Cheukting/mathqa huggingface dataset:
Question (general): in a school with 632 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
Options: a ) 150 , b ) 200 , c ) 250 , d ) 158 , e ) none
Rationale: "sol . let the number of grils be x . then , number of boys = ( 632 - x ) . then , ( 11 3 / 4 × 632 ) ⇔ 11 x + 12 ( 632 - x ) ⇔ x = 7584 - 7426 ⇔ 158 . answer d"
Answer: d
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.15 km and 0.6 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 42 , b ) 9 , c ) 7 , d ) 67 , e ) 15
Rationale: ": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.15 + 0.6 = 1.75 km = 1750 m . required time = 1750 * 3 / 125 = 42 sec . answer : a"
Answer: a
Question (general): sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 152 . if the ratio of his marks in english and maths is 1 : 5 , find his marks in science ?
Options: a ) 8 , b ) 77 , c ) 66 , d ) 55 , e ) 31
Rationale: "s : e = 1 : 3 e : m = 1 : 5 - - - - - - - - - - - - s : e : m = 1 : 3 : 15 1 / 19 * 152 = 8 answer : a"
Answer: a
Question (gain): the salary of a person was reduced by 28 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 38.9 %
Rationale: "let the original salary be $ 100 new salary = $ 72 increase on 72 = 28 increase on 100 = [ ( 28 / 72 ) 100 ] % = 38.9 % answer is e"
Answer: e
Question (general): the average height of 35 boys in a class was calculated as 183 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 181.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 183 cm . wrong total height of 35 boys = 183 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm - 106 cm ) / 35 = 183 cm - 60 / 35 cm = 183 cm - 1.71 cm = 181.29 cm . answer : b"
Answer: b
Question (physics): a is half good a work man as b and together they finish a job in 14 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 36 , e ) 48
Rationale: "c 21 wc = 1 : 2 2 x + x = 1 / 14 = > x = 1 / 42 2 x = 1 / 21 = > 21 days"
Answer: c
Question (general): each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.55 % , what fraction of the products was checked by worker y ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 8
Rationale: "x : 0.5 % is 0.05 % - points from 0.55 % . y : 0.8 % is 0.25 % - points from 0.55 % . therefore the ratio of products checked by y : x is 1 : 5 . thus , worker y checked 1 / 6 of the products . the answer is d ."
Answer: d
Question (gain): a baseball card decreased in value 40 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 46 % , e ) 72 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.6 = 60 after second year price = 60 * 0.9 = 54 final decrease = [ ( 100 - 54 ) / 100 ] * 100 = 46 % correct answer - d"
Answer: d
Question (probability): from a group of 3 boys and 3 girls , 4 children are to be randomly selected . what is the probability that equal numbers of boys and girls will be selected ?
Options: a ) 1 / 10 , b ) 4 / 9 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: prob reqd = 1 - probab of not having eq numbers prob of not having eq no ' s is = prob of having 3 boys and 1 girl or prob of having 3 girls and 1 boy = ( 1 * 3 / 15 ) + ( 3 / 15 * 1 ) = 2 / 5 reqd prob = 1 - 2 / 5 = 3 / 5 answer : d
Answer: d
Question (general): 9 years ago i was 5 times as old as my eldest son . today i am 3 times his age . how old am i now ?
