Cheukting/mathqa huggingface dataset:
Question (general): if 9 ^ y = 3 ^ 14 , what is y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: "9 ^ y = 3 ^ 2 y = 3 ^ 14 2 y = 14 y = 7 the answer is e ."
Answer: e
Question (general): how many zeroes are there at the end of the number n , if n = 90 ! + 180 ! ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "the number of zeroes at the end of 90 ! will be less than the number of zeroes at the end of 180 ! hence it is sufficient to calculate the number of zeroes at the end of 90 ! the number of zeroes = [ 90 / 5 ] + [ 90 / 25 ] + [ 90 / 125 ] = 18 + 3 + 0 = 21 the answer is c ."
Answer: c
Question (gain): ms . harris invested in fund x and fund b . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund x paid 23 % and fund b paid 17 % . the interest earned in fund b was exactly $ 200 greater than the interest earned in fund x . how much did ms . morris invest in fund x ?
Options: a ) $ 32000 , b ) $ 36000 , c ) $ 40000 , d ) $ 42000 , e ) $ 45,000
Rationale: 0.17 b - 0.23 x = 200 | * 100 17 b - 23 x = 20,000 x + b = 100,000 b = 100,000 - x 17 ( 100,000 - x ) - 23 x = 20,000 1 , 700,000 - 17 x - 23 x = 20,000 1 , 680,000 = 40 x divide by 40 first two digits : 42 . . . so answer is d .
Answer: d
Question (general): in a forest 150 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 10 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 3,000 , d ) 1,500 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 10 / 50 * 100 = 20 % . so , 150 tagged deers comprise 10 % of total # of deers - - > total # of deers = 150 * 20 = 3,500 . answer : c"
Answer: c
Question (geometry): a 11 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 5 / 8 , b ) 1 / 5 , c ) 6 / 11 , d ) 3 / 11 , e ) 2 / 5
Rationale: "a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 3 meters from either end . the probability of this is 6 / 11 . the answer is c ."
Answer: c
Question (general): if the price of a certain computer increased 30 percent from b dollars to 351 dollars , then 2 b =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = b after 30 % price increase price = b + ( 30 / 100 ) * b = 1.3 b = 351 ( given ) i . e . b = 351 / 1.3 = $ 270 i . e . 2 b = 2 * 270 = 540 answer : option a"
Answer: a
Question (general): vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 5780 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2000 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 5780 = x = 5780 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2000 . answer : c"
Answer: c
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 170 meters long if the speed of the train is 36 kmph ?
Options: a ) 54 sec , b ) 65 sec , c ) 25 sec , d ) 45 sec , e ) 27 sec
Rationale: "d = 100 + 170 = 270 s = 36 * 5 / 18 = 10 mps t = 270 / 10 = 27 sec answer : e"
Answer: e
Question (general): in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 12 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 95 , d ) 88 , e ) 93
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 12 total people can seat = 81 + 12 = 93 answer : e"
Answer: e
Question (physics): some persons can do a piece of work in 16 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "16 / ( 2 * 2 ) = 4 days answer : b"
Answer: b
Question (general): stacy was 5 days late returning items to the library . stacy had checked out 40 books , 2 movies , and 3 magazines . books are fined $ 0.25 per day , movies are fined $ 3.00 per day , and magazines are fined $ 0.50 per day . what is the average fine per item per day stacy paid ?
Options: a ) $ 0.25 , b ) $ 0.30 , c ) $ 0.35 , d ) $ 0.40 , e ) none of the above
Rationale: explanation : 40 2 3 $ 0.25 $ 3.00 $ 0.50 $ 10.00 + $ 6.00 + $ 1.50 = $ 17.50 / 45 = $ 0.39 e
Answer: e
Question (general): if an average hard drive had a capacity of 0.4 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 512 , c ) 4096 , d ) 1024 , e ) 1536
Rationale: "0.4 * 2 ^ 10 = 0.4 * 1024 = 409.6 the answer is c ."
