Cheukting/mathqa huggingface dataset:
Question (physics): 36 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) a ) 44 , b ) b ) 77 , c ) c ) 66 , d ) d ) 55 , e ) e ) 37
Rationale: "( 36 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 80 80 – 36 = 44 answer : a"
Answer: a
Question (geometry): square a has an area of 121 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 9 / 25 , b ) 1 / 5 , c ) 16 / 121 , d ) 105 / 121 , e ) 6 / 25
Rationale: "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 121 - 16 = 105 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 105 / 121 . answer : d ."
Answer: d
Question (physics): the end of a blade on an airplane propeller is 15 feet from the center . if the propeller spins at the rate of 1,320 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 200 π , b ) 240 π , c ) 300 π , d ) 450 π , e ) 1,200 π
Rationale: "distance traveled in 1 revolution = 2 π r = 2 π 15 / 5280 revolutions in one second = 1320 revolutions in 60 seconds ( one minute ) = 1320 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1320 * 60 * 2 π 15 / 5280 = 450 π d is the answer"
Answer: d
Question (general): a man whose speed is 4 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1 kmph , find his average speed for the total journey ?
Options: a ) 5 , b ) 4 , c ) 4.5 , d ) 3.75 , e ) 3
Rationale: "m = 4 s = 1 ds = 5 us = 3 as = ( 2 * 5 * 3 ) / 8 = 3.75 answer : d"
Answer: d
Question (gain): 20 % of a number is more than 40 % of 140 by 80 . find the number ?
Options: a ) 680 , b ) 620 , c ) 652 , d ) 520 , e ) 458
Rationale: "( 20 / 100 ) * x – ( 40 / 100 ) * 140 = 80 1 / 5 x = 136 x = 680 answer : a"
Answer: a
Question (physics): a certain machine produces 550 units of product p per hour . working continuously at this constant rate , this machine will produce how many units of product p in 5 days ?
Options: a ) 7,000 , b ) 24,000 , c ) 66,000 , d ) 100,000 , e ) 168,000
Rationale: "since 5 days consist of 24 * 5 hours the total is 120 hours . since every hour the machine produces 550 units of product p the total product during 120 hours is 120 * 550 = 66,000 . correct option : c"
Answer: c
Question (general): the average salary / head of all the workers ina workshop is rs . 850 , if the average salary / head of 7 technician is rs . 1000 and the average salary / head of the rest is rs . 780 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 25
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y - 7 workers . 7 x 1000 + 780 ( y - 7 ) = 850 y ⇒ 7000 + 780 y - 5460 = 850 y ⇒ 70 y = 1540 ∴ y = 22 so total number of workers = 22 c
Answer: c
Question (geometry): if the sides of a square are multiplied by sqrt ( 20 ) , the area of the original square is how many times as large as the area of the resultant square ?
Options: a ) 2 % , b ) 5 % , c ) 20 % , d ) 50 % , e ) 150 %
Rationale: "let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length sqrt ( 20 ) * x , so the area is 20 x ^ 2 . the area of the original square is 1 / 20 = 5 % times the area of the new square . the answer is b ."
Answer: b
Question (general): the average weight of 6 students decreases by 3 kg when one of them weighing 80 kg is replaced by a new student . the weight of the student is
Options: a ) 62 kg , b ) 60 kg , c ) 70 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 3 kg = > ( 80 - x ) / 6 = 3 = > x = 62 answer : a"
Answer: a
Question (physics): if 20 honey bees make 20 grams of honey in 20 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 30
Rationale: explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 20 : : 20 : x honey 20 : 1 = > 1 x 20 x x = 20 x 1 x 20 = > x = 20 . answer : c
Answer: c
Question (gain): a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 60 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 7 : 15 , b ) 7 : 10 , c ) 7 : 8 , d ) 7 : 4 , e ) 7 : 2
Rationale: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 60 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.60 = $ 36 cost = 36 / 1.6 = $ 22.5 if he wants a 60 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 22.5 well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 22.5 / 33 = 15 / 22 of a liter . if milk is 15 / 22 of the liter , then water is 7 / 22 of the liter , and the ratio of water to milk is 7 : 15 . answer choice ( a )"
Answer: a
Question (gain): in town x , 65 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 27 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 65 % , out of which 48 are employed males , hence 17 % are employed females . ( employed females ) / ( total employed people ) = 17 / 64 = 27 % answer : b ."
