Cheukting/mathqa huggingface dataset:
Question (general): what is the greatest prime factor of 4 ^ 17 - 2 ^ 29 ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 31
Rationale: i ' m happy to help with this . we know 4 = 2 ^ 2 , so 4 ^ 17 = ( 2 ^ 2 ) ^ 17 = 2 ^ ( 2 * 17 ) = 2 ^ 34 that takes advantage of a law of exponents that says ( a ^ n ) ^ m = a ^ ( n * m ) so , 4 ^ 17 - 2 ^ 29 = 2 ^ 34 - 2 ^ 29 = 2 ^ ( 29 + 5 ) - 2 ^ 29 = ( 2 ^ 29 ) * ( 2 * 6 ) - 2 ^ 29 = ( 2 ^ 6 - 1 ) * ( 2 ^ 29 ) = ( 32 - 1 ) * ( 2 ^ 29 ) = 31 * ( 2 ^ 29 ) the prime factors of 31 are 31 , so the largest prime factor is 31 , answer choice d . here ' s a blog you may find helpful . http : / / magoosh . com / gmat / 2012 / gmat - math - factors / does all that make sense ? please let me know if you have any further questions . mike wow . i am floored by how great of an explanation you provided . posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week . e
Answer: e
Question (other): jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 2 and the ratio of indian to british stamps is 4 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Rationale: "u / i = 5 / 2 i / b = 4 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 20 : 8 : 2 i . e . u : b = 20 : 2 answer : option d"
Answer: d
Question (gain): by investing in 16 % stock at 64 , one earns rs . 1500 . the investment made is ?
Options: a ) 2288 , b ) 2877 , c ) 5760 , d ) 7636 , e ) 5728
Rationale: "to earn rs . , investment = rs . 64 . to earn rs . 1500 , investment = = rs . 5760 . answer : c"
Answer: c
Question (general): a student , after his teacher ' s question , chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 344 , b ) 251 , c ) 411 , d ) 212 , e ) 120
Rationale: let x be the number he chose , then 2 ⋅ x − 138 = 102 2 x = 240 x = 120 correct answer is e ) 120
Answer: e
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 36 and 16 ?
Options: a ) 148 , b ) 210 , c ) 314 , d ) 320 , e ) 344
Rationale: prime factorization of 36 = 2 x 2 x 3 x 3 prime factorization of 16 = 2 x 2 x 2 x 2 gcf = 4 lcm = 144 sum = 148 . answer a .
Answer: a
Question (general): lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 28 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "l = r l = 3 c r = c + 28 3 c = c + 28 c = 14 the answer is e ."
Answer: e
Question (gain): a fruit seller sells mangoes at the rate of rs . 5 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 6.56 , b ) rs 9.56 , c ) rs 10.56 , d ) rs 11.56 , e ) none of these
Rationale: "explanation : 80 : 5 = 105 : x x = ( 5 × 105 / 80 ) = rs 6.56 option a"
Answer: a
Question (physics): a train covers a distance of 15 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) m , b ) m , c ) m , d ) m , e ) m
Rationale: "speed = ( 15 / 10 * 60 ) km / hr = ( 90 * 5 / 18 ) m / sec = 25 m / sec . length of the train = 25 * 6 = 150 m . answer : c"
Answer: c
Question (general): when a certain number x is divided by 66 , the remainder is 14 . what is the remainder when x is divided by 11 ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 9 , e ) 10
Rationale: "let possible value of x is 80 least possible value of x / 11 is 80 / 11 = > 7 quotient with remainder 3 thus answer is ( b ) 3"
Answer: b
Question (general): a special municipal payroll tax charges not tax on a payroll less than $ 200,000 and only 0.1 % on a company ’ s payroll above $ 200,000 . if belfried industries paid $ 400 in this special municipal payroll tax , then they must have had a payroll of ?
Options: a ) $ 180,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 400,000 , e ) $ 600,000
Rationale: "answer : e , ( with different approach ) : the 400 paid is 0.1 % of the additional amount above 200,000 . let it be x now 0.1 % of x = 400 therefore x = 400,000 total = 200,000 + x = 600,000"
Answer: e
Question (probability): there are 7 red shoes & 3 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
Options: a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 15 , d ) 7 / 15 , e ) 7 / 16
Rationale: "taking 2 red shoe the probablity is 7 c 2 from 10 shoes probablity of taking 2 red shoe is 7 c 2 / 10 c 2 = 7 / 15 answer : d"
Answer: d
Question (physics): a can do a piece of work in 8 days . b can do it in 16 days . with the assistance of c they completed the work in 4 days . find in how many days can c alone do it ?