Answer: c
Question (geometry): in may , the grounds keeper at spring lake golf club built a circular green with an area of 36 π square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 100 pi
b ) 144 pi
c ) 70
d ) 80
e ) 90
Rationale: area of circle 36 pi sq feet = pi r ^ 2 therefore r = 6 now green radi doubled i . e r = 12 area = 144 pi b
Answer: b
Question (general): a house wife saved $ 5 in buying an item on sale . if she spent $ 48 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 48 + 5 = $ 53 saving = 5 / 48 * 100 = 100 / 11 = 10 % approximately answer is c"
Answer: c
Question (gain): a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 200 , find the original price per kg ?
Options: a ) s . 7 , b ) s . 4 , c ) s . 5 , d ) s . 1 , e ) s . 9
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 200 - - - 80 ? - - - 2 = > rs . 5 answer : c"
Answer: c
Question (general): find the remainder when 6 ^ 50 is divided by 215
Options: a ) 34 , b ) 35 , c ) 36 , d ) 37 , e ) 38
Rationale: "( 6 ^ 3 ) ^ 16 * 6 ^ 2 / 215 ( 215 + 1 ) ^ 16 * 6 ^ 2 / 215 1 ^ 16 * 6 ^ 2 / 215 = 36 answer : c"
Answer: c
Question (physics): a train 140 m long is running at 60 kmph . in how much time wiu it pass a platform 260 m long ?
Options: a ) 21 sec , b ) 22 sec , c ) 23 sec , d ) 24 sec , e ) 26 sec
Rationale: "s = d / t d = 140 + 260 = 400 m s = 60 * 5 / 18 m / sec = 50 / 3 m / sec t = 400 / ( 50 / 3 ) = 1200 / 50 = 24 sec answer : d"
Answer: d
Question (general): the total marks obtained by a student in mathematics and physics is 50 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 15 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 50 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 50 + 20 ) / 2 = 35 . answer : c"
Answer: c
Question (physics): a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 70 paise per sq . metre
Options: a ) s 595 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 70 = 59500 p in rs = 59500 / 100 = rs 595 answer : a"
Answer: a
Question (general): rahul played weel in this season . his current batting averagge is 46 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 3 , d ) 6 , e ) 5
Rationale: "46 x + 78 = 54 ( x + 1 ) = > 8 x = 24 = > x = 3 answer : c"
Answer: c
Question (gain): find the simple interest on rs . 69,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 8625 , d ) 9500 , e ) none of them
Rationale: p = rs . 69000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 69,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8625 answer is c .
Answer: c
Question (general): the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 7 years hence ?
Options: a ) 22 , b ) 77 , c ) 74 , d ) 98 , e ) 71
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 7 years , their ages will be 47 and 27 . sum of their ages = 47 + 27 = 74 . answer : c"
Answer: c
Question (physics): malar and roja combined will complete a task in 35 days , but malar alone can complete same work in 60 days . calculate in how many days roja can complete this work ?
Options: a ) 85 days , b ) 45 days , c ) 90 days , d ) 84 days , e ) 95 days
Rationale: malar - 35 days = > 1 / 35 roja - 60 days = > 1 / 60 malar one day work = 1 / 35 - 1 / 60 = 1 / 84 = = > 84 days answer d
Answer: d
Question (geometry): the measure of the side of a square is quadrupled . if x represents the perimeter of the original square , what is the value of the new perimeter ?
Options: a ) 3 x
b ) 4 x
c ) 9 x
d ) 12 x
e ) 27 x
Rationale: original perimeter = x hence original side = x / 4 new side = 4 x / 4 new perimeter = 4 * 4 x / 4 = 4 x correct option : b
Answer: b
Question (general): tough and tricky questions : word problems . micheal , saren and donald decided to club together to buy a present . each of them gave equal amount of money . luckily saren negotiated a 20 % discount for the present so that each of them paid 4 dollars less . how much did they pay for a present ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: answer c . we know that saren negotiated a discount of 20 % , so each of them paid $ 4 less . since there are three people , the 20 % of the original price amounts to $ 12 . 5 times 12 $ is 60 $ , so the original price , before saren negotiated the discount , had been $ 60 . they paid $ 12 less than the base price , so they spent $ 48 .
