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Question: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 14 % , then the cost price of the article is :
A.500.
B.540.
C.555.
D.664.
e ) 5598B.
"110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 114 = rs . 540 answer : option b" | null |
Question: the speed of a boat in still water is 14 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 8 minutes is
A.1.6 km.
B.2.5 km.
C.3.6 km.
D.4 km.
e ) none of theseB.
"explanation : speed downstreams = ( 14 + 5 ) kmph = 19 kmph . distance travelled = ( 19 x 8 / 60 ) km = 2.5 km option b" | null |
Question: what is the tens digit of 6 ^ 19 ?
A.1.
B.3.
C.5.
D.7.
e ) 9E.
the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 19 has the form 5 n + 4 , so the tens digit of 6 ^ 19 is 9 . the answer is e . | null |
Question: aa is two digit number then m times its cube of aa has 1 in its tens place then what is m .
A.3.
B.4.
C.5.
D.6.
e ) 7E.
when aa = 11 7 * ( 11 ) ^ 3 = 7 * 1331 = 9317 m = 7 answer : e | null |
Question: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability w that out of the two , one is white and one is blue ?
A.15 / 56.
B.41 / 56.
C.13 / 28.
D.15 / 28.
e ) 5 / 14D.
"the required probability w = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ." | null |
Question: the curved surface of a sphere is 64 Ο cm 2 . find its radius ?
['A.8', 'B.3', 'C.4', 'D.9', 'e ) 7']C.
explanation : 4 Ο r 2 = 64 = > r = 4 answer : option c | null |
Question: dhoni spent 25 percent of his earning last month on rent and 10 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?
A.50 %.
B.55 %.
C.60 %.
D.62 %.
e ) 52.5 %E.
"say dhoni ' s earning last month was $ 100 . dhoni spent 30 percent of his earning last month on rent - - > $ 25 on rent ; 10 percent less than what he spent on rent to purchase a new dishwasher - - > $ 25 * 0.9 = $ 22.5 on the dishwasher . left over amount 100 - ( 25 + 22.5 ) = $ 52.5 answer : e" | null |
Question: a present value of a machine is $ 800 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
A.$ 900.
B.$ 810.
C.$ 915.
D.$ 715.
e ) $ 648E.
"p = $ 800 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 800 * 9 / 10 * 9 / 10 = $ 648 answer is e" | null |
Question: the effective annual rate of interest corresponding to a nominal rate of 16 % per annum payable half - yearly is ?
A.16.64 %.
B.16.07 %.
C.16.08 %.
D.16.09 %.
e ) 16.19 %A.
"amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 8 / 100 ) 2 ] = rs . 116.64 effective rate = ( 116.64 - 100 ) = 116.64 % answer : a" | null |
Question: cost of 2 bats and 3 balls is rs . 1300 . the cost of 3 bats and 2 balls is rs . 1200 . the cost of each balls is more than that of each bat by ?
A.50.
B.100.
C.110.
D.120.
e ) 130B.
2 bats + 3 ball = 1300 - - - ( 1 ) 3 bats + 3 ball = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - bats + ball = 100 = > ball - bats = 100 b | null |
Question: m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 2 , - 1 , 1 , 2 , 3 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?
A.0.
B.1 / 3.
C.2 / 5.
D.1 / 2.
e ) 3 / 5E.
answer e . total # of outcomes : 5 * 5 = 25 # of outcomes where product is - ve : ( - 6,1 ) , ( - 6,2 ) , ( - 6,3 ) . . . hence , total : 15 probability : 15 / 25 = 3 / 5 | null |
Question: what will be the vulgar fraction of 0.5
A.3 / 5.
B.1 / 2.
C.3 / 2.
D.3 / 7.
e ) 3 / 8B.
"explanation : 0.5 = 50 / 100 = 1 / 2 option b" | null |
Question: what is the total cost of 2 sandwiches at $ 2.45 each and 4 sodas at $ 0.87 each ?
A.$ 8.38.
B.$ 6.85.
C.$ 8.46.
D.$ 10.08.
e ) $ 11.85A.
"answer = a 2 * 2.45 + 4 * 0.87 = 2 ( 2.50 - 0.05 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.1 - 0.52 = 9 - 0.62 = 8.38" | null |
Question: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 50 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
A.22.
B.27.
C.45.
D.99.
e ) 12C.
"relative speed = 50 + 30 = 80 km / hr . 80 * 5 / 18 = 200 / 9 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 9 / 200 = 45 sec . answer : c" | null |
Question: set x consists of all two - digit primes and set y consists of all positive even multiples of 5 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
A.87.
B.89.
C.90.
D.92.
e ) 95A.
