Cheukting/mathqa huggingface dataset:
Question (general): a cricketer scored 138 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 46.2 % , b ) 54.54 % , c ) 63 % , d ) 56.52 % , e ) none of these
Rationale: explanation : number of runs made by running = 138 - ( 12 x 4 + 2 x 6 ) = 138 - ( 60 ) = 78 now , we need to calculate 72 is what percent of 138 . = > 78 / 138 * 100 = 56.52 % answer : d
Answer: d
Question (geometry): if the height of a triangle is decreased by 40 % , land its base is increased by 40 % , what will be the effect on its area ?
Options: a ) no change
b ) 16 % increase
c ) 8 % decrease
d ) 16 % decrease
e ) none of thes
Rationale: regd effect = ∣ ∣ 40 − 40 − 40 × 40100 ∣ ∣ % = − 16 % | 40 − 40 − 40 × 40100 | % = − 16 % i . e . , the area will decrease by 16 % answer d
Answer: d
Question (gain): p and q invested in a shop . the profits were divided in the ratio of 2 : 3 respectively . if p invested rs . 40,000 , the amount invested by q is :
Options: a ) 35000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) none
Rationale: "suppose q invested rs . y . then , 40000 / y = 2 / 3 or y = [ 40000 x 3 / 2 ] = 60000 . answer d"
Answer: d
Question (general): if taxi fares were $ 8.00 for the first 1 / 5 mile and $ 0.8 for each 1 / 5 mile there after , then the taxi fare for a 8 - mile ride was
Options: a ) $ 39.00 , b ) $ 39.10 , c ) $ 39.25 , d ) $ 39.30 , e ) $ 39.20
Rationale: in 8 miles , initial 1 / 5 mile charge is $ 8 rest of the distance = 8 - ( 1 / 5 ) = 39 / 5 rest of the distance charge = 39 ( 0.8 ) = $ 31.2 ( as the charge is 0.8 for every 1 / 5 mile ) = > total charge for 4 miles = 8 + 31.2 = 39.2 answer is e
Answer: e
Question (physics): with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity q of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."
Answer: d
Question (general): how many diagonals does a 63 - sided convex polygon have ?
Options: a ) 1890 , b ) 1953 , c ) 3780 , d ) 3843 , e ) 3906
Rationale: "a 63 - sided convex polygon has 63 vertices . if we examine a single vertex , we can see that we can connect it with 60 other vertices to create a diagonal . note : there are 60 options because we ca n ' t connect the vertex to itself , and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 63 vertices can be connected with 60 vertices to create a diagonal then . . . . . . the total number of diagonals = ( 63 ) ( 60 ) = 3780 however , before we select answer choice c , we must recognize that we have counted every diagonal twice . for example , we might connect vertex a with vertex f and count that as 1 diagonal , and at the same time we connect vertex f with vertex a and count that as 1 diagonal . of course these diagonals are the same . to account for counting each diagonal twice , we must divide 3780 by 2 to get : 1890 answer : a"
Answer: a
Question (general): in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students t in the class ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25
Rationale: the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )
Answer: c
Question (gain): uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 20 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 10 % chocolate ?
Options: a ) 18 , b ) 20 , c ) 16 , d ) 22 , e ) 24
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 90 % * total = 36 = > ( 9 / 10 ) total = 36 = > total = 360 / 9 = > total = 40 oz , from there , you must find 10 % of the total 40 oz of the mixture . 10 % * total = > ( 1 / 10 ) ( 40 ) = 4 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 20 - 4 = 16 oz chocolate left over . answer : c"
Answer: c
Question (general): the area of one square is x ^ 2 + 10 x + 25 and the area of another square is 4 x ^ 2 − 12 x + 9 . if the sum of the perimeters of both squares is 64 , what is the value of x ?
Options: a ) 0 , b ) 2 , c ) 4.8 , d ) 4.67 , e ) 10
Rationale: "spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 5 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 5 l 2 = 2 x - 3 p 1 = 4 ( x + 5 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 64 4 ( x + 5 ) + 4 ( 2 x - 3 ) = 64 . . . . . . . . . . . . > x = 4.8 answer : c"
Answer: c
Question (physics): how long does a train 100 m long traveling at 72 kmph takes to cross a tunnel of 1400 m in length ?
