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Question: the radius of the two circular fields is in the ratio 4 : 10 the area of the second field is what percent greater than the area of the first ?
['A.72 %', 'B.96 %', 'C.94 %', 'D.84 %', 'e ) 82 %']D.
r = 4 Γ― β¬ r 2 = 16 r = 10 Γ― β¬ r 2 = 100 100 Γ― β¬ Γ’ β¬ β 84 Γ― β¬ 100 - - - - ? = > 84 % . answer : d | null |
Question: a river 2 m deep and 45 m wide is flowing at the rate of 5 kmph the amount of water that runs into the sea per minute is ?
A.4500 m 3.
B.4580 m 3.
C.7500 m 3.
D.4900 m 3.
e ) 4700 m 3C.
"explanation : ( 5000 * 2 * 45 ) / 60 = 7500 m 3 answer : option c" | null |
Question: if the range q of the 6 numbers 4 , 314 , 710 and x is 12 , what is the difference between the greatest possible value of x and least possible value of x ?
A.0.
B.2.
C.12.
D.13.
e ) 15D.
the range q of a set is the difference between the largest and smallest elements of a set . without x , the difference between the largest and smallest elements of a set is 14 - 3 = 11 < 12 , which means that in order 12 to be the range of the set x must be either the smallest element so that 14 - x = 12 - - - > x = 2 or x must the largest element so that x - 3 = 12 - - > x = 15 . the the difference between the greatest possible value of x and least possible value of x is 15 - 2 = 13 . answer : d . | null |
Question: a person is traveling at 60 km / hr and reached his destiny in 4 hr . 30 m then find the distance ?
A.150 km.
B.270 km.
C.246 km.
D.196 km.
e ) 205 kmB.
"t = 4 hr 30 m = 9 / 2 hr d = t * s = 60 * 9 / 2 = 270 km answer is b" | null |
Question: if 80 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
A.10 %.
B.( 8 ) 20 %.
C.30 %.
D.50 %.
e ) 55 %E.
"i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 80 - x ) + x + ( 55 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 135 x = 55 ans : e" | null |
Question: a train 300 m long can cross an electric pole in 20 sec and then find the speed of the train ?
A.72.
B.67.
C.54.
D.26.
e ) 27C.
"length = speed * time speed = l / t s = 300 / 20 s = 15 m / sec speed = 15 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 54 kmph answer : c" | null |
Question: a train is 385 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
A.42 seconds.
B.30 seconds.
C.40 seconds.
D.50 seconds.
e ) none of theseA.
"explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 385 + 140 = 525 meter time = distance / speed = 525 β 2 / 25 = 42 seconds option a" | null |
Question: ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of a * b ?
A.10000.
B.11000.
C.19000.
D.20000.
e ) 21000B.
"yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 a * b = 110 * 100 = 11000 ans : b" | null |
Question: the distance between two cities a and b is 330 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
A.10 a . m.
B.10.30 a . m.
C.11 a . m.
D.11.30 a . m.
e ) none of theseC.
explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 330 . therefore , 60 x + 75 ( x - 1 ) = 330 . = > x = 3 . so , they meet at ( 8 + 3 ) i . e , 11 a . m . answer : c | null |
Question: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 m and a distance of one meter is left from all sides of the boundary of the length of the garden is :
A.450 sq mtrs.
B.460 sq mtrs.
C.480 sq mtrs.
D.490 sq mtrs.
e ) 470 sq mtrsC.
"length of garden = 1 + 2 * 11 + 1 = 24 m breadth of garden = 1 + 9 * 2 + 1 = 20 m area = 24 * 20 = 480 sq mtrs answer : c" | null |
Question: there are 10 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
A.156.
B.167.
C.132.
D.352.
e ) 380C.
"the total number of stations = 12 from 12 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 12 p β ways . Β² β° p β = 12 * 11 = 132 . answer : c" | null |
Question: total dinning bill of 9 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
A.21.84.
B.12.84.
C.16.98.
D.24.84.
e ) 15.84C.
"dinner bill of 9 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 9 = $ 16.98 answer : c" | null |
Question: find the length of the longest pole that can be placed in a room 12 m long 8 m broad and 9 m high .
A.13.
B.14.
C.15.
D.16.
e ) 17E.
"length of longest pole = length of the diagonal of the room = sqrt ( 12 ^ 2 + 8 ^ 2 + 9 ^ 2 = sqrt ( 289 ) = 17 m . answer is e ." | null |
Question: find the average of first 4 multiples of 8 ?
