Cheukting/mathqa huggingface dataset:
Question (other): in a class of 40 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?
Options: a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32
Rationale: "answer let a be the set of students who have enrolled for english and b be the set of students who have enrolled for german . then , ( a u b ) is the set of students who have enrolled at least one of the two subjects . as the students of the class have enrolled for at least one of the two subjects , a u b = 40 we know a u b = a + b - ( a n b ) i . e , 40 = a + 22 - 12 or a = 30 which is the set of students who have enrolled for english and includes those who have enrolled for both the subjects . however , we need to find out the number of students who have enrolled for only english = students enrolled for english - students enrolled for both german and english = 30 - 12 = 18 . choice is ( c )"
Answer: c
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 minutes , then the area of the park ( in sq . m ) is :
Options: a ) 152600 m 2 , b ) 153500 m 2 , c ) 153600 m 2 , d ) 153800 m 2 , e ) none of these
Rationale: "explanation : question seems to be typical , but trust me it is too easy to solve , before solving this , lets analyse how we can solve this . we are having speed and time so we can calculate the distance or perimeter in this question . then by applying the formula of perimeter of rectangle we can get value of length and breadth , so finally can get the area . lets solve it : perimeter = distance travelled in 8 minutes , = > perimeter = 12000 / 60 * 8 = 1600 meter . [ because distance = speed * time ] as per question length is 3 x and width is 2 x we know perimeter of rectangle is 2 ( l + b ) so , 2 ( 3 x + 2 x ) = 1600 = > x = 160 so length = 160 * 3 = 480 meter and width = 160 * 2 = 320 meter finally , area = length * breadth = 480 * 320 = 153600 answer : option c"
Answer: c
Question (gain): each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 98 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 50 , c ) 92 , d ) 96 , e ) 98
Rationale: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after some water evaporates the cucumbers become 98 % water and 2 % of non - water , so now 1 pound of non - water composes 2 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.02 = 50 pounds . answer : b ."
Answer: b
Question (gain): how much 60 % of 50 is greater than 45 % of 30 ?
Options: a ) 18 , b ) 91 , c ) 16.5 , d ) 17 , e ) 12
Rationale: "( 60 / 100 ) * 50 – ( 45 / 100 ) * 30 30 - 13.5 = 16.5 answer : c"
Answer: c
Question (geometry): rectangular tile each of size 50 cm by 40 cm must be laid horizontally on a rectangular floor of size 120 cm by 150 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 9 , b ) 15 , c ) 12 , d ) 11 , e ) 10
Rationale: "area of tile = 50 * 40 = 2000 area of floor = 120 * 150 = 18000 no of tiles = 18000 / 2000 = 9 so , the no of tile = 9 answer : a"
Answer: a
Question (physics): it takes printer a 4 more minutes more than printer b to print 40 pages . working together , the two printers can print 50 pages in 6 minutes . how long will it take printer a to print 60 pages ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "if it takes 4 more minutes for a to print 40 pages than it takes b , it takes 5 more minutes for a to print 50 pages than it takes b . thus if b is the number of minutes than b takes to print 50 pages , we can write : 1 / b + 1 / ( b + 5 ) = 1 / 6 ( since in 1 minute , they print 1 / 6 th of the 50 page job ) 6 ( 2 b + 5 ) = b ( b + 5 ) b ^ 2 - 7 b - 30 = 0 ( b - 10 ) ( b + 3 ) = 0 b = 10 thus it takes a 15 minutes to print 50 pages and 15 * 60 / 50 = 18 minutes to print 60 pages ( answer b )"
Answer: b
Question (physics): two trains of length 200 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 28 , b ) 266 , c ) 990 , d ) 20 , e ) 24
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 200 + 280 = 480 m . the time required = d / s = 480 / 20 = 24 sec . answer : e"
Answer: e
Question (general): a woodworker normally makes a certain number of parts in 24 days . but he was able to increase his productivity by 5 parts per day , and so he not only finished the job in only 22 days but also he made 80 extra parts . how many parts does the woodworker normally makes per day and how many pieces does he make in 24 days ?
Options: a ) 360 , b ) 350 , c ) 340 , d ) 370 , e ) 380
Rationale: let x be the number of parts the woodworker normally makes daily . in 24 days he makes 24 ⋅ x pieces . his new daily production rate is x + 5 pieces and in 22 days he made 22 ⋅ ( x + 5 ) parts . this is 80 more than 24 ⋅ x . therefore the equation is : 24 ⋅ x + 80 = 22 ( x + 5 ) 30 = 2 x x = 15 normally he makes 15 parts a day and in 24 days he makes 15 ⋅ 24 = 360 parts . so answer is a .
