text
stringlengths 45
2.98k
| __index_level_0__
float64 0
11.7k
β |
|---|---|
Question: a 300 meter long train crosses a platform in 33 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
A.250.
B.266.
C.230.
D.288.
e ) 271A.
"speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 33 = 50 / 3 3 ( x + 300 ) = 1650 Γ¨ x = 250 m . answer : a" | null |
Question: bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p and q , having each turn together to fill the empty drum ?
A.30.
B.45.
C.50.
D.25.
e ) 60B.
"let capacity of p be x liters then capacity of q = x / 3 liters capacity of the drum = 60 x required number of turns = 60 x / ( x + x / 3 ) = 60 x * 3 / 4 x = 45 answer is b" | null |
Question: mr . loyd wants to fence his square shaped land of 120 sqft each side . if a pole is laid every 10 ft how many poles do he need ?
A.20.
B.30.
C.48.
D.50.
e ) 60C.
"if each side is 120 feet . . then total perimeter is 120 * 4 = 480 poles every 10 feet hence no of poles = 480 / 10 = 48 answer : c" | null |
Question: if 4 / ( 1 + 3 / x ) = 1 , then x =
A.3.
B.1.
C.1 / 3.
D.- 1 / 3.
e ) - 3B.
"the expression 4 / ( 1 + 3 / x ) = 1 should have been equal to something . if 4 / ( 1 + 3 / x ) = 1 = > 4 x / ( x + 3 ) = 1 = > 4 x = x + 3 = > 3 x = 3 = > x = 1 correct option : b" | null |
Question: a 16 % stock yielding 10 % is quoted at :
A.83.33.
B.110.
C.112.
D.120.
e ) 160E.
"solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 16 , money invested = rs . ( 100 / 10 x 16 ) = rs . 160 . Γ’ Λ Β΄ market value of rs . 100 stock = rs . 160 answer e" | null |
Question: there are , in a certain league , 20 teams , and each team face another team for a total of 10 times . how many games are played in the season ?
A.1900.
B.3600.
C.2400.
D.180.
e ) 5400A.
"1 st team : 190 2 nd team : 180 3 rd team : 170 similarly the last team will play 0 therefore ( 190 + 180 + 170 . . . . 10 ) 10 ( 19 + 18 + 17 + 16 . . . . 1 ) 10 ( n ( n + 1 ) / 2 ) = 10 ( 19 * 20 / 2 ) = 1900 answer : a" | null |
Question: if integer k is equal to the sum of all even multiples of 15 between 390 and 615 , what is the greatest prime factor of k ?
A.5.
B.7.
C.8.
D.13.
e ) 17C.
"if we break down what the stem is asking what is the sum of all mult of 30 between 390 and 600 . using arithmetic progression to find n : 600 = 390 + ( n - 1 ) 30 210 + 30 = 30 n 240 = 3 n = > n = 8 the sum would be : 8 * mean mean = [ 600 + 390 ] / 2 = 495 8 * 495 c" | null |
Question: if x and y are positive integers and 3 + x + y + xy = 17 , what is the value of x + y ?
A.3.
B.5.
C.6.
D.8.
e ) 9C.
"try each answer choice . for a : 3 + 3 + xy = 17 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 3 + 5 + xy = 17 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 3 + 6 + xy = 17 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 3 + 8 + xy = 17 ; xy = 6 ( no combination of xy = 6 and x + y = 8 ) for e : 3 + 9 + xy = 17 ; xy = 5 ( impossible , 5 prime number . 1 + 5 does n ' t equal 9 ) therefore , answer c ." | null |
Question: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 54 , what is the total amount ?
A.166.
B.105.
C.178.
D.177.
e ) 210E.
"x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 54 35 - - - ? = > 210 answer : e" | null |
Question: the expenditure of a businessman increase consistently by 10 % per year . if his present expenditure is rs . 20000 then what will his expenditure be after 2 years ?
A.24500.
B.24400.
C.24300.
D.24200.
e ) 24100D.
explanation : expenditure = 20000 x 1.1 x 1.1 = 24200 answer : option d | null |
Question: farm tax is levied on the 25 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
A.15 %.
B.25 %.
C.50 %.
D.0.2083 %.
e ) noneC.
"this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 25 ) = 50 % the correct answer is ( c ) ." | null |
Question: a textile manufacturing firm employees 100 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 100 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
A.13000.
B.7000.
C.10000.
D.3500.
e ) none of theseD.
"explanation : profit = 5 , 00,000 Γ’ Λ β ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 Γ£ β ( 99 / 100 ) Γ’ Λ β 150000 Γ£ β ( 99 / 100 ) Γ’ Λ β 75000 . = > rs 2 , 68,000 . decrease in profit = > 2 , 75,000 Γ’ Λ β 2 , 71,500 = > rs . 3,500 . answer : d" | null |
Question: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 18 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
A.30 min ..
