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if 20 men can build a wall 66 metres long in 12 days , what length of a similar can be built by 86 men in 8 days ?
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if 20 men can build a wall 66 metres long in 12 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 12 * 20 ) = 189.2 mtrs
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carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 4 inches tall . how tall are the sculpture andbase together ?
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we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 4 = 38 38 / 12 = 3.17 feet
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the average of 6 no . ' s is 2.5 . the average of 2 of them is 1.1 , while the average of the other 2 is 1.4 . what is the average of the remaining 2 no ' s ?
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sum of the remaining two numbers = ( 2.5 * 6 ) - [ ( 1.1 * 2 ) + ( 1.4 * 2 ) ] = 15 - ( 2.2 + 2.8 ) = 15 - 5 = 10 required average = ( 10 / 2 ) = 5
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the sum of the first 92 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ?
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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 = 92 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 92 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 92 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 9200 + 2500 = 11700 d is the answer .
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a is an integer greater than 9 but less than 21 , b is an integer greater than 19 but less than 31 , what is the range of a / b ?
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min value of a / b will be when b is highest and a is lowest - - - > a = 10 and b = 30 so , a / b = 1 / 3 max value of a / b will be when b is lowest and a is highest - - - > a = 20 and b = 20 so , a / b = 1 range is 1 - ( 1 / 3 ) = 2 / 3 . answer should be c
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if 18 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
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let x be the number of students in the school . 0.18 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.18 x / 0.25 = 0.72 x students went to the camping which is 72 % . the answer is e
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a couple decides to have 2 children . if they succeed in having 2 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 1 girl and 1 boy ?
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sample space = 2 ^ 2 = 4 . favourable events = { bg } , { gb } , probability = 2 / 4 = 1 / 2 . ans ( a ) .
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a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 5 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
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by the question , the equation would be 150 p - 85 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 195 . answer e for me .
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a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 60 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
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i did n ' t understand how did we get 100 ? total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 60 books , thus 76 - 60 = 16 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 50 .
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a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by c are ?
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a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 15 / 25 * 100 = 60
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the average age of an adult class is 50 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 years . find what was the original average age of the class ?
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let original strength = y then , 50 y + 12 x 32 = ( y + 12 ) x 46 Γ’ β‘ β 50 y + 384 = 46 y + 552 Γ’ β‘ β 4 y = 168 Γ’ Λ Β΄ y = 42 c
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anne and katherine are both saving money from their summer jobs to buy bicycles . if anne had $ 150 less , she would have exactly 1 / 3 as much as katherine . and if katherine had twice as much , she would have exactly 3 times as much as anne . how much money have they saved together ? (
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if anne had $ 150 less , katherine would have three times more than anne . make this statement into an equation and simplify : 3 ( a β 150 ) = k 3 a β 450 = k and if katherine had twice as much , she would have three times more than anne : 2 k = 3 a substitute 3 a β 450 for k into the last equation and solve for a 2 ( 3 a β 450 ) = 3 a 6 a β 900 = 3 a β 900 = β 3 a 300 = a now substitute 300 for a into the same equation and solve for k : 2 k = 3 ( 300 ) 2 k = 900 k = 450 thus , together anne and katherine have 300 + 450 = 750 correct answer e ) $ 750
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a train crosses a platform of 120 m in 15 sec , same train crosses another platform of length 180 m in 18 sec . then find the length of the train ?
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length of the train be β x β x + 120 / 15 = x + 180 / 18 6 x + 720 = 5 x + 900 x = 180 m
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a β s speed is 32 / 27 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 ?
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we have the ratio of a β s speed and b β 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 32 meters , b covers 27 meters in that time . so if the race is 32 meters long , when a reaches the finish line , b would be 5 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 5 meters so that he doesn β t need to cover that . in that case , the time required by a ( to cover 32 meters ) would be the same as the time required by b ( to cover 27 meters ) to reach the finish line . so b should get a head start of 5 / 32 th of the race . answer ( a )
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how many cubes of 4 cm edge can be put in a cubical box of 1 m edge .
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number of cubes = 100 Γ’ Λ β 100 Γ’ Λ β 100 / 4 * 4 * 4 = 15625 note : 1 m = 100 cm
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how many integers between 324,700 and 375,600 have tens digit 1 and units digit 3 ?
