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 3 w widgets .
Options: a ) 4 , b ) 6 , c ) 18 , d ) 10 , e ) 12
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 18 days to doing 3 w widgets . answer : c"
Answer: c
Question (general): find a sum for 1 st 7 prime number ' s ?
Options: a ) 25 , b ) 28 , c ) 58 , d ) 34 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 ) = 58 note : 1 is not a prime number option c"
Answer: c
Question (physics): a and b can do a piece of work in 9 days . with the help of c they finish the work in 6 days . c alone can do that piece of work in ?
Options: a ) 33 , b ) 878 , c ) 18 , d ) 88 , e ) 11
Rationale: "c = 1 / 6 â € “ 1 / 9 = 1 / 18 = > 18 days answer : c"
Answer: c
Question (geometry): the length of a rectangular garden is three times its width . if the area of the rectangular garden is 507 square meters , then what is the width of the rectangular garden ?
Options: a ) 10
b ) 11
c ) 12
d ) 13
e ) 14
Rationale: let x be the width of the garden . 3 x ^ 2 = 507 x ^ 2 = 169 x = 13 the answer is d .
Answer: d
Question (physics): due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 30 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 5.61 , b ) b ) 8 , c ) c ) 10 , d ) d ) 15 , e ) e ) 8.19
Rationale: "old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 30 = 9 * 2 / 1 = 18 time difference = 8.19 ans : e"
Answer: e
Question (gain): 220 % of a number x is 44 . what is 44 % of x .
Options: a ) 8.8 , b ) 8.9 , c ) 6.6 , d ) 7.7 , e ) none
Rationale: solution : given , 220 % of x = 44 or , x = 20 . thus , 44 % of 20 = ( 44 * 20 ) / 100 = 8.8 answer : option a
Answer: a
Question (general): what is the smallest of 6 consecutive odd integers whose average ( arithmetic mean ) is b + 2 ?
Options: a ) b - 3 , b ) b - 6 , c ) b - 1 , d ) b , e ) b + 1
Rationale: since the numbers are consecutive odd integers , mean = median = 3 rd integer + 4 th integer / 2 and 1 st integer = 3 rd integer - 4 let ' s say 3 rd integer = n and 4 th integer = n + 2 2 n + 2 / 2 = b + 2 n = b + 1 1 st integer = b + 1 - 4 = b - 3 a is the answer
Answer: a
Question (physics): a motorcyclist goes from bombay to pune , a distance of 180 kms at an average of 20 kmph speed . another man starts from bombay by car 2 â ½ hours after the first , and reaches pune â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 1 : 9 , d ) 1 : 5 , e ) 1 : 1
Rationale: "t = 180 / 20 = 9 h t = 9 - 3 = 6 time ratio = 9 : 6 = 3 : 2 speed ratio = 2 : 3 answer : b"
Answer: b
Question (general): on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 19 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 85
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 19 more transactions than cal . jade = 66 + 19 = 85 jade handled = 85 transactions . answer : e"
Answer: e
Question (physics): in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of six metres is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 32 , b ) 34 , c ) 26 , d ) 28 , e ) 30
Rationale: "between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 6 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 6 + 6 = 34 meter answer is b ."
Answer: b
Question (physics): a garrison of 150 men has provisions for 31 days . at the end of 16 days , a reinforcement arrives , and it is now found that the provisions will last only for 5 days more . what is the reinforcement ?
Options: a ) 150 , b ) 450 , c ) 400 , d ) 600 , e ) 300
Rationale: "150 - - - - 31 150 - - - - 15 x - - - - - 5 x * 5 = 150 * 15 x = 450 150 - - - - - - - 300 answer : e"
Answer: e
Question (physics): the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 800 per sq . metre .
