Cheukting/mathqa huggingface dataset:
Question (physics): you have to send 3000 grapes 1000 kilometers from grapecity to appleland . your truck can carry 1000 grapes at a time . every time you travel a kilometer towards appleland you must pay a tax of 1 grape but you pay nothing when going in the other direction ( towards grapecity ) . what is highest number of grapes you can get to appleland ?
Options: a ) 833 , b ) 765 , c ) 665 , d ) 679 , e ) 874
Rationale: step one : first you want to make 3 trips of 1,000 grapes 333 kilometers . you will be left with 2,001 grapes and 667 kilometers to go . step two : next you want to take 2 trips of 1,000 grapes 500 kilometers . you will be left with 1,000 grapes and 167 kilometers to go ( you have to leave a grape behind ) . step three : finally , you travel the last 167 kilometers with one load of 1,000 grapes and are left with 833 grapes in appleland . correct answer is a ) 833
Answer: a
Question (physics): the sum of all consecutive odd integers from − 19 to 29 , inclusive , is
Options: a ) 125 , b ) 135 , c ) 150 , d ) 175 , e ) 235
Rationale: "the sum of the odd numbers from - 19 to + 19 is 0 . let ' s add the remaining numbers . 21 + 23 + 25 + 27 + 29 = 5 ( 25 ) = 125 the answer is a ."
Answer: a
Question (general): the contents of a certain box consist of 14 apples and 25 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 19 , e ) 20
Rationale: "the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 25 oranges , so to get to 6 oranges , we should remove 25 - 6 = 19 oranges . answer d"
Answer: d
Question (other): jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 7 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 35 : 2
Rationale: u / i = 7 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 35 : 21 : 2 i . e . u : b = 35 : 2 answer : option e
Answer: e
Question (general): how many prime numbers are between 13 / 3 and 83 / 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "13 / 3 = 4 . xxx 83 / 6 = 13 . xxx so we need to find prime numbers between 4 ( exclusive ) - 12 ( inclusive ) there are 2 prime numbers 7 11 hence answer will be ( b ) 2 b"
Answer: b
Question (gain): john makes $ 60 a week from his job . he earns a raise andnow makes $ 80 a week . what is the % increase ?
Options: a ) 15 % , b ) 33.33 % , c ) 17.8 % , d ) 19 % , e ) 21 %
Rationale: "increase = ( 20 / 60 ) * 100 = ( 1 / 3 ) * 100 = 33.33 % . b"
Answer: b
Question (other): three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 600 . their h . c . f is ?
Options: a ) 10 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 600 x = 10 the numbers are 3 * 10 , 4 * 10 , 5 * 10 hence required h . c . f . = 10 answer is a"
Answer: a
Question (physics): a boat takes 19 hours for travelling downstream from point a to point b and coming back to a point c which is at midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?
Options: a ) 180 km , b ) 127 km , c ) 178 km , d ) 188 km , e ) 111 km
Rationale: "explanation : speed in downstream = ( 14 + 4 ) km / hr = 18 km / hr ; speed in upstream = ( 14 â € “ 4 ) km / hr = 10 km / hr . let the distance between a and b be x km . then , x / 18 + ( x / 2 ) / 10 = 19 â ‡ ” x / 18 + x / 20 = 19 â ‡ ’ x = 180 km . answer : a"
Answer: a
Question (general): in a division sum , the quotient is 18 , the divisor 43 and the remainder 12 , find the dividend ?
Options: a ) 586 , b ) 766 , c ) 796 , d ) 786 , e ) 686
Rationale: "explanation : 18 * 43 + 12 = 786 answer : d"
Answer: d
Question (general): x and y are both integers . if x / y = 50.60 , then what is the sum of all the possible two digit remainders of x / y ?
Options: a ) 315 , b ) 616 , c ) 672 , d ) 900 , e ) 1024
Rationale: "remainder = 0.60 - - > 60 / 100 - - > can be written as ( 60 / 4 ) / ( 100 / 4 ) = 15 / 25 so remainders can be 15 , 30 , 45 , 60 , . . . . . 90 . we need the sum of only 2 digit remainders - - > 15 + 30 + 45 + 60 + 75 + 90 = 315 answer : a"
Answer: a
Question (general): the average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 60 kg is replaced by a new man . what is the weight of the new man ?
