Cheukting/mathqa huggingface dataset:
Question (gain): arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 20 % profit ?
Options: a ) 15.12 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32
Rationale: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 120 % of rs . 630 = 120 / 100 * 630 = rs . 756 s . p . per kg = 756 / 50 = rs . 15.12 answer : a"
Answer: a
Question (gain): double of quarter of 2 percent written as a decimal is :
Options: a ) 0.01 , b ) 0.0005 , c ) 0.25 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 2 % = 2 * ( 1 / 4 * 2 / 100 ) = 0.01 . answer : a"
Answer: a
Question (physics): a boat covers a certain distance downstream in 1 hour , while it comes back in 11 ⁄ 2 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ?
Options: a ) 14 kmph , b ) 15 kmph , c ) 13 kmph , d ) 12 kmph , e ) none of these
Rationale: "explanation : let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x - 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 11 ⁄ 2 hour . ie , distance travelled downstream in 1 hour = distance travelled upstream in 11 ⁄ 2 hour since distance = speed × time , we have ( x + 3 ) × 1 = ( x − 3 ) ( 3 / 2 ) = > 2 ( x + 3 ) = 3 ( x - 3 ) = > 2 x + 6 = 3 x - 9 = > x = 6 + 9 = 15 kmph . answer : option b"
Answer: b
Question (other): a certain bag contains 100 balls â € ” 50 white , 30 green , 8 yellow , 9 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.88 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 30 + 8 ) / 100 = 88 / 100 = 0.88 . answer is d"
Answer: d
Question (physics): if the wheel is 9 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 18 , b ) 26 , c ) 14 , d ) 18.7 , e ) 91
Rationale: "2 * 22 / 7 * 9 * x = 1056 = > x = 18.7 answer : d"
Answer: d
Question (gain): kanul spent $ 80000 in buying raw materials , $ 30000 in buying machinery and 20 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 135656 , b ) $ 137500 , c ) $ 134446 , d ) $ 123265 , e ) $ 124564
Rationale: "let the total amount be x then , ( 100 - 20 ) % of x = 80000 + 30000 80 % of x = 110000 80 x / 100 = 110000 x = $ 1100000 / 8 x = $ 137500 answer is b"
Answer: b
Question (general): the product of two numbers is 4107 . if the h . c . f . of these numbers is 37 , then the greater number is :
Options: a ) 101 , b ) 107 , c ) 111 , d ) 185 , e ) none
Rationale: "explanation let the numbers be 37 a and 37 b . then , 37 a x 37 b = 4107 ab = 3 . now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 x 1 , 37 x 3 ) i . e . , ( 37 , 111 ) . greater number = 111 . answer c"
Answer: c
Question (general): if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 3 ø 1 ) ø 2 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "3 ø 1 = 2 ^ 3 / 2 ^ 1 = 4 4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 the answer is b ."
Answer: b
Question (general): if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 63 , what is the value of x ?
Options: a ) 60 , b ) 62 , c ) 64 , d ) 61 , e ) 66
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 63 x = 61 answer : d"
Answer: d
Question (general): a movie buff owns movies on dvd and on blu - ray in a ratio of 9 : 2 . if she buys 2 more blu - ray movies , that ratio would change to 17 : 4 . if she owns movies on no other medium , what was the original number of movies in her library before the extra purchase ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 187
Rationale: "if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 9 x and b ( d ) = 2 x now from the next line the new eqn becomes 9 x / ( 2 x + 2 ) = 17 / 4 solving it 36 x = 34 x + 34 x = 17 which means m ( d ) = 153 and b ( d ) = 34 so total initially is m ( d ) + b ( d ) = 187 e"
Answer: e
Question (physics): if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 5 strokes ?
Options: a ) 31 / 32 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 left after 3 rd stroke = 1 / 2 * 1 / 4 = 1 / 8 left after 4 th stroke = 1 / 2 * 1 / 8 = 1 / 16 left after 5 th stroke = 1 / 2 * 1 / 16 = 1 / 32 so removed = 1 - 1 / 32 = 31 / 32
Answer: a
Question (physics): the ratio between the length and the breadth of a rectangular park is 4 : 1 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 1024545 m , b ) 134561 m , c ) 156787 m , d ) 15450 m , e ) 102400 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 4 x metres and breadth = 1 x metres . then , 2 ( 4 x + 1 x ) = 1600 or x = 160 . length = 640 m and breadth = 160 m . area = ( 640 x 160 ) m 2 = 102400 m e"
Answer: e
Question (general): the average weight of 9 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 76 kg , b ) 77 kg , c ) 78.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 9 × 1.5 = 13.5 kg so the weight of new person = 65 + 13.5 = 78.5 kg answer c"
Answer: c
Question (general): find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1344 ?
