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Question: the population of a town is 8000 . it decreases annually at the rate of 30 % p . a . what will be its population after 2 years ?
A.3920.
B.5120.
C.5200.
D.5400.
e ) 5500A.
"formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 70 / 100 ã — 70 / 100 = 3920 answer : a" | null |
Question: a hall is 15 meters long and 10 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
A.600.
B.700.
C.800.
D.900.
e ) 1000D.
"2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 900 the answer is d ." | null |
Question: a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points e that an individual player might have scored ?
A.7.
B.13.
C.16.
D.21.
e ) 23E.
"general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points e for 12 th player is 100 - 77 = 23 . answer : e ." | null |
Question: a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1990 on her 32 nd birthday first be eligible to retire under this provision ?
A.2003.
B.2009.
C.2005.
D.2006.
e ) 2007B.
she must gain at least 70 points , now she has 31 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1990 + 19 = 2009 . answer : b . | null |
Question: the average age of 17 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?
A.39.
B.41.
C.45.
D.42.
e ) 50B.
"age of the 15 th student = 17 * 15 - ( 14 * 5 + 16 * 9 ) = 255 - 214 = 41 years answer is b" | null |
Question: ajay can ride 50 km in 1 hour . in how many hours he can ride 1500 km ?
A.30 hrs.
B.15 hrs.
C.20 hrs.
D.25 hrs.
e ) 18 hrsA.
"1 hour he ride 50 km he ride 1500 km in = 1500 / 50 * 1 = 30 hours answer is a" | null |
Question: a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 54 inches and the width of the wall is 68 inches , what is the length of the wall , in inches ?
['A.25.7', 'B.72.7', 'C.70.7', 'D.85.7', 'e ) 56.7']D.
since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 54 ^ 2 = 2916 . area of rectangle is double of that 2 * 2916 = 5832 . now a = lw and we need find w so a / l = w ; 5832 / 68 = 85.7 answer ! answer is d | null |
Question: fresh grapes contain 80 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 40 kgs of raisins ?
A.150 kgs.
B.64 kgs.
C.72 kgs.
D.65 kgs.
e ) 70 kgsA.
"the weight of non - water in 40 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 80 = 20 % of whole weight ) , so 40 * 0.75 = x * 0.2 - - > x = 150 . answer : a ." | null |
Question: a is twice as good a work man as b and together they finish the work in 4 days . in how many days a alone can finish the work ?
A.3.
B.2.
C.7.
D.9.
e ) 6E.
"wc = 2 : 1 2 x + x = 1 / 4 = > x = 1 / 12 2 x = 1 / 6 a can do the work in 6 days . answer : e" | null |
Question: if p is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
A.10.
B.12.
C.14.
D.16.
e ) 18C.
"no need to actually find the product of 1 to 30 . just look at the numbers that have factors of 3 . 3 = 3 6 = 3 * 2 9 = 3 * 3 12 = 3 * 2 * 2 15 = 3 * 5 18 = 3 * 3 * 2 21 = 3 * 7 24 = 3 * 2 * 2 * 2 27 = 3 * 3 * 3 30 = 3 * 2 * 5 there are 14 3 ' s , so the largest factor of p for 3 k is 3 * 14 answer : c" | null |
Question: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ?
A.2 / 3.
B.1 / 3.
C.2 / 9.
D.1 / 12.
e ) 1 / 24D.
"probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( d ) answer : d" | null |
Question: a woman swims downstream 45 km and upstream 15 km taking 3 hours each time , what is the speed of the woman in still water ?
A.10.
B.12.
C.14.
D.16.
e ) 18A.
45 - - - 3 ds = 15 ? - - - - 1 15 - - - - 3 us = 5 ? - - - - 1 m = ? m = ( 15 + 5 ) / 2 = 10 answer : a | null |
Question: in order to obtain an income of rs . 1000 from 50 % stock at rs . 500 , one must make an investment of
A.rs . 17000.
B.rs . 16050.
C.rs . 15400.
D.rs . 10000.
e ) rs . 10500D.
"explanation : market value = rs . 500 . required income = rs . 1000 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 50 ( ie , 50 % of the face value 100 ) , investment = rs . 500 to obtain rs . 1000 , investment = 500 / 50 ã — 1000 = 10000 answer : option d" | null |
Question: jack and jill are marathon runners . jack can finish a marathon ( 40 km ) in 4.5 hours and jill can run a marathon in 4.0 hours . what is the ratio of their average running speed ? ( jack : jill )
A.14 / 15.
