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Question: the average marks of a class of 40 students is 44 and that of another class of 45 students is 70 . find the average marks of all the students ?
A.52.6.
B.52.4.
C.52.1.
D.69.5.
e ) 52.9D.
"sum of the marks for the class of 40 students = 40 * 44 = 1760 sum of the marks for the class of 45 students = 45 * 70 = 3150 sum of the marks for the class of 85 students = 2760 + 3150 = 5910 average marks of all the students = 5910 / 85 = 69.5 . answer : d" | null |
Question: { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number selected will be a solution of the equation ( x + 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 ?
A.1 / 12.
B.1 / 6.
C.1 / 4.
D.1 / 3.
e ) 1 / 2C.
roots of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 are x = - 5 , x = - 10 andx = 5 / 2 = 2.5 . so , three solutions present in our set of 12 distinct numbers , therefore p = 3 / 12 = 1 / 4 . answer : c . | null |
Question: a towel , when bleached , was found to have lost 20 % of its length and 10 % of its breadth . the percentage of decrease in area is
A.28 %.
B.30 %.
C.32 %.
D.38 %.
e ) 40 %A.
"let original length = x and original breadth = y . decrease in area = xy - 80 x x 90 y 100 100 = xy - 18 xy 25 = 7 xy . 25 decrease % = 7 xy x 1 x 100 % = 28 % . 25 xy a )" | null |
Question: 5 / 8 of 3 / 10 of a number is greater than 4 / 9 of 1 / 4 of the same number by 55 . what is half of that number ?
A.310.
B.312.
C.320.
D.314.
e ) 360E.
"let no . be x 5 / 8 * 3 / 10 * x - 4 / 9 * 1 / 4 * x = 55 by further solving 15 x / 80 - 4 x / 36 = 55 11 x / 144 = 55 x = 720 we have to find x / 2 = 720 / 2 = 360 answer : e" | null |
Question: the average of 10 numbers is calculated as 18 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
A.A.16.
B.B.18.
C.C.19.
D.D.22.
e ) e ) 24C.
"explanation : 10 * 18 + 36 – 26 = 190 = > 190 / 10 = 19 c )" | null |
Question: the speed of a boat in still water in 42 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 44 minutes is :
A.86.6 km.
B.46.6 km.
C.34.5 km.
D.35.6 km.
e ) 26.6 kmC.
"speed downstream = ( 42 + 5 ) = 47 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 47 = 34.5 km answer : c" | null |
Question: what is the remainder when 1024 * 1047 * 1050 * 1053 is divided by 33 ?
A.3.
B.27.
C.30.
D.21.
e ) 18A.
"take the remainder from each of 1024 / 33 , 1047 / 33 and so on . . 1024 / 33 gives remainder = 1 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 1 * 24 * 27 * 30 break them into pairs 1 * 24 / 33 gives remainder 24 and 27 * 30 / 33 gives remainder 18 so 24 * 18 / 33 gives remainder 3 . a" | null |
Question: the average of first 20 natural numbers is ?
A.10.5.
B.11.4.
C.5.3.
D.5.9.
e ) 5.1A.
"sum of 20 natural no . = 420 / 2 = 210 average = 210 / 20 = 10.5 answer : a" | null |
Question: by investing in 1623 % stock at 64 , one earns rs . 1500 . the investment made is
A.rs . 9600.
B.rs . 7500.
C.rs . 5640.
D.rs . 5760.
e ) rs . 6760D.
"explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1500 , investment needed = 64 × 3 × 1500 / 50 = 5760 answer : option d" | null |
Question: the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1240 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?
A.2480.
B.3490.
C.6785.
D.8215.
e ) 9255D.
"sum of square of n numbers is found using the formula [ n ( n + 1 ) ( 2 n + 1 ) ] / 6 we have sum of 1 st 15 numbers = 1240 we need to find sum of squares from 16 to 30 which is = sum of squares of 1 st 30 + ve integers - sum of squares of 1 st 15 + ve integers . we will get d - 8215 ; answer : d" | null |
Question: in a department store prize box , 40 % of the notes give the winner a dreamy vacation ; the other notes are blank . what is the approximate probability that 3 out of 5 people that draw the notes one after the other , and immediately return their note into the box get a dreamy vacation ?
A.0.12.
B.0.23.
C.0.35.
