Cheukting/mathqa huggingface dataset:
Question (general): running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 4 w widgets .
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 24
Rationale: "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 24 days to doing 4 w widgets . answer : e"
Answer: e
Question (general): the average of first 32 natural numbers is ?
Options: a ) 16.5 , b ) 17.5 , c ) 18.4 , d ) 15.4 , e ) 15.1
Rationale: "sum of 32 natural no . = 1056 / 2 = 55 average = 528 / 32 = 16.5 answer : a"
Answer: a
Question (physics): a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 4680 , what will be a ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 520 , c ) $ 2080 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 4680 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 4680 will be 4 : 3 : 2 . hence , a ' s share will be 4 * 4680 / 9 = 2080 . correct choice is ( c )"
Answer: c
Question (gain): by selling an article at rs . 600 , a profit of 25 % is made . find its cost price ?
Options: a ) 322 , b ) 480 , c ) 287 , d ) 192 , e ) 107
Rationale: "explanation : sp = 600 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / ( 100 + 25 ) ] = 600 * [ 100 / 125 ] = rs . 480 answer : b"
Answer: b
Question (gain): ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 1200 then loss of pyarelal ?
Options: a ) 600 , b ) 700 , c ) 1080 , d ) 900 , e ) 1000
Rationale: let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1200 , loss of pyarelal = 1200 * 9 x / 10 x = 1080 answer : c
Answer: c
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 20 m wide at the top and 12 m wide at the bottom and the area of cross - section is 800 sq m , the depth of cannel is ?
Options: a ) 76 , b ) 50 , c ) 27 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 20 + 12 ) = 800 d = 50 answer : b"
Answer: b
Question (physics): the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 95 per day . what was his wage on the 8 th day ?
Options: a ) $ 76 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 104
Rationale: average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 95 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 95 * 7 ) = 1350 - ( 609 + 665 ) = 1350 - 1274 = 76 answer a
Answer: a
Question (gain): what is the rate percent when the simple interest on rs . 1500 amount to rs . 250 in 5 years ?
Options: a ) 3.33 % , b ) 6 % , c ) 2 % , d ) 95 % , e ) 1 %
Rationale: "interest for 5 yrs = 250 interest for 1 yr = 50 interest rate = 50 / 1500 x 100 = 3.33 % answer : a"
Answer: a
Question (physics): nd the area of trapezium whose parallel sides are 20 cm and 15 cm long , and the distance between them is 14 cm ?
Options: a ) 230 cm 2 , b ) 245 cm 2 , c ) 255 cm 2 , d ) 260 cm 2 , e ) 280 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 15 ) * ( 14 ) = 245 cm 2 answer : b"
Answer: b
Question (physics): if 50 apprentices can finish a job in 4 hours , and 30 journeymen can finish the same job in 7 hours , how much of the job should be completed by 10 apprentices and 15 journeymen in one hour ?
Options: a ) 17 / 140 , b ) 29 / 180 , c ) 26 / 143 , d ) 1 / 5 , e ) 39 / 121
Rationale: "50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 7 * 2 = 14 hours ; in 1 hour 15 journeymen can finish 1 / 14 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 14 = 17 / 140 of the job . answer : a"
Answer: a
Question (general): a sum of money lent out at s . i . amounts to a total of $ 420 after 2 years and to $ 595 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 310 , b ) $ 320 , c ) $ 330 , d ) $ 340 , e ) $ 350
Rationale: "s . i for 5 years = $ 595 - $ 420 = $ 175 the s . i . is $ 35 / year s . i . for 2 years = $ 70 principal = $ 420 - $ 70 = $ 350 the answer is e ."
