Cheukting/mathqa huggingface dataset:
Question (gain): 15 litres of mixture contains 20 % alcohol and the rest water . if 2 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 23 % , c ) 18.3 % , d ) 17.64 % , e ) 21.23 %
Rationale: "alcohol in the 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 2 = 17 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 17 = 17.64 % answer is d"
Answer: d
Question (physics): two pipes p and q can fill a cistern in 10 and 15 minutes respectively . both are opened together , but at the end of 2 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "let x be the total time it takes for the cistern to fill . 2 / 10 + x / 15 = 1 x / 15 = 4 / 5 x = 12 after the first pipe is turned off , it takes 10 more minutes to fill the cistern . the answer is e ."
Answer: e
Question (general): there are 16 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 750 , b ) 900 , c ) 1050 , d ) 1200 , e ) 1350
Rationale: the number of ways to choose two teams is 16 c 2 = 16 * 15 / 2 = 120 the total number of games in the season is 10 * 120 = 1200 . the answer is d .
Answer: d
Question (general): in an examination , the percentage of students qualified to the number of students appeared from school a is 70 % . in school b , the number of students appeared is 20 % more than the students appeared from school a and the number of students qualified from school b is 50 % more than the students qualified from school a . what is the percentage of students qualified to the number of students appeared from school b ?
Options: a ) 30 % , b ) 70 % , c ) 80 % , d ) 87.5 % , e ) none
Rationale: solution let number of students appeared from school a = 100 . then , number of students qualified from school a = 70 . number of students appeared from school b = 120 . number of students qualified from school b = [ 150 / 100 x 70 ] = 105 . required percentage = [ 105 / 120 x 100 ] % = 87.5 % answer d
Answer: d
Question (physics): a man sitting in a train which is travelling at 20 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 ) 72 kmph . , d ) 92 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 20 ) kmph = 92 kmph . answer d"
Answer: d
Question (general): the area of one square is x ^ 2 + 6 x + 9 and the area of another square is 4 x ^ 2 − 20 x + 25 . if the sum of the perimeters of both squares is 52 , what is the value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the areas are ( x + 3 ) ^ 2 and ( 2 x - 5 ) ^ 2 . the lengths of the sides are x + 3 and 2 x - 5 . if we add the two perimeters : 4 ( x + 3 ) + 4 ( 2 x - 5 ) = 52 12 x = 60 x = 5 the answer is c ."
Answer: c
Question (physics): a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 130 m long ?
Options: a ) 39.2 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) none of these
Rationale: "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 130 = 490 meter time taken to cross the platform = 490 / ( 25 / 2 ) = 490 ã — 2 / 25 = 39.2 seconds answer : a"
Answer: a
Question (physics): two trains are traveling from point a to point b such that the speed of first train is 65 kmph and the speed of 2 train is 29 kmph . where is the distance b / w a and b such that the slower train reached 5 hrs late compared to the faster ?
Options: a ) 3 , b ) 65 , c ) 9 , d ) 5 , e ) 31
Rationale: answer : b
Answer: b
Question (probability): if g is to be chosen at random from the set { 5,8 , 7,1 } and k is to be chosen at random from the set { 14 , 8,3 } , what is the probability that gk will be even ?