D.0.45.
e ) 0.65B.
the probability of winning is 40 % = 40 / 100 = 2 / 5 . the probability of not winning is 60 % = 3 / 5 . p ( wwwnn ) = 5 ! 3 ! 2 ! ∗ ( 25 ) 3 ∗ ( 35 ) 2 = 144625 ≈ 23 p ( wwwnn ) = 5 ! 3 ! 2 ! ∗ ( 25 ) 3 ∗ ( 35 ) 2 = 144625 ≈ 23 ( we multiply by 5 ! 3 ! 2 ! 5 ! 3 ! 2 ! , because wwwnn scenario can occur in several ways : wwwnn , wwnwn , wnwwn , nwwwn , . . . the # of such cases basically equals to the # of permutations of 5 letters wwwnn , which is 5 ! 3 ! 2 ! 5 ! 3 ! 2 ! ) . answer : b . | null |
Question: if the volume of the cube is 729 cm 3 , then the surface area of the cube will be
['A.486 sq . cm', 'B.456 sq . cm', 'C.446 sq . cm', 'D.476 sq . cm', 'e ) none of these']A.
explanation : a 3 = 729 ; a = 9 surface area = ( 6 x 9 x 9 ) = 486 cm 2 answer : a | null |
Question: what is the rate percent when the simple interest on rs . 1600 amount to rs . 200 in 4 years ?
A.4 %.
B.3.125 %.
C.5 %.
D.6 %.
e ) 7 %B.
"interest for 1 year = 200 / 4 = 50 interest on rs 1600 p / a = 50 interest rate = 50 / 1600 * 100 = 3.125 % answer : b" | null |
Question: if the simple interest on a certain sum of money for 2 years is one – fifth of the sum , then the rate of interest per annum is
A.14 %.
B.7 %.
C.10 %.
D.15 %.
e ) 3 %C.
"explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 2 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 2 ) = 20 / 2 = 10 % answer : option c" | null |
Question: a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , c sitting together ?
A.3 / 14.
B.5 / 28.
C.3 / 28.
D.1 / 7.
e ) 9 / 28C.
total number of arrangement is = 8 ! = 40320 favorable event i . e ) a , b and c can be arranged in 3 ! and the remaining can be arranged in 6 ! since ab can be in any of the four positions . so 3 ! * 6 ! / 8 ! = 3 / 28 answer : c | null |
Question: there are 2 sections a and b in a class , consisting of 50 and 50 students respectively . if the average weight of section a is 60 kg and that of section b is 80 kg , find the average of the whole class ?
A.50.78 kg.
B.49.32 kg.
C.61.67 kg.
D.70 kg.
e ) 70.89 kgD.
"total weight of 50 + 50 students = 50 * 60 + 50 * 80 = 3000 + 4000 average weight of the class is = 7000 / 100 = 70 kg answer is d" | null |
Question: in a school with 632 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
A.150.
B.200.
C.250.
D.158.
e ) noneD.
"sol . let the number of grils be x . then , number of boys = ( 632 - x ) . then , ( 11 3 / 4 × 632 ) ⇔ 11 x + 12 ( 632 - x ) ⇔ x = 7584 - 7426 ⇔ 158 . answer d" | null |
Question: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.15 km and 0.6 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
A.42.
B.9.
C.7.
D.67.
e ) 15A.
": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.15 + 0.6 = 1.75 km = 1750 m . required time = 1750 * 3 / 125 = 42 sec . answer : a" | null |
Question: sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 152 . if the ratio of his marks in english and maths is 1 : 5 , find his marks in science ?
A.8.
B.77.
C.66.
D.55.
e ) 31A.
"s : e = 1 : 3 e : m = 1 : 5 - - - - - - - - - - - - s : e : m = 1 : 3 : 15 1 / 19 * 152 = 8 answer : a" | null |
Question: the salary of a person was reduced by 28 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
A.10 %.
B.15 %.
C.20 %.
D.25 %.
e ) 38.9 %E.
"let the original salary be $ 100 new salary = $ 72 increase on 72 = 28 increase on 100 = [ ( 28 / 72 ) 100 ] % = 38.9 % answer is e" | null |
Question: the average height of 35 boys in a class was calculated as 183 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
A.187.89 cm.
B.181.29 cm.
C.123.98 cm.
D.149.98 cm.
e ) 146.89 cmB.
"calculated average height of 35 boys = 183 cm . wrong total height of 35 boys = 183 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm - 106 cm ) / 35 = 183 cm - 60 / 35 cm = 183 cm - 1.71 cm = 181.29 cm . answer : b" | null |
Question: a is half good a work man as b and together they finish a job in 14 days . in how many days working alone b finish the job ?
A.23.
B.22.
C.21.
D.36.
e ) 48C.