"set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 10 , 20 , 30 , . . . . . . . . . . . . . . . , 70 , 80 , 90 } combining two sets , say set z set z = { 10,11 , 13 , 17 , 20,30 , . . . . . . . . . . . . . . . . . . . , 70 , 80 , 83 , 89 , 90 , 97 } range = max value - min value range ( z ) = 97 - 10 = 87 oa a is the answer ." | null |
Question: a woman complete a journey in 5 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
A.334 km ..
B.216 km ..
C.112 km ..
D.224 km ..
e ) 544 km .C.
"0.5 x / 21 + 0.5 x / 24 = 5 - - > x / 21 + x / 24 = 10 - - > x = 112 km . c" | null |
Question: a rectangular field is to be fenced on three sides leaving a side of 34 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
A.74 ft.
B.88 ft.
C.22 ft.
D.11 ft.
e ) 66 ftA.
"given that length and area , so we can find the breadth . length x breadth = area 34 x breadth = 680 breadth = 20 feet area to be fenced = 2 b + l = 2 ( 20 ) + 34 = 88 feet answer : a ) 74 ft" | null |
Question: how many shots of 1 cm radius can be prepared from a sphere of 6 cm radius ?
A.33.
B.88.
C.216.
D.288.
e ) 299C.
"4 / 3 Γ― β¬ * 6 * 6 * 6 = 4 / 3 Γ― β¬ * 1 * 1 * 1 * x x = 216 answer : c" | null |
Question: a man can do a piece of work in 5 days , but with the help of his son , he can finish it in 4 days . in what time can the son do it alone ?
A.5.
B.5 1 / 2.
C.7 1 / 2.
D.6.
e ) 20E.
"son ' s 1 day work = 1 / 4 - 1 / 5 = 1 / 20 son alone can do the work in 20 days = 20 days answer is e" | null |
Question: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the standard deviation for the exam ?
A.7.
B.6.
C.8.
D.0.
e ) 2C.
"mean - 2 sd = 58 mean + 3 sd = 98 by solving above equation we get , sd ( absolute value ) = 8 ans . c" | null |
Question: a man & his wife appear in an interview for 2 vacancies in the same post . the probability of husband ' s selection is 1 / 7 & the probability of wife ' s selection is 1 / 5 . what is the probability that only 1 of them is selected ?
A.1 / 3.
B.2 / 3.
C.2 / 7.
D.3 / 11.
e ) 4 / 5C.
let a = event that the husband is selected and b = event that the wife is selected . then , p ( a ) = 1 / 7 and p ( b ) = 1 / 5 β΄ p ( a Β― ) = ( 1 - 17 / 5 ) = 6 / 7 and = ( 1 - 1 / 5 ) = 4 / 5 required probability = p [ ( a and not b ) or ( b and not a ) ] = p [ ( a and b Β― ) or ( b and a Β― ) ] = p ( a and b Β― ) + p ( b and a Β― ) = p ( a ) . p ( b Β― ) + p ( b ) . p ( a Β― ) = ( 1 / 7 * 4 / 5 ) + ( 1 / 5 * 6 / 7 ) = 10 / 35 = 2 / 7 c | null |
Question: find the length of the wire required to go 11 times round a square field containing 27889 m 2 .
A.7348.
B.3388.
C.2667.
D.8766.
e ) 66711A.
"a 2 = 27889 = > a = 167 4 a = 668 668 * 11 = 7348 answer : a" | null |
Question: a movie buff owns movies on dvd and on blu - ray in a ratio of 7 : 2 . if she buys 4 more blu - ray movies , that ratio would change to 13 : 4 . if she owns movies on no other medium , what was the original number of movies in her library before the extra purchase ?
A.22.
B.28.
C.77.
D.99.
e ) 234E.
"if u can just keep an eye on the options 99 is the only multiple of 9 in options given . . so you can mark it wid in seconds . now coming to the process m ( d ) = 7 x and b ( d ) = 2 x now from the next line the new eqn becomes 7 x / ( 2 x + 6 ) = 11 / 4 solving it 28 x = 26 x + 52 x = 11 which means m ( d ) = 182 and b ( d ) = 52 so total initially is m ( d ) + b ( d ) = 234 e" | null |
Question: there are 25 balls in a jar . you take out 5 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ?
A.12 ..
B.9 ..
C.8 ..
D.7 ..
e ) 6 .B.
"9 = 5 blue balls + 20 / 5 answer : b" | null |
Question: a circular well with a diameter of 4 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ?
A.32 m 3.
B.36 m 3.
C.40 m 3.
D.44 m 3.
e ) 301.6E.
"solution volume = Ο r 2 h βΉ = βΊ ( 22 / 7 Γ 2 Γ 2 Γ 24 ) m 3 βΉ = βΊ 301.6 m 3 . answer e" | null |
Question: priya and her father differ in their ages by 31 years . after 8 years . if the sum of their ages will be 69 , their present ages are
A.11.
42.
B.12.
24.
