Cheukting/mathqa huggingface dataset:
Question (physics): a cistern is filled by pipe a in 10 hours and the full cistern can be leaked out by an exhaust pipe b in 15 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 50 hrs , b ) 30 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: "time taken to full the cistern = ( 1 / 10 - 1 / 15 ) hrs = 1 / 30 = 30 hrs answer : b"
Answer: b
Question (general): all the students of class are told to sit in circle shape . here the boy at the 10 th position is exactly opposite to 45 th boy . total number of boys in the class ?
Options: a ) 65 , b ) 68 , c ) 72 , d ) 70 , e ) 58
Rationale: "as half the circle shape consist of 45 - 10 = 35 boys , so total number of boys in full circle = 2 * 35 = 70 answer : d"
Answer: d
Question (general): how many integers between 2000 and 3000 that have distinct digits and increase from left to right ?
Options: a ) 10 , b ) 20 , c ) 60 , d ) 120 , e ) 600
Rationale: since the numbers must be distinct and increasing from left to right , the only arrangements we could come - up with are : 245 _ - - > 4 246 _ - - > 3 247 _ - - > 2 248 _ - - > 1 256 _ - - > 3 257 _ - - > 2 258 _ - - > 1 267 _ - - > 2 268 _ - - > 1 number of integers = 20 b
Answer: b
Question (physics): the speed of a car is 70 km in the first hour and 90 km in the second hour . what is the average speed of the car ?
Options: a ) 79 kmph , b ) 80 kmph , c ) 34 kmph , d ) 23 kmph , e ) 14 kmph
Rationale: "s = ( 70 + 90 ) / 2 = 80 kmph answer : b"
Answer: b
Question (physics): pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed z ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16
Rationale: "let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this z we get x = 8 . b ."
Answer: b
Question (physics): the length of the bridge , which a train 475 metres long and travelling at 90 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 225 m , c ) 245 m , d ) 250 m , e ) 275 m
Rationale: "speed = [ 90 x 5 / 18 ] m / sec = [ 25 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 475 + x ) / 30 = 25 = > 475 + x = 750 = > x = 275 answer : e"
Answer: e
Question (gain): a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 90 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 16.7 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 90 ( multiplying factor is 6 : ( 90 / 15 ) ) then typical dosage would be 2 * 6 = 12 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 12 ) * 100 = 16.67 % e is the answer ."
Answer: e
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 80 ps per meter is ?
Options: a ) 287 , b ) 369 , c ) 125 , d ) 200 , e ) 361
Rationale: "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.80 = rs . 200 answer : d"
Answer: d
Question (geometry): what is the smallest positive integer x , such that 1152 x is a perfect cube ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 18
Rationale: we need to make 1152 x a perfect cube , hence we need to have the powers a multiple of 3 1152 = 2 ^ 7 * 3 ^ 2 the minimum value of x for which 1152 x is a perfect cube = 2 ^ 2 * 3 = 12 correct option : d
Answer: d
Question (gain): an association of mathematics teachers has 1,600 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 14.5 % , e ) 19.6 %
Rationale: total umber of members = 1600 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1600 ) * 100 = 19.6 % answer e
Answer: e
Question (general): a no . when divided by 125 gives a remainder 40 , what remainder will be obtainedby dividingthe same no . 15 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "125 + 40 = 165 / 15 = 11 ( remainder ) b"
Answer: b
Question (geometry): the area of a triangle will be when a = 3 m , b = 4 m , c = 5 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 6 , c ) 4 , d ) 9 , e ) 1
Rationale: s = ( 3 + 4 + 5 ) / 2 = 6 answer : b
Answer: b
Question (general): a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.5 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
Options: a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 1,200 , e ) e . 2,400
Rationale: "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.5 = 300 answer : b"
Answer: b
Question (physics): if 7 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 588 , b ) 263 , c ) 120 , d ) 160 , e ) 1260
Rationale: "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 7 c 2 for vertical 8 c 2 total parallelogram is 7 c 2 * 8 c 2 = 21 * 28 = 588 answer : a"
Answer: a
Question (gain): if the a radio is sold for rs 490 and sold for rs 465.50 . find loss percentage .
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) none of them
Rationale: cost price = rs 490 , selling price = 465.50 . loss = rs ( 490 - 465.50 ) = rs 24.50 . loss % = [ ( 24.50 / 490 ) * 100 ] % = 5 % answer is b
Answer: b
Question (probability): if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first flip but not on the last 4 flips ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 16 , d ) 1 / 32 , e ) 1 / 64
Rationale: "p ( htttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 the answer is d ."
Answer: d
Question (gain): a person distributed 20 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 50000 . find his total income ?
