regisss/math_qa huggingface dataset:
Problem: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number g of people surveyed by the company ?
Options: a ) 46 , b ) g = 80 , c ) g = 90 , d ) g = 100 , e ) 200
Rationale: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."
Answer: d
Problem: the product x of two prime numbers is between 17 and 55 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 11 but less than 25 , then x =
Options: a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 65
Rationale: "option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 65 = 5 * 13 > > answer answer = e"
Answer: e
Problem: a train traveling at 72 kmph crosses a platform in 33 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 420 meters , d ) 300 meters , e ) can not be determined
Rationale: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 33 = 660 m . so , length of platform = 660 - 360 = 300 m imo , answer d"
Answer: d
Problem: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 84,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.20833 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 384000 x \ therefore required percentage = \ inline \ frac { 800 x } { 384000 } \ times 100 = 0.20833 a"
Answer: a
Problem: the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 800 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 3 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84 , b ) 1.75 , c ) 3.52 , d ) 2.46 , e ) none of these
Rationale: "here ' s how i did it . my notes from reading the problem were : 1 l a = 800 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 3 l , so 5 x = 3 - - - > x = 3 / 5 . each part is 3 / 5 of a liter . so if we have 3 parts a , we have 800 * 3 * ( 3 / 5 ) = 1440 if we have 2 parts b , we have 850 * 2 * ( 3 / 5 ) = 1020 1440 + 1020 = 2460 solving for units gives us 2.46 so the answer is d"
Answer: d
Problem: if 4 xz + yw = 10 and xw + yz = 20 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 12 . , c ) 15 . , d ) 50 . , e ) 18 .
Rationale: "( 2 x + y ) * ( 2 z + w ) = 10 + 2 ( 20 ) = 50 answer : d"
Answer: d
Problem: $ 9,000 is deposited in a savings account that pays 14 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
Options: a ) $ 11304.12 , b ) $ 12304.54 , c ) $ 11604.14 , d ) $ 10304.10 , e ) $ 9304.41
Rationale: this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 14 / 2 = 7 % now , ca = 9000 ( 1 + 7 / 100 ) ^ 2 = $ 10304.10 hence answer is d
Answer: d
Problem: a certain bacteria colony doubles in size every day for 25 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 10 , d ) 15 , e ) 24
Rationale: "if there is one bacteria colony , then it will reach the limit of its habitat in 25 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 24 times . answer : e . similar questions to practice : hope it helps ."
Answer: e
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 10 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 10 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined
Rationale: answer : a .
Answer: a
Problem: if daily wages of a man is 4 times to that of a woman , how many men should work for 25 days to earn rs . 14400 ? given that wages for 40 women for 30 days are rs . 21600 .
Options: a ) 12 , b ) 4 , c ) 6 , d ) 8 , e ) 20
Rationale: explanation : wages of 1 woman for 1 day = 21600 / 40 ã — 30 wages of 1 man for 1 day = 21600 ã — 4 / 40 ã — 30 wages of 1 man for 25 days = 21600 ã — 4 ã — 25 / 40 ã — 30 number of men = 14400 / ( 21600 ã — 4 ã — 25 / 40 ã — 30 ) = 144 / ( 216 ã — 100 / 40 ã — 30 ) = 8 answer : option d
Answer: d
Problem: jerry went to a shop and bought things worth rs . 20 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 14 , b ) 14.7 , c ) 21.3 , d ) 21.5 , e ) 21.7
Rationale: total cost of the items he purchased = rs . 20 given that out of this rs . 20 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 20 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 20 − 0.3 − x ) = 30 ⇒ ( 20 − 0.3 − x ) = 5 ⇒ x = 20 − 0.3 − 5 = 14.7 b )
Answer: b
Problem: 5005 - 5000 ÷ 10.00 = ?
Options: a ) 0.5 , b ) 50 , c ) 5000 , d ) 4505 , e ) none
Rationale: "answer given expression = 5005 - 5000 ÷ 10.00 = 5005 - 500 = 4505 correct option : d"
Answer: d
Problem: machine a takes 50 hours to complete a certain job and starts that job at 6 am . after four hour of working alone , machine a is joined by machine b and together they complete the job at 1 pm . how long would it have taken machine b to complete the job if it had worked alone for the entire job ?
Options: a ) 9 , b ) 88.88 , c ) 4.88 , d ) 2.88 , e ) 3.88
Rationale: "let us assume total job = 100 units a finishes 100 units in 50 hrs ( given ) hence a ( working rate ) = 2 units / hr now given that a works for 4 hr ( so 8 units done ) then a and b finish total work in 7 hours . hence a and b finish 92 units in 3 hours . of these 3 x 2 = 6 units were done by a . hence b did 86 units in 3 hours . hence b ( working rate ) = 86 / 3 units / hr hence b takes 100 x 3 / 86 = 3.88 hours to complete the job . answer e ."
Answer: e
Problem: a random 10 - letter code is to be formed using the letters a , b , c , d , e , f , g , h , i and i ( only the “ i ” will be used twice ) . what is the probability that a code that has the two i ’ s adjacent to one another will be formed ?