Options: a ) 45 , b ) 54 , c ) 34 , d ) 58 , e ) 56
Rationale: x - 9 = 5 ( y - 9 ) & x = 3 y x - 9 = 5 x / 3 - 45 x = 54 answer : b
Answer: b
Question (other): find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 90 = 2 : 3 answer : b"
Answer: b
Question (other): a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is 4 times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 12 : 8 , b ) 8 : 16 , c ) 9 : 16 , d ) 8 : 12 , e ) 16 : 9
Rationale: water : soap = 3 : 2 soap : salt = 12 : 8 = > for 12 soap , salt = 8 = > for 2 soap , salt = ( 8 / 12 ) * 2 = 16 / 12 = 4 / 3 so , water : soap : salt = 3 : 2 : 4 / 3 = 9 : 6 : 4 after open container , water : soap : salt = 2.25 : 6 : 4 so , water : salt = 2.25 : 4 = 9 : 16 answer : c
Answer: c
Question (other): initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many q women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number q = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"
Answer: d
Question (general): a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 225.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
Options: a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60
Rationale: "let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 225 = > 125 * s = 150 = > s = 1.2 answer d"
Answer: d
Question (gain): a and b invests rs . 3000 and rs . 5500 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 8 : 8 , b ) 9 : 8 , c ) 9 : 7 , d ) 9 : 5 , e ) 9 : 11
Rationale: "( 3 * 6 + 6 * 6 ) : ( 5.5 * 12 ) 54 : 66 = > 9 : 11 answer : e"
Answer: e
Question (gain): if a lends rs . 3150 to b at 8 % per annum and b lends the same sum to c at 12.5 % per annum then the gain of b in a period of 2 years is ?
Options: a ) 280 , b ) 295 , c ) 283.5 , d ) 245 , e ) 200
Rationale: "( 3150 * 4.5 * 2 ) / 100 = > 283.5 answer : c"
Answer: c
Question (other): apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 663 and for 36 kgs of apples is 726 then the cost of first 10 kgs of apples is
Options: a ) 100 , b ) 150 , c ) 200 , d ) 350 , e ) 450
Rationale: ans : by framing equations we get 30 l + 3 q = 663 30 l + 6 q = 726 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 20 cost of 10 kgs of apples = 10 x 20 = 200 answer : c
Answer: c
Question (general): 10 + 19
Options: a ) 29 , b ) 13 , c ) 28 , d ) 6 , e ) 2
Rationale: a
Answer: a
Question (gain): a and b started a business investing rs . 80,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 4 : 1 , b ) 3 : 2 , c ) 18 : 20 , d ) 18 : 4 , e ) 17 : 4
Rationale: "a : b = 80000 : 20000 = 8 : 2 = 4 : 1 answer : a"
Answer: a
Question (physics): a rower can row 7 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
Options: a ) 2.92 , b ) 3.04 , c ) 3.12 , d ) 3.21 , e ) 3.35
Rationale: let x be the distance to big rock . time = x / 5 + x / 9 = 1 x = 45 / 14 = 3.21 km the answer is d .
Answer: d
Question (general): the average of first 35 prime numbers is ?
Options: a ) 14.54 , b ) 15.6 , c ) 15.8 , d ) 14.7 , e ) 14.8
Rationale: "explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 ) / 11 = 160 / 11 = 14.54 ( approx ) answer is a"
Answer: a
Question (physics): a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a women alone in 18 days , how long will a boy take to complete the work ?
Options: a ) 6 days , b ) 8 days , c ) 9 days , d ) 7 days , e ) 5 days
Rationale: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 womans 1 day ’ s work = 1 / 18 ( 1 man + 1 woman ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 boys 1 day ’ s work = 1 / 3 – 2 / 9 = 3 - 2 / 9 = 1 / 9 therefore , the boy alone can finish the work in 9 days . answer : option c"
Answer: c
Question (general): the least number which should be added to 1789 so that the sum is exactly divisible by 5 , 6 , 4 and 3 is ?
Options: a ) 1 , b ) 11 , c ) 21 , d ) 31 , e ) 41
Rationale: l . c . m . of 5 , 6 , 4 and 3 = 60 . on dividing 1789 by 60 , the remainder is 49 . number to be added = ( 60 - 49 ) = 11 b )
Answer: b
Question (general): i chose a number and divide it by 8 . then i subtracted 160 from the result and got 12 . what was the number i chose ?
Options: a ) 1376 , b ) 1800 , c ) 1400 , d ) 2500 , e ) 100
Rationale: "let x be the number i chose , then x / 8 − 160 = 12 x / 8 = 172 x = 1376 answer is a ."
