Cheukting/mathqa huggingface dataset:
Question (general): a batch of cookies was divided among 3 tins : 2 / 3 of all the cookies were placed in either the blue tin or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction w of the cookies that were placed in the other tins were placed in the green tin ?
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7
Rationale: blue tin or red tin : 2 / 3 ( n ) red tin : ( 1 / 3 ) n blue tin : ( 1 / 4 ) n what the last statment meant , is it wants this fraction : ( # of cookies in green tin ) / ( # of cookies in red and green tin ) # of cookies in green tin = 2 n / 3 - n / 4 = 8 n - 3 n / 12 = 5 n / 12 # of cookies in red and green tin = n / 3 + 5 n / 12 = 9 n / 12 fraction w = 5 n / 12 * 12 / 9 n = 5 / 9 ( c )
Answer: c
Question (physics): two trains of equal lengths take 12 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 22 , b ) 13 , c ) 77 , d ) 99 , e ) 21
Rationale: "speed of the first train = 120 / 12 = 10 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 10 + 8 = 18 m / sec . required time = ( 120 + 120 ) / 18 = 13 sec . answer : b"
Answer: b
Question (general): the difference of two numbers is 11 and one - fifth of their sum is 9 . find the numbers .
Options: a ) 28 and 17 , b ) 27 and 18 , c ) 25 and 15 , d ) 27 and 15 , e ) 25 and 18
Rationale: "let the number be x and y . then , x – y = 11 - - - - ( i ) and 1 / 5 ( x + y ) = 9 = > x + y = 45 - - - - ( ii ) adding ( i ) and ( ii ) , we get : 2 x = 56 or x = 28 . putting x = 28 in ( i ) , we get : y = 17 . hence , the numbers are 28 and 17 . answer is a ."
Answer: a
Question (general): 40 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "to maximize the percentage of companies offering both , let ' s assume that all 40 % of companies which offer wireless internet also offer snacks . the answer is b ."
Answer: b
Question (physics): a boat moves down stream at the rate of 1 km in 6 minutes and upstream at the rate of 1 km in 10 minutes . the speed of current is
Options: a ) 2 kmph , b ) 3 kmph , c ) 4 kmph , d ) 5 kmph , e ) 6 kmph
Rationale: if speed ( in kmph ) of the boat = b and current = c , then in downstream time taken ( in hrs . ) = 1 / ( b + c ) = 6 / 60 = 1 / 10 or b + c = 10 - - - ( i ) & in upstream time taken ( in hrs . ) = 1 / ( b - c ) = 10 / 60 = 1 / 6 or b - c = 6 - - - ( ii ) from ( i ) & ( ii ) , b = 8 , c = 2 answer : a
Answer: a
Question (other): a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 5 : 2 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 15 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 5 : 2 - - > e : l = 5 : 2 = 20 : 8 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 20 : 15 . thus , l : s = 8 : 15 . answer : b ."
Answer: b
Question (physics): the sector of a circle has radius of 21 cm and central angle 130 o . find its perimeter ?
Options: a ) 89.7 , b ) 91.4 , c ) 91.7 , d ) 91.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 130 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 47.7 + 42 = 89.7 cm answer : a"
Answer: a
Question (general): the population of a city increases by 8 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.27 % , c ) 22.50 % , d ) 12 % , e ) none of these
Rationale: "actual increase in population = 7 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 7 / 100 ) ^ 3 = 122.5043 ∴ required percentage = 22.50 % answer : c"
Answer: c
Question (physics): pipe a can fill a tank in 3 hours . due to a leak at the bottom , it takes 9 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 4.5 , b ) 17 , c ) 18 , d ) 19 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 3 - 1 / x = 1 / 9 = > 1 / x = 1 / 3 - 1 / 9 = ( 3 - 1 ) / 9 = 2 / 9 = > x = 9 / 2 = 4.5 . answer : a"
Answer: a
Question (physics): the radius of a semi circle is 4.8 cm then its perimeter is ?
