Cheukting/mathqa huggingface dataset:
Question (other): a baseball team played 10 games and won 5 . what is the ratio of the number of games played to the number of losses ?
Options: a ) 5 : 1 , b ) 1 : 1 , c ) 20 : 4 , d ) 10 : 3 , e ) 2 : 1
Rationale: the number of games played is 10 . the number of games won is 5 , so 10 - 5 = 5 = number of game losses . answer = ! 0 : 5 = 2 : 1 answer is e
Answer: e
Question (general): 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 48 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 48 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 48 / 60 oxen = 24 days the answer is b ."
Answer: b
Question (gain): cp of 2 buffaloes are $ 30,000 . by selling 1 at a loss of 15 % and other at a profit of 19 % , he foundthat sp of both buffaloes is the same . find the cp of each ?
Options: a ) $ 10,500 , b ) $ 10,500 , c ) $ 11,500 , d ) $ 12,000 , e ) $ 12,500
Rationale: "let the c . p of 1 st buffalo = x ∴ c . p of 2 nd buffalo = 30,000 - x s . p of 1 st buffalo = ( 100 - loss % ) - - - - - - - - - - - - - - - - - - - x c . p 100 s . p = 100 - 15 x - - - - - - - - - - - = 85 x / 100 100 s . p of 2 nd buffalo = ( 100 - profit % ) - - - - - - - - - - - - - - - - - - - - - x c . p 100 s . p = ( 100 + 19 ) ( 30,000 - x ) 119 ( 30,000 - x ) - - - - - - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - 100 100 s . p of 1 st buffalo = s . p of 2 nd buffalo 85 x / 100 = 119 ( 30,000 - x ) / 100 ⇒ 85 x = 119 ( 30,000 - x ) ⇒ 85 x = 3 , 570,000 - 119 x ⇒ 85 x + 119 x = 3 , 570,000 ⇒ 204 x = 3 , 570,000 ⇒ x = 3 , 570,000 / 204 ⇒ x = $ 17,500 c . p of 1 st buffalo = $ 17,500 c . p of 2 nd buffalo = 30,000 - 17,500 = $ 12,500 e"
Answer: e
Question (gain): the purchase price of an article is $ 48 . in order to include 10 % of cost for overhead and to provide $ 12 of net profit , the markup should be
Options: a ) 15 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "cost price of article = 48 $ % of overhead cost = 10 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 10 = 35 % answer c"
Answer: c
Question (probability): in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 8 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 134 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Rationale: "the probability of survival for each of the first 3 months of life is 1 - 1 / 8 = 7 / 8 , so of 200 newborn 200 * 7 / 8 * 7 / 8 * 7 / 8 = ~ 134 is expected to survive . answer : a ."
Answer: a
Question (gain): increasing the original price of a certain item by 15 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 50.0 , d ) 52.5 , e ) 43.75
Rationale: "we ' re told that the original price of an item is increased by 15 % and then that price is increased by 25 % . . . . if . . . . starting value = $ 100 + 15 % = 100 + . 15 ( 100 ) = 115 + 25 % = 115 + . 25 ( 115 ) = 115 + 28.75 = 143.75 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 43.75 / 100 = 43.75 % final answer : e"
Answer: e
Question (general): find the least number must be subtracted from 378461 so that remaining no . is divisible by 13 ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 6 , e ) 8
Rationale: "on dividing 378461 by 13 we get the remainder 5 , so 5 should be subtracted b"
Answer: b
Question (gain): the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 40 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 896 , d ) $ 870 , e ) $ 660
Rationale: let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 140 % of $ 640 = $ 896 . c
Answer: c
Question (general): a certain pair of used shoes can be repaired for $ 11.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 28.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?