Answer: a
Question (general): solve for x and check : - 12 x = 72
Options: a ) - 4 , b ) - 2 , c ) - 6 , d ) - 12 , e ) none of these
Rationale: "solution : dividing each side by - 12 , we obtain ( - 12 x / - 12 ) = ( 72 / - 12 ) therefore : x = - 6 check : - 12 x = 72 ( - 12 * - 6 ) = 72 72 = 72 answer : c"
Answer: c
Question (general): a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 40 , how many horses are there ?
Options: a ) 8 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: legs 8 * 4 = 32 now half on their horses so remaining on the walk so 4 men 4 men has 8 legs so , 8 + 32 = 40 legs walking answer : a
Answer: a
Question (physics): workers at a campaign office have 3000 fliers to send out . if they send out 1 / 5 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ?
Options: a ) 1800 , b ) 800 , c ) 1100 , d ) 1200 , e ) 1900
Rationale: "( 1 / 5 ) * 3000 = 600 remaining = 3000 - 600 = 2400 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 2400 = 600 remaining now = 2400 - 600 = 1800 answer : option a"
Answer: a
Question (general): find the average of first 20 multiples of 7 ?
Options: a ) 73.5 , b ) 70.5 , c ) 63.5 , d ) 54.5 , e ) 40.5
Rationale: "required average = 7 ( 1 + 2 + 3 + … … . + 20 ) / 20  ( 7 * 20 * 21 ) / ( 20 * 2 )  ( 147 / 2 ) = 73.5 . answer a 73.5"
Answer: a
Question (geometry): the diagonal of a rhombus are 70 m and 160 m . its area is :
Options: a ) 1940 , b ) 4800 , c ) 5600 , d ) 5200 , e ) 5000
Rationale: "area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 70 ã — 160 ) cm ( power ) 2 = 70 ã — 80 = 5600 cm ( power ) 2 answer is c ."
Answer: c
Question (gain): 50 % of a number is more than 40 % of 120 by 180 . find the number ?
Options: a ) 456 , b ) 480 , c ) 420 , d ) 445 , e ) 320
Rationale: "( 50 / 100 ) * x – ( 40 / 100 ) * 120 = 180 1 / 2 x = 228 x = 456 answer : a"
Answer: a
Question (gain): sheela deposits rs . 5000 in bank savings account . if this is 20 % of her monthly income . what is her monthly income in ?
Options: a ) 22000 , b ) 20000 , c ) 25000 , d ) 22235 , e ) none of these
Rationale: "explanation : 20 % of income = rs . 5000 100 % of income = 5000 x 100 / 20 = rs . 25000 answer : c"
Answer: c
Question (general): there are 4 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 8 , c ) 40 , d ) 60 , e ) 120
Rationale: "each person is one participant of 4 games . so there are in all 4 * 4 = 16 instances of one participant games . but each game has 2 participants so total number of games = 16 / 2 = 8 b"
Answer: b
Question (physics): a 24 ' ' x 24 ' ' square metal plate needs to be fixed by a carpenter on to a wooden board . the carpenter uses nails all along the edges of the square such that there are 25 nails on each side of the square . each nail is at the same distance from the neighboring nails . how many nails does the carpenter use ?
Options: a ) 94
b ) 95
c ) 96
d ) 97
e ) 98
Rationale: every corner will have one , 4 corners will have 4 + and for 4 sides 23 no of nails = 4 + ( 4 * 23 ) = 96 answer : c
Answer: c
Question (general): the sum of the ages of 5 children born at the intervals of 3 year each is 50 year . what is the age of the eldest child ?
Options: a ) 16 year , b ) 8 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 â ‡ ” 5 x = 20 â ‡ ” x = 4 . â ˆ ´ age of the eldest child = x + 12 = 4 + 12 = 16 years . answer a"
Answer: a
Question (general): let the number which when multiplied by 15 is increased by 280 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: "solution let the number be x . then , 15 x - x = 280 ‹ = › 14 x = 280 x ‹ = › 20 . answer b"
Answer: b
Question (general): in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 105 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 105 5 x - 20 = 105 5 x = 125 x = 25 the answer is b ."