C.15.
42.
D.16.
19.
e ) 33.
44A.
a 11 , 42 let the age of priya = x years then , the age of her father = ( x + 31 ) years atq , ( x + 8 ) + ( x + 31 + 8 ) = 69 2 x + 47 = 69 2 x = 69 β 47 = 22 x = 11 the age of priya = 11 years the age of her father = 11 + 31 = 42 years | null |
Question: if 7 spiders make 7 webs in 7 days , then how many days are needed for 1 spider to make 1 web ?
A.1.
B.7.
C.3.
D.14.
e ) 16B.
"explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 7 : 1 ( webs ) 1 : 7 } : : x : 7 β 7 Γ 1 Γ 7 = 1 Γ 7 Γ x β x = 7 answer : option b" | null |
Question: the price of lunch for 13 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
A.11.73.
B.12.
C.13.85.
D.14.
e ) 15.87C.
"clearly c is the answer i used poe here lets consider option ( c ) 13 * 13.85 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo c" | null |
Question: a shopkeeper sold an article at $ 1800 with 20 % profit . then find its cost price ?
A.$ 1000.
B.$ 1500.
C.$ 1850.
D.$ 1600.
e ) $ 2000B.
"cost price = selling price * 100 / ( 100 + profit ) c . p . = 1800 * 100 / 120 = $ 1500 answer is b" | null |
Question: find the principle on a certain sum of money at 5 % per annum for 2 years if the amount being rs . 1120 ?
A.1018.
B.1067.
C.1977.
D.1056.
e ) 1097A.
"1120 = p [ 1 + ( 5 * 2 ) / 100 ] p = 1018 answer : a" | null |
Question: a man swims downstream 24 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?
A.8.
B.5.
C.24.
D.12.
e ) 36B.
"24 - - - 4 ds = 6 ? - - - - 1 16 - - - - 4 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : b" | null |
Question: when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 38 , what is the remainder when k is divided by 7 ?
A.2.
B.4.
C.3.
D.5.
e ) 6C.
"cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 38 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 38 ) 17 is the only common number in both the sets . hence k = 17 answer : c" | null |
Question: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 6000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
A.s . 375.
B.s . 400.
C.s . 600.
D.s . 750.
e ) s . 850D.
"c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 6000 ) = rs . 750 answer = d" | null |
Question: a can do a job in 9 days and b can do it in 27 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
A.22 days.
B.18 days.
C.22 6 / 2 days.
D.27 days.
e ) 9 daysB.
"1 / 9 + 1 / 27 = 3 / 27 = 1 / 9 9 / 1 = 9 * 2 = 18 days answer : b" | null |
Question: what will be the remainder when 13 ^ 36 is divided by 2196 ?
A.0.
B.1.
C.12.
D.2195.
e ) 5B.
"in such qs , best is to get the dividend and divisor in some friendly figures . . 13 ^ 36 = ( 13 ^ 3 ) ^ 12 = 2197 ^ 12 = ( 2196 + 1 ) ^ 12 when ( 2196 + 1 ) ^ 12 is divided by 2196 , all terms in the expansion are divisible by 2196 except 1 ^ 12 , so the remainder will be 1 answer : b" | null |
Question: for what value of x , is | x β 5 | + | x + 5 | + | x | = 27 ?
A.0.
B.3.
C.- 3.
D.9.
e ) - 9D.
"for what value of x , is | x β 5 | + | x + 5 | + | x | = 27 ? it ' s easiest just to plug in answer choices : ( d ) : 9 | x β 5 | + | x + 5 | + | x | = 27 ? | 9 - 5 | + | 9 + 5 | + | 9 | = 27 ? | 4 | + | 14 | + | 9 | = 27 ( d )" | null |
Question: if an organization were to sell n tickets for a theater production , the total revenue from ticket sales would be 20 percent greater than the total costs of the production . if the organization actually sold all but 5 percent of the n tickets , the total revenue from ticket sales was what percent greater than the total costs of the production ?
A.4 %.
B.10 %.
C.14 %.
D.15 %.
e ) 18 %C.
let cost of prod for 1 ticket = 1 so cop for n tickets = n so for selling n tickets , sp = 1.2 * n = 1.2 n so sp of 1 ticket = 1.2 sp of 95 % tickets = 1.2 * 0.95 n so profit % = ( 1.2 * 0.95 n - n ) / n * 100 = 0.14 * 100 = 14 % answer - c | null |
Question: virginia , adrienne , and dennis have taught history for a combined total of 96 years . if virginia has taught for 9 more years than adrienne and for 12 fewer years than dennis , for how many years has dennis taught ?
A.23.
B.32.
C.35.