Options: a ) 80 kg , b ) 83 kg , c ) 70 kg , d ) 75 kg , e ) 85 kg
Rationale: "since the average has increased by 1.5 kg , the weight of the man who stepped in must be equal to 60 + 10 x 1.5 60 + 15 = 75 kg ans : ' d '"
Answer: d
Question (gain): a shopkeeper sold an article at $ 1050 and gained a 20 % profit . what was the cost price ?
Options: a ) $ 835 , b ) $ 845 , c ) $ 855 , d ) $ 865 , e ) $ 875
Rationale: "let x be the cost price . 1.2 x = 1050 x = 1050 / 1.2 = 875 the answer is e ."
Answer: e
Question (general): niall ' s income is 60 % less than rex ' s income , and sam ' s income is 25 % less than niall ' s income . if rex gave 60 % of his income to sam and 40 % of his income to niall , niall ' s new income would be what fraction of sam ' s new income ?
Options: a ) 8 / 9 , b ) 11 / 12 , c ) 8 / 13 , d ) 11 / 13 , e ) 12 / 13
Rationale: we can take some easy numbers and make calculations simpler . let r ( rex ' s income ) = 100 q ( niall ' s income ) = 40 % r = 40 s ( sam ' s income ) = 75 % q = ( 3 / 4 ) * 40 = 30 now , if rex gives 40 % to niall - - > q = 40 + 40 = 80 60 % given to sam - - > s = 30 + 60 = 90 the ratio is : q / s = 80 / 90 = 8 / 9 = a
Answer: a
Question (general): if 2 a = 4 b = 10 , then 40 ab =
Options: a ) 50 , b ) 100 , c ) 250 , d ) 450 , e ) 500
Rationale: 2 a * 4 b = 10 * 10 = 100 8 ab = 100 i . e . 40 ab = 500 answer : option e
Answer: e
Question (general): rahim bought 52 books for rs . 1200 from one shop and 32 books for rs . 480 from another . what is the average price he paid per book ?
Options: a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 20 , e ) s . 10
Rationale: "average price per book = ( 1200 + 480 ) / ( 52 + 32 ) = 1680 / 84 = rs . 20 answer : d"
Answer: d
Question (general): a rower whose speed is 4 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 2 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 6 , b ) 4 , c ) 9 , d ) 3 , e ) 2
Rationale: "time upstream = d / 2 time downstream = d / 6 total time = d / 2 + d / 6 = 2 d / 3 average speed = 2 d / ( 2 d / 3 ) = 3 km / hr the answer is d ."
Answer: d
Question (general): if 2 ^ 5 , 4 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 26 , b ) 39 , c ) 42 , d ) 208 , e ) 156
Rationale: "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 4 * 4 = 208 smash d"
Answer: d
Question (general): if 3 < x < 6 < y < 11 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 < x < 6 < y < 11 ; 3 < x y < 11 3 + y < x + 11 y - x < 8 . positive integer difference is 7 ( for example y = 10.5 and x = 3.5 ) answer : e ."
Answer: e
Question (general): chris age after 20 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 5
Rationale: chris present age = x after 20 years = x + 20 5 years back = x - 5 x + 20 = 5 ( x - 5 ) x = 5 answer is e
Answer: e
Question (general): if x is an integer and 2.134 × 10 ^ x is less than 2 , 200,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "x is an integer and 2.134 × 10 x is less than 2 , 200,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 2 , 200,000 to remain true , the greatest number is 2 , 134,000 , which makes x = 6 b . 6"
Answer: b
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 15 m wide at the top and 9 m wide at the bottom and the area of cross - section is 636 sq m , the depth of cannel is ?
