Cheukting/mathqa huggingface dataset:
Question (other): mrs . evans gave a test to her freshmen economics class , which has 30 students enrolled and 25 of them answered question 1 correctly . if 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?
Options: a ) 30 , b ) 28 , c ) 26 , d ) 22 , e ) 19
Rationale: total number of enrolled students = 30 number of students who did not take test = 5 hence , number of students who took test = 30 - 5 = 25 number of students who answered q 2 correctly = 22 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 22 . number of students who answered both q 1 & q 2 correctly = 22 . answer : d
Answer: d
Question (general): what is the smallest number which when diminished by 12 , is divisible 8 , 12 , 22 and 24 ?
Options: a ) 276 , b ) 295 , c ) 230 , d ) 225 , e ) 245
Rationale: "required number = ( lcm of 8 , 12 , 22 and 24 ) + 12 = 264 + 12 = 276 answer : option a"
Answer: a
Question (general): k is a 3 digit number such that the the ratio of the number to the sum of its digits is least . what is the difference between the hundreds and tens digit ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: explanation : this is only possible only when the hundreds digit has the least value and tens and units has the highest value . so we could get the highest possible sum but possible lowest number . so by this logic this number could only be 199 . so the difference is 8 . note : remember a number given as abc i . e abc = ax 100 + bx 10 + c . so 123 = 1 x 100 + 2 x 10 + 3 . answer : b
Answer: b
Question (general): ♠ n denotes the number obtained when n is rounded to the nearest tenth . for example ♠ 4.31 = 4.3 ♠ 2.423 - ♠ 3.421 =
Options: a ) 1.05 , b ) 1.04 , c ) - 0.8 , d ) - 1.0 , e ) - 0.1
Rationale: ♠ 2.423 - ♠ 3.421 2.4 - 3.2 = - 0.8 answer : c
Answer: c
Question (other): if 1 tic equals 5 tacs and 2 tacs equal 8 tocs , what is the ratio of one tic to one toc ?
Options: a ) 15 / 2 , b ) 20 / 1 , c ) 5 / 6 , d ) 3 / 10 , e ) 1 / 15
Rationale: "tic = 5 * tac and 2 * tac = 8 * toc ; 2 * tic = 10 * tac and 10 * tac = 40 * toc - - > 2 * tic = 40 * toc - - > tic / toc = 40 / 2 = 20 / 1 . answer : b ."
Answer: b
Question (physics): one hour after yolanda started walking from x to y , a distance of 65 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 5 miles per hour and bob â s was 7 miles per hour , how many miles had bob walked when they met ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 5 ( t + 1 ) miles . these distances must sum to 65 miles , so 7 t + 5 ( t + 1 ) = 65 , which may be solved for t as follows 7 t + 5 ( t + 1 ) = 65 7 t + 5 t + 5 = 65 12 t = 60 t = 5 ( hours ) therefore , bob had walked 7 t = 7 ( 5 ) = 35 miles when they met . the best answer is e ."
Answer: e
Question (gain): if 30 % of 100 is greater than 50 % of a number by 10 , then the number is ?
Options: a ) 40 , b ) 30 , c ) 60 , d ) 80 , e ) 50
Rationale: "let the number be x 30 % of 100 - 50 % of x = 10 50 / 100 x = ( 30 / 100 * 100 ) - 10 x / 2 = 20 x = 40 answer is a"
Answer: a
Question (general): there were 35 students in a hostel . due to the admission of 7 new students , he expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by rs 1 . what was the original expenditure of the mess ?
Options: a ) 125 , b ) 321 , c ) 561 , d ) 852 , e ) 420
Rationale: "let the original average expenditure be rs . x . then , 42 ( x - 1 ) - 35 x = 42 ; 7 x = 84 ; x = 12 . original expenditure = rs . ( 35 x 12 ) = rs . 420 . . ans : e"
Answer: e
Question (physics): at a speed of 40 miles per hour , a certain car uses 1 gallon of gasoline every 40 miles . if the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 40 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 5 / 12 , c ) 7 / 12 , d ) 2 / 3 , e ) 25 / 36
Rationale: "gas used = ( 5 hours ) * ( 40 miles / hour ) * ( 1 gallon / 40 miles ) = 5 gallons portion used = ( 5 ) / 12 = 5 / 12 ans b"
Answer: b
Question (general): niharika covers a distance in 30 min , if she drives at a speed of 60 km / h on an average . find the speed at which she must drive at to reduce the time of the journey by 30 % .