Options: a ) 70 sec , b ) 60 sec , c ) 82 sec , d ) 75 sec , e ) 62 sec
Rationale: d = 1400 + 100 = 1500 m s = 72 * 5 / 18 = 20 t = 1500 * 1 / 20 = 75 sec answer : d
Answer: d
Question (physics): a person walks from one end to the other of a 60 - meter long moving walkway at a constant rate in 30 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 48 , b ) 60 , c ) 72 , d ) 84 , e ) 96
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 30 ( v + x ) = 60 then 120 ( v + x ) = 240 120 ( v - x ) = 60 when we add the two equations : 240 v = 300 v = 5 / 4 time = 60 / ( 5 / 4 ) = 48 seconds the answer is a ."
Answer: a
Question (general): mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 22 miles , how many miles was mike ' s ride ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 22 ) = $ 13 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 13 0.25 * x = 10.5 x = 42 miles the answer is c ."
Answer: c
Question (other): if g and d are both integers , g > d , and - 3 g > 19 , then the largest value of d would be ?
Options: a ) - 5 , b ) - 6 , c ) - 7 , d ) - 8 , e ) - 10
Rationale: no , your thinking is incorrect . when we know that g > d and g < - 6.33 , the largest value of g can be - 7 while if g = - 7 , then largest value of d < - 7 will be - 8 . for negative numbers , - 7 > - 8 and - 8 > - 10 . you are right in saying that d can take any value less than - 7 - - - > d could be - 8 , - 9 , - 10 . . . . and out of all these values , - 8 is the greatest . look at the numbers on the number line . for any 2 numbers , the ones on the right are greater than the ones on the left : . . . . . . . - 11 - 10 - 9 - 8 - 7 - 6 - 5 . . . . . 0 1 2 3 4 5 6 . . . ( - 11 < - 10 , - 10 < - 8 , 4 < 5 etc ) . so , as per the question if d < g and g = - 7 , then d ' s largest ' possible ' value has to be - 8 . - 10 is smaller than - 8 = d
Answer: d
Question (gain): what is the dividend from tony ' s stock , if he invested rs . 3200 at 85 to obtain an income of rs . 250 .
Options: a ) 4 , b ) 7.6 , c ) 6.6 , d ) 7.6 , e ) 9.6
Rationale: by investing rs . 3200 , income = rs . 250 by investing rs . 85 , income = 250 ã — 85 / 3200 = 6.6 ie , dividend = 6.6 % answer is c .
Answer: c
Question (physics): a is twice as good a workman as b and together they finish a piece of work in 14 days . the number of days taken by a alone to finish the work is :
Options: a ) 11 , b ) 21 , c ) 28 , d ) 42 , e ) none of these
Rationale: "( a ' s 1 day ' s work ) : ( b ' s 1 day ' s work ) = 2 : 1 ( a + b ) ' s 1 day ' s work = 1 / 14 divide 1 / 14 in the ratio 2 : 1 a ' s 1 day ' s work = ( 1 / 14 x 2 / 3 ) = 1 / 21 hence , a alone can finish the work in 21 days . correct option : b"
Answer: b
Question (general): a test has 160 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ?
Options: a ) 23 , b ) 25 , c ) 27 , d ) 29 , e ) 31
Rationale: a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 160 . thus 5 c < = 320 and so c < = 64 . then 40 < = c < = 64 and c can have 25 possible values . the answer is b .
Answer: b
Question (physics): a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution . if 65 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ?
Options: a ) 7.50
b ) 8.75
c ) 7.75
d ) 9.50
e ) 9.75
Rationale: we are given that a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of glucose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of glucose would be in the container when we have 45 cubic centimeters of solution , we can set up a proportion . we can say : “ 15 grams of glucose is to 100 cubic centimeters of solution as x grams of glucose is to 65 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 15 / 100 = x / 65 when we cross multiply we obtain : ( 15 ) ( 65 ) = 100 x 975 = 100 x 9.75 = x there are 9.75 grams of glucose in the solution in the container . the answer is e .
Answer: e
Question (gain): the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 150 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 150 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 150 ) * 100 / 500 = 30 % answer : option e"
Answer: e
Question (gain): if a man lost 4 % by selling oranges at the rate of 60 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 11 , b ) 28 , c ) 39 , d ) 40 , e ) 43
Rationale: "96 % - - - - 60 144 % - - - - ? 96 / 144 * 60 = 40 answer : d"
Answer: d
Question (physics): a man can row 9 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 6.24 km , b ) 6 km , c ) 8.84 km , d ) 5.66 km , e ) 10 km
Rationale: "m = 9 s = 1.2 ds = 10.2 us = 7.8 x / 10.2 + x / 7.8 = 1 x = 4.42 d = 4.42 * 2 = 8.84 answer : c"
Answer: c
Question (physics): a train speeds past a pole in 15 sec and a platform 100 m long in 25 sec , its length is ?