D.41.
e ) 42E.
let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 12 = > a = ( d - 12 ) - 9 = d - 21 d - 9 + d - 21 + d = 96 = > 3 d = 96 + 30 = 126 = > d = 42 answer e | null |
Question: the average salary of 20 people in the shipping department at a certain firm is $ 1000 . the salary of 10 of the employees is $ 600 each and the salary of 6 of the employees is $ 200 each . what is the average salary of the remaining employees ?
A.$ 2500.
B.$ 3200.
C.$ 4500.
D.$ 5000.
e ) $ 5200B.
"total salary . . . 20 * 1000 = 20000 10 emp @ 600 = 6000 6 emp @ 200 = 1200 remaing 4 emp salary = 20000 - 6000 - 1200 = 12800 average = 12800 / 4 = 3200 answer is b" | null |
Question: an aeroplane covers a certain distance of 670 kmph in 6 hours . to cover the same distance in 6 1 / 4 hours , it must travel at a speed of
A.440.
B.540.
C.643.
D.740.
e ) 250C.
"speed of aeroplane = 670 kmph distance travelled in 6 hours = 670 * 6 = 4020 km speed of aeroplane to acver 4020 km in 25 / 4 = 4020 * 4 / 25 = 643 km answer c ." | null |
Question: a cube is divided into 216 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
['A.72', 'B.84', 'C.96', 'D.108', 'e ) 120']C.
each side of the cube has 6 x 6 = 36 cubelets . only the interior cubelets are painted one colour . on each side , 4 x 4 = 16 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 16 = 96 the answer is c . | null |
Question: a sum fetched a total simple interest of $ 4061.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
A.$ 8829.
B.$ 2840.
C.$ 6578.
D.$ 7782.
e ) $ 8926E.
"e 8926 principal = $ 100 x 4016.25 / 9 x 5 = $ 406125 / 45 = $ 8926 ." | null |
Question: the average of 5 consecutive odd numbers is 55 . what is the difference between the highest and lowest numbers ?
A.2.
B.5.
C.8.
D.9.
e ) 10C.
explanation : let the numbers be x , x + 2 , x + 4 , x + 6 and x + 8 . then , ( x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) ) / 5 = 55 5 x + 20 = 275 x = 255 / 5 = 51 . so , required difference = ( 51 + 8 ) 51 = 8 answer : c | null |
Question: in a class of 25 students in an examination in maths 3 students scored 95 marks each , 5 get zero each and the average of the rest was 45 . what is the average of the whole class ?
A.A.47.
B.B.45.6.
C.C.42.
D.D.48.
e ) e ) 49C.
"explanation : total marks obtained by a class of 25 students = 3 * 95 + 5 * 0 + 17 * 45 = 1050 average marks of whole class = 1050 / 25 = 42 answer : option c" | null |
Question: 18.05 Γ£ β 0.001 = ?
A.0.1805.
B.0.01805.
C.1.805.
D.0.001805.
e ) none of theseB.
"18.05 Γ£ β 0.001 = ? or , ? = 0.01805 answer b" | null |
Question: a school has 4 section of chemistry in class x having 40 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
A.50.25.
B.52.25.
C.51.25.
D.53.25.
e ) none of the aboveB.
"required average marks = 40 Γ 50 + 35 Γ 60 + 45 Γ 55 + 42 Γ 45 / 40 + 35 + 45 + 42 = 2000 + 2100 + 2475 + 1890 / 162 = 8465 β 162 = 52.25 answer b" | null |
Question: ajay can walk 7 km in 1 hour . in how many hours he can walk 80 km ?
A.5 hrs.
B.11.4 hrs.
C.15.5 hrs.
D.20.4 hrs.
e ) 30 hrsB.
"1 hour he walk 8 km he walk 80 km in = 80 / 7 * 1 = 11.4 hours answer is b" | null |
Question: the percentage profit earned by selling an article for rs . 1320 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
A.3000.
B.1230.
C.2000.
D.1625.
e ) 3400D.
"c . p . be rs . x . then , ( 1320 - x ) / x * 100 = ( x - 1280 ) / x * 100 1320 - x = x - 1280 2 x = 2600 = > x = 1300 required s . p . = 125 % of rs . 1300 = 125 / 100 * 1300 = rs . 1625 . anser d" | null |
Question: the compound ratio of 5 : 1 , 3 : 1 and 2 : 5 ?
A.6 : 1.
B.1 : 3.
C.1 : 5.
D.1 : 1.
e ) 1 : 6A.
5 / 1 * 3 / 1 * 2 / 5 = 30 / 5 6 : 1 answer : a | null |
Question: 130 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
A.8 days.
B.6 days.
C.7 days.
D.9 days.
e ) 13 daysE.
"1 women ' s 1 day work = 1 / 910 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 910 + 10 / 140 ) = 1 / 13 5 women and 10 children will complete the work in 13 days . answer : e" | null |
Question: a grocer has a sale of rs . 3435 , rs . 3920 , rs . 3855 , rs . 4230 and rs . 3560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ?