B.41 min ..
C.17 min ..
D.23 min ..
e ) 25 min .A.
"the ratio is 2 : 3 = gym : ride , so ( 18 ) ( 3 / 2 ) = 27 minutes at the gym , and 27 + 18 = 45 minutes exercise , so ( 2 / 3 ) ( 45 ) = 30 minutes yoga . answer : a" | null |
Question: when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 8 , the quotient is 3 y and the remainder is 1 . what is the value of 13 y β x ?
A.2.
B.3.
C.4.
D.5.
e ) 6B.
( 1 ) x = 11 y + 4 ( 2 ) 2 x = 24 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 13 y - 3 = x 13 y - x = 3 the answer is b . | null |
Question: what is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad ?
['A.814', 'B.266', 'C.287', 'D.999', 'e ) 661']A.
explanation : length of largest tile = h . c . f . of 1517 cm and 902 cm = 41 cm . area of each tile = required number of tiles = = 814 answer : a ) 814 | null |
Question: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is seven times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
A.1 : 1.
B.2 : 3.
C.3 : 2.
D.9 : 4.
e ) 63 : 8E.
"water : soap = 3 : 2 soap : salt = 21 : 2 = > for 21 soap , salt = 2 = > for 2 soap , salt = ( 2 / 21 ) * 2 = 4 / 21 so , water : soap : salt = 3 : 2 : 4 / 21 = 63 : 42 : 4 after open container , water : soap : salt = 31.5 : 42 : 4 so , water : salt = 31.5 : 4 = 63 : 8 e" | null |
Question: if a drawing has an outer circle of diameter 30 and an inner circle of diameter 24 , then what fraction of outer circle ' s surface is not covered by the inner circle ?
['A.3 / 6', 'B.8 / 24', 'C.14 / 16', 'D.9 / 25', 'e ) 2 / 3']D.
the questions asks us to find the surface which is not covered by the inner circle i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the inner circle = pi * r ^ 2 , where r = 12 = > pi * 144 area of the outer circle = pi * 225 surface not covered by the inner circle = pi * 225 - pi * 144 = pi * 81 fraction of outer circle ' s surface is not covered by the inner circle = pi * 81 / total area of the outer circle = > pi * 81 / pi * 225 = 9 / 25 answer is d | null |
Question: the sum of three consecutive even numbers is 366 . find the middle number of the three ?
A.111.
B.123.
C.122.
D.152.
e ) 142C.
"middle number = 366 / 3 = 122 ans c" | null |
Question: x can finish a work in 24 days . y can finish the same work in 16 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?
A.3.
B.5.
C.6.
D.8.
e ) 9E.
"work done by x in 1 day = 1 / 24 work done by y in 1 day = 1 / 16 work done by y in 10 days = 10 / 16 = 5 / 8 remaining work = 1 β 5 / 8 = 3 / 8 number of days in which x can finish the remaining work = ( 3 / 8 ) / ( 1 / 24 ) = 9 e" | null |
Question: some of 45 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?
A.2 / 5.
B.1 / 4.
C.1 / 5.
D.1 / 7.
e ) 2 / 3B.
"let total paint = 1 let amount replaced = x 45 ( 1 - x ) + 25 x = 40 x = 1 / 4 answer : b" | null |
Question: what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ?
A.e = 5.
B.e = 9.
C.e = 10.
D.e = 20.
e ) 30D.
"what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20" | null |
Question: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 59 ?
A.3944.
B.920.
C.7290.
D.6928.
e ) 4012E.
"explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 59 = rs . 4012 . answer : option e" | null |
Question: if the sum of two numbers is 45 and the h . c . f and l . c . m of these numbers are 4 and 5 respectively , then the product of the reciprocals is equal to :
A.20 / 20.
B.1 / 1.
C.2 / 30.
D.11 / 20.
e ) 1 / 20E.
"let the numbers be a and b . then , a + b = 45 and ab = 5 * 4 = 20 . required product = 1 / a * 1 / b = 1 / ab = 1 / 20 = 1 / 20 . answer : e" | null |
Question: at jerri β s pet shop , 60 cups of bird seed are used every 5 days to feed 20 parakeets . how many cups of bird seed would be required to feed 10 parakeets for 5 days ?
A.45.6.
B.20.
C.9.
D.30.
e ) 65D.
let ' s go step - by - step . 60 cups are used over a 5 day period , which means 12 cups a day . this feeds 20 parakeets , which means each parakeet needs . 60 of a cup every day . for 10 parakeets , we need 10 * . 60 cups = 6 cups a day . over 5 days , we need 30 cups . choice d . | null |
Question: find the value of x : 2 x Β² β 4 .
A.0,2.
B.- 2,2.
C.- 2,1.