"c 21 wc = 1 : 2 2 x + x = 1 / 14 = > x = 1 / 42 2 x = 1 / 21 = > 21 days" | null |
Question: each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.55 % , what fraction of the products was checked by worker y ?
A.1 / 3.
B.1 / 4.
C.1 / 5.
D.1 / 6.
e ) 1 / 8D.
"x : 0.5 % is 0.05 % - points from 0.55 % . y : 0.8 % is 0.25 % - points from 0.55 % . therefore the ratio of products checked by y : x is 1 : 5 . thus , worker y checked 1 / 6 of the products . the answer is d ." | null |
Question: a baseball card decreased in value 40 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
A.28 %.
B.30 %.
C.32 %.
D.46 %.
e ) 72 %D.
"consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.6 = 60 after second year price = 60 * 0.9 = 54 final decrease = [ ( 100 - 54 ) / 100 ] * 100 = 46 % correct answer - d" | null |
Question: from a group of 3 boys and 3 girls , 4 children are to be randomly selected . what is the probability that equal numbers of boys and girls will be selected ?
A.1 / 10.
B.4 / 9.
C.1 / 2.
D.3 / 5.
e ) 2 / 3D.
prob reqd = 1 - probab of not having eq numbers prob of not having eq no ' s is = prob of having 3 boys and 1 girl or prob of having 3 girls and 1 boy = ( 1 * 3 / 15 ) + ( 3 / 15 * 1 ) = 2 / 5 reqd prob = 1 - 2 / 5 = 3 / 5 answer : d | null |
Question: 9 years ago i was 5 times as old as my eldest son . today i am 3 times his age . how old am i now ?
A.45.
B.54.
C.34.
D.58.
e ) 56B.
x - 9 = 5 ( y - 9 ) & x = 3 y x - 9 = 5 x / 3 - 45 x = 54 answer : b | null |
Question: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
A.2 : 0.
B.2 : 3.
C.2 : 1.
D.2 : 2.
e ) 2 : 8B.
"by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 90 = 2 : 3 answer : b" | 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 4 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 quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ?
A.12 : 8.
B.8 : 16.
C.9 : 16.
D.8 : 12.
e ) 16 : 9C.
water : soap = 3 : 2 soap : salt = 12 : 8 = > for 12 soap , salt = 8 = > for 2 soap , salt = ( 8 / 12 ) * 2 = 16 / 12 = 4 / 3 so , water : soap : salt = 3 : 2 : 4 / 3 = 9 : 6 : 4 after open container , water : soap : salt = 2.25 : 6 : 4 so , water : salt = 2.25 : 4 = 9 : 16 answer : c | null |
Question: initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many q women are currently in the room ?
A.12.
B.14.
C.15.
D.24.
e ) 36D.
"the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number q = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d" | null |
Question: a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 225.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
A.$ 0.60.
B.$ 0.80.
C.$ 1.00.
D.$ 1.20.
e ) $ 1.60D.
"let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 225 = > 125 * s = 150 = > s = 1.2 answer d" | null |
Question: a and b invests rs . 3000 and rs . 5500 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
A.8 : 8.
B.9 : 8.
C.9 : 7.
D.9 : 5.
e ) 9 : 11E.
"( 3 * 6 + 6 * 6 ) : ( 5.5 * 12 ) 54 : 66 = > 9 : 11 answer : e" | null |
Question: if a lends rs . 3150 to b at 8 % per annum and b lends the same sum to c at 12.5 % per annum then the gain of b in a period of 2 years is ?
A.280.
B.295.
C.283.5.
D.245.
e ) 200C.
"( 3150 * 4.5 * 2 ) / 100 = > 283.5 answer : c" | null |
Question: apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 663 and for 36 kgs of apples is 726 then the cost of first 10 kgs of apples is
A.100.
B.150.
C.200.
D.350.
e ) 450C.
ans : by framing equations we get 30 l + 3 q = 663 30 l + 6 q = 726 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 20 cost of 10 kgs of apples = 10 x 20 = 200 answer : c | null |
Question: 10 + 19
A.29.
B.13.
C.28.
D.6.
e ) 2A.
a | null |
Question: a and b started a business investing rs . 80,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
A.4 : 1.
B.3 : 2.
C.18 : 20.
D.18 : 4.
e ) 17 : 4A.
"a : b = 80000 : 20000 = 8 : 2 = 4 : 1 answer : a" | null |
Question: a rower can row 7 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
A.2.92.
B.3.04.
C.3.12.