Options: a ) 87 days , b ) 20 days , c ) 26 days , d ) 19 days , e ) 16 days
Rationale: "c = 1 / 4 - 1 / 8 - 1 / 16 = 1 / 16 = > 16 days answer : e"
Answer: e
Question (geometry): the radius of a cylinder is 10 m , height 15 m . the volume of the cylinder is :
Options: a ) 2200 , b ) 5500 , c ) 3300 , d ) 1100 , e ) 4714.3
Rationale: "cylinder volume = ï € r ( power 2 ) h = 22 / 7 ã — 10 ã — 10 ã — 15 = 4714.3 m ( power 3 ) answer is e ."
Answer: e
Question (general): mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 47 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 6 % , c ) 15 % , d ) 17 % , e ) 20 %
Rationale: "let me try a simpler one . lets assume that candidate got 47 % votes and total votes is 100 . candidate won = 47 remaining = 53 to get 50 % , candidate requires 3 votes from 100 which is 3 % and 3 votes from 53 . 3 / 53 = . 056 = 5.6 % which is approx 6 % . hence the answer is b ."
Answer: b
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.50 km and 1.25 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 12 , b ) 77 , c ) 66 , d ) 99 , e ) 11
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.50 + 1.25 = 2.75 km = 2750 m . required time = 2750 * 3 / 125 = 66 sec . answer : c"
Answer: c
Question (physics): what is the cost of leveling the field in the form of parallelogram at the rate of rs . 30 / 10 sq . metre , whose base & perpendicular distance from the other side being 64 m & 74 m respectively ?
Options: a ) s . 6000 , b ) s . 6300 , c ) s . 4736 , d ) s . 6480 , e ) s . 7000
Rationale: "area of the parallelogram = length of the base * perpendicular height = 64 * 74 = 4736 m . total cost of levelling = rs . 4736 c"
Answer: c
Question (physics): sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 70 ps per meter is ?
Options: a ) 287 , b ) 369 , c ) 175 , d ) 279 , e ) 361
Rationale: "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.70 = rs . 175 answer : c"
Answer: c
Question (general): when 1 / 20 % of 4,000 is subtracted from 1 / 20 of 4,000 , the difference is
Options: a ) 50 , b ) 198 , c ) 380 , d ) 398 , e ) 400
Rationale: "1 / 20 % of 4000 = 2 1 / 20 of 4000 = 200 200 - 2 = 198 ans : b"
Answer: b
Question (physics): what percent is 2 minutes 24 seconds of an hour ?
Options: a ) 6 % , b ) 8 % , c ) 4 % , d ) 2 % , e ) 9 %
Rationale: "2 mt 24 s = 144 s ( 144 * 100 ) / ( 60 * 60 ) = 4 % answer : c"
Answer: c
Question (general): what is the remainder when 43 * 49 is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 43 * 49 ) / 8 } } = remainder of ( 43 / 8 ) * remainder of ( 49 / 8 ) = 3 * 1 = 3 answer : b"
Answer: b
Question (general): the difference between a number and its two - fifth is 510 . what is 60 % of that number ?
Options: a ) 512 , b ) 510 , c ) 514 , d ) 516 , e ) 518
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 60 % of 850 = 510 . answer : b"
Answer: b
Question (general): a 40 - liter solution of alcohol and water is 5 percent alcohol . if 5.5 liters of alcohol and 4.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 9 % , b ) 11 % , c ) 13 % , d ) 15 % , e ) 17 %
Rationale: "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 5.5 ) / 50 = 7.5 / 50 = 15 % the answer is d ."
Answer: d
Question (general): in the first round of the elections , the only two candidates got exactly the same number of votes . during the second round , 16000 votes switched from the first candidate to the second one . the total number of votes remained the same in both rounds , and no other votes switched sides . if , in the second round , the winning candidate got 5 times as many votes as the other candidate , how many people have voted in each round ?