Options: a ) 84.71 kmph . , b ) 85.74 kmph . , c ) 83.71 kmph . , d ) 85.71 kmph . , e ) 84.71 kmph .
Rationale: given speed = 60 kmph . it means niharika covered 60 km in 60 min ( 1 hour ) . so , in 30 min he will cover 30 km . 30 % time reduced = 30 - 30 % of 30 = 21 min . thus , niharika needs to cover 30 km in 21 min ( 0.35 hour ) . speed * time = distance . speed * 0.35 = 30 speed = 85.71 kmph . answer : option d
Answer: d
Question (physics): rahul ' s housing colony have one tap , working alone at its maximum constant rate , can fill a certain tank in 230 seconds . a second tap , working alone at its maximum constant rate , can fill the same tank in 234 seconds . if both taps work together at their respective maximum constant rates , the time it will take to fill the tank is closest to
Options: a ) 116 seconds , b ) 150 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds
Rationale: tap 1 : 230 secs tap 2 : 234 secs considering the average of these 2 taps : 232 secs . so 1 tap can fill the tank in 232 secs , so 2 taps can fill the tank in 232 / 2 = 116 secs . closest answer is a .
Answer: a
Question (probability): a certain junior class has 1,000 students and a certain senior class has 600 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 40,000 , b ) 1 / 10,000 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "total number of ways of choosing one student from each group is = 600 * 1000 number of cases in which a sibling pair will be got is = 60 thus the probability that the 2 students selected will be a sibling pair is = 60 / ( 600 * 1000 ) = 1 / 10,000 b"
Answer: b
Question (general): what is the remainder when 8 ^ 1 + 8 ^ 2 + 8 ^ 3 + . . . + 8 ^ 9 is divided by 2 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) none of the above , e ) 5
Rationale: "notice that in the brackets we have the sum of 9 even multiples of 2 , which yields remainder of 0 upon division by 2 . answer : d"
Answer: d
Question (physics): a can do a work in 20 days , b in 30 days . a alone start the work after 10 days he left work . in how many days b can finish the work ?
Options: a ) 30 days , b ) 25 days , c ) 20 days , d ) 10 days , e ) 15 days
Rationale: "10 days work of a = 10 / 20 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 b can finish 1 / 2 work = 30 * 1 / 2 = 15 days answer is e"
Answer: e
Question (physics): there are 24 students in chad â € ™ s class . he brought 27 cookies to pass out for his birthday . how many cookies will each student get ? will there be any cookies left over ?
Options: a ) 1 - 9 , b ) 1 - 7 , c ) 2 - 8 , d ) 1 - 3 , e ) 3 - 10
Rationale: 27 / 24 = 1 r 3 chad will give each student 1 cookie and there will be 3 cookies left over correct answer d
Answer: d
Question (gain): a shopkeeper sells 450 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) 12 , b ) 27 , c ) 29 , d ) 45 , e ) 21
Rationale: sp per metre = 18000 / 450 = rs . 40 loss per metre = rs . 5 cp per metre = 40 + 5 = rs . 45 . answer : d
Answer: d
Question (general): a vessel of capacity 2 litre has 20 % of alcohol and another vessel of capacity 6 litre had 55 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 37 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: "20 % of 2 litres = 0.4 litres 55 % of 6 litres = 3.3 litres therefore , total quantity of alcohol is 3.7 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 37 % a"
Answer: a
Question (physics): a man goes from a to b at a speed of 35 kmph and comes back to a at a speed of 28 kmph . find his average speed for the entire journey ?