D.3.21.
e ) 3.35D.
let x be the distance to big rock . time = x / 5 + x / 9 = 1 x = 45 / 14 = 3.21 km the answer is d . | null |
Question: the average of first 35 prime numbers is ?
A.14.54.
B.15.6.
C.15.8.
D.14.7.
e ) 14.8A.
"explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 ) / 11 = 160 / 11 = 14.54 ( approx ) answer is a" | null |
Question: a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a women alone in 18 days , how long will a boy take to complete the work ?
A.6 days.
B.8 days.
C.9 days.
D.7 days.
e ) 5 daysC.
"explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 womans 1 day ’ s work = 1 / 18 ( 1 man + 1 woman ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 boys 1 day ’ s work = 1 / 3 – 2 / 9 = 3 - 2 / 9 = 1 / 9 therefore , the boy alone can finish the work in 9 days . answer : option c" | null |
Question: the least number which should be added to 1789 so that the sum is exactly divisible by 5 , 6 , 4 and 3 is ?
A.1.
B.11.
C.21.
D.31.
e ) 41B.
l . c . m . of 5 , 6 , 4 and 3 = 60 . on dividing 1789 by 60 , the remainder is 49 . number to be added = ( 60 - 49 ) = 11 b ) | null |
Question: i chose a number and divide it by 8 . then i subtracted 160 from the result and got 12 . what was the number i chose ?
A.1376.
B.1800.
C.1400.
D.2500.
e ) 100A.
"let x be the number i chose , then x / 8 − 160 = 12 x / 8 = 172 x = 1376 answer is a ." | null |
Question: solve for x and check : - 12 x = 72
A.- 4.
B.- 2.
C.- 6.
D.- 12.
e ) none of theseC.
"solution : dividing each side by - 12 , we obtain ( - 12 x / - 12 ) = ( 72 / - 12 ) therefore : x = - 6 check : - 12 x = 72 ( - 12 * - 6 ) = 72 72 = 72 answer : c" | null |
Question: a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 40 , how many horses are there ?
A.8.
B.12.
C.14.
D.16.
e ) 18A.
legs 8 * 4 = 32 now half on their horses so remaining on the walk so 4 men 4 men has 8 legs so , 8 + 32 = 40 legs walking answer : a | null |
Question: workers at a campaign office have 3000 fliers to send out . if they send out 1 / 5 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ?
A.1800.
B.800.
C.1100.
D.1200.
e ) 1900A.
"( 1 / 5 ) * 3000 = 600 remaining = 3000 - 600 = 2400 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 2400 = 600 remaining now = 2400 - 600 = 1800 answer : option a" | null |
Question: find the average of first 20 multiples of 7 ?
A.73.5.
B.70.5.
C.63.5.
D.54.5.
e ) 40.5A.
"required average = 7 ( 1 + 2 + 3 + … … . + 20 ) / 20 ( 7 * 20 * 21 ) / ( 20 * 2 ) ( 147 / 2 ) = 73.5 . answer a 73.5" | null |
Question: the diagonal of a rhombus are 70 m and 160 m . its area is :
A.1940.
B.4800.
C.5600.
D.5200.
e ) 5000C.
"area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 70 ã — 160 ) cm ( power ) 2 = 70 ã — 80 = 5600 cm ( power ) 2 answer is c ." | null |
Question: 50 % of a number is more than 40 % of 120 by 180 . find the number ?
A.456.
B.480.
C.420.
D.445.
e ) 320A.
"( 50 / 100 ) * x – ( 40 / 100 ) * 120 = 180 1 / 2 x = 228 x = 456 answer : a" | null |
Question: sheela deposits rs . 5000 in bank savings account . if this is 20 % of her monthly income . what is her monthly income in ?
A.22000.
B.20000.
C.25000.
D.22235.
e ) none of theseC.
"explanation : 20 % of income = rs . 5000 100 % of income = 5000 x 100 / 20 = rs . 25000 answer : c" | null |
Question: there are 4 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?
A.10.
B.8.
C.40.
D.60.
e ) 120B.
"each person is one participant of 4 games . so there are in all 4 * 4 = 16 instances of one participant games . but each game has 2 participants so total number of games = 16 / 2 = 8 b" | null |
Question: a 24 ' ' x 24 ' ' square metal plate needs to be fixed by a carpenter on to a wooden board . the carpenter uses nails all along the edges of the square such that there are 25 nails on each side of the square . each nail is at the same distance from the neighboring nails . how many nails does the carpenter use ?
