Cheukting/mathqa huggingface dataset:
Question (other): the ratio of pens to pencils is 5 to 6 . there are 9 more pencils than pens . how many pencils are there ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 9 x = 9 the number of pencils is 54 . the answer is d .
Answer: d
Question (geometry): the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the width of this rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c"
Answer: c
Question (general): if the average of 10 digits is 80 and the average of 6 of them is 58 , calculate the average of the remaining 4 numbers ?
Options: a ) 119 , b ) 117 , c ) 116 , d ) 113 , e ) 115
Rationale: "explanation : total of the 10 digits - 10 * 80 = 800 total of the 6 digits - 6 * 58 = 348 total of the remaining 4 digits - 800 - 348 = 452 average of the remaining 4 numbers = 452 / 4 = 113 answer : d"
Answer: d
Question (gain): 1 / 2 is what percent of 1 / 3
Options: a ) 150 % , b ) 200 % , c ) 250 % , d ) 300 % , e ) 400 %
Rationale: "explanation : 1 / 2 / 1 / 3 * 100 = 1 / 2 * 3 / 1 * 100 = 150 % answer : option a"
Answer: a
Question (physics): 39 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 15 , e ) 14
Rationale: "first codition = total hours to complete the work = 39 persons * 12 days * 5 hr second codition = total hours to complete the work = 30 persons * x days * 6 hr since the work is still the same so 39 * 12 * 5 = 30 * x * 6 x = 13 answer : c"
Answer: c
Question (general): 2 : 3 : : 23 : ?
Options: a ) 25 , b ) 28 , c ) 22 , d ) 29 , e ) 30
Rationale: "d 29 3 is the next prime number after 2 . similarly , 29 is the next prime number after 23 ."
Answer: d
Question (general): the product of two numbers is 220 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 23 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 220 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 220 ) = 729 x + y = 27 . option c"
Answer: c
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 300 resolutions .
Options: a ) 421 m , b ) 422 m , c ) 423 m , d ) 424 m , e ) 425 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 300 resolutions . = 300 * 2 * 22 / 7 * 22.4 = 42200 cm = 422 m answer : b"
Answer: b
Question (general): the ratio between x and y is 7 / 9 ; x is increased by 4 and y is decreased by 4 , what is the ratio between the new values of x and y ?
Options: a ) 7 / 9 , b ) 14 / 9 , c ) 7 / 18 , d ) 11 / 13 , e ) it can not be determined
Rationale: "ratio = 7 k / 9 k = 7 / 9 , 14 / 18 , etc . x is increased by 4 and y is decreased by 4 - - > ( 7 k + 4 ) / ( 9 k - 4 ) new ratio can be 11 / 15 , 18 / 14 , etc . answer : e"
Answer: e
Question (physics): an outlet pipe empties a tank which is full in 10 hours . if the inlet pipe is kept open , which lets liquid in at the rate of 8 litres / min then outlet pipe would take 6 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 12800 litres , c ) 12100 litres , d ) 11200 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 8 * 60 = 480 liters / hour ; net outflow rate when both pipes operate would be x - 480 liters / hour . capacity of the tank = x * 10 hours = ( x - 480 ) * ( 10 + 6 ) hours 10 x = ( x - 480 ) * 16 - - > x = 1280 - - > capacity = 10 x = 12800 liters . answer : b"
Answer: b
Question (physics): karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many y miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him y : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer ."
Answer: d
Question (general): ( 3108 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 331 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9268 ) / 28 = 331 option c"
Answer: c
Question (general): for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 8 and the price of a student ticket was $ 4 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 20960 , b ) $ 21920 , c ) $ 22680 , d ) $ 28500 , e ) $ 29160
Rationale: "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 30 - - > x = 27 * 30 and 3 x = 3 * ( 27 * 30 ) = 27 * 90 . therefore , the total revenue from ticket sales that day was 27 * 30 * 4 + 27 * 90 * 8 = $ 22,680 . answer : c ."
Answer: c
Question (general): a train ride from two p to town q costs $ 6.85 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.85 . what is the cost of a bus ride from town p to town q ?