Options: a ) rs . 15,550 , b ) rs . 15,600 , c ) rs . 16,500 , d ) rs . 17,600 , e ) rs . 17,900
Rationale: area of the floor = ( 5.5 × 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 800 × 22 ) = rs . 17600 . answer : option d
Answer: d
Question (general): employees of a certain company are each to receive a unique 8 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , 6 , and 7 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 1220 , b ) 1840 , c ) 2160 , d ) 2480 , e ) 2760
Rationale: "there are 6 ! ways to make codes starting with 12 . there are 6 ! ways to make codes starting with 24 . there are 6 ! ways to make codes starting with 36 . the number of codes is 3 * 6 ! = 2160 . the answer is c ."
Answer: c
Question (general): if x is 13 percent greater than 80 , then x =
Options: a ) 88.8 , b ) 90.4 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "13 % of 80 = ( 80 * 0.13 ) = 10.4 11 % greater than 80 = 80 + 10.4 = 90.4 answer is clearly b ."
Answer: b
Question (general): an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 3 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "n ( n + 1 ) to be divisible by 3 either n or n + 1 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 2 , or 3 . thus , the overall probability is 2 / 3 . answer : d ."
Answer: d
Question (probability): in a throw of a coin probability of getting a head .
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 1 / 2
Rationale: "s = { h , t } e = { h } probability = n ( e ) / n ( s ) = 1 / 2 correct option is e"
Answer: e
Question (general): how many numbers from 10 to 40 are exactly divisible by 3 ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 10 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 . 10 numbers . 10 / 3 = 3 and 40 / 3 = 13 = = > 13 - 3 = 10 . therefore 10 digits d )"
Answer: d
Question (physics): in a dairy farm , 45 cows eat 45 bags of husk in 45 days . in how many days one cow will eat one bag of husk ?
Options: a ) 34 days , b ) 45 days , c ) 46 days , d ) 50 days , e ) none of these
Rationale: "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 45 bags 45 1 ] : : 45 : x = > x ∗ 45 ∗ 1 = 45 ∗ 1 ∗ 45 = > x = 45 option b"
Answer: b
Question (physics): how many pieces of 85 cm length can be cut from a rod of 17 meters long ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: number of pieces = 1700 / 85 = 20 the answer is d .
Answer: d
Question (general): in the land of oz only one or two - letter words are used . the local language has 64 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 128
Rationale: "the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 64 letters is 64 ; the number of 2 letter words ( xx ) that can be made from 64 letters is 64 * 64 , since each x can take 64 values . total : 64 + 64 * 64 . similarly : the number of 1 letter words ( x ) that can be made from 63 letters is 63 ; the number of 2 letter words ( xx ) that can be made from 63 letters is 63 * 63 , since each x can take 63 values . total : 63 + 63 * 63 . the difference is ( 64 + 64 * 64 ) - ( 63 + 63 * 63 ) = 128 . answer : e ."
Answer: e
Question (physics): while working alone at their constant rates , computer x can process 240 files in 8 hours , and computer y can process 240 files in 6 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 3 , b ) 3.4 , c ) 3.8 , d ) 4 , e ) 4.5
Rationale: "both computers together process files at a rate of 240 / 8 + 240 / 6 = 30 + 40 = 70 files per hour . the time required to process 240 files is 240 / 70 which is about 3.4 hours the answer is b ."
