Cheukting/mathqa huggingface dataset:
Question (general): company x provides bottled water to its employees in 5 liter bottles , $ 3 each . at least how many 5 l bottles must company x buy monthly , so that new contract with $ 50 fixed monthly rate and $ 1 for 20 l bottle each paid off ? ( assume that no other costs apply )
Options: a ) 15 , b ) 17 , c ) 19 , d ) 20 , e ) 21
Rationale: let the no . of 5 liter bottles be x , so the no . of 20 l bottles will be x / 4 ( to equate the vol . ) since the total cost will be equal , 3 x = 50 + x / 4 so x = 18.18 or 19 . answer is ( c ) .
Answer: c
Question (general): if a ( a - 7 ) = 8 and b ( b - 7 ) = 8 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 2 , d ) 7 , e ) 48
Rationale: "i . e . if a = - 1 then b = 8 or if a = 8 then b = - 1 but in each case a + b = - 1 + 8 = 7 answer : option d"
Answer: d
Question (gain): by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 30 % ?
Options: a ) s . 429 , b ) s . 480 , c ) s . 429 , d ) s . 488 , e ) s . 419
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 30 % = 30 % of 640 = rs . 192 sp = cp - loss = 640 - 192 = rs . 448 answer : d"
Answer: d
Question (gain): if the cost price of 50 articles is equal to the selling price of 15 articles , then the gain or loss percent is ?
Options: a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 233
Rationale: "percentage of profit = 35 / 15 * 100 = 233 % answer : e"
Answer: e
Question (general): if the function q is defined by the formula q = 5 e / ( 4 x ( z ^ 2 ) ) , by what factor will q be multiplied if e is quadrupled , x is doubled , and z is tripled ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27
Rationale: we just need to find the factor thats all , e - > quadrupled - > 4 e x - > doubled - > 2 x z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 e is in numerator , and x * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b
Answer: b
Question (physics): a man rows his boat 95 km downstream and 60 km upstream , taking 2 hours each time . find the speed of the stream ?
Options: a ) 76 kmph , b ) 6 kmph , c ) 9 kmph , d ) 8 kmph , e ) 4 kmph
Rationale: "speed downstream = d / t = 95 / ( 2 ) = 48 kmph speed upstream = d / t = 60 / ( 2 ) = 30 kmph the speed of the stream = ( 48 - 30 ) / 2 = 9 kmph answer : c"
Answer: c
Question (gain): a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 6 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 88.6 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 6 % of 400 = 24 therefore , total number of rotten fruits = 90 + 24 = 114 therefore number of fruits in good condition = 1000 - 114 = 886 therefore percentage of fruits in good condition = ( 886 / 1000 × 100 ) % = ( 88600 / 1000 ) % = 88.6 % answer : b"
Answer: b
Question (general): if a farmer sells 20 of his chickens , his stock of feed will last for 3 more days than planned , but if he buys 15 more chickens , he will run out of feed 4 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 90 , e ) 100
Rationale: let x = total feed required for the planned period n = number of chicken t = total time of the planned feed x = nt 1 ) x = ( n - 15 ) * ( t + 4 ) 2 ) x = ( n + 20 ) * ( t - 3 ) equating 1 & 2 ( n - 15 ) * ( t + 4 ) = ( n + 20 ) * ( t - 3 ) 7 n = 35 t n = 5 t x = n * n / 5 substituting this value in 1 n * n / 5 = ( n - 15 ) * ( n / 5 + 4 ) 5 n = 300 n = 60 b
Answer: b
Question (general): which number can we add to 987654 to get a number exactly divisible by 456 ?
Options: a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 42
Rationale: "987654 / 456 = 2165 with a remainder of 414 . we need to add 456 - 414 = 42 the answer is e ."
Answer: e
Question (general): if 25 % of a number is subtracted from a second number , the second number reduces to its 4 - sixth . what is the ratio of the first number to the second number ?
Options: a ) 5 : 3 , b ) 4 : 3 , c ) 6 : 3 , d ) 3 : 4 , e ) 5 : 4
Rationale: explanation : let the numbers be p & q q - p / 4 = 4 q / 6 = > q - 4 q / 6 = p / 4 = > 2 q / 6 = p / 4 = > p / q = 4 / 3 answer b
Answer: b
Question (gain): the weight of a glass of jar is 10 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 5 / 9
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 10 g weight of coffee beans = 90 g weight of jar and remaining beans = 60 g weight of remaining beans = 50 g fraction remaining = 50 / 90 = 5 / 9 answer is e ."
Answer: e
Question (physics): the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of rs . 800 per sq . metre .
