Cheukting/mathqa huggingface dataset:
Question (other): a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 23788 , d ) 10500 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 6 = 6 months . so there profit ratio = ( 3500 ã — 12 ) : ( 6 x ) = 2 : 3 â ‡ ’ x = 10500 answer : d"
Answer: d
Question (gain): the population of a village is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 10000 , b ) 12000 , c ) 13000 , d ) 14000 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 × 120 / 100 = 14400 e"
Answer: e
Question (general): in a class of 30 students , 5 students did not borrow any books from the library , 12 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 5 , b ) 8 , c ) 15 , d ) 18 , e ) 20
Rationale: the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 32 - 12 = 20 books . answer : e .
Answer: e
Question (physics): two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 3 hours ?
Options: a ) 2.4 . , b ) 3.6 . , c ) 4.8 . , d ) 5.5 . , e ) 6.4
Rationale: "w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 3 hrs = 4 × rate of each carpenter x time = 4 × 2 / 5 × 3 = 4.8 desks c is the correct answer ."
Answer: c
Question (other): mr . kutty has only hens and sheep . if the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep ?
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 6 : 13 , d ) 13 : 6 , e ) none of these
Rationale: let the total number of hens and sheep be x and y respectively . i . e . , x + y = 38 and 2 x + 4 y = 100 ∴ ratio = 13 : 6 answer d
Answer: d
Question (physics): a boat covers a certain distance downstream in 1 hour , while it comes back in 1.30 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ?
Options: a ) 10 , b ) 13 , c ) 11 , d ) 08 , e ) 15
Rationale: "let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x − 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 1 1 ⁄ 2 hour . i . e . , distance travelled downstream in 1 hour = distance travelled upstream in 1 1 ⁄ 2 hour since distance = speed × time , we have ( x + 3 ) × 1 = ( x − 3 ) 3 / 2 ⇒ 2 ( x + 3 ) = 3 ( x − 3 ) ⇒ 2 x + 6 = 3 x − 9 ⇒ x = 6 + 9 = 15 kmph answer is e ."
Answer: e
Question (general): if x is a positive number and 1 / 4 the square root of x is equal to 3 x , then x =
Options: a ) 1 / 16 , b ) 12 , c ) 1 / 12 , d ) 144 , e ) 1 / 144
Rationale: "1 / 4 of sqrt ( x ) = 3 x , which means that sqrt ( x ) = 12 x or x = 144 x ^ 2 - > divide by x 1 = 144 x x = 1 / 144 e ."
Answer: e
Question (general): a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 15 days starting with sunday is
Options: a ) 280 , b ) 285 , c ) 290 , d ) 295 , e ) 570
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 15 ) = ( 8550 / 15 ) = 570 answer : option e"
Answer: e
Question (probability): in how many ways can 11 books on english and 9 books on french be placed in a row on a shelf so that two books on french may not be together ?
Options: a ) 220 . , b ) 240 , c ) 260 , d ) 280 , e ) 300
Rationale: we have 11 english and 9 french books , no french books should be adjacent . imagine 11 english books in a row and empty slots like below : * e * e * e * e * e * e * e * e * e * e * e * now if 9 french books would be placed in 12 empty slots , all french books will be separated by english books . so we can ` ` choose ' ' 9 empty slots from 12 available for french books , which is 12 c 9 = 220 . ans : a _________________
Answer: a
Question (general): if 35 percent of 400 is 20 percent of x , then x =
Options: a ) 200 , b ) 350 , c ) 700 , d ) 900 , e ) 1,400
Rationale: "5 / 100 ( 400 ) = 2 / 10 ( x ) x = 700 . . answer : c"
Answer: c
Question (geometry): the side of a rhombus is 26 m and length of one of its diagonals is 20 m . the area of the rhombus is ?
Options: a ) 488
b ) 429
c ) 418
d ) 480
e ) 410
Rationale: 262 – 102 = 242 d 1 = 20 d 2 = 48 1 / 2 * 20 * 48 = 480 answer : d
Answer: d
Question (general): 80 370 ? 1550 2440 3530
Options: a ) 900 , b ) 840 , c ) 750 , d ) 860 , e ) 960
Rationale: "10 ^ 2 - 20 = 80 20 ^ 2 - 30 = 370 30 ^ 2 - 40 = 860 40 ^ 2 - 50 = 1550 50 ^ 2 - 60 = 2440 60 ^ 2 - 70 = 3530 . answer : d"
Answer: d
Question (gain): how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 4 - percent solution ?