A.20.
B.12.6.
C.22.5.
D.31.3.
e ) 40.8A.
"average = ( 8 + 16 + 24 + 32 ) / 4 = 20 answer is a" | null |
Question: if 9 ^ y = 3 ^ 14 , what is y ?
A.2.
B.3.
C.4.
D.5.
e ) 7E.
"9 ^ y = 3 ^ 2 y = 3 ^ 14 2 y = 14 y = 7 the answer is e ." | null |
Question: how many zeroes are there at the end of the number n , if n = 90 ! + 180 ! ?
A.15.
B.18.
C.21.
D.24.
e ) 27C.
"the number of zeroes at the end of 90 ! will be less than the number of zeroes at the end of 180 ! hence it is sufficient to calculate the number of zeroes at the end of 90 ! the number of zeroes = [ 90 / 5 ] + [ 90 / 25 ] + [ 90 / 125 ] = 18 + 3 + 0 = 21 the answer is c ." | null |
Question: ms . harris invested in fund x and fund b . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund x paid 23 % and fund b paid 17 % . the interest earned in fund b was exactly $ 200 greater than the interest earned in fund x . how much did ms . morris invest in fund x ?
A.$ 32000.
B.$ 36000.
C.$ 40000.
D.$ 42000.
e ) $ 45,000D.
0.17 b - 0.23 x = 200 | * 100 17 b - 23 x = 20,000 x + b = 100,000 b = 100,000 - x 17 ( 100,000 - x ) - 23 x = 20,000 1 , 700,000 - 17 x - 23 x = 20,000 1 , 680,000 = 40 x divide by 40 first two digits : 42 . . . so answer is d . | null |
Question: in a forest 150 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 10 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
A.150.
B.750.
C.3,000.
D.1,500.
e ) 2,500C.
"the percentage of tagged deer in the second sample = 10 / 50 * 100 = 20 % . so , 150 tagged deers comprise 10 % of total # of deers - - > total # of deers = 150 * 20 = 3,500 . answer : c" | null |
Question: a 11 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
A.5 / 8.
B.1 / 5.
C.6 / 11.
D.3 / 11.
e ) 2 / 5C.
"a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 3 meters from either end . the probability of this is 6 / 11 . the answer is c ." | null |
Question: if the price of a certain computer increased 30 percent from b dollars to 351 dollars , then 2 b =
A.540.
B.570.
C.619.
D.649.
e ) 700A.
"before price increase price = b after 30 % price increase price = b + ( 30 / 100 ) * b = 1.3 b = 351 ( given ) i . e . b = 351 / 1.3 = $ 270 i . e . 2 b = 2 * 270 = 540 answer : option a" | null |
Question: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 5780 , how much amount did raghu invest ?
A.1287.
B.2887.
C.2000.
D.1129.
e ) 1192C.
"let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 5780 = x = 5780 / 2.89 = 2000 therefore , amount invested by raghu is rs . 2000 . answer : c" | null |
Question: how many seconds will a train 100 meters long take to cross a bridge 170 meters long if the speed of the train is 36 kmph ?
A.54 sec.
B.65 sec.
C.25 sec.
D.45 sec.
e ) 27 secE.
"d = 100 + 170 = 270 s = 36 * 5 / 18 = 10 mps t = 270 / 10 = 27 sec answer : e" | null |
Question: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 12 people all together . how many people can sit in a bus ?
A.52.
B.49.
C.95.
D.88.
e ) 93E.
"right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 12 total people can seat = 81 + 12 = 93 answer : e" | null |
Question: some persons can do a piece of work in 16 days . two times the number of these people will do half of that work in ?
A.3.
B.4.
C.5.
D.6.
e ) 8B.
"16 / ( 2 * 2 ) = 4 days answer : b" | null |
Question: stacy was 5 days late returning items to the library . stacy had checked out 40 books , 2 movies , and 3 magazines . books are fined $ 0.25 per day , movies are fined $ 3.00 per day , and magazines are fined $ 0.50 per day . what is the average fine per item per day stacy paid ?
A.$ 0.25.
B.$ 0.30.
C.$ 0.35.
D.$ 0.40.
e ) none of the aboveE.
explanation : 40 2 3 $ 0.25 $ 3.00 $ 0.50 $ 10.00 + $ 6.00 + $ 1.50 = $ 17.50 / 45 = $ 0.39 e | null |
Question: if an average hard drive had a capacity of 0.4 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
A.256.
B.512.
C.4096.
D.1024.
e ) 1536C.