Answer: b
Question (general): the average of 6 no . ' s is 3.95 . the average of 2 of them is 4.4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 3.6 , d ) 5.6 , e ) 5.7
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4.4 * 2 ) + ( 3.85 * 2 ) ] = 7.20 . required average = ( 7.2 / 2 ) = 3.6 . c"
Answer: c
Question (physics): two tains of equal lengths take 10 seconds and 20 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 20 , e ) 13.3
Rationale: "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 20 ] m / sec = 6 m / sec . relative speed = ( 12 + 6 ) = m / sec = 18 m / sec . ∴ required time = ( 120 + 120 ) / 18 secc = 13.3 sec . answer e"
Answer: e
Question (physics): the speed of a train including stoppages is 90 kmph and excluding stoppages is 120 kmph . of how many minutes does the train stop per hour ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: explanation : t = 30 / 120 * 60 = 15 answer : option e
Answer: e
Question (general): the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 30 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 47.5 % , c ) 35 % , d ) 32.5 % , e ) 30 %
Rationale: price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 30 percent is reduced which means the new price is merely 70 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 7 / 10 ) p = 21 / 40 p is the new price after both deduction which is 52.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 47.5 % of p . so answer is b = 47.5 %
Answer: b
Question (physics): a certain industrial loom weaves 0.128 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.128 : 15 : : 1 : x = > 0.128 * x = 15 = > x = 15 / 0.128 = > x = 117 answer : d
Answer: d
Question (general): # p is defined as 2 p + 20 for any number p . what is p , if # ( # ( # p ) ) = 12 ?
Options: a ) – 16 , b ) – 44 , c ) 10 , d ) 16 , e ) 18
Rationale: # p = 2 p + 20 - - - > # ( # p ) = 2 ( 2 p + 20 ) + 20 = 4 p + 60 and thus # ( 4 p + 60 ) = 2 ( 4 p + 60 ) + 20 = 8 p + 140 = 12 - - - > 8 p = - 128 - - - > p = - 16 , a is the correct answer .
Answer: a
Question (general): when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 175
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 14 , divided by the divisor j . 0.08 = 14 / j 0.08 * j = 14 j = 14 / 0.08 = 1400 / 8 = 700 / 4 = 350 / 2 = 175 so j = 175 , answer = e ."
Answer: e
Question (general): a seller of used cars has 10 cars to sell and each of his clients selected 2 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 8 , b ) 10 , c ) 15 , d ) 14 , e ) 16
Rationale: "ifno caris selected more than once then the number of clients = 10 / 2 = 5 but since every car is being selected three times so no . of clients must be thrice as well = 5 * 3 = 15 answer : option c"
Answer: c
Question (other): two numbers are in respectively 10 % and 40 % more than a third number . the ratio of the two numbers is ?
Options: a ) 11 : 14 , b ) 7 : 9 , c ) 17 : 25 , d ) 15 : 26 , e ) 2 : 3
Rationale: let the 3 rd number be x then , first number = 110 % of x = 110 x / 100 = 11 x / 10 second number = 140 % of x = 140 x / 100 = 7 x / 5 ratio of first two numbers = 11 x / 10 : 7 x / 5 = 11 : 14 answer is a
Answer: a
Question (gain): find the number of shares that can be bought for rs . 8200 if the market value is rs . 20 each with brokerage being 2.8 % .
Options: a ) 237 , b ) 270 , c ) 398.8 , d ) 166 , e ) 111
Rationale: "explanation : cost of each share = ( 20 + 2.8 % of 20 ) = rs . 20.56 therefore , number of shares = 8200 / 20.56 = 398.8 answer : c"
Answer: c
Question (physics): a 300 meter long train crosses a platform in 27 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 150 m , b ) 278 m , c ) 350 m , d ) 228 m , e ) 282 m
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 27 = 50 / 3 3 ( x + 300 ) = 1350 è x = 150 m . answer : a"
Answer: a
Question (general): the average age of a family of 6 members is 34 years . if the age of the youngest member is 7 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 12 , e ) 27
Rationale: "present age of total members = 6 x 34 = 204 7 yrs back their ages were = 6 x 7 = 42 ages at the birth of youngest member = 204 - 42 = 162 therefore , avg age at the birth of youngest member = 162 / 6 = 27 . answer : e"
Answer: e
Question (general): the average salary of 15 people in the shipping department at a certain firm is $ 20,000 . the salary of 5 of the employees is $ 20,000 each and the salary of 4 of the employees is $ 16,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 19,250 , b ) $ 18,500 , c ) $ 18,000 , d ) $ 15,850 , e ) $ 22,600
Rationale: "total salary . . . 15 * 20 k = 300 k 5 emp @ 20 k = 100 k 4 emp @ 16 k = 64 k remaing 6 emp sal = 300 k - 100 k - 64 k = 136 k average = 136 k / 6 = 22600 ans : e"
Answer: e
Question (general): find the value of x in ( x / 5 ) + 3 = 4 .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: ( x / 5 ) + 3 = 4 . subtracting both sides with 3 gives x / 5 = 1 multiplying both sides by 5 gives x = 5 answer : e
Answer: e
Question (physics): if a can do a work in 10 days and a and b can do a same piece of job in 5 days . in how days can do a work b alone ?