Options: a ) 1 , b ) 5 , c ) 8 , d ) 4 , e ) 3
Rationale: method - 1 gk will be even when 1 ) g is even and k is odd , probability of g even is ( 1 / 4 ) and probability of k odd is ( 1 / 3 ) , so probability of case ( 1 ) = ( 1 / 4 ) * ( 1 / 3 ) = ( 1 / 12 ) 2 ) g is odd and k is even , probability of g odd is ( 3 / 4 ) and probability of k even is ( 2 / 3 ) , so probability of case ( 2 ) = ( 3 / 4 ) * ( 2 / 3 ) = ( 6 / 12 ) 3 ) g is even and k is even , probability of g even is ( 1 / 4 ) and probability of k even is ( 2 / 3 ) , so probability of case ( 1 ) = ( 1 / 4 ) * ( 2 / 3 ) = ( 2 / 12 ) total favorable probability = ( 1 / 12 ) + ( 6 / 12 ) + ( 2 / 12 ) = ( 12 / 12 ) = 1 answer : option a
Answer: a
Question (geometry): the cost of painting the whole surface area of a cube at the rate of 13 paise per sq . cm is rs . 343.98 . then the volume of the cube is
Options: a ) 8500 cm 3
b ) 9000 cm 3
c ) 9250 cm 3
d ) 9261 cm 3
e ) none
Rationale: solution surface area = ( 34398 / 13 ) ‹ = › 2646 cm 3 ‹ = › 6 a 2 = 2646 ‹ = › a 2 = 441 ‹ = › a = 21 . so , volume = ( 21 x 21 x 21 ) cm 3 = 9261 cm 3 . answer d
Answer: d
Question (physics): a man can row 8 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 7.82 km , b ) 6 km , c ) 5.76 km , d ) 5.66 km , e ) 10 km
Rationale: "m = 8 s = 1.2 ds = 9.2 us = 6.8 x / 9.2 + x / 6.8 = 1 x = 3.91 d = 3.91 * 2 = 7.82 answer : a"
Answer: a
Question (general): the difference between the place values of two fives in the numerical 86510529 is
Options: a ) 0 , b ) 4905 , c ) 49050 , d ) 490500 , e ) none of them
Rationale: "required difference = ( 500000 - 500 ) = 490500 . answer is d"
Answer: d
Question (general): if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 56 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 17 , d ) 29 , e ) 39
Rationale: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 56 = > 45 - [ 28 - { 37 - 15 + * } ] = 56 45 - [ 28 - 37 + 15 - * ] = 56 = > 45 [ 43 - 37 - * ] = 56 45 - [ 6 - * ] = 56 = > 45 - 6 + * = 56 39 + * = 56 = > * = 56 - 39 = 17 answer : c"
Answer: c
Question (general): 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration w of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration w would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"
Answer: d
Question (general): how much percentage 80 is of 480 ?
Options: a ) 16.5 , b ) 14.33 , c ) 12.5 , d ) 15.8 , e ) 16.66
Rationale: 80 * 100 / 480 = 16.66 % answer e
Answer: e
Question (gain): a present value of a machine is $ 2000 . its value depletiation rate is 20 % per annum then find the machine value before 2 years ?
Options: a ) $ 3125 , b ) $ 2945 , c ) $ 3012 , d ) $ 2545 , e ) $ 3150
Rationale: "p = $ 2000 r = 20 % t = 2 years machine value before 2 years = p / [ ( 1 - r / 100 ) ^ t ] = 2000 * 5 / 4 * 5 / 4 = $ 3125 answer is a"
Answer: a
Question (gain): if xerox paper costs 5 cents a sheet and a buyer gets 10 % discount on all xerox paper one buys after the first 2000 papers and 20 % discount after first 10000 papers , how much will it cost to buy 25000 sheets of xerox paper ?
Options: a ) $ 1250 , b ) $ 1060 , c ) $ 1350 , d ) $ 900 , e ) $ 1000
Rationale: "for first 2000 pages - cost 5 cents / paper for 2001 - 10000 - cost 4.5 cents / paper for 10000 + - 4 cents / paper so cost = ( 5 cents * 2000 ) + ( 4.5 cents * 8000 ) + ( 4 cents * 15000 ) = $ 1060 alternatively , ( 0.05 x 2000 ) + ( 0.045 x 8000 ) + ( 0.04 x 15000 ) = 1,060 answer : b"
Answer: b
Question (gain): 3 persons invested rs . 9000 in a joint business . the second person invested rs . 1000 more than the first and the third rs . 1000 more than second . after two years , they gained rs . 1800 . how much third person will get ?
Options: a ) 400 , b ) 800 , c ) 600 , d ) 1200 , e ) 1000
Rationale: first persons investment = x second persons investment = x + 1000 third persons investments = x + 2000 x + x + 1000 + x + 2000 = 9000 3 x = 6000 x = 2000 ratio = 2000 : 3000 : 4000 2 : 3 : 4 4 / 9 * 1800 = 800 answer : b
Answer: b
Question (physics): bombay express left delhi for bombay at 14.30 hrs , travelling at a speed of 60 kmph and rajdhani express left delhi for bombay on the same day at 16.30 hrs , travelling at a speed of 80 kmph . how far away from delhi will the two trains meet ?