Options: a ) $ 1.50 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20
Rationale: "let x be the cost of a bus ride . x + ( x + 685 ) = 985 2 x = 300 x = $ 1.50 the answer is a ."
Answer: a
Question (other): compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 222 grams of compound x ?
Options: a ) 54 , b ) 185 , c ) 250 , d ) 270 , e ) 322
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 222 gms of x have 222 * 10 / 12 = 185 gms of b and 222 - 185 = 37 gms of a . cross check : - a / b = 37 / 185 = 2 / 10 ( as given ) ans b"
Answer: b
Question (physics): a train 100 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 ) 6 sec , b ) 9 sec , c ) 12 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 100 m at 50 / 3 m / sec = 100 * 3 / 50 sec = 6 sec answer : a"
Answer: a
Question (general): how many multiples of 8 are less than 1600 , and also multiples of 64 ?
Options: a ) 25 , b ) 28 , c ) 62 , d ) 83 , e ) 89
Rationale: the lcm of 8 and 64 is 64 . divide 1600 / 64 = 25 . xxx . so a is your answer .
Answer: a
Question (other): what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 50 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "36 = 3 ^ 2 * 2 ^ 2 . 36 ^ 50 = 3 ^ 100 * 2 ^ 100 the answer is a ."
Answer: a
Question (general): find k if 32 / k = 4 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 32 / k = 4 and 32 / 8 = 4 , then k = 8 correct answer c"
Answer: c
Question (general): exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 14 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 35 , c ) 39 , d ) 42 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 7 and 14 ( in order 3 / 7 and 5 / 14 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 14 , which is 98 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 98 people in the room . therefore there are 3 / 7 * 98 = 42 people in the room under the age of 21 . answer : d ."
Answer: d
Question (general): in a group of ducks and cows , the total number of legs are 36 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 36 more than twice the number of heads = > 2 ( d + 2 c ) = 36 + 2 ( c + d ) = > d + 2 c = 18 + c + d = > 2 c = 18 + c = > c = 18 i . e . , total number of cows = 18 answer is d ."
Answer: d
Question (physics): the radius of a semi circle is 6.6 cm then its perimeter is ?
Options: a ) 32.7 , b ) 32.4 , c ) 22.4 , d ) 33.9 , e ) 32.1
Rationale: "36 / 7 r = 6.6 = 33.9 answer : d"
Answer: d
Question (general): the total age of a and b is 12 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 15 , d ) 20 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 12 a - c = 12 answer is b"
Answer: b
Question (gain): a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party w . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "s = 100 not ( w and b ) = 35 only w = 20 ( w and b ) / b = 1 / 2 let ( w and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
Answer: a
Question (physics): pipe a fills a tank in 6 minutes . pipe b can fill the same tank 2 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 0.5 , b ) 1.0 , c ) 1.5 , d ) 2.0 , e ) 2.5
Rationale: "a ' s rate is 1 / 6 and b ' s rate is 1 / 3 . the combined rate is 1 / 6 + 1 / 3 = 1 / 2 the pipes will fill the tank in 2 minutes . the answer is d ."
Answer: d
Question (general): the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8600 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 4100 , b ) s . 4270 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8600 = 34400 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 2400 salary of may is rs . 6500 salary of january = rs . 4100 answer : a"
Answer: a
Question (general): what is the tens digit of 7 ^ 545 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 0
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 546 = 4 * 136 + 1 the ten ' s digit will be 0 . answer e"
Answer: e
Question (general): set a consists of all the prime numbers between 6 and 42 . what is the range of set a ?
Options: a ) 16 , b ) 34 , c ) 16.6 , d ) 17 , e ) 23
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 41 lowest number = 7 range = highest - lowest = 41 - 7 = 34 option b"
Answer: b
Question (general): a certain elevator has a safe weight limit of 2000 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: lets assume there are 2 x people . half of them have average weight of 200 and other half has 230 . maximum weight is = 2000 so 200 * x + 230 * x = 2000 = > 430 x = 2000 = > x is approximately equal to 5 . so total people is 2 * 5 = 10 we are not taking 10 as answer because say 10 th person has minimum of 200 weight then 200 * 5 + 230 * 5 = 2150 ( which is more than 2000 ) answer c .