B.15 / 14.
C.8 / 9.
D.5 / 4.
e ) can not be determinedC.
"average speed of jack = distance / time = 40 / ( 9 / 2 ) = 80 / 9 average speed of jill = 40 / ( 4.0 ) = 10 ratio of average speed of jack to jill = ( 80 / 9 ) / 10 = 8 / 9 answer c" | null |
Question: a snooker tournament charges $ 45.00 for vip seats and $ 15.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 300 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
A.212.
B.240.
C.220.
D.230.
e ) 225C.
"let no of sits in vip enclosure is x then x * 45 + 15 ( 300 - x ) = 7500 or 30 x = 7500 - 4500 , x = 3000 / 30 = 100 vip = 100 general 220 c" | null |
Question: the length of a rectangular floor is more than its breadth by 100 % . if rs . 600 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?
A.15.0 m ..
B.14.4 m ..
C.12.0 m ..
D.16.2 m ..
e ) 16.5 m .B.
"let the length and the breadth of the floor be l m and b m respectively . l = b + 100 % of b = l + 1 b = 2 b area of the floor = 600 / 3 = 200 sq m l b = 200 i . e . , l * l / 2 = 108 l 2 = 216 = > l = 14.4 m . answer : b" | null |
Question: 5 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?
A.2988.
B.2776.
C.4400.
D.4675.
e ) 881D.
"x * ( 95 / 100 ) * ( 80 / 100 ) = 3553 x = 4675 answer : d" | null |
Question: what is the sum of the odd integers from 35 to 55 , inclusive ?
A.495.
B.550.
C.555.
D.600.
e ) 605A.
"the mean is 45 . sum = mean ( # of elements ) there are 11 odd numbers between 35 - 55 inclusive . 11 * 45 = 495 a" | null |
Question: every monday , marina eats one croissant and every tuesday she eats two croissants . on each subsequent day of the week , she eats a number of croissants equal to the sum of the croissants eaten on the two previous days , with the exception that if she eats more than 4 croissants on any particular day , the next day she will eat only one croissant . at the end of the week ( which runs from monday through sunday ) , the cycle resets , and marina goes back to eating one croissant on monday , two on tuesday , and so forth . if a particular month begins on a saturday , how many croissants will marina eat on the 30 th of that month ?
A.1.
B.2.
C.3.
D.5.
e ) 6A.
she eat as follow mon - 1 tue - 2 wed - 3 thr - 5 fri - 1 ( since she had more than 4 previous day ) sat - 6 sunday - 1 ( since she had more than 4 previous day ) so 30 th day of month she will have 1 . answer is a | null |
Question: a boy swims downstream 48 km and upstream 12 km taking 6 hours each time ; what is the speed of the current ?
A.1.
B.2.
C.3.
D.4.
e ) 5C.
"48 - - - 6 ds = 8 ? - - - - 1 12 - - - - 6 us = 2 ? - - - - 1 s = ? s = ( 8 - 2 ) / 2 = 3 answer : c" | null |
Question: if the sides of a cube are in the ratio 5 : 3 . what is the ratio of their diagonals ?
['A.5 : 9', 'B.9 : 3', 'C.5 : 4', 'D.3 : 5', 'e ) 5 : 3']E.
explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 5 : 3 d 1 : d 2 = 5 : 3 where √ 3 cancelled both side answer : e | null |
Question: the average weight of 26 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
A.49.05.
B.42.25.
C.50.
D.51.25.
e ) 52.25A.
"explanation : average weight of 26 boys = 50.25 total weight of 26 boys = 50.25 × 26 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 26 ) + ( 45.15 × 8 ) total boys = 26 + 8 = 34 average weight of all the boys = ( 50.25 × 26 ) + ( 45.15 × 8 ) / 34 = 49.05 answer : option a" | null |
Question: a one - foot stick is marked in 1 / 4 and 1 / 5 portion . how many total markings will there be , including the end points ?
A.18.
B.16.
C.13.
D.9.
e ) 11D.
lcm of 20 = 20 1 / 4 marking are ( table of 5 ) 0 . . . . . . 5 . . . . . . 10 . . . . . 15 . . . . . . 20 ( total = 5 ) 1 / 5 marking are ( table of 4 ) 0 . . . . . . . 4 . . . . . . 8 . . . . . . 12 . . . . . . . . 16 . . . . . . 20 ( total = 6 ) overlapping markings are 0 . . . . . . . . 20 ( total = 2 ) total markings = 5 + 6 - 2 = 9 answer = d | null |
Question: find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years ?