Options: a ) 38.9 kmph , b ) 38.8 kmph , c ) 38.1 kmph , d ) 37.1 kmph , e ) 37.8 kmph
Rationale: "distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 35 ) + ( d / 28 ] = ( 2 d ) / [ 11 d / 140 ) = > 38.1 kmph . answer : c"
Answer: c
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 22 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square .
Options: a ) 23.56 , b ) 33.0 , c ) 23.55 , d ) 23.53 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 22 + 20 ) = 84 cm parameter of the square = 84 cm i . e . 4 a = 84 a = 21 diameter of the semicircle = 21 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) 21 = 1 / 2 ( 22 / 7 ) ( 21 ) = 66 / 2 = 33 cm answer : b"
Answer: b
Question (general): a certain lab experiments with white and brown mice only . in one experiment , 2 / 5 of the mice are brown . if there are 12 white mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 20 , b ) 12 , c ) 15 , d ) 18 , e ) 16
Rationale: "let total number of mice = m number of brown mice = 2 / 5 m number of white mice = 3 / 5 m = 12 = > m = 20 answer a"
Answer: a
Question (geometry): the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the length and width of this rectangle .
Options: a ) w = 15 and l = 20
b ) w = 25 and l = 30
c ) w = 35 and l = 40
d ) w = 45 and l = 50
e ) w = 55 and l = 60
Rationale: l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer a
Answer: a
Question (gain): last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.6 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.6 ( x ) + 0.5 ( 1 - x ) = 0.75 0.1 x = 0.75 - 0.5 x = 0.25 / 0.1 x = 1 / 4 therefore the answer is a : 1 / 4 ."
Answer: a
Question (general): the total number of digits used in numbering the pages of a book having 346 pages is
Options: a ) 732 , b ) 990 , c ) 1098 , d ) 930 , e ) 1405
Rationale: "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 247 ) = ( 9 + 180 + 741 ) = 930 . answer : d"
Answer: d
Question (gain): a light has a rating of 110 watts , it is replaced with a new light that has 30 % higher wattage . how many watts does the new light have ?
Options: a ) 143 , b ) 145 , c ) 156 , d ) 134 , e ) 100
Rationale: "final number = initial number + 30 % ( original number ) = 110 + 30 % ( 110 ) = 110 + 33 = 143 . answer a"
Answer: a
Question (physics): a train 150 m long crosses a platform 100 m long in 10 sec ; find the speed of the train ?
Options: a ) 100 , b ) 70 , c ) 95 , d ) 90 , e ) 85
Rationale: "d = 150 + 100 = 250 t = 10 s = 250 / 10 * 18 / 5 = 90 kmph . answer : d"
Answer: d
Question (physics): calculate the time it will take for a train that is 240 meter long to pass a bridge of 130 meter length , if the speed of the train is 50 km / hour ?
Options: a ) 21.64 seconds , b ) 22.64 seconds , c ) 23.64 seconds , d ) 26.64 seconds , e ) 35.64 seconds
Rationale: "speed = 35 km / hr = 50 * ( 5 / 18 ) m / sec = 13.89 m / sec total distance = 240 + 130 = 370 meter time = distance / speed = 370 * ( 1 / 13.89 ) = 26.64 seconds answer : d"
Answer: d
Question (other): there are 200 doctors and nurses at a hospital . if the ratio of doctors to nurses is 4 to 6 , how many nurses are at the hospital ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "the number of nurses at the hospital is ( 6 / 10 ) * 200 = 120 . the answer is b ."
Answer: b
Question (gain): milk contains 5 % water . what content of pure milk should be added to 10 liters of milk to reduce this to 2 % ?