"0.4 * 2 ^ 10 = 0.4 * 1024 = 409.6 the answer is c ." | null |
Question: in may , the grounds keeper at spring lake golf club built a circular green with an area of 36 Ο square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
['A.100 pi', 'B.144 pi', 'C.70', 'D.80', 'e ) 90']B.
area of circle 36 pi sq feet = pi r ^ 2 therefore r = 6 now green radi doubled i . e r = 12 area = 144 pi b | null |
Question: a house wife saved $ 5 in buying an item on sale . if she spent $ 48 for the item , approximately how much percent she saved in the transaction ?
A.8 %.
B.9 %.
C.10 %.
D.11 %.
e ) 12 %C.
"actual price = 48 + 5 = $ 53 saving = 5 / 48 * 100 = 100 / 11 = 10 % approximately answer is c" | null |
Question: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 200 , find the original price per kg ?
A.s . 7.
B.s . 4.
C.s . 5.
D.s . 1.
e ) s . 9C.
"100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 200 - - - 80 ? - - - 2 = > rs . 5 answer : c" | null |
Question: find the remainder when 6 ^ 50 is divided by 215
A.34.
B.35.
C.36.
D.37.
e ) 38C.
"( 6 ^ 3 ) ^ 16 * 6 ^ 2 / 215 ( 215 + 1 ) ^ 16 * 6 ^ 2 / 215 1 ^ 16 * 6 ^ 2 / 215 = 36 answer : c" | null |
Question: a train 140 m long is running at 60 kmph . in how much time wiu it pass a platform 260 m long ?
A.21 sec.
B.22 sec.
C.23 sec.
D.24 sec.
e ) 26 secD.
"s = d / t d = 140 + 260 = 400 m s = 60 * 5 / 18 m / sec = 50 / 3 m / sec t = 400 / ( 50 / 3 ) = 1200 / 50 = 24 sec answer : d" | null |
Question: the total marks obtained by a student in mathematics and physics is 50 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
A.15.
B.25.
C.35.
D.45.
e ) 55C.
"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 50 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 50 + 20 ) / 2 = 35 . answer : c" | null |
Question: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 70 paise per sq . metre
A.s 595.
B.s 780.
C.s 880.
D.s 480.
e ) s 980A.
"area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 70 = 59500 p in rs = 59500 / 100 = rs 595 answer : a" | null |
Question: rahul played weel in this season . his current batting averagge is 46 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
A.8.
B.10.
C.3.
D.6.
e ) 5C.
"46 x + 78 = 54 ( x + 1 ) = > 8 x = 24 = > x = 3 answer : c" | null |
Question: find the simple interest on rs . 69,000 at 16 2 / 3 % per year for 9 months .
A.7500.
B.6500.
C.8625.
D.9500.
e ) none of themC.
p = rs . 69000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 69,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8625 answer is c . | null |
Question: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 7 years hence ?
A.22.
B.77.
C.74.
D.98.
e ) 71C.
"a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 7 years , their ages will be 47 and 27 . sum of their ages = 47 + 27 = 74 . answer : c" | null |
Question: malar and roja combined will complete a task in 35 days , but malar alone can complete same work in 60 days . calculate in how many days roja can complete this work ?
A.85 days.
B.45 days.
C.90 days.
D.84 days.
e ) 95 daysD.
malar - 35 days = > 1 / 35 roja - 60 days = > 1 / 60 malar one day work = 1 / 35 - 1 / 60 = 1 / 84 = = > 84 days answer d | null |
Question: the measure of the side of a square is quadrupled . if x represents the perimeter of the original square , what is the value of the new perimeter ?
['A.3 x', 'B.4 x', 'C.9 x', 'D.12 x', 'e ) 27 x']B.
original perimeter = x hence original side = x / 4 new side = 4 x / 4 new perimeter = 4 * 4 x / 4 = 4 x correct option : b | null |
Question: tough and tricky questions : word problems . micheal , saren and donald decided to club together to buy a present . each of them gave equal amount of money . luckily saren negotiated a 20 % discount for the present so that each of them paid 4 dollars less . how much did they pay for a present ?
A.20.
B.36.
C.48.
D.60.
e ) 72C.
answer c . we know that saren negotiated a discount of 20 % , so each of them paid $ 4 less . since there are three people , the 20 % of the original price amounts to $ 12 . 5 times 12 $ is 60 $ , so the original price , before saren negotiated the discount , had been $ 60 . they paid $ 12 less than the base price , so they spent $ 48 . | null |
Question: a train passes a station platform in 36 sec and a man standing on the platform in 25 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
A.767 m.
