Cheukting/mathqa huggingface dataset:
Question (general): on a certain date , pat invested $ 6000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24000 , in how many years total will the total value of the investment plus interest increase to $ 48000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: 24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a .
Answer: a
Question (general): equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 6 full and other jar 1 / 5 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 1 / 3 , d ) 7 / 12 , e ) 2 / 3
Rationale: "same amount of water made bigger jar 1 / 6 full , thenthe same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 6 + 1 / 6 = 2 / 6 = 1 / 3 full . answer : c ."
Answer: c
Question (physics): abel can complete a work in 10 days , ben in 14 days and carla in 15 days . all of them began the work together , but abel had to leave after 2 days and ben 3 days before the completion of the work . how long did the work last ?
Options: a ) 6 , b ) 7 , c ) 7 10 / 29 , d ) 9 , e ) 10
Rationale: "abel in the 2 days that he worked completed 1 / 5 of the job = 4 / 5 remains then if ben had to leave 3 days before the completion , this means that carla had to work alone for these 3 days in which she completed 1 / 5 of the job . now together , ben and carla completed the job in ( 1 / 14 + 1 / 15 ) ( t ) = 3 / 5 29 / 210 ( t ) = 3 / 5 - - - > t = 126 / 29 therefore , these 4 10 / 29 days worked plus the 3 days that carla had to work by herself add to 7 10 / 29 days answer : c"
Answer: c
Question (geometry): what is the smallest positive integer that can be multiplied by 432 to make it a perfect square ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 11
Rationale: "432 = 2 ^ 4 * 3 ^ 2 * 3 therefore the smallest integer to multiplied to 1008 to make it a perfect square is 3 . answer b ."
Answer: b
Question (general): the price of lunch for 14 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12.85 , c ) 13.8 , d ) 14 , e ) 15.87
Rationale: "clearly b is the answer i used poe here lets consider option ( b ) 14 * 12.85 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo b"
Answer: b
Question (general): the difference between the place values of two sevens in the numeral 69758472 is
Options: a ) 0 , b ) 100 , c ) 6993 , d ) 699930 , e ) none of these
Rationale: "required difference = ( 700000 - 70 ) = 699930 answer : option d"
Answer: d
Question (probability): in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turnon to be white , if all possible hypothesis concerning thecolor of theballs that initiallyin the bag were equally possible ?
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 3 / 5 , d ) 3 / 8 , e ) 4 / 9
Rationale: since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b
Answer: b
Question (physics): 1000 men have provisions for 20 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 12.8 , b ) 12.6 , c ) 12.5 , d ) 12.2 , e ) 16.6
Rationale: "1000 * 20 = 1200 * x x = 16.6 . answer : e"
Answer: e
Question (probability): a meeting has to be conducted with 3 managers . find the number of ways in which the managers be selected from among 6 managers , if 2 managers will not attend the meeting together ?
Options: a ) 18 , b ) 20 , c ) 16 , d ) 22 , e ) 24
Rationale: "we can either choose all 3 people from 4 manager who have no problems or choose 2 from the 4 and 1 from the 2 managers who have a problem sitting together so 4 c 3 + ( 4 c 2 * 2 c 1 ) this is 4 + 12 = 16 answer : c"
Answer: c
Question (gain): the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is ?
Options: a ) 500 , b ) 277 , c ) 266 , d ) 188 , e ) 123
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 112 = rs . 500 answer : a"
Answer: a
Question (general): the total marks obtained by a student in mathematics and physics is 90 and his score in chemistry is 30 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 90 and c - p = 30 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 90 + 30 ) / 2 = 60 . answer : e"
Answer: e
Question (general): if x is less than y by 20 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 66.66 % , e ) none of these
Rationale: using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 20 % ) = > 20 / ( 100 - 20 ) * 100 = 25 % answer : b
Answer: b
Question (general): a picnic attracts 200 persons . there are 20 more men than women , and 20 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 65 , c ) 110 , d ) 130 , e ) 200
Rationale: adult + children = 200 let , children = y then , adult = y + 20 i . e . y + ( y + 20 ) = 200 i . e . y = 900 i . e . adult = 90 + 20 = 110 adults include only men and women i . e . men + women = 110 let women , w = x then men , m = x + 20 i . e . x + ( x + 20 ) = 2 x + 20 = 110 i . e . x = 45 i . e . men , m = 45 + 20 = 65 answer : option b
Answer: b
Question (general): the smallest fraction , which each of 6 / 7 , 5 / 14 , 10 / 21 will divide exactly is :
Options: a ) 30 / 7 , b ) 30 / 98 , c ) 60 / 147 , d ) 50 / 294 , e ) 52 / 294
Rationale: required fraction = l . c . m of 6 / 7 , 5 / 14 , 10 / 21 = ( l . c . m of 6 , 5 , 10 ) / ( h . c . f of 7 , 14 , 21 ) = 30 / 7 answer : a
Answer: a
Question (gain): what is rate of interest if principal . amount be 400 , simple interest 180 and time 2 year .