Options: a ) 1 / 10 , b ) 1 / 8 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 2
Rationale: total number of combinations possible = 10 ! / 2 ! 10 ! / 2 ! total favorable combinations = 9 ! 9 ! - we have considered the two is as one element . since we have two is , they can interchange their positions , without affecting the code . probability = 9 ! / ( 10 ! / 2 ! ) = 9 ! ∗ 2 ! / 10 ! = 1 / 59 ! / ( 10 ! / 2 ! ) = 9 ! ∗ 2 ! / 10 ! = 1 / 5 ans : c
Answer: c
Problem: at the end of the day , february 14 th , a florist had 90 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 15 of which were white and 10 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
Options: a ) 20 % , b ) 75 % , c ) 50 % , d ) 33.3 % , e ) 80 %
Rationale: r + w + p = 90 s + l = 90 1 / 3 * 90 = 30 short - stemmed white = 15 short - stemmed pink = 10 = > short - stemmed red = 5 10 / p = 5 / r = > r = p / 2 , p = 2 r so total long stemmed = 60 and long stemmed red + long stemmed pink = 60 so long stemmed red / long stemmed = ? total white = 15 ( as no long stemmed white ) = > r + 2 r + 15 = 90 = > 3 r = 75 and r = 25 long stemmed r = 25 - 5 = 20 so long stemmed red / r = 20 / 60 = 33.3 % answer - d
Answer: d
Problem: the average salary / head of allthe workers in a workshop is rs . 1200 , if the average salary / head of 10 technician is rs . 1400 and the average salary / head of the rest is rs . 900 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 17 , c ) 15 , d ) 19 , e ) 21
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 10 technician + sum of salary for other y - 10 workers . 10 x 1400 + 900 ( y - 10 ) = 1200 y ⇒ 14000 + 900 y - 9000 = 1200 y ⇒ 300 y = 5000 ∴ y = 17 so total number of workers = 17 b
Answer: b
Problem: two cubes have their volumes are in the ratio 1 : 27 . find the ratio of their surface area ?
Options: a ) 1 : 2
b ) 2 : 3
c ) 1 : 9
d ) 2 : 7
e ) 3 : 11
Rationale: let their edges be a and b then , a ^ 3 / b ^ 3 = 1 / 27 ( a / b ) ^ 3 = ( 1 / 3 ) ^ 3 a / b = 1 / 3 ratio of their surface areas = 6 a ^ 2 / 6 b ^ 2 = ( a / b ) ^ 2 = 1 / 9 = 1 : 9 answer is c
Answer: c
Problem: if the integer n has exactly 4 positive divisors , including 1 and n , how many positive divisors does n ^ 3 have ?
Options: a ) 16 , b ) 11 , c ) 10 , d ) 20 , e ) 9
Rationale: take the example of 6 . . . it has 4 positive divisors ( 1,2 , 3,4 ) now , take the example of 216 . . . it has 16 divisors . . so a is the ans
Answer: a
Problem: the number 181 can be written as sum of the squares of 2 different positive integers . what is the difference of these 2 different integers ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 4 , e ) 5
Rationale: "sum of the squares of 2 different positive integers = 181 10 ^ 2 + 9 ^ 2 = 181 now , differene of these 2 different integers = 10 - 9 = 1 ans - c"
Answer: c
Problem: if you roll a fair - sided die twice , what is the probability of getting a double ( 5,5 ) ?
Options: a ) 1 / 24 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 18 , e ) 1 / 3 !
Rationale: "total no . in two dice ( 1,1 ) , ( 2,2 ) . . . . . ( 6 , ) total number of events = 6 * 6 total events of getting same pair ( 5,5 ) = 6 probability = 6 / 6 * 6 = 1 / 6 = 1 / 3 ! e"
Answer: e
Problem: a father and his son are waiting at a bus stop in the evening . there is a lamp post behind them . the lamp post , the father and his son stand on the same straight line . the father observes that the shadows of his head and his son ’ s head are incident at the same point on the ground . if the heights of the lamp post , the father and his son are 6 metres , 1.8 metres and 0.9 metres respectively , and the father is standing 2.1 metres away from the post , then how far ( in metres ) is the son standing from his father ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.45 , e ) none of these
Rationale: explanation : l is the lamp post position , f is father and s is son ’ s position . x is the point where the shadow falls . ld = 0.9 = son ’ s height , lb = 1.8 = father ’ s height . so ab = 6 – 1.8 = 4.2 also bc = lf = 2.1 we observe that ∆ abc ~ ∆ ade ( two triangles are similar ) . hence , the corresponding sides are proportional . so , ab / ad = dc / de . 4.2 / 5.1 = 2.1 / de . de = 5.1 * 2.1 / 4.2 = 5.1 / 2 = 2.55 . ls = de = 2.55 fs = ls – lf = 2.55 – 2.1 = 0.45 . answer : d
Answer: d
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 2.25 each . if none of the 40 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 160 , b ) $ 150 , c ) $ 280 , d ) $ 200 , e ) $ 180
Rationale: "if 40 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 80 books amount received for sold books = 80 * 2.25 = $ 180 answer : e"
Answer: e
Problem: a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 5 per sq m ?