B.240 m.
C.187 m.
D.176 m.
e ) 165 mE.
"speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 25 = 375 m . let the length of the platform be x m . then , ( x + 375 ) / 36 = 15 = > x = 165 m . answer : e" | null |
Question: a club wants to mix 25 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
A.30.
B.40.
C.50.
D.60.
e ) 70C.
"let number of pounds of 5 $ candy to be used be w 6 = ( 25 * 8 + 5 * w ) / ( 25 + w ) = > 150 + 6 w = 200 + 5 w = > w = 50 answer c" | null |
Question: if pintu is coded as 79523 in a certain code language , how would you code lumbo in the same language ?
A.13426.
B.14236.
C.13436.
D.33426.
e ) 15263D.
"1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . lumbo is 33426 . . . answer : d" | null |
Question: a shopkeeper has 280 kg of apples . he sells 30 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
A.24 %.
B.25 %.
C.26 %.
D.28 %.
e ) 35 %A.
"if the total quantity was 100 then 30 x 20 % + 60 x 30 % = 24 this profit will remain same for any total quantity unless the % of products remains the same . hence ' a ' is the answer" | null |
Question: pradeep has to obtain 20 % of the total marks to pass . he got 390 marks and failed by 25 marks . the maximum marks are
A.300.
B.2075.
C.800.
D.1000.
e ) 3900B.
"explanation : let their maximum marks be x . then , 20 % of x = 390 + 25 = > 20 / 100 x = 415 x = ( 41500 / 20 ) x = 2075 . answer : b" | null |
Question: 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 . 6500 ?
A.rs . 5870.
B.rs . 5991.
C.rs . 8870.
D.rs . 6850.
e ) none of theseC.
"explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6500 * 6 ) β 30,130 ] = rs . ( 39000 β 30,130 ) = rs . 8870 answer c" | null |
Question: if 30 men take 15 days to to complete a job , in how many days can 25 men finish that work ?
A.18.
B.17.
C.16.
D.15.
e ) 14A.
ans . 18 days | null |
Question: if 7 a = 8 b and ab β 0 , what is the ratio of a / 8 to b / 7 ?
A.16 / 14.
B.8 / 7.
C.1.
D.7 / 8.
e ) 64 / 49C.
"a nice fast approach is the first find a pair of numbers that satisfy the given equation : 7 a = 8 b here ' s one pair : a = 8 and b = 7 what is the ratio of a / 8 to b / 7 ? in other words , what is the value of ( a / 8 ) / ( b / 7 ) ? plug in values to get : ( a / 8 ) / ( b / 7 ) = ( 8 / 8 ) / ( 7 / 7 ) = 1 / 1 = 1 c" | null |
Question: an empty fuel tank is filled with brand z gasoline . when the tank is 3 / 4 empty , it is filled with brand y gasoline . when the tank is half empty again , it is filled with brand z gasoline . when the tank is half empty again , it is filled with brand y gasoline . at this time , what percent of the gasoline in the tank is brand z ?
A.40 %.
B.41 %.
C.43.75 %.
D.42 %.
e ) 44 %C.
"work with fraction of brand z in the tank . 1 st step : brand z is 1 2 nd step : brand z is 1 / 2 3 rd step : brand z is ( 3 / 4 ) * ( 1 / 2 ) + 1 / 2 = 7 / 8 4 th step : brand z is ( 1 / 2 ) * ( 7 / 8 ) = 7 / 16 = 43.75 % answer ( c )" | null |
Question: what will be the fraction of 20 %
A.1 / 4.
B.1 / 5.
C.1 / 10.
D.1 / 8.
e ) none of aboveB.
"explanation : it will 20 * 1 / 100 = 1 / 5 answer : option b" | null |
Question: a cistern is filled by a tap in 6 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
A.81.
B.85.
C.88.
D.91.
e ) 95D.
"filling rate - leak rate = net rate 1 / 6.5 - leak rate = 1 / 7 leak rate = 2 / 13 - 1 / 7 = 1 / 91 the answer is d ." | null |
Question: 3 candidates contested in an election and received 4136 , 7636 , 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?
A.45 %.
B.49 %.
C.50 %.
D.51 %.
e ) 62 %C.
total number of votes polled = 4136 + 7636 + 11628 = 23400 required percentage = 11628 * 100 / 23400 = 50 % answer is c | null |
Question: in a hostel , the number of students decreased by 12 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
A.19 %.
B.15 %.
