Cheukting/mathqa huggingface dataset:
Question (other): water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 90 grams of water ?
Options: a ) 16 , b ) 90 , c ) 112 , d ) 128 , e ) 142
Rationale: "solution : we are given that the ratio of hydrogen to oxygen in water , by mass , is 2 : 16 . using our ratio multiplier we can re - write this as 2 x : 16 x . we can now use these expressions to determine how much oxygen is in 90 grams of water . 2 x + 16 x = 90 18 x = 90 x = 5 since x is 5 , we know that there are 16 x 5 = 80 grams of oxygen in 90 grams of water . answer b ."
Answer: b
Question (physics): suppose 3 monkeys take 3 minutes to eat 3 bananas . how many monkeys would it take to eat 6 bananas in 6 minutes ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 3 , e ) 13
Rationale: "one monkey takes 3 min to eat 1 banana , so in 6 mins 1 monkey will eat 2 bananas , so for 6 bananas in 6 min we need 6 / 2 = 3 monkeys answer : d"
Answer: d
Question (gain): a dessert recipe calls for 50 % melted chocolate and 50 % raspberry puree to make a particular sauce . a chef accidentally makes 15 cups of the sauce with 40 % melted chocolate and 60 % raspberry puree instead . how many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50 % of each ?
Options: a ) 1.5 , b ) 2.5 , c ) 3 , d ) 4.5 , e ) 5
Rationale: we have 15 cups of sauce with 4040 choc and 6060 rasb cups of choc = 0.4 ∗ 15 = 6 cups of rasb = 0.6 ∗ 15 = 9 now let say we removed x cup of original mix and replaced with x cups of choc . therefore final number of cups of choc = 6 − 0.4 x + x now this number of cup should be 50 % of total = 15 / 2 = 7.5 therefore 6 − 0.4 x + x = 7.5 on solving x = 2.5 answer : b
Answer: b
Question (other): if x and y are both odd prime numbers andx < y , then how many different positive integer factors does 2 xyhave ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 12 , e ) 8
Rationale: "x and y are both odd prime numbers - it means either x or y is not 2 and since prime numbers have only two factors - 1 and the number itself x and y each will have ( 1 + 1 ) = 2 factors hence 2 xy will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors e is the answer"
Answer: e
Question (general): 1 , 6 , 24 , 60 , 120 , 210 , ___ ?
Options: a ) 336 , b ) 366 , c ) 330 , d ) 660 , e ) 770
Rationale: "it follow the pattern like this . . 2 ^ 3 - 2 = 6 3 ^ 3 - 3 = 24 4 ^ 3 - 4 = 60 5 ^ 3 - 5 = 120 6 ^ 3 - 6 = 210 so . . . 7 ^ 3 - 7 = 336 answer : a"
Answer: a
Question (other): there are 30 students in a classroom . the ratio of the # of girls to boys was 1 : 2 , how many boys are there ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: # of girls = x # of boys = 2 x x + 2 x = 30 3 x = 30 x = 30 / 3 = 10 boys = 2 x = 2 * 10 = 20 answer : c
Answer: c
Question (other): 99 ! how many zero ' s ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: 99 ! = 99 / 5 = 19 = 19 / 5 = 3 so 99 ! has ( 19 + 3 = 22 zeroes ) answer : c
Answer: c
Question (physics): in a kilometer race , a beats b by 40 meters or 8 seconds . what time does a take to complete the race ?