A.500.
B.1000.
C.6000.
D.7000.
e ) 2000E.
"total sale for 5 months = rs . ( 3435 + 3920 + 3855 + 4230 + 3560 ) = rs . 19000 . required sale = rs . [ ( 3500 x 6 ) - 19000 ] = rs . ( 21000 - 19000 ) = rs . 2000 answer : option e" | null |
Question: a number of 55 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?
A.10.
B.12.
C.15.
D.16.
e ) 19E.
to maximize # of boxes we should minimize marbles per box : 17 * 3 + 1 * 4 + 1 * 5 = 50 - - > 17 + 1 + 1 = 19 . answer : e . | null |
Question: the length of a side of a hexagon is 7 inches . what is the perimeter ?
A.48.
B.42.
C.44.
D.45.
e ) 40B.
"hexagon . it means 6 equal sides . p = 6 ( 7 ) = 42 inches answer b" | null |
Question: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 25 , and 30 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
A.4 / 11.
B.1 / 2.
C.15 / 22.
D.150 / 11.
e ) 11 / 4D.
"p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 25 + 1 / 30 = 11 / 150 therefore they take 150 / 11 ratio = 150 / 11 = d" | null |
Question: how many numbers from 45 to 110 are exactly divisible by 12 ?
A.5.
B.7.
C.6.
D.11.
e ) 12C.
"option ' c ' 45 / 12 = 3 and 110 / 12 = 9 = = > 9 - 3 = 6 numbers" | null |
Question: 40 is subtracted from 60 % of a number , the result is 50 . find the number ?
A.150.
B.330.
C.277.
D.279.
e ) 712A.
"( 60 / 100 ) * x β 40 = 50 6 x = 900 x = 150 answer : a" | null |
Question: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 108 . find the number of notes of rs . 50 denomination .
A.15.
B.21.
C.17.
D.19.
e ) 97E.
"total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 108 - x now , 50 * x + 500 * ( 108 - x ) = 10350 50 x + 54000 - 500 x = 10350 - 450 x = - 43650 x = 97 . no . of 50 rupees note = 97 . answer : option e" | null |
Question: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day 5 miles per hour for 6 hours . how many miles in total did she walk ?
A.68.
B.44.
C.58.
D.60.
e ) 62A.
first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 5 miles per hour and 6 hours - 30 miles total 18 + 20 + 30 = 68 answer : option a . | null |
Question: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 878 in 4 years . the sum is :
A.500.
B.698.
C.626.
D.910.
e ) noneC.
"sol . s . i . for 1 year = rs . ( 878 - 815 ) = rs . 63 . s . i . for 3 years = rs . ( 63 * 3 ) = rs . 189 . Γ’ Λ Β΄ principal = rs . ( 815 - 189 ) = rs . 626 answer c" | null |
Question: after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 85 % full . if the original contents of the reservoir totaled 220 billion gallons , the reservoir was approximately what percentage full before the storm ?
A.45 %.
B.48 %.
C.55 %.
D.58 %.
e ) 65 %C.
"when the storm deposited 120 billion gallons , volume of water in the reservoir = 220 + 120 = 340 billion gallons if this is only 85 % of the capacity of the reservoir , the total capacity of the reservoir = 340 / 0.85 = 400 billion gallons therefore percentage of reservoir that was full before the storm = ( 220 / 400 ) * 100 = 55 % option c" | null |
Question: find the value of 72517 x 9999 = m ?
A.345434667.
B.246465757.
C.465767867.
D.725097483.
e ) 645354643D.
"72518 x 9999 = 72517 x ( 10000 - 1 ) = 72517 x 10000 - 72517 x 1 = 725170000 - 72517 = 725097483 d" | null |
Question: 10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 2907 , how much was it in the beginning ?
A.A.3800.
B.B.4200.
C.C.4400.
D.D.4500.
e ) e ) 4600A.
"x * ( 90 / 100 ) * ( 85 / 100 ) = 2907 x = 3800 answer : a" | null |
Question: average of 5 numbers is 20 , and the sum of 3 of the numbers is 48 , what is the average of the other 2 numbers ?
A.24.
B.34.
C.29.
D.35.
e ) 26E.
let the five numbers be a , b , c , d , e . then their average is ( a + b + c + d + e ) / 5 = 20 a + b + c = 48 ( 48 + d + e ) / 5 = 20 48 + d + e = 100 d + e = 52 average = 52 / 2 = 26 ans e | null |
Question: the population of a city increases by 4 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
A.9 %.
B.9.27 %.
C.27 %.
D.12 %.
e ) none of theseB.
"actual increase in population = 3 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 3 / 100 ) ^ 3 = 109.2727 β΄ required percentage = 9.27 % answer : b" | null |
Question: a rectangle measures 8 cm on length and its diagonal measures 17 cm . what is the perimeter of the rectangle ?