['A.94', 'B.95', 'C.96', 'D.97', 'e ) 98']C.
every corner will have one , 4 corners will have 4 + and for 4 sides 23 no of nails = 4 + ( 4 * 23 ) = 96 answer : c | null |
Question: the sum of the ages of 5 children born at the intervals of 3 year each is 50 year . what is the age of the eldest child ?
A.16 year.
B.8 year.
C.10 year.
D.none of these.
e ) 9 yearA.
"solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 â ‡ ” 5 x = 20 â ‡ ” x = 4 . â ˆ ´ age of the eldest child = x + 12 = 4 + 12 = 16 years . answer a" | null |
Question: let the number which when multiplied by 15 is increased by 280 .
A.14.
B.20.
C.26.
D.28.
e ) 30B.
"solution let the number be x . then , 15 x - x = 280 ‹ = › 14 x = 280 x ‹ = › 20 . answer b" | null |
Question: in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 105 ?
A.24.
B.25.
C.26.
D.27.
e ) 28B.
"let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 105 5 x - 20 = 105 5 x = 125 x = 25 the answer is b ." | null |
Question: at 15 : 00 there were 22 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 8 students left the lab , how many students were in the computer lab at 15 : 44 ?
A.7.
B.14.
C.25.
D.27.
e ) 32E.
"initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 32 e" | null |
Question: 475.124 x 15.98 ÷ 8.001 + 33.33 = ?
A.983.578.
B.659.121.
C.781.189.
D.656.112.
e ) 456.512A.
"explanation : ? = 475.124 x ( 15.98 ÷ 8.001 ) + 33.33 ≈ ( 475.124 x 16 / 8 ) + 33.33 ≈ 950.248 + 33.33 ≈ 983.578 answer : option a" | null |
Question: 20 men can cut 30 trees in 4 hours . if 4 men leave the job , how many trees will be cut in 6 hours ?
A.24.
B.36.
C.48.
D.22.
e ) 32B.
"20 men - working 4 hrs - cut 30 trees 1 men - working 1 hr - cuts = 30 / 20 * 4 thus 16 men - working 6 hrs - cut = 30 * 16 * 6 / 20 * 4 = 36 trees answer is b" | null |
Question: 4 dices are thrown at the same time . what is the probability of getting only 2 dices showing the same face ?
A.4 / 9.
B.5 / 9.
C.11 / 18.
D.7 / 9.
e ) none of the aboveB.
probability of getting two same faces : 1 and 1 / 6 for other two faces , probabilities : 5 / 6 and 4 / 6 respectively . the dice combinations can be arranged in 4 ! / 2 ! ways total probability = 1 * 1 / 6 * 5 / 6 * 4 / 6 * 4 ! / 2 ! = 5 / 9 answer : b | null |
Question: mr . loyd wants to fence his square shaped land of 60 sqft each side . if a pole is laid every 12 ft how many poles do he need ?
A.20.
B.30.
C.40.
D.50.
e ) 60A.
"if each side is 120 feet . . then total perimeter is 60 * 4 = 240 poles every 12 feet hence no of poles = 240 / 12 = 20 answer : a" | null |
Question: the average of first six prime numbers greater than 20 is ?
A.10.
B.20.
C.30.
D.40.
e ) 34E.
"23 + 29 + 31 + 37 + 41 + 43 = 204 / 6 = 34 answer : e" | null |
Question: a boat having a length 7 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
A.100 kg.
B.120 kg.
C.89 kg.
D.80 kg.
e ) 210 kgE.
"volume of water displaced = ( 7 x 3 x 0.01 ) m 3 = 0.21 m 3 . mass of man = volume of water displaced x density of water = ( 0.21 x 1000 ) kg = 210 kg . answer : e" | null |
Question: 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 50 overs to reach the target of 282 runs ?
A.6.25.
B.5.5.
C.7.4.
D.5.
e ) 6D.
"explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 50 run rate needed = 250 / 50 = 5 answer : option d" | null |
Question: the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 0.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?
A.$ 2.00.
B.$ 3.00.
C.$ 3.50.
D.$ 4.00.
e ) $ 5.00A.
"number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 0.50 + 0.50 ( x − 2 ) = 0.50 + . 5 * 3 = 0.5 + 1.5 = 2 $ answer a" | null |
Question: if a : b : : 3 : 7 , then what is ( 5 a + 2 b ) : ( a - 2 b ) ?
A.57 : 11.
B.- 57 : 11.
C.11 : 10.
D.- 29 : 11.
e ) - 1 : 10D.
"a / b = 3 / 7 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 2 ] / [ ( a / b ) - 2 ] = [ 5 * ( 3 / 7 ) + 2 ] / [ ( 3 / 7 ) - 2 ] = - 29 / 11 answer : d" | null |
Question: in a group of 100 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
A.0.1.