Options: a ) a ) 452000 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 1000000 , e ) e ) 652000
Rationale: "3 children got = 3 * 20 % = 60 % wife got = 30 % orphan house = 5 % total = 60 + 30 + 5 = 95 % remaining = 100 - 95 = 5 % 5 % = 50000 100 % = 50000 * 100 / 5 = $ 1000000 answer is d"
Answer: d
Question (general): the average ( arithmetic mean ) of the even integers from 0 to 60 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 30 inclusive ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 60 is 60 / 2 = 30 the average of the even numbers from 0 to 30 is 30 / 2 = 15 the answer is b ."
Answer: b
Question (physics): a train 200 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 10 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 9 , e ) 5
Rationale: "speed of train relative to man = 60 + 10 = 70 km / hr . = 70 * 5 / 18 = 175 / 9 m / sec . time taken to pass the men = 200 * 9 / 175 = 10 sec . answer : c"
Answer: c
Question (general): what is the least number which should be added to 2697 so that the sum is exactly divisible by 5 , 6 , 4 , and 3 ?
Options: a ) 3 , b ) 11 , c ) 19 , d ) 27 , e ) 35
Rationale: "l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 2697 by 60 , the remainder is 57 . the number to be added = 60 - 57 = 3 . the answer is a ."
Answer: a
Question (general): on dividing number by 357 , we get 39 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 0 , b ) 3 , c ) 5 , d ) 11 , e ) 13
Rationale: "let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x 2 = ( 5 k + 3 ) 2 = ( 25 k 2 + 30 k + 9 ) = 5 ( 5 k 2 + 6 k + 1 ) + 4 on dividing x 2 by 5 , we get 4 as remainder . answer : c"
Answer: c
Question (general): how many even number in the range between 10 to 150 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 47
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 , 10 , 12,14 . . . 150 using ap formula , we can say 150 = 10 + ( n - 1 ) * 2 or n = 71 . for 6 , 12,18 , . . . 96 using ap formula , we can say 150 = 12 + ( n - 1 ) * 6 or n = 24 . hence , only divisible by 2 but not 3 = 71 - 24 = 47 . hence , answer e"
Answer: e
Question (physics): a is twice as good as b . and together they finish a piece of work in 20 days . in how many days will a alone finish the work
Options: a ) 30 , b ) 25 , c ) 12 , d ) 10 , e ) 32
Rationale: "( a ' s 1 day work ) : ( b ' s 1 day work ) = 2 : 1 a + b 1 day work = 1 / 20 a ' s 1 day work = ( 1 / 20 ) * ( 2 / 3 ) = 1 / 30 a alone can finish the work in 30 days answer is a"
Answer: a
Question (gain): a tradesman sold an article at a loss of 20 % . if the selling price had been increased by $ 100 , there would have been a gain of 5 % . what was the cost price of the article ?
Options: a ) $ 100 , b ) $ 200 , c ) $ 300 , d ) $ 400 , e ) $ 500
Rationale: "let c . p . be $ x then , ( 105 % of x ) - ( 80 % of x ) = 100 or 25 % of x = 100 x / 4 = 100 x = 400 c . p . = $ 400 correct option is d"
Answer: d
Question (gain): a shop keeper marked 20 % above the cost price and offered 15 % discount then find it ' s net profit ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 15 %
Rationale: net profit = 20 - 15 + ( 20 * ( - 15 ) / 100 ) = 2 % answer is a
Answer: a
Question (gain): if 0.5 % of a = 65 paise , then the value of a is ?
Options: a ) rs . 130 , b ) rs . 17 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: answer ∵ 0.5 / 100 of a = 65 / 100 ∴ a = rs . ( 65 / 0.5 ) = rs . 130 correct option : a
Answer: a
Question (general): suppose a , b , and c are positive integers with a < b < c such that 1 / a + 1 / b + 1 / c = 1 . what is a + b + c ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 11 , e ) no such integers exist
Rationale: first note that we must have 1 / a < 1 , so a > 1 . since 1 / a > 1 / b > 1 / c , we must also have 1 / a > 1 / 3 ; so a < 3 . thus , a / 2 . now 1 / b + 1 / c = 1 / 2 where 2 < b < c . similar to before , 1 / b > 1 / 4 , so b < 4 . thus , b = 3 . with a = 2 and b = 3 we have 1 / 2 + 1 / 3 + 1 / c = 1 , which is satisfied when c = 6 . to conclude , a + b + c = 2 + 3 + 6 = 11 . correct answer d
Answer: d
Question (general): what is the smallest number which when diminished by 24 , is divisible 5 , 10 , 15 and 20 ?
Options: a ) 276 , b ) 84 , c ) 88 , d ) 90 , e ) 342
Rationale: "required number = ( lcm of 5 , 10 , 15 and 20 ) + 24 = 60 + 24 = 84 option b"
Answer: b
Question (geometry): a 6 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point ?