Options: a ) 6500 , b ) 2779 , c ) 2779 , d ) 3900 , e ) 2781
Rationale: "area = ( l + b â € “ d ) d ( 80 + 60 â € “ 10 ) 10 = > 1300 m 2 1300 * 5 = rs . 6500 answer : a"
Answer: a
Problem: at their respective rates , pump a , b , and c can fulfill an empty tank , or pump - out the full tank in 2 , 3 , and 6 hours . if a and b are used to pump - out water from the half - full tank , while c is used to fill water into the tank , in how many hours , the tank will be empty ?
Options: a ) 2 / 3 , b ) 1 , c ) 3 / 4 , d ) 3 / 2 , e ) 2
Rationale: rate of a = 1 / 2 tank / hour ; rate of b = 1 / 3 tank / hour ; rate of c = 1 / 6 tank / hour . combined rate when a and b are used to pump - out water , while c is used to fill water into the tank is 1 / 2 + 1 / 3 - 1 / 6 = 2 / 3 tank hour . so , to empty the full tank 3 / 2 hours ( reciprocal of rate ) are needed . to empty the half - full tank half of that time would be needed : 1 / 2 * 3 / 2 = 3 / 4 hours . answer : c .
Answer: c
Problem: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 108 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) none of these
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 108 km time taken = distance / speed = 108 / 27 = 4 hours . answer : option b"
Answer: b
Problem: company c sells a line of 25 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 12000 , b ) 13000 , c ) 14000 , d ) 15000 , e ) 16000
Rationale: "the average price of 25 products is $ 1,200 means that the total price of 25 products is 25 * 1,200 = $ 30,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 400 + 14 * 1,000 = $ 18,000 . therefore , the greatest possible selling price of the most expensive product is $ 30,000 - $ 18,000 = $ 12,000 . answer : a ."
Answer: a
Problem: a man purchased earphone on friday . but he forgot how much it cost . the data he have are mean expenditure of all 7 days is 500 . expenditure on mon , tue , wed , thurs , sat , sun are 450600 , 400500 , 550300 . on friday he purchased 3 things one earphone , one pen and one notebook . pen cost 30 and notebook cost 50 . then what is cost of earphone ?
Options: a ) 620 , b ) 530 , c ) 450 , d ) 470 , e ) 500
Rationale: solution let expenditure on friday be x ( 450 + 600 + 400 + 500 + x + 550 + 300 ) / 7 = 500 2800 + x = 3500 x = 700 pen + notebook + earphone = 700 earphone = 700 - 80 = 620 answer a
Answer: a
Problem: what percent is 6 gm of 1 kg ?
Options: a ) 1.5 % , b ) 0.5 % , c ) 0.6 % , d ) 3.5 % , e ) 4 %
Rationale: "1 kg = 1000 gm 6 / 1000 × 100 = 600 / 1000 = 3 / 5 = 0.6 % c )"
Answer: c
Problem: a train 300 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 6 sec . , b ) 7 sec . , c ) 9 sec . , d ) 18 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 300 m at ( 50 / 3 ) m / sec = ( 300 x 3 / 50 ) sec = 18 sec . answer d"
Answer: d
Problem: how many prime numbers are between 51 / 13 and 89 / 9 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "51 / 13 = 4 - 89 / 9 = 10 - prime numbers between 4 and 10 are 5 and 7 - sign signifies that the number is marginally less . answer c"
Answer: c
Problem: company c sells a line of 25 products with an average retail price of $ 1,400 . if none of these products sells for less than $ 420 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 16000 , b ) 11400 , c ) 13200 , d ) 15400 , e ) 16800
Rationale: "the average price of 25 products is $ 1,400 means that the total price of 25 products is 25 * 1,200 = $ 35,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 420 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 420 + 14 * 1,000 = $ 18,200 . therefore , the greatest possible selling price of the most expensive product is $ 35,000 - $ 18,200 = $ 16,800 . answer : e"
Answer: e
Problem: a soccer team played 130 games and won 60 percent of them . how many games did it win ?
Options: a ) 84 , b ) 94 , c ) 100 , d ) 125 , e ) 78
Rationale: "60 % of 130 = x 0.60 * 130 = x 78 = x answer : e"
Answer: e
Problem: what least no . must be subtracted from 5026 so that remaining no . is divisible by 5 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 1
Rationale: explanation : on dividing 5026 by 5 we get the remainder 1 , so 1 should be subtracted option e
Answer: e
Problem: a gambler has won 40 % of his 40 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 70 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "let x be the number of additional games the gambler needs to play . 0.4 ( 40 ) + 0.7 x = 0.6 ( x + 40 ) 0.1 x = 8 x = 80 the answer is d ."