Options: a ) 10 , b ) 12.5 , c ) 25 , d ) 22.5 , e ) 14.5
Rationale: "s . i = ( p * r * t ) / 100 180 = 800 r / 100 r = 180 / 8 = 22.5 % answer d"
Answer: d
Question (general): find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3 .
Options: a ) 131 , b ) 197 , c ) 207 , d ) 219 , e ) 227
Rationale: "let ' n ' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3 . required number = ( lcm of 11 and 12 ) - ( common difference of divisors and remainders ) = ( 132 ) - ( 1 ) = 131 . answer : a"
Answer: a
Question (physics): david biked 16 1 / 3 miles in 2 hours and 20 minutes . what was his average rate of speed in miles per hour ?
Options: a ) 7 , b ) 7 2 / 3 , c ) 8 1 / 3 , d ) 9 , e ) 9 1 / 3
Rationale: d = 16 ( 1 / 3 ) = 49 / 3 t = 2 ( 1 / 3 ) = 7 / 3 s = d / t = 7 answer = a
Answer: a
Question (general): if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 6 k , what is one possible value for k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 3 or k = 6 . all the answers are positive , so we choose k = 2 . answer = d"
Answer: d
Question (general): a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 50 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined
Rationale: "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 50 % = 50 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 50 - c = 100 c = 10 option b ."
Answer: b
Question (gain): find the compound interest on rs . 16,000 at 20 % per annum for 9 months , compounded quartely .
Options: a ) rs . 2522 , b ) rs . 2512 , c ) rs . 2572 , d ) rs . 2592 , e ) none
Rationale: "solution principal = rs . 16,000 ; time = 9 months = 3 quarters ; amount = rs . [ 16000 x ( 1 + 5 / 100 ) ³ ] = [ 16000 x 21 / 20 x 21 / 20 x 21 / 20 ] = rs . 18522 . c . i = rs . ( 18522 - 16000 ) = rs . 2522 . answer a"
Answer: a
Question (general): find the ones digit of 73 ^ 330
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 330 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer b ."
Answer: b
Question (general): the mean of 50 observations was 36 . it was found later that an observation 28 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.0 , b ) 36.5 , c ) 36.1 , d ) 36.2 , e ) 36.8
Rationale: "explanation : correct sum = ( 36 * 50 + 28 - 23 ) = 1825 . correct mean = = 1805 / 50 = 36.1 answer : c ) 36.1"
Answer: c
Question (general): the rate of interest on a sum of money is 9 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occured on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 1,125 , b ) 2,000 , c ) 2,100 , d ) 2,250 , e ) 2,540
Rationale: "explanation : i 1 = ( p x 3 x 9 ) / 100 = 10 p / 37 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 10 p / 37 + 4 p / 25 + p / 20 = 540 12 p / 25 = 540 p = 1125 answer : option a"
Answer: a
Question (physics): in a games hour 4 different types of players came to the ground ? cricket 22 , hokey 15 , football 21 , softball 19 . how many players are present in the ground ?
Options: a ) 70 , b ) 52 , c ) 62 , d ) 77 , e ) 79
Rationale: "total number of players = 22 + 15 + 21 + 19 = 77 answer is d"
Answer: d
Question (other): an alloy is to contain copper and zinc in the ratio 5 : 3 . the zinc required to be melted with 40 kg of copper is ?