Options: a ) 120 km , b ) 360 km , c ) 480 km , d ) 500 km , e ) none
Rationale: sol . suppose they meet x hours after 14.30 hrs . then , 60 x = 80 ( x - 2 ) or x = 8 . ∴ required distance = ( 60 x 8 ) km = 480 km . answer c
Answer: c
Question (gain): a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 600 , what is the reduced price for kg ?
Options: a ) 30 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 600 * ( 25 / 100 ) = 150 - - - - 5 ? - - - - 1 = > rs . 30"
Answer: a
Question (general): the numbers { 1 , 3 , 6 , 7 , 7 , 7 } are used to form 3 2 - digit numbers . if the sum of these 3 numbers is a prime number p , what is the largest possible value of p ?
Options: a ) 97 , b ) 151 , c ) 209 , d ) 211 , e ) 219
Rationale: what is the largest possible sum of these three numbers that we can form ? maximize the first digit : 76 + 73 + 71 = 220 = even , so not a prime . let ' s try next largest sum , switch digits in 76 and we ' ll get : 67 + 73 + 71 = 211 = prime . answer : d .
Answer: d
Question (general): what is the sum of the digits of integer k , if k = ( 10 ^ 40 - 46 )
Options: a ) 351 , b ) 360 , c ) 363 , d ) 369 , e ) 378
Rationale: "there are 41 digits in 10 ^ 4 when we subtract 46 from it , there will be 40 digits left . 10 ^ 4 can be written as 9999999 . . . . ( 40 times ) + 1 so , 10 ^ 40 - 46 = 9999999 . . . . ( 40 times ) + 1 - 46 = 9999999 . . . . ( 40 times ) - 45 consider the last 2 digits , 99 - 45 = 54 the last 2 digits will be 54 . and our number would be 99999 . . . . . . 99954 with 2 less 9 s after subtraction . number of 9 s left are 38 and the last two digits are 54 the sum of the digits will be ( 38 * 9 ) + 5 + 4 = 351 answer : - a"
Answer: a
Question (other): a person want to give his money of $ 2700 to his 3 children a , b , c in the ratio 5 : 6 : 9 . what is the a + c share ?
Options: a ) $ 1890 , b ) $ 2002 , c ) $ 3500 , d ) $ 1500 , e ) $ 5640
Rationale: "a ' s share = 2700 * 5 / 20 = $ 675 c ' s share = 2700 * 9 / 20 = $ 1215 a + d = $ 1890 answer is a"
Answer: a
Question (general): let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 81 th number in this set ?
Options: a ) 605 , b ) 608 , c ) 613 , d ) 616 , e ) 645
Rationale: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 81 th number = 8 * ( 81 - 1 ) + 5 = 645 answer = e"
Answer: e
Question (general): how many multiples of 5 are there between 0 and 358 ?
Options: a ) 54 , b ) 75 , c ) 76 , d ) 71 , e ) 58
Rationale: "5 * 1 = 5 5 * 71 = 355 total number of multiples = ( 71 + 1 ) = 72 answer d"
Answer: d
Question (gain): a bowl was filled with 10 ounces of water , and 0.012 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 6 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 012 * 50 = . 012 * 100 / 2 = 1.2 / 2 = . 6 percent of the original amount of water evaporated during this period = ( . 6 / 10 ) * 100 % = 6 % answer d"
Answer: d
Question (other): the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 1 / 9 is given by ?
Options: a ) 7 / 98 , b ) 1 / 48 , c ) 4 / 189 , d ) 1 / 96 , e ) 1 / 68
Rationale: "2 / 3 * 6 / 7 * 1 / 3 * 1 / 9 = 12 / 567 = 4 / 189 answer : c"
Answer: c
Question (general): a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 9 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 39 , b ) 33 , c ) 27 , d ) 21 , e ) 10
Rationale: "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 9 = > m = 27 answer c"
Answer: c
Question (general): company z has 61 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .
Options: a ) 6 , b ) 7 , c ) 13 , d ) 9 , e ) 12
Rationale: say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 61 . now , plug options for x . only c and e give an integer value for y . but only for c x > y as needed . answer : c .
Answer: c
Question (general): when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 17 ] * [ 4 ] = ?