D.0,4.
e ) - 1,4B.
that quadratic is factored as follows : 2 x Β² β 4 = ( 2 x β 2 ) ( x + 2 ) . now , it is easy to see that the second factor will be 0 when x = β 2 . as for the value of x that will make 2 x β 4 = 0 , we must solve that equation we have : 2 x = 4 x = 2 the solutions are : x = - 2 and 2 b | null |
Question: a jar of 180 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
A.16.
B.18.
C.20.
D.22.
e ) 24B.
"180 = 18 * 10 = 20 * 9 there are 18 people in the group today . the answer is b ." | null |
Question: a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is :
A.18.
B.17.
C.76.
D.85.
e ) 86D.
"let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d" | null |
Question: the average of first 5 multiples of 5 is
A.3.
B.6.
C.9.
D.12.
e ) 15E.
solution average = 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 75 / 5 . = 15 answer e | null |
Question: a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 50 percent of the drive from the center , what percent of the round - trip has the technician completed ?
A.70.
B.65.
C.60.
D.75.
e ) 80D.
"round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 50 % of 50 % i . e 25 % . so he completed 50 + 25 = 75 % of total trip . d" | null |
Question: the difference of two numbers is 1415 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
A.A.270.
B.B.280.
C.C.290.
D.D.300.
e ) e ) 310B.
let the smaller number be x . then larger number = ( x + 1415 ) . x + 1415 = 6 x + 15 5 x = 1400 x = 280 smaller number = 280 . b ) | null |
Question: the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 25 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
A.32.5.
B.77.78.
C.48.
D.65.
e ) 67.5B.
"1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 56.25 4 ) now 56.25 has to be added byx % in order to equal the original price . 56.25 + ( x % ) 56.25 = 100 . solving this eq for x , we get x = 77.78 ans is b ." | null |
Question: there is a 50 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 50 cm , how many insects were still left after the race was over ?
A.0.
B.4.
C.6.
D.8.
e ) 11E.
"only the prime numbers greater than 10 and less than 50 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , and 47 . the total is 11 . the answer is e ." | null |
Question: of the 180 people at a party , 70 were women , and 30 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?
A.40.
B.50.
C.60.
D.70.
e ) 100E.
"total people at party = 180 women = 70 so men 180 - 70 = 110 no . of pple who tried appetizer = 180 - 50 ( given info ) = 130 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 130 - 30 = 100 correct option e" | null |
Question: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 25 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
A.12.5 minutes ..
B.25 minutes.
C.35 minutes ..
D.35 minutes.
e ) 75 minutesA.
"if the distance between the two houses is d . then speed of danny = ( d / 25 ) speed of steve = ( d / 50 ) [ steve takes 50 minutes to reach danny ' s house . double the time taken by danny ) obviously speed of danny is twice that of steve . now in order to cover distance ( d / 2 ) [ they meet in middle ] , steve will take : ( d / 2 ) / ( d / 50 ) = 25 minutes . distance is same and danny ' s speed is twice of steve . thus he will take 12.5 minutes to cover this same distance . steve take 25 - 12.5 = 12.5 minutes longer . a is the answer ." | null |
Question: we run a business that rents out canoes and kayaks . a canoe rental costs $ 15 per day , and a kayak rental costs $ 18 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 405 in revenue . how many more canoes than kayaks were rented out ?
A.5.
B.6.
C.7.
D.8.
e ) 9A.
"let x be the number of canoes . then 2 x / 3 is the number of kayaks . 15 x + ( 2 x / 3 ) * 18 = 405 15 x + 12 x = 405 27 x = 405 x = 15 ( canoes ) 2 x / 3 = 10 ( kayaks ) there were 15 - 10 = 5 more canoes rented out . the answer is a ." | null |
Question: how many positive integers between 1 and 200 are there such that they are multiples of 17 ?
A.9.
B.11.
C.13.
D.10.
e ) 8B.
"multiples of 17 = 17 , 34,51 , - - - - - 187 number of multiples of 17 = > 17 * 11 = 187 answer is b" | null |
Question: in a company the manager wants to give some gifts to all of the workers . in each block there are about 100 workers are there . the total amount for giving the gifts for all the workers is $ 4000 . the worth of the gift is $ 4 . how many blocks are there in the company ?
A.12.
B.10.
C.15.
D.17.
e ) 20B.
each employee will get a gift worth of = $ 4 total employees = 4000 / 4 = 1000 total blocks = 1000 / 100 = 10 correct option is b | null |
Question: in what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
A.2.
B.7.
C.8.
D.6.
e ) 9D.
"t = 60 / 36 * 18 / 5 = 6 sec answer : d" | null |
Question: three pipes a , b and c can fill a tank from empty to full in 30 minutes , 20 minutes and 10 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution p in the liquid in the tank after 3 minutes ?
A.3 / 11.
B.2 / 11.
C.1 / 11.
D.4 / 11.
e ) 1 / 11B.