Options: a ) 15,000 , b ) 25,000 , c ) 40,000 , d ) 48,000 , e ) 60,000
Rationale: let a be the first candidate and b be the second one . given x + 16000 = 5 ( x - 16000 ) = > x = 24000 2 x = 48000 imo option d .
Answer: d
Question (physics): in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 120 marks , how many questions does he answer correctly ?
Options: a ) 20 , b ) 10 , c ) 30 , d ) 50 , e ) 40
Rationale: "let the number of correct answers be x then , number of wrong answers = ( 80 - x ) 4 x – ( 80 - x ) = 120 = > 4 x – 80 + x = 120 = > 5 x = 200 = > x = 200 / 5 = 40 i . e . , he does 40 questions correctly answer is e ."
Answer: e
Question (physics): after striking the floor , a rubber ball rebounds to 4 / 5 th of the height from which it has fallen . find the total distance that it travels before coming to rest if it has been gently dropped from a height of 120 metres .
Options: a ) 540 m , b ) 960 m , c ) 1080 m , d ) 1020 m , e ) 1120 m
Rationale: solution : the first drop is 120 metres . after this the ball will rise by 96 metres and fall by 96 metres . this process will continue in the form of infinite gp with common ratio 0.8 and first term 96 . the required answer is given by the formula : a / ( 1 - r ) now , [ { 120 / ( 1 / 5 ) } + { 96 / ( 1 / 5 ) } ] = 1080 m . answer c
Answer: c
Question (gain): a sum was put a simple interest at a certain rate for 5 years . had it been put at 2 % higher rate , it would have fetched rs . 250 more . the sum is :
Options: a ) s . 2000 , b ) s . 2500 , c ) s . 3000 , d ) s . 3500 , e ) s . 4000
Rationale: "explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 2 ) ã — 5 / 100 â ˆ ’ x ã — r ã — 5 / 100 = 250 â ‡ ’ x ã — 2 ã — 5 / 100 = 250 â ‡ ’ x ã — 5 / 100 = 125 â ‡ ’ 5 x = 12500 â ‡ ’ x = 2500 answer : option b"
Answer: b
Question (general): what is the largest 4 digit number exactly divisible by 35 ?
Options: a ) 4676 , b ) 4678 , c ) 9975 , d ) 9504 , e ) 9936
Rationale: "largest 4 digit number = 9999 9999 ÷ 35 = 285 , remainder = 24 hence largest 4 digit number exactly divisible by 88 = 9999 - 24 = 9975 answer : c"
Answer: c
Question (physics): a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 105 km downstream .
Options: a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 105 / 21 = 5 hours option b"
Answer: b
Question (general): the sum of the average ( arithmetic mean ) of the even integers from 0 to 100 inclusive and the average ( arithmetic mean ) of the even integers from 0 to 50 inclusive ?
Options: a ) 15 , b ) 125 , c ) 25 , d ) 75 , e ) 50
Rationale: so , according to a mean of a set of even numbers from 0 to 100 = ( 0 + 100 ) / 2 = 50 and mean of a set of even numbers from 0 to 50 = ( 0 + 50 ) / 2 = 25 sum = 50 + 25 = 75 answer : d .
Answer: d
Question (geometry): mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 30 ft how many poles do he need ?
Options: a ) 20
b ) 30
c ) 40
d ) 50
e ) 60
Rationale: if each side is 120 feet . . then total perimeter is 150 * 4 = 600 poles every 20 feet hence no of poles = 600 / 20 = 30 answer : b
Answer: b
Question (general): when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.50 for every box , and if the university needs 1.92 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 150 , b ) $ 200 , c ) $ 320 , d ) $ 650 , e ) $ 810
Rationale: "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 1 , 920,000 / 4800 = 400 boxes total cost = 400 × $ 0.5 = $ 200 the answer is b ."
Answer: b
Question (gain): find the simple interest on rs . 68,800 at 16 2 / 3 % per annum for 9 months .
Options: a ) s . 8600 , b ) s . 8000 , c ) s . 7500 , d ) s . 7000 , e ) s . 6500
Rationale: "p = rs . 68800 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 68,800 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8600 answer is a ."
Answer: a
Question (geometry): the area of square abcd above is 22 . the shaded region is the intersection of the square and a circular region centered at c . what is the area of the shaded region ?