Options: a ) 35 , b ) 33 1 / 3 , c ) 21 , d ) 16 2 / 3 , e ) 15
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 4 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 4 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 4 x = 6 since you need a 15 l solution , you must evaporate 21 of the original 50 l solution to get a 4 % solution . answer is c ."
Answer: c
Question (probability): three coins are tossed . find the probability of at least 1 head and 1 tail ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 7 / 8 , e ) 1 / 8
Rationale: "n ( s ) = 2 ^ 3 = 8 . . . . ( 3 coins tossed ) let e is the event of getting at least 1 head and 1 tail n ( e ) = tth , htt , tht , hht , hth , thh = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 8 = 3 / 4 ans - c"
Answer: c
Question (general): 10 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 90 , b ) 98 , c ) 35 , d ) 99 , e ) 80
Rationale: "though 2 * ( 10 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 9 , so he ' ll play 18 matches . similarly , second guy has to play with the rest of 8 as his 2 games with the first guy are already played . so he plays 16 matches . this continues like this and the total matches are 18 + 16 + 14 . . . + 2 18 + 16 + . . . + 2 = 2 ( 9 + 8 + . . . + 1 ) = 2 ( ( 9 * 10 ) / 2 ) = 9 * 10 = 90 . answer : a"
Answer: a
Question (geometry): john is building a rectangular fence around a garden . the length will be 5 feet shorter than its width . if the total area of the garden is 176 square feet , what is the length of the diagonal ( in feet ) ?
Options: a ) between 18 and 19
b ) between 19 and 20
c ) between 20 and 21
d ) between 21 and 22
e ) between 22 and 23
Rationale: to solve this , we first need to set up an equation for the area of the garden . if x is the width , then we have x ( x - 5 ) = 176 . by putting the equation in standard form , we get x ^ 2 - 5 x - 176 = 0 . by using the quadratic formula , we get roots of - 11 and 16 . we know that x is the width , and x - 5 is the length , so by using the roots , we get 16 as the width ( x ) , and 11 as the length ( x - 5 ) . once we have this , we can use the pythagorean theorem to solve for the diagonal . plugging in the length and width , we will get d ^ 2 = 16 ^ 2 + 11 ^ 2 = 256 + 121 = 377 the square root of 377 is less than 20 , since 20 ^ 2 = 400 . going down a number , we can compute 19 ^ 2 = 361 < 377 . therefore , the length of the diagonal must be between 19 and 20 . the correct answer is b .
Answer: b
Question (other): divide $ 450 among a , b in the ratio 1 : 4 . how many $ that a get ?
Options: a ) $ 90 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: "sum of ratio terms = 1 + 4 = 5 a = 450 * 1 / 5 = $ 90 answer is a"
Answer: a
Question (general): 88 % of 370 + 24 % of 210 - ? = 118
Options: a ) 256 , b ) 258 , c ) 268 , d ) 358 , e ) none of these
Rationale: "let 88 % of 370 + 240 % of 210 - x = 118 then , x = ( 88 / 100 * 370 ) + ( 24 / 100 * 210 ) - 118 - 325.60 + 50.40 - 118 = 376 - 118 = 258 correct option : b"
Answer: b
Question (physics): a train passes a platform in 22 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 40 , b ) 50 , c ) 60 , d ) 30 , e ) 20
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 12 = > 300 + l = 15 × 22 = 330 = > l = 330 - 300 = 30 meter answer is d ."