Answer: d
Problem: 50 % of a number is added to 200 , the result is the same number . find the number ?
Options: a ) 300 , b ) 288 , c ) 400 , d ) 129 , e ) 281
Rationale: "( 50 / 100 ) * x + 200 = x x / 2 + 200 = x x + 400 = 2 x x = 400 answer : c"
Answer: c
Problem: there is a square with side ‘ a ’ and one octagon is inscribed in it . what will be perimeter of octagon .
Options: a ) 8 a / 3
b ) 7 a / 3
c ) 5 a / 3
d ) a / 3
e ) 11 a / 3
Rationale: well if it ' s a regular octagon then it actually trisects each side of the square in which 1 / 3 of the lenght of the side of the square is the length of one side of the octagon . if any one has a doubt he can draw the figure and see it going this way lenght of a side of a octagon is a / 3 and thus perimeter would be 8 a / 3 . answer : a
Answer: a
Problem: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction x of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
Options: a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14
Rationale: "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus x = 11 / 14 of the remaining votes must be against . answer : a ."
Answer: a
Problem: the speed of the boat in still water in 12 kmph . it can travel downstream through 54 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 8 hours , b ) 6 hours , c ) 4 hours , d ) 5 hours , e ) 9 hours
Rationale: "still water = 12 km / hr downstream = 54 / 3 = 18 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 18 / 2 = 6 km / hr so time taken in upstream = 545 / 6 = 9 hrs answer : e"
Answer: e
Problem: if shares of two persons in profits are rs . 400 and rs . 600 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "profit = time * capital so 400 : 600 = 2 : 3 answer : b"
Answer: b
Problem: each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , thirty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 40 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: "let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.3 i + 0.8 f = 0.4 ( i + f ) 0.4 f = 0.1 i f = 0.25 i this means that for every 4 incandescent bulbs , there is 1 fluorescent bulb . the percent of bulbs that are switched on which are incandescent is : 0.3 i / ( 0.3 i + 0.8 f ) = 0.3 i / ( 0.3 i + 0.8 * 0.25 i ) = 0.3 i / 0.5 i = 3 / 5 = 60 % . the answer is d ."
Answer: d
Problem: a train 300 m long is running at a speed of 99 km / hr . in what time will it pass a bridge 195 m long ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "speed = 99 * 5 / 18 = 55 / 2 m / sec total distance covered = 300 + 195 = 495 m required time = 495 * 2 / 55 = 18 sec answer : b"
Answer: b
Problem: f ( x ) is a function such that f ( 2 x + 1 ) = 2 f ( x ) + 1 for all real numbers x and f ( 0 ) = 2 . find the value of f ( 3 ) .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: f ( 2 x + 1 ) = 2 f ( x ) + 1 : given f ( 3 ) = 2 f ( 1 ) + 1 : x = 1 in a f ( 1 ) = 2 f ( 0 ) + 1 : x = 0 in a f ( 3 ) = 11 : substitute correct answer b
Answer: b
Problem: evaluate 28 % of 450 + 45 % of 260
Options: a ) 232 , b ) 243 , c ) 252 , d ) 262 , e ) 282
Rationale: "explanation : = ( 28 / 100 ) * 450 + ( 45 / 100 ) * 260 = 126 + 117 = 243 answer : option b"
Answer: b
Problem: what is the units digit of ( 44 ^ 4 ) ( 33 ^ 5 ) ( 21 ^ 6 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "the units digit of 44 ^ 4 is the units digit of 4 ^ 4 which is 6 . the units digit of 33 ^ 5 is the units digit of 3 ^ 5 which is 3 . the units digit of 21 ^ 6 is the units digit of 1 ^ 6 which is 1 . the units digit of 6 * 3 * 1 is 8 . the answer is e ."
Answer: e
Problem: the largest 4 digit number exactly divisible by 55 is ?
Options: a ) 9935 , b ) 9939 , c ) 9944 , d ) 9955 , e ) 9960
Rationale: "largest 4 - digit number = 9999 55 ) 9999 ( 181 9955 answer : d"
Answer: d
Problem: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 2662 in 3 years . find the rate percent ?
Options: a ) 23 % , b ) 10 % , c ) 32 % , d ) 98 % , e ) 31 %
Rationale: "2420 - - - 242 100 - - - ? = > 10 % answer : b"
Answer: b
Problem: a car started running at a speed of 36 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 45 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: "a 45 km the total distance covered by the car in the first 10 hours = 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 + 54 = sum of 10 terms in ap whose first term is 36 and last term is 54 = 10 / 2 [ 36 + 54 ] = 450 km ."
