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Question: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 60 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
A.80 %.
B.32 %.
C.48 %.
D.84 %.
e ) 92 %A.
"this is easiest to solve with a bell - curve histogram . m here is equal to Β΅ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 60 % is one st . dev , then on either side of m we have 60 / 2 = 30 % . so , 30 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 30 = 80 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 80 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it a" | null |
Question: 8 kilograms of rice costing rs . 16 per kg is mixed with 4 kilograms of rice costing rs . 22 per kg . what is the average price of the mixture ?
A.20.
B.18.
C.16.
D.19.
e ) 17B.
p 1 = rs . 16 per kg , p 2 = rs . 22 per kg , q 1 = 8 kg , q 2 = 4 kg now , p = ( p 1 q 1 + p 2 q 2 ) / ( q 1 + q 2 ) average price of the mixture = 8 * 16 + 4 * 22 / 12 = 128 + 88 / 12 = 216 / 12 = 18 answer : b | null |
Question: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 70 metres ?
A.22 seconds.
B.65 seconds.
C.78 seconds.
D.12 seconds.
e ) 14 secondsE.
"speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 70 / 5 = 14 seconds . answer : e" | null |
Question: if the numbers 1 to 99 are written on 99 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
A.1 / 50.
B.1 / 25.
C.1 / 99.
D.1.
e ) 2C.
"there are 25 primes , 73 composite numbers from 1 to 100 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 99 . answer : c" | null |
Question: a trader purchased two colour televisions for a total of rs . 35000 . he sold one colour television at 30 % profit and the other 40 % profit . find the difference in the cost prices of the two televisions if he made an overall profit of 32 % ?
A.21000.
B.21009.
C.21029.
D.21298.
e ) 21098A.
let the cost prices of the colour television sold at 30 % profit and 40 % profit be rs . x and rs . ( 35000 - x ) respectively . total selling price of televisions = x + 30 / 100 x + ( 35000 - x ) + 40 / 100 ( 35000 - x ) = > 130 / 100 x + 140 / 100 ( 35000 - x ) = 35000 + 32 / 100 ( 35000 ) x = 28000 35000 - x = 7000 difference in the cost prices of televisions = rs . 21000 answer : a | null |
Question: an article is bought for rs . 775 and sold for rs . 900 , find the gain percent ?
A.11.1 %.
B.12.1 %.
C.13.1 %.
D.15.1 %.
e ) 16.1 %E.
"775 - - - - 125 100 - - - - ? = > 16.1 % answer : e" | null |
Question: 9 ! / ( 9 - 3 ) ! = ?
A.336.
B.346.
C.356.
D.366.
e ) 504E.
9 ! / ( 9 - 3 ) ! = 9 ! / 6 ! = 9 * 8 * 7 = 504 . hence , the correct answer is e . | null |
Question: if 213 Γ 16 = 3408 , then 1.6 Γ 21.3 is equal to :
A.0.3408.
B.3.408.
C.34.08.
D.340.8.
e ) none of theseC.
"solution 1.6 Γ 21.3 = ( 16 / 10 x 213 / 10 ) = ( 16 x 213 / 100 ) = 3408 / 100 = 34.08 . answer c" | null |
Question: if the simple interest on a sum of money for 5 years at 18 % per annum is rs . 900 , what is the compound interest on the same sum at the rate and for the same time ?
A.rs . 1287.76.
B.rs . 1284.76.
C.rs . 1587.76.
D.rs . 1266.76.
e ) rs . 1283.76A.
"sum = ( 900 * 100 ) / ( 5 * 18 ) = rs . 1 , 000.00 c . i . on rs . rs . 1 , 000.00 for 5 years at 18 % = rs . 2 , 287.76 . = rs . 2 , 287.76 - 1 , 000.00 = rs . 1287.76 answer : a" | null |
Question: the true discount on a bill due 9 months hence at 16 % per annum is rs . 150 . the amount of the bill is
A.1200.
B.1764.
C.1400.
D.1354.
e ) none of theseC.
explanation : let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 150 . x Γ£ β 16 Γ£ β ( 9 / 12 ) Γ£ β ( 1 / 100 ) = 150 or x = 1250 . p . w . = rs . 1250 sum due = p . w . + t . d . = rs . ( 1250 150 ) = rs . 1400 answer : c | null |
Question: andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.81 . what is the median gasoline price ?
A.$ 1.
B.$ 1.81.
C.$ 1.92.
D.$ 2.13.
e ) $ 2.15B.
"ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.81 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.81 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b" | null |
Question: a freight elevator can carry a maximum load of 1100 pounds . sean , who weighs 200 pounds , is in the elevator with two packages weighing 150 pounds and 280 pounds . if he needs to fit 3 more packages in the elevator that weigh as much as possible without exceeding the elevator limit , what is the difference between their average and the average of the two packages already in the elevator ?
A.59.
B.85.
C.190.
D.215.
e ) 210A.
the average of existing 2 package is 150 + 280 / 2 = 430 / 2 = 215 remaining allowed weight = 1100 - 200 - 430 = 470 . allowed per package = 470 / 3 = 156 so difference in average of existing and allowable = 215 - 156 = 59 hence a | null |
Question: power windows : 60 % anti - lock brakes : 25 % cd player : 75 % the table above shows the number of vehicles at bill ' s car dealership that have certain features . no vehicle has all 3 features , but 10 % have power windows and anti - lock brakes , 15 % have anti - lock brakes and a cd player , and 22 % have power windows and a cd player . what percent of the vehicles at bill ' s car dealership have a cd player but no power windows or anti - lock brakes ?
A.25.
B.18.
C.11.
D.38.
e ) 0D.
answer : d were looking for the number of cars with a cd player but no other features . we know that 40 % of the cars have a cd player , 15 % have a cd player and anti - lock brakes , while 22 % have a cd player and power windows . since no car has all three features , those account for all of the possibilities except for what were looking for . if a car has a cd player , it must either have anti - lock brakes , power windows , or no other features . since the total of cars with a cd player is 75 % , we can set up the following equation : 75 = 15 + 22 + x x = 38 , choiced . | null |
Question: a train 360 m long is running at a speed of 60 km / hr . in what time will it pass a bridge 140 m long ?
A.40 sec.
B.30 sec.
C.26 sec.
D.27 sec.
e ) 34 secB.
"speed = 60 * 5 / 18 = 50 / 3 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 3 / 50 = 30 sec answer : b" | null |
Question: the value of ( log 9 27 + log 8 32 ) is :
A.7 / 2.
B.19 / 6.
C.5 / 3.
D.7.
e ) 8C.
let log 9 27 = x . then , 9 x = 27 = > ( 32 ) x = 33 = > 2 x = 3 = > x = 3 / 2 let log 8 32 = y . then 8 y = 32 = > ( 23 ) y = 25 = > 3 y = 5 = > y = 5 / 3 answer : c | null |
Question: a meal cost $ 37.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
A.41 - 43.
B.39 - 41.
C.38 - 40.
D.37 - 39.
e ) 36 - 37A.
"10 % ( 37.5 ) = 3.75 15 % ( 37.5 ) = 5.625 total amount could have been 37.5 + 3.75 and 37.5 + 5.625 = > could have been between 41.25 and 43.125 = > approximately between 41 and 43 answer is a ." | null |
Question: find the slope of the line perpendicular to the line y = ( 1 / 4 ) x - 7
A.1.
B.2.
C.- 4.
D.4.
e ) 5C.
"two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 4 . if m is the slope of the line perpendicular to the given line , then m Γ ( 1 / 4 ) = - 1 solve for m m = - 4 correct answer c ) - 4" | null |
Question: a person can row at 9 kmph and still water . he takes 7 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
A.60 km.
B.87 km.
C.33 km.
D.67 km.
e ) 20 kmC.
"let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 7.5 = > x / 10 + x / 8 = 15 / 2 = > ( 4 x + 5 x ) / 40 = 15 / 2 = > x = 33 km . answer : c" | null |
Question: walking with 4 / 5 of my usual speed , i miss the bus by 4 minutes . what is my usual time ?
A.16 min.
B.26 min.
C.34 min.
D.20 min.
e ) 12 minA.
"speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 5 1 - - - - - - - - 4 4 - - - - - - - - - ? Γ¨ 16 answer : a" | null |
Question: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 22 in two years , at the same percent rate per annum ?
A.s . 520.
B.s . 480.
C.s . 420.
D.s . 100.
e ) s . 200D.
explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 22 % rate per annum = [ ( ci β si ) / ( si in 1 year ) ] * 100 = [ ( 22 β 20 ) / 20 ] * 100 = 10 % p . a . let the principal be rs . x time = t = 2 years % rate = 10 % p . a . si = ( prt / 100 ) 20 = ( x * 10 * 2 ) / 100 x = rs . 100 answer : d | null |
Question: if x / ( 11 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
A.22.
B.33.
C.44.
D.66.
e ) 99D.
x / ( 11 p ) = odd prime number x = odd prime number * 11 p least value of x = lowest odd prime number * 11 * lowest value of p = 3 * 11 * 2 = 66 answer d | null |
Question: 9 persons went to a hotel for taking their meals . 8 of them spent rs . 12 each on their meals and the ninth spent rs . 8 more than the average expenditure of all the 9 . what was the total money spent by them .