Options: a ) [ 22 ] , b ) [ 44 ] , c ) [ 105 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 17 ] * [ 4 ] = ( 2 * 17 + 1 ) ( 4 / 2 + 1 ) = [ 105 ] . ans - c"
Answer: c
Question (general): a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 155 . find the unknown rate of two towels ?
Options: a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600
Rationale: 10 * 155 = 1550 3 * 100 + 5 * 150 = 1050 1550 – 1050 = 500 c
Answer: c
Question (general): the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 7 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 25 , b ) 35 , c ) 75 , d ) 80 , e ) 79
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 7 = 75 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 â € “ 316 = 4 a = e + 4 = 75 + 4 = 79 e"
Answer: e
Question (general): if there are 4 peanuts in a box and mary puts 4 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "4 + 4 = 8 correct answer is a ) 8"
Answer: a
Question (physics): maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 50 kilometers , maxwell ' s walking speed is 3 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 33.3 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 50 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 3 = 9 kms / hr time taken = 50 / 9 = 5.55 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 5.55 = 33.3 kms . . . answer - d"
Answer: d
Question (general): the average marks of 30 students in a class is 60 . but a student mark is wrongly noted as 90 instead of 15 then find the correct average marks ?
Options: a ) 55.65 , b ) 57.5 , c ) 62.5 , d ) 45.25 , e ) 50
Rationale: correct avg marks = 60 + ( 15 - 90 ) / 30 avg = 60 - 2.5 = 57.5 answer is b
Answer: b
Question (physics): there are two inlets and one outlet to a cistern . one of the inlets takes 2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern . both of the inlets are turned on at 9 : 00 am with the cistern completely empty , and at 10 : 00 am , the outlet is turned on and it takes 1 more hour to fill the cistern completely . how much time does the outlet working alone takes to empty the cistern when the cistern is full ?
Options: a ) 2 hours , b ) 2.5 hours , c ) 3 hours , d ) 3.5 hours , e ) 4 hours
Rationale: the combined inflow rate of the two inlets is 1 / 2 + 1 / 4 = 3 / 4 cistern / hour . thus , working together , it takes 4 / 3 hours ( time is reciprocal of rate ) to fill the cistern . from 9 : 00 am to 10 : 00 am , so in 1 hours , the inlet pipes will fill ( time ) * ( rate ) = 1 * 3 / 4 = 3 / 4 th of the cistern . then the outlet is turned on and the remaining 1 / 4 th of the cistern is filled in 1 hour . letting x to be the rate of the outlet , we would have : 3 / 4 - x = 1 / 4 - - > x = 1 / 2 cistern / hour , which means that it takes 2 hours the outlet working alone to empty the cistern . answer : a
Answer: a
Question (other): if log 0.318 = 0.3364 and log 0.317 = 0.33320 then log 0.319 = ?
Options: a ) 0.33365 , b ) 0.3368 , c ) 0.3396 , d ) 0.3369 , e ) 0.3469
Rationale: log 0.318 / log 0.317 = log ( 0.318 - 0.317 ) = log 0.001 = 0.3364 / 0.33320 = 1.0096 now , log 0.318 * log 0.001 = log ( 0.318 + 0.001 ) = log 0.319 = 0.3364 * 1.0096 = 0.3396 so option c answer : c
Answer: c
Question (general): the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 50 ( 50,000 / 1,000 = 50 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 50 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 6 = 64 , i . e . the population has to double 6 times . since it takes the population 2 minutes to double once it takes 6 * 2 minutes = 12 minutes to double nine times . thus , solution b = 12 is correct ."
Answer: b
Question (physics): a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 900 m long ?
Options: a ) 200 sec , b ) 210 sec , c ) 167 sec , d ) 197 sec , e ) 179 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2100 m t = d / s t = 2100 / 10 t = 210 sec answer : b"
Answer: b
Question (general): we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 368 . how many math books did we buy ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: m + h = 80 h = 80 - m 4 m + 5 h = 368 4 m + 5 * ( 80 - m ) = 368 m = 32 the answer is b .
Answer: b
Question (physics): how many seconds will a 420 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 30 km / hr ?