['A.44 cm', 'B.42 cm', 'C.46 cm', 'D.49 cm', 'e ) 41 cm']C.
second side = β 17 power 2 - 8 power 2 = β 289 - 64 = 15 cm perimeter = 2 ( l + b ) = 2 ( 8 + 5 ) cm = 2 ( 23 ) = 46 cm answer is c . | null |
Question: $ 6,000 is deposited in a savings account that pays 10 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
A.$ 6615.15.
B.$ 6615.00.
C.$ 6714.10.
D.$ 6655.55.
e ) $ 6698.20B.
"this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 10 / 2 = 5 % now , ca = 6000 ( 1 + 5 / 100 ) ^ 2 = $ 6615.00 hence answer is b" | null |
Question: a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 5 % on conveyance . if his savings at the end of the month is rs . 1200 , then his salary per month in rupees is :
A.4000.
B.6000.
C.8000.
D.10000.
e ) none of theseC.
"total expenditure = 40 + 25 + 15 + 5 = 85 % saving = ( 100 - 85 ) = 15 % 15 / 100 Γ salary = 1200 , salary = 8000 rs . answer : c ." | null |
Question: in 1982 and 1983 , company b β s operating expenses were $ 10.0 million and $ 12.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b β s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
A.3 %.
B.16 2 / 3 %.
C.25 %.
D.21 3 / 7 %.
e ) 60 %D.
"profit in 1982 = 15.6 - 10 = 5.6 million $ profit in 1983 = 18.8 - 12 = 6.8 million $ percentage increase in profit = ( 6.8 - 5.6 ) / 5.6 * 100 % = 21 3 / 7 % answer d" | null |
Question: a train running at the speed of 48 km / hr crosses a pole in 9 seconds . what is the length of the train ?
A.140.
B.130.
C.120.
D.170.
e ) 160C.
"speed = ( 48 x 5 / 18 ) m / sec = ( 40 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( 40 / 3 x 9 ) m = 120 m . answer is c ." | null |
Question: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts seven hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
A.3.
B.4.5.
C.4.
D.D.5.5.
e ) e ) 14E.
"the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 7 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 7 + t ) = 40 * t t = 21 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 21 / 60 = 14 hrs time taken by a = 7 + t = 7 + 21 = 28 hrs time taken by k = 14 hrs so k starts 28 - 14 = 14 hrs after a . ( answer e )" | null |
Question: the average height of 35 boys in a class was calculated as 185 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.178.27 cm.
B.183.29 cm.
C.978.29 cm.
D.178.89 cm.
e ) 176.29 cmB.
"calculated average height of 35 boys = 185 cm . wrong total height of 35 boys = 185 * 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 = 185 cm - ( 166 cm - 106 cm ) / 35 = 185 cm - 60 / 35 cm = 185 cm - 1.71 cm = 183.29 cm . answer : b" | null |
Question: the cost to park a car in a certain parking garage is $ 10.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
A.$ 1.09.
B.$ 1.67.
C.$ 2.225.
D.$ 2.47.
e ) $ 2.50D.
"total cost of parking for 10 hours = 10 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 10 + 7 * 1.75 = 22.25 thus the average parking price = 22.25 / 9 = 2.47 $ d is the correct answer ." | null |
Question: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 205 ?
A.1,108.
B.2,100.
C.2,140.
D.2,124.
e ) 2,256C.
"i think it should be c . i can buy 8 250 - pack for rs 22.95 * 8 = $ 183.60 now , i can buy 7 20 - pack for 3.05 * 7 = $ 21.35 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 7 = 2140" | null |
Question: a train which has 410 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
A.56 sec.
B.41 sec.
C.36 sec.
D.29 sec ..
e ) 19 sec .B.
"time taken to cross a moving person = length of train / relative speed time taken = 410 / ( ( 45 - 9 ) ( 5 / 18 ) = 410 / 36 * ( 5 / 18 ) = 410 / 10 = 41 sec answer : b" | null |
Question: the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - half of the males and three - fourths of the females in the class ?
A.218.
B.226.
C.234.
D.242.
e ) 250C.
"1 / 2 * 2 / 5 + 3 / 4 * 3 / 5 = 4 / 20 + 9 / 20 = 13 / 20 the number of degrees is 13 / 20 * 360 = 234 degrees the answer is c ." | null |
Question: a man can row upstream at 25 kmph and downstream at 45 kmph , and then find the speed of the man in still water ?
A.11.
B.77.
C.30.
D.88.
e ) 35E.
"us = 25 ds = 45 m = ( 45 + 25 ) / 2 = 35 answer : e" | null |
Question: the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is :
A.2377.
B.1683.
C.2677.
D.9972.
e ) 1611B.
