Cheukting/mathqa huggingface dataset:
Question (physics): calculate the time it will take for a full tank to become completely empty due to a leak given that the tank could be filled in 7 hours , but due to the leak in its bottom it takes 8 hours to be filled ?
Options: a ) 59 hours , b ) 54 hours , c ) 59 hours , d ) 56 hours , e ) 26 hours
Rationale: part filled without leak in 1 hour = 1 / 7 part filled with leak in 1 hour = 1 / 8 work done by leak in 1 hour = 1 / 7 â ˆ ’ 1 / 8 = 56 hours answer : d
Answer: d
Question (physics): a is 2 times as fast as b . a alone can do the work in 20 days . if a and b working together in how many days will the work be completed ?
Options: a ) 23 , b ) 13 , c ) 21 , d ) 24 , e ) 25
Rationale: "a can finish 1 work in 20 days b can finish 1 / 2 work in 20 days - since a is 2 faster than b this means b can finish 1 work in 20 * 2 days = 40 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 40 / ( 20 + 40 ) = 13 days so answer is b"
Answer: b
Question (general): company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.2 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 3 / 8 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: "the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.2 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 24 hours . total hours = 64 . then the fraction would be 24 / 64 = 3 / 8 . therefore answer a ."
Answer: a
Question (physics): a train leaves mumabai at 9 am at a speed of 30 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 60 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 27 , b ) 279 , c ) 60 , d ) 278 , e ) 379
Rationale: when the second train leaves mumbai the first train covers 30 * 1 = 30 km so , the distance between first train and second train is 30 km at 10.00 am time taken by the trains to meet = distance / relative speed = 30 / ( 60 - 30 ) = 1 hours so , the two trains meet at 11 a . m . the two trains meet 1 * 60 = 60 km away from mumbai . answer : c
Answer: c
Question (general): a = 4 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get 2 different values and answer is c . . . ."
Answer: c
Question (general): a envelop weight 8.5 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.6 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg
Rationale: "800 * 8.5 6800.0 gm 6.8 kg answer : b"
Answer: b
Question (gain): in a city , 35 % of the population is composed of migrants , 20 % of whom are from rural areas . of the local population , 48 % is female while this figure for rural and urban migrants is 30 % and 40 % respectively . if the total population of the city is 728400 , what is its female population ?
Options: a ) 324138 , b ) 248888 , c ) 378908 , d ) 277880 , e ) 379010
Rationale: explanation : total population = 728400 migrants = 35 % of 728400 = 254940 local population = ( 728400 - 254940 ) = 473460 . rural migrants = 20 % of 254940 = 50988 urban migrants = ( 254940 - 50988 ) = 203952 female population = 48 % of 473460 + 30 % of 50988 + 40 % of 203952 = 324138 answer : a
Answer: a
Question (general): a batsman scored 120 runs whichincluded 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets ?
Options: a ) 40 % , b ) 50 % , c ) 65 % , d ) 68 % , e ) 70 %
Rationale: "number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 120 - ( 60 ) = 60 now , we need to calculate 60 is what percent of 120 . = > 60 / 120 * 100 = 50 % b"
Answer: b
Question (general): 397 x 397 + 104 x 104 + 2 x 400 x 104 = x ?
Options: a ) 234341 , b ) 235633 , c ) 234677 , d ) 315656 , e ) 251501
Rationale: "given exp . = ( 397 ) 2 + ( 104 ) 2 + 2 x 397 x 104 = ( 397 + 104 ) 2 = ( 501 ) 2 = ( 500 + 1 ) 2 = ( 5002 ) + ( 1 ) 2 + ( 3 x 500 x 1 ) = 250000 + 1 + 1500 = 251501 e"
Answer: e
Question (general): the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 3 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 44 / 7 , b ) 9 / 8 , c ) 25 / 8 , d ) 3 / 4 , e ) 7 / 8
Rationale: "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 3 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 3 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 3 * 2 b * b 3 b - 2 b ^ 2 = 6 b ^ 2 3 b = 8 b ^ 2 b = 3 / 8 = 3 / 8 so , a = 2 b = 3 / 4 the correct answer is d ."