C.25 %.
D.40 %.
e ) 5.3 %E.
"cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 12 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.88 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.88 * 1.2 ) = > f ( new ) = 0.9469 f therefore the new cost of food must be 94.69 % of the old cost , or the cost of food must decrease by 5.3 % ( option e )" | null |
Question: if the radius of a cylinder is made 3 times and so is the height , what is the new volume of the cylinder divided by the old one ?
A.27 ..
B.2 ..
C.6 ..
D.4 ..
e ) 10 .A.
"let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 3 r ) ^ 2 ( 3 h ) v ' = 27 v a ) 27" | null |
Question: the sum of number of boys and girls in a school is 1150 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
A.50.
B.40.
C.60.
D.92.
e ) 70D.
"we have x + x % of 1150 = 1150 x + x / 100 * 1150 = 1150 25 / 2 * x = 1150 x = 1150 * 2 / 25 = 92 answer is d" | null |
Question: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 35 days to complete the same work . then q alone can do it in
A.20.
B.22.
C.25.
D.28.
e ) 30D.
"work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 35 work done by p , q and r in 1 day = 1 / 10 + 1 / 35 = 9 / 70 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day Γ£ β 2 = 9 / 70 = > work done by p in 1 day = 9 / 140 = > work done by q and r in 1 day = 9 / 140 hence work done by q in 1 day = 9 / 140 Γ’ β¬ β 1 / 35 = 1 / 28 so q alone can do the work in 28 days answer is d ." | null |
Question: kim has 3 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 6 shoes , what is the probability that she will select 2 shoes of the same color ?
A.2 / 5.
B.1 / 5.
C.1 / 9.
D.1 / 10.
e ) 1 / 25B.
"total pairs = 6 c 2 = 15 ; same color pairs = 3 c 1 * 1 c 1 = 3 ; prob = 1 / 5 ans b" | null |
Question: simplify : 3005 - 3000 + 10
A.2505.
B.2509.
C.2705.
D.2508.
e ) none of themC.
3005 - 3000 + 10 = 3005 - ( 3000 / 10 ) = 3005 - 300 = 2705 . answer is c | null |
Question: a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 8 / 15 . how many tennis balls did the retailer order originally .
A.110.
B.114.28.
C.140.
D.160.
e ) 214B.
white : yellow = x : ( x + 50 ) = 8 : 15 - - > 15 x = 8 x + 400 - - > x = 57.14 . the total # of balls originally x + x = 57.14 + 57.14 = 114.28 . answer : b . | null |
Question: when a merchant imported a certain item , he paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 94.50 , what was the total value of the item ?
A.$ 2,350.
B.$ 2,850.
C.$ 3,250.
D.$ 3,400.
e ) $ 3,750A.
let x be the value in excess of $ 1,000 . 0.07 x = 94.5 x = $ 1,350 the total value was $ 1,350 + $ 1,000 = $ 2,350 . the answer is a . | null |
Question: how many numbers are divisible by both 2 and 3 up to 300 ?
A.50.
B.100.
C.150.
D.200.
e ) 250A.
divide 300 by 6 , as the numbers which are divisible by both 2 and 3 are also divisible by 6 . the quotient obtained after dividing 300 by 6 is 50 , hence answer is 50 . option a | null |
Question: the result when a number subtracted from 150 is the same as the number added to 68 . what is the number ?
A.110.
B.100.
C.109.
D.218.
e ) 210C.
answer let the number be x . then , x - 68 = 150 - x Γ’ β‘ β 2 x = 150 + 68 = 218 Γ’ β‘ β 2 x = 218 Γ’ Λ Β΄ x = 109 correct option : c | null |
Question: the radius of a cylinder is 9 m , height 12 m . the volume of the cylinder is :
A.2200.
B.5500.
C.3054.9.
D.1100.
e ) 4400C.
"cylinder volume = Γ― β¬ r ( power 2 ) h = 22 / 7 Γ£ β 9 Γ£ β 9 Γ£ β 12 = 3054.9 m ( power 3 ) answer is c ." | null |
Question: how many numbers up to 300 and 700 are divisible by 2 , 3 and 7 both together ?
A.9.
B.10.
C.11.
D.12.
e ) 13A.
( 700 β 300 ) / 42 = 9 22 / 42 = > 9 numbers answer : a | null |
Question: if x * y = xy β 2 ( x + y ) for all integers x and y , then 3 * ( β 3 ) =
A.β 16.
B.β 9.
C.β 4.
D.4.
e ) 16B.