A.272.22.
B.128.29.
C.306.04.
D.198.39.
e ) 212.22C.
"explanation : a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c" | null |
Question: the average score of a cricketer in 2 matches is 30 and in other 3 matches is 40 . then find the average score in all the 5 matches ?
A.25.
B.27.
C.30.
D.35.
e ) 36E.
average in 5 matches = ( 2 * 30 + 3 * 40 ) / 2 + 3 = 60 + 120 / 5 = 180 / 5 = 36 answer is e | null |
Question: two spherical balls lie on the ground touching . if one of the balls has a radius of 9 cm , and the point of contact is 10 cm above the ground , what is the radius of the other ball ( in centimeters ) ?
A.50 / 4.
B.70 / 6.
C.80 / 7.
D.90 / 8.
e ) 100 / 9D.
"a straight line will join the two centers and the point of contact , thus making similar triangles . 1 / 9 = ( r - 10 ) / r r = 9 r - 90 r = 90 / 8 the answer is d ." | null |
Question: in what ratio must tea at rs . 62 per kg be mixed with tea at rs . 72 per kg so that the mixture must be worth rs . 64.50 per kg ?
A.3 : 1.
B.2 : 1.
C.5 : 2.
D.3 : 2.
e ) 3 : 4A.
mean price = ( 72 - 64.5 = 7.5 ) ( 64.5 - 62 = 2.5 ) req ratio = 7.5 : 2.5 = 3 : 1 answer a | null |
Question: a solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm . the height of the cone is :
['A.8 cm', 'B.6 cm', 'C.4 cm', 'D.3 cm', 'e ) none']D.
sol . let the height of the cone be h cm . then , 1 / 3 ∏ * 6 * 6 * h = 4 / 3 ∏ * 3 * 3 * 3 ⇒ h = [ 36 * 3 / 36 ] = 3 cm . answer d | null |
Question: the present worth of rs . 2310 due years hence , the rate of interest being 15 % per annum , is :
A.rs . 1440.
B.rs . 1750.
C.rs . 1680.
D.rs . 1840.
e ) none of theseC.
"explanation : p . w . = rs . [ 100 × 2310 / 100 + ( 15 × 52 ) ] = rs . 1680 . answer : c" | null |
Question: if x is the median of the set { 8 / 2 , 11 / 3 , 27 / 9 , 21 / 5 , x } , x could be
A.4.
B.17 / 5.
C.16 / 5.
D.30 / 7.
e ) 31 / 7A.
the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 11 / 3 = 3 . something , 28 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( a ) | null |
Question: how many seconds will a train 100 meters long take to cross a bridge 140 meters long if the speed of the train is 36 kmph ?
A.26.
B.24.
C.25.
D.82.
e ) 27B.
"explanation : d = 100 + 140 = 240 s = 36 * 5 / 18 = 10 mps t = 240 / 10 = 24 sec answer : option b" | null |
Question: while working alone at their constant rates , computer x can process 240 files in 12 hours , and computer y can process 240 files in 6 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
A.3.
B.3.5.
C.4.
D.4.5.
e ) 5C.
"both computers together process files at a rate of 240 / 12 + 240 / 6 = 20 + 40 = 60 files per hour . the time required to process 240 files is 240 / 60 = 4 hours the answer is c ." | null |
Question: a and b together can complete work in 6 days . a alone starts working and leaves it after working for 4 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
A.4.
B.12.
C.5.
D.6.
e ) 7B.
"explanation : ( a + b ) one day work = 1 / 6 now a does half of the work in 4 days so a can complete the whole work in 8 days a ’ s one day work = 1 / 8 b ’ s one day work = 1 / 6 - 1 / 8 = 2 / 48 = 1 / 24 b alone can complete the work in 24 days so half of the work in 12 days answer : option b" | null |
Question: in town x , 64 percent of the population are employed , and 46 percent of the population are employed males . what percent of the employed people in town x are females ?
A.16 %.
B.25 %.
C.28 %.
D.40 %.
e ) 52 %C.
we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 46 are employed males , hence 18 % are employed females . ( employed females ) / ( total employed people ) = 18 / 64 = 28 % answer : c . | null |
Question: the lcm of two numbers is 2310 and hcf is 55 . if one of the numbers is 210 . then what is the other number ?