Answer: a
Question (general): julian owes his classmate jenny 20 dollars . if he borrows 8 dollars how much will he owe her ?
Options: a ) 28 , b ) 12 , c ) - 28 , d ) 12 , e ) 0
Rationale: add how he has already borrowed and how much he is going to borrow - 20 + - 8 correct answer c ) - 28
Answer: c
Question (general): country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 20 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 10 % . if ron imported a $ 20,000 imported car and ended up paying $ 2500 in taxes , what is the first tier ' s price level ?
Options: a ) $ 6000 , b ) $ 5500 , c ) $ 5000 , d ) $ 5700 , e ) $ 5800
Rationale: "let t be the tier price , p be total price = 20000 per the given conditions : 0.20 t + 0.10 ( p - t ) = 2500 0.20 t + 0.10 * 20000 - 0.10 t = 2500 0.10 t + 2000 = 2500 0.10 t = 2500 - 2000 = 500 t = 500 / 0.10 = 5000 answer c"
Answer: c
Question (general): the sum of ages of 5 children born at the intervals of 8 years each is 90 years . what is the age of the youngest child ?
Options: a ) 2 , b ) 9 , c ) 6 , d ) 4 , e ) 0
Rationale: "let the ages of children be x , ( x + 8 ) , ( x + 16 ) , ( x + 24 ) and ( x + 32 ) years . then , x + ( x + 8 ) + ( x + 16 ) + ( x + 24 ) + ( x + 32 ) = 90 5 x = 10 x = 2 . age of the youngest child = x = 2 years . answer : a"
Answer: a
Question (general): if a and b are the roots of the equation x 2 - 9 x + 20 = 0 , find the value of a 2 + b 2 + ab ?
Options: a ) 57 , b ) 59 , c ) 61 , d ) 63 , e ) 65
Rationale: "a 2 + b 2 + ab = a 2 + b 2 + 2 ab - ab i . e . , ( a + b ) 2 - ab from x 2 - 9 x + 20 = 0 , we have a + b = 9 and ab = 20 . hence the value of required expression ( 9 ) 2 - 20 = 61 . option c"
Answer: c
Question (general): for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 96 θ 33 ) θ 17 ) - ( 94 θ ( 33 θ 17 ) ) ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "( ( 96 θ 33 ) θ 17 ) the remainder of 96 divided by 33 is 30 ; the remainder of 30 divided by 17 is 13 ; ( 97 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 94 divided by 16 is 1 . 13 - 2 = 11 . answer : d ."
Answer: d
Question (gain): a man bought 40 shares of rs . 60 at 6 discount , the rate of dividend being 12 1 / 2 % the rate of interest obtained is
Options: a ) 13.89 % , b ) 15.5 % , c ) 14 % , d ) 14.25 % , e ) 14.95 %
Rationale: "explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 6 = rs . 54 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 60 × 25 / 2 × 100 = rs . 7.5 total dividend = ( 40 × 7.5 ) ie , he got a dividend of ( 40 × 7.5 ) for an investment of rs . ( 40 × 54 ) interest obtained = 40 × 7.5 × 100 / 40 × 54 = 13.89 % answer : option a"
Answer: a
Question (general): the unit digit in the product ( 224 * 607 * 214 * 863 ) is :
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 4 * 7 * 4 * 3 ) = 6 answer : c"
Answer: c
Question (general): a number is increased by 70 % and then decreased by 70 % . find the net increase or decrease per cent .
Options: a ) 49 % , b ) 18 % , c ) 17 % , d ) 13 % , e ) 16 %
Rationale: let the number be 100 . increase in the number = 70 % = 70 % of 100 = ( 70 / 100 ã — 100 ) = 70 therefore , increased number = 100 + 70 = 170 this number is decreased by 70 % therefore , decrease in number = 70 % of 170 = ( 70 / 100 ã — 170 ) = 11900 / 100 = 119 therefore , new number = 170 - 119 = 51 thus , net decreases = 100 - 51 = 49 hence , net percentage decrease = ( 49 / 100 ã — 100 ) % = ( 4900 / 100 ) % = 49 % answer : a
Answer: a
Question (physics): a train which has 400 m long , is running 50 kmph . in what time will it cross a person moving at 14 kmph in same direction ?