Options: a ) 32.51 , b ) 32.4 , c ) 32.1 , d ) 32.92 , e ) 24.69
Rationale: "36 / 7 r = 4.8 = 24.69 answer : e"
Answer: e
Question (other): the number of stamps that p and q had were in the ratio of 9 : 2 respectively . after p gave q 33 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 6 : 5 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 11 , b ) 33 , c ) 45 , d ) 67 , e ) 80
Rationale: "p started with 9 k stamps and q started with 2 k stamps . ( 9 k - 33 ) / ( 2 k + 33 ) = 6 / 5 45 k - 12 k = 178 + 165 33 k = 343 k = 11 p has 9 ( 11 ) - 33 = 66 stamps and q has 2 ( 11 ) + 33 = 55 stamps . the answer is a ."
Answer: a
Question (physics): a man can row a distance of 5 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 40 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 , e ) 5
Rationale: explanation : he covered 5 km in 1 hour , so he might cover 40 km in 8 hours . but he took 10 hours . he would have saved 10 â € “ 8 = 2 hours . answer : a
Answer: a
Question (general): how many 3 - digit numerals end with a digit that represents a prime number ?
Options: a ) 16 , b ) 80 , c ) 160 , d ) 180 , e ) 400
Rationale: "prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways total = 4 * 10 * 10 = 400 ans : e"
Answer: e
Question (physics): machine a and machine b process the same work at different rates . machine c processes work as fast as machines a and b combined . machine d processes work 3 times as fast as machine c ; machine d ’ s work rate is also exactly 4 times machine b ’ s rate . assume all 4 machines work at fixed unchanging rates . if machine a works alone on a job , it takes 6 hours and 20 minutes . if all 4 machines work together on the same job simultaneously , how many minutes will it take all of them to complete it ?
Options: a ) 15 , b ) 17 , c ) 19 , d ) 21 , e ) 24
Rationale: c = a + b d = 3 c = 3 ( a + b ) = 4 b then b = 3 a and c = 4 a the combined rate of the four machines is a + 3 a + 4 a + 12 a = 20 a machine a can complete the work in 380 minutes , so its rate is 1 / 380 of the work per minute . the combined rate is 20 / 380 = 1 / 19 so the work will be completed in 19 minutes . the answer is c .
Answer: c
Question (general): in a fuel station the service costs $ 1.50 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 410 $ , d ) 430 $ , e ) 447 $
Rationale: 12 * 1.50 + 0.65 * 12 * 55 = 447 hence - e
Answer: e
Question (physics): cole drove from home to work at an average speed of 60 kmh . he then returned home at an average speed of 90 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "let the distance one way be x time from home to work = x / 60 time from work to home = x / 90 total time = 2 hrs ( x / 60 ) + ( x / 90 ) = 2 solving for x , we get x = 72 time from home to work in minutes = ( 72 ) * 60 / 60 = 72 minutes ans = c"
Answer: c
Question (general): a certain sum of money is divided among a , b and c so that for each rs . a has 80 paisa , b has 65 paisa and c 40 paisa . if c ' s share is rs . 40 , find the sum of money ?
Options: a ) rs . 185 , b ) rs . 410 , c ) rs . 285 , d ) rs . 385 , e ) rs . 475
Rationale: "a : b : c = 80 : 65 : 40 = 16 : 13 : 8 8 - - - - 40 37 - - - - ? = > rs . 185 answer : a"
Answer: a
Question (probability): from a group of 5 boys and 5 girls , 6 children are to be randomly selected . what is the probability that 3 boys and 3 girls will be selected ?
Options: a ) 4 / 15 , b ) 6 / 17 , c ) 8 / 19 , d ) 10 / 21 , e ) 12 / 23
Rationale: "the total number of ways to choose 6 children from 10 is 10 c 6 = 210 the number of ways to choose 3 boys and 3 girls is 5 c 3 * 5 c 3 = 10 * 10 = 100 p ( 3 boys and 3 girls ) = 100 / 210 = 10 / 21 the answer is d ."
Answer: d
Question (geometry): what is the area of square field whose side of length 14 m ?