Answer: b
Question (physics): at 15 : 00 there were 22 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 8 students left the lab , how many students were in the computer lab at 15 : 44 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 32
Rationale: "initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 32 e"
Answer: e
Question (general): 475.124 x 15.98 ÷ 8.001 + 33.33 = ?
Options: a ) 983.578 , b ) 659.121 , c ) 781.189 , d ) 656.112 , e ) 456.512
Rationale: "explanation : ? = 475.124 x ( 15.98 ÷ 8.001 ) + 33.33 ≈ ( 475.124 x 16 / 8 ) + 33.33 ≈ 950.248 + 33.33 ≈ 983.578 answer : option a"
Answer: a
Question (physics): 20 men can cut 30 trees in 4 hours . if 4 men leave the job , how many trees will be cut in 6 hours ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 22 , e ) 32
Rationale: "20 men - working 4 hrs - cut 30 trees 1 men - working 1 hr - cuts = 30 / 20 * 4 thus 16 men - working 6 hrs - cut = 30 * 16 * 6 / 20 * 4 = 36 trees answer is b"
Answer: b
Question (probability): 4 dices are thrown at the same time . what is the probability of getting only 2 dices showing the same face ?
Options: a ) 4 / 9 , b ) 5 / 9 , c ) 11 / 18 , d ) 7 / 9 , e ) none of the above
Rationale: probability of getting two same faces : 1 and 1 / 6 for other two faces , probabilities : 5 / 6 and 4 / 6 respectively . the dice combinations can be arranged in 4 ! / 2 ! ways total probability = 1 * 1 / 6 * 5 / 6 * 4 / 6 * 4 ! / 2 ! = 5 / 9 answer : b
Answer: b
Question (geometry): mr . loyd wants to fence his square shaped land of 60 sqft each side . if a pole is laid every 12 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "if each side is 120 feet . . then total perimeter is 60 * 4 = 240 poles every 12 feet hence no of poles = 240 / 12 = 20 answer : a"
Answer: a
Question (general): the average of first six prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 34
Rationale: "23 + 29 + 31 + 37 + 41 + 43 = 204 / 6 = 34 answer : e"
Answer: e
Question (physics): a boat having a length 7 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 100 kg , b ) 120 kg , c ) 89 kg , d ) 80 kg , e ) 210 kg
Rationale: "volume of water displaced = ( 7 x 3 x 0.01 ) m 3 = 0.21 m 3 . mass of man = volume of water displaced x density of water = ( 0.21 x 1000 ) kg = 210 kg . answer : e"
Answer: e
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 50 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 5.5 , c ) 7.4 , d ) 5 , e ) 6
Rationale: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 50 run rate needed = 250 / 50 = 5 answer : option d"
Answer: d
Question (general): the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 0.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?
Options: a ) $ 2.00 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00
Rationale: "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 0.50 + 0.50 ( x − 2 ) = 0.50 + . 5 * 3 = 0.5 + 1.5 = 2 $ answer a"
Answer: a
Question (general): if a : b : : 3 : 7 , then what is ( 5 a + 2 b ) : ( a - 2 b ) ?
Options: a ) 57 : 11 , b ) - 57 : 11 , c ) 11 : 10 , d ) - 29 : 11 , e ) - 1 : 10
Rationale: "a / b = 3 / 7 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 2 ] / [ ( a / b ) - 2 ] = [ 5 * ( 3 / 7 ) + 2 ] / [ ( 3 / 7 ) - 2 ] = - 29 / 11 answer : d"
Answer: d
Question (general): in a group of 100 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
Options: a ) 0.1 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85
Rationale: number of people whose age is less than 20 is given by 100 - 90 = 10 probability p that a person selected at random from the group is less than 20 is given by 10 / 100 = 0.1 correct answer a
Answer: a
Question (gain): an article is bought for rs . 1200 and sold for rs . 800 , find the loss percent ?