Options: a ) 15 kg , b ) 20 kg , c ) 8 kg , d ) 24 kg , e ) 32 kg
Rationale: let the required quantity of copper be x kg 5 : 3 : : 40 : x 5 x = 40 * 3 x = 24 kg answer is d
Answer: d
Question (gain): if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 348 , the cost of the article is
Options: a ) 289 , b ) 231 , c ) 200 , d ) 40 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 348 = 2 x / 20 = 2 = > x = 40 answer : d"
Answer: d
Question (general): solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 200 milliliters of solution x to create a solution that is 20 percent alcohol by volume ?
Options: a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600
Rationale: "20 % is an equal distance between 10 % and 30 % . thus there should be equal parts of both solutions . we should add 200 ml of solution y . the answer is a ."
Answer: a
Question (general): the ratio 6 : 3 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 80 % , d ) 200 % , e ) none
Rationale: "solution 6 : 3 = 6 / 3 = ( 6 / 3 x 100 ) % . = 200 % . answer d"
Answer: d
Question (general): the average weight of 8 person ' s increases by 6 kg when a new person comes in place of one of them weighing 40 kg . what might be the weight of the new person ?
Options: a ) 80 kg , b ) 85 kg , c ) 90 kg , d ) 88 kg , e ) 110 kg
Rationale: "total weight increased = ( 8 x 6 ) kg = 48 kg . weight of new person = ( 40 + 48 ) kg = 88 kg . answer : d"
Answer: d
Question (general): a and b are two partially filled buckets of water . if 8 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 8 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 88 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let bucket a be a and bucket b be b scenario 1 a - 8 = 1 / 3 ( b + 8 ) - - - - > 3 a - 24 = b + 8 scenario 2 b - 8 = 1 / 2 ( a + 8 ) - - - - - > 2 b - 16 = a + 8 from scenario 1 , b = 3 a - 32 substitute b with this information in stmt 2 2 ( 3 a - 32 ) - 16 = a + 8 - - - - - - > 6 a - 64 - 16 = a + 8 - - - - - - > 6 a - a = 80 + 8 - - - > 5 a = 88 a = 88 / 5 , answer choice a"
Answer: a
Question (physics): 16 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ?
Options: a ) 23 , b ) 27 , c ) 20 , d ) 27 , e ) 11
Rationale: "16 * 25 = 20 * x = > x = 20 days answer : c"
Answer: c
Question (physics): a man traveled a total distance of 900 km . he traveled one - third of the whole trip by plane and the distance traveled by train is one - half of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?
Options: a ) 400 km , b ) 450 km , c ) 500 km , d ) 550 km , e ) 600 km
Rationale: "total distance traveled = 900 km . distance traveled by plane = 300 km . distance traveled by bus = x distance traveled by train = x / 2 x + x / 2 + 300 = 900 3 x / 2 = 600 x = 400 km the answer is a ."
Answer: a
Question (general): if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 30
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 18
Rationale: "p ã · 44 = 432 = > p = 432 * 44 = 19008 p / 30 = 19008 / 30 = 633 , remainder = 18 e"
Answer: e
Question (gain): in country z , 18 % of the people do not have a university diploma but have the job of their choice , and 25 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 37 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 18 % job of choice total = 40 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 25 % of 60 % = 15 % . we can also see that 30 % of the people have their job of choice and a diploma ( 40 % - 18 % = 22 % ) . 22 % + 15 % = 37 % . therefore 37 % of the people in country z have a diploma . ans a"
Answer: a
Question (other): if 0.5 of a number is equal to 0.09 of another number , the ratio of the numbers i
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 20 , d ) 3 : 7 , e ) 9 : 50
Rationale: sol . 0.5 a = 0.09 b â ‡ ” a / b = 0.09 / 0.50 = 9 / 50 â ˆ ´ a : b = 9 : 50 . answer e
Answer: e
Question (physics): two trains t 1 and t 2 start simultaneously from two stations x and y respectively towards each other . if they are 70 km apart both 3 and 6 hours after start , then find the distance between the two stations .
Options: a ) 210 km , b ) 240 km , c ) 220 km , d ) 180 km , e ) 190 km
Rationale: in first 3 hours t 1 travels r km and t 2 travels s km . after 6 hours they traveled r + s + 70 + 700 2 ( r + s ) = r + s + 140 r + s = 140 hence distance between xy is r + s + 70 = 140 + 70 = 210 answer : a
Answer: a
Question (general): among 7 numbers the average of first 4 numbers is 13 and the average of last 4 numbers is 15 . the sum of last 3 numbers is 55 . the square of the fourth number is equal to the last number then what is the last number ?