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the integers are : 324,713 324,813 etc . . . 375,513 the number of integers is 3756 - 3247 = 509 the answer is a .
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find the area of trapezium whose parallel sides are 12 cm and 16 cm long , and the distance between them is 14 cm ?
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area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 12 + 16 ) * ( 14 ) = 196 cm 2
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if the space diagonal of cube c is 5 inches long , what is the length , in inches , of the diagonal of the base of cube c ?
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n cube c , let ' s say that each side has side length x so , the diagonal = β ( x Β² + x Β² + x Β² ) = β ( 3 x Β² ) here , we ' re told that the diagonal has length 5 , so we can write : 5 = β ( 3 x Β² ) square both sides to get : 25 = 3 x Β² divide both sides by 3 to get : 25 / 3 = x Β² square root both sides : β ( 25 / 3 ) = x or . . . . ( β 25 ) / ( β 3 ) = x simplify : 5 / ( β 3 ) = x
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a train running at the speed of 58 km / hr crosses a pole in 9 sec . what is the length of the train ?
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speed = 58 * 5 / 18 = 145 / 9 m / sec length of the train = speed * time = 145 / 9 * 9 = 145 m
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if x and y are both odd prime numbers and x < y , how many distinct positive integer w factors does 2 xy have ?
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since 2 xy prime w factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
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if it takes 4 identical printing presses exactly 6 hours to print 8000 newspapers , how long would it take 2 of these presses to print 6000 newspapers ?
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4 presses - 8,000 newspapers - 6 hours ; 2 presses - 4,000 newspapers - 6 hours ; ( 360 mins ) 2 presses - 6,000 newspapers - 360 / 4000 * 6000 = 540 mins = 9 hrs
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if ( t - 8 ) is a factor of t ^ 2 - kt - 43 , then k =
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t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 3 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ) ( t + m ) d
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a batsman in his 12 th innings makes a score of 55 and thereby increases his average by 1 runs . what is his average after the 12 th innings if he had never been β not out β ?
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let β x β be the average score after 12 th innings β 12 x = 11 Γ ( x β 1 ) + 55 β΄ x = 44 answer c
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find large number from below question the difference of two numbers is 2415 . on dividing the larger number by the smaller , we get 21 as quotient and the 15 as remainder
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let the smaller number be x . then larger number = ( x + 2415 ) . x + 2415 = 21 x + 15 20 x = 2400 x = 120 large number = 120 + 2415 = 2535
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in an examination , a student scores 3 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 30 questions and secures 130 marks , the no of questions he attempts correctly is :
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let the number of correct answers be x . number of incorrect answers = ( 60 β x ) . 3 x β ( 30 β x ) = 130 = > 4 x = 160 = > x = 40
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a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 2.3 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
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72 km / hr = 1.2 km / min the total distance is 2.4 km . 2.4 / 1.2 = 2 minutes the answer is a .
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a garrison of 2000 men has provisions for 40 days . at the end of 20 days , a reinforcement arrives , and it is now found that the provisions will last only for 10 days more . what is the reinforcement ?
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2000 - - - - 40 2000 - - - - 20 x - - - - - 10 x * 10 = 2000 * 20 x = 4000 2000 - - - - - - - 2000
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five bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 seconds respectively . in 20 minutes , how many times do they toll together ?
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l . c . m of 2 , 4,6 , 8,10 is 240 . i . e after each 2 min they will toll together . so in 20 min they will toll 10 times . as they have initially tolled once , the answer will be 10 + 1 = 11 .
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we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 600 . how many green hats did we buy ?
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let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 600 . 6 ( 85 - g ) + 7 g = 600 . 510 - 6 g + 7 g = 600 . g = 600 - 510 = 90 . the answer is b .
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if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 750 responses are needed , what is the minimum number of questionnaires that should be mailed ?
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let x be the minimum number of questionnaires to be mailed . 0.6 x = 750 x = 1250 the answer is d .