Options: a ) 16 % , b ) 35 % , c ) 33 % , d ) 18 % , e ) 12 %
Rationale: "1200 - - - - 400 100 - - - - ? = > 33 % answer : c"
Answer: c
Question (general): how much is 80 % of 45 is greater than 4 / 5 of 25 ?
Options: a ) 15 , b ) 57 , c ) 16 , d ) 16 , e ) 73
Rationale: "( 80 / 100 ) * 45 â € “ ( 4 / 5 ) * 25 36 - 20 = 16 answer : c"
Answer: c
Question (physics): a small water pump would take 3 hours to fill an empty tank . a larger pump would take 3 / 4 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
Options: a ) 3 / 4 , b ) 3 / 5 , c ) 5 / 7 , d ) 1 / 2 , e ) 4 / 5
Rationale: "rate of the small pump is 1 / 3 tank / hour rate of the larger pump is 1 / ( 3 / 4 ) or 4 / 3 tank / hour ; combined rate of the two pumps is 1 / 3 + 4 / 3 = 5 / 3 tank / hour , together they will fill the empty tank in 1 / ( 5 / 3 ) ) = 3 / 5 hours ( time = job / rate ) . answer : b"
Answer: b
Question (general): if p ( a ) = 5 / 7 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 7 / 25 , b ) 3 / 25 , c ) 8 / 25 , d ) 2 / 7 , e ) 3 / 17
Rationale: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 5 / 7 . 2 / 5 p ( a n b ) = 2 / 7 . d"
Answer: d
Question (general): divide rs . 5500 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 1 / 5 as a and c together . a ' s share is ?
Options: a ) 1227 , b ) 1268 , c ) 1375 , d ) 1200 , e ) 1210
Rationale: "a + b + c = 5500 a = 1 / 3 ( b + c ) ; b = 1 / 5 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 5500 = > 1375 answer : c"
Answer: c
Question (general): in digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 100 cu . m , b ) 1000 cu . m , c ) 10000 cu . m , d ) 2000 cu . m , e ) 4000 cu . m
Rationale: "20 * 10 * 5 = 1000 answer : b"
Answer: b
Question (physics): in traveling from a dormitory to a certain city , a student went 1 / 3 of the way by foot , 3 / 5 of the way by bus , and the remaining 2 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 120
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 3 x + 3 / 5 x + 2 x - 1 / 3 x - 3 / 5 x = 2 x = 30 km option : a"
Answer: a
Question (physics): a factory produces 6500 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 1375 toys , b ) 2375 toys , c ) 1300 toys , d ) 1375 toys , e ) 2375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 6500 / 5 = 1300 toys correct answer c"
Answer: c
Question (gain): a farmer spent $ 37 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.70
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 37 = $ 14.8 on chicken feed , thus he spent the remaining 37 - 14.8 = $ 22.2 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 14.8 - - > x = $ 18.5 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 18.5 + 22.2 = $ 40.7 . answer : e"
Answer: e
Question (gain): the charge for a single room at hotel p is 20 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 12.5 % , d ) 50 % , e ) 150 %
Rationale: "let rate in r = 100 x then p = 80 x g = 100 y p = 90 y thus 80 x = 90 y or x = 1.125 y ans r = 112.5 y so increase = 12.5 % answer : c"
Answer: c
Question (geometry): the ratio of the volumes of two cubes is 729 : 125 . what is the ratio of their total surface areas ?
Options: a ) 81 : 21 , b ) 81 : 22 , c ) 81 : 24 , d ) 81 : 25 , e ) 81 : 29
Rationale: "ratio of the sides = 3 √ 729 : 3 √ 125 = 9 : 5 ratio of surface areas = 9 ^ 2 : 5 ^ 2 = 81 : 25 answer : option d"
Answer: d