Options: a ) 40 sec , b ) 35 sec , c ) 33 sec , d ) 42 sec , e ) 41 sec
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 400 / ( ( 50 - 14 ) ( 5 / 18 ) = 400 / 36 * ( 5 / 18 ) = 400 / 10 = 40 sec answer : a"
Answer: a
Question (general): how many even 4 - digit integers greater than 8000 are there such that all their digits are different ?
Options: a ) 240 , b ) 369 , c ) 469 , d ) 520 , e ) 599
Rationale: case 1 : numbers starting with 8 followed by even number the hundreds digit can take 4 numbers ( 0,2 , 4,6 ) so 4 ways the unit digit can take remaining 3 even numbers left after using 2 , to be even so 3 ways . the tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways total = 4 * 3 * 7 = 84 case 2 : numbers starting with 8 followed by odd number the hundreds digit can take 5 numbers ( 1 , 3,5 , 7,9 ) so 5 ways the unit digit can take remaining 4 even numbers ( 0,2 , 4,6 ) to be even so 4 ways . the tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways total = 5 * 4 * 7 = 140 case 3 : numbers starting with 9 followed by even number the hundreds digit can take 5 numbers ( 0 , 2,4 , 6,8 ) so 5 ways the unit digit can take remaining 4 even numbers left after using 1 , to be even so 3 ways . the tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways total = 5 * 3 * 7 = 105 case 4 : numbers starting with 9 followed by odd number the hundreds digit can take 4 numbers ( 1,3 , 5,7 ) so 4 ways the unit digit can take 5 numbers ( 0 , 2,4 , 6,8 ) to be even so 5 ways . the tens digit can take remaining 7 numbers left after using 3 numbers so 7 ways total = 4 * 5 * 7 = 140 hence 84 + 140 + 105 + 140 = 469 , correct answer is c
Answer: c
Question (geometry): a certain farmer pays $ 60 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet ? ( 43,560 square feet = 1 acre )
Options: a ) $ 5,330 , b ) $ 3,360 , c ) $ 1,350 , d ) $ 600 , e ) $ 150
Rationale: basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 600 ( d )
Answer: d
Question (gain): today joelle opened an interest - bearing savings account and deposited $ 6,000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
Options: a ) $ 6715 , b ) $ 5615 , c ) $ 6415 , d ) $ 6615 , e ) $ 6315
Rationale: interest for 1 st year = 6000 * 5 / 100 = 300 interest for 2 nd year = 6300 * 5 / 100 = 315 total = 6000 + 300 + 315 = 6615 answer : d
Answer: d
Question (general): what is x if x + 2 y = 100 and y = 25 ?
Options: a ) 25 , b ) 50 , c ) 75 , d ) 100 , e ) 4
Rationale: "substitute y by 25 in x + 2 y = 100 x + 2 ( 25 ) = 100 x + 50 = 100 if we substitute x by 50 in x + 50 = 100 , we have 50 + 50 = 100 . hence x = 50 correct answer b"
Answer: b
Question (physics): a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 3 days . in how many days b alone can do the work ?
Options: a ) 5 days , b ) 7 days , c ) 12 days , d ) 4.5 days , e ) 10 days
Rationale: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 3 x = 4.5 days answer : option d"
Answer: d
Question (physics): a tiger is 50 of its own leaps behind a deer . the tiger takes 5 leaps per minutes to deer ’ s 4 . if the tiger and the deer cover 8 m and 5 m per leap respectively , what distance will the tiger have to run before it catches the deer ?
Options: a ) 600 m , b ) 700 m , c ) 800 m , d ) 1000 m , e ) 1200 m
Rationale: tiger takes 5 leaps / m and deer takes 4 leaps / m thus , tiger runs at the speed of 5 x 8 = 40 m / min and deer runs at the speed of 4 x 5 = 20 m / min tiger is 50 leaps behind , which is 50 x 8 = 400 m relative speed of tiger and deer is = 20 m / min thus , 400 / 20 = 20 m thus , the tiger will catch deer = 20 x 40 = 800 m answer : c
Answer: c
Question (physics): a man can row upstream at 25 kmph and downstream at 39 kmph , and then find the speed of the man in still water ?