B.0.55.
C.0.65.
D.0.75.
e ) 0.85A.
number of people whose age is less than 20 is given by 100 - 90 = 10 probability p that a person selected at random from the group is less than 20 is given by 10 / 100 = 0.1 correct answer a | null |
Question: an article is bought for rs . 1200 and sold for rs . 800 , find the loss percent ?
A.16 %.
B.35 %.
C.33 %.
D.18 %.
e ) 12 %C.
"1200 - - - - 400 100 - - - - ? = > 33 % answer : c" | null |
Question: how much is 80 % of 45 is greater than 4 / 5 of 25 ?
A.15.
B.57.
C.16.
D.16.
e ) 73C.
"( 80 / 100 ) * 45 â € “ ( 4 / 5 ) * 25 36 - 20 = 16 answer : c" | null |
Question: a small water pump would take 3 hours to fill an empty tank . a larger pump would take 3 / 4 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
A.3 / 4.
B.3 / 5.
C.5 / 7.
D.1 / 2.
e ) 4 / 5B.
"rate of the small pump is 1 / 3 tank / hour rate of the larger pump is 1 / ( 3 / 4 ) or 4 / 3 tank / hour ; combined rate of the two pumps is 1 / 3 + 4 / 3 = 5 / 3 tank / hour , together they will fill the empty tank in 1 / ( 5 / 3 ) ) = 3 / 5 hours ( time = job / rate ) . answer : b" | null |
Question: if p ( a ) = 5 / 7 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
A.7 / 25.
B.3 / 25.
C.8 / 25.
D.2 / 7.
e ) 3 / 17D.
"p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 5 / 7 . 2 / 5 p ( a n b ) = 2 / 7 . d" | null |
Question: divide rs . 5500 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 1 / 5 as a and c together . a ' s share is ?
A.1227.
B.1268.
C.1375.
D.1200.
e ) 1210C.
"a + b + c = 5500 a = 1 / 3 ( b + c ) ; b = 1 / 5 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 5500 = > 1375 answer : c" | null |
Question: in digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be ?
A.100 cu . m.
B.1000 cu . m.
C.10000 cu . m.
D.2000 cu . m.
e ) 4000 cu . mB.
"20 * 10 * 5 = 1000 answer : b" | null |
Question: in traveling from a dormitory to a certain city , a student went 1 / 3 of the way by foot , 3 / 5 of the way by bus , and the remaining 2 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
A.30.
B.45.
C.60.
D.90.
e ) 120A.
"whole trip = distance by foot + distance by bus + distance by car x = 1 / 3 x + 3 / 5 x + 2 x - 1 / 3 x - 3 / 5 x = 2 x = 30 km option : a" | null |
Question: a factory produces 6500 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
A.1375 toys.
B.2375 toys.
C.1300 toys.
D.1375 toys.
e ) 2375 toysC.
"to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 6500 / 5 = 1300 toys correct answer c" | null |
Question: a farmer spent $ 37 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
A.$ 37.80.
B.$ 38.50.
C.$ 39.20.
D.$ 39.50.
e ) $ 40.70E.
"a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 37 = $ 14.8 on chicken feed , thus he spent the remaining 37 - 14.8 = $ 22.2 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 14.8 - - > x = $ 18.5 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 18.5 + 22.2 = $ 40.7 . answer : e" | null |
Question: the charge for a single room at hotel p is 20 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 ?
A.15 %.
B.20 %.
C.12.5 %.
D.50 %.
e ) 150 %C.
"let rate in r = 100 x then p = 80 x g = 100 y p = 90 y thus 80 x = 90 y or x = 1.125 y ans r = 112.5 y so increase = 12.5 % answer : c" | null |
Question: the ratio of the volumes of two cubes is 729 : 125 . what is the ratio of their total surface areas ?
A.81 : 21.
B.81 : 22.
C.81 : 24.
D.81 : 25.
e ) 81 : 29D.
"ratio of the sides = 3 √ 729 : 3 √ 125 = 9 : 5 ratio of surface areas = 9 ^ 2 : 5 ^ 2 = 81 : 25 answer : option d" | null |
Question: how many multiples of 10 are there between 10 and 290 ?
A.8.
B.18.
C.27.
D.51.
e ) 60C.
