Cheukting/mathqa huggingface dataset:
Question (general): a line has a slope of 3 / 4 and intersects the point t ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?
Options: a ) ( 40,0 ) , b ) ( 30,0 ) , c ) ( 0,40 ) , d ) ( 40,30 ) , e ) ( 0,30 )
Rationale: "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point t of intersection is ( 40,0 ) . a is the correct answer ."
Answer: a
Question (gain): the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 8337 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6725 , b ) rs . 6727 , c ) rs . 6908 , d ) rs . 6725 , e ) rs . 6947.5
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8337 ( 100 / 120 ) = rs . 6947.5 answer : e"
Answer: e
Question (physics): two drivers began their journey with the same amount of petrol in their cars at the same time . the only difference is that the first driver � s car could drive 4 hours in that amount of petrol and the second one could drive 5 hours . however , they only drove for some time and found that the amount of petrol that was left in one of the cars was 4 times the petrol left in the other one . for how long had they driven at this point of time ?
Options: a ) 3.75 hours , b ) 5.45 hours , c ) 7.10 hours , d ) 4.75 hours , e ) 3.33 hours
Rationale: a 3.75 hours while you can solve it as you like , a simple mathematical equation can be used to find out . let m be the amount of petrol initially . let n be the time for which they drove . according to the question , the amount of petrol used by first car in n hours = mn / 4 the amount of petrol used by second car in n hours = mn / 5 hence , the amount of petrol left in the first car = ( m - mn / 4 ) the amount of petrol left in the second car = ( m - mn / 5 ) as per the details given in the question , we can form the below equation : m - mn / 5 = 4 ( m - mn / 4 ) n = 15 / 4 or 3.75 hours . hence , both the drivers have driven the car for 3.75 hours at that particular time .
Answer: a
Question (other): the ratio of two numbers is 5 : 9 . if each number is decreased by 5 , the ratio becomes 5 : 11 . find the numbers .
Options: a ) 30 , 19 , b ) 21 , 37 , c ) 15 , 34 , d ) 15 , 27 , e ) none of these
Rationale: "explanation : let the two numbers be 5 x and 9 x . ( 5 x - 5 ) / ( 9 x - 5 ) = 5 : 11 ( 5 x - 5 ) * 11 = ( 9 x - 5 ) * 5 55 x – 55 = 45 x – 25 10 x = 30 x = 3 therefore , the numbers are 15 and 27 . answer : d"
Answer: d
Question (physics): tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 11 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 190 , c ) 132 , d ) 170 , e ) 60
Rationale: "c 132 sum = ( n x n ) + n hence , 11 x 11 = 121 + 11 = 132"
Answer: c
Question (general): the average height of 12 girls out of a class of 20 is 161 cm . and that of the remaining girls is 158 cm . the average height of the whole class is :
Options: a ) 142.3 cms , b ) 162.3 cms , c ) 160.5 cms , d ) 142.8 cms , e ) 159.8 cms
Rationale: "explanation : average height of the whole class = ( 12 × 161 + 8 × 158 / 20 ) = 159.8 cms answer e"
Answer: e
Question (general): find out the c . i on rs . 9000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 550.87 , b ) 506.07 , c ) 506.04 , d ) 506.03 , e ) 306.01
Rationale: "a = 9000 ( 51 / 50 ) 3 = 9550.87 9000 - - - - - - - - - - - 550.87 answer : a"
Answer: a
Question (geometry): the length of rectangle is thrice its breadth and its perimeter is 56 m , find the area of the rectangle ?
Options: a ) 432 , b ) 212 , c ) 252 , d ) 992 , e ) 147
Rationale: "2 ( 3 x + x ) = 56 l = 21 b = 7 lb = 21 * 7 = 147 answer : e"
Answer: e
Question (general): in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . the duration of the flight is
Options: a ) 3 hr . , b ) 5 hr . , c ) 2 hr . , d ) 7 hr . , e ) 1 hr .
Rationale: "e 1 hr . let the duration of the flight be x hours . then , 600 / x - 600 / 0.5 x = 200 - - > 600 / x - 1200 / ( 2 x + 1 ) = 200 - - > x ( 2 x + 1 ) = 3 - - > 2 x ^ 2 + x - 3 = 0 - - > ( 2 x + 3 ) ( x - 1 ) = 0 - - > x = 1 hr ."
Answer: e
Question (gain): money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 2200 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 19,800 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 22,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 2200 triples to $ 6600 , in 28 years , it will again triple to $ 6600 * 3 = $ 19,800 answer b"
Answer: b
Question (physics): a rocket soars for 12 seconds at 150 meters per second . it then plummets 600 meters in 3 seconds . what is the average speed of the rocket in meters per second ?