Answer: e
Question (physics): donovan and michael are racing around a circular 300 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 6 , b ) 9 , c ) 8 , d ) 7 , e ) 10
Rationale: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 300 / 45 = > 60 / 9 2 . speed / rate of michael = distance / time = > 300 / 40 = > 30 / 4 relative speed between them = 30 / 4 - 60 / 9 = > 270 - 240 / 36 = 30 / 36 = 5 / 6 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 300 , relative rate = 5 / 6 total time taken by micheal to surpass donovan = distance / rate = > 300 * 6 / 5 = > 1800 / 5 = > 360 no . of laps taken by michael = total time / michael ' s rate = > 360 / 40 = > 9 hence correct answer is 9 laps . b"
Answer: b
Question (general): the average age of a group of persons going for picnic is years . fifteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is
Options: a ) 5 , b ) 10 , c ) 15 , d ) 40 , e ) 50
Rationale: solution let the initial number of persons be x . then 16 x + 15 x 15 = 15.5 ( x + 20 ) = 0.5 x = 7.5 x = 15 . answer c
Answer: c
Question (general): the average of 10 numbers was calculated as 19 . it is discovered later on that while calculating the average , one number , namely 76 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "10 * 19 - 26 + 76 = 240 240 / 10 = 24 the answer is d ."
Answer: d
Question (gain): anand and deepak started a business investing rs . 22,500 and rs . 35,000 respectively . out of a total profit of rs . 13,800 , deepak ’ s share is _____
Options: a ) 5400 , b ) 3797 , c ) 27877 , d ) 2772 , e ) 9911
Rationale: explanation : ratio of their investments = 22500 : 35000 = 9 : 14 so deepak ' s share = 923923 × 13800 = rs . 5,400 answer : a
Answer: a
Question (general): of the 3,600 employees of company x , 3 / 4 are clerical . if the clerical staff were to be reduced by 4 / 5 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 37 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: "let ' s see , the way i did it was 3 / 4 are clerical out of 3600 so 2700 are clerical 2700 reduced by 4 / 5 is 2700 * 4 / 5 so it reduced 2160 people , so there is 540 clerical people left but since 2160 people left , it also reduced from the total of 3600 so there are 1440 people total since 540 clerical left / 1440 people total you get ( a ) 37 %"
Answer: a
Question (general): the sum of the squares of three numbers is 41 , while the sum of their products taken two at a time is 20 . their sum is :
Options: a ) 10 , b ) 5 , c ) 9 , d ) 15 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 138 xy + yz + zx = 131 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 41 + ( 2 * 20 ) ( x + y + z ) ^ 2 = 81 so x + y + z = 9 answer : c"
Answer: c
Question (general): when a merchant imported a certain item , she 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 $ 109.90 , what was the total value of the item ?
Options: a ) $ 1940 , b ) $ 2150 , c ) $ 2360 , d ) $ 2570 , e ) $ 2780
Rationale: let x be the value of the item . 0.07 * ( x - 1000 ) = 109.90 x = 2570 the answer is d .
Answer: d
Question (general): a cyclist rides a bicycle 9 km at an average speed of 12 km / hr and again travels 12 km at an average speed of 9 km / hr . what is the average speed for the entire trip ?
Options: a ) 9.5 , b ) 9.8 , c ) 10.1 , d ) 10.6 , e ) 11.2
Rationale: "distance = 21 km time = 9 / 12 + 12 / 9 = ( 81 + 144 ) / 108 = 225 / 108 = 25 / 12 hours average speed = ( 21 * 12 ) / 25 = 10.1 km / h the answer is c ."
Answer: c
Question (other): tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 173 per kg , the price of the third variety per kg will be
Options: a ) rs . 169.50 , b ) rs . 1700 , c ) rs . 195.50 , d ) rs . 180 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 173 / 22.50 = 1 = â € º x - 173 = 22.50 = â € º x = 195.50 . hence , price of the third variety = rs . 195.50 per kg . answer c"
Answer: c
Question (gain): 110 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 150 , d ) 155 , e ) 165
Rationale: "final number = initial number + 50 % ( original number ) = 110 + 50 % ( 110 ) = 110 + 55 = 165 . answer e"
Answer: e
Question (physics): in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 8 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 24 standard orders ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "the choices give away the answer . . 36 machines take 4 hours to fill 8 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 24 / 8 = 6 ans b"
Answer: b
Question (general): a textile manufacturing firm employees 50 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 50 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 5000 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 − ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 × ( 49 / 50 ) − 150000 × ( 49 / 50 ) − 75000 . = > rs 2 , 68,000 . decrease in profit = > 2 , 75,000 − 2 , 68,000 = > rs . 7,000 . answer : b"
Answer: b
Question (general): find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 4 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1346 , c ) 1378 , d ) 1635 , e ) 1815
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 4 x + 15 3 x = 1350 x = 450 large number = 450 + 1365 = 1815 e"
Answer: e
Question (physics): sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 216 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 6
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 216 per week 36 x = 216 x = 6 correct option : e"
Answer: e
Question (gain): by selling 15 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ?