Answer: b
Question (general): out of 3 consecutive odd numbers 9 times the first number is equal to addition of twice the third number and adding 9 to twice the second . what is the first number ?
Options: a ) 20 / 21 , b ) 23 / 25 , c ) 24 / 23 , d ) 22 / 5 , e ) 21 / 5
Rationale: description : = > 9 x = 2 ( x + 2 ) + 9 + 2 ( x + 4 ) = > 9 x = 4 x + 21 = > 5 x = 21 x = 21 / 5 answer e
Answer: e
Question (physics): find the lcm of 23 , 46,827
Options: a ) 227 , b ) 83 , c ) 23 , d ) 827 , e ) none of these
Rationale: explanation : whenever we have to solve this sort of question , remember the formula . lcm = \ \ begin { aligned } \ \ frac { hcf of denominators } { lcm of numerators } \ \ end { aligned } so answers will be option 2 , please also give attention to the difference in formula of hcf and lcm answer : option b
Answer: b
Question (general): at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 42 liters of forest green to change it to verdant green ?
Options: a ) 14 , b ) 12 , c ) 15 , d ) 11 , e ) 10
Rationale: "42 liter of forset green have 24 liter of blue and 18 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 24 / ( 18 + x ) = ¾ 54 + 3 x = 96 = > x = 14 answer : a"
Answer: a
Question (general): a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 300,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,250 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "0.04 x + 0.09 y = 300000 [ 1 ] 0.04 x = 0.80 * 300000 = 240000 [ 2 ] 240000 + 0.09 y = 300000 - - > 0.09 y = 60000 [ 3 ] 240000 / 12 = 20000 [ 4 ] 60000 / 12 = 5000 [ 5 ] adding [ 4,5 ] we get : 25000 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.25 , ans a"
Answer: a
Question (geometry): a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is
Options: a ) 3220 , b ) 4830 , c ) 5120 , d ) 6420 , e ) none
Rationale: "solution clearly , l = ( 48 - 16 ) m = 32 m ‹ = › b = ( 36 - 16 ) m = 20 m , ‹ = › h = 8 m . . volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 . answer c"
Answer: c
Question (general): 1,2 , 3,2 , 4,6 , 4,8 , _____
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "divide the series : 1 , 2,3 2 , 4,6 4,8 , ? so it is 12 answer : c"
Answer: c
Question (gain): there were two candidates in an election . winner candidate received 62 % of votes and won the election by 312 votes . find the number of votes casted to the winning candidate ?
Options: a ) 806 , b ) 744 , c ) 912 , d ) 1200 , e ) 1400
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 312 62 % - - - - - - - - ? = > 806 answer : a"
Answer: a
Question (general): 5358 x 52 = ?
Options: a ) 272258 , b ) 272358 , c ) 278616 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 2 ) = 5358 x 50 + 5358 x 2 = 267900 + 10716 = 278616 . c )"
Answer: c
Question (general): if x / ( 9 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 54 , b ) 33 , c ) 44 , d ) 66 , e ) 99
Rationale: "x / ( 9 p ) = odd prime number x = odd prime number * 9 p least value of x = lowest odd prime number * 9 * lowest value of p = 3 * 9 * 2 = 54 answer a"
Answer: a
Question (general): rs . 900 is divided among maya , annie , saiji so that maya receives half as much as annie and annie half as much as saiji . then saiji ’ s share is :
Options: a ) rs . 200 , b ) rs . 300 , c ) rs . 400 , d ) rs . 600 , e ) rs . 500
Rationale: let saiji = x . then , annie = x / 2 and maya = x / 4 . therefore , maya : annie : saiji = x / 4 : x / 2 : x = 1 : 2 : 4 . therefore , saiji ’ s share = rs . 900 * 4 / 9 = rs . 400 . answer : c
Answer: c
Question (physics): a company has two models of computers , model m and model n . operating at a constant rate , a model m computer can complete a certain task in 24 minutes and a model n computer can complete the same task in 12 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model m computers were used ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 8 , e ) 6
Rationale: let ' s say 1 work is processing 24 gb of data . model m : 1 gb per min model n : 2 gb per min working together , 1 m and 1 n = 3 gb per min so , 8 times as many computers would work at 18 gb per min . so no . of m = 8 answer is d
Answer: d
Question (physics): a and b together can do a work in 4 days . a alone can do it in 20 days . what time b will take to do the work alone ?