Answer: c
Question (physics): a train passes a station platform in 36 sec and a man standing on the platform in 25 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 ) 187 m , d ) 176 m , e ) 165 m
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 25 = 375 m . let the length of the platform be x m . then , ( x + 375 ) / 36 = 15 = > x = 165 m . answer : e"
Answer: e
Question (general): a club wants to mix 25 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 25 * 8 + 5 * w ) / ( 25 + w ) = > 150 + 6 w = 200 + 5 w = > w = 50 answer c"
Answer: c
Question (general): if pintu is coded as 79523 in a certain code language , how would you code lumbo in the same language ?
Options: a ) 13426 , b ) 14236 , c ) 13436 , d ) 33426 , 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 . . . lumbo is 33426 . . . answer : d"
Answer: d
Question (gain): a shopkeeper has 280 kg of apples . he sells 30 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 30 x 20 % + 60 x 30 % = 24 this profit will remain same for any total quantity unless the % of products remains the same . hence ' a ' is the answer"
Answer: a
Question (general): pradeep has to obtain 20 % of the total marks to pass . he got 390 marks and failed by 25 marks . the maximum marks are
Options: a ) 300 , b ) 2075 , c ) 800 , d ) 1000 , e ) 3900
Rationale: "explanation : let their maximum marks be x . then , 20 % of x = 390 + 25 = > 20 / 100 x = 415 x = ( 41500 / 20 ) x = 2075 . answer : b"
Answer: b
Question (general): a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6500 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 8870 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6500 * 6 ) – 30,130 ] = rs . ( 39000 – 30,130 ) = rs . 8870 answer c"
Answer: c
Question (physics): if 30 men take 15 days to to complete a job , in how many days can 25 men finish that work ?
Options: a ) 18 , b ) 17 , c ) 16 , d ) 15 , e ) 14
Rationale: ans . 18 days
Answer: a
Question (general): if 7 a = 8 b and ab ≠ 0 , what is the ratio of a / 8 to b / 7 ?
Options: a ) 16 / 14 , b ) 8 / 7 , c ) 1 , d ) 7 / 8 , e ) 64 / 49
Rationale: "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 7 a = 8 b here ' s one pair : a = 8 and b = 7 what is the ratio of a / 8 to b / 7 ? in other words , what is the value of ( a / 8 ) / ( b / 7 ) ? plug in values to get : ( a / 8 ) / ( b / 7 ) = ( 8 / 8 ) / ( 7 / 7 ) = 1 / 1 = 1 c"
Answer: c
Question (gain): an empty fuel tank is filled with brand z gasoline . when the tank is 3 / 4 empty , it is filled with brand y gasoline . when the tank is half empty again , it is filled with brand z gasoline . when the tank is half empty again , it is filled with brand y gasoline . at this time , what percent of the gasoline in the tank is brand z ?
Options: a ) 40 % , b ) 41 % , c ) 43.75 % , d ) 42 % , e ) 44 %
Rationale: "work with fraction of brand z in the tank . 1 st step : brand z is 1 2 nd step : brand z is 1 / 2 3 rd step : brand z is ( 3 / 4 ) * ( 1 / 2 ) + 1 / 2 = 7 / 8 4 th step : brand z is ( 1 / 2 ) * ( 7 / 8 ) = 7 / 16 = 43.75 % answer ( c )"
Answer: c
Question (gain): what will be the fraction of 20 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 8 , e ) none of above
Rationale: "explanation : it will 20 * 1 / 100 = 1 / 5 answer : option b"
Answer: b
Question (physics): a cistern is filled by a tap in 6 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 81 , b ) 85 , c ) 88 , d ) 91 , e ) 95
Rationale: "filling rate - leak rate = net rate 1 / 6.5 - leak rate = 1 / 7 leak rate = 2 / 13 - 1 / 7 = 1 / 91 the answer is d ."
