ^ 2 + ( 2 ) ^ 3 + ( 2 ^ 4 ) + ( 2 ^ 5 ) ] = - [ 4 + 8 + 16 + 32 ] = - 60 answer = b = - 60"
Answer: b
Question (general): how many even number in the range between 20 to 100 inclusive are not divisible by 3
Options: a ) 28 , b ) 30 , c ) 31 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 20 , 22,24 . . . 100 using ap formula , we can say 100 = 20 + ( n - 1 ) * 2 or n = 41 . for 6 , 24,36 . . . 96 using ap formu 24 la , we can say 96 = 24 + ( n - 1 ) * 6 or n = 13 . hence , only divisible by 2 but not 3 = 41 - 13 = 28 . hence , answer a"
Answer: a
Question (physics): a clock shows the time as 9 a . m . if the minute hand gains 7 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 63 min , d ) 50 min , e ) 55 min
Rationale: "there are 9 hours in between 9 a . m . to 6 p . m . 9 * 7 = 63 minutes . answer : c"
Answer: c
Question (gain): how much interest will $ 10,000 earn in 9 months at an annual rate of 4 % ?
Options: a ) $ 300 , b ) $ 350 , c ) $ 450 , d ) $ 550 , e ) $ 650
Rationale: soln : - 9 months = 3 / 4 of year ; 4 % = 4 / 100 = 1 / 25 ; $ 10,000 ( principal ) * 1 / 25 ( interest rate ) * 3 / 4 ( time ) = $ 300 . answer : a
Answer: a
Question (physics): if the perimeter of a rectangular garden is 700 m , its length when its breadth is 100 m is ?
Options: a ) 299 m , b ) 777 m , c ) 200 m , d ) 250 m , e ) 128 m
Rationale: "2 ( l + 100 ) = 700 = > l = 250 m answer : d"
Answer: d
Question (general): you have been given a physical balance and 7 weights of 40 , 42 , 36 , 33 , 47 , 52 and 67 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 169 kgs .
Options: a ) 163 , b ) 166 , c ) 162 , d ) 164 , e ) 165
Rationale: "67 + 52 + 47 = 166 answer : e"
Answer: e
Question (general): the average of first five multiples of 7 is
Options: a ) 21 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "solution average = 7 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 105 / 5 . = 21 answer a"
Answer: a
Question (gain): a shopkeeper loses 15 % , if an article is sold for rs . 102 . what should be the selling price of the article to gain 20 % ?
Options: a ) rs . 146 , b ) rs . 144 , c ) rs . 129 , d ) rs . 123 , e ) rs . 128
Rationale: "given that sp = rs . 102 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 102 ) / 85 = 20 * 6 = rs . 120 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 120 * 120 ) / 100 = rs . 144 answer : b"
Answer: b
Question (general): sum of the squares of 3 no . ' s is 62 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 18 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 62 + 2 * 131 a + b + c = √ 324 = 18 d"
Answer: d
Question (physics): some persons can do a piece of work in 12 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "12 / ( 2 * 2 ) = 3 days answer : a"
Answer: a
Question (general): how many multiples of 4 are there between 12 and 92 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 3 up to 4 * 23 . 23 - 3 + 1 = 21 . the answer is a ."
Answer: a
Question (general): a metered rikshaw charges rs 13.50 for the first 1 km and 2.50 per 1 / 3 km there after . what would the charge if this rikshaw is hired for 13 kms ? in approx ? ?
Options: a ) 103.5 rs , b ) 104.5 rs , c ) 105.5 rs , d ) 106.5 rs , e ) 107.5 rs
Rationale: for 1 st km : rs . 13.50 ramaining distance : 13 - 1 = 12 km 1 / 3 km costs 2.5 rs 1 km costs ( 2.5 * 3 ) remaining 12 km costs ( 2.5 * 3 ) * 12 = 90 rs total cost = 90 + 13.5 = 103.5 rs answer : a
Answer: a
Question (physics): two pipes a and b separately fill in 15 / 2 min and 5 min respactively and third pipe c can empty of 14 l / m if all the pipes are open when the cistern is full , it is emptied in 1 hr . how many litres does the cistern hold ?
Options: a ) 40 , b ) 30 , c ) 50 , d ) 80 , e ) 54
Rationale: let total water in cistern = x liter speed of a = 2 x / 15 l / m ( speed = liter / time ) speed of b = x / 5 l / m speed of c = 14 l / m according to question x + ( x / 5 + 2 x / 15 ) * 60 = 60 * 14 x + = 60 * 14 x = 40 liter answer : a
Answer: a
Question (physics): if 4 men can colour 48 m long cloth in 2 days , then 6 women can colour 36 m long cloth in ?
Options: a ) day , b ) day , c ) days , d ) days , e ) days
Rationale: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 6 = 1 day . b )"
Answer: b
Question (probability): from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a black card and the second card is a king ?
Options: a ) 1 / 26 , b ) 1 / 13 , c ) 3 / 52 , d ) 3 / 26 , e ) 15 / 26
Rationale: "p ( black card ) = 1 / 2 p ( king ) = 1 / 13 p ( black card then a king ) = 1 / 2 * 1 / 13 = 1 / 26 the answer is a ."
Answer: a