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if the price of 357 apples is rs . 1517.25 , what will be the approximate price of 49 dozens of such apples
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let the required price be x more apples , more price ( direct proportion ) hence we can write as apples 357 : ( 49 Γ 12 ) } : : 1517.25 : x β 357 x = ( 49 Γ 12 ) Γ 1517.25 β x = ( 49 Γ 12 Γ 1517.25 ) / 357 = ( 7 Γ 12 Γ 1517.25 ) / 51 = ( 7 Γ 4 Γ 1517.25 ) / 17 = 7 Γ 4 Γ 89.25 β 2500 . answer a
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if 9 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
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let the required no of hectares be x . then men - - - hectares - - - days 9 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 9 * 30 / 24 * 80 x = 400
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two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 144 seconds . the length of each train is :
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the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 Γ 518 = 259 m / s in 144 secs the total distance traveled is 144 x 25 / 9 = 400 m . therefore the length of each train is = 400 / 2 = 200 m . answer d
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if an investor puts $ 900 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
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1.05 * 1.05 * 900 = $ 992.25 the answer is d .
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if the wheel is 21 cm then the number of revolutions to cover a distance of 1056 cm is ?
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2 * 22 / 7 * 21 * x = 1056 = > x = 8
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for each color copy , print shop x charges $ 1.25 and print shop y charges $ 2.75 . how much greater is the charge for 60 color copies at print shop y than at print shop x ?
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the difference in the two prices is $ 2.75 - $ 1.25 = $ 1.50 for each color copy . each color copy will cost an extra $ 1.50 at print shop y . 60 * $ 1.50 = $ 90 the answer is b .
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a train 180 m long running at 75 kmph crosses a platform in 40 sec . what is the length of the platform ?
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d = 75 * 5 / 18 = 40 = 833 Γ’ β¬ β 150 = 683
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a train is 327 meter long is running at a speed of 40 km / hour . in what time will it pass a bridge of 122 meter length ?
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speed = 40 km / hr = 40 * ( 5 / 18 ) m / sec = 100 / 9 m / sec total distance = 327 + 122 = 449 meter time = distance / speed = 449 * ( 9 / 100 ) = 40.41 seconds .
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if x + y = 2 x - 2 z , x - 2 y = 4 z and x + y + z = 21 , what is the value of z / y ?
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x + y = 2 x - 2 z x - y = 2 z - - - - - - - - - - 1 x - 2 y = 4 z - - - - - - - - - 2 subtracting equation 1 from equation 2 2 z = - y z / y = - 0.5 c is the answer
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if a person walks at 16 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
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let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 16 16 x = 10 x + 200 6 x = 200 x = 33.3 km .
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if teena is driving at 55 miles per hour and is currently 7.5 miles behind coe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of coe ?
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this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . coe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena can cover 7.5 miles in 30 mins teena will cover 15 miles in 60 mins so answer 30 + 60 = 90 mins . d
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in a 500 m race , the ratio of the speeds of two contestants a and b is 2 : 4 . a has a start of 300 m . then , a wins by :
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to reach the winning post a will have to cover a distance of ( 500 - 300 ) m , i . e . , 200 m . while a covers 2 m , b covers 4 m . while a covers 200 m , b covers 4 x 200 / 2 m = 400 m . thus , when a reaches the winning post , b covers 400 m and therefore remains 100 m behind . a wins by 100 m .
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the two lines y = x and x = - 8 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
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the point of intersection is ( - 8 , - 8 ) . the triangle has a base of length 8 and a height of 8 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 8 * 8 = 32 the answer is b .
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a school has received 60 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
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let us suppose there are 100 people . 40 % of them donated $ 16000 ( 400 * 40 ) $ 16000 is 60 % of total amount . so total amount = 16000 * 100 / 60 remaining amount is 40 % of total amount . 40 % of total amount = 16000 * ( 100 / 60 ) * ( 40 / 100 ) = 32000 / 3 this amount has to be divided by 60 ( remaining people are 60 ) so per head amount is 32000 / 3 / 60 = 32000 / 180 = 1600 / 9 = $ 177.78 ;
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the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 58 , and last 6 numbers is 65 then find 6 th number ?