Options: a ) 22 , b ) 37 , c ) 32 , d ) 27 , e ) 18
Rationale: "us = 25 ds = 39 m = ( 39 + 25 ) / 2 = 32 answer : c"
Answer: c
Question (general): if the sum of two numbers is 60 and the h . c . f and l . c . m of these numbers are 3 and 120 respectively , then the sum of the reciprocal of the numbers is equal to :
Options: a ) 2 / 9 , b ) 4 / 5 , c ) 1 / 6 , d ) 6 / 6 , e ) 3 / 9
Rationale: "let the numbers be a and b . then , a + b = 60 and ab = 3 * 120 = 360 . required sum = 1 / a + 1 / b = ( a + b ) / ab = 60 / 360 = 1 / 6 . answer : c"
Answer: c
Question (general): last year department store x had a sales total for december that was 2 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 1 / 4 , b ) 4 / 15 , c ) 2 / 13 , d ) 4 / 11 , e ) 4 / 5
Rationale: "let avg for 11 mos . = 10 therefore , dec = 20 year total = 11 * 10 + 20 = 130 answer = 20 / 130 = 2 / 13 = c"
Answer: c
Question (physics): a worker earns $ 24 on the first day and spends $ 18 on the second day . the worker earns $ 24 on the third day and spends $ 18 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 72 ?
Options: a ) 9 , b ) 12 , c ) 17 , d ) 21 , e ) 24
Rationale: "every two days , the net total is $ 6 . after 16 days , the worker will have $ 48 . on day 17 , the worker will receive $ 24 for a net total of $ 72 . the answer is c ."
Answer: c
Question (general): in a class of students , 2 / 3 of the number of girls is equal to 1 / 5 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 5 / 3 , e ) 7 / 3
Rationale: ( 2 / 3 ) g = ( 1 / 5 ) ( b + g ) 10 g = 3 b + 3 g 7 g = 3 b b / g = 7 / 3 . the answer is e .
Answer: e
Question (general): jaya two digits age when appended with the two digits age of amitabh the 4 digits number formed is a perfect square . what is the the sum of the 4 digits no . ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: min no could be = 7 ( 1024 ) let jaya has two digits number = 10 and amitabh has two digits number = 24 after appending = 1024 which is perfect square of 32 and sum of four digits number 1024 = 7 answer : b
Answer: b
Question (general): pure milk costs 3.60 per litre . a milkman adds water to 25 litres of pure milk and sells the mixture at 3 per litre . how many litres of water does he add ?
Options: a ) 2 litres , b ) 5 litres , c ) 7 litres , d ) 11 litres , e ) none of these
Rationale: in mixture , quantity of pure milk / quantity of water = 3 − 0 / 3.6 − 3 = 3 / 0.6 = 5 / 1 since in every 5 litres of milk , he adds 1 litre of water . ∴ in every 25 litres of milk , he adds 5 litres of water . answer b
Answer: b
Question (physics): machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 12000 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 60 / 7
Rationale: for 1 hour - machine a rate - 2000 envelopes machine b + c rate - 2400 envelopes since a + c = 3000 envelopes a ' s rate is 2000 envelopes as above , c has a rate of 1000 envelopes per hour . which makes machine b ' s rate as 1400 envelopes per hour . thus , it will take 8 hours to manufacture 12000 envelopes . answer : - e
Answer: e
Question (general): what is 2 4 / 3 - 3 1 / 4 divided by 2 / 3 - 1 / 6 ?
Options: a ) 5 / 4 , b ) 2 / 3 , c ) 1 / 6 , d ) 5 / 2 , e ) 1 / 8
Rationale: "2 4 / 3 - 3 1 / 4 = 10 / 3 - 13 / 4 = ( 40 - 39 ) / 12 = 1 / 12 2 / 3 - 1 / 6 = ( 4 - 1 ) / 6 = 3 / 6 = 1 / 2 so 1 / 12 / 1 / 2 = 2 / 12 = 1 / 6 answer - c"
Answer: c
Question (general): the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 6 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 45 , b ) 65 , c ) 75 , d ) 78 , e ) 90
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 6 = 74 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 – 316 = 4 a = e + 4 = 74 + 4 = 78 d"
Answer: d
Question (physics): the length of the bridge , which a train 160 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 255 , b ) 267 , c ) 245 , d ) 277 , e ) 215
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 160 + x ) / 30 = 25 / 2 = > 2 ( 160 + x ) = 750 = > x = 215 m . answer : e"
Answer: e
Question (general): 32 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 26 , c ) 42 , d ) 27 , e ) 14
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 32 = 14 answer : e"
Answer: e
Question (physics): pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 9 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 33 , b ) 77 , c ) 18 , d ) 99 , e ) 66
Rationale: "let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 9 = > 1 / x = 1 / 6 - 1 / 9 = ( 3 - 2 ) / 18 = 1 / 18 = > x = 18 . answer : c"
Answer: c
Question (general): if x / y = 3 and ( 2 a - x ) / ( 5 b - y ) = 3 , then the value of a / b is ?