Options: a ) 1000 , b ) 2217 , c ) 1200 , d ) 2777 , e ) 2991
Rationale: "1344 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1200 answer : c"
Answer: c
Question (gain): there are 100 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of manager to 98 % ?
Options: a ) 1 , b ) 2 , c ) 50 , d ) 49 , e ) 97
Rationale: "we have 99 managers and 1 director . that 1 director to compose 2 % of the total number of people , there must be 50 people in the room , hence 50 managers must leave . answer : c ."
Answer: c
Question (general): a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , b receives :
Options: a ) s . 11,000 , b ) s . 11,300 , c ) s . 11,500 , d ) s . 11,700 , e ) s . 11,900
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . b ' s share = rs . ( 35000 x 17 / 50 ) = rs . 11,900 . e"
Answer: e
Question (general): how many 3 digit positive integers e exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ."
Answer: e
Question (gain): 6.2 is what percent of 1000 ?
Options: a ) 62 % , b ) 6.2 % , c ) 0.62 % , d ) 0.062 % , e ) 0.0062 %
Rationale: "10 % of 1000 is 100 . 6.2 is way less than 100 ( 10 % of 1000 ) . so it can not be 62 % of 1000 . eliminate option a 1 % of 1000 is 10 . 6.2 is less than 10 . so it cant be 6.2 % . eliminate option b ( 0.5 % ) i . e . half of 1 % of 1000 is 5 . but 6.2 is greater than 5 . . so it has to be greater than 0.5 % . . . hence answer is 0.62 % , answer : c"
Answer: c
Question (physics): a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 12 cm . what is the length of the wire ?
Options: a ) 6 cm , b ) 14 cm , c ) 16 cm , d ) 23 cm , e ) 29 cm
Rationale: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 12 ) ^ 2 * h = ( 4 / 3 ) π ( 12 ) ^ 3 = > h = 16 cm answer : c"
Answer: c
Question (physics): a van takes 6 hours to cover a distance of 252 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 28 kmph , b ) 60 kmph , c ) 70 kmph , d ) 80 kmph , e ) 90 kmph
Rationale: "time = 6 distence = 252 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 252 / 9 = 28 kmph a"
Answer: a
Question (general): the ages of two persons differ by 28 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 40,12 , b ) 20,10 , c ) 25,15 , d ) 30,10 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 28 ) years . 5 ( x - 5 ) = ( x + 28 - 5 ) or 4 x = 48 or x = 12 . their present ages are 40 years and 12 years option a"
Answer: a
Question (general): 3 x + y = 21 , and x + 3 y = 1 . find the value of 2 x + 2 y
Options: a ) 20 , b ) 18 , c ) 16 , d ) 11 , e ) 5
Rationale: "add these two equations 4 x + 4 y = 22 divide by 2 ( to get 2 x + 2 y ) answer will be d . 11"
Answer: d
Question (physics): x can finish a work in 20 days . y can finish the same work in 15 days . yworked for 9 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "work done by x in 1 day = 1 / 20 work done by y in 1 day = 1 / 15 work done by y in 9 days = 9 / 15 = 3 / 5 remaining work = 1 – 3 / 5 = 2 / 5 number of days in which x can finish the remaining work = ( 2 / 5 ) / ( 1 / 20 ) = 8 d"
Answer: d
Question (general): thomas worked in the factory @ 4550 / - per week . owner told him to give the amount after one month . then how much amount will be paid to thomas ?