Options: a ) 2.15 , b ) 4.2 , c ) 5.18 , d ) 3.75 , e ) 4.2
Rationale: "40 % - - - 15 160 % - - - ? 40 / 160 * 15 = 3.75 answer : d"
Answer: d
Question (physics): find the area of a cuboid of length 10 cm , breadth 8 cm . and height 6 cm .
Options: a ) 400 cm cube , b ) 410 cm cube , c ) 420 cm cube , d ) 430 cm cube , e ) 480 cm cube
Rationale: "area of a cuboid = lxbxh = 10 cm x 8 cm x 6 cm = 480 cm cube answer : e"
Answer: e
Question (gain): a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 8 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 87.8 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 8 % of 400 = 8 / 100 × 400 = 3200 / 100 = 32 therefore , total number of rotten fruits = 90 + 32 = 122 therefore number of fruits in good condition = 1000 - 122 = 878 therefore percentage of fruits in good condition = ( 878 / 1000 × 100 ) % = ( 87800 / 1000 ) % = 87.8 % answer : b"
Answer: b
Question (gain): in an election , candidate a got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate
Options: a ) 356000 , b ) 356500 , c ) 357000 , d ) 400000 , e ) none of these
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357000 c )"
Answer: c
Question (general): of 30 applicants for a job , 12 had at least 4 years ' experience , 19 had degrees , and 6 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 30 - 6 = 24 aub = a + b - aib aib = 19 + 12 - 24 = 7 answer d"
Answer: d
Question (geometry): the circumferences of two circles are 264 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 29960 sq m , b ) 33880 sq m , c ) 43120 sq m , d ) 27680 sq m , e ) 12786 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 264 and 2 ∏ l = 704 s = 264 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 132 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 132 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 132 - 352 ) ( 132 + 352 ) / ∏ = ( 220 ) ( 484 ) / ( 22 / 7 ) = 33880 sq m answer : b"
Answer: b
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.25 km and 1.00 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 48 , b ) 9 , c ) 7 , d ) 67 , e ) 54
Rationale: ": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.25 + 1.0 = 2.25 km = 2250 m . required time = 2250 * 3 / 125 = 54 sec . answer : e"
Answer: e
Question (gain): a reduction of 25 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 2.8 , b ) 2.3 , c ) 2.5 , d ) 3.3 , e ) 2.9
Rationale: "100 * ( 25 / 100 ) = 25 - - - 10 ? - - - 1 = > rs . 2.5 100 - - - 75 ? - - - 2.5 = > rs . 3.3 answer : d"
Answer: d
Question (gain): if 15 % of 30 % of 50 % of a number is 90 , then what is the number ?
Options: a ) 4000 , b ) 3050 , c ) 4400 , d ) 4500 , e ) none of these
Rationale: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 90 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 90 = > a = 10 * 20 * 10 * 2 = 4000 . answer : a"
Answer: a
Question (general): a certain box has 9 cards and each card has one of the integers from 1 to 9 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 9 cards ?
Options: a ) 1 / 36 , b ) 1 / 15 , c ) 1 / 18 , d ) 1 / 9 , e ) 2 / 9
Rationale: "the average of the numbers is 5 . the total number of ways to choose 2 cards from 9 cards is 9 c 2 = 36 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } the probability is 2 / 36 = 1 / 18 the answer is c ."