Answer: d
Question (physics): john goes to his office by car at a speed of 40 kmph and reaches 8 minutes earlier . if he goes at a speed of 30 kmph , he reaches 4 mins late . what is the distance from his house to office ?
Options: a ) 18 km , b ) 20 km , c ) 22 km , d ) 24 km , e ) 30 km
Rationale: let his office time be 10 a . m . he reaches office at 8 minutes earlier when he travels at 40 kmph = > he reaches at 9 : 52 a . m he reaches his office 4 minutes late when travels at 30 kmph speed = > he reaches at 10.04 a . m the time difference is ( 10.04 – 9.52 ) = 12 minutes let the distance be d and time = distance speed t 1 – t 2 = 12 minutes = 12 / 60 hours = 1 / 5 hours d / 30 – d / 40 = 1 / 5 ( 4 d - 3 d ) / 120 = 1 / 5 d = 24 km
Answer: d
Question (general): a certain list consists of 11 different numbers . if n is in the list and n is 5 times the average ( arithmetic mean ) of the other 10 numbers in the list , then n is what fraction of the sum of the 11 numbers in the list ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 4 , d ) 3 / 5 , e ) 1 / 6
Rationale: "series : a 1 , a 2 . . . . a 10 , n sum of a 1 + a 2 + . . . + a 10 = 10 * x ( x = average ) so , n = 5 * x hence , a 1 + a 2 + . . + a 10 + n = 15 x so , the fraction asked = 5 x / 15 x = 1 / 3 answer is a"
Answer: a
Question (gain): compound interest of rs . 4000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .
Options: a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 630 , e ) none of the above
Rationale: 10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 4000 [ 1 + ( 5 / 100 ) ] ^ 3 - 4000 = 4000 [ ( 21 / 20 ) ^ 3 - 1 ] = 4000 ( 9261 - 8000 ) / 8000 = 4 * 1261 / 8 = 630 answer : d
Answer: d
Question (physics): find the length of the longest pole that can be placed in an indoor stadium 24 m long , 18 m wide and 16 m high
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "sqrt ( 1156 ) = 34 becoz max length is cuboid diagonal d = sqrt ( l ^ 2 + b ^ 2 + h ^ 2 ) where l lenght b breadth & h height answer : d"
Answer: d
Question (physics): one hour before john started walking from p to q , a distance of 13 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 9 miles , d ) 9,6 miles , e ) 12 miles
Rationale: "ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 13 - 3 = 10 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 10 miles so it will take them 10 / 5 = 2 hours to meet . in 2 hrs , ann would have covered 2 hrs * 3 miles per hour = 6 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 6 = 9 miles . answer ( c )"
Answer: c
Question (gain): sheela deposits rs . 3800 in bank savings account . if this is 22 % of her monthly income . what is her monthly income in ?
Options: a ) 22000 , b ) 20000 , c ) 25123 , d ) 17272 , e ) none of these
Rationale: "explanation : 22 % of income = rs . 3800 100 % of income = 3800 x 100 / 22 = rs . 17272 answer : d"
Answer: d
Question (physics): one pipe can fill a pool 1.5 times faster than a second pipe . when both pipes are opened , they fill the pool in four hours . how long would it take to fill the pool if only the slower pipe is used ?
Options: a ) 11.25 , b ) 11.52 , c ) 1.25 , d ) 9 , e ) 10
Rationale: "say the rate of the slower pipe is r pool / hour , then the rate of the faster pipe would be 1.5 r = 3 r / 2 . since when both pipes are opened , they fill the pool in four hours , then their combined rate is 1 / 4 pool / hour . thus we have that r + 3 r / 2 = 1 / 4 - - > r = 1 / 10 pool / hour - - > time is reciprocal of rate thus it ' s 10 / 1 = 10 hours . answer : e ."