Options: a ) 10 , b ) 20 , c ) 5 , d ) 15 , e ) 9
Rationale: a ' s one day work = 1 / 10 a + b = 1 / 5 ( one day work ) b = ( 1 / 5 ) - a = ( 1 / 5 ) - ( 1 / 10 ) = 1 / 10 ( one day work ) b can done a work in 10 days . answer option a
Answer: a
Question (physics): pipe a and pipe b fill water into a tank of capacity 1000 litres , at a rate of 200 l / min and 50 l / min . pipe c drains at a rate of 25 l / min . pipe a is open for 1 min and closed , then pipe b is open for 2 min and closed . further the pipe c is opened and drained for another 2 min . this process is repeated until the tank is filled . how long will it take to fill the tank ?
Options: a ) 15 , b ) 17 , c ) 18 , d ) 56 , e ) 20
Rationale: "tank capacity : 1000 l , 1 st - 200 l / min for 1 min , volume filled : 200 l 2 nd - 100 l / min for 2 min , volume filled : 100 l 3 rd ( water draining ) : 25 l / min * 2 : 50 l total : ( 200 + 100 ) - 50 = 250 l filled for 1 cycle number of 250 in 1000 l tank : 1000 / 250 = 4 time taken to fill : 4 * total time = 4 * 5 = 20 ( option e )"
Answer: e
Question (physics): a car traveled 480 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 22 , e ) 27
Rationale: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 462 miles will be covered in 462 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 480 / h = > 336 / c = 480 / ( c + 6 ) = > 336 c + 336 * 6 = 480 c = > c = 336 * 6 / 144 = 14 answer a ."
Answer: a
Question (general): what is the least number should be added to 1056 , so the sum of the number is completely divisible by 26 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "( 1056 / 26 ) gives remainder 16 10 + 16 = 26 , so we need to add 10 a"
Answer: a
Question (general): what is the smallest number which , when increased by 5 , is divisible by 7 , 8 , and 24 ?
Options: a ) 148 , b ) 153 , c ) 158 , d ) 163 , e ) 168
Rationale: "lcm ( 7 , 8,24 ) = 24 x 7 = 168 so the least divisible number is 168 , and the number we are looking for is 168 - 5 = 163 . the answer is d ."
Answer: d
Question (geometry): the length of a rectangle is reduced by 15 % . by what % would the width have to be increased to maintain the original area ?
Options: a ) 10 %
b ) 20 %
c ) 17.6 %
d ) 30 %
e ) 35 %
Rationale: sol . required change = ( 15 * 100 ) / ( 100 - 15 ) = 17.6 % c
Answer: c
Question (general): abi decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month . if abi ' s savings by the end of the year from these monthly savings were 6 times the amount she spent per month , what should be the fraction of her salary that she spent each month ?