Answer: c
Question (general): what is the 6 th digit to the right of the decimal point in the decimal equivalent of 16 / 45 ?
Options: a ) 5 , b ) 12 , c ) 2 , d ) 35 , e ) 4
Rationale: "16 / 45 = 0.3555 . . . . 35 is non - terminating repeating decimal . the 22 nd digit to the right of decimal point will be 5 . answer a"
Answer: a
Question (gain): a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 13600 after a year ?
Options: a ) 3630 , b ) 9232 , c ) 8828 , d ) 2387 , e ) 4080
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 13600 = 4080 answer : e"
Answer: e
Question (physics): two trains 120 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.16 , b ) 7.16 , c ) 7.07 , d ) 7.15 , e ) 7.11
Rationale: "t = ( 120 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.07 answer : c"
Answer: c
Question (general): the average weight of 4 pigs is 15 kg . weight less than 16 kg is considered as under weight . what maximum no . of pig can be under weight .
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: sum of all four pigs weigh = 60 kg it is possible that all four pigs are underweight . because the average is 15 kg which itself underweight . answer e
Answer: e
Question (physics): a can do a job in 30 days and b in 40 days . if they work on it together for 10 days , then the fraction of the work that is left is ?
Options: a ) 2 / 11 , b ) 3 / 13 , c ) 5 / 12 , d ) 7 / 10 , e ) 6 / 15
Rationale: "a ' s 1 day work = 1 / 30 b ' s 1 day work = 1 / 40 a + b 1 day work = 1 / 30 + 1 / 40 = 7 / 120 a + b 4 days work = 7 / 120 * 10 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 answer is c"
Answer: c
Question (gain): a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 15 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 204 , b ) $ 216 , c ) $ 220 , d ) $ 230 , e ) $ 240
Rationale: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 15 emlpoyee paid = . 85 * 240 = 204 $ answer a"
Answer: a
Question (other): the compound ratio of 1 : 4 , 2 : 5 and 1 : 6 ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 10 , d ) 1 : 30 , e ) 1 : 60
Rationale: 1 / 4 * 2 / 5 * 1 / 6 = 1 / 60 1 : 60 answer : e
Answer: e
Question (gain): the true discount on a bill due 9 months hence at 16 % per annum is rs . 189 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1575 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 189 . ∴ x 16 x 9 / 12 x 1 / 100 } = 189 or x = 1575 . ∴ p . w . = rs . 1575 . answer b"
Answer: b
Question (general): in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 35 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 25
Rationale: 12 * 35 = 420 420 % 21 = 20 answer : d
Answer: d
Question (general): tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 3 ?
Options: a ) 3 / 10 , b ) 1 / 2 , c ) 2 / 5 , d ) 3 / 7 , e ) 1 / 6
Rationale: "here , s = { 1 , 2,3 , . . . . . . , 19,20 } e = event getting a multiple of 3 = { 3,6 , 9,12 , 15,18 } probability = 6 / 20 = 3 / 10 correct option is a"
Answer: a
Question (general): the sum of the digits of [ ( 10 ^ x ) ^ y ] - 64 = 279 . what is the value of xy ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: 1000 − 64 = 936 . whatever xy is you finish with 36 = = > 3 + 6 = 9 therefore , 279 − 9 = 270 and 270 / 9 = 30 now you add the last two digits ( 3 and 6 ) answer is 30 + 2 = 32 answer : e
Answer: e
Question (gain): a corporation paid $ 7 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 150 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 150 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 20 % , d ) 23 % , e ) 43 %
Rationale: "initial ratio of federal taxes to gross profits : 7 / 50 = 0.14 final ratio : 30 / 150 = 0.2 thus , the percentage change : ( 0.2 - 0.14 ) / 0.14 * 100 = 6 / 14 * 100 = 3 / 7 * 100 = just less than 50 % . answer : e"
Answer: e
Question (physics): jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 5.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 4 / 5 , d ) 42 / 55 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / ( 11 / 2 ) = 84 / 11 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 84 / 11 ) / 10 = 84 / 110 = 42 / 55 answer d"
Answer: d