Options: a ) 140 , b ) 150 , c ) 155 , d ) 160 , e ) 175
Rationale: when soaring , the rocket travels a total distance of 1800 m ( 150 m / s for 12 s ) while plummeting the rockets travel distance of 600 m in 3 s the total distance traveled is 2400 m ( 1800 + 600 ) the time taken to travel this distance is 15 s ( 12 + 3 ) average speed = 2400 / 15 = 160 ans : ( option d )
Answer: d
Question (general): for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers w are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a
Answer: a
Question (general): a no . when divided by 224 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "224 + 43 = 267 / 17 = 12 ( remainder ) e"
Answer: e
Question (physics): 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours x will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) x = 5 . , d ) x = 6 . , e ) 8 .
Rationale: "c . 5 hrs if there were 10 beavers it qould have taken double x = 6 hrs . . so closest to that option is 5 ."
Answer: c
Question (general): the product of two numbers is 168 and the sum of these two numbers is 26 . what is the largest of these two numbers ?
Options: a ) 22 , b ) 77 , c ) 88 , d ) 12 , e ) 62
Rationale: "let the numbers be x and ( 26 – x ) . therefore , x ( 26 – x ) = 168 x 2 – 26 x + 168 = 0 ( x – 14 ) ( x – 12 ) = 0 x = 14 or x = 12 so , the numbers are 14 and 12 . answer : d"
Answer: d
Question (general): a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 700.00 . what would be the approximate hourly charge to rent computer b ?
Options: a ) $ 9.40 , b ) $ 10.00 , c ) $ 13.20 , d ) $ 17.80 , e ) $ 22.10
Rationale: "pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 700 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 700 / 70 = 10 b"
Answer: b
Question (physics): in a survey of 330 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 37 / 66 , b ) 8 / 41 , c ) 9 / 348 , d ) 1 / 8 , e ) 41 / 91
Rationale: "- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 276 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 330 we have to find not part time and not uninsured . in other words not part time and insured = x / 330 = ( 276 - 104 + 13 ) / 330 = 37 / 66 answer is a ."
Answer: a
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 896 grams per kg , what is his percent ?
Options: a ) 22 % , b ) 25 % , c ) 77 % , d ) 99 % , e ) 11.6 %
Rationale: "896 - - - 104 100 - - - ? = > 11.6 % answer : e"
Answer: e
Question (other): jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the numbers will be even ?
Options: a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 2 , e ) 12 / 21
Rationale: probability that the number on first die is even = 3 / 6 [ because 3 out of 6 faces are even ] probability that the number on second die is even = 3 / 7 [ because 3 out of 7 faces are even ] probability that both dice result in odd numbers = ( 3 / 6 ) * ( 3 / 7 ) = 3 / 14 answer : option a
Answer: a
Question (gain): what will be the compound interest on a sum of rs . 26000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.22 , b ) s . 10823.20 , c ) s . 10123.20 , d ) s . 10123.29 , e ) s . 10528.13
Rationale: "explanation : amount = [ 26000 * ( 1 + 12 / 100 ) 3 ] = 26000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 36528.13 - 26000 ) = rs . 10528.13 answer : e"
Answer: e
Question (general): which number need to add to 859622 to get a no . exactly divisible by 456 ?
Options: a ) 345466 , b ) 465767 , c ) 565676 , d ) 645469 , e ) 859622
Rationale: "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e"
Answer: e
Question (general): a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent r of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is r = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Question (physics): a cistern is filled by pipe a in 10 hours and the full cistern can be leaked out by an exhaust pipe b in 12 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 50 hrs , b ) 60 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: "time taken to full the cistern = ( 1 / 10 - 1 / 12 ) hrs = 1 / 60 = 60 hrs answer : b"
Answer: b
Question (geometry): here is 15 dots . if you select 3 dots randomly , what is the probability that 3 dots make a triangle ?
Options: a ) 440 / 455 , b ) 412 / 455 , c ) 434 / 455 , d ) 449 / 455 , e ) 438 / 455
Rationale: total ways of selecting 3 dots out of 15 is 15 c 3 = 455 if 3 dots are collinear then triangle may not be formed . now look at the above diagram . if we select any 3 dots from the red lines they may not form a triangle . they are 3 x 5 c 3 = 30 . if we select the three letters from blue lines , they may not form a triangle . they are in total 5 ways . also there are 6 others lines which do n ' t form a triangle . also another two orange lines . total = 30 + 5 + 6 + 2 = 43 . so we can form a triangle in 455 - 43 = 412 . so answer could be 412 / 455 . answer : b
Answer: b
Question (general): in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 3 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 8 * 1 + 3 * 2 = 14 books . the 7 students who borrowed at least three books borrowed 40 - 14 = 26 books . if 6 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 26 - 18 = 8 books . the answer is a ."