"part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 30 + 1 / 20 + 1 / 10 ) = 11 / 20 part filled by a in 3 minutes = 3 / 30 required ratio = 3 / 30 * 20 / 11 = 2 / 11 answer : b" | null |
Question: a man buys 54 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
A.7.6 %.
B.7.7 %.
C.16.21 %.
D.13.6 %.
e ) 7.8 %C.
"explanation : let marked price be re . 1 each c . p . of 54 pens = rs . 46 s . p . of 54 pens = 99 % of rs . 54 = rs . 53.46 profit % = ( profit / c . p . ) x 100 profit % = ( 7.46 / 46 ) x 100 = 16.21 % answer : c" | null |
Question: find the area of a cuboid of length 15 cm , breadth 10 cm . and height 16 cm .
A.2400 cm cube.
B.2410 cm cube.
C.2420 cm cube.
D.2430 cm cube.
e ) 2480 cm cubeA.
"area of a cuboid = lxbxh = 15 cm x 10 cm x 16 cm = 2400 cm cube answer : a" | null |
Question: a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 6 days . in how many days b alone can do the work ?
A.5 days.
B.7 days.
C.12 days.
D.9 days.
e ) 10 daysD.
"explanation : a β s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 6 x = 9 days answer : option d" | null |
Question: the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 15 and 41 inclusive .
A.351.
B.392.
C.410.
D.424.
e ) 450B.
"we ' re dealing with a sequence of consecutive odd integers : 15 to 41 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 15 + 41 = 56 2 ) now look at the ' next smallest ' and the ' next biggest ' : 17 + 39 = 56 now we have proof that there is no middle term . we have 7 bunches of 56 . 7 ( 56 ) = 392 b" | null |
Question: the cost price of a radio is rs . 1800 and it was sold for rs . 1430 , find the loss % ?
A.18 %.
B.20.5 %.
C.30 %.
D.45 %.
e ) 12 %B.
"1800 - - - - 370 100 - - - - ? = > 20.5 % answer : b" | null |
Question: when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in z hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of z ?
A.3 / 4.
B.1 [ 1 / 5 ].
C.1 [ 2 / 5 ].
D.1 [ 3 / 4 ].
e ) 2B.
"rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * z = 1 = > x = 1 / z when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / z = 4 / 3 = > 1 / z = ( 8 - 3 ) / 6 = 5 / 6 = > z = 6 / 5 = 1 [ 1 / 5 ] answer b" | null |
Question: a work crew of 6 men takes 8 days to complete one - half of a job . if 9 men are then added to the crew and the men continue to work at the same rate , how many days will it take the enlarged crew to do the rest of the job ?
A.2.
B.3.
C.3 1 / 5.
D.4.
e ) 4 4 / 5C.
"suppose 1 man can do work in x days . . so 4 men will do in . . 6 / x = 1 / 8 * 1 / 2 as half job is done x = 96 now 9 more are added then 15 / 96 = 1 / 2 * 1 / d for remaining half job d = 3 1 / 5 number of days c" | null |
Question: what is the dividend . divisor 17 , the quotient is 8 and the remainder is 5
A.A.145.
B.B.141.
C.C.150.
D.D.153.
e ) e ) 158B.
"d = d * q + r d = 17 * 8 + 5 d = 136 + 5 d = 141 answer : b" | null |
Question: a searchlight on top of the watch - tower makes 3 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 15 seconds ?
A.1 / 4.
B.1 / 3.
C.1 / 2.
D.2 / 3.
e ) 3 / 4A.
"3 revolutions per minute = 1 revolution every 20 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 20 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 15 seconds ) = 1 - p ( man in dark for max of 15 seconds ) = 1 - 15 / 20 = 1 - 3 / 4 = 1 / 4 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 20 seconds because that is the max . in this approach it would be 5 / 20 seconds = 1 / 4 . answer is a" | null |
Question: john and amanda stand at opposite ends of a straight road and start running towards each other at the same moment . their rates are randomly selected in advance so that john runs at a constant rate of 3 , 4 , or 5 miles per hour and amanda runs at a constant rate of 3 , 4 , 5 , 6 , or 7 miles per hour . what is the probability that john has traveled farther than amanda by the time they meet ?
A.1 / 2.
B.1 / 3.
C.1 / 5.
D.2 / 15.
e ) 4 / 15C.
john will run farther if he runs at 5 mph and amanda runs at 4 mph or 3 mph . in this case , p ( john runs farther ) = 1 / 3 * 2 / 5 = 2 / 15 john will run farther if he runs at 4 mph and amanda runs at 3 mph . in this case , p ( john runs farther ) = 1 / 3 * 1 / 5 = 1 / 15 p ( john runs farther ) = 2 / 15 + 1 / 15 = 3 / 15 = 1 / 5 the answer is c . | null |
Question: the average of numbers 0.64205 , 0.64203 , 0.64202 and 0.64201 is ?
A.0.64202.