Answer: a
Problem: the average age of a class of 20 students is 18 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 years , b ) 41 years , c ) 42 years , d ) 43 years , e ) 44 years
Rationale: "if age of the teacher was 18 , average would not have changed . since average increased by 2 , age of the teacher = 18 + 22 × 1 = 40 answer : a"
Answer: a
Problem: the profits of qrs company rose 30 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 56 % , d ) 62 % , e ) 80 %
Rationale: "assume 100 in march , then 130 in april as 30 % increase , then 104 in may as 20 % decrease from april , and then 156 in june which is 150 % of 104 . so overall increase is from 100 to 156 is 56 % answer c"
Answer: c
Problem: if the radius of a circle is increased by 20 % then the area is increased by :
Options: a ) 44 % , b ) 120 % , c ) 144 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 120 / 100 r then area = pi * ( 120 r / 100 ) 2 area = 144 r / 100 that is area increases from 100 to 144 = increase in area = 44 % answer : a"
Answer: a
Problem: one half of a two digit number exceeds its one third by 7 . what is the sum of the digits of the number ?
Options: a ) a ) 3 , b ) b ) 5 , c ) c ) 7 , d ) d ) 9 , e ) e ) 10
Rationale: "x / 2 – x / 3 = 7 = > x = 46 4 + 6 = 10 answer : e"
Answer: e
Problem: the sum of two consecutive numbers is 37 . what are they ?
Options: a ) 18 and 19 , b ) 18 and 21 , c ) 18 and 23 , d ) 19 and 20 , e ) none
Rationale: "two consecutive numbers are like 8 and 9 , or 51 and 52 . let x , then , be the first number . then the number after it is x + 1 . the problem states that their sum is 37 : word problem = 37 2 x = 37 − 1 = 36 . x = 36 2 = 18 . the two numbers are 18 and 19 . option is a"
Answer: a
Problem: a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
Options: a ) 45 , b ) 40 , c ) 39 , d ) 37 , e ) 38
Rationale: "explanation : let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 . answer : b"
Answer: b
Problem: if 40 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 10 % , c ) 5 % , d ) 14 % , e ) 25 %
Rationale: 40 % of ( x - y ) = 30 % of ( x + y ) ( 40 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 4 ( x - y ) = 3 ( x + y ) x = 7 y x = 7 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 7 y ) x 100 ) = 14 % answer is d .
Answer: d
Problem: one fast typist type some matter in 4 hrs and another slow typist type the same matter in 6 hrs . if both do combine in how much time they will take to finish .
Options: a ) 10 hr , b ) 1 hr , c ) 2 hr 24 mins , d ) 3 hr 4 mins , e ) 4 hr 10 mins
Rationale: "fast ' s 1 hr work = 1 / 4 slow ' s 1 hr work = 1 / 6 1 / 4 + 1 / 6 = 5 / 12 they ll finish in 12 / 5 hrs = 2 2 / 5 = = > 2 hr 24 mins answer : c"
Answer: c
Problem: there are 20 players on a rugby team . if the average weight of the players is 180 pounds , what will be the new average height if a 210 pound player will join the team ?
Options: a ) 185 , b ) 183.22 , c ) 184.96 , d ) 181.43 , e ) 182.78
Rationale: ( sum of the 20 weights ) / 20 = 180 sum of the 20 weights = 3600 new sum = 3600 + 210 = 3810 new average = 3810 / 21 = 181.43 ans : d
Answer: d
Problem: if in a 20 over cricket match , there were no wide balls , no wides , no extras and no overthrows . what is the maximum number of runs that a batsman can score in an ideal case scenario ?
Options: a ) 663 , b ) 720 , c ) 625 , d ) 640 , e ) none
Rationale: solution : 663 explanation : for an ideal case , the batsman will hit a six on each ball . but if he hits six on the last ball of the over , the strike will change in the next over . thus , the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over . thus the total runs that he can score in each over : 6 * 5 + 3 = 33 but this will have to go like it only till the 19 th over . in the last over , he can hit a six in the last ball as well as that will be the last ball of the match . thus runs for the last over will be 6 * 6 = 36 . hence the maximum runs = 33 * 19 + 36 = 663 answer a
Answer: a
Problem: what annual payment will discharge a debt of rs . 1025 due in 2 years at the rate of 5 % compound interest ?
Options: a ) rs . 550 , b ) rs . 551.25 , c ) rs . 560 , d ) rs . 560.75 , e ) rs . 660.75
Rationale: "let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1025 820 x + 1025 * 441 x = 551.25 so , value of each installment = rs . 551.25 answer : b"
Answer: b
Problem: after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 5130 . what was the number of original inhabitants ?
Options: a ) 7300 , b ) 7600 , c ) 7900 , d ) 8200 , e ) 8500
Rationale: "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5130 ( 27 / 40 ) * x = 5130 x = 5130 * 40 / 27 = 7600 the answer is b ."
Answer: b
Problem: 40 is subtracted from 70 % of a number , the result is 30 . find the number ?
Options: a ) 150 , b ) 997 , c ) 266 , d ) 288 , e ) 100
Rationale: "( 70 / 100 ) * x – 40 = 30 7 x = 700 x = 100 answer : e"
Answer: e
Problem: find the greatest number that will divide 28 , 128 and 147 leaving 10 , 2 and 3 as remainders respectively
Options: a ) 19 , b ) 17 , c ) 13 , d ) 9 , e ) 18
Rationale: "explanation : answer will be hcf of ( 28 - 10 , 128 - 2 , 147 - 3 ) hcf of ( 18 , 126 , 144 ) = 18 option e"
Answer: e
Problem: if a train , travelling at a speed of 120 kmph , crosses a pole in 6 sec , then the length of train is ?