Options: a ) 6 days , b ) 8 days , c ) 12 days , d ) 10 days , e ) 5 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 4 a alone can do 1 day ' s work = 1 / 20 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 4 ) - ( 1 / 20 ) = 5 days answer : option e"
Answer: e
Question (physics): in a kilometer race , a beats b by 200 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 180 sec , b ) 190 sec , c ) 290 sec , d ) 490 sec , e ) 40 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 200 = 50 sec . time taken by a = 50 - 10 = 40 sec . answer : e"
Answer: e
Question (physics): if a car went the first third of the distance at 80 kmh , the second third at 15 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 30 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 15 and 48 ) so : 240 = 80 * t 1 = 3 hrs 240 = 15 * t 2 = 16 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 24 hrs d = rt ( 240 * 3 ) = r * 24 r = 30 answer : a"
Answer: a
Question (gain): x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 6 . if x invested rs . 5,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 15,000 , e ) none
Rationale: solution suppose y invested rs . y then , 5000 / y = 2 / 6 â € ¹ = â € º y = ( 5000 ã — 6 / 2 ) . â € ¹ = â € º y = 15000 . answer d
Answer: d
Question (general): in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 100 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 100 5 x - 20 = 100 5 x = 120 x = 24 the answer is a .
Answer: a
Question (gain): an article is bought for rs . 600 and sold for rs . 900 , find the gain percent ?
Options: a ) 33 1 / 7 % , b ) 33 1 / 6 % , c ) 50 % , d ) 38 1 / 3 % , e ) 33 2 / 3 %
Rationale: "600 - - - - 300 100 - - - - ? = > 50 % answer : c"
Answer: c
Question (general): mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 7 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "if n = 8 mark sold 1 box and ann sold 6 boxes total 7 < 8 answer : e"
Answer: e
Question (general): total 15 cows 5 cow gives each 2 liter milk 5 cow gives each 3 / 4 liter milk 5 cow gives each 1 / 4 liter milk this is split into 3 son per each 5 cows & 5 liter milk how ?
Options: a ) 10 , b ) 5 , c ) 15 , d ) 7.5 , e ) 12.5
Rationale: "5 cow 2 liter each = 10 liter 5 cow 3 / 4 liter each = 3 / 4 = 0.75 * 5 = 3.75 5 cow 1 / 4 liter each = 1 / 4 = 0.25 * 5 = 1.25 add 10 + 3.75 + 1.25 = 15 milk split into 3 son each 5 liter then 15 / 3 = 5 answer : b"
Answer: b
Question (general): given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 19 = f ( x – 4 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: 2 ( 3 x - 5 ) - 19 = 3 ( x - 4 ) - 5 3 x = 12 x = 4 the answer is b .
Answer: b
Question (general): a committee is reviewing a total of 20 x black - and - white films and 8 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?
Options: a ) 40 / 41 , b ) 20 / 41 , c ) 30 / 41 , d ) 60 / 41 , e ) 80 / 41
Rationale: "say x = y = 10 . in this case we would have : 20 x = 200 black - and - white films ; 8 y = 80 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 2 black - and - white films and all 80 color films , thus total of 82 films were selected . color films thus compose 80 / 82 = 40 / 41 of the selected films . answer : a"
Answer: a
Question (general): if | 4 x + 2 | = 46 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 1 , c ) 4 , d ) - 5 , e ) 6
Rationale: "there will be two cases 4 x + 2 = 46 or 4 x + 2 = - 46 = > x = 11 or x = - 12 sum of both the values will be - 12 + 11 = - 1 answer is b"
Answer: b
Question (general): there are 780 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 130 , b ) 100 , c ) 125 , d ) 175 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 780 . hence , we have m + f = 780 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 780 / 3 = 260 solving the three equations yields the solution f = 260 , m = 520 , and d = 260 . the number of female democratic participants equals half the female participants equals 260 / 2 = 130 . answer : a"
Answer: a
Question (other): there are 680 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 425 , b ) 345 , c ) 375 , d ) 380 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 680 . hence 3 x + 5 x = 680 solve for x 8 x = 680 x = 85 number of boys 3 x = 3 × 85 = 255 number of girls 5 x = 5 × 85 = 425 a"
Answer: a
Question (general): in a clothing store , there are 6 different colored neckties ( orange , yellow , green , blue , and indigo ) and 5 different colored shirts ( orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability that all of the boxes will contain a necktie and a shirt of the same color ?