A.rs . 115.
B.rs . 116.
C.rs . 117.
D.rs . 118.
e ) noneC.
solution : let the average expenditure of all the nine be x . then , 12 Γ 8 + ( x + 8 ) = 9 x . therefore , x = 13 . total money spent , = 9 x = rs . ( 9 Γ 13 ) = rs . 117 answer : option c | null |
Question: a cube of edge 6 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
A.1 : 25.
B.1 : 36.
C.1 : 52.
D.1 : 522.
e ) noneB.
"sol . required ratio = 6 * 1 * 1 / 6 * 6 * 6 = 1 / 36 = 1 : 36 . answer b" | null |
Question: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 36 . what is the difference between the two digits of that number ?
A.4.
B.5.
C.6.
D.8.
e ) 9A.
"sol . let the ten β s digit be x and unit β s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 36 β 9 ( x - y ) = 36 β x - y = 4 answer a" | null |
Question: a snail , climbing a 66 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
A.42.
B.63.
C.77.
D.80.
e ) 91B.
"total transaction in two days = 4 - 2 = 2 feet in 62 days it will climb 62 feet on the 63 rd day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 63 b" | null |
Question: if 6 pr = 360 and if 6 cr = 15 , find r ?
A.5.
B.6.
C.4.
D.3.
e ) 2C.
solution : npr = ncr οΏ½ r ! 6 pr = 15 * r ! 360 = 15 * r ! r ! = 360 / 15 = 24 r ! = 4 * 3 * 2 * 1 = > r ! = 4 ! therefore , r = 4 . answer : option c | null |
Question: what is the sum of all remainders obtained when the first 130 natural numbers are divided by 9 ?
A.397.
B.401.
C.403.
D.412.
e ) 399D.
"a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 412 . answer : d ." | null |
Question: by selling 90 pens , a trader gains the cost of 15 pens . find his gain percentage ?
A.16.66 %.
B.17.66 %.
C.18.66 %.
D.19.66 %.
e ) 20.66 %A.
"let the cp of each pen be rs . 1 . cp of 90 pens = rs . 90 profit = cost of 15 pens = rs . 15 profit % = 15 / 90 * 100 = 16.66 % answer : a" | null |
Question: how many paying stones , each measuring 2 m * 2 m are required to pave a rectangular court yard 30 m long and 18 m board ?
A.99.
B.18.
C.135.
D.17.
e ) 12C.
"30 * 18 = 2 * 2 * x = > x = 135 answer : c" | null |
Question: a jogger running at 9 km / hr along side a railway track is 250 m ahead of the engine of a 100 m long train running at 99 km / hr in the same direction . in how much time will the train pass the jogger ?
A.14 sec.
B.67 sec.
C.98 sec.
D.36 sec.
e ) 23 secA.
"speed of train relative to jogger = 99 - 9 = 90 km / hr . = 90 * 5 / 18 = 25 m / sec . distance to be covered = 250 + 100 = 350 m . time taken = 350 / 25 = 14 sec . answer : a" | null |
Question: a train 200 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 20 seconds . the speed of the train is ?
A.36.
B.50.
C.88.
D.66.
e ) 23E.
"speed of the train relative to man = ( 200 / 20 ) m / sec = 5 m / sec . [ 5 * ( 18 / 5 ) ] km / hr = 18 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 18 = = > x = 23 km / hr . answer : e" | null |
Question: a pupil ' s marks were wrongly entered as 73 instead of 65 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
A.18.
B.82.
C.16.
D.27.
e ) 29C.
"let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 65 ) = > x / 2 = 8 = > x = 16 . answer : c" | null |
Question: the average salary of 16 people in the shipping department at a certain firm is $ 20,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 16,000 each . what is the average salary of the remaining employees ?
A.$ 18,714.
B.$ 18,500.
C.$ 18,000.
D.$ 15,850.
e ) $ 12,300A.
total salary . . . 16 * 20 k = 320 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 7 emp sal = 320 k - 125 k - 64 k = 131 k average = 131 k / 7 = 18714 ans : a | null |
Question: a shopkeeper sold an article at $ 100 with 30 % profit . then find its cost price ?
A.$ 120.
B.$ 100.
C.$ 91.
D.$ 77.
e ) $ 69D.
"cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 130 = $ 77 ( approximately ) answer is d" | null |
Question: in an election between two candidates , the first candidate got 80 % of the votes and the second candidate got 480 votes . what was the total number of votes ?
A.1600.
B.1800.
C.2000.
D.2200.
e ) 2400E.