Options: a ) 281 , b ) 125 , c ) 200 , d ) 266 , e ) 121
Rationale: "d = 120 * 5 / 18 * 6 = 200 m answer : c"
Answer: c
Problem: sakshi can do a piece of work in 5 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 4 , b ) 16 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 5 : x ⇒ x = ( 5 x 4 / 5 ) ⇒ x = 4 days . hence , tanya takes 16 days is complete the work . answer a"
Answer: a
Problem: two pipes a and b can separately fill a cistern in 60 minutes and 80 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 100 min , c ) 240 min , d ) 120 min , e ) 130 min
Rationale: 1 / 40 - ( 1 / 60 + 1 / 80 ) = - 1 / 240 third pipe can empty in 240 minutes answer : c
Answer: c
Problem: 13 buckets of water fill a tank when the capacity of each bucket is 51 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 17 litres ?
Options: a ) 39 , b ) 28 , c ) 23 , d ) 12 , e ) 24
Rationale: "capacity of the tank = ( 13 × 51 ) litre number of buckets required of capacity of each bucket is 17 litre = 13 × 51 / 17 = 13 × 3 = 39 answer is a"
Answer: a
Problem: a candidate appearing for an examination has to secure 55 % marks to pass paper i . but he secured only 45 marks and failed by 25 marks . what is the maximum mark for paper i ?
Options: a ) 127 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: he secured 45 marks nd fail by 25 marks so total marks for pass the examinatn = 70 let toal marks x x * 55 / 100 = 70 x = 127 answer : a
Answer: a
Problem: by selling 15 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 4 , e ) 10
Rationale: "80 % - - - 15 120 % - - - ? 80 / 120 * 15 = 10 answer : e"
Answer: e
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 10 cm ?
Options: a ) 827 cm 2 , b ) 216 cm 2 , c ) 285 cm 2 , d ) 178 cm 2 , e ) 190 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 10 ) = 190 cm 2 answer : e"
Answer: e
Problem: a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money n did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: "notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ n = 20 answer : b"
Answer: b
Problem: two trains leave a station traveling the same direction . train a leaves the station traveling at a constant speed of 60 mph , and train b leaves the station traveling at a constant speed of 80 mph . if both trains maintain constant speeds , in how many minutes will train b overtake train a if train a left 40 minutes prior to train b ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: we can use d = rt [ distance = rate * time ] train a will have traveled for 40 minutes longer than train b when b overtakes a , so time of train a : t + 40 minutes = t + ( 2 / 3 ) hours ( use hours since the rate is in hours ) time of train b : t rate of train a : 60 mph rate of train b : 80 mph the distances traveled by each will be equal when train b overtakes train a , so we can set the right sides of d = rt equal for the two trains ( rate of train a ) * ( time of train a ) = ( rate of train b ) * ( time of train b ) 60 * ( t + 2 / 3 ) = 80 * t 60 t + 40 = 80 t 40 = 20 t 2 = t 2 hours = 120 minutes d
Answer: d
Problem: if the average of 5 positive integers is 50 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 58 , c ) 49 , d ) 48 , e ) 44
Rationale: sum of 5 integer ( a , b , c , d , e ) = 5 * 50 = 250 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 250 i . e . 5 a = 240 i . e . a = 48 i . e . largest e = 48 + 10 = 58 answer : option b
Answer: b
Problem: what is the smallest number which , when increased by 7 , is divisible by 8 , 11 , and 24 ?
Options: a ) 264 , b ) 257 , c ) 269 , d ) 270 , e ) 282
Rationale: "lcm ( 8 , 11,24 ) = 24 x 11 = 264 so the least divisible number is 264 , and the number we are looking for is 264 - 7 = 257 . the answer is b ."
Answer: b
Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 210 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 356 , c ) 452 , d ) 416 , e ) 546
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 210 x = 42 total number of students = 13 x = 13 * 42 = 546 answer is e"
Answer: e
Problem: the grade point average of one third of the classroom is 15 ; the grade point average of the rest is 18 . what is the grade point average of the whole class ?
