Cheukting/mathqa huggingface dataset:
Question (other): in a class , 7 students like to play basketball and 5 like to play cricket . 3 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 9 , e ) 22
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 7 + 5 - 3 = 9 d )"
Answer: d
Question (probability): a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 22 ) * ( 6 ) , which indeed is 6 / 22 . e"
Answer: e
Question (physics): jerry travels 8 miles at an average speed of 40 miles per hour , stops for 12 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
Options: a ) 42 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5
Rationale: "total time taken by jerry = ( 8 / 40 ) * 60 minutes + 12 minutes + ( 20 / 60 ) * 60 minutes = 44 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 44 / 60 ) hours = 28 * 60 / 44 = 42 miles per hour answer : option a"
Answer: a
Question (physics): 8 men can dig a pit in 20 days . if a men work half as much again as a boy , then 4 men and 9 boys can dig a similar pit . fint the days for 15 boys can dig ?
Options: a ) 17 , b ) 10 , c ) 15 , d ) 20 , e ) 16
Rationale: 1 man = 3 / 2 boys ( 4 men + 9 boys ) = 15 boys 8 men = [ ( 3 / 2 ) + 8 ] = 12 boys now , 12 boys can dig the pit in 20 days . 15 boys can dig = 16 days . answer is option e
Answer: e
Question (gain): a man invests in a 16 % stock at 128 . the interest obtained by him is
Options: a ) 22.5 % , b ) 42.5 % , c ) 12.5 % , d ) 62.5 % , e ) 82.5 %
Rationale: by investing rs 128 , income derived = rs . 16 by investing rs . 100 , income derived = = rs . 12.5 interest obtained = 12.5 % answer : c
Answer: c
Question (other): in what ratio must tea at rs . 60 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 63 per kg ?
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 7 : 3 , e ) none
Rationale: "required ratio = 700 : 300 = 7 : 3 answer d"
Answer: d
Question (gain): how many pounds of salt at 80 cents / lb must be mixed with 40 lbs of salt that costs 35 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 5 , b ) 15 , c ) 40 , d ) 50 , e ) 25
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 35 cents / lb ( salt 1 ) with 80 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 80 - 40 ) / ( 40 - 35 ) = 8 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 5 lbs . answer ( a )"
Answer: a
Question (physics): how long does a train 120 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?
Options: a ) 33 , b ) 72 , c ) 52 , d ) 82 , e ) 62
Rationale: explanation : t = ( 660 + 120 ) / 54 * 18 / 5 t = 52 answer : option c
Answer: c
Question (probability): if 2 cards are selected at random from the deck of 52 cards then what is the probability of one of the selected cards will be king and other will be 10 ? a deck of cards has a total of 52 cards , consisting of 4 suits ; ( spades ( black ) , hearts ( red ) , diamond ( red ) s , and clubs ( black ) ) ; and 13 cards including 1 king , 1 queen and 1 jack in each suit
Options: a ) 8 / 2652 , b ) 18 / 2652 , c ) 1 / 2652 , d ) 12 / 2652 , e ) 16 / 2652
Rationale: 2 possible cases : king - 10 or 10 - king ( 4 kings and 4 10 ) . either way , the total probability = 2 ( king - 10 ) = 2 ( 4 / 52 * 4 / 51 ) = 18 / 2652 . b is the correct answer .
Answer: b
Question (physics): a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 10 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 20 , b ) 19 , c ) 18 , d ) 17 , e ) 16
Rationale: "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 10 + 9 = 19 . the answer is b ."
Answer: b
Question (general): 60 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 4 like all . how many people like apple ?
Options: a ) 47 , b ) 46 , c ) 54 , d ) 58 , e ) 67
Rationale: "orange + mango - apple = 7 mango + apple - orange = 10 apple = 60 orange + mango + apple = 4 60 + 10 + 4 - 7 = 67 like apple answer : e"
Answer: e
Question (gain): bhanu spends 30 % of his income on petrol on scooter 20 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 2287 , b ) 140 , c ) 128 , d ) 797 , e ) 123
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 20 % ( 700 ) = rs . 140 answer : b"
Answer: b
Question (general): the average of the first 5 multiples of 9 is :
Options: a ) 20 , b ) 27 , c ) 28 , d ) 30 , e ) none of these
Rationale: solution : required average = ( total sum of multiple of 9 ) / 5 = ( 9 + 18 + 27 + 36 + 45 ) / 5 = 27 note that , average of 9 and 45 is also 27 . and average of 18 and 36 is also 27 . answer : option b
Answer: b
Question (other): 13 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 2184
Rationale: "no . of ways of picking 2 biology books ( from 13 books ) = 13 c 2 = ( 13 * 12 ) / 2 = 78 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 78 * 28 = 2184 ( option e )"
Answer: e
Question (general): real - estate salesman z is selling a house at a 20 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 20 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 20 percent discount . salesman y ' s final price is what fraction of salesman x ' s final price ?