Options: a ) 53 , b ) 28 , c ) 27 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 15 + 9 ) = 636 d = 53 answer : a"
Answer: a
Question (physics): a train passes a station platform in 36 sec and a man standing on the platform in 24 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 767 m , b ) 240 m , c ) 180 m , d ) 176 m , e ) 186 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 24 = 360 m . let the length of the platform be x m . then , ( x + 360 ) / 36 = 15 = > x = 180 m . answer : c"
Answer: c
Question (gain): the weight of a glass of jar is 30 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 7
Rationale: let weight of jar filled with beans = 100 g weight of jar = 30 g weight of coffee beans = 70 g weight of jar and remaining beans = 60 g weight of remaining beans = 30 g fraction remaining = 30 / 70 = 3 / 7 answer is e .
Answer: e
Question (gain): what will be the fraction of 12.5 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 8 , e ) none of above
Rationale: "explanation : it will 12.5 * 1 / 100 = 1 / 8 answer : option d"
Answer: d
Question (gain): a number increased by 15 % gives 1150 . the number is
Options: a ) 250 , b ) 1000 , c ) 450 , d ) 500 , e ) 520
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 15 % = 115 % 115 % - - - - - - - > 1150 ( 115 × 100 = 1150 ) 100 % - - - - - - - > 1000 ( 100 × 100 = 1000 ) b )"
Answer: b
Question (physics): a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 390 m long platform ?
Options: a ) 19 , b ) 27 , c ) 51 , d ) 47 , e ) 28
Rationale: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 390 ) / 36 * 5 / 18 = 51 min . answer : c"
Answer: c
Question (general): the average of 7 numbers is 23 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 115 , e ) e ) 145
Rationale: "explanation : average of new numbers = 23 * 5 = 115 answer : option d"
Answer: d
Question (general): if taxi fares were $ 3.00 for the first 1 / 5 mile and $ 0.20 for each 1 / 5 mile there after , then the taxi fare for a 4 - mile ride was
Options: a ) $ 6.80 , b ) $ 6.50 , c ) $ 16.80 , d ) $ 6.85 , e ) $ 61.80
Rationale: "in 4 miles , initial 1 / 5 mile charge is $ 3 rest of the distance = 4 - ( 1 / 5 ) = 19 / 5 rest of the distance charge = 19 ( 0.2 ) = $ 3.8 ( as the charge is 0.2 for every 1 / 5 mile ) = > total charge for 4 miles = 3 + 3.8 = 6.8 answer is a"
Answer: a
Question (physics): if 8 men or 12 women can do a piece of work in 35 days , in how many days can the same work be done by 6 men and 11 women ?
Options: a ) 10 days , b ) 11 days , c ) 13 days , d ) 15 days , e ) 21 days
Rationale: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 35 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 35 = 1 / 420 so , 20 women work = 20 / 420 = 1 / 21 ans : 21 days answer : e"
Answer: e
Question (general): the total age of a and b is 18 years more than the total age of b and c . c is how many year younger than
Options: a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 18 years
Rationale: "given that a + b = 182 + b + c = > a â € “ c = 18 + b â € “ b = 18 = > c is younger than a by 18 years answer : e"
Answer: e
Question (physics): one pump drains one - half of a pond in 1 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.2 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "the tricky part here , i believed is one half hour = 1 / 2 . then everything would be easy . we have the 1 st pump working rate / hour = 1 / 2 : 1 = 1 / 2 working rate of 2 pumps : 1 / 2 : 1 / 2 = 1 . working rate of 2 nd pump : 1 - 1 / 2 = 1 / 2 - - > time taken for the 2 nd pump to finish : 1 : 1 / 2 = 2 / 1 = 2 hours . c"
Answer: c
Question (general): the greatest number which on dividing 1657 and 2037 leaves remainders 9 and 5 respectively , is :
Options: a ) 16 , b ) 127 , c ) 235 , d ) 305 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1657 - 9 ) and ( 2037 - 5 ) = h . c . f . of 1648 and 2032 = 16 . answer : a"
Answer: a
Question (geometry): a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 10 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 2387 , b ) 1298 , c ) 1128 , d ) 1237 , e ) 1200
Rationale: "l * 30 = 1200 l = 40 40 + 30 + 50 = 120 120 * 10 = 1200 e"
Answer: e
Question (geometry): the length of a rectangle is 2 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?