"it should be mentioned whether 10 and 290 are inclusive . if 10 and 290 are inclusive , then the answer is ( 290 - 10 ) / 10 + 1 = 29 . if 10 and 290 are not inclusive , then the answer is ( 280 - 20 ) / 10 + 1 = 27 . since oa is c , then we have not inclusive case ." | null |
Question: what is the remainder when 1041 * 1047 * 1050 * 1053 is divided by 33 ?
A.3.
B.27.
C.30.
D.21.
e ) 18D.
"take the remainder from each of 1041 / 33 , 1047 / 33 and so on . . 1044 / 33 gives remainder = 18 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 18 * 24 * 27 * 30 break them into pairs 18 * 24 / 33 gives remainder 3 and 27 * 30 / 33 gives remainder 18 so 3 * 18 / 33 gives remainder 21 . d" | null |
Question: if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 170 , what is the value of a − c ?
A.− 120.
B.− 100.
C.100.
D.135.
e ) it can not be determined from the information givenA.
"a + b = 220 b + c = 340 a - c = - 120 . imo option a ." | null |
Question: line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 144 ) . what is the slope of line m ?
A.- 2.
B.- 1.
C.0.
D.1.
e ) 2D.
the midpoint of ( 2,8 ) and ( 14,4 ) is ( 8,6 ) . the slope of a line through ( 0 , - 2 ) and ( 8,6 ) is ( 6 - ( - 2 ) ) / ( 8 - 0 ) = 8 / 8 = 1 the answer is d . | null |
Question: the average weight of a , b and c is 60 kg . if the average weight of a and b be 70 kg and that of b and c be 50 kg , then the weight of b is :
A.50 kg.
B.60 kg.
C.55 kg.
D.57 kg.
e ) 62 kgB.
"explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 60 x 3 ) = 180 â € ¦ . ( i ) a + b = ( 70 x 2 ) = 140 â € ¦ . ( ii ) b + c = ( 50 x 2 ) = 100 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 240 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 60 . b â € ™ s weight = 60 kg . answer b" | null |
Question: length of a rectangular plot is 22 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
A.51 m.
B.61 m.
C.71 m.
D.81 m.
e ) 91 mB.
"let breadth = x metres . then , length = ( x + 22 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 22 ) + x ] = 200 2 x + 22 = 100 2 x = 78 x = 39 . hence , length = x + 22 = 61 m b" | null |
Question: a reduction of 20 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 600 , what is the reduced price for kg ?
A.20.
B.40.
C.36.
D.30.
e ) 35D.
"600 * ( 20 / 100 ) = 120 - - - - 4 ? - - - - 1 = > rs . 30 answer : d" | null |
Question: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 2500 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
A.2160.
B.2350.
C.2000.
D.2300.
e ) none of theseC.
"explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 2500 = 18000 exp in % = 100 - 10 = 90 % , 18000 = 90 % saving = 10 % = 18000 x 10 / 90 = rs . 2000 answer : c" | null |
Question: jim drove 384 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
A.113 miles.
B.432 miles.
C.456 miles.
D.816 miles.
e ) 767 milesD.
"the number of miles to drive to finish his journey is given by 1200 - 384 = 816 miles correct answer d" | null |
Question: find the product of the local value and absolute value of 4 in 564823
A.1600.
B.8000.
C.16000.
D.12000.
e ) 18000C.
explanation : place value = local value face value = absolute value the place value of 4 in 564823 is 4 x 1000 = 4000 the face value of 4 in 564823 is nothing but 4 . = > 4000 x 4 = 16000 answer : option c | null |
Question: the banker â € ™ s gain on a sum due 3 years hence at 10 % per annum is rs . 60 . the banker â € ™ s discount is
A.rs . 960.
B.rs . 840.
C.rs . 1020.
D.rs . 760.
e ) rs . 260E.
"solution t . d = ( b . g x 100 / r x t ) = rs . ( 60 x 100 / 10 x 3 ) = rs . 200 . b . d = rs ( 200 + 60 ) = rs . 260 . answer e" | null |
Question: robert ' s salary was decreased by 70 % and subsequently increased by 70 % . how much percentage does he lose ?
A.10 %.
B.20 %.
C.25 %.
D.30 %.
e ) 49 %E.
"let original salary be $ 100 salary after decreasing 70 % = 100 - 100 x 70 / 100 = $ 30 salary after increasing 70 % on $ 30 = 30 + 30 x 70 / 100 = $ 51 percentage of loss = 100 - 51 = 49 % answer : e" | null |
Question: a train covers a distance of 54 km in 15 min . if it takes 8 sec to pass a telegraph post , then the length of the train is ?
A.470.
B.480.
C.490.
D.500.
e ) 510B.