"let v be the total number of votes . 0.2 v = 480 v = 2400 the answer is e ." | null |
Question: peter invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 4 years and to $ 500 at the end of another 2 years . what was the rate of interest in which he invested his sum ?
A.12 %.
B.12.5 %.
C.67 %.
D.25 %.
e ) 33 %D.
"lets assume the principal amount ( initial amount invested ) to be p rate of interest to berand time as t . we need to find r now after a time of 4 years the principal p amounts to $ 400 and after a time of 6 years ( question says after another 6 years so 4 + 2 ) p becomes $ 500 . formulating the above data amount ( a 1 ) at end of 4 years a 1 = p ( 1 + 4 r / 100 ) = 400 amount ( a 2 ) at end of 6 years a 2 = p ( 1 + 2 r / 100 ) = 500 dividing a 2 by a 1 we get ( 1 + 4 r / 100 ) / ( 1 + 2 r / 100 ) = 5 / 4 after cross multiplication we are left with 4 r = 100 which gives r = 25 % option : d" | null |
Question: twenty - one dots are evenly spaced on the circumference of a circle . how many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle ?
['A.1299', 'B.1305', 'C.1311', 'D.1317', 'e ) 1323']E.
the total number of ways we can choose three dots is 21 c 3 = 1330 . we can form seven equilateral triangles from these twenty - one dots . there are 1330 - 7 = 1323 combinations which do not form an equilateral triangle . the answer is e . | null |
Question: if the area of circle is 616 sq cm then its circumference ?
['A.76', 'B.55', 'C.88', 'D.21', 'e ) 11']C.
the area of circle = pie * r ^ 2 = 616 = > r = 14 2 * 22 / 7 * 14 = 88 answer : c | null |
Question: the ratio of boarders to day scholars at a school is 7 to 16 . however , after a few new students join the initial 560 boarders , the ratio changed to 1 to 2 , respectively . if no boarders became day scholars and vice versa , and no students left the school , how many boarders joined the school ?
A.48.
B.64.
C.70.
D.80.
e ) 84D.
let day scholars be ds and boarders be b given b / ds = 7 / 16 - - - > eq 1 initially b = 560 and x be new boarders joined then from eq 1 , we get ds = 16 / 7 * 560 = 1280 now , new ration is 560 + x / ds = 1 / 2 560 + x / 1280 = 1 / 2 = > 1120 + 2 x = 1280 = > 2 x = 160 = > x = 80 ans option d | null |
Question: when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 6 . when n is divided by ( p + 2 ) , the quotient is 15 and the remainder is 3 . what is the value of n ?
A.151.
B.331.
C.168.
D.691.
e ) 871C.
n / p = 18 6 / p = 18 p + 6 n / ( p + 2 ) = 15 2 / ( p + 2 ) = 15 p + 30 + 3 solving these two equations we get p = 9 n = 168 answer is c . | null |
Question: in an examination , 25 % of total students failed in hindi , 35 % failed in english and 40 % in both . the percentage of these who passed in both the subjects is :
A.10 %.
B.20 %.
C.60 %.
D.80 %.
e ) 50 %D.
"pass percentage = 100 - ( 25 + 35 - 40 ) = 100 - 20 = 80 answer : d" | null |
Question: population of a city in 20004 was 1400000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city at the end of the year 2007
A.354354.
B.545454.
C.465785.
D.456573.
e ) 2818075 / 2E.
"required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 2818075 / 2 e" | null |
Question: the slant height of a cone is 15 cm and radius of the base is 3 cm , find the curved surface of the cone ?
A.26.
B.134.
C.141.
D.190.
e ) 28C.
"Ο * 15 * 3 = 141 answer : c" | null |
Question: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 340 m long ?
A.56 sec.
B.42 sec.
C.45 sec.
D.48 sec.
e ) 50 secA.
"speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 340 = 700 m required time = 700 * 2 / 25 = 56 sec answer : a" | null |
Question: if ( 55 ^ 55 + 55 ) is divided by 56 , then the remainder is : ?
A.54.
B.55.
C.53.
D.56.
e ) 57A.
solution : ( x ^ n + 1 ) is divisible by ( x + 1 ) , when n is odd . . ' . ( 55 ^ 55 + 1 ) is divisible by ( 55 + 1 ) = 56 . when ( 55 ^ 55 + 1 ) + 54 is divided by 56 , the remainder is 54 . answer a | null |
Question: g ( x ) is defined as the product of all even integers k such that 0 < k β€ x . for example , g ( 14 ) = 2 Γ 4 Γ 6 Γ 8 Γ 10 Γ 12 Γ 14 . if g ( a ) is divisible by 4 ^ 11 , what is the smallest possible value for a ?