Options: a ) 30 square inches , b ) 75 square inches , c ) 68 square inches , d ) 89 square inches , e ) 32 square inches
Rationale: "if the width is 4 in and the length is 2 times the width , then the length is 2 * 4 = 8 in the area is given by 4 * 8 = 32 square inches correct answer e"
Answer: e
Question (other): the ratio between the sale price and the cost price of an article is 7 : 4 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 3 : 4 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 25
Rationale: "c . p . = rs . 4 x and s . p . = rs . 7 x . then , gain = rs . 3 x required ratio = 3 x : 4 x = 3 : 4 a"
Answer: a
Question (general): barbata invests $ 2400 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2400 + 0.05 * 2400 + x + 0.08 x = 2400 + x + 0.06 ( 2400 + x ) 0.05 * 2400 + 0.08 x = 0.06 x + 0.06 * 2400 0.02 x = 2400 ( 0.06 - 0.05 ) x = 2400 * 0.01 / 0.02 = 1200 ans : ` ` a ' '"
Answer: a
Question (gain): if a speaks the truth 30 % of the times , b speaks the truth 40 % of the times . what is the probability that at least one will tell the truth
Options: a ) 0.58 , b ) 0.9 , c ) 1.9 , d ) 2.2 , e ) 2.3
Rationale: "probability of a speaks truth p ( a ) = 3 / 10 ; false = 7 / 10 probability of b speaks truth p ( b ) = 4 / 10 ; false = 6 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 7 / 10 ) * ( 6 / 10 ) ] = 1 - 42 / 100 = 1 - 0.42 = 0.58 answer : a"
Answer: a
Question (geometry): a certain farmer pays $ 30 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 370 feet by 605 feet ? ( 43,560 square feet = 1 acre )
Options: a ) $ 5,330 , b ) $ 3,360 , c ) $ 1,350 , d ) $ 360 , e ) $ 154.1
Rationale: basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 154.1 ( e )
Answer: e
Question (general): difference between a two - digit number and the number obtained by interchanging the two digits is 36 , what is the difference between two numbers
Options: a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 14
Rationale: explanation : let the ten digit be x , unit digit is y . then ( 10 x + y ) - ( 10 y + x ) = 36 = > 9 x - 9 y = 36 = > x - y = 4 . option b
Answer: b
Question (general): the average score of a cricketer in 6 matches is 27 and in other 4 matches is 32 . then find the average score in all the 10 matches ?
Options: a ) 25 , b ) 27 , c ) 30 , d ) 29 , e ) 42
Rationale: "average in 10 matches = ( 6 * 27 + 4 * 32 ) / 6 + 4 = 162 + 128 / 10 = 290 / 10 = 29 answer is d"
Answer: d
Question (gain): rs . 900 amounts to rs . 920 in 3 years at simple interest . if the interest is increased by 3 % , it would amount to how much ?
Options: a ) rs . 1056 , b ) rs . 1001 , c ) rs . 2056 , d ) rs . 1026 , e ) rs . 1856
Rationale: "( 900 * 3 * 3 ) / 100 = 81 920 + 81 = 1001 answer : b"
Answer: b
Question (general): the average expenditure of a labourer for 10 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 180 , b ) 100 , c ) 112 , d ) 110 , e ) none of the above
Rationale: "income of 10 months = ( 10 × 85 ) – debt = 850 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 1120 average monthly income = 1120 ÷ 10 = 112 answer c"
Answer: c
Question (probability): a store has 10 bottles of juice , including 5 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 4 / 9 , b ) 6 / 11 , c ) 8 / 15 , d ) 10 / 21 , e ) 12 / 25
Rationale: "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 5 c 3 * 5 c 3 = 10 * 10 = 100 p ( selling 3 bottles of apple juice ) = 100 / 210 = 10 / 21 the answer is d ."