A.715.
B.825.
C.330.
D.605.
e ) 465D.
"first number * second number = lcm * hcf other number = 2310 * 55 / 210 = 11 * 55 = 605 answer : d" | null |
Question: what is the sum of all possible solutions to | x - 2 | ^ 2 + | x - 2 | = 20 ?
A.- 1.
B.6.
C.7.
D.8.
e ) 14D.
"denote | x - 2 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 2 | , so it ' s an absolute value and thus can not be negative . y = | x - 2 | = 4 - - > x = 6 or x = - 2 . the sum = 8 answer : d ." | null |
Question: a and b invests rs . 2500 and rs . 4000 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.11 : 5.
B.15 : 16.
C.15 : 2.
D.9 : 9.
e ) 11 : 1B.
"( 2.5 * 6 + 5 * 6 ) : ( 4 * 12 ) 45 : 48 = > 15 : 16 answer : b" | null |
Question: find the average of first 4 multiples of 11 ?
A.10.
B.12.6.
C.27.5.
D.31.3.
e ) 40.8C.
"average = ( 11 + 22 + 33 + 44 ) / 4 = 27.5 answer is c" | null |
Question: a car traveled from san diego to san francisco at an average speed of 54 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
A.24 ..
B.32 ..
C.36 ..
D.42 ..
e ) 44 .C.
let the time taken be = x one way distance = 54 x total distance traveled = 2 * 54 x = 108 x total time taken = x + 2 x = 3 x average speed = 108 x / 3 x = 36 answer : c | null |
Question: a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 8 hours longer than the first half , how many hours did it take the runner to run the second half ?
A.10.
B.12.
C.16.
D.20.
e ) 24C.
"the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 8 t 1 = 8 and so t 2 = 16 . the answer is c ." | null |
Question: a pump will fill a tank in 3 hours . because of a leak in the tank , it took 3 hours 30 min to fill the tank . in what time the leak can drain out all the water of the tank and will make tank empty ?
A.20 hrs.
B.21 hrs.
C.22 hrs.
D.23 hrs.
e ) 24 hrsB.
work done for 1 hr without leak = 1 / 3 work done with leak = 31 / 2 = = > 7 / 2 work and leak in 1 hr = 2 / 7 work leak in 1 hr = 1 / 3 - 2 / 7 = 1 / 21 so 21 hrs answer b | null |
Question: the area of a square garden is q square feet and the perimeter is p feet . if q = p + 21 , what is the perimeter of the garden in feet ?
['A.24', 'B.28', 'C.32', 'D.36', 'e ) 40']B.
let x be the length of one side of the square garden . x ^ 2 = 4 x + 21 x ^ 2 - 4 x - 21 = 0 ( x - 7 ) ( x + 3 ) = 0 x = 7 , - 3 p = 4 ( 7 ) = 28 the answer is b . | null |
Question: a train 100 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
A.28.
B.50.
C.88.
D.41.
e ) 12D.
"speed of the train relative to man = ( 100 / 10 ) m / sec = ( 10 ) m / sec . [ ( 10 ) * ( 18 / 5 ) ] km / hr = 36 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 36 = = > x = 41 km / hr . answer : d" | null |
Question: a positive number x is multiplied by 2 , and this product is then divided by 4 . 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 ) 1 / 2A.
"we need to produce an equation from the information given in the problem stem . we are first given that x is multiplied by 2 and then the product is divided by 3 . this gives us : 2 x / 3 next we are given that the positive square root of the result ( which is 2 x / 3 ) is equal to x . this gives us √ ( 2 x / 3 ) = x 2 x / 3 = x ^ 2 2 x = 3 x ^ 2 3 x ^ 2 – 2 x = 0 x ( 3 x – 2 ) = 0 x = 0 or 3 x – 2 = 0 3 x = 2 x = 9 / 4 because x is positive , x = 9 / 4 . the answer is a ." | null |
Question: how many multiples of 3 are there between 10 and 100 , exclusive ?
A.30.
B.29.
C.28.
D.31.
e ) 33A.
"3 * 4 = 12 3 * 33 = 99 total multiples = ( 33 - 4 ) + 1 = 30 exclude 10 and 100 = 30 answer is a" | null |
Question: an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 28 gallons of ethanol , how many gallons of fuel a were added ?
A.160.
B.150.
C.100.