Answer: c
Question (physics): a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3360 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 380 , b ) s . 600 , c ) s . 420 , d ) s . 400 , e ) s . 480
Rationale: explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3360 × ( 1 / 8 ) = 420 answer : option c
Answer: c
Question (gain): 90 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 135 , d ) 140 , e ) 160
Rationale: "final number = initial number + 50 % ( original number ) = 90 + 50 % ( 90 ) = 90 + 45 = 135 . answer c"
Answer: c
Question (general): rahim bought 55 books for rs . 1500 from one shop and 60 books for rs . 340 from another . what is the average price he paid per book ?
Options: a ) s . 17 , b ) s . 18 , c ) s . 16 , d ) s . 11 , e ) s . 10
Rationale: "average price per book = ( 1500 + 340 ) / ( 55 + 60 ) = 1840 / 115 = rs . 16 answer : c"
Answer: c
Question (general): the average of 10 numbers was calculated as 16 . it is discovered later on that while calculating the average , one number , namely 46 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "10 * 16 - 26 + 46 = 180 180 / 10 = 18 the answer is a ."
Answer: a
Question (physics): a taxi company charges $ 1.25 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 1 / 3 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 1.25 for the first quarter - mile , we will have $ 3.65 left to spend on quarter - mile intervals . since $ 3.65 / $ 0.15 = 24.33 we can buy 24.33 more quarter - miles , and will travel 25.33 quarter miles in all : 25.33 × 1 / 4 = 6 1 / 3 miles . the correct answer is choice ( e ) ."
Answer: e
Question (physics): a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 27 days , c ) 26.67 days , d ) 16 days , e ) 12 days
Rationale: "answer a can complete a project in 20 days . so , a will complete 1 / 20 th of the project in a day . b can complete a project in 30 days . so , b will complete 1 / 30 th of the project in a day . let the total number of days taken to complete the project be x days . b worked for all x days . however , a worked for ( x - 10 ) days because a quits 10 days before the project is completed . in a day , a completes 1 / 20 th of the project . therefore , a would have completed x − 10 / 20 th of the project in ( x - 10 ) days . in a day , b completes 130130 th of the project . therefore , b would have completed x / 30 h of the project in x days . ∴ x − 10 / 20 + x / 30 = 1 or x = 18 . choice a"
Answer: a
Question (physics): 60 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 170 litres , e ) none of these
Rationale: explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 60 = 80 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 80 = 120 litres . answer c
Answer: c
Question (general): what is the remainder when 8 ^ 714 is divided by 5 ?
Options: a ) 2 , b ) 3 , c ) 1 , d ) 0 , e ) 4
Rationale: "8 ^ 0 = 1 8 ^ 1 = 8 8 ^ 2 = 64 8 ^ 3 = 512 8 ^ 4 = 4096 8 ^ 5 = . . . . . 8 and so on after ignoring the first last - digit of 8 ^ 0 = 1 , in a recurring last - digit pattern of 8,4 , 2,6 , 8,4 , 2,6 . . . . 715 / 4 = 178 ( with a remainder 2 ) so the last number is a 4 . so when 8 ^ 714 is divided by 5 the remainder is 4 , ans = e"
Answer: e
Question (general): 20.20 / 2000 is equal to :
Options: a ) 1.01252677 , b ) 0.013466667 , c ) 0.125266677 , d ) 0.126256677 , e ) 0.12725776
Rationale: "20.20 / 2000 = 2525 / 200000 = 0.013466667 answer : b"
Answer: b
Question (physics): a bus trip of 450 miles would have taken 1 hour less if the average speed s for the trip had been greater by 5 miles per hour . what was the average speed s , in miles per hour , for the trip ?