Options: a ) 719 / 720 , b ) 1 / 120 , c ) 2 / 233 , d ) 3 / 543 , e ) 1 / 720
Rationale: 5 ties and 5 shirts . . . red tie can take any of 5 shirts . . orange can take any of the remaining 4 shirts yellow any of remaining 3 . . and so on till last indigo chooses the 1 remaining . . total ways = 5 * 4 * 3 * 2 * 1 = 120 out of this 120 , only 1 way will have same colour tie and shirt . . prob = 1 / 120 b
Answer: b
Question (physics): 325 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 13 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "26 trees have 25 gaps between them , required distance ( 325 / 25 ) = 13 a"
Answer: a
Question (general): in the coordinate plane , points ( x , 1 ) and ( 4 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x + y =
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: "line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 1 ) = ( 4 , 1 ) and ( 4 , y ) = ( 4,1 ) - - > x + y = 4 + 1 = 5 . answer : d"
Answer: d
Question (general): the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 45 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 60
Rationale: "20 x + 45 = 21 ( x – 5 ) x = 60 answer : e"
Answer: e
Question (general): q and f represent two distinct digits . if the number 457 q 89 f is divisible by 36 , what is the value of ( q + f ) ?
Options: a ) a ) 9 , b ) b ) 3 , c ) c ) 12 , d ) d ) 6 , e ) e ) 10
Rationale: a no . divisible by 36 means it is div by 49 . to be div by 4 last 2 digits to be multiple of 4 so , f could be either 2 or 6 only similarly for a number to be div by 9 its sum must be multiple of 9 first . filtering we find q could be either 1 , 47 only . to be divisible by 9 only 1 works . ( if we choose f = 6 then q have to be 6 but as per condition qf are distinct ) so q = 1 f = 2 ans : - 3 . b
Answer: b
Question (general): the total population of dogs in a community is estimated to be 50 % male and 50 % female . the total number of black dogs is 20 % greater than the total number of male black dogs . if the total number of female dogs is 8 times more than the number of female black dogs what percentage of male dogs is black ?
Options: a ) 84.4 , b ) 70.2 , c ) 80.1 , d ) 60.8 , e ) 62.5
Rationale: since we are dealing in percentage let us pick 100 as the number of black male dogs . that means that the total number of black dogs is = 120 ( 20 % more ) , therefore the number of black female dogs is 20 . the total number of female dogs is 8 x the number of black female = 20 * 8 = 160 female dogs . male dogs are 50 % of the dogs , and because there are 160 female dogs , then there must also be 160 male dogs therefore percentage of male dogs that are black = 100 / 160 * 100 = 62.5 correct option is e
Answer: e
Question (geometry): when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 0.3 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0003 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 0.3 then x = 0.3 / 1000 = 0.0003 . the answer is d"
Answer: d
Question (general): the ratio 25 : 50 expressed as percent equals to
Options: a ) 50 % , b ) 85 % , c ) 25 % , d ) 75 % , e ) none of above
Rationale: "explanation : actually it means 25 is what percent of 50 , which can be calculated as , ( 25 / 50 ) * 100 = 25 * 2 = 50 answer : option a"
Answer: a
Question (general): a man is 22 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 19 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 22 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 22 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 20 answer : d"
Answer: d
Question (physics): 18 beavers , working together in a constant pace , can build a dam in 8 hours . how many hours will it take 36 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 8 .
Rationale: "total work = 18 * 8 = 144 beaver hours 36 beaver * x = 144 beaver hours x = 144 / 36 = 4 answer : b"
Answer: b
Question (general): 2 + 4
Options: a ) 8 , b ) 13 , c ) 28 , d ) 6 , e ) 2
Rationale: d
Answer: d
Question (physics): maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 30 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 30 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 30 / 10 = 3 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 3 = 18 kms . . . answer - b"
Answer: b
Question (physics): a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 6 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 24 hr , e ) 26 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 6 ) = 1 / 26 leak will empty the tank in 26 hrs . answer : e"
Answer: e
Question (general): 10 people went to a hotel for combine dinner party 5 of them spent rs . 20 each on their dinner and rest spent 4 more than the average expenditure of all the 10 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 1492 , d ) 240 , e ) none of these
Rationale: "solution : let average expenditure of 10 people be x . then , 10 x = 20 * 5 + 5 * ( x + 4 ) ; or , 10 x = 20 * 5 + 5 x + 20 ; or , x = 24 ; so , total money spent = 24 * 10 = rs . 240 . answer : option d"
Answer: d