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6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 58 + 6 * 65 - 11 * 60 = 78 answer is a
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each month a retailer sells 100 identical items . on each item he makes a profit of $ 30 that constitutes 16 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
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for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 16 % of the cost : sell price = cost + $ 20 sell price = $ 125 + $ 20 thus , the sell price is $ 145 for each item . selling all 100 items gives the retailer . . . 100 ( $ 20 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 145 ) = $ 7.25 discount $ 137.75 = $ 125 + $ 12.75 now , the retailer makes a profit of just $ 12.75 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 12.75 ( x ) = $ 2,000 x = 2,000 / 12.75 x = 156.8627 = 157 items a
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4 dice are thrown simultaneously on the board . find the probability show the same face .
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the total number of elementary events associated to the random experiments of throwing four dice simultaneously is : = 6 Γ 6 Γ 6 Γ 6 = 64 = 6 Γ 6 Γ 6 Γ 6 = 64 n ( s ) = 64 n ( s ) = 64 let xx be the event that all dice show the same face . x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) = 6 hence required probability , = n ( x ) n ( s ) = 664 = n ( x ) n ( s ) = 664 = 1 / 216 c
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if a 3 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
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the area a of the large cube is 3 * 3 * 6 = 54 square cm . the area of the 27 small cubes is 27 * 6 = 54 * 3 = 3 a , an increase of 200 % . the answer is d .
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the population of a town is 8000 . it decreases annually at the rate of 10 % p . a . what will be its population after 2 years ?
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formula : ( after = 100 denominator ago = 100 numerator ) 8000 Γ£ β 90 / 100 Γ£ β 90 / 100 = 6480
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jim β s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.15 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
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let the fixed charge of jim β s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 15 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 15 = 2.25 + 9 * . 15 = 3.6 $ answer c
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in a certain city , 70 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 80 percent of the registered voters who are democrats and 30 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
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say there are total of 100 registered voters in that city . thus 70 are democrats and 30 are republicans . 70 * 0.80 = 56 democrats are expected to vote for candidate a ; 30 * 0.30 = 9 republicans are expected to vote for candidate a . thus total of 56 + 9 = 65 registered voters are expected to vote for candidate a , which is 65 % of the total number of registered voters .
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a and b can do a piece of work in 7 days . with the help of c they finish the work in 4 days . c alone can do that piece of work in ?
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c = 1 / 4 Γ’ β¬ β 1 / 7 = 3 / 28 = > 28 / 3 = 9 1 / 3 days
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the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 9 minutes , then the area of the park ( in sq . m ) is :
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perimeter = distance covered in 9 min . = ( 12000 / 60 ) x 9 m = 1800 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1800 or x = 180 . length = 540 m and breadth = 360 m . area = ( 540 x 360 ) m 2 = 194400 m 2 .
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a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 80 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
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the actual answer is obtained by multiplying 180 % by 70 % and subtracting 100 % from this total . that is : 180 % Γ 70 % = 126 % ; 126 % β 100 % = 26 % .
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pipe a can fill a tank in 16 hrs and pipe b can fill it in 24 hrs . if both the pipes are opened in the empty tank . in how many hours will it be fill 5 / 4 th of that tank ?
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part filled a in 1 hr = ( 1 / 16 ) part filled b in 1 hr = ( 1 / 24 ) part filled by ( a + b ) together in 1 hr = ( 1 / 16 ) + ( 1 / 24 ) = 5 / 48 so , the tank will be full in 48 / 5 hrs time taken to fill exact quarter tank = ( 48 / 5 ) * ( 5 / 4 ) = 12 hrs
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a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 504 . find the sum ?
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let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 504 = > 36 x / 100 - 24 x / 100 = 504 = > 12 x / 100 = 840 = > x = 4200 .
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the average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
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total age increased = ( 8 * 2 ) years = 16 years . sum of ages of two new men = ( 21 + 23 + 16 ) years = 60 years average age of two new men = ( 60 / 2 ) years = 30 years .
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a boy traveled from the village to the post - office at the rate of 12.5 kmph and walked back at the rate of 2 kmph . if the whole journey took 5 hours 48 minutes , find the distance of the post - office from the village .
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solution : average speed = 2 xy / ( x + y ) km / hr = ( 2 * 12.5 * 2 ) / ( 12.5 + 2 ) km / hr = 50 / 14.5 km / hr . total distance = ( 50 / 14.5 * 29 / 5 ) km . = 20 km . required distance = 20 / 2 = 10 km .