Options: a ) 9500 , b ) 17500 , c ) 18200 , d ) 19500 , e ) 6750
Rationale: total salary paid to thomas in one week : 4550 / - salary for one day : 4550 / 7 = 650 / - total for one month = 650 / - * 30 days = 19500 / - answer is option ( d )
Answer: d
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.6 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 6.5 , c ) 6.15 , d ) 7 , e ) 8
Rationale: "10 overs - run rate = 3.6 runs scored in first 10 overs = 36 remaining overs 40 total runs to be scored = 282 32 runs already scored 282 - 36 = 246 246 runs to be scored in 40 overs let required runrate be x 40 * x = 246 x = 246 / 40 x = 6.15 the required runrate is 6.15 answer : c"
Answer: c
Question (general): in a tree , 3 / 5 of the birds are parrots while the rest are toucans . if 1 / 3 of the parrots are female and 3 / 4 of the toucans are female , what fraction of the birds in the tree are male ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 5 , d ) 3 / 10 , e ) 7 / 10
Rationale: the fraction of birds that are male parrots is ( 2 / 3 ) ( 3 / 5 ) = 2 / 5 . the fraction of birds that are male toucans is ( 1 / 4 ) ( 2 / 5 ) = 1 / 10 . the total fraction of male birds is 2 / 5 + 1 / 10 = 1 / 2 . the answer is a .
Answer: a
Question (gain): working together at their respective constant rates , machine a and machine b can produce 1,800 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1,800 unit total would it produce ?
Options: a ) 25 , b ) 33 , c ) 30 , d ) 67 , e ) 75
Rationale: "1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 1800 units in 24 hrs , so it can produce 1800 * 8 / 24 = 600 units is 8 hrs . 600 is 30 % of 1800 . c is the answer"
Answer: c
Question (probability): a coin is tossed 6 times . what is the probability of getting exactly 5 heads ?
Options: a ) 3 / 8 , b ) 3 / 16 , c ) 5 / 16 , d ) 3 / 32 , e ) 7 / 64
Rationale: "the number of possible outcomes is 2 ^ 6 = 64 there are 6 ways to get exactly 5 heads . p ( exactly 5 heads ) = 6 / 64 = 3 / 32 the answer is d ."
Answer: d
Question (general): at a supermarket , john spent 1 / 4 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 6 on bakery products . if he spent the remaining $ 6 on candy , how much did john spend at the supermarket ?
Options: a ) $ 24 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180
Rationale: "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 4 of his money on fresh fruits and vegetables , or ( 1 / 4 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 6 on bakery products , or ( 1 / 6 ) t . we are also given that he spent the remaining $ 6 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 4 ) t + ( 1 / 3 ) t + ( 1 / 6 ) t + 6 = t to get rid of the fractions we can multiply the entire equation by 12 , and we obtain : 3 t + 4 t + 2 t + 72 = 12 t 9 t + 72 = 12 t 72 = 3 t t = 24 john spent $ 24 at the supermarket . answer : a"
Answer: a
Question (physics): a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 13 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 13 + 12 = 25 . the answer is c .
Answer: c
Question (physics): the population of a bacteria colony doubles every day . if it was started 6 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 128
Rationale: "2 ^ 6 ( 2 ) = 2 ^ 7 = 128 the answer is e ."
Answer: e
Question (gain): in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 7500 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 2700 , c ) 2900 , d ) 2200 , e ) 2300
Rationale: "b number of valid votes = 80 % of 7500 = 6000 . valid votes polled by other candidate = 45 % of 6000 = ( 45 / 100 x 6000 ) = 2700 ."
Answer: b
Question (gain): the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 48.0 billion from $ 85.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 30.4 , c ) 43.5 , d ) 32.5 , e ) 33.8
Rationale: $ 85 - $ 48 = 37 $ ( 37 / 85 ) * 100 = 43.5 % answer : c
Answer: c
Question (general): 10 ^ 23 - 7 is divided by 6 , remainder is ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: anything power by 10 we got 10 and some zeros after that . ( i . e , 1000000000000000 . . . . ) on that , we minus 7 means , we must get last two digits is 93 . and 93 is divided by 6 , we get reminder 3 . answer : a
Answer: a
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 60 questions and secures 110 marks , the no of questions he attempts correctly is :
Options: a ) 34 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "explanation : let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 110 = > 5 x = 170 = > x = 34 answer : a"
Answer: a
Question (general): the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 3.6 miles in the sixth 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 30 , b ) 34 , c ) 38 , d ) 42 , e ) 46
Rationale: "( 3.6 miles / 8 minutes ) * 60 minutes / hour = 27 mph let x be the original speed . x - 5 ( 3 ) = 27 x = 42 mph the answer is d ."