Options: a ) 25 , b ) 63 , c ) 40 , d ) 45 , e ) 60
Rationale: "explanation : speed of train relatively to man = ( 30 - 6 ) km / hr = 24 km / hr = ( 24 x 5 / 18 ) m / sec = 6.66 m / sec time taken to pass the man = ( 420 / 6.66 ) sec = 63 sec . answer : b"
Answer: b
Question (general): if x + y = 25 and x 2 y 3 + y 2 x 3 = 25 , what is the value of xy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: xy = 1 as x + y = 25 x 2 y 3 + y 2 x 3 = 25 x 2 y 2 ( y + x ) = 25 substituting x + y x 2 y 2 = 1 xy = 1 answer : a
Answer: a
Question (general): there is a 30 % increase in the price of an article in the first year , a 20 % decrease in the second year and a 10 % increase in the next year . if the final price of the article is rs . 2288 , then what was the price of the article initially ?
Options: a ) rs . 2008 , b ) rs . 2022 , c ) rs . 2000 , d ) rs . 2029 , e ) rs . 2021
Rationale: let the price of the article , four years age be rs . 100 in the 1 st year , price of the article = 100 + 30 = rs . 130 . in the 2 nd year , price = 130 - 20 % of 130 = 130 - 26 = rs . 104 . in the 3 rd year , price = 104 + 10 % of 104 = 104 + 10.4 = rs . 114.40 . but present price of the article is rs . 2288 for 114.4 - - - > 100 ; 2288 - - - > ? required price = ( 2288 * 100 ) / 114.4 = 20 * 100 = rs . 2000 . answer : c
Answer: c
Question (general): if p ( a ) = 2 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 7 / 25 , b ) 4 / 25 , c ) 8 / 25 , d ) 2 / 13 , e ) 3 / 17
Rationale: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 2 / 5 . 2 / 5 p ( a n b ) = 4 / 25 . b"
Answer: b
Question (general): if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 64 and ( y - 1 ) ^ 2 is less than 64 , what is the sum of the maximum possible value of xy and the minimum possible value of xy ?
Options: a ) - 16 , b ) - 18 , c ) 0 , d ) 14 , e ) 16
Rationale: "( x + 1 ) ^ 2 < = 64 x < = 7 x > = - 9 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 9 × - 6 = 54 minimum possible value of xy is - 9 × 8 = - 72 - 72 + 54 = - 18 answer : b"
Answer: b
Question (gain): if the difference between compound interest ( interest compounded yearly ) and simple interest on a sum for 2 years at 10 % p . a . is rs . 150 then sum is
Options: a ) rs . 12000 , b ) rs . 15000 , c ) rs . 13000 , d ) rs . 10000 , e ) rs . 14000
Rationale: compund interest = p [ 1 + r / 100 ] ^ t - p ci = p [ 21 / 100 ] simple interest = ptr / 100 si = p [ 20 / 100 ] difference p [ 21 / 100 ] - p [ 20 / 100 ] = 150 p = 15000 answer : b
Answer: b
Question (physics): a leak in the bottom of a tank can empty the full tank in 7 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 7960 , c ) 8290 , d ) 6048 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 7 - 1 / 12 ) = 5 / 84 work done by the inlet in 1 min . = ( 5 / 84 × 1 / 60 ) = 0.000992 volume of 0.000992 part = 6 litres . therefore , volume of whole = ( ( 1 / 0.000992 ) × 6 ) ‹ = › 6048 litres . answer d"
Answer: d
Question (probability): in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 500 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 340 , b ) 346 , c ) 352 , d ) 365 , e ) 370
Rationale: number of newborns that can die in first month = 1 / 10 * 500 = 50 survived = 450 number of newborns that can die in second month = 1 / 10 * 450 = 45 survived = 405 number of newborns that can die in third month = 1 / 10 * 405 = 40 survived = 365 answer : d
Answer: d
Question (probability): kim has 5 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 10 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25
Rationale: "total pairs = 10 c 2 = 45 ; same color pairs = 5 c 1 * 1 c 1 = 5 ; prob = 1 / 9 or 2 / 10 * 1 / 9 * 5 = 1 / 9 ans c"
Answer: c
Question (general): the mean of 50 observations was 36 . it was found later that an observation 45 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.24 , b ) 36.14 , c ) 36.24 , d ) 36.44 , e ) none
Rationale: "solution correct sum = ( 36 x 50 + 45 - 23 ) = 1822 . â ˆ ´ correct mean = 1822 / 50 = 36.44 . answer d"
Answer: d