Options: a ) 17 , b ) 19 , c ) 21 , d ) 23 , e ) 25
Rationale: "let n = total students in class total points for 1 / 3 class = 15 n / 3 = 5 n total points for 2 / 3 class = 18 * 2 n / 3 = 12 n total points for whole class = 5 n + 12 n = 17 n 17 n total class points / n total students = 17 grade point average for total class answer : a"
Answer: a
Problem: arjun started a business with rs . 10,000 and is joined afterwards by anoop with rs . 40 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "suppose anoop joined after 3 months . then , 10000 * 12 = 40000 * ( 12 – x ) = > x = 9 . answer : e"
Answer: e
Problem: if the operation @ is defined for all a and b by the equation a @ b = ( a - b ) / 5 , then ( 3 @ - 2 ) @ 6 = ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) - 2 , e ) - 1
Rationale: work within the parenthesis first so solve ( 3 @ - 2 ) first ( 3 @ - 2 ) = ( 3 - ( - 2 ) ) / 5 = ( 3 + 2 ) / 5 = 1 now take 1 plug back into equation and solve the rest ( 1 @ 6 ) = ( 1 - 6 ) / 5 = - 5 / 5 = - 1 so - 1 is the answer . . . . this question is merely testing order of operations remember pemdas answer is option : e
Answer: e
Problem: what is the ratio of 5 / 7 to the product 3 * ( 7 / 3 ) ?
Options: a ) 3 : 7 , b ) 1 : 3 , c ) 5 : 49 , d ) 1 : 7 , e ) 3 : 49
Rationale: "3 / 7 / 21 / 3 = 5 / 49 . . . imo option c ."
Answer: c
Problem: a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 15 sec . what is the length of the goods train ?
Options: a ) 299 , b ) 277 , c ) 276 , d ) 270 , e ) 50
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 15 sec . let the length of the train be x meters . then , ( x + 250 ) / 15 = 20 x = 50 m . answer : e"
Answer: e
Problem: a goods train runs at the speed of 72 km / hr and crosses a 290 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 278 , b ) 166 , c ) 151 , d ) 230 , e ) 109
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 290 ) / 26 = 20 x = 230 m . answer : d"
Answer: d
Problem: the contents of a certain box consist of 24 oranges and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be oranges ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 46 , e ) 50
Rationale: oranges = ( oranges + kiwi + x ) * 0.3 24 = ( 30 + 24 + x ) * 0.3 x = 26 . answer : b .
Answer: b
Problem: if s is the sum of reciprocals of a list of consecutive integers from 55 to 64 , inclusive , s is approximately equal to
Options: a ) 0.16 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) 0.5
Rationale: we need to find the approximate value of 1 / 55 + 1 / 56 + 1 / 57 + 1 / 58 + 1 / 59 + 1 / 60 + 1 / 61 + 1 / 62 + 1 / 63 + 1 / 64 . now , the sum of these 10 terms will be very close to 10 times 1 / 60 , which is 0.016 * 10 = 0.16 . answer : a .
Answer: a
Problem: the sector of a circle has radius of 28 cm and central angle 135 o . find its perimeter ?
Options: a ) 122 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 28 ) + 2 ( 28 ) = 66 + 56 = 122 cm answer : a"
Answer: a
Problem: a swimmer swims downstream 55 km and upstream 10 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 4.6 , b ) 4.5 , c ) 4.4 , d ) 4.3 , e ) 4.2
Rationale: 55 - - - 5 ds = 11 ? - - - - 1 10 - - - - 5 us = 2 ? - - - - 1 s = ? s = ( 11 - 2 ) / 2 = 4.5 answer : b
Answer: b
Problem: what is the sum of the greatest common factor and the lowest common multiple of 16 and 72 ?
Options: a ) 142 , b ) 152 , c ) 124 , d ) 160 , e ) 184
Rationale: "prime factorization of 16 = 2 x 2 x 2 x 2 . prime factorization of 72 = 2 x 2 x 2 x 3 x 3 gcf = 8 lcm = 144 sum = 152 . answer b ."
Answer: b
Problem: a is half good a work man as b and together they finish a job in 13 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 39 / 2 , d ) 36 , e ) 48
Rationale: c 39 / 2 wc = 1 : 2 2 x + x = 1 / 13 = > x = 1 / 39 2 x = 2 / 39 = > 39 / 2 days
Answer: c
Problem: 33 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 18 , e ) 19
Rationale: let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 33 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 33 x 5 x 12 x = ( 33 x 5 x 12 ) / ( 30 x 6 ) x = 11 answer b
Answer: b
Problem: the diagonal of a rectangle is √ 41 cm and its area is 20 sq . cm . the perimeter of the rectangle must be :
Options: a ) 18
b ) 28
c ) 38
d ) 48
e ) 58
Rationale: explanation : l 2 + b 2 = 41 also , lb = 20 ( l + b ) 2 = l 2 + b 2 + 2 lb = 41 + 40 = 81 ( l + b ) = 9 perimeter = 2 ( l + b ) = 18 cm . answer : a
Answer: a
Problem: the pilot of a small aircraft with a 60 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 10 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 5 , b ) 12 , c ) 2 , d ) 4 , e ) 6
Rationale: "actual miles / gallon is = 480 / 60 = 8 miles / gallon . current engine miles / gallon is 10 miles / gallon . additional 2 miles / gallon is required to match the actual mileage . answer : c"
Answer: c
Problem: there is a square with sides of 12 . what is the circumference of the biggest circle that can be cut out of this square ?