"3 * ( - 3 ) = 3 * ( - 3 ) - 2 ( 3 + ( - 3 ) ) = - 9 - 0 = - 9 option ( b )" | null |
Question: total 90 cows 30 cow gives each 2 liter milk 30 cow gives each 3 / 4 liter milk 30 cow gives each 1 / 4 liter milk this is split into 3 son per each 30 cows & 30 liter milk how ?
A.10.
B.12.
C.15.
D.16.
e ) 30E.
"30 cow 2 liter each = 60 liter 30 cow 3 / 4 liter each = 3 / 4 = 0.75 * 30 = 22.5 30 cow 1 / 4 liter each = 1 / 4 = 0.25 * 30 = 7.5 add 60 + 22.5 + 7.5 = 90 milk split into 3 son each 30 liter then 90 / 3 = 30 answer : e" | null |
Question: the ratio between the length and the breadth of a rectangular park is 1 : 3 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
A.124545 m.
B.134561 m.
C.156787 m.
D.15450 m.
e ) 120000 mE.
"perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 1 x metres and breadth = 3 x metres . then , 2 ( 1 x + 3 x ) = 1600 or x = 200 . length = 200 m and breadth = 600 m . area = ( 600 x 200 ) m 2 = 120000 m e" | null |
Question: the ratio of two quantities is incorrect when written as 10 to 14 . how should this ratio be written ?
A.5 : 14.
B.10 : 7.
C.20 : 24.
D.5 : 7.
e ) it can not be determined from the information givenD.
a ratio should be reduced to the lowest common denominator . 10 : 14 means 10 x : 14 x which can be written as 5 ( 2 ) : 7 ( 2 ) . . . answer : d | null |
Question: cereal a is 11 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
A.1 : 2.
B.2 : 3.
C.1 : 3.
D.1 : 4.
e ) 3 : 4A.
"2 % is 3 % - points below 5 % and 11 % is 6 % - points above 5 % . the ratio of a : b should be 3 : 6 = 1 : 2 . the answer is a ." | null |
Question: in a family 16 people eat only vegetarian , 9 people eat only non veg . , 12 people eat both veg and non veg . . how many people eat veg in the family ?
A.28.
B.26.
C.22.
D.31.
e ) 21A.
total people eat veg = only veg + both veg and non veg total = 16 + 12 = 28 answer = a | null |
Question: if the price of sugar rises from rs . 10 per kg to rs . 11 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
A.9 %.
B.20 %.
C.25 %.
D.30 %.
e ) noneA.
"sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x Γ 11 = x = 91 kg . β΄ reduction in consumption = 9 % . answer a" | null |
Question: the sum of the even numbers between 1 and n is 85 * 86 , where n is an odd number , then n = ?
A.163.
B.171.
C.179.
D.185.
e ) 191B.
"let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 85 * 86 then a = 85 and n = 171 . the answer is b ." | null |
Question: total dinning bill of 6 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
A.21.84.
B.22.84.
C.23.84.
D.24.84.
e ) 25.48E.
dinner bill of 6 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 6 = $ 25.48 answer : e | null |
Question: in a t . v . factory , an average of 63 tvs are produced per day for the fist 25 days of the months . a few workers fellill for the next 5 daysreducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?
A.35.
B.33.
C.48.
D.50.
e ) 52B.
production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 63 = 165 Γ’ Λ Β΄ average for last 5 days = 165 / 5 = 33 b | null |
Question: a part - time employee β s hourly wage was increased by 25 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
A.9 %.
B.15 %.
C.20 %.
D.50 %.
e ) 100 %C.
"let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 25 % wage increase , the employee makes $ 1.25 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.25 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.25 to get : new # of hours = 100 / 1.25 β 80 hours so , the number of hours decreases from 100 hours to ( approximately ) 80 hours . this represents a 20 % decrease ( approximately ) . answer : c" | null |
Question: a man rows his boat 120 km downstream and 92 km upstream , taking 4 hours each time . find the speed of the stream ?
A.6 kmph.
B.4 kmph.
C.2 kmph.
D.8 kmph.
e ) 1 kmphB.
"speed downstream = d / t = 120 / ( 4 ) = 30 kmph speed upstream = d / t = 92 / ( 4 ) = 23 kmph the speed of the stream = ( 30 - 23 ) / 2 = 4 kmph answer : b" | null |
Question: a student completes a 3 part exam as follows . the student completes sections a in 4 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
A.10 : 3.
B.9 : 2.
C.7 : 1.