Options: a ) 20.8 , b ) 21.46 , c ) 21.74 , d ) 22.3 , e ) 21.4
Rationale: "1 ) cost of repairing = 11.5 ( for one year ) , therefore for 2 years it would be $ 23 . 2 ) cost of new pair which will last for 2 years is $ 28 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoeinitial value would be the cost of repairing the old shoe . i . e ( 28 - 23 ) / ( 23 ) * 100 = 21.74 % . ans is c"
Answer: c
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 80 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 ) 40 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 80 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 80 / 10 = 8 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 8 = 40 kms . . . answer - c"
Answer: c
Question (physics): renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 4 days . in what time suma can do it alone ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 17
Rationale: "renu ’ s one day ’ s work = 1 / 6 suma ’ s one day ’ s work = 1 / 4 - 1 / 6 = 1 / 12 suma can do it alone in 12 days . answer : b"
Answer: b
Question (physics): working at their respective constant rates , machine a makes 100 copies in 8 minutes and machine b makes 150 copies in 10 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 425 , c ) 675 , d ) 825 , e ) 750
Rationale: "machine a can produce 100 * 30 / 8 = 375 copies and , machine b can produce 150 * 30 / 10 = 825 copies total producing 700 copies . d is the answer"
Answer: d
Question (other): q - 1 ) of the 84 parents who attended a meeting at a school , 25 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic . if the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise children during the picnic nor volunteered to bring refreshments , how many of the parents volunteered to bring refreshments ?
Options: a ) 25 , b ) 36 , c ) 38 , d ) 45 , e ) 42
Rationale: i used the following formula : total = group 1 + group 2 + neither - both using the information from the question stem , we have : 84 total people 25 who supervise ( group 1 ) x who neither supervise nor bring refreshments 1.5 x people who bring refreshments ( group 2 ) 11 who supervise and bring refreshments ( both ) therefore . . . 84 = 25 + 1.5 x + x - 11 solving , we get x = 28 since we want the value of those who bring refreshments and supervise : 1.5 ( 28 ) = 42 answer is e
Answer: e
Question (general): in a mayoral election , candidate x received 1 / 4 more votes than candidate y , and candidate y received 1 / 6 fewer votes than z . if z received 24,000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22000 , c ) 24000 , d ) 25000 , e ) 32000
Rationale: "z = 24 - - > y received 1 / 4 fewer votes than z - - > y = z - 1 / 6 * z = 20 ; x received 1 / 4 more votes than y - - > x = y + 1 / 4 * y = 25 . answer : d ."
Answer: d
Question (physics): excluding stoppages , the speed of a bus is 72 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 8 min , c ) 9 min , d ) 10 min , e ) 55.8 min
Rationale: "due to stoppages , it covers 9 km less . time taken to cover 67 km = ( 67 / 72 ) x 60 = 55.8 min answer : e"
Answer: e
Question (physics): two cars are driving toward each other . the first car is traveling at a speed of 60 km / h , which is 25 % slower than the second car ' s speed . if the distance between the cars is 770 km , how many hours will it take until the two cars meet ?
Options: a ) 4 , b ) 4.5 , c ) 5 , d ) 5.5 , e ) 6
Rationale: "the speed of the first car is 60 km / h . the speed of the second car is 60 / 0.75 = 80 km / h . the two cars complete a total of 140 km each hour . the time it takes the cars to meet is 770 / 140 = 5.5 hours . the answer is d ."
Answer: d
Question (probability): in 15 year ’ s time the combined age of my 4 brothers will be 107 . what will it be in 6 year ’ s time ?
Options: a ) 65 , b ) 87 , c ) 71 , d ) 60 , e ) 66
Rationale: c 71 combined age in 15 years = 107 . 4 × 15 = 60 , therefore combined age now is 107 – 60 = 47 . in 6 years time , therefore , combined age will be 47 + 24 ( 4 × 6 ) = 71 .
Answer: c
Question (general): if sharon ' s weekly salary increased by 10 percent , she would earn $ 330 per week . if instead , her weekly salary were to increase by 8 percent , how much would she earn per week ?
Options: a ) rs . 424 , b ) rs . 524 , c ) rs . 324 , d ) rs . 350 , e ) rs . 354
Rationale: "soln : - ( 330 / 110 ) 108 = 324 in this case long division does not take much time . ( 330 / 110 ) 108 = 324 answer : c"
Answer: c
Question (gain): the compound interest on $ 27,000 at 11 % p . a is $ 11,000 . find out the period ( in years ) ?