A.22.
B.24.
C.28.
D.32.
e ) 44B.
"g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b" | null |
Question: the least common multiple of positive integer m and 3 - digit integer n is 690 . if n is not divisible by 3 and m is not divisible by 2 , what is the value of n ?
A.115.
B.230.
C.460.
D.575.
e ) 690B.
the lcm of n and m is 690 = 2 * 3 * 5 * 23 . m is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to m . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b . | null |
Question: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is :
A.rs . 50.
B.rs . 160.
C.rs . 200.
D.rs . 225.
e ) rs . 325C.
"let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c" | null |
Question: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent f of the distribution is less than m + d ?
A.16 %.
B.32 %.
C.48 %.
D.84 %.
e ) 92 %D.
"d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , f = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d" | null |
Question: the difference between the local value and the face value of 9 in the numeral 62975148 is
A.899999.
B.899991.
C.899891.
D.899981.
e ) 899000B.
"explanation : ( local value of 9 ) - ( face value of 9 ) = ( 900000 - 9 ) = 899991 b )" | null |
Question: a man complete a journey in 10 hours . he 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.220 km.
B.224 km.
C.230 km.
D.234 km.
e ) 255 kmB.
"( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 x / 21 + x / 24 = 20 15 x = 168 x 20 x = [ 168 x 20 / 15 ] = 224 km answer is b" | null |
Question: the compound ratio of 3 : 4 , 3 : 2 and 4 : 5 ?
A.1 : 9.
B.1 : 7.
C.1 : 2.
D.9 : 10.
e ) 1 : 4D.
"3 / 4 * 3 / 2 * 4 / 5 = 9 / 10 = 9 : 10 answer : d" | null |
Question: the true discount on a bill of rs . 2460 is rs . 360 . what is the banker ' s discount ?
A.rs . 432.
B.rs . 422.
C.rs . 412.
D.rs . 442.
e ) none of theseB.
"explanation : f = rs . 2460 td = rs . 360 pw = f - td = 2460 - 360 = rs . 2100 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2100 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2460 for unexpired time = 360 / 2100 Γ 2460 = 0.17 Γ 2460 = rs . 422 answer : option b" | null |
Question: a number is doubled and 5 is added . if the resultant is trebled , it becomes 111 . what is that number ?
A.12.
B.29.
C.27.
D.16.
e ) 99D.
"explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 111 6 x + 15 = 111 6 x = 96 x = 16 answer : d" | 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 . 700 more than d , what is b ' s share ?
A.rs . 500.
B.rs . 1400.
C.rs . 2000.
D.rs . 2500.
e ) none of the aboveB.
"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 = 700 x = 700 . b ' s share = rs . 2 x = rs . ( 2 x 700 ) = rs . 1400 . answer = b" | null |
Question: if the simple interest on a sum of money for 5 years at 9 % per annum is rs . 800 , what is the compound interest on the same sum at the rate and for the same time ?
A.rs . 947.55.
B.rs . 957.55.
C.rs . 857.55.
D.rs . 657.55.
e ) rs . 357.55B.
"sum = ( 800 * 100 ) / ( 5 * 9 ) = rs . 1 , 777.78 c . i . on rs . rs . 1 , 777.78 for 5 years at 9 % = rs . 2 , 735.33 . = rs . 2 , 735.33 - 1 , 777.78 = rs . 957.55 answer : b" | null |
Question: find the difference between c . i and s . i on a sum of money rs . 2000 for 2 years . at 4 % p . a
A.rs . 2.20.
B.rs . 3.20.
C.rs . 4.20.
D.rs . 5.20.
e ) rs . 3.25B.
p 9 r / 100 ) ^ 2 = 2000 ( 4 / 100 ) ^ 2 = rs . 3.20 answer : b | null |
Question: if 5 machines can produce 20 units in 10 hours , how long would it take 10 machines to produce 100 units ?
A.25.
B.30.
C.35.
D.24.
e ) 96A.
"5 machines would produce 100 units in 50 hours . increasing the amount of machines by 2 would mean dividing 50 hours by 2 . 50 / 2 = 25 answer : a" | null |
Question: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2340 , what will be a ' s share of the earnings ?
A.$ 1100.
B.$ 520.
C.$ 1040.
D.$ 1170.
e ) $ 630C.
"explanatory answer a , b and c will share the amount of $ 2340 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 2340 will be 4 : 3 : 2 . hence , a ' s share will be 4 * 2340 / 9 = 1040 correct choice is ( c )" | null |
Question: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.00 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
A.s . 666.
B.s . 1140.
C.s . 999.
D.s . 1085.
e ) s . 1020A.