Answer: d
Question (general): a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 136 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 24 , b ) 33 , c ) 55 , d ) 77 , e ) 88
Rationale: let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 136 = > . 1 x + 3 / 4 x = 136 = > x = 160 160 - 136 = pure gala = 24 . a
Answer: a
Question (general): at a monthly meeting , 1 / 3 of the attendees were males and 4 / 5 of the male attendees arrived on time . if 5 / 6 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 1 / 6 , b ) 2 / 15 , c ) 3 / 20 , d ) 7 / 30 , e ) 8 / 45
Rationale: "males who did not arrive on time are 1 / 5 * 1 / 3 = 1 / 15 of the attendees . females who did not arrive on time are 1 / 6 * 2 / 3 = 1 / 9 of the attendees . the fraction of all attendees who did not arrive on time is 1 / 15 + 1 / 9 = 8 / 45 the answer is e ."
Answer: e
Question (gain): a shopkeeper sold an book offering a discount of 5 % and earned a profit of 30 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 136.8 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 130 let marked price be $ x . then , 95 / 100 x = 130 x = 13000 / 95 = $ 136.8 now , s . p . = $ 136.8 , c . p . = $ 100 profit % = 136.8 % . d"
Answer: d
Question (general): a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 300 and $ 200 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "the smallest amount that the company can spend is the lcm of 300 and 200 , which is 600 for each , which is total 1200 . the number of 1 st type of computers which costing $ 300 = 600 / 300 = 2 . the number of 2 nd type of computers which costing $ 200 = 600 / 200 = 3 . total = 2 + 3 = 5 answer is b ."
Answer: b
Question (general): if p is a prime number greater than 3 , find the remainder when p ^ 2 + 14 is divided by 12 .
Options: a ) 6 , b ) 1 , c ) 3 , d ) 8 , e ) 7
Rationale: "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 14 = 36 n ^ 2 + 12 n + 1 + 14 = 36 n ^ 2 + 12 n + 12 + 3 if p = 6 n - 1 , then p ^ 2 + 14 = 36 n ^ 2 - 12 n + 1 + 14 = 36 n ^ 2 - 12 n + 12 + 3 when divided by 12 , it must leave a remainder of 3 . the answer is c ."
Answer: c
Question (probability): three unbiased coins are tossed . what is the probability of getting 3 heads and 1 tail ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 1 / 2 , e ) 1 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { hhh , hth , thh , hht } p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 1 / 2 answer is d"
Answer: d
Question (general): find 95 × × 98
Options: a ) 93 / 198 , b ) 93 / 12 , c ) 93 / 13 , d ) 93 / 10 , e ) 93 / 11
Rationale: "here both numbers are less than 100 . so they are deficient of - 5 and - 2 compared with 100 . so answer : d"
Answer: d
Question (general): 5 + 5
Options: a ) 9 , b ) 12 , c ) 20 , d ) 10 , e ) 0
Rationale: d
Answer: d
Question (general): a certain ball team has an equal number of right - and left - handed players . on a certain day , one - third of the players were absent from practice . of the players at practice that day , one - third were right handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of left handed players who were not at practice ?
Options: a ) 1 / 3 , b ) 5 / 1 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2
Rationale: "say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 6 absent and 12 present . of the players at practice that day , one - third were right - handed - - > 12 * 1 / 3 = 4 were right - handed and 8 left - handed . the number of right - handed players who were not at practice that day is 9 - 4 = 5 . the number of left - handed players who were not at practice that days is 9 - 8 = 1 . the ratio = 5 / 1 . answer : b"
Answer: b
Question (other): bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 42 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 10 , e ) 12
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 42 = 6 k + 4 p = > k = 5 , p = 3 total red ' s in bag a will be 2 k = 10 d"
Answer: d
Question (general): a man has some hens and cows . if the number of heads be 42 and the number of feet equals 124 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "explanation : let number of hens = h and number of cows = c number of heads = 42 = > h + c = 42 - - - ( equation 1 ) number of feet = 124 = > 2 h + 4 c = 124 = > h + 2 c = 62 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 62 - 42 = > c = 20 substituting the value of c in equation 1 , we get h + 22 = 42 = > h = 42 - 20 = 22 i . e . , number of hens = 22 answer : a"
Answer: a