B.0.64204.
C.0.642022.
D.0.642028.
e ) noneD.
"answer average = ( 0.64205 + 0.64203 + 0.64202 + 0.64201 ) / 4 = 2.56811 / 4 = 0.642028 correct option : d" | null |
Question: two bullet train s 140 m and 210 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
A.15.8 sec ..
B.12.6 sec ..
C.11.8 sec ..
D.10.8 sec ..
e ) 08.8 sec .B.
"relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 210 ) m = 350 m . required time = 350 x 9 / 250 = 54 / 5 = 12.6 sec . answer b" | null |
Question: 4 friends are pooling their money for pizza . emma has 8 dollars . daya has 25 % more money than emma , jeff has 2 / 5 of the money daya has , and brenda has 4 more dollars than jeff . how much money does brenda have ?
A.14.
B.6.
C.7.
D.8.
e ) 10D.
d 8 emma has 8 dollars . daya has 25 % more dollars than emma . daya = 8 + 8 x 25 % = 8 + 8 x . 25 = 8 + 2 = 10 jeff has 2 / 5 of what daya has . = 10 x 2 / 5 = 4 brenda has 4 more dollars than jeff . = 4 + 4 = 8 brenda has 8 dollars . the correct answer is d . | null |
Question: in one alloy there is 12 % chromium while in another alloy it is 8 % . 35 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
A.8.8 %.
B.9.75 %.
C.9.2 %.
D.8.6 %.
e ) 8.4 %B.
"the amount of chromium in the new 35 + 45 = 80 kg alloy is 0.12 * 35 + 0.08 * 45 = 7.8 kg , so the percentage is 7.8 / 80 * 100 = 9.75 % . answer : b ." | null |
Question: mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 26 miles , how many miles was mike ' s ride ?
A.20.
B.30.
C.36.
D.46.
e ) 54D.
"the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 26 ) = $ 14 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 14 0.25 * x = 11.5 x = 46 miles the answer is d ." | null |
Question: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.91 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
A.9 %.
B.10 %.
C.11 %.
D.12 %.
e ) 15 %C.
"let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.91 9.9 - 45 x + 36 x = 8.91 9 x = 0.99 x = 0.11 the answer is c ." | null |
Question: find the simple interest on $ 10000 at 4 % per annum for 12 months ?
A.$ 400.
B.$ 500.
C.$ 650.
D.$ 710.
e ) $ 1000A.
"p = $ 10000 r = 4 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 4 * 1 / 100 = $ 400 answer is a" | null |
Question: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 3 m 3 , then the rise in the water level in the tank will be :
A.20 cm.
B.25 cm.
C.35 cm.
D.18.75 cm.
e ) none of theseD.
"explanation : total volume of water displaced = ( 3 x 50 ) m 3 = 150 m 3 rise in water level = 150 / 40 Γ£ β 20 = 0.1875 m = 18.75 cm answer : d" | null |
Question: a contractor undertakes to built a walls in 50 days . he employs 40 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
A.60.
B.30.
C.35.
D.20.
e ) none of theseA.
"40 men complete 0.4 work in 25 days . applying the work rule , m 1 Γ d 1 Γ w 2 = m 2 Γ d 2 Γ w 1 we have , 40 Γ 25 Γ 0.6 = m 2 Γ 25 Γ 0.4 or m 2 = 40 Γ 25 Γ 0.6 / 25 Γ 0.4 = 60 men answera" | null |
Question: the average weight of 6 person ' s increases by 4.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
A.160 kg.
B.175 kg.
C.180 kg.
D.102 kg.
e ) 190 kgD.
"total weight increased = ( 6 x 4.5 ) kg = 27 kg . weight of new person = ( 75 + 27 ) kg = 102 kg option d" | null |
Question: a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start ?
A.A.2.
B.B.5.
C.C.7.
D.D.5.
e ) e ) 1E.
"explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 60 40 d = 20 rs = 60 β 40 = 20 t = 20 / 10 = 1 hours answer : option e" | null |
Question: sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1500 , what is the gain percent ?
A.10 %.
B.15 %.
C.20 %.
D.25 %.
e ) 30 %D.
"selling price / total cost = 1500 / 1200 = 1.25 the gain percent is 25 % . the answer is d ." | null |
Question: a , b , c , d , e are the 5 electronic shops in the naza market , which have 20 , 30 , 60 , 80 and 50 t . v . sets with them respectively , then the average number of t . v . sets in each shop is
A.24.
B.48.
C.50.
D.60.
e ) noneB.
answer average number of t . v . sets = ( 20 + 30 + 60 + 80 + 50 ) / 5 = 48 correct option : b | null |
Question: a no . when divided by 281 gives a remainder 160 , what remainder will be obtainedby dividingthe same no . 21 ?
A.21.
B.22.
C.23.
D.24.
e ) 25A.