Options: a ) 221 , b ) 190 , c ) 192 , d ) 191 , e ) 121
Rationale: "time taken by b run 1000 meters = ( 1000 * 8 ) / 40 = 200 sec . time taken by a = 200 - 8 = 192 sec . answer : c"
Answer: c
Question (geometry): the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 4500 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40 , b ) b . 100 , c ) c . 400 , d ) d . 1,000 , e ) e . 2,000
Rationale: "the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 4500 pi r = 15 so area = 4 . pi . r ^ 2 = 900 . pi = 900 x 3.14 = 2000 ( approx ) e"
Answer: e
Question (physics): in what time will a train 300 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 9.7 sec , c ) 3.5 sec , d ) 2.9 sec , e ) 7.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 300 / 40 = 7.5 sec . answer : e"
Answer: e
Question (gain): anand and deepak started a business investing rs . 2250 and rs . 3200 respectively . out of a total profit of rs . 1380 , deepak ' s share is :
Options: a ) 3776 , b ) 810.27 , c ) 815.21 , d ) 688.12 , e ) 267.1
Rationale: ratio of their shares = 2250 : 3200 = 45 : 64 deepak ' s share = 13800 * 64 / 109 = rs . 810.27 . answer : b
Answer: b
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 77.14 cm , b ) 25.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 23.57 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 18 + 14 ) = 64 cm parameter of the square = 64 cm i . e . 4 a = 64 a = 16 diameter of the semicircle = 16 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 16 ) = 1 / 2 ( 22 / 7 ) ( 16 ) = 352 / 14 = 25.14 cm to two decimal places answer : b"
Answer: b
Question (probability): find the probability that a leap year selected at random will not have 53 sundays
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Rationale: "there are 366 days in a leap year : 52 weeks and 2 more days . so , 52 sundays and 2 days . these 2 days can be : { mon , tue } , { tue , wed } , { wed , thu } , { thu , fri } , { fri , sat } , { sat , sun } and { sun , mon } ( 7 cases ) . in order to have 53 sundays we should have either { sat , sun } or { sun , mon } case . the probability of that is 2 / 7 . so , probability of not having 53 sundays is 1 - 2 / 7 = 5 / 7 answer : b ."
Answer: b
Question (physics): a can do a piece of work in 3 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 5
Rationale: "a ' s 1 hour ' s work = 1 / 3 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 3 + 1 / 3 ) = 2 / 3 . b ' s 1 hour ' s work = ( 2 / 3 - 1 / 2 ) = 1 / 6 . therefore a alone will take 6 hours to do the work . d"
Answer: d
Question (geometry): the area of the floor of a room is 20 m 2 that of a longer wall 15 m 2 and of the shorter wall 12 m 2 , find the edge of the new cube ?
Options: a ) 450 m 3
b ) 100 m 2
c ) 60 m 3
d ) 400 m 3
e ) 500 m 3
Rationale: lb = 20 ; lh = 15 ; fh = 12 ( lbh ) 2 = 20 * 15 * 12 = > lbh = 60 m 3 answer : c
Answer: c
Question (physics): in a 200 m race , if a gives b a start of 25 metres , then a wins the race by 10 seconds . alternatively , if a gives b a start of 45 metres the race ends in a dead heat . how long does a take to run 200 m ?
Options: a ) 100 seconds , b ) 112.5 seconds , c ) 77.5 seconds , d ) 87.5 seconds , e ) none
Rationale: explanatory answer a gives b a start of 25 metres and still wins the race by 10 seconds . alternatively , if a gives b a start of 45 metres , then the race ends in a dead heat . therefore , the additional 20 metres start given to b compensates for the 10 seconds . i . e . , b runs 20 metres in 10 seconds . hence , b will take 100 seconds to run 200 metres . we know that a gives b a start of 45 metres . b will take 22.5 seconds to run this 45 metres as b runs 20 metres in 10 seconds or at the speed of 2 m / s . hence , a will take 22.5 seconds lesser than b or 100 - 22.5 = 77.5 seconds to complete the race . answer c
Answer: c
Question (physics): if a farmer wants to plough a farm field on time , he must plough 340 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 280 , b ) 490 , c ) 720 , d ) 435 , e ) 679
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 340 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 340 x = 85 ( x + 2 ) + 40 255 x = 210 x = 0.823 so the farmer planned to have the work done in 6 days , and the area of the farm field is 340 ( 0.823 ) = 280 hectares correct answer a"
Answer: a
Question (physics): p is 60 % more efficient than q . p can complete a work in 26 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: the work done by p in 1 day = 1 / 26 let work done by q in 1 day = q q × ( 160 / 100 ) = 1 / 26 q = 100 / ( 26 × 160 ) = 10 / ( 26 × 16 ) the work done by p and q in 1 day = 1 / 26 + 10 / ( 26 × 16 ) = 26 / ( 26 × 16 ) = 1 / 16 p and q together can do the work in 16 days . the answer is c .