D.80.
e ) 50C.
"say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 28 gallons then 0.12 a + 0.16 ( 200 - a ) = 28 - - > a = 100 . answer : c ." | null |
Question: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 14 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
A.2.
B.4.
C.5.
D.6.
e ) 8A.
total distance = 14 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 10 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 10 / 10 = 1 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 1 = 4 + 4 = 8 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 8 / 4 = 2 hrs . . . answer a | null |
Question: the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 2 / 5 of that total . what was the price of the basic computer ?
A.1300.
B.1600.
C.1750.
D.1900.
e ) 2000A.
"let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 2 / 5 of that new total price : p = 2 / 5 * $ 3,000 = $ 1200 . plug this value in the first equation : c + 1200 = $ 2,500 - - > c = $ 1,300 . answer : a ." | null |
Question: in a lottery there are 20 prizes and 35 blanks . a lottery is drawn at random . what is the probability of getting a prize
A.2 / 13.
B.4 / 11.
C.5 / 11.
D.6 / 11.
e ) 3 / 13B.
"total draws = prizes + blanks = 20 + 35 = 55 probability of getting a prize = 20 / 55 = 4 / 11 correct option is b" | null |
Question: lloyd normally works 7.5 hours per day and earns $ 3.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
A.$ 33.75.
B.$ 42.00.
C.$ 51.75.
D.$ 54.00.
e ) $ 70.00B.
"daily working hour * regular rate + overtime * increased rate 7.5 * 3.5 + 3 * 3.5 * 1.5 = 42 answer b" | null |
Question: tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many e kilometers per hour did tammy walk on the second day ?
A.3.
B.3.5.
C.4.
D.4.5.
e ) 6C.
ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5 | null |
Question: the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 462 the other is
A.330.
B.300.
C.270.
D.150.
e ) 350D.
"the other number = l . c . m * h . c . f / given number = 2310 * 30 / 462 = 150 answer is d ." | null |
Question: a reduction of 22 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
A.s . 2.82.
B.s . 2.4.
C.s . 2.5.
D.s . 2.2.
e ) s . 2.1A.
"100 * ( 22 / 100 ) = 22 - - - 10 ? - - - 1 = > rs . 2.2 100 - - - 78 ? - - - 2.2 = > rs . 2.82 answer : a" | null |
Question: a person incurs a loss of 5 % be selling a watch for rs . 1140 . at what price should the watch be sold to earn 5 % profit .
A.rs . 1200.
B.rs . 1230.
C.rs . 1260.
D.rs . 1290.
e ) rs . 1270C.
explanation : let the new s . p . be x , then . ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) = > ( 951 / 140 = 105 / x ) = > x = 1260 answer is c | null |
Question: patanjali 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 she walked the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?
A.24.
B.44.
C.58.
D.60.
e ) 62E.
patanjali walked 18 miles on the first day , walking 3 miles per hour i . e . total time of walk on day - 1 = 18 / 3 = 6 hours second day time of walk = 6 - 1 = 5 hours and speed = 3 + 1 = 4 miles per hour i . e . distance walked on second day = 5 * 4 = 20 miles third day time of walk = 6 hours and speed = 4 miles per hour i . e . distance walked on second day = 6 * 4 = 24 miles total distance travelled on three days = 18 + 20 + 24 = 62 answer : option e | null |
Question: the current in a river is 10 mph . a boat can travel 50 mph in still water . how far up the river can the boat travel if the round trip is to take 5 hours ?
A.120.
B.100.
C.96.
D.85.
e ) 150A.
upstream speed = 50 - 10 = 40 mph downstream speed = 50 + 10 = 60 mph d / 40 + d / 60 = 5 hours solving for d we get d = 120 answer : a | null |
Question: 60 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
A.33.
B.45.
C.26.
D.28.
e ) 19B.
"explanation : let the two parts be ( 60 - x ) and x . then , 10 ( 60 - x ) + 22 x = 780 = > 12 x = 180 = > x = 15 . bigger part = ( 60 - x ) = 45 . answer : b ) 45" | null |
Question: the sum of two number is 25 and their difference is 13 . find their product .
A.114.
B.104.
C.315.
D.350.
e ) 400A.
"let the numbers be x and y . then , x + y = 25 and x - y = 13 . 4 xy = ( x + y ) 2 - ( x - y ) 2 = ( 25 ) 2 - ( 13 ) 2 = ( 625 - 169 ) = = 456 = > 114 answer a" | null |
Question: a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 5 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
A.2.5 %.