"explanation : l . c . m . of 5 , 6 , 7 , 8 = 840 . { \ color { blue } \ therefore } required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . { \ color { blue } \ therefore } required number = ( 840 x 2 + 3 ) = 1683 . answer : b ) 1683" | null |
Question: 1 men takes 37 $ to eat a pizza in restaurant such that it have discount multiple of 4 if u eat more pizza . discount increase by multiple of 4 every pizza u eat . for 1 pizza 0 % off . for 2 pizza % off for 3 pizza 8 % off . pizza without discount is 10 $ . how much that man eats the pizza .
A.2.
B.3.
C.4.
D.5.
e ) 6B.
solution : b . for 1 pizza 10 $ . for 2 pizza 10 $ + 9.6 $ ( 4 % off ) = 19.6 , for 3 pizza 19.6 + 9.2 ( 8 % off ) = 28.8 , for 4 pizza 28.8 + 8.8 ( 12 % off ) = 37.6 . so he have 37 so he cant eat 4 th pizza . | null |
Question: 5 people can write 25 book in 20 days working 8 hour a day . then in how many day 125 can be written by 75 people ?
A.25 / 3.
B.19 / 3.
C.20 / 3.
D.25 / 3.
e ) 22 / 3C.
"work per day epr hour per person = 25 / ( 20 * 8 * 5 ) / / eq - 1 people = 75 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 125 / ( p * 8 * 75 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 20 / 3 answer : c" | null |
Question: if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 46 ?
A.11.
B.12.
C.13.
D.14.
e ) 15A.
"four wheeler = 11 * 4 = 44 ( max ) 2 wheel = 1 so no of 4 wheeler = 11 answer : a" | null |
Question: three 6 faced dice are thrown together . the probability that exactly two dice show the same number on them is
A.5 / 15.
B.5 / 12.
C.5 / 19.
D.5 / 12.
e ) 5 / 11B.
"using question number 11 and 12 , we get the probability as 1 - ( 1 / 36 + 5 / 9 ) = 5 / 12 answer : b" | null |
Question: a train 250 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?
A.150 m.
B.200 m.
C.250 m.
D.270 m.
e ) 300 mC.
"d = 72 * 5 / 18 = 25 = 500 β 250 = 250 m answer : c" | null |
Question: a 9 % stock yields 8 % . the market value of the stock is :
A.rs . 72.
B.rs . 92.
C.rs . 112.50.
D.rs . 116.50.
e ) none of theseC.
"solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 9 , investment = rs . ( 100 / 8 x 9 ) = rs . 112.50 β΄ market value of rs . 100 stock = rs . 112.50 answer c" | null |
Question: one side of a rectangular field is 15 m and one of its diagonal is 18 m . find the area of the field .
A.100.
B.120.
C.150.
D.148.5.
e ) noneD.
"solution other side = β ( 18 ) 2 - ( 15 ) 2 = β 324 - 225 = β 99 = 9.9 m . β΄ area = ( 15 x 9.9 ) m 2 = 148.5 m 2 . answer d" | null |
Question: in one hour , a boat goes 19 km / hr along the stream and 9 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
A.12 kmph.
B.13 kmph.
C.14 kmph.
D.15 kmph.
e ) 16 kmphC.
explanation : let the speed downstream be a km / hr and the speed upstream be b km / hr , then speed in still water = 1 / 2 ( a + b ) km / hr rate of stream = 1 / 2 ( a β b ) km / hr speed in still water = 1 / 2 ( 19 + 9 ) kmph = 14 kmph . answer : option c | null |
Question: the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 40 , what is the possible maximum range of the temperatures ?
A.100.
B.25.
C.40.
D.45.
e ) 75A.
"average = 60 , sum of temperatures = 60 * 5 = 300 as the min temperature is 40 , max would be 300 - 4 * 40 = 140 - - > the range = 140 ( max ) - 40 ( min ) = 100 answer : a" | null |
Question: find out the square of a number which when doubled exceeds its one sixth by 11 ?
A.36.
B.25.
C.19.
D.26.
e ) 17A.
"a let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 6 ) + 11 = > 12 p = p + 66 = > p = 6 p ^ 2 = 6 ^ 2 = 36 . answer : a" | null |
Question: a train overtakes two persons who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . find the length of train ?
A.45 m.
B.50 m.
C.55 m.
D.60 m.
e ) 65 mB.
"explanation : first person speed = 2 * ( 5 / 18 ) = 5 / 9 m / sec second person speed = 4 * ( 5 / 18 ) = 10 / 9 m / sec let the length of train is x metre and speed is y m / sec then , x / y β 5 / 9 = 9 = > 9 y β 5 = x = > 9 y β x = 5 . . . . . ( i ) also , x / y β 10 / 9 = 10 90 y β 9 x = 100 . . . . . ( ii ) from ( i ) and ( ii ) , we get , x = 50 so length of train is 50 metre option b" | null |
Question: a number is doubled and 9 is added . if resultant is trebled , it becomes 63 . what is that number
A.6.