Options: a ) 158 m , b ) 150 m , c ) 110 m , d ) 130 m , e ) 157 m
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 100 ) / 25 = x / 15 = > x = 150 m . answer : b"
Answer: b
Question (physics): two trains 300 m and 450 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.6 , b ) 27 , c ) 10.4 , d ) 10.8 , e ) 10.1
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 300 + 450 = 750 m . required time = 700 * 9 / 250 = 27 sec . answer : b"
Answer: b
Question (gain): a shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 3 a rupee . find his net profit or loss percent ?
Options: a ) 33 4 / 3 % , b ) 33 1 / 7 % , c ) 50 % , d ) 32 1 / 3 % , e ) 60 %
Rationale: the total number of mangoes bought by the shopkeeper be 18 . if he buys 6 a rupee , his cp = 3 he selling at 3 a rupee , his sp = 6 profit = sp - cp = 6 - 3 = 3 profit percent = 3 / 6 * 100 = 50 % answer : c
Answer: c
Question (gain): what percent of 180 is 45 ?
Options: a ) 0.25 % , b ) 4 % , c ) 25 % , d ) 40 % , e ) 250 %
Rationale: "here ' s an algebraic approach . let p = the required percent . this means p / 100 = the percent as a fraction . so , ` ` what percent of 180 is 45 ? ' ' becomes ` ` ( p / 100 ) of 180 = 45 or : ( p / 100 ) ( 180 ) = 45 divide both sides by 180 to get : p / 100 = 45 / 180 simplify right side : p / 100 = 1 / 4 multiply both sides by 100 to get : p = 25 answer : c"
Answer: c
Question (physics): if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 15 men in 3 days ?
Options: a ) 65 mtr . , b ) 52 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 42 mtr .
Rationale: "20 men is 6 days can build 112 metres 15 men in 3 days can build = 112 * ( 15 / 20 ) x ( 3 / 6 ) = 42 meters answer : e ."
Answer: e
Question (physics): b completes a work in 3 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 2.31 days , b ) 4.31 days , c ) 5.31 days , d ) 6.31 days , e ) 7.31 days
Rationale: 1 / 3 + 1 / 10 = 13 / 30 30 / 13 = 2.31 days answer : a
Answer: a
Question (gain): a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 20,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,000 , e ) s . 7,500
Rationale: a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 20000 x 3 / 10 = rs . 6,000 . d
Answer: d
Question (physics): nick took a bus from home to market , that travels at 80 kmph . while walking back at 8 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 60 kmph . find the average speed .
Options: a ) 49.5 kmph , b ) 49.0 kmph , c ) 48.5 kmph , d ) 48.0 kmph , e ) none of these
Rationale: let the distance be 2 x ( one way ) time taken by bus = 2 x / 80 , by walking = x / 8 , by cycling = x / 60 hours : . average speed = total distance / total time = 8 x / x / 40 + x / 8 + x / 60 = 8 * 60 / 1.5 + 7.5 + 1 = 12.0 answer : d
Answer: d
Question (physics): a boat having a length 6 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 100 kg , b ) 120 kg , c ) 89 kg , d ) 180 kg , e ) 110 kg
Rationale: "volume of water displaced = ( 6 x 3 x 0.01 ) m 3 = 0.18 m 3 . mass of man = volume of water displaced x density of water = ( 0.18 x 1000 ) kg = 180 kg . answer : d"
Answer: d
Question (general): a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 1551 , what is the value of n ?
Options: a ) 22 , b ) 38 , c ) 62 , d ) 94 , e ) 672
Rationale: "factorise 1551 . . 3 * 11 * 47 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 47 = 94 . . ans : d"
Answer: d
Question (general): 0.999999 + 0.111111 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.111 , e ) 1.11111
Rationale: "0.999999 + 0.111111 = 0.999999 + 0.11111 + 0.000001 = ( 0.999999 + 0.000001 ) + 0.11111 = 1 + 0.11111 = 1.11111 e"
Answer: e
Question (gain): if the cost price of 10 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 40 % gain , d ) 60 % loss , e ) 50 % loss
Rationale: "explanation : 10 cp = 25 sp cost price cp = 25 selling price sp = 10 formula = ( sp - cp ) / cp * 100 = ( 10 - 25 ) / 25 * 100 = 60 % loss answer : option d"
Answer: d
Question (general): what is the unit digit in 7 ^ 105 ?
Options: a ) 9 , b ) 7 , c ) 3 , d ) 8 , e ) 5
Rationale: "unit digit in 7 ^ 105 = unit digit in [ ( 7 ^ 4 ) ^ 26 x 7 ] but , unit digit in ( 7 ^ 4 ) ^ 26 = 1 unit digit in 7 ^ 105 = ( 1 x 7 ) = 7 . answer b ) 7 ."