Options: a ) 18 − 9 / 4 ∗ π
b ) 22 − 11 / 2 ∗ π
c ) 9 + 9 / 4 ∗ π
d ) 9 + 9 / 2 ∗ π
e ) 9 / 2 − 9 / 4 ∗ π
Rationale: = square - quarter circle = 22 - pi * 22 / 4 = 22 - pi * 11 / 2 answer : b
Answer: b
Question (general): in the list 1 , 2 , 3 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ?
Options: a ) 2 / 9 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 11 , e ) 7 / 9
Rationale: "mode : the mode of any set is the term which has the highest frequency ( occurrence ) highest frequent term in the set is 5 ( with frequency 4 ) hence mode = 5 four terms ( 1 , 2 , 3 , 4 ) out of a total of 11 terms are less than mode of the set . fraction of set that are less than mode of set = 4 / 11 answer : option d"
Answer: d
Question (general): a soft drink company had 6000 small and 14000 big bottles in storage . if 20 % of small 23 % of big bottles have been sold , then the total bottles remaining in storage is
Options: a ) 15360 , b ) 15720 , c ) 15060 , d ) 14930 , e ) 16075
Rationale: "6000 + 14000 - ( 0.2 * 6000 + 0.22 * 14000 ) = 15720 . answer : b ."
Answer: b
Question (physics): express a speed of 72 kmph in meters per second ?
Options: a ) 10 mps , b ) 76 mps , c ) 20 mps , d ) 97 mps , e ) 16 mps
Rationale: "72 * 5 / 18 = 20 mps answer : c"
Answer: c
Question (general): there are 10 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?
Options: a ) 33 , b ) 36 , c ) 39 , d ) 42 , e ) 45
Rationale: "10 c 2 = 45 the answer is e ."
Answer: e
Question (general): if two of the 4 expressions x + y , x + 5 y , x - y , 5 x + y are chosen at random , what is the probability that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: there are total 4 c 2 = 64 c 2 = 6 ways to choose 2 equations out of 4 at random . we want the product of 2 equations in format x 2 − ( by ) 2 x 2 − ( by ) 2 , where b is a constant coefficient of term y 2 y 2 . also note equation does not contain any xyxy term . there are only 2 equations , ( x + y ) & ( x - y ) which gives the product x 2 − y 2 x 2 − y 2 . product of all other equations will contain term xyxy so answer = 1 / 6 ans : e
Answer: e
Question (general): bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 7 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 19 left in his pocket . what was the value of n ?
Options: a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68
Rationale: "started to test answer d if he had 60 , then he spent 15 at hardware store now he was left with 45 $ he spent 7 dollars on cleaning , thus he remained with 38 $ he then spent 1 / 2 of 38 , or 19 , and was left with 19 . hence , the only option that can be right is a ."
Answer: a
Question (physics): a man swims downstream 48 km and upstream 32 km taking 8 hours each time ; what is the speed of the current ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "48 - - - 8 ds = 6 ? - - - - 1 32 - - - - 8 us = 4 ? - - - - 1 s = ? s = ( 6 - 4 ) / 2 = 1 answer : a"
Answer: a
Question (physics): how many seconds will a 100 m 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 ) 11 sec , b ) 6 sec , c ) 77 sec , d ) 14 sec , e ) 12
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 100 * 3 / 50 = 6 sec . answer : b"
Answer: b
Question (other): in a colony of 70 residents , the ratio of the number of men and women is 4 : 3 . among the women , the ratio of the educated to the uneducated is 1 : 4 . if the ratio of the number of educated to uneducated persons is 8 : 27 , then find the ratio of the number of educated to uneducated men in the colony ?