Options: a ) 16200 , b ) 16350 , c ) 16500 , d ) 16750 , e ) 16250
Rationale: "area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = rs . 800 hence , total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer is c ."
Answer: c
Question (general): the sum of the even numbers between 1 and n is 105 * 106 , where n is an odd number , then n = ?
Options: a ) 187 , b ) 193 , c ) 199 , d ) 205 , e ) 211
Rationale: let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 105 * 106 then a = 105 and n = 211 . the answer is e .
Answer: e
Question (general): in township k each property is taxed at 8 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 24,000 , by how much will the property tax increase ?
Options: a ) $ 32 , b ) $ 50 , c ) $ 320 , d ) $ 400 , e ) $ 500
Rationale: "property tax as a percentage of its assessed value = 8 % increase in assessed value of the property = 24000 - 20000 = 4,000 $ increase in property tax = ( 8 / 100 ) * 4000 = 320 $ answer c"
Answer: c
Question (general): o mow a grass field a team of mowers planned to cover 15 hectares a day . after 4 working days they increased the daily productivity by 33 × 13 % 33 × 13 % , and finished the work 1 day earlier than it was planned . a ) what is the area of the grass field ? b ) how many days did it take to mow the whole field ? c ) how many days were scheduled initially for this job ?
Options: a ) 387 , b ) 39 , c ) 37 , d ) 20 , e ) 28
Rationale: hint : see problem 20 and solve by yourself . answer : a ) 120 hectares ; b ) 7 days ; c ) 8 days . answer : d
Answer: d
Question (geometry): if ( 20 ) ² is subtracted from the square of a number , the answer so obtained is 4321 . what is the number ?
Options: a ) 68
b ) 69
c ) 70
d ) 71
e ) 72
Rationale: x ^ 2 = 4321 + 400 = 4721 4761 = 69 * 69 x = 69 answer : b
Answer: b
Question (general): how many integers between 1 and 10 ^ 17 are such that the sum of their digits is 2 ?
Options: a ) 133 , b ) 143 , c ) 153 , d ) 163 , e ) 173
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 16 and there are 17 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 16 thus , the total number of integers is 1 + 2 + . . . + 16 + 17 = 17 * 18 / 2 = 153 the answer is c ."
Answer: c
Question (physics): excluding stoppages , the speed of a bus is 60 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 10 min , b ) 12 min , c ) 18 min , d ) 20 min , e ) 15 min
Rationale: "due to stoppages , it covers 15 km less . time taken to cover 15 km = ( 15 / 60 x 60 ) min = 15 min answer : e"
Answer: e
Question (general): the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is rs . 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is :
Options: a ) 4050 , b ) 3500 , c ) 4000 , d ) 4500 , e ) 5000
Rationale: let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) subtracting ( ii ) from ( iv ) , we get p = 4000 . p ' s monthly income = rs . 4000 . answer : c
Answer: c
Question (general): if ( 1 / 2 ) ^ 23 ( 1 / 81 ) ^ k = 1 / 18 ^ 23 , then k =
Options: a ) 8 , b ) 12 , c ) 16 , d ) 24 , e ) 46 / 4
Rationale: "i ' m going to focus on denominator only . . ( 2 ^ 23 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 23 ( 2 ^ 23 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 23 ( 2 ^ 23 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 23 ) . ( 3 ^ 2 ) ^ 23 hence 4 k = 46 k = 46 / 4 answer e i hope it ' s quite clear"
Answer: e
Question (physics): the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 90 per day . what was his wage on the 8 th day ?
Options: a ) $ 83 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 111
Rationale: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 90 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 90 * 7 ) = 1350 - ( 609 + 630 ) = 1350 - 1239 = 111 answer e"
Answer: e
Question (gain): a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 80 % ?
Options: a ) 10.8 , b ) 20.8 , c ) 28.8 , d ) 18.8 , e ) 17.8
Rationale: "c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 480 % of re . 1 = rs . 24 / 5 for rs . 24 / 5 , toffees sold = 6 . for re . 1 , toffees sold = 6 x 24 / 5 = 28.8 . answer c"
Answer: c
Question (general): find the average of all the numbers between 11 and 34 which are divisible by 10 ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 15
Rationale: "average = ( 20 + 30 ) 2 = 50 / 2 = 25 answer is c"
Answer: c
Question (general): a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 400 shares of the company ' s stock ?
Options: a ) $ 208 , b ) $ 96 , c ) $ 104 , d ) $ 120 , e ) $ 240
Rationale: "eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 400 - - > $ 208 answer is a"
Answer: a
Question (geometry): the content of several smaller cylinders ( 3 meter diameter and 6 meter height ) were to be emptied into a larger cylinder ( 20 meter diameter and 10 meter height ) , how many smaller cylinders will fill up the larger cylinder ?