"281 + 160 = 441 / 21 = 21 ( remainder ) a" | null |
Question: in the rectangular coordinate system , points ( 16 , 0 ) and ( β 16 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
A.2.
B.4.
C.8.
D.16.
e ) none of the aboveD.
"d it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 16 d" | null |
Question: the speed of a railway engine is 74 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of compartments that can be carried by the engine is :
A.49.
B.18.
C.16.
D.17.
e ) 19E.
"the reduction in speed is directly proportional to the square root of the number of compartments attached doesreductionmean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 74 - k * sqrt ( n ) wherekis a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 74 - k * sqrt ( 9 ) = 74 - 3 k k = 16.67 now , we need to know : what value of n makes s go to zero ? 0 = 74 - 16.67 * sqrt ( n ) 16.67 * sqrt ( n ) = 74 sqrt ( n ) = 4.44 n = 4.44 ^ 2 > 19 with 20 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 19 is the maximum number of cars the engine can pull and still move . e" | null |
Question: the sum of even numbers between 1 and 31 is
A.16.
B.128.
C.240.
D.512.
e ) noneC.
"solution required numbers are 2 , 4 , 6 , . . 30 . this is an a . p containing 15 terms . required sum = n / 2 ( first term + last term ) βΉ = βΊ 15 / 2 ( 2 + 30 ) βΉ = βΊ 240 . answer c" | null |
Question: find value for x from below equation ? x + 1 = - 3
A.1.
B.- 4.
C.- 1.
D.2.
e ) 3B.
"1 . subtract 1 from both sides : x + 1 - 1 = - 3 - 1 2 . simplify both sides : x = - 4 b" | null |
Question: if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 50 , what is the value of c Γ’ Λ β a ?
A.25.
B.10.
C.90.
D.14.
e ) it can not be determined from the information givenB.
"the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 100 - - 2 subtracting 1 from 2 we have c - a = 10 ; answer : b" | null |
Question: a certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday ( inc . the first day it was planted ) . if this plant grew by 30 % b / w the 4 th day and 10 th day after it was planted , how many feet per day does the plant grow
A.A.2.
B.B.4.5.
C.C.0.69.
D.D.5.5.
e ) e ) 3C.
if the plant is 11 feet tall when it is planted , it will be 11 + k feet tall at the end of the day ( where k is the constant length it grows by every day ) . similarly , at the end of the 4 th day the plant must be 11 + 4 k feet tall and at the end of the 10 th day it must be 11 + 10 k feet tall . therefore 6 k = 0.3 ( 11 + 4 k ) = > k = 0.69 therefore the plant grows by 0.69 feet every day . option ( c ) | null |
Question: 6,61 , 212,507 , _ ?
A.974.
B.994.
C.954.
D.845.
e ) 754B.
"( 2 ) 3 - 2 = 6 ( 4 ) ^ 3 - 3 = 61 ( 6 ) ^ 3 - 4 = 212 ( 8 ) ^ 3 - 5 = 507 ( 10 ) ^ 3 - 6 = 994 answer : b" | null |
Question: john and steve are speed walkers in a race . john is 14 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john β s final push ?
A.13 seconds.
B.17 seconds.
C.26 seconds.
D.32 seconds.
e ) 51 secondsD.
"let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 14 + 2 - - - > 0.5 t = 16 - - - > t = 32 seconds . d is the correct answer ." | null |
Question: the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing theaverage by 4 year . find what was theoriginal strength of class ?
A.11.
B.12.
C.17.
D.19.
e ) 21B.
"let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 β 40 y + 384 = 36 y + 432 β 4 y = 48 β΄ y = 12 b" | null |
Question: running at the same constant rate , 5 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
A.648.
B.1,800.
C.2,160.
D.10,800.
e ) 64,800C.
"5 machines produce 270 bottles per minute ; 1 machine produces 270 / 5 = 54 bottles per minute ; 10 machines produce 54 * 10 = 540 bottles per minute ; in 4 minutes 10 machines produce 540 * 4 = 2,160 bottles . answer : c ." | null |
Question: the radius of the wheel of a bus is 100 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
A.175.
B.250.
C.300.
D.330.
e ) none of theseA.
"radius of the wheel of bus = 100 cm . then , circumference of wheel = 2 Γ― β¬ r = 200 Γ― β¬ = 628.57 cm distance covered by bus in 1 minute = 66 Γ’ Β β 60 Γ£ β 1000 Γ£ β 100 cms distance covered by one revolution of wheel = circumference of wheel = 440 cm Γ’ Λ Β΄ revolutions per minute = 6600000 / 60 Γ£ β 628.57 = 175 answer a" | null |
Question: what is the smallest positive integer x , such that 1944 x is a perfect cube ?
A.4.
B.3.
C.8.
D.12.
e ) 18B.