Options: a ) 1 : 7 , b ) 2 : 3 , c ) 1 : 8 , d ) 2 : 3 , e ) 1 : 3
Rationale: number of men in the colony = 4 / 7 * 70 = 40 . number of women in the colony = 3 / 7 * 70 = 40 . number educated women in the colony = 1 / 5 * 30 = 6 . number of uneducated women in the colony = 4 / 5 * 50 = 24 . number of educated persons in the colony = 8 / 35 * 70 = 16 . as 6 females are educated , remaining 10 educated persons must be men . number of uneducated men in the colony = 40 - 10 = 30 . number of educated men and uneducated men are in the ratio 10 : 30 i . e . , 1 : 3 . answer : e
Answer: e
Question (geometry): a cube of edge 5 cm is cut into cubes of each edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to
Options: a ) 1 : 5
b ) 1 : 25
c ) 1 : 125
d ) 1 : 625
e ) none
Rationale: solution required ratio = ( 6 x 1 x 1 / 6 x 5 x 5 ) ‹ = › 1 / 25 ‹ = › 1 : 125 . answer b
Answer: b
Question (general): find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 7 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1346 , c ) 1590 , d ) 1635 , e ) 1489
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 7 x + 15 6 x = 1350 x = 225 large number = 225 + 1365 = 1590 c"
Answer: c
Question (general): alex age after 13 years will be 10 times his age 10 years back . what is the present age of alex ?
Options: a ) 15 , b ) 13 , c ) 20 , d ) 21 , e ) 26
Rationale: let alex ' s present age be x alex ' s age after 17 years = x + 17 alex ' s age 10 years back = x - 10 x + 17 = 10 ( x - 10 ) x = 13 rajeev ' s present age = 13 years answer is b
Answer: b
Question (general): when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of q ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . q * 23 + 39 = 25 * ( q + 1 ) q = 7 ans . ( a )"
Answer: a
Question (general): how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 60 m long and 16 1 / 2 m board ?
Options: a ) 99 , b ) 18 , c ) 16 , d ) 198 , e ) 15
Rationale: "60 * 33 / 2 = 5 / 2 * 2 * x = > x = 198 answer : d"
Answer: d
Question (general): the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 7 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 23 years , b ) 24 years , c ) 25 years , d ) 26 years , e ) 27 years
Rationale: "explanation let the average age of the whole team by x years . 11 x â € “ ( 26 + 33 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 50 2 x = 50 x = 25 . so , average age of the team is 25 years . answer c"
Answer: c
Question (general): if 6 ^ k + 6 ^ k = ( 6 ^ 9 ) ^ ( 6 ^ 9 ) - 6 ^ k , then k = ?
Options: a ) 11 / 3 , b ) 11 / 2 , c ) 242 , d ) 6 ^ 11 - 1 , e ) 3 ^ 11 - 1
Rationale: "6 ^ k + 6 ^ k = ( 6 ^ 9 ) ^ 6 ^ 9 - 6 ^ k 6 * ( 6 ^ k ) = 6 ^ ( 36 * 6 ^ 9 ) = 6 ^ ( 6 ^ 2 * 6 ^ 9 ) = 6 ^ ( 6 ^ 11 ) 6 ^ k + 1 = 6 ^ ( 6 ^ 11 ) so k + 1 = 6 ^ 11 so k = 6 ^ 11 - 1 answer is d"
Answer: d
Question (physics): there are 12 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 132 , b ) 145 , c ) 165 ` , d ) 400 , e ) 300
Rationale: "the total number of stations = 12 from 12 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 12 p 2 ways . 12 p 2 = 12 * 11 = 870 answer : a"
Answer: a
Question (other): the ratio of three numbers is 2 : 3 : 5 and their sum is 150 . the second number of the three numbers is ?
Options: a ) 24 , b ) 26 , c ) 27 , d ) 29 , e ) 45
Rationale: "2 : 3 : 5 total parts = 10 10 parts - - > 150 1 part - - - - > 15 the second number of the three numbers is = 3 * 15 = 45 answer : e"
Answer: e
Question (general): 10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 3213 , how much was it in the beginning ?
Options: a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600
Rationale: "x * ( 90 / 100 ) * ( 85 / 100 ) = 3213 x = 4200 answer : b"
Answer: b
Question (general): a jogger running at 9 km / hr along side a railway track is 180 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 89 , b ) 20 , c ) 36 , d ) 88 , e ) 30
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 180 + 120 = 300 m . time taken = 300 / 10 = 30 sec . answer : option e"
Answer: e
Question (gain): 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 6 mat - weavers in 6 days ?
Options: a ) 25 , b ) 9 , c ) 39 , d ) 61 , e ) 16
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 6 : : 4 : x days 4 : 6 4 * 4 * x = 6 * 6 * 4 x = ( 6 * 6 * 4 ) / ( 4 x 4 ) x = 9 . answer is b ."
Answer: b