Options: a ) 60 , b ) 52 , c ) 5 , d ) 25 , e ) 125
Rationale: let the numbers be a , b , c , d , e , f , g d + e + f + g = 15 * 4 = 60 e + f + g = 55 , 60 - 55 = 5 so the fourth number is 5 . the square is 25 . the answer is option d .
Answer: d
Question (general): a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 12 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 28 , e ) 32
Rationale: "since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 12 r / 2 = 12 r = 24 the answer is c ."
Answer: c
Question (general): the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum q of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just q = 900 : the answer is c ."
Answer: c
Question (general): a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 126 . find the number of notes of rs . 50 denomination .
Options: a ) 115 , b ) 121 , c ) 117 , d ) 119 , e ) 121
Rationale: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 126 - x now , 50 * x + 500 * ( 126 - x ) = 10350 50 x + 63000 - 500 x = 10350 - 450 x = - 52650 x = 117 . no . of 50 rupees note = 117 . answer : option c"
Answer: c
Question (gain): a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 33 . find the profit percentage ?
Options: a ) 65 % , b ) 50 % , c ) 59 % , d ) 40 % , e ) 53 %
Rationale: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 165 ( 33 * 5 ) profit percentage = ( 165 - 100 ) / 100 * 100 = 65 % answer : a"
Answer: a
Question (other): each factor of 230 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "210 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 3 / 16 . answer : d"
Answer: d
Question (physics): 3 different containers contain 496 litres , 403 litres and 713 litres of mixtures of milk and water respectively . what biggest measure can measure all the different quantities exactly ?
Options: a ) 30 litres , b ) 31 litres , c ) 32 litres , d ) 33 litres , e ) 34 litres
Rationale: 403 ) 713 ( 1 403 - - - - - - - - - 310 ) 403 ( 1 310 - - - - - - - - - - 93 ) 310 ( 3 279 - - - - - - - - 31 ) 93 ( 3 93 - - - - - - - x so answer is 31 litres . . . . . . answer : b
Answer: b
Question (physics): 12 persons can complete the work in 18 days . after working for 6 days , 4 more persons added to complete the work fast . in how many more days they will complete the work ?
Options: a ) 10 days , b ) 9 days , c ) 8 days , d ) 7 days , e ) 6 days
Rationale: total work 12 * 18 = 216 units after 6 days work finished 6 * 12 = 72 units remaining work 216 - 72 = 144 units remaing days = 144 ( 12 + 4 ) = 9 days answer : b
Answer: b
Question (general): there are 870 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 145
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 870 . hence , we have m + f = 870 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 870 / 3 = 290 solving the three equations yields the solution f = 290 , m = 580 , and d = 290 . the number of female democratic participants equals half the female participants equals 290 / 2 = 145 . answer : e"
Answer: e
Question (general): is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 37 , then how old is b ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 14
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 37 5 x = 35 = > x = 7 hence , b ' s age = 2 x = 14 years . answer : e"
Answer: e
Question (gain): a and b invests rs . 10000 each , a investing for 9 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 21000 , find their shares ?
Options: a ) 1300,1500 , b ) 9000,12000 , c ) 7290,8000 , d ) 15000,12000 , e ) 72821,75000
Rationale: "the ratio of their profits a : b = 9 : 12 = 3 : 4 share of a in the total profit = 3 / 7 * 21000 = rs . 9000 share of b in the total profit = 4 / 7 * 21000 = rs . 12000 answer : b"
Answer: b
Question (general): a batsman scored 150 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 66.66 % , e ) 70 %
Rationale: "explanation : number of runs made by running = 150 - ( 5 x 4 + 5 x 6 ) = 150 - ( 50 ) = 100 now , we need to calculate 100 is what percent of 150 . = > 100 / 150 * 100 = 66.66 % option d"
Answer: d
Question (physics): speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7380 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 937.1 hours , c ) 915 hours , d ) 905 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7380 / 18 + 7380 / 14 = 410 + 527.1 = 937.1 hours answer : option b"
Answer: b