D.8 : 3.
e ) 11 : 2C.
"the time spent on section b and section c is 28 minutes each . the ratio of c to a is 28 : 4 = 7 : 1 the answer is c ." | null |
Question: a is twice as good a workman as b and they took 10 days together to do the work b alone can do it in .
A.25 days.
B.88 days.
C.30 days.
D.11 days.
e ) 13 daysC.
wc = 2 : 1 2 x + x = 1 / 10 x = 1 / 30 = > 30 days answer : c | null |
Question: which number can we add to 425897 to get a number exactly divisible by 456 ?
A.3.
B.5.
C.7.
D.9.
e ) 11C.
"425897 / 456 = 933 with a remainder of 449 . we need to add 456 - 449 = 7 the answer is c ." | null |
Question: the speed at which a man can row a boat in still water is 9 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ?
A.16 seconds.
B.34 seconds.
C.14 seconds.
D.18 seconds.
e ) 15 secondsD.
"speed of the boat downstream = 9 + 3 = 12 kmph = 12 * 5 / 18 = 10 / 3 m / s hence time taken to cover 60 m = 60 * 3 / 10 = 18 seconds . answer : d" | null |
Question: the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 588 feet squared , what is the difference between the length and the width of the roof ?
A.28 ..
B.40 ..
C.42 ..
D.44 ..
e ) 46 .A.
"answer is a : 28 let w be the width , so length is 3 w . therefore : w * 3 w = 588 , solving for , w = 14 , so 3 w - w = 2 w = 2 * 14 = 28" | null |
Question: a train covers a distance of 12 km in 10 minutes . if it takes 8 seconds to pass a telegraph post , then the length of the train is
A.100 m.
B.120 m.
C.140 m.
D.160 m.
e ) 170 cmD.
"explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 8 ) m = 160 m answer : option d" | null |
Question: how many numbers from 15 to 65 are exactly divisible by 5 ?
A.5.
B.7.
C.9.
D.10.
e ) 12D.
"option ' d ' 15 / 5 = 3 and 65 / 5 = 13 = = > 13 - 3 = 10 numbers" | null |
Question: if the area of a circle decreases by 66 % , then the radius of a circle decreases by
A.20 %.
B.18 %.
C.36 %.
D.64 %.
e ) none of theseE.
"if area of a circle decreased by x % then the radius of a circle decreases by ( 100 β 10 β 100 β x ) % = ( 100 β 10 β 100 β 66 ) % = ( 100 β 10 β 64 ) % = 100 - 58 = 42 % answer e" | null |
Question: two cards are drawn together from a pack of 52 cards the probability that one is the spade and one is a heart is ?
A.85 / 852.
B.45 / 69.
C.18 / 456.
D.13 / 102.
e ) 23 / 125D.
"let s be the sample space then n ( s ) = 52 c 2 = ( 52 * 51 ) / ( 2 * 1 ) = 1326 let e be the event of getting 1 spade kings and 1 heart let n ( e ) = number of ways of chossing 1 spade out of 13 and 1 heart out of 13 = ( 13 c 1 * 13 c 1 ) = 13 * 13 = 169 p ( e ) = n ( e ) / n ( s ) = 169 / 1326 = 13 / 102 answer ( d )" | null |
Question: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 15 more transactions than cal . how much transactions did jade handled ?
A.80.
B.81.
C.82.
D.83.
e ) 84B.
solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 Γ 10 % = 90 + 90 Γ 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 Γ 99 = 66 jade handled 15 more transactions than cal . jade = 66 + 15 = 81 jade handled = 81 transactions . answer : b | null |
Question: peter invests a sum of money and gets back an amount of $ 815 in 3 years . david invests an equal amount of money and gets an amount of $ 850 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
A.670.
B.664.
C.698.
D.744.
e ) 710E.
"since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 850 - 815 = 35 interest earned for 3 years = 35 * 3 = 105 amount invested = 815 - 105 = 710 answer : e" | null |
Question: a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.2 m and its walls are 5 cm thick . the thickness of the bottom is :
A.90 cm.
B.2 dm.
C.1 m.
D.1.1 cm.
e ) none of theseB.
"explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) Γ ( 260 - 10 ) Γ ( 120 - x ) ] = 8000 Γ 1000 = > 320 Γ 250 Γ ( 120 - x ) = 8000 Γ 1000 = > ( 120 - x ) = 8000 Γ 1000 / 320 = 100 = > x = 20 cm = 2 dm . answer : b" | null |
Question: the sector of a circle has perimeter 83 cm and central angle 225 o . find its radius ?