Answer: e
Question (general): 3 photographers , lisa , mike and norm , take photos of a wedding . the total of lisa and mikes photos is 60 less than the sum of mike ' s and norms . if norms photos number 10 more than twice the number of lisa ' s photos , then how many photos did norm take ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 110 , e ) 80
Rationale: l + m = m + n - 60 / n = 2 l + 10 60 = m + n - l - m 60 = n - l 60 = 2 l + 10 - l 50 = l 2 ( 50 ) + 10 = 110 d
Answer: d
Question (geometry): the area of a rectangle is 360 sq . m . if its length is increased by 10 m and its width is decreased by 6 m , then its area does not change . find the perimeter of the original rectangle .
Options: a ) 74 m
b ) 75 m
c ) 76 m
d ) 77 m
e ) 78 m
Rationale: let l and b are the length and width of the original rectangle . since , l * b = 360 sq . m - ( 1 ) now , a / c to the problem ( l + 10 ) * ( b - 6 ) = 360 sq . m therefore , b = 6 ( 1 + l / 10 ) - ( 2 ) l * l + 10 l - 600 = 0 { by using equations 1 and 2 } thereafter , ( l - 20 ) ( l + 30 ) = 0 hence , l = 20 m b = 18 m { by using equation 2 } now , perimeter of the original rectangle = 2 ( l + b ) = 2 ( 20 + 18 ) = 76 m answer : c
Answer: c
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 39 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 39 / 3 = 13 kmph answer : b"
Answer: b
Question (geometry): in measuring the sides of a rectangle , one side is taken 7 % in excess , and the other 6 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.58 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 61 / 57 ) x ( 47 / 50 ) y = ( 867 / 862 ) ( xy ) error in measurement = ( 867 / 862 ) xy - xy = ( 5 / 862 ) xy error percentage = [ ( 5 / 862 ) xy ( 1 / xy ) 100 ] % = ( 29 / 50 ) % = 0.58 % . answer is e ."
Answer: e
Question (geometry): how many squares are there between 2011 to 2300 ? ? ? ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: nos . are 2025 , 2116 , 2209 answers is 3 answer : a
Answer: a
Question (general): the average age of a group of 10 students is 14 years . if 5 more students join the group , the average age rises by 1 year . the average age of the new students is :
Options: a ) 22 , b ) 38 , c ) 11 , d ) 17 , e ) 91
Rationale: explanation : total age of the 10 students = 10 × 14 = 140 total age of 15 students including the newly joined 5 students = 15 × 15 = 225 total age of the new students = 225 − 140 = 85 average age = 85 / 5 = 17 years answer : d
Answer: d
Question (general): average expenditure of a person for the first 3 days of a week is rs . 310 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 390 , d ) 430 , e ) none
Rationale: "explanation : assumed mean = rs . 310 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 310 + rs . 40 = rs . 350 correct option : a"
Answer: a
Question (physics): if the perimeter of a rectangular garden is 800 m , its length when its breadth is 100 m is ?
Options: a ) 286 m , b ) 899 m , c ) 300 m , d ) 166 m , e ) 187 m
Rationale: "2 ( l + 100 ) = 800 = > l = 300 m answer : c"
Answer: c
Question (gain): two equal sums of money were invested , one at 4 % and the other at 4.5 % . at the end of 7 years , the simple interest received from the latter exceeded to that received from the former by 31.50 . each sum was :
Options: a ) 1200 , b ) 600 , c ) 750 , d ) 900 , e ) none of these
Rationale: difference of s . i . = √ 31.50 let each sum be x . then x × 4 1 / 2 × 7 / 100 − x × 4 × 7 / 100 = 31.50 or 7 ⁄ 100 x × 1 ⁄ 2 = 63 ⁄ 2 or x = 900 answer d
Answer: d
Question (general): shekar scored 76 , 65 , 82 , 67 and 75 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 73
Rationale: "explanation : average = ( 76 + 65 + 82 + 67 + 75 ) / 5 = 365 / 5 = 73 hence average = 73 answer : e"
Answer: e
Question (general): tickets for all but 100 seats in a 10000 - seat stadium were sold . of the tickets sold , 30 % were sold at half price and the remaining tickets were sold at the full price of $ 2 . what was the total revenue from ticket sales ?