Options: a ) 2.5 , b ) 3 1 / 4 , c ) 3 , d ) 2 3 / 4 , e ) 4
Rationale: "amount = 27,000 + 11,000 = 38,000 . . . . . . . . . now by using compound interest formula we get , 27,000 * ( 111 / 100 ) ^ n = 38000 = = = = > n = = 3 1 / 4 years ans - b"
Answer: b
Question (general): 1,5 , 13,25 , __
Options: a ) 26 , b ) 30 , c ) 31 , d ) 41 , e ) 43
Rationale: "series increased by 1 1 + ( 4 * 1 ) = 1 + 4 = 5 5 + ( 4 * 2 ) = 5 + 8 = 13 13 + ( 4 * 3 ) = 13 + 12 = 25 25 + ( 4 * 4 ) = 25 + 16 = 41 answer : d"
Answer: d
Question (general): ages of two persons differ by 18 years . if 4 years ago , the elder one was 4 times as old the younger one , find their present age
Options: a ) 6,24 , b ) 9,27 , c ) 10,28 , d ) 18,36 , e ) 19,37
Rationale: explanation : let the age of younger person be x , then elder person ' s age is ( x + 18 ) = > 4 ( x - 4 ) = ( x + 18 - 4 ) [ 4 years before ] = > 4 x - 16 = x + 14 = > x = 10 . so elder person ' s age is x + 18 = 28 answer : option c
Answer: c
Question (general): if 13 = 13 w / ( 1 - w ) , then ( 4 w ) 2 =
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 , d ) 2 , e ) 4
Rationale: "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 4 w = 2 4 w * 2 = 2 * 2 = 4 answer : e"
Answer: e
Question (general): in a recent head - to - head run - off election , 10,000 absentee ballets were cast . 2 / 3 of the absentee ballets were thrown out and 2 / 5 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 / 3 * 3 / 5 ( total absentee votes ) = 1 / 5 ( total votes ) = 1 / 5 * 10000 = 2000 answer is a"
Answer: a
Question (physics): a bicycle wheel has a diameter of 0.61 m . how many complete revolutions does it make in 1 km ?
Options: a ) 246 , b ) 522 , c ) 1408 , d ) 710 , e ) 223
Rationale: "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.61 m ) = 522.1 . hence 522 complete revolutions . answer b"
Answer: b
Question (gain): nitin borrowed some money at the rate of 6 % p . a . for the first 3 years , 9 % p . a . for the next 5 years and 13 % p . a . for the period beyond 8 years . if the total interest paid by him at the end of 11 years is rs . 8160 , how much money did he borrow ?
Options: a ) 8000 , b ) 2787 , c ) 27766 , d ) 9976 , e ) 21671
Rationale: let the sum be rs . x . then , [ ( x * 6 * 3 ) / 100 ] + [ ( x * 9 * 5 ) / 100 ] + [ ( x * 13 * 3 ) / 100 ] = 8160 18 x + 45 x + 39 x = ( 8160 * 100 ) 102 x = 816000 = > x = 8000 . answer : a
Answer: a
Question (other): the ratio between the sale price and the cost price of an article is 6 : 2 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 23 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 2 : 1
Rationale: "c . p . = rs . 2 x and s . p . = rs . 6 x . then , gain = rs . 4 x required ratio = 4 x : 2 x = 2 : 1 e"
Answer: e
Question (general): a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1200 in total compensation , how many total hours did he work that week ?
Options: a ) 60 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 1200 - 640 = 560 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 560 / 28 = 20 total hrs = 40 + 20 = 60 answer a 60"
Answer: a
Question (general): if 5 ^ 29 * 4 ^ 15 = 2 * 10 ^ n , what is the value of n ?
Options: a ) 11 , b ) 21 , c ) 22 , d ) 29 , e ) 32
Rationale: my attempt : 5 ^ ( 29 ) * 4 ^ ( 15 ) = 2 * 10 ^ p 5 ^ ( 29 ) * 2 ^ ( 30 ) = 2 * ( 2 * 5 ) ^ p 5 ^ ( 29 ) * 2 ^ ( 30 ) = 2 * 2 ^ ( p ) * 5 ^ ( p ) 5 ^ ( 29 ) * 2 ^ ( 30 ) = 2 ^ ( p + 1 ) * 5 ^ ( p ) = > ( p + 1 ) = 30 = > p = 29 answer : 29 ( d )
Answer: d
Question (physics): a man is standing on a railway bridge which is 180 m long . he finds that a train crosses the bridge in 20 seconds but himself in 8 seconds . find the length of the train and its speed .