Options: a ) 29 / 32 , b ) 28 / 31 , c ) 30 / 31 , d ) 40 / 41 , e ) 34 / 15
Rationale: "let the retail price be = x selling price of z = 0.80 x selling price of x = 0.80 * 0.80 x = 0.64 x selling price of y = ( ( 0.80 x + 0.64 x ) / 2 ) * 0.80 = 0.72 x * 0.80 = 0.58 x 0.58 x = k * 0.64 x k = 0.58 / 0.64 = 58 / 64 = 29 / 32 answer : a"
Answer: a
Question (general): how many integers between 100 and 160 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 32 , b ) 27 , c ) 25 , d ) 35 , e ) 29
Rationale: "the total numbers between 100 and 160 , inclusive , is 61 . 3 * 34 = 102 and 3 * 53 = 159 so the number of multiples of 3 is 20 . 5 * 20 = 100 and 5 * 32 = 160 so the number of multiples of 5 is 13 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 10 = 150 so the number of multiples of 15 is 4 . thus the total number is 61 - 20 - 13 + 4 = 32 . the answer is a ."
Answer: a
Question (general): calculate the share of y , if rs . 690 is divided among x , y and z in the ratio 5 : 7 : 11 ?
Options: a ) 190 , b ) 160 , c ) 120 , d ) 151 , e ) 150
Rationale: "5 + 7 + 11 = 23 690 / 23 = 30 so y ' s share = 5 * 30 = 150 answer : e"
Answer: e
Question (gain): you hold some gold in a vault as an investment . over the past year the price of gold increases by 52 % . in order to keep your gold in the vault , you must pay 6 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 42.88 $ , b ) 43 % , c ) 45 % , d ) 45.5 % , e ) 46.3 %
Rationale: ( 100 % + 52 % ) * ( 100 % - 6 % ) = 152 * 0.94 = 142.88 % an increase of 42.88 % your gold holdings have increased in value by 42.88 % . the answer is a
Answer: a
Question (gain): a tank contains 9,000 gallons of a solution that is 6 percent sodium chloride by volume . if 3,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 6 % , b ) 7 % , c ) 8 % , d ) 9 % , e ) 10 %
Rationale: "we start with 9,000 gallons of a solution that is 6 % sodium chloride by volume . this means that there are 0.06 x 9,000 = 54 gallons of sodium chloride . when 3,000 gallons of water evaporate we are left with 6,000 gallons of solution . from here we can determine what percent of the 6,000 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 540 / 6,000 ) x 100 = ? 9 / 100 x 100 = ? = 9 % answer is d ."
Answer: d
Question (gain): a sum fetched a total simple interest of rs . 750 at the rate of 6 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 2600 , b ) 2500 , c ) 2900 , d ) 2800 , e ) 2700
Rationale: "sol . principal = rs . [ 100 * 750 / 6 * 5 ] = rs . [ 75000 / 30 ] = rs . 2500 . answer b"
Answer: b
Question (general): robert ate 12 chocolates , nickel ate 3 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2
Rationale: 12 - 3 = 9 . answer is c
Answer: c
Question (physics): in what time will a train 140 meters long cross an electric pole , if its speed is 210 km / hr
Options: a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 2.4 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 210 * ( 5 / 18 ) = 58 m / sec time = distance / speed = 140 / 58 = 2.4 seconds option d"
Answer: d
Question (physics): there are two cars . one is 300 miles north of the other . simultaneously , the car to the north is driven westward at 20 miles per hour and the other car is driven eastward at 60 miles per hour . how many miles apart are the cars after 5 hours ?