Answer: d
Question (general): 3 candidates contested in an election and received 4136 , 7636 , 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?
Options: a ) 45 % , b ) 49 % , c ) 50 % , d ) 51 % , e ) 62 %
Rationale: total number of votes polled = 4136 + 7636 + 11628 = 23400 required percentage = 11628 * 100 / 23400 = 50 % answer is c
Answer: c
Question (general): in a hostel , the number of students decreased by 12 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 5.3 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 12 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.88 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.88 * 1.2 ) = > f ( new ) = 0.9469 f therefore the new cost of food must be 94.69 % of the old cost , or the cost of food must decrease by 5.3 % ( option e )"
Answer: e
Question (geometry): if the radius of a cylinder is made 3 times and so is the height , what is the new volume of the cylinder divided by the old one ?
Options: a ) 27 . , b ) 2 . , c ) 6 . , d ) 4 . , e ) 10 .
Rationale: "let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 3 r ) ^ 2 ( 3 h ) v ' = 27 v a ) 27"
Answer: a
Question (general): the sum of number of boys and girls in a school is 1150 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 92 , e ) 70
Rationale: "we have x + x % of 1150 = 1150 x + x / 100 * 1150 = 1150 25 / 2 * x = 1150 x = 1150 * 2 / 25 = 92 answer is d"
Answer: d
Question (physics): p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 35 days to complete the same work . then q alone can do it in
Options: a ) 20 , b ) 22 , c ) 25 , d ) 28 , e ) 30
Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 35 work done by p , q and r in 1 day = 1 / 10 + 1 / 35 = 9 / 70 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 9 / 70 = > work done by p in 1 day = 9 / 140 = > work done by q and r in 1 day = 9 / 140 hence work done by q in 1 day = 9 / 140 â € “ 1 / 35 = 1 / 28 so q alone can do the work in 28 days answer is d ."
Answer: d
Question (probability): kim has 3 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 6 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 = 6 c 2 = 15 ; same color pairs = 3 c 1 * 1 c 1 = 3 ; prob = 1 / 5 ans b"
Answer: b
Question (general): simplify : 3005 - 3000 + 10
Options: a ) 2505 , b ) 2509 , c ) 2705 , d ) 2508 , e ) none of them
Rationale: 3005 - 3000 + 10 = 3005 - ( 3000 / 10 ) = 3005 - 300 = 2705 . answer is c
Answer: c
Question (general): a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 8 / 15 . how many tennis balls did the retailer order originally .
Options: a ) 110 , b ) 114.28 , c ) 140 , d ) 160 , e ) 214
Rationale: white : yellow = x : ( x + 50 ) = 8 : 15 - - > 15 x = 8 x + 400 - - > x = 57.14 . the total # of balls originally x + x = 57.14 + 57.14 = 114.28 . answer : b .
Answer: b
Question (general): when a merchant imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 94.50 , what was the total value of the item ?
Options: a ) $ 2,350 , b ) $ 2,850 , c ) $ 3,250 , d ) $ 3,400 , e ) $ 3,750
Rationale: let x be the value in excess of $ 1,000 . 0.07 x = 94.5 x = $ 1,350 the total value was $ 1,350 + $ 1,000 = $ 2,350 . the answer is a .
Answer: a
Question (other): how many numbers are divisible by both 2 and 3 up to 300 ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: divide 300 by 6 , as the numbers which are divisible by both 2 and 3 are also divisible by 6 . the quotient obtained after dividing 300 by 6 is 50 , hence answer is 50 . option a
Answer: a
Question (general): the result when a number subtracted from 150 is the same as the number added to 68 . what is the number ?