Options: a ) 2 / 3
b ) 3 / 4
c ) 4 / 5
d ) 5 / 6
e ) 6 / 7
Rationale: the longer wire will form a square with an area more than 1 if the wire is cut at a point within two meters of either end . the probability of this is 4 / 6 = 2 / 3 . the answer is a .
Answer: a
Question (gain): in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 42 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 245 , c ) 150 , d ) 300 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 42 , so 0.14 * { total } = 42 - - > { total } = 300 . answer : d ."
Answer: d
Question (physics): a goods train runs at the speed of 72 km / hr and crosses a 300 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 382 , b ) 782 , c ) 278 , d ) 270 , e ) 220
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 300 ) / 26 = 20 x = 220 m . answer : e"
Answer: e
Question (general): two sets of 3 consecutive positive integers have exactly one integer in common . the sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set ?
Options: a ) 4 , b ) 7 , c ) 6 , d ) 12 , e ) it can not be determined from the information given .
Rationale: "a = ( 2 , 3,4 ) , sum of this = 9 b = ( 4 , 5,6 ) , sum of this = 15 , the differenct between 15 - 9 = 6 hence , 6 is the answer i . e . c"
Answer: c
Question (general): the average mark of the students of a class in a particular exam is 60 . if 5 students whose average mark in that exam is 44 are excluded , the average mark of the remaining will be 80 . find the number of students who wrote the exam ?
Options: a ) 12 , b ) 10 , c ) 7 , d ) 9 , e ) 8
Rationale: "let the number of students who wrote the exam be x . total marks of students = 60 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 60 x - ( 5 * 44 ) = 80 ( x - 5 ) 180 = 20 x = > x = 9 answer : d"
Answer: d
Question (gain): in how many years will a sum of money doubles itself at 18 % per annum on simple interest ?
Options: a ) 5.9 % , b ) 5.5 % , c ) 6 % , d ) 6.4 % , e ) 7.5 %
Rationale: "p = ( p * 18 * r ) / 100 r = 5.5 % answer : b"
Answer: b
Question (physics): how many pieces of 75 cm can be cut from a rope 55.5 meters long ?
Options: a ) 30 , b ) 40 , c ) 60 , d ) none , e ) 74
Rationale: "explanation : total pieces of 75 cm that can be cut from a rope of 55.5 meters long is = ( 55.5 meters ) / ( 75 cm ) = ( 55.5 meters ) / ( 0.75 meters ) = 74 answer : e"
Answer: e
Question (general): a merchant gains or loses , in a bargain , a certain sum . in a second bargain , he gains 380 dollars , and , in a third , loses 70 . in the end he finds he has gained 250 dollars , by the 3 together . how much did he gain or lose bv the first ?
Options: a ) 80 , b ) 60 , c ) - 60 , d ) - 70 , e ) none
Rationale: in this sum , as the profit and loss are opposite in their nature , they must be distinguished by contrary signs . if the profit is marked + , the loss must be - . let x = the sum required . then according to the statement x + 380 - 70 = 250 and x = - 60 . answer c
Answer: c
Question (gain): population is 20000 . pop increases by 10 % every year , then the pop after 3 years is ?
Options: a ) 26630 , b ) 26640 , c ) 36620 , d ) 26620 , e ) 26820
Rationale: population after 1 st year = 20000 * 10 / 100 = 2000 = = = > 20000 + 2000 = 22000 population after 2 nd year = 22000 * 10 / 100 = 2200 = = = > 22000 + 2200 = 24200 population after 3 rd year = 24200 * 10 / 100 = 2420 = = = > 24200 + 2420 = 26620 answer : d
Answer: d
Question (other): find the number of different prime factors of 6440
Options: a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "explanation : l . c . m of 6440 = 2 x 2 x 2 x 5 x 7 x 23 2 , 5 , 7,23 number of different prime factors is 4 . answer : option a"
Answer: a
Question (physics): a train traveling at 72 kmph crosses a platform in 31 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 260 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 31 = 620 m . so , length of platform = 620 - 360 = 260 m imo , answer b"
Answer: b
Question (probability): wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 5 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
Options: a ) 1 / 4 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22
Rationale: p ( 1 and not 2 ) = 5 / 8 * ( 1 - 3 / 5 ) = 1 / 4 answer : a .
Answer: a
Question (general): what is the remainder when 7 ^ 74 - 5 ^ 74 is divided by 12 ?
Options: a ) 1 , b ) 0 , c ) 2 , d ) 3 , e ) none of these
Rationale: "easiest way for me : 7 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 12 * 4 + 1 ) ^ 37 - ( 12 * 2 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : b"
Answer: b
Question (general): joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 35 . he was allowed to drop his lowest score . after doing so , his average test score improved to 40 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80
Rationale: the arithmetic mean of 4 equally weighted tests was 35 . so what we can assume is that we have 4 test scores , each 35 . he dropped his lowest score and the avg went to 40 . this means that the lowest score was not 35 and other three scores had given the lowest score 5 each to make it up to 35 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 35 . so the lowest score = 35 - 15 = 20 answer ( a )
Answer: a
Question (physics): there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 10 days more ?