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the sum of the numbers is 177 . if the ratio between the first and the second be 5 : 3 and that between the second and third be 4 : 9 , then find the second number ?
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given ratios 5 : 3 4 : 9 20 : 12 : 27 the second number = 177 / ( 20 + 12 + 27 ) * 15 = 45 answer is c
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if the height of a cone is increased by 190 % then its volume is increased by ?
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100 %
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a green lizard can travel from the green cave to the blue cave in 108 minutes ; the blue lizard can travel from the blue cave to the green cave in 25 % less time . if the green lizard started to travel 7.5 minutes before the blue lizard , how many minutes after the blue lizard , will the green lizard pass the middle line ?
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time take by the green lizard to cover the distance between the caves = 108 mins time take by the green lizard to cover half the distance = 108 / 2 = 54 mins time take by the blue lizard to cover the distance between the caves = 108 x 3 / 4 = 81 mins time take by the blue lizard to cover half the distance = 81 / 2 = 40.5 mins now the green lizard had been travelling for 7.5 mins when the blue lizard started . therefore when the blue lizard starts to move the green lizard will have to cover 54 - 7.5 = 46.5 mins worth of distance at its current speed . difference in time when they both reach the mid point = 46.5 - 40.5 = 6 mins . e is the correct answer .
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working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 16 , and 18 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
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p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 16 + 1 / 18 = 17 / 144 therefore they take 144 / 17 ratio = 144 / 17 = d
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the first year , two cows produced 8100 litres of milk . the second year their production increased by 15 % and 10 % respectively , and the total amount of milk increased to 9100 litres a year . how many litres were milked from each cow each year ?
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let x be the amount of milk the first cow produced during the first year . then the second cow produced ( 8100 β x ) ( 8100 β x ) litres of milk that year . the second year , each cow produced the same amount of milk as they did the first year plus the increase of 15 % 15 % or 10 % 10 % . so 8100 + 15100 β
x + 10100 β
( 8100 β x ) = 91008100 + 15100 β
x + 10100 β
( 8100 β x ) = 9100 therefore 8100 + 320 x + 110 ( 8100 β x ) = 91008100 + 320 x + 110 ( 8100 β x ) = 9100 120 x = 190120 x = 190 x = 3800 x = 3800 therefore , the cows produced 3800 and 4300 litres of milk the first year , and 4370 and 4730 litres of milk the second year , respectively .
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sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 2.5 per pound , and german chocolate cost $ 1.5 per pound . if the total the she spent on chocolate was $ 15 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
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if there were all the expensive ones 2.5 . . . . there would be 15 / 2.5 or 6 of them but since 1.5 $ ones are also there , answer has to be > 6 . . . . if all were 1.5 $ ones , there will be 15 / 1.5 or 10 . . . so only 8 is left ans b . .
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an integer n between 1 and 99 , inclusive , is to be chosen at random . what is the probability that n ( n + 2 ) will be divisible by 3 ?
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n ( n + 2 ) to be divisible by 3 either n or n + 2 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } , . . . , { 97 , 98 , 99 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 } n can be : 1 , or 3 . thus , the overall probability is 2 / 3 .
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find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 15 per cubic meter ?
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22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 15 = 1485
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a car started running at a speed of 28 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 .
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a 37 km the total distance covered by the car in the first 10 hours = 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in ap whose first term is 28 and last term is 46 = 10 / 2 [ 28 + 46 ] = 370 km .
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find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2
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( 4 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 3 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 3 x 11 ^ 2 = 2 ^ 22 x 7 ^ 3 x 11 ^ 2 total number of prime factors = ( 22 + 3 + 2 ) = 27 . answer is d .
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for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 7 of whom are females , by how much does the index for the females exceed the index for the males in the group ?
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index for females = ( 20 - 7 ) / 20 = 13 / 20 = 0.65 index for males = ( 20 - 13 / 20 = 7 / 20 = 0.35 index for females exceeds males by 0.65 - 0.35 = 0.3
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the sum of the squares of three numbers is 138 , while the sum of their products taken two at a time is 131 . their sum is :
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let the numbers be a , b and c . then , a 2 + b 2 + c 2 = 138 and ( ab + bc + ca ) = 131 ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) 138 + 2 * 131 = 400 ( a + b + c ) = Γ’ Λ Ε‘ 400 = 20
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the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 14 % ?