Answer: a
Question (general): a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 4 - inch increase in the length of the shoe . if the largest size of this shoe is 30 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?
Options: a ) 9.25 , b ) 11.75 , c ) 13.25 , d ) 15.75 , e ) 17.25
Rationale: "let x be the length of the size 8 shoe . then 0.3 x = 9 / 4 x = 90 / 12 = 15 / 2 inches the size 15 shoe has a length of 15 / 2 + 7 / 4 = 37 / 4 = 9.25 inches the answer is a ."
Answer: a
Question (geometry): what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 11 , 60 and 61 ?
Options: a ) 6.5 , b ) 12.5 , c ) 28 , d ) 30.5 , e ) 40
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 61 / 2 = 30.5 ans . d"
Answer: d
Question (gain): a man spends 50 % of his income on food , 15 % on children education and 50 % of the remaining on house rent . what percent of his income he is left with ?
Options: a ) 17.5 % , b ) 16 % , c ) 15.4 % , d ) 12.6 % , e ) 13.5 %
Rationale: "let the total income be x then , income left = ( 100 - 50 ) % of x - [ 100 - ( 50 + 15 ) ] % of x = 50 % of 35 % of x = 17.5 % of x answer is a"
Answer: a
Question (physics): a car covers a distance of 624 km in 3 hours . find its speed ?
Options: a ) 104 , b ) 277 , c ) 298 , d ) 269 , e ) 208
Rationale: 624 / 3 = 208 kmph answer : e
Answer: e
Question (physics): it was calculated that 50 men could complete a piece of work in 10 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 20 days . , b ) 15 days . , c ) 22 days . , d ) 30 days . , e ) 18 days .
Rationale: "one day work = 1 / 10 one man ’ s one day work = 1 / ( 10 * 50 ) now : no . of workers = 25 one day work = 25 * 1 / ( 10 * 50 ) the total no . of days required to complete the work = ( 50 * 10 ) / 25 = 20 answer : a"
Answer: a
Question (other): at a supermarket , the ratio of the number of shampoos to the number of soaps is 8 to 5 , and the ratio of the number of drinks to the number of shampoos is 3 to 4 . if the ratio of the soaps to the number of cereals is 9 to 2 , what is the ratio of the number of drinks to the number of cereals ?
Options: a ) 4 : 3 , b ) 15 : 6 , c ) 45 : 16 , d ) 15 : 4 , e ) 27 : 5
Rationale: sh : soaps = 8 : 5 drinks : sh = 3 : 4 = > 6 : 8 drinks : sh : soaps = 6 : 8 : 5 soaps : cer = 9 : 2 = > 9 * 5 : 2 * 5 = 45 : 10 now , drinks : sh : soaps = > 6 * 9 : 8 * 9 : 5 * 9 = 54 : 72 : 45 drinks : sh : soaps : cer = 54 : 72 : 45 : 10 drinks : cer = 54 : 10 = > 27 : 5 e
Answer: e
Question (general): xy = 1 then what is ( 5 ^ ( x + y ) ^ 2 ) / ( 5 ^ ( x - y ) ^ 2 )
Options: a ) 2 , b ) 625 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 5 ^ 4 = 625 answer b"
Answer: b
Question (general): gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 2 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: "g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 8 w 10 + 5 x = 8 ( x + 1 ) x = 2 / 3 ratio of gold with copper = 1 : 2 / 3 = 3 : 2 answer is a"
Answer: a
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 400 is required to paint the floor at the rate of rs . 3 / sq m , what would be the length of the floor ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 400 / 3 = 133.33 sq m l b = 133.33 i . e . , l * l / 3 = 133.33 l ^ 2 = 400 > l = 20 . c"
Answer: c
Question (general): a baker charges n dollars for a birthday cake . next week , she intends to earn 320 dollars selling cakes . if she were to reduce the price of the cake by 20 percent , she would have to sell two more cakes to earn the same amount of revenue . how many cakes does she intend to sell next week ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: we ' re told that by selling cakes at n dollars / cake , a baker will make $ 320 . reducing the price by 20 % and selling 2 more cakes will also make her $ 320 . we ' re asked for the original number of cakes that the baker intends to sell . $ 320 is a rather interesting number . based on the answer choices , we ' re almost certainly dealing with integer values for the number of cakes and the price per cake . as such , 6 is probably not going to be part of the solution ( either as 4 and 6 cakes or as 6 and 8 cakes ) . as such , we can avoid answers b and c . . . . let ' s test answer d : 8 cakes if . . . . original cakes = 8 8 ( n ) = $ 320 , so n = $ 40 / cake 20 % off = $ 8 off = 40 - 8 = $ 32 / cake + 2 more cakes = 8 + 2 = 10 cakes 10 ( 32 ) = $ 320 this is an exact match for what we were told , so this must be the answer . final answer : d
Answer: d
Question (gain): a sum of money deposited at c . i . amounts to rs . 1820 in 4 years and to rs . 2402 in 5 years . find the rate percent ?