Options: a ) 220 , b ) 760 , c ) 990 , d ) 880 , e ) 660
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 10 x * 10 = 760 * 20 x = 1520 760 - - - - - - - 760 answer : b"
Answer: b
Question (physics): the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 15 metres ?
Options: a ) 5 , b ) 10 , c ) 3 , d ) 12 , e ) 6
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 15 / 5 = 3 seconds . answer : c"
Answer: c
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 723 grams per kg , what is his percent ?
Options: a ) 38.3 % , b ) 25 % , c ) 77 % , d ) 99 % , e ) 12 %
Rationale: "723 - - - 277 100 - - - ? = > 38.3 % answer : a"
Answer: a
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 800 more than d , what is b ' s share ?
Options: a ) rs . 1600 , b ) rs . 1500 , c ) rs . 2000 , d ) rs . 2500 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 800 x = 800 . b ' s share = rs . 2 x = rs . ( 2 x 800 ) = rs . 1600 . answer = a"
Answer: a
Question (gain): an error 4 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?
Options: a ) 4.05 % , b ) 4.02 % , c ) 8.16 % , d ) 3 % , e ) 2 %
Rationale: "percentage error in calculated area = ( 4 + 4 + ( 4 ã — 4 ) / 100 ) % = 8.16 % answer : c"
Answer: c
Question (other): if the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 5 , what is the ratio of apples to cucumbers ?
Options: a ) 4 : 15 , b ) 1 : 3 , c ) 2 : 5 , d ) 4 : 5 , e ) 7 : 6
Rationale: "apples : bananas = 4 : 3 bananas : cucumbers = 1 : 5 = 3 : 15 so if i have bananas , i ' d have 4 apples and 15 cucumbers apples : cucumbers = 4 : 15 answer : a"
Answer: a
Question (general): if ( t - 8 ) is a factor of t ^ 2 - kt - 40 , then k =
Options: a ) 16 , b ) 1 , c ) 2 , d ) 6 , e ) 14
Rationale: "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 1 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ) ( t + m ) b"
Answer: b
Question (general): a certain number when divided by 95 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 95 + 25 = 120 / 15 = 8 ( remainder ) d"
Answer: d
Question (physics): p alone can complete a job in 4 days . the work done by q alone in one day is equal to one - third of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 1.5 , b ) 2.0 , c ) 2.5 , d ) 3.0 , e ) 3.5
Rationale: p ' s rate is 1 / 4 q ' s rate is 1 / 12 the combined rate is 1 / 4 + 1 / 12 = 1 / 3 if they work together , the job will take 3 days . the answer is d .
Answer: d
Question (gain): a man ' s speed with the current is 12 km / hr and the speed of the current is 2 km / hr . the man ' s speed against the current is
Options: a ) 8 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "man ' s rate in still water = ( 12 - 2 ) km / hr = 10 km / hr . man ' s rate against the current = ( 10 - 2 ) km / hr = 8 km / hr . answer : a"
Answer: a
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 242 runs ?
Options: a ) 6.25 , b ) 5.25 , c ) 6.29 , d ) 6.39 , e ) 6.13
Rationale: "required run rate = [ 242 - ( 3.2 * 10 ) ] / 40 = 210 / 40 = 5.25 answer : b"
Answer: b
Question (physics): the population of a bacteria colony doubles every day . if it was started 8 days ago with 4 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 131072 , e ) 409600
Rationale: "4 ^ 8 ( 2 ) = 131072 the answer is d ."
Answer: d
Question (probability): a coin is tossed six times . what is the probability that there is at the least one tail ?
Options: a ) 63 / 64 , b ) 31 / 37 , c ) 31 / 18 , d ) 31 / 10 , e ) 31 / 19
Rationale: let p ( t ) be the probability of getting least one tail when the coin is tossed six times . = there is not even a single tail . i . e . all the outcomes are heads . = 1 / 64 ; p ( t ) = 1 - 1 / 64 = 63 / 64 answer : a
Answer: a
Question (geometry): how many 3 x 3 x 3 cubes could fit in a 10 x 24 x 16 box ?
Options: a ) 150 , b ) 145 , c ) 138 , d ) 142 , e ) 175
Rationale: the answer is d ) 142 . the 10 x 24 x 16 box has an area of 3840 . if you divide it by 27 ( the total of the 3 x 3 x 3 smaller cube ) you get 142.2 . this means you could fit 142 whole cubes in the larger box .
Answer: d