B.17.67 %.
C.28.3 %.
D.36 %.
e ) 73.6 %D.
fiction novels = 5,508 transferred to another location = 6,120 transferred fiction novels = 1,101 non transferred fiction novels = 4,407 percent of the remaining collection was fiction novels = 4,407 / ( 18360 - 6120 ) * 100 = > 36.004 . . . % hence answer will be ( d ) | null |
Question: there is one 4 - digit whole number n , such that the last 4 digits of n 2 are in fact the original number n
A.8476.
B.7376.
C.9376.
D.7378.
e ) 9466C.
c 9376 looking at the last digit , the last digit must be either 0 , 1 , 5 or 6 . then looking at the last two digits , the last two digits must be either 0001 , 25 or 76 . then looking at the last three digits , the last three digits must be either 00001 , 625 or 376 . then looking at the last four digits , the last four digits must be either 0000001 , 0625 or 9376 . out of those , only 9376 is a 4 digit number | null |
Question: when two dice are tossed , what is the probability that the total score is a prime number ?
A.1 / 6.
B.3.
C.5 / 12.
D.7 / 12.
e ) 9 / 12C.
total number of outcomes possible = 36 probability of total score is a prime number = 15 p ( e ) = 15 / 36 = 5 / 12 answer : c | null |
Question: running at the same constant rate , 6 identical machines can produce a total of 420 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
A.648.
B.1800.
C.2800.
D.10800.
e ) 10900C.
"let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 420 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 420 x = ( 10 x 4 x 420 ) / ( 6 ) x = 2800 . answer : c" | null |
Question: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 5 days more ?
A.2280.
B.2240.
C.2299.
D.2288.
e ) 2266A.
"760 - - - - 22 760 - - - - 20 x - - - - - 5 x * 5 = 760 * 20 x = 3040 760 - - - - - - - 2280 answer : a" | null |
Question: the ratio of the volumes of two cubes is 216 : 343 . what is the ratio of their total surface areas ?
A.81 : 12.
B.31 : 36.
C.81 : 22.
D.8 : 19.
e ) 1 : 11B.
"ratio of the sides = ³ √ 216 : ³ √ 343 = 6 : 7 ratio of surface areas = 62 : 72 = 31 : 36 answer : b" | null |
Question: the length and breadth of a rectangle is increased by 10 % and 30 % respectively . what is the increase in the area ?
A.43.0.
B.44.0.
C.43.5.
D.45.0.
e ) 42.0A.
"100 * 100 = 10000 110 * 130 = 14300 - - - - - - - - - - 4300 10000 - - - - - - - 4300 100 - - - - - - - 43.00 answer a" | null |
Question: the distance between 2 cities a and b is 1000 km . a train starts from a at 11 a . m . and travels towards b at 100 km / hr . another starts from b at 12 p . m . and travels towards a at 150 km / hr . at what time do they meet ?
A.11 am ..
B.12 p . m ..
C.3 pm ..
D.4 p . m ..
e ) 1 p . m .D.
"suppose they meet x hrs after 11 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 11 + 5 = 4 p . m . answer is d" | null |
Question: in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 65 , what is the greatest possible value of b × a ?
A.0.
B.5.
C.10.
D.15.
e ) 25C.
"you should notice that 65 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 2 = 10 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : c ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . c" | null |
Question: if k is the greatest positive integer such that 3 ^ k is a divisor of 15 ! then k =
A.3.
B.4.
C.5.
D.6.
e ) 7D.
for solving this type of tasks we can use such approach 15 / 3 = 5 15 / 3 ^ 2 = 1 and remainder and 3 ^ 3 is more than 15 so we stop on second exponent 5 + 1 = 6 so maximum value of k = 6 and answer is d | null |
Question: how many of the integers between 15 and 55 are even ?
A.21.
B.20.
C.11.
D.10.
e ) 9B.
"number start between 15 to 55 is 40 numbers half of them is even . . which is 20 answer : b" | null |
Question: count the numbers between 10 - 99 which yield a remainder of 5 when divided by 8 and also yield a remainder of 1 when divided by 6 ?
A.one.
B.three.
C.two.
D.five.
e ) fourE.