Answer: d
Question (gain): in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 184 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 434 , e ) 460
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 184 = > 4 x / 10 = 184 = > 4 x = 1840 = > x = 460 . answer : e"
Answer: e
Question (physics): a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts four hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 8 , d ) d ) 5.5 , e ) e ) 5
Rationale: "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 4 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 4 + t ) = 40 * t t = 12 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 12 / 60 = 8 hrs time taken by a = 4 + t = 4 + 12 = 16 hrs time taken by k = 8 hrs so k starts 16 - 8 = 8 hrs after a . ( answer c )"
Answer: c
Question (physics): a and b together can complete work in 5 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 8 , c ) 15 , d ) 6 , e ) 7
Rationale: "explanation : ( a + b ) one day work = 1 / 5 now a does half of the work in 3 days so a can complete the whole work in 6 days a ’ s one day work = 1 / 6 b ’ s one day work = 1 / 5 - 1 / 6 = 1 / 30 b alone can complete the work in 30 days so half of the work in 15 days answer : option c"
Answer: c
Question (physics): a rectangular plot measuring 15 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 46 m , b ) 26 m , c ) 26 m , d ) 56 m , e ) 25 m
Rationale: "perimeter of the plot = 2 ( 15 + 50 ) = 130 m no of poles = 130 / 5 = 26 m answer : b"
Answer: b
Question (physics): if a train , travelling at a speed of 270 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 281 m , b ) 325 m , c ) 117 m , d ) 375 m , e ) 350 m
Rationale: "d d = 270 * 5 / 18 * 5 = 375 m"
Answer: d
Question (general): a certain car uses one gallon of gasoline every 36 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 40 %
Rationale: "4 miles on the highway = 4 / 36 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 36 + 4 / 20 = 14 / 45 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 14 / 45 - 8 / 36 ) / ( 8 / 36 ) = 0.40 . answer : e ."
Answer: e
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along theoundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 145010 m , b ) 146400 m , c ) 153600 m , d ) 164500 m , e ) 167550 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m c"
Answer: c
Question (gain): the calendar of the year 2060 can be used again in the year ?
Options: a ) 2081 , b ) 2083 , c ) 2088 , d ) 1971 , e ) 1973
Rationale: "explanation : given year 2060 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2060 + 28 = 2088 answer : c"
Answer: c
Question (general): mixture a is 40 percent alcohol , and mixture b is 80 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 50 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 1.5 , b ) 1.7 , c ) 2.3 , d ) 2.5 , e ) 2.4
Rationale: "( 80 - 50 ) / ( 50 - 40 ) = qa / qb 30 / 10 = qa / qb 3 / 1 = qa / qb qa = ( 3 / 5 ) * 4 = 12 / 5 = 2.4 approx answer : e"
Answer: e
Question (geometry): the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 75 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75 % , b ) 80 % , c ) 145 % , d ) 150 % , e ) 180 %
Rationale: "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 75 percent to make square c length of each side of square c = 1.75 * 20 = 35 area of c = 35 ^ 2 = 1225 difference in areas of c and cummulative areas of a and b = 1225 - ( 400 + 100 ) = 725 percent is the area of square c greater than the sum of the areas of squares a and b = ( 725 / 500 ) * 100 % = 145 % answer c"
Answer: c
Question (general): the temperature of a certain cup of coffee 15 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 15 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 15 a ) + 60 60 = 120 * ( 2 ^ - 15 a ) 60 / 120 = 2 ^ - 15 a 1 / 2 = 2 ^ - 15 a 2 ^ - 1 = 2 ^ - 15 a - 1 = - 15 a 1 / 15 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 15 * 30 ) + 60 f = 120 * ( 2 ^ - 2 ) + 60 f = 120 * ( 1 / 2 ^ 2 ) + 60 f = 120 * 1 / 4 + 60 f = 30 + 60 = 90 answer e !"
Answer: e
Question (general): p and q are the only two applicants qualified for a short - term research project that pays 480 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 5 , b ) $ 8 , c ) $ 11 , d ) $ 14 , e ) $ 17
Rationale: "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 480 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 480 / 30 = $ 16 p ' s hourly wage is 480 / ( t - 10 ) = $ 24 which is $ 8 per hour more . the answer is b ."
Answer: b
Question (geometry): the area of the largest circle that can be drawn inside a rectangle with sides 18 cm by 14 cm is
Options: a ) 237
b ) 154
c ) 2376
d ) 198
e ) 171
Rationale: explanation : the diameter is equal to the shortest side of the rectangle . so radius = 14 / 2 = 7 cm . answer : b ) 154
Answer: b
Question (gain): what profit percent is made by selling an article at a certain price , if by selling at 1 / 3 rd of that price , there would be a loss of 20 % ?