Options: a ) 20
b ) 10
c ) 50
d ) 74
e ) 73
Rationale: calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h larger cylinder volume = 3141.59 smaller cylinder volume = 42.41 therefore the number of cylinders b that can be filled to capacity = 3141.59 / 42.41 = 74.1 answer is d 74 smaller cylinders can be filled to capacity .
Answer: d
Question (general): if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 840 , what is the least possible value of n ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: 840 = 2 * 2 * 2 * 3 * 5 * 7 , so n must be at least 7 . the answer is c .
Answer: c
Question (general): among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 10 % of listco ' s sales staff . listco employs 72 level - 1 employees , 30 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ?
Options: a ) 108 , b ) 42 , c ) 56 , d ) 32 , e ) 58
Rationale: "i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 72 and that c and l 1 = 0.10 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.10 x = 30 , therefore the grand total is 300 . now we know that l 2 is 300 - 72 = 228 . we also learn that c and no c are equally represented thus 150 each . therefore no c and no l 2 will be 150 - 42 = 108 . thus a is the correct answer choice"
Answer: a
Question (geometry): a semicircle has a radius of 9 . what is the approximate perimeter of the semicircle ?
Options: a ) 16 , b ) 25 , c ) 33 , d ) 46 , e ) 58
Rationale: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 9 + 2 * 9 which is about 46 . the answer is d ."
Answer: d
Question (physics): a can do piece of work in 15 days and b in 20 days they finished the work with the assistance of c in 5 days and got rs . 45 as their wages find the share for each in wages ?
Options: a ) 11 , 12,13 , b ) 15 , 11,13 , c ) 15 , 11.25 , 18.75 , d ) 11 , 15.25 , 18.75 , e ) none of these
Rationale: explanation : a ’ s 1 day work = 1 / 3 b ’ s 1 day work = 1 / 4 c ’ s 1 day work = 1 - 1 / 4 - 1 / 3 = 5 / 12 a ’ s share = 45 * 1 / 3 = 15 b ’ s share = 45 * 1 / 4 = 11.25 c ’ s share = 45 * 5 / 12 = 18.75 answer : option c
Answer: c
Question (general): if the average ( arithmetic mean ) of a and b is 210 , and the average of b and c is 160 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 210 = = = > a + b = 420 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 420 - 320 = = = > a + b - b - c = 100 = = = > a - c = 100 answer : c"
Answer: c
Question (general): calculate 469158 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4691110842
Rationale: "answer 469158 x 9999 = 469157 x ( 10000 - 1 ) = 4691580000 - 469158 = 4691110842 . option : e"
Answer: e
Question (gain): 33 1 / 3 % of 210 ?
Options: a ) 70 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 210 = 70 a )"
Answer: a
Question (gain): on a certain transatlantic crossing , 20 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 40 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 66.6 %
Rationale: "0.20 p = rt + c 0.4 ( rt ) = no c = > 0.60 ( rt ) had c 0.20 p = 0.60 ( rt ) rt / p = 1 / 3 = 33 % answer - a"
Answer: a
Question (general): a man has some hens and cows . if the number of heads be 48 and the number of feet equals 136 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 26 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 136 heads : x * 1 + y * 1 = 48 implies , 2 x + 4 y = 136 and x + y = 48 solving these two equations , we get x = 28 and y = 20 therefore , hens are 28 . answer : e"
Answer: e
Question (general): hillary and eddy are climbing to the summit of mt . everest from a base camp 5,100 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 1100 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 14.0 , b ) 9.0 , c ) 10.0 , d ) 11.0 , e ) 12.0
Rationale: "solution : h stopped 800 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance between them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . e"
Answer: e
Question (gain): an error 6 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is
Options: a ) 12.04 % , b ) 14.14 % , c ) 12.36 % , d ) 12.26 % , e ) 15.5 %
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 106 x 106 ) cm 2 . ( a 2 - a 1 ) = [ ( 106 ) 2 - ( 100 ) 2 ] = ( 106 + 100 ) x ( 106 - 100 ) = 1236 cm 2 . percentage error = 12.36 % d"
Answer: d
Question (physics): a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 190 m long ?