Options: a ) 300 , b ) 360 , c ) 400 , d ) 450 , e ) 500
Rationale: here , drawing a quick sketch of the ' actions ' described will end in a diagonal line that you canbuilda right triangle around : the right triangle will have a base of 400 and a height of 300 . the hidden pattern here is a 3 / 4 / 5 right triangle ( the 300 lines up with the ' 3 ' and the 400 lines up with the ' 4 ' ) . in this way , you can deduce that each side is ' 100 times ' bigger than it ' s corresponding side : 3 / 4 / 5 becomes 300 / 400 / 500 thus the distance between the two cars is the length of the hypotenuse of this larger right triangle . . . final answer : e
Answer: e
Question (gain): an investment compounds annually at an interest rate of 34.1 % what is the smallest investment period by which time the investment will more than triple in value ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 9 , e ) 12
Rationale: assume initial amount is x annual interest is 34.1 % so after 1 year the amount will become x * ( 100 + 34.1 ) / 100 = > x * 4 / 3 now we need to find n for x * ( 4 / 3 ) ^ n = 3 x ; or in other words n = 4 answer : b
Answer: b
Question (physics): the cross - section of a water channel is a trapezium in shape . if the channel is 12 meters wide at the top and 6 meters wide at the bottom and the area of cross - section is 630 square meters , what is the depth of the channel ( in meters ) ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "1 / 2 * d * ( 12 + 6 ) = 630 d = 70 the answer is c ."
Answer: c
Question (physics): a bicycle wheel has a diameter of 0.51 m . how many complete revolutions does it make in 1 km ?
Options: a ) 246 , b ) 448 , c ) 1408 , d ) 710 , e ) 624
Rationale: 1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.51 m ) = 624.5 . hence 624 complete revolutions . answer e
Answer: e
Question (geometry): triangle atriangle b are similar triangles with areas 1536 units square and 1734 units square respectively . the ratio of there corresponding height would be
Options: a ) 9 : 10 , b ) 17 : 19 , c ) 23 : 27 , d ) 16 : 17 , e ) 15 : 23
Rationale: "let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 1536 / 1734 ( x ^ 2 / y ^ 2 ) = ( 16 * 16 * 6 ) / ( 17 * 17 * 7 ) ( x ^ 2 / y ^ 2 ) = 16 ^ 2 / 17 ^ 2 x / y = 16 / 17 ans = d"
Answer: d
Question (physics): x can finish a work in 20 days . y can finish the same work in 16 days . y worked for 12 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 2 , b ) 3 , c ) 9 , d ) 5 , e ) 8
Rationale: "work done by x in 1 day = 1 / 20 work done by y in 1 day = 1 / 16 work done by y in 12 days = 12 / 16 = 3 / 4 remaining work = 1 – 3 / 4 = 1 / 4 number of days in which x can finish the remaining work = ( 1 / 4 ) / ( 1 / 20 ) = 5 d"
Answer: d
Question (general): if the average of 10 consecutive integers is 20.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 24 , e ) 25
Rationale: the average falls between the 5 th and 6 th integers , integer 5 = 20 , integer 6 = 21 . counting up to the tenth integer we get 25 . answer : e
Answer: e
Question (general): sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 55 marks . how many sums did sandy get correct ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 55 5 x = 115 x = 23 the answer is c ."
Answer: c
Question (general): a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money m did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: "notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ m = 20 answer : b"
Answer: b
Question (gain): last year elaine spent 10 % of her annual earnings on rent . this year she earned 15 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
Options: a ) 252.5 , b ) 364.5 , c ) 367.5 , d ) 375 , e ) 345
Rationale: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 10 of this on rent . this year she earned 15 % more , or $ 115 . she would ' ve spent 30 % of this on rent , or $ 34.5 do $ 34.5 / $ 10 this will give you 345 % e is the correct answer ."
Answer: e
Question (other): sandy is younger than molly by 8 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 18 , b ) 27 , c ) 36 , d ) 45 , e ) 54
Rationale: "s = m - 8 s / m = 7 / 9 9 s = 7 m 9 ( m - 8 ) = 7 m m = 36 the answer is c ."