"take out the factors of 1944 that will come 2 ^ 3 * 3 ^ 3 * 3 ^ 2 . for perfect cube you need every no . raise to the power 3 . for 1944 to be a perfect cube , need 1 3 that means = 3 b is the answer ." | null |
Question: if n is an integer and 101 n ^ 2 is less than or equal to 6400 , what is the greatest possible value of n ?
A.7.
B.8.
C.9.
D.10.
e ) 11A.
101 * n ^ 2 < = 6400 n ^ 2 < = 6400 / 101 which will be less than 81 since 6400 / 100 = 64 which is the square of 9 next closest value of n where n ^ 2 < = 64 is 7 ans a | null |
Question: a number whose fifth part increased by 5 is equal to its fourth part diminished by 5 is ?
A.160.
B.180.
C.200.
D.220.
e ) noneC.
"answer let the number be n . then , ( n / 5 ) + 5 = ( n / 4 ) - 5 β ( n / 4 ) - ( n / 5 ) = 10 β ( 5 n - 4 n ) / 20 = 10 β΄ n = 200 option : c" | null |
Question: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 390 m long ?
A.38 sec.
B.35 sec.
C.44 sec.
D.40 sec.
e ) 60 secE.
"explanation : speed = 45 km / hr = 45 Γ ( 10 / 36 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 390 = 750 meter time taken to cross the platform = 750 / ( 25 / 2 ) = 750 Γ 2 / 25 = 60 seconds answer : option e" | null |
Question: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 500 more than d , what is a ' s share ?
A.rs . 2500.
B.rs . 1000.
C.rs . 1500.
D.rs . 2000.
e ) noneA.
sol . let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 500 β x = 500 . β΄ a ' s share = rs . 5 x = rs . ( 5 x 500 ) = rs . 2500 . answer a | null |
Question: a certain high school has 500 students . of these students , 50 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
A.430.
B.440.
C.450.
D.460.
e ) 470B.
"we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 50 y = 20 z = 10 so , we have 50 students taking music , 20 taking art and 10 taking both music and art . 40 student taking just music 10 student taking just art 10 student taking both music and art total = 60 students we ' re asked for the total number of students who are taking neither course . that is 500 - 60 = 440 . b" | null |
Question: praveen starts business with rs . 3920 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari β s contribution in the capital ?
A.s . 10080.
B.s . 8000.
C.s . 8500.
D.s . 9000.
e ) s . 6000A.
"let hari β s capital be rs . x . then , 3920 * 12 / 7 x = 2 / 3 = > 14 x = 141120 = > x = 10080 . answer : a" | null |
Question: the ratio between b and y is 7 / 9 ; b and y are increased by 4 , what is the ratio between the new values of b and y ?
A.7 / 9.
B.14 / 9.
C.7 / 18.
D.11 / 13.
e ) it can not be determinedE.
ratio = 7 k / 9 k = 7 / 9 , 14 / 18 , etc . b and y are increased by 4 - - > ( 7 k + 4 ) / ( 9 k + 4 ) new ratio can be 11 / 13 , 18 / 22 , etc . answer : e | null |
Question: the difference between simple interest and compound interest on rs . 1200 for one year at 10 % per annum reckoned half yearly is
A.2.
B.7.
C.3.
D.0.
e ) 8B.
"explanation : s . i = rs . ( 1200 x 10 x 1 / 100 ) = rs . 120 . c . i = rs [ ( 1200 x 1 + 5 / 100 ) Β² - 1200 ] = rs . 123 . difference = rs . [ 123 - 120 ] = rs . 3 . answer : b" | null |
Question: a woman can do a piece of work in 40 days . man is 25 % more efficient than woman . in how many days a man can do the same piece of work ?
A.32 days.
B.36 days.
C.38 days.
D.40 days.
e ) 53 daysA.
the ratio of the efficiencies of a woman and man = 100 : 125 = 4 : 5 the ratio of the days taken by woman and man to finish the work = 5 : 4 woman takes 32 days to finish the work . = > 5 parts = 40 the number of days taken by man to finish the work = 4 parts = 40 / 5 x 4 = 32 days a | null |
Question: if a ^ 2 + b ^ 2 = 144 and ab β 0 , then the greatest possible value for b is between
A.16 and 13.
B.12 and 3.
C.11 and 4.
D.10 and 5.
e ) 9 and 6B.
since a β 0 , greatest possible value for b will be less than 12 but closer to it . so it lies between 11 and 12 answer : b | null |
Question: the ratio between the present ages of a and b is 3.5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
A.14 : 4.
B.13 : 0.
C.15 : 11.
D.13 : 12.
e ) 13 : 17C.
"let the present ages of a and b be 3.5 x and 3 x years respectively . then , ( 3.5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 0.5 x = 8 = > x = 16 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 60 : 44 = 15 : 11 . answer : c" | null |
Question: ram , who is half as efficient as krish , will take 21 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
A.16 days.
B.12 days.