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let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 86 gain % = 22 / 64 * 100 = 34.375 % .
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the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
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let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( β ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places
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in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students e in the class ?
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the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )
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a car travels first 160 km at 64 km / hr and the next 160 km at 80 km / hr . what is the average speed for the first 320 km of the tour ?
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car travels first 160 km at 64 km / hr time taken to travel first 160 km = distancespeed = 16064 car travels next 160 km at 80 km / hr time taken to travel next 160 km = distancespeed = 16080 total distance traveled = 160 + 160 = 2 Γ 160 total time taken = 16064 + 16080 average speed = total distance traveledtotal time taken = 2 Γ 16016064 + 16080 = 2164 + 180 = 2 Γ 64 Γ 8080 + 64 = 2 Γ 64 Γ 80144 = 2 Γ 8 Γ 8018 = 6409 = 71.11 km / hr
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a prize of $ 800 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
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total value of the prize = $ 800 number of people = 20 2 / 5 of 800 ( = $ 320 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 800 - 320 = $ 480 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 480 - 140 = $ 340 , hence e is the correct answer .
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simple interest on a certain sum of money for 3 years at 10 % per annum is half the compound interest on rs . 6500 for 2 years at 14 % per annum . the sum placed on simple interest is
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solution c . i . = rs [ 6500 x ( 1 + 14 / 100 ) Γ’ Β² - 6500 ] rs . ( 6500 x 114 / 100 x 114 / 100 - 6500 ) = rs . 1947.4 . sum = rs . [ 973.7 x 100 / 3 x 10 ] = rs . 3245.67 . answer e
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mary works in a restaurant a maximum of 50 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
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mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 30 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 30 ) = $ 300 . the total amount is $ 160 + $ 300 = $ 460 answer c 460 .
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an outlet pipe empties a tank which is full in 5 hours . if the inlet pipe is kept open , which lets water in at the rate of 4 litres / min then outlet pipe would take 3 hours longer . find the capacity of the tank .
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let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 4 * 60 = 240 liters / hour ; net outflow rate when both pipes operate would be x - 240 liters / hour . capacity of the tank = x * 5 hours = ( x - 240 ) * ( 5 + 3 ) hours 5 x = ( x - 240 ) * 8 - - > x = 640 - - > capacity = 5 x = 3200 liters .
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you buy a piece of land with an area of Γ’ Λ Ε‘ 625 , how long is one side of the land plot ?
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try filling the numbers into the answer y x y = find the closest to 625 . answer e
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in a division sum , the remainder is 4 and the divisor is 2 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is :
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diver = ( 4 * 3 ) + 2 = 14 2 * quotient = 14 quotient = 7 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 7 ) + 2 = 100 c
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if the sum of two numbers is 42 and their product is 437 , then find the absolute difference between the numbers .
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let the numbers be x and y . then , x + y = 42 and xy = 437 x - y = sqrt [ ( x + y ) 2 - 4 xy ] = sqrt [ ( 42 ) 2 - 4 x 437 ] = sqrt [ 1764 β 1748 ] = sqrt [ 16 ] = 4 . required difference = 4 . answer is b .
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for dinner , cara ate 240 grams of bread which was 8 times as much bread as she ate for lunch , and 6 times as much bread as she ate for breakfast . how much bread did cara eat in total ?
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for breakfast , cara ate 240 / 6 = 40 grams . for lunch , cara ate 240 / 8 = 30 grams . for dinner , cara ate 240 grams . the total is 40 + 30 + 240 = 310 grams . the answer is b .
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a rectangular box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn . the area of the lawn is 2109 sq . m . what is the width of the road ?
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total area of cross roads = 60 x + 40 x β x 2 but total area of the cross roads = 291 m 2 hence , 60 x + 40 x β x 2 = 291 β 100 x β x 2 = 291 β x 2 β 100 x + 291 = 0 β ( x β 97 ) ( x β 3 ) = 0 β x = 3
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if 50 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
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let 50 % of a = 1 / 3 b then 50 a / 100 = 1 b / 3 a / 2 = b / 3 a / b = 2 / 3 a : b = 2 : 3 answer is e
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the speed at which a man can row a boat in still water is 25 kmph . if he rows downstream , where the speed of current is 11 kmph , what time will he take to cover 80 metres ?