Answer: c
Question (gain): if the cost price is 92 % of sp then what is the profit %
Options: a ) 8.70 % , b ) 8.60 % , c ) 8.10 % , d ) 8.30 % , e ) 8.27 %
Rationale: "sol . sp = rs 100 : then cp = rs 92 : profit = rs 8 . profit = { ( 8 / 92 ) * 100 } % = 8.70 % answer is a ."
Answer: a
Question (gain): a sum was put a simple interest at a certain rate for 7 years . had it been put at 2 % higher rate , it would have fetched rs . 350 more . the sum is :
Options: a ) s . 500 , b ) s . 1000 , c ) s . 1500 , d ) s . 2000 , e ) s . 2500
Rationale: "explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 2 ) ã — 7 / 100 â ˆ ’ x ã — r ã — 7 / 100 = 350 â ‡ ’ x ã — 2 ã — 7 / 100 = 350 â ‡ ’ x ã — 7 / 100 = 175 â ‡ ’ 7 x = 17500 â ‡ ’ x = 2500 answer : option a"
Answer: a
Question (geometry): the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 34 - inch flat - screen television than a square 27 - inch flat - screen television ?
Options: a ) 106.75 , b ) 213.5 , c ) 427 , d ) 729 , e ) 1,156
Rationale: "diagonal of a square = √ 2 * side of square = > side = diagonal / ( √ 2 ) area of square = s * s = ( diagonal ^ 2 ) / 2 difference of both tv ' s = ( 34 ^ 2 - 27 ^ 2 ) / 2 = 427 answer : c"
Answer: c
Question (general): â ˆ š 1.5625 = ?
Options: a ) 1.05 , b ) 1.25 , c ) 1.45 , d ) 1.55 , e ) 1.65
Rationale: explanation : 1 | 1.5625 ( 1.25 | 1 | - - - - - - - 22 | 56 | 44 | - - - - - - - 245 | 1225 | 1225 | - - - - - - - | x | - - - - - - - 1.5625 = 1.25 . answer is b
Answer: b
Question (general): the tax on a commodity is diminished by 20 % but its consumption is increased by 20 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 4 % , d ) 12 % , e ) 14 %
Rationale: "100 * 100 = 10000 80 * 120 = 9600 10000 - - - - - - - 400 100 - - - - - - - ? = 4 % answer : c"
Answer: c
Question (physics): three cubes of metal whose edges are 9 , 12 and 18 cm respectively , are melted and one new cube is made . find the edge of the new cube ?
Options: a ) 20.2 , b ) 77 , c ) 66 , d ) 18 , e ) 99
Rationale: "93 + 123 + 183 = a 3 = > a = 20.2 answer : a"
Answer: a
Question (general): find ( 7 x + 4 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 4 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 4 y ) / ( 3 y - 2 y ) = > 25 y / y = 25 answer : b"
Answer: b
Question (general): the price of lunch for 12 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12 , c ) 13.8 , d ) 14 , e ) 15
Rationale: "clearly e is the answer i used poe here lets consider option ( e ) 12 * 15 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo e"
Answer: e
Question (gain): the banker ' s gain on a sum due 3 years hence at 12 % per annum is rs . 270 . the banker ' s discount is :
Options: a ) rs . 960 , b ) rs . 760 , c ) rs . 840 , d ) rs . 1020 , e ) rs . 1615
Rationale: t . d = ( b . gx 100 ) / ( r / t ) = ( 270 x 100 ) / ( 12 x 3 ) = rs . 750 b . d . = rs . ( 750 + 270 ) = rs . 1020 . answer : d
Answer: d
Question (gain): a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 26000 , then the share of a is ?
Options: a ) s . 14028 , b ) s . 14000 , c ) s . 14003 , d ) s . 14029 , e ) s . 24029
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 26000 share of b = 7 / 13 ( 26000 ) = rs . 14000 answer : b"
Answer: b
Question (gain): by selling 150 apples , a fruit - seller gains the selling price of 30 apples . find the gain percent ?
Options: a ) 30 % , b ) 58 % , c ) 25 % , d ) 60 % , e ) 12 %
Rationale: "option c explanation : sp = cp + g 150 sp = 150 cp + 30 sp 120 sp = 150 cp 120 - - - 30 cp 100 - - - ? = > 25 %"
Answer: c
Question (general): a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 70 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "explanation : let number of horses = number of men = x . then , number of legs = 4 x + 2 x ( x / 2 ) = 5 x . so , 5 x = 70 or x = 14 . answer : c"
Answer: c
Question (general): 617 x 617 + 583 x 583 = ?