Options: a ) $ 16,830 , b ) $ 17,820 , c ) $ 18,000 , d ) $ 19,800 , e ) $ 21,780
Rationale: 10000 seats - - > full price : half price = 7000 : 3000 price when all seats are filled = 14000 + 3000 = 17000 100 seats are unsold - - > loss due to unfilled seats = 30 + 2 * 70 = 170 revenue = 17000 - 170 = 16830 answer : a
Answer: a
Question (gain): a and b started a business investing rs . 10,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 3 : 2 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 2 , e ) 18 : 4
Rationale: "a : b = 10000 : 20000 = 1 : 2 answer : d"
Answer: d
Question (gain): rs . 6000 is lent out in two parts . one part is lent at 7 % p . a simple interest and the other is lent at 9 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 9 : 3 , b ) 9 : 5 , c ) 5 : 8 , d ) 5 : 4 , e ) 9 : 2
Rationale: "let the amount lent at 7 % be rs . x amount lent at 9 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 9 / 100 ( 6000 - x ) = 540 - 2 x / 100 = > 540 - 1 / 50 x = 450 = > x = 4500 amount lent at 10 % = 1500 required ratio = 4500 : 1500 = 9 : 3 answer : a"
Answer: a
Question (physics): a man sitting in a train which is travelling at 15 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 97 kmph . , d ) 80 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 15 ) kmph = 97 kmph . answer c"
Answer: c
Question (other): there are 35 student in a school . 20 if them speek hindi 19 of them speak eng 9 of them speak both , then how many student neithe speak eng nor speak hindi
Options: a ) 28 , b ) 30 , c ) 32 , d ) 35 , e ) none of these
Rationale: total number of students = 35 no of hindi speaking students ( h ) = 20 no of english speaking students ( e ) = 19 h intersection e = 9 thus h union e = 20 + 19 - 9 = 30 thus number of student neithe speak eng nor speak hindi = 35 - 30 = 5 answer : e
Answer: e
Question (general): a student chose a number , multiplied it by 2 , then subtracted 152 from the result and got 102 . what was the number he chose ?
Options: a ) 127 , b ) 100 , c ) 129 , d ) 160 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 152 = 102 2 x = 254 x = 127 correct answer a"
Answer: a
Question (gain): the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 50 feet wide by 150 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
Options: a ) 1000 min , b ) 1200 min , c ) 1300 min , d ) 1400 min , e ) 1600 min
Rationale: volume of pool = 50 * 150 * 10 cu . ft , 80 % full = 50 * 150 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 50 * 150 * 10 * 0.8 / 60 min = 1000 min a
Answer: a
Question (general): if a is an integer greater than 9 but less than 26 and b is an integer greater than 14 but less than 31 , what is the range of a / b ?
Options: a ) 1 , b ) 1 / 2 , c ) 5 / 6 , d ) 2 / 3 , e ) 4 / 3
Rationale: "range of a / b = max ( a / b ) - min ( a / b ) to get max ( a / b ) = > max ( a ) / min ( b ) = 25 / 15 to get min ( a / b ) = > min ( a ) / max ( b ) = 10 / 30 range = 25 / 15 - 10 / 30 = 4 / 3"
Answer: e
Question (gain): if the cost price is 40 % of selling price . then what is the profit percent .