Options: a ) 10 liters , b ) 15 liters , c ) 20 liters , d ) 18 liters , e ) 22 liters
Rationale: "quantity of water in 10 liters = 5 % of 10 liters = 0.5 liters let x liters of pure milk be added . then , 0.5 / ( 10 + x ) = 2 / 100 2 x = 30 x = 15 liters answer is b"
Answer: b
Question (physics): the current in a river is 4 mph . a boat can travel 18 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 85.5 miles , c ) 96 miles , d ) 100 miles , e ) 112 miles
Rationale: "upstream speed = 18 - 4 = 14 mph downstream speed = 18 + 4 = 22 mph d / 14 + d / 22 = 10 hours solving for d we get d = 85.5 answer : b"
Answer: b
Question (general): a batsman scored 90 runs which included 2 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 40 % , b ) 50 % , c ) 57 % , d ) 60 % , e ) 80 %
Rationale: "explanation : number of runs made by running = 90 - ( 2 x 4 + 5 x 6 ) = 90 - ( 38 = 52 now , we need to calculate 38 is what percent of 90 . = > 52 / 90 * 100 = 57 % option c"
Answer: c
Question (general): for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 2835 what is the least possible value of k ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: "2835 = 3 * 3 * 3 * 3 * 5 * 7 thus k must include numbers at least up to the number 9 so that there are at least four appearances of 3 ( that is : 3 , 6 , and 9 = 3 * 3 ) . the answer is c ."
Answer: c
Question (other): in a class of 120 students , 25 did not opt for math . 10 did not opt for science and 2 did not opt for either . how many students of the class opted for both math and science ?
Options: a ) 63 , b ) 95 , c ) 77 , d ) 87 , e ) 48
Rationale: "120 students total 25 did not opt for math 10 did not opt for science 2 did not opt for either total of 95 students in math and 8 did not opt for sci but did for math 95 - 8 = 87 87 students of the class opted for both math and science answer : d . 87"
Answer: d
Question (other): the ratio of three numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: "let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e"
Answer: e
Question (general): at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 8.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 5.40
Rationale: "manager wages per hour = $ 8.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 8.50 ) = = > $ 4.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 4.25 = ( 20 * ( $ 4.25 ) ) / 100 - - > ( $ 85 ) / 100 - - > $ 0.85 therefore , chef wages per hour = $ 4.25 + $ 0.85 = = > $ 5.10 difference of wages between manager and chef = $ 8.50 - $ 5.10 = = > $ 3.40 answer : c"
Answer: c
Question (general): 101 ã — 101 + 99 ã — 99 = ?
Options: a ) 10002 , b ) 20004 , c ) 20002 , d ) 20102 , e ) 20202
Rationale: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1012 + 992 = ( 100 + 1 ) 2 + ( 100 â ˆ ’ 1 ) 2 = 2 ( 1002 + 12 ) = 2 ( 10000 + 1 ) = 20002 . answer : option c"
Answer: c
Question (gain): in a village of 2,600 people , 800 people are over 70 years old and 850 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a female or younger than 70 years old ?
Options: a ) 231 / 260 , b ) 117 / 130 , c ) 51 / 65 , d ) 23 / 32 , e ) 11 / 16
Rationale: "the number of people younger than 70 years old is 2600 - 800 = 1800 the number of females older than 70 years old is 0.6 * 850 = 510 the number of people who are either female or younger than 70 is 1800 + 510 = 2310 . p ( a person is younger than 70 or male ) = 2310 / 2600 = 231 / 260 the answer is a ."
Answer: a
Question (gain): jaclyn buys $ 40 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 950 , b ) 1234 , c ) 1289 , d ) 1345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 = 40000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 950 answer : a"
Answer: a
Question (gain): 60 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 14.4 , b ) 180 / 7 , c ) 50.4 , d ) 60 , e ) 90
Rationale: "60 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 60 ) * 100 = 60 square feet answer : option d"
Answer: d
Question (general): a case contains c cartons . each carton contains b boxes , and each box contains 500 paper clips . how many paper clips are contained in 2 cases ?
Options: a ) 500 bc , b ) 500 b / c , c ) 1000 bc , d ) 1000 b / c , e ) 1000 / bc
Rationale: "2 cases * c cartons / case * b boxes / carton * 500 clips / box = 1000 bc paper clips the answer is c ."
Answer: c
Question (physics): a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 8 hours of the journey .