Options: a ) 15 / 2 , b ) - 2 , c ) 1 , d ) 2 , e ) 3
Rationale: "x = 3 y 2 a - 3 y = 3 ( 5 b - y ) 2 a - 3 y = 15 b - 3 y 2 a = 15 b a / b = 15 / 2 answer : a"
Answer: a
Question (general): what could be the range of a set consisting of odd multiples of 7 ?
Options: a ) 21 , b ) 24 , c ) 35 , d ) 62 , e ) 70
Rationale: "a set of odd multiples of 7 would be something like 7 , 21 , 35 , 49 . . . . the range would always be an even number multiple of 7 . answer : e"
Answer: e
Question (other): a man invests some money partly in 4 % stock at 48 and partly in 10 % stock at 110 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 4 : 5 , d ) 6 : 5 , e ) none
Rationale: "solution for an income of rs . 1 in 9 % stock at 96 , investment = rs . ( 48 / 4 ) = rs . 12 . for an income of rs . 1 in 12 % stock at 120 , investment = rs . ( 110 / 10 ) = rs . 10 . ∴ ratio of investments = 12 : 10 = 6 : 5 answer d"
Answer: d
Question (general): what least number must be added to 1096 , so that the sum is completely divisible by 23 ?
Options: a ) 2 , b ) 1 , c ) 3 , d ) 5 , e ) 8
Rationale: "1096 / 23 = 47.6 - - that is 23 * 47 = 1081 now , 1096 - 1081 = 15 to get completely divided by 23 add 8 to 1096 ans - e"
Answer: e
Question (general): the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 5 : 4 . if the oil bill for february had been $ 45 more , the corresponding ratio would have been 3 : 2 . how much was the oil bill for january ?
Options: a ) $ 60 , b ) $ 90 , c ) $ 120 , d ) $ 150 , e ) $ 180
Rationale: 5 : 4 = 15 : 12 and 3 : 2 = 18 : 12 . an increase in $ 45 increases the ratio by 3 : 12 . therefore an increase in $ 15 increases the ratio by 1 : 12 . therefore , january ' s bill was 12 ( $ 15 ) = $ 180 . the answer is e .
Answer: e
Question (physics): trains a and b start simultaneously from stations 450 miles apart , and travel the same route toward each other on adjacent parallel tracks . if train a and train b travel at a constant rate of 50 miles per hour and 50 miles per hour , respectively , how many miles will train a have traveled when the trains pass each other , to the nearest mile ?
Options: a ) 112 , b ) 133 , c ) 150 , d ) 167 , e ) 225
Rationale: "since we know the distance ( 450 ) and the combined rate ( 100 ) , we plug it into the formula : distance = rate * time 450 = 100 * time we can solve for the time they will meet cause we added the rate of train a and train b together . so the time will be 450 / 100 from dividing 100 on both sides to isolate time in the equation above . time will be 4.5 hours so now you can plug that in for train a ’ s distance . distance = rate * time distance = 50 * 4.5 distance = 225 according to answer choice e ."
Answer: e
Question (general): a theater box office sold an average ( arithmetic mean ) of 64 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 80 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 3 : 7 , d ) 7 : 12 , e ) 4 : 5
Rationale: "deviation from the mean for the daytime staff = 80 - 64 = 16 . deviation from the mean for the evening staff = 64 - 60 = 4 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 4 : 16 = 1 : 4 . the answer is b ."
Answer: b
Question (physics): 12 welders work at a constant rate they complete an order in 3 days . if after the first day , 9 welders start to work on the other project , how many more days the remaining welders will need to complete the rest of the order ?
Options: a ) 5 , b ) 2 , c ) 8 , d ) 4 , e ) 6
Rationale: 1 . we need to find out the time taken by 3 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 12 * 3 = 36 days 4 . but on day 1 twelve workers had already worked finishing 1 / 3 of the job . so 3 workers have to finish only 2 / 3 of the job . 5 . total time taken by 3 workers can be got from formula used at ( 2 ) . i . e . , 3 * total time taken = 36 . total time taken by 3 workers to finish the complete job is 36 / 3 = 12 days . 6 . time taken by 6 workers to finish 2 / 3 of the job is 2 / 3 * 12 = 8 days . the answer is choice c
Answer: c