"speed = ( 54 / 15 * 60 ) km / hr = ( 216 * 5 / 18 ) m / sec = 60 m / sec . length of the train = 60 * 8 = 480 m . answer : option b" | null |
Question: the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number e ?
A.60.
B.80.
C.40.
D.120.
e ) 160B.
"( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = e answer : b" | null |
Question: what is the remainder when you divide 2 ^ 200 - 3 by 7 ?
A.1.
B.2.
C.3.
D.4.
e ) 5A.
answer is a . this is very similar to the 32 ^ 32 ^ 32 - 3 divided by 7 question . | null |
Question: the ratio of three numbers is 2 : 3 : 4 and their sum is 180 . the second number of the three numbers is ?
A.24.
B.60.
C.27.
D.29.
e ) 30B.
"2 : 3 : 4 total parts = 9 9 parts - - > 180 1 part - - - - > 20 the second number of the three numbers is = 3 * 20 = 60 answer : b" | null |
Question: if ( log 5 5 ) ( log 4 9 ) ( log 3 2 ) is equal to
A.1.
B.3 / 2.
C.2.
D.5.
e ) 7A.
solution given expression = log 9 / log 4 × log 2 / log 3 ‹ = › log 3 ² / log 2 ² × log 2 / log 3 = 2 log 3 / 2 log 2 × log 2 / log 3 = 1 . answer a | null |
Question: the total marks obtained by a student in mathematics and physics is 32 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
A.40.
B.26.
C.27.
D.28.
e ) 22B.
"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 32 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 32 + 20 ) / 2 = 26 . answer : b" | null |
Question: in the rectangular coordinate system , if the line x = 4 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
A.3.
B.2.
C.1 / 2.
D.1 / 3.
e ) 1 / 4C.
"x = 4 y + 5 , and thus y = x / 4 - 5 / 4 the slope is 1 / 4 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 4 and thus p = 1 / 2 the answer is c ." | null |
Question: the average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student . the weight of the student is
A.62 kg.
B.60 kg.
C.64 kg.
D.72 kg.
e ) none of theseC.
explanation : let the weight of student be x kg . given , difference in average weight = 8 kg = > ( 96 - x ) / 4 = 8 = > x = 64 answer : c | null |
Question: if 4 men working 10 hours a day earn rs . 800 per week , then 9 men working 6 hours a day will earn how much per week ?
A.rs 840.
B.rs 1320.
C.rs 1080.
D.rs 1680.
e ) none of theseC.
"explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 800 : x hence 4 * 10 * x = 9 * 6 * 800 or x = 9 * 6 * 800 / 4 * 10 = 1080 answer : c" | null |
Question: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 4.5 ) , ( 8 , 0 ) , ( 0 , - 4.5 ) , ( - 8 , 0 ) ?
A.56.
B.72.
C.112.
D.116.
e ) 120B.
"ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 4.5 + 4.5 = 9 area = 1 / 2 * 16 * 9 = 72 b is the answer" | null |
Question: a theater box office sold an average ( arithmetic mean ) of 63 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 78 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?
A.2 : 3.
B.1 : 4.
C.1 : 5.
D.6 : 11.
e ) 4 : 7C.
deviation from the mean for the daytime staff = 78 - 63 = 15 . deviation from the mean for the evening staff = 63 - 60 = 3 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 3 : 15 = 1 : 5 . the answer is c . | null |
Question: pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 9 : 00 am and pipe b at 10 : 00 am , at what time will the pool be full ?
A.19 : 00.
B.17 : 00.
C.16 : 00.
D.18 : 00.
e ) 20 : 00A.
pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 9 : 00 a . m and pipe b at 10 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 10 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 9 : 00 a . m , pool is full at 19 : 00 hrs answer : a | null |
Question: a train running at the speed of 100 km / hr crosses a pole in 9 sec . what is the length of the train ?
A.298 m.
B.250 m.
C.208 m.
D.988 m.
e ) 299 mB.
"speed = 100 * 5 / 18 = 250 / 9 m / sec length of the train = speed * time = 250 / 9 * 9 = 250 m answer : b" | null |
Question: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 45 meters . how many times did the ball bounce ?
A.5.
B.4.
C.7.
D.8.
e ) 9B.
"going down = 16 m going up = 8 - - > total = 24 going down = 8 - - > total = 32 going up = 4 - - > total = 36 going down = 4 - - > total = 40 going up = 2 - - > total = 42 going down = 2 - - > total = 44 going up = 1 - - > total = 45 ( caught ) no of bounce = 4 answer : b" | null |
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