Options: a ) 40 sec , b ) 42 sec , c ) 44 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 190 = 550 m required time = 550 * 2 / 25 = 44 sec answer : c"
Answer: c
Question (general): in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is :
Options: a ) 86 , b ) 88 , c ) 92 , d ) 94 , e ) 96
Rationale: "divisor = ( 6 * 3 ) + 2 = 20 5 * quotient = 20 quotient = 4 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 4 ) + 6 = 86 . 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 . the present age of this son is
Options: a ) 21 years , b ) 22 years , c ) 20 years , d ) 24 years , e ) 26 years
Rationale: "explanation : let ' s son age is x , then father age is x + 22 . = > 2 ( x + 2 ) = ( x + 22 + 2 ) = > 2 x + 4 = x + 24 = > x = 20 years option c"
Answer: c
Question (physics): a train 55 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 5 sec , c ) 4 sec , d ) 6 sec , e ) 3 sec
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 55 * 3 / 55 ] sec = 3 sec answer : e"
Answer: e
Question (gain): how long will a boy take to run round a square field of side 60 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 72 sec , d ) 25 sec , e ) 39 sec
Rationale: "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 60 * 4 = 240 m time taken = 240 * 3 / 10 = 72 sec answer is c"
Answer: c
Question (general): in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 6 eggs . if the cost of each pound of rice is $ 0.24 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.20 , b ) 0.24 , c ) 20 , d ) 24 , e ) 55
Rationale: "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 24 cents ; a half - liter of kerosene costs as much as 6 eggs - - > 6 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 12 eggs = 12 / 12 * 24 = 24 cents . answer : d ."
Answer: d
Question (physics): murali travelled from city a to city b at a speed of 40 kmph and from city b to city c at 60 kmph . what is the average speed of murali from a to c given that the ratio of distances between a to b and b to c is 1 : 2 ? a . 48 kmph
Options: a ) 33 , b ) 360 / 7 , c ) 28 , d ) 27 / 8 , e ) 16
Rationale: let the distances between city a to b and b to c be x km and 2 x km respectively . total time taken to cover from a to c = ( x ) / 40 + ( 2 x ) / 60 = ( 3 x + 4 x ) / 120 = 7 x / 120 average speed = ( x + 2 x ) / ( 7 x / 120 ) = 360 / 7 kmph . answer : b
Answer: b
Question (general): a ’ s speed is 30 / 17 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 17 , b ) 13 / 30 , c ) 17 / 30 , d ) 11 / 30 , e ) 11 / 13
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 30 meters , b covers 17 meters in that time . so if the race is 30 meters long , when a reaches the finish line , b would be 13 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 13 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 30 meters ) would be the same as the time required by b ( to cover 17 meters ) to reach the finish line . so b should get a head start of 13 / 30 th of the race . answer ( b )"
Answer: b
Question (gain): a cycle is bought for rs . 670 and sold for rs . 780 , find the gain percent ?
Options: a ) 70 % , b ) 20 % , c ) 16 % , d ) 19 % , e ) 80 %
Rationale: "explanation : 670 - - - - 110 100 - - - - ? = > 16 % answer : c"
Answer: c
Question (general): the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 22 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347.6 , b ) 987.6 , c ) 941.6 , d ) 637.6 , e ) 667.6
Rationale: "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 22 = 2 r a = 12 / 5 r and r = 66 a = 158.4 required total cost = 4 * 158.4 + 3 * 66 + 5 * 22 = 633.6 + 198 + 110 = $ 941.60 c"
Answer: c
Question (gain): a shopkeeper sold an article offering a discount of 5 % and earned a profit of 20.65 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 27 % , c ) 30 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 120.65 let marked price be rs . x . then , 95 / 100 x = 120.65 x = 12065 / 95 = rs . 127 now , s . p . = rs . 127 , c . p . = rs . 100 profit % = 27 % . answer : b"
Answer: b
Question (physics): two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 90 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 12 sec , b ) 24 sec , c ) 30 sec , d ) 60 sec , e ) 62 sec
Rationale: "relative speed = 90 + 30 = 120 km / hr . 120 * 5 / 18 = 100 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 100 = 30 sec . answer : c"
Answer: c
Question (general): john was thrice as old as tom 6 years ago . john will be 7 / 5 times as old as tom in 6 years . how old is tom today ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 7 / 5 * ( t + 6 ) 5 j + 30 = 7 t + 42 5 ( 3 t - 12 ) + 30 = 7 t + 42 8 t = 72 t = 9 the answer is b ."
Answer: b
Question (physics): workers at a campaign office have 2000 fliers to send out . if they send out 1 / 10 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ?
Options: a ) 300 , b ) 1350 , c ) 1100 , d ) 1200 , e ) 1900
Rationale: "( 1 / 10 ) * 2000 = 200 remaining = 2000 - 200 = 1800 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 1800 = 450 remaining now = 1800 - 450 = 1350 answer : option b"
Answer: b