Options: a ) 10 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "( s + 5 ) ( t - 1 ) = 450 s * t = 450 solving both the equations , we get : s = 45 or - 50 since speed should be positive , s = 45 hence , option c"
Answer: c
Question (general): an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters w long ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3
Rationale: let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1
Answer: b
Question (physics): i flew my tiny seaplane to visit my mother . on the flight up , i flew at 110 mph . on the way home , i flew 72 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 91 mph , c ) 88 mph , d ) 100 mph , e ) 99 mph
Rationale: "( 110 mph + 72 mph ) / 2 = 91 mph correct answer is : b"
Answer: b
Question (other): a starts business with rs . 35000 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ’ s contribution in the capital ?
Options: a ) 22378 , b ) 279889 , c ) 2788 , d ) 9000 , e ) 2882
Rationale: explanation : ratio in which profit is to be divided = 2 : 3 assume that b ' s contribution to the capital = b ⇒ 3500 × 12 : b × 7 = 2 : 3 ⇒ 3500 × 12 / 7 b = 2 / 3 ⇒ b = ( 3500 × 12 × 3 ) / ( 2 × 7 ) = 500 × 6 × 3 = 9000 answer : d
Answer: d
Question (general): if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 55 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 16 , d ) 29 , e ) 39
Rationale: 45 - [ 28 - { 37 - ( 15 - * ) } ] = 55 = > 45 - [ 28 - { 37 - 15 + * } ] = 55 45 - [ 28 - 37 + 15 - * ] = 55 = > 45 [ 43 - 37 - * ] = 55 45 - [ 6 - * ] = 55 = > 45 - 6 + * = 55 39 + * = 55 = > * = 55 - 39 = 16 answer : c
Answer: c
Question (general): what is the remainder of q = 3 ^ 19 when divided by 10 ?
Options: a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9
Rationale: "i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , q = when divided by 10 , the remainder must be 7 . d"
Answer: d
Question (other): find the fraction which has the same ratio to 2 / 5 that 3 / 8 has to 1 / 5
Options: a ) 1 / 15 , b ) 3 / 4 , c ) 5 / 8 , d ) 9 / 6 , e ) 8 / 7
Rationale: "p : 2 / 5 = 3 / 8 : 1 / 5 as the product of the means is equal to the product of the extremes . p * 1 / 5 = 2 / 5 * 3 / 8 p * 1 / 5 = 6 / 40 p = 3 / 4 = > p = 3 / 4 answer : b"
Answer: b
Question (general): what is the remainder when 1271 * 1275 * 1277 * 1289 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 9 , d ) 11 , e ) 7
Rationale: "1271 * 1275 * 1277 * 1285 = ( 1272 - 1 ) ( 1272 + 3 ) ( 1284 - 7 ) ( 1284 + 5 ) = ( multiple of 12 - 1 ) ( multiple of 12 + 3 ) ( multiple of 12 - 7 ) ( multiple of 12 + 1 ) now , if we expand this expression all terms but the last one will have a multiple of 12 in them , thus will leave no remainder upon division by 12 , the last term will be ( - 1 ) ( 3 ) ( - 7 ) ( 5 ) = 105 . thus the question becomes : what is the remainder upon division of 105 by 12 ? the answer to this question is 9 . answer : c ."
Answer: c
Question (general): in a class of 27 students in an examination in maths 5 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49.3
Rationale: explanation : total marks obtained by a class of 25 students = 5 * 95 + 3 * 0 + 19 * 45 = 1330 average marks of whole class = 1330 / 27 = 49.3 answer : option e
Answer: e
Question (physics): a man sitting in a train which is traveling at 56 kmph observes that a goods train , traveling in opposite direction , takes 15 seconds to pass him . if the goods train is 410 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 42 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 410 / 15 m / sec = ( ( 410 / 15 ) × ( 18 / 5 ) ) kmph = 98 kmph . speed of goods train = ( 98 - 56 ) kmph = 42 kmph answer : option d"
Answer: d
Question (gain): a trader marked the selling price of an article at 12 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 10.5 % , c ) 11 % , d ) 12.5 % , e ) 9.8
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 112 * 100 ] % = 9.8 % answer e"
Answer: e