Options: a ) 720578 , b ) 80578 , c ) 80698 , d ) 81268 , e ) none of them
Rationale: "= ( 617 ) ^ 2 + ( 583 ) ^ 2 = ( 600 + 17 ) ^ 2 + ( 600 - 17 ) ^ 2 = 2 [ ( 600 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 360000 + 289 ] = 2 x 360289 = 720578 answer is a"
Answer: a
Question (geometry): what positive number , when squared , is equal to the cube of the positive square root of 15 ?
Options: a ) 64 , b ) 32 , c ) 8 , d ) 6 , e ) 2
Rationale: "let the positive number be x x ^ 2 = ( ( 15 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 36 = > x = 6 answer d"
Answer: d
Question (general): a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability t that a + b is prime ?
Options: a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9
Rationale: "total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes t = 15 / 36 . answer : c ."
Answer: c
Question (gain): a man invested rs . 14400 in rs . 100 shares of a company at 20 % premium . if the company declares 7 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 840 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 7 / 100 x 12000 ) = rs . 840 . answer b
Answer: b
Question (physics): a boy standing idle sounds a whistle to his friend at a distance of 1200 m moving away from him in a speeding car at 108 kms / hr . find the duration after which his friend is going to hear him . ( speed of sound = 330 m / sec ) .
Options: a ) 3.6 secs , b ) 4.00 secs , c ) 40 secs , d ) 45 secs , e ) none of these
Rationale: if friend hears sound after t secs , then 330 * t = 1200 + ( 108 * 5 / 18 ) * t 300 t = 1200 t = 4 secs answer : b
Answer: b
Question (general): if ' a ' and ' b ' are non - zero numbers such that their sum is 6 times the product , what is the value of 1 / a + 1 / b ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 12
Rationale: a + b = 6 ab 1 / a + 1 / b = ( b + a ) / ( ab ) = 6 . the answer is b .
Answer: b
Question (other): two integers are in the ratio of 1 to 4 . if 12 is added to the smaller number , the ratio becomes 1 to 2 . find the larger integer .
Options: a ) 8 , b ) 16 , c ) 32 , d ) 48 , e ) 54
Rationale: one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 12 to the smaller integer makes the ratio 1 to 2 , then 2 ( x + 12 ) = y . substituting y = 4 x into the second equation yields 2 x + 24 = 4 x . so , x = 12 ( smaller integer ) and , y = 4 x = 48 ( larger integer ) so d is the correct answer . another option is to test the answer choices . a ) the larger number is 8 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 2 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 2 ) , we get 14 . so , the new ratio is 14 to 8 which is the same as 7 to 4 . no good . we want a resulting ratio of 1 to 2 eliminate a b ) the larger number is 16 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 4 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 4 ) , we get 16 so , the new ratio is 16 to 16 which is 1 to 1 . no good . we want a resulting ratio of 1 to 2 eliminate b c ) the larger number is 32 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 8 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 8 ) , we get 20 so , the new ratio is 20 to 32 which is 5 to 8 . no good . we want a resulting ratio of 1 to 2 eliminate c d ) the larger number is 48 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 12 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 12 ) , we get 24 so , the new ratio is 24 to 48 . this is the same as the ratio of 1 to 2 therefore ( d ) is correct e ) the larger number is 54 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 13.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 54 . eliminate e therefore d is the only correct choice .
Answer: d
Question (gain): if the annual increase in the population of a town is 10 % and the present number of people is 11000 , what will the population be in 2 years ?
Options: a ) 12100 , b ) 15240 , c ) 12456 , d ) 11452 , e ) 13310
Rationale: "the required population is = 11000 ( 1 + 10 / 100 ) ^ 2 = 11000 * 11 / 10 * 11 / 10 = 13310 answer is e"
Answer: e
Question (physics): shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 60 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 30 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 30 , d ) 40 , e ) 46
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 30 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 30 hence answer is c"
Answer: c
Question (gain): the owner of a furniture shop charges his customer 15 % more than the cost price . if a customer paid rs . 6400 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 5565 , b ) rs . 6298 , c ) rs . 6290 , d ) rs . 6725 , e ) rs . 6708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 6400 ( 100 / 115 ) = rs . 5565 . answer : a"
Answer: a
Question (physics): a train speeds past a pole in 15 seconds and a platform 140 meters long in 25 seconds . what is the length of the train ( in meters ) ?