A.21 cm.
B.15 cm.
C.14 cm.
D.24 cm.
e ) 28 cmC.
let radius = x cm perimeter of the sector = length of the arc + 2 ( radius ) 83 = ( 225 / 360 * 2 * 22 / 7 * x ) + 2 ( x ) 83 = 55 x / 14 + 2 x 83 = 83 x / 14 1162 = 83 x x = 14 answer : c | null |
Question: a transport company β s 120 buses running 20 hrs a day consume 360 of fuel in a day . in the next 3 days , the company will invest in 30 more green buses that use 30 % less fuel . how many lts of fuel will be consumed in a 5 day week after the new buses are added to the fleet ?
A.3060.
B.1.
512.
C.1800.
D.1260.
e ) 3,312E.
old buses use 360 * 5 days = 1,800 lts new buses use ( 0.70 * 360 ) / 120 * 5 days * 30 buses = 1,512 lts total fuel is 3,312 lts answer is e | null |
Question: at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses at the restaurant ? ( assume that all boxes are filled to capacity . )
A.96.
B.240.
C.56.
D.384.
e ) 480E.
"1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can just ` ` add 28 s ' ' until we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e" | null |
Question: in a certain alphabet , 9 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
A.7.
B.8.
C.14.
D.20.
e ) 28A.
"we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 9 + 24 = 33 ; next , we find the total # of letters without line : 40 - 33 = 7 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 7 - 0 = 7 . a" | null |
Question: if a train , travelling at a speed of 90 kmph , crosses a pole in 4 sec , then the length of train is ?
A.281.
B.125.
C.288.
D.100.
e ) 121D.
"d = 90 * 5 / 18 * 4 = 100 m answer : d" | null |
Question: john ' s bank ' s saving amount is decreased 20 % due to loan payment and current balance is rs . 24000 . find the actual balance before deduction ?
A.8000.
B.8500.
C.9000.
D.9500.
e ) 30000E.
"20 % decreased 80 % balance = 24000 100 % = 24000 / 80 * 100 = 30000 answer : e" | null |
Question: 987.650 - ? + 56.98 = 126.654
A.A.899.015.
B.B.752.804.
C.C.714.642.
D.D.629.906.
e ) 917.976E.
"explanation : 917.976 answer : option e" | null |
Question: two employees x and y are paid a total of rs . 700 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
A.s . 200.18.
B.s . 240.18.
C.s . 290.18.
D.s . 300.18.
e ) s . 318.18E.
"let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 700 but x = 120 % of y = 120 y / 100 = 12 y / 10 β΄ 12 y / 10 + y = 700 β y [ 12 / 10 + 1 ] = 700 β 22 y / 10 = 700 β 22 y = 7000 β y = 7000 / 22 = rs . 318.18 e )" | null |
Question: james took a 3 - hour bike ride . in the second hour he travlled 12 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
A.54.0.
B.54.9.
C.55.5.
D.37.0.
e ) 63.0D.
"let the distance travelled in the first hour be x . thus , 1.2 x = 12 , x = 10 . now , the distance travelled in the 3 rd hour = 12 + 1 / 4 Γ’ Λ β 12 = 15 therefore 12 + 15 + 10 = 37 answer : d" | null |
Question: in a group of 100 cars , 47 cars do not have air conditioning . if at least 53 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?
A.45.
B.47.
C.49.
D.51.
e ) 53B.
"lets assume ac = 53 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 53 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 53 . . we have to assign atleast 6 tocars with ac and racing stripes . hence ac = 53 - 6 = 47 . the answer is b" | null |
Question: how many bricks each measuring 22 cm x 10.25 cm x 8 cm , will be needed to build a wall 9 m x 7 m x 10.5 m
A.5600.
B.3066.
C.3055.
D.7200.
e ) none of theseB.
"explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 900 x 700 x 10.5 ) / ( 22 x 10.25 x 8 ) = 3066 answer : b" | null |
Question: 60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 56 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ?
A.12.
B.18.
C.32.
D.40.
e ) 44C.
"let ' s take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 32 ( 44 - 12 ) must be those with four screens or more c is the answer" | null |
Question: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 600 resolutions ?
A.844.8 m.
B.704 m.
C.774 m.
D.714 m.
e ) 744 mA.
in one resolution , the distance covered by the wheel is its own circumference . distance covered in 600 resolutions . = 600 * 2 * 22 / 7 * 22.4 = 84480 cm = 844.8 m answer : a | null |
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