"answer = e ) four numbers between 10 - 99 giving remainder 5 when divided by 8 = 13 , 21 , 29 , 37 , 45 , 53 , 61 , 69 , 77 , 85 , 93 the above numbers giving remainder 1 when divided by 6 = 13 , 37 , 61 , 85 = 4" | null |
Question: a train 510 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
A.40.
B.52.
C.26.
D.21.
e ) 14B.
"speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 510 + 140 = 650 m required time = 650 * 2 / 25 = 52 sec answer : b" | null |
Question: if ryan and smith car ratio is 5 : 8 . ryan bought 6 new car and smith bought 2 new car . now , smith has 18 car . what is their car ratio now ?
A.5 : 4.
B.3 : 2.
C.8 : 9.
D.6 : 5.
e ) 7 : 5C.
current no . of smith car = 8 x + 2 = 18,8 x = 16 , x = 2 . current car ratio = 10 + 6 / 18 = 16 / 18 = 8 : 9 . answer c | null |
Question: a ( 7 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 15 . what is the value of w ?
A.3 ..
B.4 ..
C.5 ..
D.6 ..
e ) 9 .B.
"y = x ^ 2 + 15 w ^ 3 = 7 ^ 2 + 15 w ^ 3 = 64 w = 4 answer b" | null |
Question: the timing of a college is from 12 p . m to 4.10 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
A.52 minutes.
B.45 minutes.
C.46 minutes.
D.48 minutes.
e ) 44 minutesC.
"explanation : total time a student spends in college = 4 hours 10 minutes = 250 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 250 â € “ 20 ) / 5 = 46 minutes answer c" | null |
Question: the grade point average of one third of the classroom is 45 ; the grade point average of the rest is 60 . what is the grade point average of the whole class ?
A.54.
B.55.
C.60.
D.65.
e ) 70B.
let n = total students in class total points for 1 / 3 class = 45 n / 3 = 15 n total points for 2 / 3 class = 60 * 2 n / 3 = 40 n total points for whole class = 15 n + 40 n = 55 n 63 n total class points / n total students = 55 grade point average for total class answer : b | null |
Question: 63 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
A.21.
B.23.
C.24.
D.25.
e ) 26A.
"according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 63 x 12 x 5 = 30 x 6 x x x = 21 hence , the number of days = 21 . answer : a" | null |
Question: marcella has 24 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
A.21.
B.20.
C.19.
D.16.
e ) 15C.
"marcella has 24 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 24 pairs of shoes minus the 5 ' destroyed ' pairs yields 19 pairs that still fulfill the requirements . answer : c" | null |
Question: the sum of the squares of three numbers is 138 , while the sum of their products take two at a time is 131 . find the sum ?
A.10.
B.30.
C.20.
D.50.
e ) 40C.
"formula is ( a + b + c ) ^ 2 = ( a ^ 2 ) + ( b ^ 2 ) + ( c ^ 2 ) + 2 ( ab + bc + ca ) = 138 + ( 2 * 131 ) the sum of the three numbers a + b + c = √ 400 = 20 answer is option c" | null |
Question: two trains are approaching each other at 60 mph each . the length of each train is 1 / 6 miles . when the two locomotives ( engines ) meet , how many seconds will it take for them to pass each other completely ?
A.8 sec.
B.11 sec.
C.12 sec.
D.10 sec.
e ) 15 secD.
total distance to cover = 2 * ( 1 / 6 ) = 2 / 6 miles relative speed = 60 + 60 = 120 mph time taken = ( 2 / 6 ) / 120 * 3600 = 10 sec . answer : d | null |
Question: a courtyard is 25 meter long and 15 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
A.22877.
B.27778.
C.18750.
D.27999.
e ) 17799C.
"number of bricks = courtyard area / 1 brick area = ( 2500 × 1500 / 20 × 10 ) = 18750 answer : c" | null |
Question: a team won 50 percent of its first 60 games in a particular season , and 80 percent of its remaining games . if the team won a total of 70 percent of its games that season , what was the total number of games that the team played ?
A.75.
B.90.
C.120.
D.150.
e ) 180E.
"70 % is 20 % - points above 50 % and 10 % - points below 80 % . thus the ratio of ` ` the first 60 games ' ' to ` ` remaining games ' ' is 1 : 2 . so the team played a total of 60 + 120 = 180 games . the answer is e ." | null |
Question: if k and w are the dimensions of a rectangle that has area 48 , and if k and w are integers such that k > w , what is the total number of possible values of k ?
A.four.
B.three.
C.two.
D.five.
e ) sixA.