"a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 β 6 = 666 * 1.0 = 666 answer : a" | null |
Question: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 5 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
A.25 km.
B.30 km.
C.40 km.
D.50 km.
e ) 60 kmA.
"number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 5 = 25 km imo , correct answer is ` ` a . ' '" | null |
Question: a positive number x is multiplied by 10 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
A.9 / 4.
B.3 / 2.
C.4 / 3.
D.2 / 3.
e ) 10 / 3E.
"sq rt ( 10 x / 3 ) = x = > 10 x / 3 = x ^ 2 = > x = 10 / 3 ans - e" | null |
Question: if 90 % of a = 30 % of b and b = c % of a , then the value of c is ?
A.900.
B.800.
C.600.
D.300.
e ) noneD.
"answer β΅ 90 a / 100 = 30 b / 100 = ( 30 / 100 ) x ac / 100 β΄ c = 100 x ( 100 / 30 ) x ( 90 / 100 ) = 300 correct option : d" | null |
Question: in a group of dogs and people , the number of legs was 28 more than twice the number of heads . how many dogs were there ? [ assume none of the people or dogs is missing a leg . ]
A.4.
B.7.
C.12.
D.14.
e ) 28D.
if there were only people , there would be exactly twice the number of legs as heads . each dog contributes two extra legs over and above this number . so 28 extra legs means 14 dogs . correct answer d | null |
Question: in a company , 50 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
A.85 %.
B.80 %.
C.75 %.
D.70 %.
e ) 65 %B.
"the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 50 % of all employees are women , so non - union women are 50 % - 18 % = 32 % 40 % of all employees are non - union . the percent of non - union employees who are women is 32 % / 40 % = 80 % the answer is b ." | null |
Question: 9 log 9 ( 4 ) = ?
A.1.
B.2.
C.3.
D.4.
e ) 5D.
"exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 4 ) = 4 correct answer d" | null |
Question: the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 5 ?
A.96.
B.106.
C.128.
D.137.
e ) 122D.
"average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 5 = 37 runs total runs = new avg x new no . of innings = 37 * 21 = 777 runs made in the 11 th inning = 777 - 640 = 137 answer : d" | null |
Question: yearly subscription to professional magazines cost a company $ 840.00 . to make a 30 % cut in the magazine budget , how much less must be spent ?
A.654.
B.655.
C.656.
D.588.
e ) 658D.
"total cost 840 840 * 30 / 100 = 252 so the cut in amount is 252 the less amount to be spend is 840 - 252 = 588 answer : d" | null |
Question: the area of a square is 4900 sq cm . find the ratio of the breadth and the length of a rectangle whose length is same the side of the square and breadth is 20 cm less than the side of the square ?
A.5 : 8.
B.5 : 10.
C.5 : 13.
D.5 : 7.
e ) 5 : 16D.
"let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4900 a = ( 4900 ) ^ 1 / 2 = 70 l = a and b = a - 20 b : l = a - 20 : a = 50 : 70 = 5 : 7 answer : d" | null |
Question: a man walking at a rate of 10 km / hr crosses a bridge in 18 minutes . the length of the bridge is ?
A.1521.
B.3000.
C.1667.
D.1254.
e ) 1112B.
"speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 18 * 60 = 3000 m answer is b" | null |
Question: the inner circumference of a circular race track , 14 m wide , is 440 m . find radius of the outer circle .
['A.84', 'B.86', 'C.82', 'D.80', 'e ) none of them']A.
let inner radius be r metres . then , 2 ( 22 / 7 ) r = 440 = r = ( 440 x ( 7 / 44 ) ) = 70 m . radius of outer circle = ( 70 + 14 ) m = 84 m . answer is a | null |
Question: r is the set of positive even integers less than 20 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
['A.none', 'B.two', 'C.three', 'D.five', 'e ) seven']C.
squares < 20 { 1,4 , 9,16 } s = { 1,4 , 9,16 } r = { 2 , . . . . . 18 } hence c . | null |
Question: elena β s bread recipe calls for 3 ounces of butter for each 4 cups of flour used . she needs to make 7 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
A.1.
B.4.
C.9.
D.13.
e ) 28E.
"solving through algebra route : 3 b + 4 f = x amount if we multiply this equation with 7 we get : 21 b + 28 f = 7 x therefore , we got 21 ounces of butter and 7 x amount of quantity when we use 28 ounces of floor . ans : e" | null |
Question: find the area , diameter = 13 m .
A.132.00 square meter.
B.132.04 square meter.
C.132.78 square meter.
D.132.24 square meter.
e ) 113.43 square meterC.