Answer: c
Question (general): when x is multiplied by 3 , the result is 4 more than the result of subtracting x from 16 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 5 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 4 = 16 - x or , 4 x = 20 or , x = 5 . answer : c"
Answer: c
Question (general): in a certain school , 25 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 36 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 120 , d ) 150 , e ) 100
Rationale: "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 25 ) % of x = 75 % of x . 75 % of x = 36 + 2 / 3 of 36 75 / 100 x = 60 x = 80 . answer : option b"
Answer: b
Question (physics): how many seconds will a 600 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 48 , b ) 36 , c ) 26 , d ) 11 , e ) 18
Rationale: "explanation : here distance d = 600 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 36 sec . answer : b"
Answer: b
Question (physics): a train covers a distance of 12 km in 10 minutes . if it takes 9 seconds to pass a telegraph post , then the length of the train is
Options: a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 180 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 9 ) m = 180 m answer : option e"
Answer: e
Question (geometry): the radius of a cylindrical vessel is 7 cm and height is 1 cm . find the whole surface of the cylinder ?
Options: a ) 352 , b ) 771 , c ) 440 , d ) 767 , e ) 1981
Rationale: "r = 7 h = 1 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 8 ) = 352 answer : a"
Answer: a
Question (physics): machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 5600 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 60 / 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 5600 envelopes b will take 5600 / 1400 hrs = 4 hrs so the answer is choice c"
Answer: c
Question (general): if the probability of rain on any given day in chicago during the summer is 25 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 7 inclusive ?
Options: a ) 1 / 16 , b ) 3 / 32 , c ) 5 / 32 , d ) 3 / 64 , e ) 7 / 64
Rationale: "one possible case is : rainy - rainy - rainy - not rainy . the probability of this case is 1 / 4 * 1 / 4 * 1 / 4 * 3 / 4 = 3 / 256 the number of possible cases is 4 c 3 = 4 . p ( exactly 3 rainy days ) = 4 * 3 / 256 = 3 / 64 the answer is d ."
Answer: d
Question (general): what is the difference between the place value and face value of 4 in the numeral 46 ?
Options: a ) 36 , b ) 45 , c ) 52 , d ) 44 , e ) 39
Rationale: difference between the place value and face value of 4 = 40 - 4 = 36 answer is a
Answer: a
Question (general): in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 1,000 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 9,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 50 % , b ) 40 % , c ) 20 % , d ) 30 % , e ) 10 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 1000 : 9000 - - - - - > 1 : 9 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 10 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 10 ) * 100 - - - > 10 % answer : e"
Answer: e
Question (general): a person travels from p to q a speed of 30 km / hr and returns by increasing his speed by 30 % . what is his average speed for both the trips ?
Options: a ) 33 , b ) 77 , c ) 48 , d ) 99 , e ) 34.5
Rationale: "speed on return trip = 130 % of 30 = 39 km / hr . average speed of trip = 30 + 39 / 2 = 69 / 2 = 34.5 km / hr answer : e"
Answer: e
Question (general): the sum of all the integers f such that - 26 < f < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: "easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 f = - 49 . d is the answer ."
Answer: d
Question (general): the average expenditure of a labourer for 6 months was 70 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 i
Options: a ) 69 , b ) 72 , c ) 75 , d ) 78 , e ) 80
Rationale: "income of 6 months = ( 6 × 70 ) – debt = 420 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 690 average monthly income = 690 ÷ 10 = 69 answer a"
Answer: a
Question (general): a student chose a number , multiplied it by 8 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 30 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "solution : let xx be the number he chose , then 8 ⋅ x − 138 = 102 8 x = 240 x = 30 answer a"
Answer: a
Question (general): a man has rs . 192 in the denominations of one - rupee notes , 5 - rupee notes and 10 - rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?
Options: a ) 37 , b ) 36 , c ) 22 , d ) 90 , e ) 28
Rationale: let number of notes of each denomination be x . then , x + 5 x + 10 x = 192 16 x = 192 x = 12 . hence , total number of notes = 3 x = 36 . answer : b
Answer: b
Question (general): how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 40 percent butterfat to obtain milk that is 20 percent butterfat ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 16 , e ) 28
Rationale: "equate the fat : 0.1 x + 0.4 * 8 = 0.2 ( x + 8 ) - - > x = 16 . answer : d ."
Answer: d
Question (general): the price of lunch for 15 people was $ 211.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.78 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 211 is for 115 then we have to calculate for 100 for 115 211 for 100 x so by cross multiplication we get 115 x = 100 * 211 = > x = 100 * 211 / 110 by simplifying we get x as 191.81 which is the price of lunch before gratuity so the gratuity is 19.19 so as the question ask the average price person excluding gratuity is 191.81 / 15 = 12.78 so our answer is b )"
Answer: b