Options: a ) 30 % , b ) 31 % , c ) 34 % , d ) 19 % , e ) 50 %
Rationale: "1820 - - - 582 100 - - - ? = > 31 % answer : b"
Answer: b
Question (general): an assembly line produces 30 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 52 , e ) 56
Rationale: "the time to produce the first 60 cogs is 60 / 30 = 2 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 3 hours = 40 cogs per hour . the answer is a ."
Answer: a
Question (gain): if the cost price of 44 chocolates is equal to the selling price of 24 chocolates , the gain percent is :
Options: a ) 83.55 % , b ) 83.33 % , c ) 80 % , d ) 83.39 % , e ) 84.33 %
Rationale: explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 24 chocolates = rs . 24 ; s . p . of 24 chocolates = rs . 44 . . ' . gain % = 20 * 100 / 24 = 83.33 % answer : b
Answer: b
Question (gain): 90 percent of your marbles are a solid color . 5 percent of your marbles are solid yellow . what percentage of your marbles are a solid color other than yellow ?
Options: a ) 5 , b ) 15 , c ) 85 , d ) 90 , e ) 95
Rationale: 90 percent are solid colors including solid yellow . 5 percent are solid yellow . 90 % - 5 % = 85 % , so 85 percent are a solid color other than yellow = > ( c )
Answer: c
Question (physics): when m divided by 288 , the remainder is 47 . find the remainder when the same m is divided by 24 ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 26
Rationale: 23 option d
Answer: d
Question (geometry): the length of rectangle is thrice its breadth and its perimeter is 112 m , find the area of the rectangle ?
Options: a ) 432 sq m , b ) 356 sq m , c ) 452 sq m , d ) 588 sq m , e ) 525 sq m
Rationale: "2 ( 3 x + x ) = 112 l = 42 b = 14 lb = 42 * 14 = 588 answer : d"
Answer: d
Question (geometry): in measuring the sides of a rectangle , one side is taken 5 % in excess and the other 4 % in deficit . find the error percent in the area , calculate from the those measurements .
Options: a ) 0.9 % , b ) 0.8 % , c ) 0.3 % , d ) 0.2 % , e ) 0.5 %
Rationale: "explanation : let x and y be the sides of the rectangle then correct area = = error % = answer : b ) 0.8 %"
Answer: b
Question (geometry): we have a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 144 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?
Options: a ) a 216 , b ) b 196 , c ) c 170 , d ) d 140 , e ) e 121
Rationale: "l = 144 / 12 = 12 ft w = 72 / 12 = 6 ft area of paper = 72 area of cube = 12 * side ^ 2 side of cube = 6 v of cube = 216"
Answer: a
Question (physics): working at constant rate , pump x pumped out half of the water in a flooded basement in 7 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 10 , b ) b . 12 , c ) c . 34 , d ) d . 18 , e ) e . 24
Rationale: "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 34 hours c"
Answer: c
Question (general): if k is an integer and 0.00010101 x 10 ^ k is greater than 1000 , what is the least possible value of k ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "0.00010101 * 10 ^ k > 1000 we need to move the decimal point to the right 7 places to get 1010.1 this is equivalent to multiplying by 10 ^ 7 . the answer is b ."
Answer: b
Question (general): the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 30 kg , b ) 31 kg , c ) 37 kg , d ) 39 kg , e ) 41 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 . . . . ( i ) a + b = ( 40 x 2 ) = 80 . . . . ( ii ) b + c = ( 43 x 2 ) = 86 . . . . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 . . . . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 31 . b ' s weight = 31 kg b )"
Answer: b
Question (gain): a car is purchased on hire - purchase . the cash price is $ 22 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 515 , d ) $ 528 , e ) $ 537
Rationale: "explanation : cash price = $ 22 000 deposit = 10 % ã — $ 22 000 = $ 2200 loan amount = $ 22000 â ˆ ’ $ 2200 number of payments = 60 = $ 19800 i = p * r * t / 100 i = 11880 total amount = 19800 + 11880 = $ 31680 regular payment = total amount / number of payments = 528 answer : d"
Answer: d