"diameter = 13 meter . radius = diameter / 2 . = 13 / 2 . = 6.5 meter . area of a circle = Γ― β¬ r 2 . here , pi ( Γ― β¬ ) = 3.14 meter , radius ( r ) = 6.5 area of a circle = 3.14 Γ£ β 6.5 Γ£ β 6.5 . = 3.14 Γ£ β 42.25 . = 132.78 square meter answer : c" | null |
Question: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 45 , find the other ?
A.100.
B.160.
C.120.
D.200.
e ) 150B.
"other number = 12 * 600 / 45 = 160 answer is b" | null |
Question: in a can , there is a mixture of milk and water in the ratio 4 : 3 . if the can is filled with an additional 8 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?
A.40.
B.36.
C.32.
D.28.
e ) 24B.
"let c be the capacity of the can . ( 4 / 7 ) * ( c - 8 ) + 8 = ( 2 / 3 ) * c 12 c - 96 + 168 = 14 c 2 c = 72 c = 36 the answer is b ." | null |
Question: according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 272 6 ounces servings of orange juice ?
A.A.25.
B.B.34.
C.C.50.
D.D.67.
e ) e ) 100B.
"its b . total juice rquired = 272 * 6 = 1632 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1632 / 48 = 34 . answer b" | null |
Question: to produce an annual income of rs . 1200 from a 12 % stock at 90 , the amount of stock needed is :
A.rs . 10,000.
B.rs . 10,800.
C.rs . 14,400.
D.rs . 16,000.
e ) none of theseA.
solution for an income of rs . 12 , stock needed = rs . 100 . for an income of rs . 1200 , stock needed = rs . 100 / 12 x 1200 = 10000 answer a | null |
Question: if the least common addition of two prime numbers x and y is 10 , where x > y , then the value of 2 x + y is
A.7.
B.9.
C.14.
D.17.
e ) 21D.
"( x + y ) = 10 and both x an y are prime . the only values of x and y can be 7 and 3 ( x = 7 and y = 3 ) 2 x + y = 2 * 7 + 3 = 17 correct option : d" | null |
Question: what is the length of a bridge ( in meters ) , which a train 156 meters long and travelling at 45 km / h can cross in 40 seconds ?
A.308.
B.320.
C.332.
D.344.
e ) 356D.
"speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 40 seconds , the train can travel 25 / 2 * 40 = 500 meters 500 = length of train + length of bridge length of bridge = 500 - 156 = 344 meters the answer is d ." | null |
Question: a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
A.2 / 11.
B.4 / 15.
C.6 / 17.
D.8 / 21.
e ) 10 / 25D.
"the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 6 c 3 * 4 c 3 = 20 * 4 = 80 p ( selling 3 bottles of apple juice ) = 80 / 210 = 8 / 21 the answer is d ." | null |
Question: if 10 men can reap 120 acres of land in 15 days , how many acres of land can 20 men reap in 30 days ?
A.120.
B.240.
C.360.
D.1200.
e ) 480E.
"10 men 120 acres 15 days 20 men ? 30 days 120 * 20 / 10 * 30 / 15 120 * 2 * 2 120 * 4 = 480 answer : e" | null |
Question: the profit earned by selling an article for 852 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
A.960.
B.975.
C.1,200.
D.920.
e ) none of theseB.
"let the profit or loss be x and 852 β x = 448 + x or , x = 404 β 2 = 202 \ cost price of the article = 852 β x = 448 + x = 650 \ sp of the article = 650 Γ 150 β 100 = 975 answer b" | null |
Question: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 6 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
A.2 : 9.
B.2 : 7.
C.1 : 6.
D.1 : 1.
e ) 1 : 3D.
"( 10 / 100 ) a + ( 2 / 100 ) b = ( 6 / 100 ) ( a + b ) 4 a = 4 b = > a / b = 1 / 1 answer is d ." | null |
Question: zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 7 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 7 questions did zachary answer correctly ?
A.6.
B.7.
C.8.
D.9.
e ) 10B.
"i got two equations : 3 x - 2 y = 25 x + y = 7 3 x - 2 ( 7 - x ) = 25 3 x - 14 + 2 x = 25 5 x = 39 x = 7.8 or between 7 and 8 . ( ans b )" | null |
Question: find the least number which when divided by 35 and 11 leaves a remainder of 1 in each case .
A.366.
B.236.
C.367.
D.365.
e ) 386E.
"explanation : the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 35 , 11 ) + 1 = 386 . answer : e" | null |
Question: the speed of a car is 90 km in the first hour and 75 km in the second hour . what is the average speed of the car ?
A.89 kmph.
B.82.5 kmph.
C.75 kmph.
D.65 kmph.
e ) 77 kmphB.