Options: a ) 225 , b ) 196 , c ) 266 , d ) 288 , e ) 261
Rationale: "14 * 14 = 196 sq m answer : b"
Answer: b
Question (general): 3 types of tea the a , b , c costs rs . 95 / kg , 100 / kg and 70 / kg respectively . how many kgs of each should be blended to produce 100 kg of mixture worth rs . 90 / kg , given that the quantities of band c are equal
Options: a ) 70 , 1515 , b ) 50 , 2525 , c ) 60 , 2020 , d ) 40 , 3030 , e ) 20 , 3030
Rationale: given quantities of b and c are equal . therefore instead of considering them as a different quantities take average of both and consider it as a single entity . so the cost of the mixture ` ` d ' ' ( equal quantities of ` ` b ' ' and ` ` c ' ' ) is 170 / 2 = 85 rs / kg now the tea contains only ` ` a ' ' of 95 rs / per and ` ` d ' ' of 85 rs / kg . it is clearly seen that ` ` a ' ' is 5 more and ` ` d ' ' is 5 less than the required cost per kg . therefore 50 / 50 will go well . a = 50 kg and d = 50 kg . ( d = b & c in equal ratio ) . therefore b & c = 25 kg each . ( a : b : c ) = ( 50 , 2525 ) answer : b
Answer: b
Question (general): # p is defined as 2 p - 20 for any number p . what is p , if # ( # ( # p ) ) = 6 ?
Options: a ) – 108 , b ) – 44 , c ) 10 , d ) 16 , e ) 18.25
Rationale: # p = 2 p - 20 - - - > # ( # p ) = 2 ( 2 p - 20 ) - 20 = 4 p - 60 and thus # ( 4 p - 60 ) = 2 ( 4 p - 60 ) - 20 = 8 p - 140 = 6 - - - > 8 p = 146 - - - > p = 18.25 , e is the correct answer .
Answer: e
Question (gain): a watch was sold at a loss of 9 % . if it was sold for rs . 220 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 1000 , b ) 2876 , c ) 1977 , d ) 2778 , e ) 1692
Rationale: "91 % 104 % - - - - - - - - 13 % - - - - 220 100 % - - - - ? = > rs . 1692 answer : e"
Answer: e
Question (physics): two persons a and b can complete a piece of work in 30 days and 60 days respectively . if they work together , what part of the work will be completed in 10 days ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 5 / 3
Rationale: a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 60 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 60 = 1 / 20 the part of the work completed in 10 days = 10 ( 1 / 20 ) = 1 / 2 . answer : d
Answer: d
Question (physics): by travelling at 30 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 19 kmph , b ) 15 kmph , c ) 12 kmph , d ) 20 kmph , e ) 23 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 30 * 3 x = 90 x km he covered 2 / 3 * 90 x = 60 x km in 1 / 3 * 3 x = x hours so , the remaining 30 x km , he has to cover in 2 x hours . required speed = 30 x / 2 x = 15 kmph . answer : b"
Answer: b
Question (gain): 33 1 / 3 % of 270 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 270 = 90 b )"
Answer: b
Question (gain): mr . hernandez , who was a resident of state x for only 8 months last year , had a taxable income of $ 22,500 for the year . if the state tax rate were 6 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 900 , b ) $ 720 , c ) $ 600 , d ) $ 300 , e ) $ 60
Rationale: "total tax for the year = 22,500 x 6 % = 1350 as stated annual tax is prorated as per the duration of stay . prorated tax = 1350 ( 8 / 12 ) = 900 answer a"
Answer: a
Question (gain): in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1300 employees , then the no . of female employees who are computer literate ?
Options: a ) 546 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1300 female employees , 60 % of 1300 . = ( 60 * 1300 ) / 100 = 780 . then male employees , = 520 50 % of male are computer literate , = 260 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1300 ) / 100 = 806 computer literate . thus , female computer literate = 806 - 260 = 546 . answer : option a"
Answer: a
Question (general): each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 5 and the 4 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Options: a ) 48 , b ) 66 , c ) 76 , d ) 78 , e ) 72
Rationale: "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 4 and 5 are adjacent - consider 4 and 5 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 4 and 5 can be arranged as 45 or 54 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : e"
Answer: e
Question (physics): susan drove an average speed of 15 miles per hour for the first 40 miles of a tripthen at a average speed of 60 miles / hr for the remaining 20 miles of the trip if she made no stops during the trip what was susan ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 20 , c ) 45 , d ) 50 , e ) 55
Rationale: avg . speed = total distance / total time total distance = 60 miles total time = 40 / 15 + 20 / 60 = 3 avg . speed = 20 . answer - b
Answer: b
Question (geometry): the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 480 m , its area is ?
Options: a ) 150 , b ) 240 , c ) 277 , d ) 261 , e ) 281
Rationale: "5 x + 12 x + 13 x = 480 = > x = 16 a = 80 , b = 192 , c = 208 s = ( 80 + 192 + 208 ) / 2 = 240 answer : b"
Answer: b
Question (physics): the perimeter of a semi circle is 113 cm then the radius is ?