Options: a ) 296 km , b ) 352 km , c ) 642 km , d ) 742 km , e ) 382 km
Rationale: "the total distance covered by the car in the first 8 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 = sum of 8 terms in ap whose first term is 30 and last term is 44 = 8 / 2 [ 30 + 44 ] = 296 km . answer : a"
Answer: a
Question (gain): a , b and c start a business with each investing rs 20000 . after 5 months a withdraws rs 5000 , b withdraws rs 4000 and c invests rs 6000 more . at the end of the year , a total profit of rs 69900 was recorded . find the share of a .
Options: a ) 20000 , b ) 21500 , c ) 20500 , d ) 22000 , e ) 21000
Rationale: a : b : c = ( 20000 × 5 + 15000 × 7 ) : ( 20000 × 5 + 16000 × 7 ) : ( 20000 × 5 + 26000 × 7 ) = ( 20 × 5 + 15 × 7 ) : ( 20 × 5 + 16 × 7 ) : ( 20 × 5 + 26 × 7 ) = 205 : 212 : 282 a ' s share = 69900 × 205 / ( 205 + 212 + 282 ) = 69900 × 205 / 699 = 20500 answer is c .
Answer: c
Question (gain): the c . p of 15 books is equal to the s . p of 20 books . find his gain % or loss % ?
Options: a ) 25 % loss , b ) 16 2 / 8 % loss , c ) 16 3 / 3 % loss , d ) 36 2 / 3 % loss , e ) 56 2 / 3 % loss
Rationale: "15 cp = 20 sp 20 - - - 5 cp loss 100 - - - ? = > 25 % loss answer : 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 . 6647 , how much amount did raghu invest ?
Options: a ) 2300 , 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 = 6647 = x = 6647 / 2.89 = 2300 therefore , amount invested by raghu is rs . 2300 . answer : a"
Answer: a
Question (gain): sonika bought a v . c . r . at the list price of 18,800 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 20,304 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,800 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,800 = 8 ⁄ 100 × 18800 = 1504 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,800 + 1504 = 20,304 . answer a"
Answer: a
Question (gain): a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 42 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 48 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.42 m = = > revenue = price x quantity = 0.48 ( m + w ) = = > profit = 0.48 ( m + w ) - 0.42 m = 0.2 * ( 0.42 m ) [ 20 % of cost ] = = > 0.48 m + 0.48 w - 0.42 m = 0.084 m = = > 0.024 m = 0.48 w = = > m / w = 0.48 / 0.024 = 20 - - or - - w / m = 1 / 20 a is correct ."
Answer: a
Question (general): 4524 - ? = 2456
Options: a ) 2058 , b ) 2069 , c ) 2072 , d ) 2089 , e ) none of these
Rationale: "explanation : none of these answer : option e"
Answer: e
Question (general): in a weight - lifting competition , the total weight of joe ' s two lifts was 600 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options: a ) 225 , b ) 275 , c ) 300 , d ) 350 , e ) 400
Rationale: "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 600 pounds . we sum the two variables to obtain : f + s = 600 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 600 3 f = 900 f = 300 answer is c"
Answer: c
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 12 cm .
Options: a ) 335 cm 2 , b ) 228 cm 2 , c ) 285 cm 2 , d ) 825 cm 2 , e ) 725 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 12 ) = 228 cm 2 answer : b"
Answer: b
Question (geometry): in measuring the sides of a rectangle , one side is taken 8 % in excess , and the other 7 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.44 % , d ) 0.6 % , e ) 0.8 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 27 / 25 ) x ( 40 / 43 ) y = ( 913 / 909 ) ( xy ) error in measurement = ( 913 / 909 ) xy - xy = ( 4 / 909 ) xy error percentage = [ ( 4 / 909 ) xy ( 1 / xy ) 100 ] % = ( 11 / 25 ) % = 0.44 % . answer is c ."
Answer: c
Question (general): what is the 9 th digit to the right of the decimal point in the decimal equivalent of 48 / 11 ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 2
Rationale: "48 / 11 = 4.3636 . . . . 36 is non - terminating repeating decimal . the 9 th digit to the right of decimal point will be 3 . answer a"
Answer: a