"s = ( 90 + 75 ) / 2 = 82.5 kmph b" | null |
Question: a larger cube has 64 cubic inch as a volume and in the cube there are 64 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas β sum of the 64 smaller cubes and the surface area of the larger cube , in square inch ?
A.54.
B.64.
C.81.
D.288.
e ) 120D.
"volume of larger cube = 64 = 4 ^ 3 side of larger cube = 4 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 4 ^ 2 = 96 surface area of 27 smaller cubes = 64 * 6 * 1 = 384 difference = 384 - 96 = 288 answer : d" | null |
Question: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 8 hours to fill the tank . the leak can drain all the water of the tank in ?
A.17 hr.
B.19 hr.
C.10 hr.
D.34 hr.
e ) 36 hrD.
"work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 8 ) = 1 / 34 leak will empty the tank in 34 hrs . answer : d" | null |
Question: two buses each 3125 m long are running in opposite directions on parallel roads . their speeds are 40 km / hr and 35 km / hr respectively . find the time taken by the slower bus to pass the driver of the faster one ?
A.50 sec.
B.66 sec.
C.48 sec.
D.55 sec.
e ) 45 secA.
relative speed = 40 + 35 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 3125 + 3125 = 6250 m . required time = 6250 * 6 / 125 = 50 sec . answer : a | null |
Question: if the perimeter of a rectangular garden is 500 m , its length when its breadth is 100 m is ?
A.299 m.
B.777 m.
C.200 m.
D.167 m.
e ) 150 mE.
"2 ( l + 100 ) = 500 = > l = 150 m answer : e" | null |
Question: a man goes from a to b at a speed of 15 kmph and comes back to a at a speed of 12 kmph . find his average speed for the entire journey ?
A.13.7 kmph.
B.13.3 kmph.
C.13.8 kmph.
D.13.9 kmph.
e ) 12.3 kmphB.
distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 15 ) + ( d / 12 ] = ( 2 d ) / [ 9 d / 60 ) = > 13.3 kmph . answer : b | null |
Question: a cube is divided into 729 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that the cube is coloured with green colour on one set of adjacent faces , red on the other set of adjacent faces , blue on the third set . so , how many cubelets are there which are painted with exactly one colour ?
A.293.
B.294.
C.295.
D.296.
e ) 298B.
"total cubes created are 729 so a plane of big cube has 9 * 9 cubes out of that ( n - 2 ) * ( n - 2 ) = 7 * 7 = 49 are painted only one side and a cube has six sides = 6 * 49 = 294 answer : b" | null |
Question: in a mixed college 160 students are there in one class . out of this 160 students 3 / 4 students are girls . how many boys are there ?
A.40.
B.60.
C.80.
D.120.
e ) 140A.
"total number of students : 160 total girls : 160 * 3 / 4 = 120 total boys : 160 - 120 = 40 answer is a" | null |
Question: the perimeter of a triangle is 60 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
A.A.72.
B.B.828.
C.C.729.
D.D.75.
e ) e ) 35D.
"explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 60 / 2 = 35 cm 2 answer : option d" | null |
Question: the product z of two prime numbers is between 10 and 30 . if one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24 , then what is z ?
A.21.
B.15.
C.14.
D.10.
e ) 6A.
"the smallest possible product is 21 which is 3 * 7 . all other products are too big . the answer is a ." | null |
Question: how many integers from 0 to 44 , inclusive , have a remainder of 1 when divided by 3 ?
A.13.
B.16.
C.17.
D.18.
e ) 19A.
"explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 43 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 43 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 42 or , n - 1 = 12 or , n = 13 a" | null |
Question: he total marks obtained by a student in physics , chemistry and mathematics is 150 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
A.55.
B.65.
C.75.
D.85.
e ) 95C.
"let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 150 + p c + m = 150 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 150 / 2 = 75 . answer : c" | null |
Question: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 7 hours to fill the tank . the leak can drain all the water of the tank in ?
A.17 hr.
B.19 hr.
C.10 hr.
D.24 hr.
e ) 30 hrE.
"work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 7 ) = 1 / 30 leak will empty the tank in 30 hrs . answer : e" | null |
Question: a ranch has both horses and ponies . exactly 5 / 7 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 3 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
A.33.
B.37.
C.41.
D.45.
e ) 49D.
"5 / 7 * p are ponies with horseshoes , so p is a multiple of 7 . 2 / 3 * 5 / 7 * p = 10 / 21 * p are icelandic ponies with horseshoes , so p is a multiple of 21 . the minimum value of p is 21 . then h = p + 3 = 24 . the minimum number of horses and ponies is 45 . the answer is d ." | null |
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