Options: a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 230
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 140 = 25 * ( x / 15 ) 10 x = 2100 x = 210 meters the answer is c ."
Answer: c
Question (general): it takes 3 workers a total of 15 hours to build a giant machine with each worker working at the same rate . if 5 workers start to build the machine at 11 : 00 am , and one extra worker per hour is added beginning at 1 : 00 pm , at what time will the machine be complete ?
Options: a ) 4 : 30 , b ) 4 : 45 , c ) 5 : 00 , d ) 5 : 15 , e ) 5 : 30
Rationale: "3 workers build 1 / 15 of a machine in one hour . 1 worker builds 1 / 45 of a machine in one hour . in the first 2 hours , 5 workers build 5 * ( 1 / 45 ) * 2 = 10 / 45 of a machine . from 1 : 00 to 2 : 00 , 6 workers build another 6 / 45 . the total is 16 / 45 . from 2 : 00 to 3 : 00 , 7 workers build another 7 / 45 . the total is 23 / 45 . from 3 : 00 to 4 : 00 , 8 workers build another 8 / 45 . the total is 31 / 45 . from 4 : 00 to 5 : 00 , 9 workers build another 9 / 45 . the total is 40 / 45 . to build another 5 / 45 , 10 workers need ( 5 / 10 ) * 60 minutes which is 30 minutes . the machine is complete at 5 : 30 . the answer is e ."
Answer: e
Question (general): on the number line , if x is halfway between - 11 and 5 , and if y is halfway between - 3 and 7 , what number is halfway between x and y ?
Options: a ) - 1.5 , b ) - 0.5 , c ) 0.5 , d ) 1.5 , e ) 2.5
Rationale: "x = - 3 and y = 2 . the answer is b ."
Answer: b
Question (physics): john and david work at a hospital with 4 other workers . for an internal review , 2 of the 4 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ?
Options: a ) 1 / 14 , b ) 1 / 20 , c ) 1 / 13 , d ) 1 / 7 , e ) 1 / 6
Rationale: "probability that john and david will both be chosen out of 8 workers = ( 2 / 4 ) * ( 1 / 3 ) = 1 / 6 answer e"
Answer: e
Question (general): if w / x = 5 / 7 and w / y = 4 / 7 , then ( x + y ) / y =
Options: a ) 1 / 2 , b ) 7 / 3 , c ) 6 / 7 , d ) 1 / 5 , e ) 11 / 13
Rationale: "ratio 1 : 7 w = 5 x ratio 2 : 7 w = 4 y 5 x = 4 y x = 4 y / 3 ( x + y ) / y = ( ( 4 y / 3 ) + y ) / y = y ( 4 / 3 + 1 ) / y = 7 / 3 answer is b"
Answer: b
Question (general): a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 6 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 6 ( 1 - x ) p 12 xp = 6 p - 6 xp 18 xp = 6 p x = 1 / 3 the answer is d ."
Answer: d
Question (general): the product of two numbers is 4107 . if the h . c . f of these numbers is 37 , then the greater number is :
Options: a ) 101 , b ) 107 , c ) 111 , d ) 112 , e ) 113
Rationale: "let the numbers be 37 a and 37 b . then , 37 a * 37 b = 4107 = > ab = 3 now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 * 1 , 37 * 3 ) i . e . , ( 1 , 111 ) . greater number = 111 . answer : c"
Answer: c
Question (general): marts income is 60 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "tim = 100 mary ' s income is 60 percent more than tims income ; mary ' s income = t + 0.6 t = 1.6 t = 1.6 * 100 = 160 tims income is 40 percent less than juans income . 100 is 40 % less than juan ' s income 100 = j - 0.4 j 100 = 0.6 j j = 100 / 0.6 = 1000 / 6 what percentage of juans income is marts income ( 160 / ( 1000 / 6 ) ) * 100 = ( 160 * 6 * 100 ) / 1000 = 96 % answer : c"
Answer: c