Options: a ) 75.4
b ) 31.42
c ) 36
d ) 18.85
e ) 37.7
Rationale: circumference of a circle = c = 2 ï € r square is 12 wide , so circle ' s diameter would be 12 , and radius would be 6 c = 2 ï € 6 which is approximately 37.7 answer is e
Answer: e
Problem: convert 0.36 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 17 / 50 , d ) 9 / 25 , e ) none
Rationale: "answer 0.36 = 36 / 100 = 9 / 25 correct option : d"
Answer: d
Problem: a box contain the number of balls which is as much greater than 44 is less than 70 . the number of balls is ?
Options: a ) 47 , b ) 114 , c ) 74 , d ) 67 , e ) 57
Rationale: answer let the number be x . then , x - 44 = 70 - x â ‡ ’ 2 x = 70 + 44 = 114 â ‡ ’ 2 x = 114 â ˆ ´ x = 57 correct option : e
Answer: e
Problem: robert ' s salary was decreased by 20 % and subsequently increased by 20 % . how much percentage does he lose ?
Options: a ) 4 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: "let original salary be $ 100 salary after decreasing 20 % = 100 - 100 x 20 / 100 = $ 80 salary after increasing 20 % on $ 80 = 80 + 80 x 20 / 100 = $ 96 percentage of loss = 100 - 96 = 4 % answer : a"
Answer: a
Problem: the average of temperatures at noontime from monday to friday is 55 ; the lowest one is 45 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "there are 5 days so the sum of temperature can be 55 * 5 = 275 lowest is 45 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 45 = 180 . on the fifth day it is 275 - 180 = 95 range is therefore 95 - 45 = 40 answer c"
Answer: c
Problem: 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 6 .
Options: a ) 150 , b ) 152 , c ) 154 , d ) 159 , e ) 144
Rationale: "d = d * q + r d = 17 * 9 + 6 d = 153 + 6 d = 159 answer d"
Answer: d
Problem: what is the probability that the sum of two dice will yield a 5 , and then when both are thrown again , their sum will again yield a 5 ? assume that each die has 4 sides with faces numbered 1 to 4 .
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 3
Rationale: "solution - rolling dices is an independent event . the combinations to get 5 are ( 1,4 ) , ( 4,1 ) , ( 2,3 ) , ( 3,2 ) , and total combinations of both dices is 16 . the probability of getting 5 in first attempt is 4 / 16 = 1 / 4 . probability of getting 5 again in second attempt = ( 1 / 4 ) * ( 1 / 4 ) = 1 / 16 . ans d"
Answer: d
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2400 ?
Options: a ) s . 800 , b ) s . 810 , c ) s . 820 , d ) s . 900 , e ) s . 920
Rationale: "2400 * 1 / 3 = 800 option a"
Answer: a
Problem: yesterday ' s closing prices of 2,420 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 484 , b ) 726 , c ) 1,100 , d ) 1,320 , e ) 1,694
Rationale: "lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 2420 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) & ( 2 ) to get h = 1320 . d is answer ."
Answer: d
Problem: a shopkeeper sells 200 metres of cloth for rs . 12000 at a loss of rs . 12 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 59 , b ) s . 72 , c ) s . 62 , d ) s . 50 , e ) s . 13
Rationale: "sp per metre = 12000 / 200 = rs . 60 loss per metre = rs . 12 cp per metre = 60 + 12 = rs . 72 answer : b"
Answer: b
Problem: before 7 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 54 , d ) 60 , e ) 70
Rationale: "a - 7 = 4 ( b - 7 ) - - > a - 4 b = - 21 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 29 - - > a = 3 ( 22 ) = 99 a - b = 99 - 29 = 70 answer : e"
Answer: e
Problem: a pipe can empty 2 / 3 rd of a cistern in 12 mins . in 6 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 3 / 7 , c ) 4 / 9 , d ) 3 / 8 , e ) 1 / 3
Rationale: "2 / 3 - - - - 12 ? - - - - - 6 = = > 1 / 3 e"
Answer: e
Problem: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6400 ?
Options: a ) rs . 5870 , b ) rs . 8270 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6400 * 6 ) – 30,130 ] = rs . ( 38400 – 30,130 ) = rs . 8270 answer b"
Answer: b
Problem: 1401 x 1401 = ?
Options: a ) 1962800 , b ) 1962801 , c ) 1960000 , d ) 1951611 , e ) 1951613
Rationale: "1401 x 1401 = ( 1401 ) 2 = ( 1400 + 1 ) 2 = ( 1400 ) 2 + ( 1 ) 2 + ( 2 x 1400 x 1 ) = 1960000 + 1 + 2800 = 1960001 + 2800 = 1962801 . b )"
Answer: b
Problem: the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 9 and 39 inclusive .
Options: a ) 351 , b ) 384 , c ) 410 , d ) 424 , e ) 450
Rationale: "we ' re dealing with a sequence of consecutive odd integers : 9 to 39 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 9 + 39 = 48 2 ) now look at the ' next smallest ' and the ' next biggest ' : 11 + 37 = 48 now we have proof that there is no middle term . we have 8 bunches of 48 8 ( 48 ) = 384 b"
Answer: b