Options: a ) 6 / 9 , b ) 5 / 3 , c ) 2 / 3 , d ) 4 / 3 , e ) 5 / 3
Rationale: let abi ' s monthly savings = s abi ' s monthly pay = p abi ' s monthly expenditure = p - s abi ' s savings by the end of the year from these monthly savings were six times the amount she spent per month 12 s = 6 * ( p - s ) = > 2 s = p - s = > p = 3 s abi ' s monthly expenditure = p - s = 3 s - s = 2 s fraction of her salary that abi spent each month = 2 s / 3 s = p - s / p = 2 / 3 . answer is c
Answer: c
Question (general): 3 people who work full - time are to work together on a project , but their total time on the project is to be equivalent to that of only one person working full - time . if one of the people is budgeted for 1 / 2 of his time to the project and a second person for 1 / 3 of her time , what part of the third worker ' s time should be budgeted to this project ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 6 , d ) 1 / 8 , e ) 1 / 9
Rationale: explanation : one - half ( 1 / 2 ) plus one - third ( 1 / 3 ) equals five - sixths ( 5 / 6 ) , so one - sixth ( 1 / 6 ) of the third worker ' s time should be budgeted to the project in order for the total time to be equivalent to that of one person working full - time . if x 2 - x - 6 = 0 , then ( x + 2 ) ( x - 3 ) = 0 , so x = - 2 or x = 3 . correct answer : a
Answer: a
Question (other): the compound ratio of 1 : 2 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 3 : 5 , e ) 1 : 4
Rationale: "1 / 2 * 3 / 2 * 4 / 5 = 3 / 5 = 3 : 5 answer : d"
Answer: d
Question (physics): in an examination , a student scores 3 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 120 questions and secures 180 marks , the number of questions he attempts correctly , is :
Options: a ) 45 , b ) 90 , c ) 80 , d ) 75 , e ) 70
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 120 â € “ x ) . 3 x â € “ ( 120 â € “ x ) = 180 or 4 x = 300 or x = 75 answer : d"
Answer: d
Question (physics): a train 240 m long , running with a speed of 108 km / hr will pass a tree in ?
Options: a ) 8 sec , b ) 16 sec , c ) 18 sec , d ) 14 sec , e ) 12 sec
Rationale: "speed = 108 * 5 / 18 = 30 m / sec time taken = 240 * 1 / 30 = 8 sec answer : a"
Answer: a
Question (gain): salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 22 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 35 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.22 0.2 x = 0.12 x = 0.6 = 60 % the answer is d ."
Answer: d
Question (gain): we had $ 350 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 440 , b ) $ 460 , c ) $ 480 , d ) $ 500 , e ) $ 520
Rationale: "let x be the amount of money we started with . 0.7 x = 350 x = 500 the answer is d ."
Answer: d
Question (gain): a baseball card decreased in value 30 % 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 ) 37 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.7 = 70 after second year price = 70 * 0.9 = 63 final decrease = [ ( 100 - 63 ) / 100 ] * 100 = 37 % correct answer - b"
Answer: b
Question (geometry): when the oil from a circular cylinder leaked , the formula for the speed of the leak is v = kh ^ 2 , where h was the height of the remaining oil and k was constant . if the height of the cylinder is 4 , the speed of the leak is v â € ™ , when the height of the oil remaining is 12 , what was the speed of the leak , in terms of v â € ™ ?
Options: a ) 9 v â € ™
b ) 4 v â € ™
c ) v â € ™ / 2
d ) v â € ™ / 4
e ) v â € ™
Rationale: when h = 4 v = v ' so v ' = k . 16 hence k = v ' / 16 now when h = 12 v = ( v ' / 16 ) . 12 ^ 2 v = v ' . 144 / 16 v = 9 v ' ans : a
Answer: a
Question (general): the population of bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1000 to 500000 bacteria ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 18 , e ) 20
Rationale: 2000 ^ 12000 ^ 22000 ^ 32000 ^ 4 . . . . . . . 2000 ^ 9 population increases in this sequence taking 9 * 2 = 18 answer : d
Answer: d
Question (gain): what is 15 % of 2 / 3 of 0.8 ?
Options: a ) 0.08 , b ) 0.8 , c ) 9 , d ) 90 , e ) none of the above
Rationale: "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 8 / 10 ) = 240 / 3000 = 0.08 option a"
Answer: a