Answer: b
Question (gain): julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 112 and $ 120 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 784 , c ) 1080 , d ) 1200 , e ) 1440
Rationale: $ 112 for 2 years = $ 56 per year . extra $ 8 yearned with the compound interest is the percent yearned on percent . so , $ 8 is yearned on $ 56 , which means that the interest = 7 % . this on the other hand means that half of the savings = 56 * 7 = $ 392 . twice of that = $ 784 . answer : b .
Answer: b
Question (general): if 70 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 40 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "70 % of ( x - y ) = 30 % of ( x + y ) ( 70 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 7 ( x - y ) = 3 ( x + y ) 4 x = 10 y x = 5 / 2 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / ( 5 / 2 ) y ) x 100 ) = 40 % answer is b ."
Answer: b
Question (general): a man spends 1 / 3 rd of his salary on food . he spends 1 / 4 th on rent and 1 / 5 th on cloths . if he is left with 1760 , then who much salary does he earn .
Options: a ) 8120 , b ) 8123 , c ) 8222 , d ) 8322 , e ) 8422
Rationale: "let salary be x total spent = ( x / 3 + x / 4 + x / 5 ) = ( 47 / 60 ) * x left = ( x - 47 x / 60 ) = ( 13 / 60 ) * x given , ( 13 / 60 ) * x = 1760 x = ( 1760 * 60 ) / 13 = 8123.077 = 8123 ( approax ) answer : b"
Answer: b
Question (general): what is the least value of x , so that 2 x 5476 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 2
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 5 + 4 + 7 + 6 = 24 + x least value of x may be ' 3 ' , so that the total 24 + 3 = 27 is divisible by 9 . answer : option d"
Answer: d
Question (other): the length of the ribbon was originally 55 cm . it was reduced in the ratio 11 : 7 . what is its length now ?
Options: a ) 6 cm , b ) 12 cm , c ) 35 cm , d ) 44 cm , e ) none of these
Rationale: explanation : length of ribbon originally = 55 cm let the original length be 11 x and reduced length be 7 x . but 11 x = 55 cm x = 55 / 11 cm = 5 cm therefore , reduced length = 7 x cm = 7 5 cm = 35 cm answer : c
Answer: c
Question (physics): at 12.00 hours , j starts to walk from his house at 6 kmph . at 13.30 , p follows him from j ' s house on his bicycle at 8 kmph . when will j be 3 km behind p ?
Options: a ) 19.39 , b ) 19.3 , c ) 19.32 , d ) 19.33 , e ) 19.36
Rationale: by the time p starts j is 1.5 hr x 6 = 9 km away from his house . j is 3 km behind when p is 3 km ahead of him . ie . , p has to cover 12 km . so he takes 12 / ( 8 - 6 ) = 6 hrs after 13.30 . so the required time is 19.30 hrs answer : b
Answer: b
Question (physics): how many seconds will a 800 m long train take to cross a man walking with a speed of 5 km / hr in the direction of the moving train if the speed of the train is 65 km / hr ?
Options: a ) 30 , b ) 50 , c ) 66 , d ) 44 , e ) 48
Rationale: "speed of train relative to man = 65 - 5 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 800 * 3 / 50 = 48 sec . answer : e"
Answer: e
Question (physics): the sum of five consecutive even numbers is 500 . find the middle number of the five ?
Options: a ) 140 , b ) 66 , c ) 100 , d ) 99 , e ) 120
Rationale: "middle number = 500 / 5 = 100 ans c"
Answer: c
Question (physics): a and b together can do a piece of work in 6 days and a alone can do it in 14 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 15 days , c ) 21 / 2 days , d ) 21 days , e ) 22 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 14 work in 1 day b alone can do ( 1 / 6 - 1 / 14 ) = 2 / 21 work in 1 day = > complete work can be done in 21 / 2 days by b answer : option c"
Answer: c
Question (physics): triathlete dan runs along a 2 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 8 miles per hour and swims at a rate of 6 miles per hour , what is his average rate for the entire trip in miles per minute ?
Options: a ) 1 / 9 , b ) 2 / 15 , c ) 3 / 15 , d ) 1 / 4 , e ) 3 / 8
Rationale: "dan travels 4 miles round trip . running part : ( 2 / 8 = 1 / 4 * 60 = 15 minutes ) swimming part : ( 2 / 6 = 1 / 3 * 60 = 20 minutes ) 4 miles in ( 15 + 20 ) minutes 4 / 35 = 1 / 9 mile per minute answer : 1 / 9 mile per minute"
Answer: a