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speed of the boat downstream = 25 + 11 = 36 kmph = 36 * 5 / 18 = 10 m / s hence time taken to cover 80 m = 80 / 10 = 8 seconds .
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for a particular american football game , the probability of a team ' s quarterback throwing a completed pass on each throw is 3 / 10 . what is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50 % .
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rule of subtraction : p ( a ) = 1 - p ( a ' ) rule of multiplication : p ( a β© b ) = p ( a ) p ( b ) the probability that the quarterback throws a completed pass at least once in 2 throws is 1 - ( 7 / 10 ) ^ 2 = 1 - 49 / 100 = 51 / 100 > 50 %
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a and b can do a work in 8 hours and 12 hours respectively . a starts the work at 6 am and they work alternately for one hour each . when will the work be completed ?
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work done by a and b in the first two hours , working alternately = first hour a + second hour b = 1 / 8 + 1 / 12 = 5 / 24 . total time required to complete the work = 2 * 24 / 5 = 9.6 days .
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in a weight - lifting competition , the total weight of joe ' s two lifts was 1800 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
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this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1800 pounds . we sum the two variables to obtain : f + s = 1800 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f β 300 = s we can now plug in ( 2 f β 300 ) for s into the first equation , so we have : f + 2 f β 300 = 1800 3 f = 2100 f = 700 answer is e .
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a train covers a distance of 12 km in 10 min . if it takes 1 sec to pass a telegraph post , then the length of the train is ?
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speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 1 = 20 m .
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in a division , divident is 729 , divisior is 38 and quotient is 19 . find the remainder .
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729 = 38 x 19 + r 729 = 722 + r r = 729 - 722 = 7
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compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 330 grams of compound x ?
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total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 330 gms of x have 330 * 10 / 12 = 275 gms of b and 330 - 275 = 55 gms of a . cross check : - a / b = 55 / 275 = 2 / 10 ( as given ) ans d
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the average salary of all the workers in a workshop is rs . 9000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
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let the total number of workers be x . then , 9000 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = > 3000 x = 42000 = x = 14 .
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find the sum of first 30 natural numbers
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sum of n natural numbers = n ( n + 1 ) 2 = 30 ( 30 + 1 ) 2 = 30 ( 31 ) 2 = 465
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a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 3 : 1 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 4 : 3 , respectively . how many more acres of land were planted with tobacco under the new system ?
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we have ratio in 5 : 3 : 1 and this is shifted to 2 : 4 : 3 ( c : s : t ) if we observe the ratio of the tobacco increased by 2 times ( 3 - 1 ) t = 1 / 9 * 1350 = 150 . since tobacco increased by 2 times . . we get 150 * 2 = 300 . answer d is the answer . .
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the charge for a single room at hotel p is 70 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
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p = 0.3 r = 0.9 g r = 0.9 g / 0.3 = 3 g thus r is 200 % greater than g . the answer is d .
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average of 10 matches is 34 , how many runs one should should score to increase his average by 4 runs .
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average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 34 ) = 418 - 340 = 78
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what least number should be added to 1021 , so that the sum is completely divisible by 25 ?
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1021 Γ£ Β· 25 = 40 with remainder = 21 21 + 4 = 25 . hence 4 should be added to 1021 so that the sum will be divisible by 25
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in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 0 vers to reach the target of 282 runs ?
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sol . required run rate = 282 β ( 3.2 Γ 10 / 40 ) = 240 / 40 = 6.25 . answer a
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how many positive integers less than 50 are multiples of 6 but not multiples of 8 ?
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the lcm of 6 and 8 is 24 . if x < 50 and x is divisible by 6 not by 8 - - > x is not divisible by 24 . from 1 - - > 50 , we have 2 numbers which is divisible by 24 : 24 , 48 . from 1 - - > 50 , we have ( 48 - 6 ) / 6 + 1 = 8 numbers divisible by 6 . therefore , our answer is 8 - 2 = 6 numbers . b
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a reduction of 10 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
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800 * ( 10 / 100 ) = 80 - - - - 5 ? - - - - 1 = > rs . 16
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