C.8 days.
D.7 days.
e ) 18 daysD.
"number of days taken by ram to complete task = 21 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 24 days is 21 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 21 w / 3 w = 7 days answer d" | null |
Question: calculate the l . c . m of 7 / 10 , 8 / 9 , 3 / 8 , 5 / 12 is :
A.840.
B.70.
C.740.
D.140.
e ) 940A.
required l . c . m = l . c . m . of 7 , 8 , 3 , 5 / h . c . f . of 10 , 9 , 8 , 12 = 840 / 1 = 840 answer is a | null |
Question: a circular mat with diameter 18 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ?
['A.5 / 12', 'B.3 / 5', 'C.1 / 2', 'D.3 / 8', 'e ) 5 / 6']D.
so we are looking for the area of the cloth over the area of the table area of the cloth = ( pi ) ( r ) ^ 2 which is about ( 3 ) ( 9 ) ( 9 ) area of the table = ( 24 ) ( 24 ) so the quick way to estimate is looking at the fraction like this : ( 3 / 24 ) ( 81 / 24 ) i hope this is easy to follow , so with some simplification i get ( 1 / 8 ) ( 3 ) = ( 3 / 8 ) answer is d | null |
Question: a man swims downstream 36 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
A.7.
B.8.
C.9.
D.2.
e ) 4C.
"36 - - - 3 ds = 12 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 12 + 6 ) / 2 = 9 answer : c" | null |
Question: the cash realised on selling a 14 % stock is rs . 109.25 , brokerage being 1 / 4 % is ?
A.366.
B.106.
C.102.
D.109.
e ) 122D.
"cash realised = rs . ( 109.25 - 0.25 ) = rs . 109 . answer : d" | null |
Question: the price of maruti car rises by 30 percent while the sales of the car come down by 20 % . what is the percentage change in the total revenue ?
A.- 4 %.
B.- 2 %.
C.+ 4 %.
D.+ 2 %.
e ) none of theseC.
solution : let initial price of maruti car be rs . 100 . as price increases 30 % , price of car will become , ( 100 + 30 % of 100 ) = rs . 130 . due to increase in price , sales is down by 20 % . it means , it is going make 20 % less revenue as expected after increment of price . so , new revenue = ( 130 - 20 % of 130 ) = rs . 104 . the initial revenue was rs . 100 which becomes rs . 104 at the end . it means there is 4 % increment in the total revenue . mind calculation method : 100 = = 30 % β ( price effect ) = = > 130 = = 20 % β ( sales effects ) = = > 104 . hence , 4 % rises . answer : option c | null |
Question: if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 21 ( q + 1 ) , what is the least possible value of p + q ?
A.36.
B.42.
C.44.
D.46.
e ) noneA.
"17 ( p + 1 ) = 21 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 21 / 17 - - > the least positive value of p + 1 is 21 , so the least value of p is 20 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 20 + 16 = 36 . answer : a ." | null |
Question: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ?
A.1 / 3.
B.2 / 5.
C.3 / 4.
D.3 / 2.
e ) 2 / 3B.
"a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 5 / 4 ) * 4 = 2 / 5 the answer is b ." | null |
Question: two numbers are in the ratio 3 : 4 . if their l . c . m . is 84 . what is sum of the numbers ?
A.49.
B.56.
C.76.
D.84.
e ) 85A.
"explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 84 = > 12 x = 84 = > x = 84 / 12 = 7 sum of the numbers = 3 x + 4 x = 7 x = 7 x 7 = 49 answer : option a" | null |
Question: three rugs have a combined area of 212 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?
A.18 square meters.
B.20 square meters.
C.24 square meters.
D.28 square meters.
e ) 30 square metersC.
"total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 212 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 24 . answer : c ." | null |
Question: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction q of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
A.11 / 14.
B.13 / 18.
C.4 / 7.
D.3 / 7.
e ) 3 / 14A.
"if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus q = 11 / 14 of the remaining votes must be against . answer : a ." | null |
Question: for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 20000 , my total savings for the two - year is
A.s . 8000.
B.s . 9000.
C.s . 9900.
D.s . 9990.
e ) s . 11000E.
"sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 20000 + 35000 ) = 66000 - 55000 = rs . 11000 e" | null |
Question: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 12 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
A.156.
B.146.
C.158.
D.187.
e ) 160A.
"a 156 sum = ( n x n ) + n hence , 12 x 12 = 144 + 12 = 156" | null |
Question: during a certain season , a team won 70 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
A.180.
B.170.
C.156.
D.150.
e ) 100E.
"we are first given that a team won 70 percent of its first 100 games . this means the team won 0.7 x 100 = 70 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t β 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t β 100 ) = number of wins for remaining games 0.5 t β 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 70 + 0.5 t β 50 = 0.7 t 20 = 0.2 t 200 = 2 t 100 = t answer is e ." | null |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.