Options: a ) 10 m / sec , b ) 15 m / sec , c ) 18 m / sec , d ) 19 m / sec , e ) 25 m / sec
Rationale: if length of train is l and speed of train is s , then l / s = 8 ( l + 180 ) / s = 20 ( l + 180 ) / l = 20 / 8 = 5 / 2 2 l + 360 = 5 * l 3 * l = 360 l = 120 mtrs s = l / 8 = 120 / 8 = 15 m / sec answer : b
Answer: b
Question (general): if 2 ^ k = 4 , then 2 ^ ( 2 k + 2 ) =
Options: a ) 29 , b ) 45 , c ) 81 , d ) 64 , e ) 18
Rationale: "2 ^ k = 4 2 ^ 2 k = 4 ^ 2 2 ^ 2 k = 16 2 ^ ( 2 k + 2 ) = 2 ^ 2 k * 2 ^ 2 = 16 * 4 = 64 answer : d"
Answer: d
Question (geometry): a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 60 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?
Options: a ) 13 , b ) 33 , c ) 50 , d ) 51 , e ) 60
Rationale: "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 60 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 30 cents . fraction of spirit is 1 / 2 . 30 = k * ( 1 / 2 ) k = 60 cost per liter = 60 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 60 * ( 1 / 3 ) * 3 = 50 cents e . 60 cents"
Answer: e
Question (general): the average marks of a class of 28 students is 40 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 52.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 52.1
Rationale: "sum of the marks for the class of 28 students = 28 * 40 = 1120 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 78 students = 1120 + 3000 = 4120 average marks of all the students = 4120 / 78 = 52.8 answer : c"
Answer: c
Question (general): free notebooks were distributed equally among children of a class . the number of notebooks each child got was one - eighth of the number of children . had the number of children been half , each child would have got 16 notebooks . total how many notebooks were distributed ?
Options: a ) 256 , b ) 512 , c ) 432 , d ) 352 , e ) 640
Rationale: let total number of children be x . then , x * ( 1 / 8 ) x = ( x / 2 ) x 16 x = 64 . number of notebooks = ( 1 / 8 ) x ^ 2 = ( 1 / 8 ) x 64 x 64 = 512 . answer is b .
Answer: b
Question (general): if 7800 / 3.25 = 2400 , then 780.0 / 32.5 is equal to ?
Options: a ) 21 , b ) 28 , c ) 26 , d ) 25 , e ) 24
Rationale: "answer given expression 780.0 / 32.5 = 7800 / 325 = 7800 / ( 3.25 x 100 ) = 2400 / 100 = 24 correct option : e"
Answer: e
Question (physics): tim and é lan are 120 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 30 miles . , b ) 35 miles . , c ) 45 miles . , d ) 60 miles . , e ) 80 miles .
Rationale: "tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice e meet the 2 : 1 ( tim : elan = 80 : 40 ) ratio of maintaining total distance traveled 120 miles so correct answer e"
Answer: e
Question (general): the sum of the first 40 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 6,500 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 40 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 40 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 40 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 4000 + 2500 = 6500 a is the answer ."
Answer: a
Question (geometry): the diagonals of a rhombus are 14 cm and 20 cm . find its area ?
Options: a ) 176 , b ) 190 , c ) 140 , d ) 278 , e ) 292
Rationale: "1 / 2 * 14 * 20 = 140 answer : c"
Answer: c
Question (geometry): what is the perimeter of a triangle with sides 7 and 5 that has the maximum possible area ?
Options: a ) 12 + √ 7
b ) 12 + 4 √ 7
c ) 12 + √ 47
d ) 12 + 4 √ 47
e ) 12 + √ 74
Rationale: we can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle . then the third side is the hypotenuse with a length of √ ( 49 + 25 ) = √ 74 the perimeter is 12 + √ 74 the answer is e .
Answer: e
Question (general): if x and y are positive integers and 20 x = 10 y what is the least possible value of xy ?