Options: a ) 17 , b ) 28 , c ) 19 , d ) 11 , e ) 22
Rationale: "36 / 7 r = 113 = > r = 22 answer : e"
Answer: e
Question (physics): a boat having a length 4 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 12 kg , b ) 120 kg , c ) 72 kg , d ) 96 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 4 x 3 x 0.01 ) m 3 = 0.12 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.12 x 1000 ) kg = 120 kg . answer : b"
Answer: b
Question (physics): a train 450 m long running at 108 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 271 , b ) 266 , c ) 350 , d ) 277 , e ) 300
Rationale: "length of the platform = 108 * 5 / 18 * 25 = 750 – 450 = 300 answer : e"
Answer: e
Question (general): when the price of sugar was increased by 32 % , a family reduced its consumption in such a way that the expenditure on sugar was only 10 % more than before . if 30 kg were consumed per month before , find the new monthly consumption .
Options: a ) 20 kg , b ) 25 kg , c ) 30 kg , d ) 35 kg , e ) none of these
Rationale: since , expenditure = price × consumption ∴ 110 % of 30 = 132 ⁄ 100 × new consumption ⇒ 110 ⁄ 100 × 30 = 132 ⁄ 100 × new consumption ⇒ new consumption = 25 kg answer b
Answer: b
Question (general): find the 25 th term of an arithmetic progression whose first term is 5 and the common difference is 7 .
Options: a ) 145 , b ) 38 , c ) 173 , d ) 156 , e ) 189
Rationale: n th term of a . p = a + ( n - 1 ) * d = 5 + ( 25 - 1 ) * 7 , = 5 + 168 = 173 . answer : c
Answer: c
Question (general): in a graduating class , 40 percent of the students are male . in this class , 50 percent of the male students and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.56 , b ) 0.62 , c ) 0.68 , d ) 0.74 , e ) 0.8
Rationale: let x be the total number of students . the number students who are younger than 25 is 0.5 * 0.4 x + 0.7 * 0.6 x = 0.62 x the answer is b .
Answer: b
Question (general): the function g ( a ) is defined for integers a such that if a is even , g ( a ) = a / 2 and if a is odd , g ( a ) = a + 5 . given that g ( g ( g ( g ( g ( a ) ) ) ) ) = 19 , how many possible values for a would satisfy this equation ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 11
Rationale: let me define terms : in g ( a ) = r a is argument , r is result , g ( ) is function , in g ( g ( g ( g ( g ( a ) ) ) ) ) , g 1 is inner most , g 5 is outermost for identification . from definition of function g , we can deduce that : if result is even then two possibilities for argument = 1 even 1 odd if result is odd then one possibility for argument = 1 even since final result = 19 = odd possibilities : g 1 : 1 even g 2 : 1 * ( even , odd ) = 1 even 1 odd g 3 : 1 * ( even , odd ) + 1 even = 2 even 1 odd g 4 : 2 * ( even , odd ) + 1 even = 3 even 2 odd g 5 : 3 * ( even , odd ) + 2 even = 5 even 3 odd = total 8 ans d it is !
Answer: d
Question (general): there are 16 bees in the hive , then 9 more fly . how many bees are there in all ?
Options: a ) 7 , b ) 33 , c ) 12 , d ) 17 , e ) 25
Rationale: 16 + 9 = 25 . answer is e .
Answer: e
Question (general): seller selling an apple for rs . 20 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 21 , d ) 18 , e ) 20
Rationale: "sp = 20 loss = cp 21 loss = cp − sp = cp − 20 ⇒ cp 21 = cp − 20 ⇒ 20 cp 21 = 20 ⇒ cp 21 = 1 ⇒ cp = 21 c"
Answer: c
Question (general): what are the last two digits of ( 301 * 402 * 503 * 604 * 645 * 547 * 448 * 349 ) ^ 2
Options: a ) 96 , b ) 76 , c ) 56 , d ) 36 , e ) 00
Rationale: ( ( 301 * 402 * 503 * 604 * 645 ) * ( 547 * 448 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 5,7 , 8,9 ; 6 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,45 and final three as 47 * 48 * 49 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 45 ) ( 56 * 49 ) ) ^ 2 = ( 00 * 44 ) ^ 2 = 00 ^ 2 = 00 hence answer is e
Answer: e
Question (general): nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1.15 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 22 , b ) $ 27.6 , c ) $ 30 , d ) $ 36 , e ) $ 40
Rationale: "b its is . let price = x ( x - 1.15 ) 8 = 6 x x = 4.6 hence total money = 6 * 4.6 = 27.6"
Answer: b
Question (gain): a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 60 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 12 % , d ) 20 % , e ) 80 %
Rationale: the actual answer is obtained by multiplying 160 % by 70 % and subtracting 100 % from this total . that is : 160 % × 70 % = 112 % ; 112 % − 100 % = 12 % . answer : c
Answer: c
Question (probability): a fair coin is tossed 3 times . what is the probability of getting at least 2 tails ?