Options: a ) 140 % , b ) 29 % , c ) 70 % , d ) 27 % , e ) 28 %
Rationale: "sp 2 = 1 / 3 sp 1 cp = 100 sp 2 = 80 1 / 3 sp 1 = 80 sp 1 = 240 100 - - - 240 = > 140 % answer : a"
Answer: a
Question (general): a certain company had a total annual expenditure of 1.89 ∗ 10 ^ 7 on employee salaries last year . if the company employed 420 people , what was the average employee salary ?
Options: a ) $ 20,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 40,000 , e ) $ 45,000
Rationale: "given : total annual expenditure of 1.89 ∗ 10 ^ 7 on employee salaries total employees = 420 observe that 420 * 4 = 1890 therefore try to bring the numerator in terms of 1890 average salary = ( 1890 * 10 ^ 4 ) / 420 = 4.5 * 10 ^ 4 = 45,000 option e"
Answer: e
Question (physics): the timing of a college is from 12 p . m to 4.00 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 4 hours 00 minutes = 240 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 240 â € “ 20 ) / 5 = 44 minutes answer e"
Answer: e
Question (other): a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 4 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
Options: a ) 2 , b ) 9 , c ) 15 , d ) 18 , e ) 30
Rationale: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 4 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 4 ) = 0.08 t - - > 60 + 6 ( t - 4 ) = 8 t - - > t = 18 . answer : d ."
Answer: d
Question (geometry): three solid cubes of sides 1 cm , 6 cm and 8 cm are melted to form a new cube . find the surface area of the cube so formed
Options: a ) 486
b ) 366
c ) 299
d ) 278
e ) 1888
Rationale: explanation : volume of new cube = = edge of new cube = = 9 cm surface area of the new cube = ( 6 x 9 x 9 ) = 486 answer : a ) 486
Answer: a
Question (gain): a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 12 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 21 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 12 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 22 / 25 = ( 1 + p % ) profit % = 21 % b"
Answer: b
Question (general): in a recent head - to - head run - off election , 12,000 absentee ballets were cast . 1 / 2 of the absentee ballets were thrown out and 1 / 2 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000
Rationale: "1 / 2 * 1 / 2 ( total absentee votes ) = 1 / 4 ( total votes ) = 1 / 4 * 12000 = 3000 answer is b"
Answer: b
Question (gain): the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is
Options: a ) rs . 500 , b ) rs . 515 , c ) rs . 550 , d ) rs . 600 , e ) none
Rationale: "solution 110 % of s . p . = 616 ‹ = › s . p . = ( 616 x 100 / 110 ) . ‹ = › rs . 560 . c . p . ‹ = › rs . ( 100 / 112 x 560 ) ‹ = › rs . 500 . answer a"
Answer: a
Question (physics): a man swims downstream 45 km and upstream 25 km taking 5 hours each time , what is the speed of the man in still water ?
Options: a ) 17 , b ) 24 , c ) 7 , d ) 24 , e ) 20
Rationale: "45 - - - 5 ds = 9 ? - - - - 1 25 - - - 5 us = 5 ? - - - - 1 m = ? m = ( 9 + 5 ) / 2 = 14 / 2 = 7 answer : c"
Answer: c
Question (physics): the length of a bridge in meters , which a train 90 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 145 , b ) 215 , c ) 265 , d ) 285 , e ) 375
Rationale: 45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 90 = 375 meters x = 285 meters the answer is d .
Answer: d
Question (general): if 3 < x < 6 < y < 8 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: 3 < x < 6 < y < 8 ; 3 < x y < 8 3 + y < x + 8 y - x < 5 . positive integer difference is 4 ( for example y = 7.5 and x = 3.5 ) answer : b .
Answer: b
Question (general): a couple decides to have 4 children . if they succeed in having 4 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 2 girls and 2 boys ?
Options: a ) 3 / 8 , b ) 1 / 4 , c ) 3 / 16 , d ) 1 / 8 , e ) 1 / 16
Rationale: "no of ways of getting p ( ggbb ) is 4 ! / 2 ! * 2 ! ; total no of ways is 2 ^ n = 2 ^ 4 = 16 ; 6 / 16 = 3 / 8 ; we can consider this question to a coin that is flipped for 4 times . what is the probability of getting exactly two heads . p ( all out comes ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 ; p ( favorable outcomes ) = 4 ! / ( 2 ! * 2 ! ) = 6 / 16 = 3 / 8 ; answer : a"
Answer: a