Options: a ) 14 , b ) 28 , c ) 63 , d ) 84 , e ) 100
Rationale: "20 x = 10 y = > x / y = 1 / 2 = > 2 x = y 2 ( 3 ) = 1 ( 3 ) = > x * y = 9 but it is not given 2 ( 10 ) = 1 ( 10 ) = > x * y = 100 e"
Answer: e
Question (general): find the greatest number which on dividing 1661 and 2045 , leaves a reminder of 10 and 13 respectively
Options: a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 150
Rationale: explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 1661 - 10 ) and ( 2045 - 13 ) = hcf ( 1651 , 2032 ) = 127 option b
Answer: b
Question (gain): the price of a t . v . set worth rs . 40000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 22678 , b ) 26699 , c ) 26788 , d ) 19000 , e ) 39000
Rationale: "money paid in cash = rs . 1000 balance payment = ( 40000 - 1000 ) = rs . 39000 answer : e"
Answer: e
Question (gain): 3 candidates in an election and received 2136 , 7636 and 11628 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 45 % , b ) 49 % , c ) 54 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 2136 + 7636 + 11628 ) = 21260 so , required percentage = 11628 / 21260 * 100 = 54 % c"
Answer: c
Question (general): find the number of terms in an arithmetic progression with the first term 2 and the last term being 62 , given that common difference is 2 .
Options: a ) 31 , b ) 40 , c ) 22 , d ) 27 , e ) 25
Rationale: the n th term = a + ( n - 1 ) * d 62 = 2 + ( n - 1 ) * 2 , 62 – 2 = ( n - 1 ) * 2 , n = 60 / 2 + 1 = 31 . answer : a
Answer: a
Question (general): a , b , c , d , and e are positive consecutive integers and a < b < c < d < e . if the sum of a + b is one less than e , and the product of ab is one more than d , then what is the value of c ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: since the integers are consecutive , we can write each as the previous integer + 1 . for example , b = a + 1 , and c = b + 1 . we can also reverse this : a + 1 = b , and b + 1 = c . since ab = d + 1 , we can also write this ab = e . since a + b = e - 1 , then a + b = ab - 1 . find the pair of consecutive integers whose sum is one less than its product . these numbers are 2 and 3 ( sum : 5 ; product : 6 ) . now that we know how the series starts , we can find the value of c . if the first two numbers are 2 and 3 , the third number is 4 ( option b ) .
Answer: b
Question (physics): a train is 360 meter long is running at a speed of 36 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 50 seconds , b ) 29 seconds , c ) 40 seconds , d ) 11 seconds , e ) 12 seconds
Rationale: "speed = 36 km / hr = 36 * ( 5 / 18 ) m / sec = 10 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 1 / 10 ) = 50 seconds answer : a"
Answer: a
Question (general): 15 times a positive integer is more than its square by 56 , then the positive integer is
Options: a ) 13 , b ) 8 , c ) 11 , d ) 12 , e ) 14
Rationale: explanation : let the number be x . then , 15 x = x 2 + 56 = > x 2 - 15 x + 56 = 0 = > ( x - 7 ) ( x - 8 ) = 0 = > x = 7 or 8 answer : option b
Answer: b
Question (gain): a shopkeeper has 280 kg of apples . he sells 35 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 35 x 20 % + 60 x 30 % = 25 this profit will remain same for any total quantity unless the % of products remains the same . hence ' b ' is the answer"
Answer: b
Question (physics): a train running at 1 / 5 of its own speed reached a place in 10 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 8 hrs , b ) 10 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: "new speed = 1 / 5 of usual speed new time = 5 / 1 of usual time 5 / 1 of usual time = 10 hrs usual time = 10 * 1 / 5 = 2 hrs time saved = 10 - 2 = 8 hrs answer is a"
Answer: a
Question (gain): a number exceeds 20 % of itself by 40 . the number is
Options: a ) 50 , b ) 60 , c ) 80 , d ) 320 , e ) none
Rationale: "explanation : let the answer be ' a ' then a − 20 / 100 a = 40 ⇒ 5 a − a = 200 ⇒ a = 50 ⇒ a = 50 correct option : a"
Answer: a