Answer: d
Question (gain): in an office , 20 percent of the workers have at least 5 years of service , and a total of 16 workers have at least 10 years of service . if 90 percent of the workers have fewer than 10 years of service , how many of the workers have at least 5 but fewer than 10 years of service ?
Options: a ) 32 , b ) 64 , c ) 50 , d ) 144 , e ) 160
Rationale: "( 10 / 100 ) workers = 16 = > number of workers = 160 ( 20 / 100 ) * workers = x + 16 = > x = 32 answer a"
Answer: a
Question (general): when a student joe , weighing 45 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?
Options: a ) 7.5 kg , b ) 11 kg , c ) 30 kg , d ) 36.5 kg , e ) 71 kg
Rationale: "after two persons leave the group the average remains the same . that means the weight of the two persons = 45 + 30 = 75 so , the average the two persons = 37.5 that gives the answer 45 - 37.5 = 7.5 answer a"
Answer: a
Question (probability): what is the probability of getting a sum 9 from two throws of dice
Options: a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 12 , d ) 2 / 9 , e ) none of these
Rationale: "explanation : total number of cases = 6 * 6 = 36 favoured cases = [ ( 3,6 ) , ( 4,5 ) , ( 6,3 ) , ( 5,4 ) ] = 4 so probability = 4 / 36 = 1 / 9 answer : b"
Answer: b
Question (general): if pintu is coded as 79523 in a certain code language , how would you code buntu in the same language ?
Options: a ) 13426 , b ) 23523 , c ) 13436 , d ) 14263 , e ) 15263
Rationale: "1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . buntu is 23523 . . . answer : b"
Answer: b
Question (other): if neha is 10 both sonali and priyanka is 15 both sadaf and tanu is 10 . how much is prinka by the same system ?
Options: a ) 8 , b ) 11 , c ) 10 , d ) 15 , e ) 6
Rationale: c prinka is 10 , in a system that awards five for each vowel .
Answer: c
Question (general): if ( a + b ) = 14 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 14 = > a = 14 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 14 - b + 3 - c = > 17 - ( b + c ) = > 17 - 9 = 8 . option b . . ."
Answer: b
Question (gain): during a sale , the price of a pair of shoes is marked down 13 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 90 %
Rationale: "assume the price = 100 price during sale = 87 price after sale = 100 percent increase = 13 / 87 * 100 = 15 % approx . correct option : d"
Answer: d
Question (physics): machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 4200 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 60 / 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 4200 envelopes b will take 4200 / 1400 hrs = 3 hrs so the answer is choice b"
Answer: b
Question (general): the average weight of 8 persons increases by 4.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 101 kg
Rationale: "total weight increased = ( 8 x 4.5 ) kg = 36 kg . weight of new person = ( 65 + 36 ) kg = 101 kg . answer : e"
Answer: e
Question (general): if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 60 , what is the value of c â ˆ ’ a ?
Options: a ) 25 , b ) 30 , c ) 90 , d ) 140 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 120 - - 2 subtracting 1 from 2 we have c - a = 30 ; answer : b"
Answer: b
Question (physics): the lcm and hcf of two numbers are 100000 and 10000 respectively . find the larger of the two numbers if their sum is 110000 .
Options: a ) 100000 , b ) 46 , c ) 577 , d ) 577 , e ) 767
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 100000 * 10000 = 1000000000 so the answer which we are looking for has to be a factor of 1000000000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 1000000000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Question (general): when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum r of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . r = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616 . b"
Answer: b
Question (general): a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 5 years ago ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let ' s say age of richard isr age of david isd age of scott iss now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 5 years ago ? i . e . d - 5 = 14 - 5 = 9 years answer : option a"
Answer: a
Question (general): car dealership x , the total profit from sales increased by 15 percent over the previous years , while the number of cars sold decreased by 15 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 18 % , b ) 20 % , c ) 22 % , d ) 35.29 % , e ) 55 %
Rationale: "let profit be x and cars sold be y originally profit / car = x / y now it is 1.15 x / 0.85 y = 115 / 85 ( x / y ) increase in profit per car = ( ( 30 / 85 ) ( x / y ) ) / ( x / y ) * 100 = 35.29 % answer = d"
Answer: d