Options: a ) 150 % , b ) 120 % , c ) 130 % , d ) 200 % , e ) none of these
Rationale: "explanation : let the s . p = 100 then c . p . = 40 profit = 60 profit % = ( 60 / 40 ) * 100 = 150 % . answer : a"
Answer: a
Question (general): when positive integer x is divided by positive integer y , the remainder is 12 . if x / y = 75.12 , what is the value of y ?
Options: a ) 84 , b ) 98 , c ) 51 , d ) 65 , e ) 100
Rationale: "when positive integer x is divided by positive integer y , the remainder is 12 - - > x = qy + 12 ; x / y = 75.12 - - > x = 75 y + 0.12 y ( so q above equals to 75 ) ; 0.12 y = 12 - - > y = 100 . answer : e ."
Answer: e
Question (general): the cost to park a car in a certain parking garage is $ 20.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 3.58 , b ) $ 1.67 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 2.50
Rationale: "total cost of parking for 9 hours = 20 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 20 + 7 * 1.75 = 32.25 thus the average parking price = 32.25 / 9 = 3.58 $ a is the correct answer ."
Answer: a
Question (general): the unit digit in the product ( 611 * 704 * 912 * 261 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 1 * 4 * 2 * 1 ) = 2 answer : a"
Answer: a
Question (physics): two trains are moving in opposite directions with speed of 150 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds
Options: a ) 56 , b ) 48 , c ) 47 , d ) 30 , e ) 25
Rationale: "explanation : relative speed = 150 + 90 = 240 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 240 hr = 1 / 120 hr = 3600 / 120 seconds = 30 seconds answer : option d"
Answer: d
Question (physics): a train 60 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 2 , e ) 3
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 60 * 3 / 55 = 3 sec . answer e"
Answer: e
Question (general): if the sum and difference of two numbers are 20 and 10 respectively , then the difference of their square is :
Options: a ) 12 , b ) 28 , c ) 160 , d ) 200 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 20 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 20 * 10 = 200 . answer : d"
Answer: d
Question (gain): a 340 - liter solution of kola is made from 75 % water , 5 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 12 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 6 % . , b ) 7.5 % . , c ) 19.6 % . , d ) 10.5 % . , e ) 11 % .
Rationale: "denominator : 340 + 12 + 3.2 + 6.8 = 362 numerator : 340 ( 1 - . 75 - . 05 ) + 3.2 340 ( 0.2 ) + 3.2 68 + 3.2 71.2 ratio : 71.2 / 362 = 0.196 answer : c"
Answer: c
Question (general): the average mark of the students of a class in a particular exam is 90 . if 2 students whose average mark in that exam is 45 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam ?
Options: a ) 10 , b ) 40 , c ) 20 , d ) 30 , e ) 25
Rationale: "let the number of students who wrote the exam be x . total marks of students = 90 x . total marks of ( x - 2 ) students = 95 ( x - 2 ) 90 x - ( 2 * 45 ) = 95 ( x - 2 ) 100 = 5 x = > x = 20 answer : c"
Answer: c
Question (general): a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 250 more than a :
Options: a ) 2348 , b ) 7250 , c ) 2767 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 250 total earning = \ inline \ frac { 58 xy } { 100 } = 7250 answer : b ) rs . 7250"
Answer: b
Question (general): when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 11 , the remainder is 9 . what is the smallest positive integer k such that k + n is a multiple of 33 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "n = 3 p + 1 = 11 q + 9 n + 2 = 3 p + 3 = 11 q + 11 n + 2 is a multiple of 3 and 11 , so it is a multiple of 33 . the answer is a ."
Answer: a
Question (physics): a copy machine , working at a constant rate , makes 35 copies per minute . a second copy machine , working at a constant rate , makes 75 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 90 , b ) 2,700 , c ) 3,300 , d ) 5,400 , e ) 324,000
Rationale: "together the two machines make 35 + 75 = 110 copies per minute . so , in half an hour they will make 110 * 30 = 3,300 copies . answer : c ."
Answer: c