B.10.
C.12.
D.14.
e ) 15A.
"explanation : = > 3 ( 2 x + 9 ) = 63 = > 2 x + 9 = 21 = > x = 6 answer : option a" | null |
Question: a = 5 ^ 10 - 625 ^ 2 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
A.none.
B.one.
C.two.
D.three.
e ) fourC.
this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get 2 different values and answer is c . . . . | null |
Question: a 80 cm long wire is to be cut into two pieces so that one piece will be 3 / 5 th of the other , how many centimeters will the shorter piece be ?
A.A.30.
B.B.20.
C.C.83.
D.D.21.
e ) e ) 52A.
"explanation : 1 : 3 / 5 = 5 : 3 3 / 8 * 80 = 30 answer : option a" | null |
Question: a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 25 days starting with sunday is
A.342.
B.285.
C.290.
D.295.
e ) 275A.
"explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 Γ 5 + 240 Γ 25 / 30 ) = ( 8550 / 25 ) = 342 answer : option a" | null |
Question: a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 12 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
A.3 / 8.
B.2 / 5.
C.1 / 5.
D.3 / 5.
e ) 3 / 4C.
"x * 6 / 100 * 1 + ( 20000 - x ) * 12 / 100 * 1 = 1440 6 x - 12 x = 144000 - 240000 = > - 6 x = - 96000 = > x = 16000 so 4000 / 20000 = 1 / 5 answer - c" | null |
Question: the ratio , by volume , of soap to alcohol to water in a certain solution is 6 : 30 : 90 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 150 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
A.1200.
B.1300.
C.1500.
D.1800.
e ) 1900D.
"soap : alcohol initial ratio soap : alcohol : water - - > 6 : 30 : 90 initial soap : alcohol = 6 / 30 = 6 : 30 after doubled soap : alcohol = 2 * 6 / 30 = 12 / 30 = 12 : 30 initial soap : water = 6 / 90 = 6 : 90 after halved soap : water : 1 / 2 * 6 / 90 = 3 / 90 = 3 : 90 = 12 : 360 after soap : alcohol : water - - > 12 : 30 : 360 given alcohol 150 cubic centimeter . ratio is 60 : 150 : 1800 ( 12 : 30 : 360 ) for 150 cubic centimeter of alcohol - - - 1800 cu cm water is required . answer - d" | null |
Question: a waiter ' s salary consists of his salary and tips . during one week his tips were 7 / 4 of his salary . what fraction of his income came from tips ?
A.4 / 9.
B.5 / 4.
C.5 / 8.
D.5 / 9.
e ) 7 / 11E.
"income = salary ( s ) + tips = s + s * 7 / 4 = s * 11 / 4 tips = s * 7 / 4 fraction of his income came from tips = ( s * 7 / 4 ) / ( s * 11 / 4 ) = 7 / 11 answer : e" | null |
Question: the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than
A.14 years.
B.12 years.
C.56 years.
D.66 years.
e ) 15 yearsE.
"given that a + b = 15 + b + c = > a Γ’ β¬ β c = 15 + b Γ’ β¬ β b = 15 = > c is younger than a by 15 years answer : e" | null |
Question: three numbers are in the ratio 4 : 5 : 6 and their product is 76680 . the largest number is
A.30.
B.24.
C.26.
D.28.
e ) 22B.
"explanation : let the number be 4 x , 5 x and 6 x . then , ( 4 x ) ( 5 x ) ( 6 x ) = 2880 = > 120 x 3 = 7680 = > x 3 = 64 = > x = 4 so , largest number is 6 x = 24 answer : option b" | null |
Question: a bag has 9 green balls and 23 pink balls . how many green balls should be added to the bag so that the ratio of green balls and pink balls in the bag becomes 1 : 1 ?
A.10.
B.11.
C.12.
D.13.
e ) 14E.
suppose x green balls need to be added . then , the number of green balls becomes 9 + x , and the number of pink balls remains the same , 23 . but now the ratio of green and pink balls is 1 : 1 this means , ( 9 + x ) / 23 = 1 / 1 solving this we get x = 14 . ans e | null |
Question: what is the value of 100 p 2 ?
A.9801.
B.12000.
C.5600.
D.9900.
e ) none of theseD.
"explanation : 100 p 2 = 100 x 99 = 9900 . answer : option d" | null |
Question: convert 2 / 5 to a decimal
A.0.1.
B.0.2.
C.0.3.
D.0.4.
e ) 0.5D.
"divide 2 by 5 : 2 / 5 = 0.4 answer : 2 / 5 = 0.4 ( d )" | null |
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