Options: a ) 110 , b ) 100 , c ) 109 , d ) 218 , e ) 210
Rationale: answer let the number be x . then , x - 68 = 150 - x â ‡ ’ 2 x = 150 + 68 = 218 â ‡ ’ 2 x = 218 â ˆ ´ x = 109 correct option : c
Answer: c
Question (geometry): the radius of a cylinder is 9 m , height 12 m . the volume of the cylinder is :
Options: a ) 2200 , b ) 5500 , c ) 3054.9 , d ) 1100 , e ) 4400
Rationale: "cylinder volume = ï € r ( power 2 ) h = 22 / 7 ã — 9 ã — 9 ã — 12 = 3054.9 m ( power 3 ) answer is c ."
Answer: c
Question (other): how many numbers up to 300 and 700 are divisible by 2 , 3 and 7 both together ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: ( 700 – 300 ) / 42 = 9 22 / 42 = > 9 numbers answer : a
Answer: a
Question (general): if x * y = xy – 2 ( x + y ) for all integers x and y , then 3 * ( – 3 ) =
Options: a ) – 16 , b ) – 9 , c ) – 4 , d ) 4 , e ) 16
Rationale: "3 * ( - 3 ) = 3 * ( - 3 ) - 2 ( 3 + ( - 3 ) ) = - 9 - 0 = - 9 option ( b )"
Answer: b
Question (general): total 90 cows 30 cow gives each 2 liter milk 30 cow gives each 3 / 4 liter milk 30 cow gives each 1 / 4 liter milk this is split into 3 son per each 30 cows & 30 liter milk how ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 30
Rationale: "30 cow 2 liter each = 60 liter 30 cow 3 / 4 liter each = 3 / 4 = 0.75 * 30 = 22.5 30 cow 1 / 4 liter each = 1 / 4 = 0.25 * 30 = 7.5 add 60 + 22.5 + 7.5 = 90 milk split into 3 son each 30 liter then 90 / 3 = 30 answer : e"
Answer: e
Question (physics): the ratio between the length and the breadth of a rectangular park is 1 : 3 . 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 ) 124545 m , b ) 134561 m , c ) 156787 m , d ) 15450 m , e ) 120000 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 1 x metres and breadth = 3 x metres . then , 2 ( 1 x + 3 x ) = 1600 or x = 200 . length = 200 m and breadth = 600 m . area = ( 600 x 200 ) m 2 = 120000 m e"
Answer: e
Question (other): the ratio of two quantities is incorrect when written as 10 to 14 . how should this ratio be written ?
Options: a ) 5 : 14 , b ) 10 : 7 , c ) 20 : 24 , d ) 5 : 7 , e ) it can not be determined from the information given
Rationale: a ratio should be reduced to the lowest common denominator . 10 : 14 means 10 x : 14 x which can be written as 5 ( 2 ) : 7 ( 2 ) . . . answer : d
Answer: d
Question (general): cereal a is 11 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 1 : 3 , d ) 1 : 4 , e ) 3 : 4
Rationale: "2 % is 3 % - points below 5 % and 11 % is 6 % - points above 5 % . the ratio of a : b should be 3 : 6 = 1 : 2 . the answer is a ."
Answer: a
Question (other): in a family 16 people eat only vegetarian , 9 people eat only non veg . , 12 people eat both veg and non veg . . how many people eat veg in the family ?
Options: a ) 28 , b ) 26 , c ) 22 , d ) 31 , e ) 21
Rationale: total people eat veg = only veg + both veg and non veg total = 16 + 12 = 28 answer = a
Answer: a
Question (general): if the price of sugar rises from rs . 10 per kg to rs . 11 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 9 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 11 = x = 91 kg . ∴ reduction in consumption = 9 % . answer a"
Answer: a
Question (general): the sum of the even numbers between 1 and n is 85 * 86 , where n is an odd number , then n = ?
Options: a ) 163 , b ) 171 , c ) 179 , d ) 185 , e ) 191
Rationale: "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 85 * 86 then a = 85 and n = 171 . the answer is b ."
Answer: b