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 1 / 2 , d ) 3 / 4 , e ) 1 / 4
Rationale: "let ' s find the probability of 2 tails , 3 tails p ( ttt ) = ( ( 1 / 2 ) ^ 3 = 1 / 8 . p ( htt ) = ( 3 ! / 2 ! ) * ( 1 / 2 ) ^ 3 = 3 / 8 total probablity = 1 / 8 + 3 / 8 = 1 / 2 answer ( c )"
Answer: c
Question (gain): a 75 - liter solution of cool - drink is made from 10 % jasmine water . if 3.5 liters of jasmine and 9.5 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 12.5 % , b ) 14 % , c ) 15.5 % , d ) 17 % , e ) 18.5 %
Rationale: "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.1 ( 75 ) + 3.5 ) / 88 = 11 / 88 = 1 / 8 = 12.5 % the answer is a ."
Answer: a
Question (physics): a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 1200 m long ?
Options: a ) 200 sec , b ) 240 sec , c ) 167 sec , d ) 197 sec , e ) 179 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2400 m t = d / s t = 2400 / 10 t = 240 sec answer : b"
Answer: b
Question (physics): a 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform .
Options: a ) 310 meter , b ) 335 meter , c ) 345 meter , d ) 350 meter , e ) none of these
Rationale: "explanation : speed = distance / time = 300 / 18 = 50 / 3 m / sec let the length of the platform be x meters then distance = speed ∗ time x + 300 = 50 / 3 ∗ 39 = > 3 ( x + 300 ) = 1950 = > x = 350 meters option d"
Answer: d
Question (physics): a and b go around a circular track of length 100 m on a cycle at speeds of 18 kmph and 36 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 198 sec , c ) 178 sec , d ) 665 sec , e ) 20 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 100 / ( 18 * 5 / 18 ) , 100 / ( 36 * 5 / 18 ) } = lcm ( 20 , 10 ) = 20 sec . answer : e"
Answer: e
Question (general): zoey won the lottery and got $ 7 , 348340 . she wants to split it among herself and 5 friends evenly . how much money must she add if she wants to split it evenly ?
Options: a ) $ 3 , b ) $ 2 , c ) $ 9 , d ) $ 1 , e ) $ 4
Rationale: zoey and her 5 friends is 6 people in all . $ 7 , 348340 must be divisible by 6 if she wants to split it evenly . the money is divisible by 6 if it ' s divisible by 2 and 3 . 7 + 3 + 4 + 8 + 3 + 4 + 0 = 29 . 2 and 3 cant go into 29 . adding 1 dollar makes it 30 . 2 and 3 can go into 30 so 6 can also . the answer is d .
Answer: d
Question (general): in a certain code language , ' book ' is coded as ' pencil ' , ' pencil ' is coded as ' mirror ' , ' mirror ' is coded as ' board ' . then what is useful to write on a paper ?
Options: a ) 2 , b ) 6278 , c ) 277 , d ) 281 , e ) 22
Rationale: we use pencil to write on a paper but here pencil is coded as mirror . so , the answer is mirror . answer : a
Answer: a
Question (geometry): what is the angle between the hands of a clock when time is 8 : 40 ?
Options: a ) 65 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 100 deg
Rationale: "angle between two hands = 40 h - 11 / 2 m = 40 * 8 - 40 * 11 / 2 = 320 - 220 = 100 deg answer : e"
Answer: e
Question (general): how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 6 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the numbers should be of the form 6 c + 3 . the minimum is 3 when c = 0 . the maximum is 45 when c = 7 . there are 8 such numbers . the answer is d ."
Answer: d