"kw = 48 = 48 * 1 = 24 * 2 = 16 * 3 = 12 * 4 - - > k can take 4 values . answer : a" | null |
Question: a number when divided by 5 , gives 45 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 10
A.A.5.
B.B.3.
C.C.4.
D.D.6.
e ) e ) 7A.
"explanation : p ÷ 5 = 45 = > p = 45 * 5 = 225 p / 10 = 225 / 10 = 22 , remainder = 5 answer : option a" | null |
Question: a certain elevator has a safe weight limit of 1950 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 190 pounds and the average weight of the others being 200 pounds ?
A.7.
B.8.
C.9.
D.10.
e ) 11D.
"lets assume there are 2 x people . half of them have average weight of 190 and other half has 200 . maximum weight is = 1950 so 190 * x + 200 * x = 1950 = > 390 x = 1950 = > x is approximately equal to 5 . so total people is 2 * 5 = 10 answer d ." | null |
Question: a and b invests rs . 8000 and rs . 12000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
A.32 : 99.
B.82 : 31.
C.8 : 15.
D.34 : 89.
e ) 35 : 21C.
a : b ( 8000 * 4 ) + ( 4000 * 8 ) : ( 12000 * 6 ) + ( 9000 * 6 ) 64000 : 120000 8 : 15 answer : c | null |
Question: the height of the wall is 6 times its width and length of the wall is 7 times its height . if the volume of the wall be 86436 cu . m . its width is
A.4 m.
B.5 m.
C.6 m.
D.7 m.
e ) 8 mD.
"explanation : let width = x then , height = 6 x and length = 42 x 42 x ã — 6 x ã — x = 86436 x = 7 answer : d" | null |
Question: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 2000 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
A.$ 3,750.
B.$ 5,600.
C.$ 8,100.
D.$ 18,000.
e ) $ 22,500D.
"x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 2000 triples to $ 6000 , in 28 years , it will again triple to $ 6000 * 3 = $ 18,000 answer d" | null |
Question: a man buys rs . 44 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
A.s . 12.
B.s . 15.
C.s . 18.
D.s . 21.
e ) s . 33E.
"dividend on rs . 44 = rs . 9 / 100 x 44 = rs . 3.96 . rs . 12 is an income on rs . 100 . rs . 3.96 is an income on rs . 100 / 12 x 3.96 = rs . 33 . answer : option e" | null |
Question: water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 1 / 16 meters . what is value of the radius in meters ?
A.1 / 4.
B.2.
C.4.
D.8.
e ) 12C.
"10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 1 / 16 ) which is about 16 r = 4 the answer is c ." | null |
Question: the duplicate ratio of 4 : 5 is ?
A.1 : 2.
B.1 : 4.
C.1 : 8.
D.1 : 18.
e ) 16 : 25E.
4 ^ 2 : 5 ^ 2 = 16 : 25 answer : e | null |
Question: how many different ways can 2 students be seated in a row of 5 desks , so that there is always at least one empty desk between the students ?
A.2.
B.3.
C.4.
D.6.
e ) 12E.
"6 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 6 x 2 = 12 e" | null |
Question: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?
A.90 kg.
B.55 kg.
C.45 kg.
D.85 kg.
e ) 25 kgA.
"explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 70 + 20 ) kg = 90 kg . answer : a" | null |
Question: if the function q is defined by the formula q = 5 w / ( 4 h ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , h is doubled , and z is tripled ?
A.1 / 9.
B.2 / 9.
C.4 / 9.
D.3 / 9.
e ) 2 / 27B.
"we just need to find the factor thats all , w - > quadrupled - > 4 w h - > doubled - > 2 h z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and h * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b" | null |
Question: ( 856942 x 555 ) = ?
A.484638125.
B.474638130.
C.474638135.
D.475602810.
e ) 484638145D.
856942 x 555 = 475602810 ans d | null |
Question: the radius of a wheel is 20.4 cm . what is the distance covered by the wheel in making 400 resolutions ?
A.512.448 m.
B.704 m.
C.510.448 m.
D.706 m.
e ) 204 mA.
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 400 resolutions . = 400 * 2 * 22 / 7 * 20.4 = 51244.8 cm = 512.448 m answer : a" | null |
Question: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did c get in a profit of rs . 2490 ?
A.s . 332.
B.s . 498.
C.s . 822.
D.s . 812.
e ) s . 810B.
"let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 c ' s share in the profit of rs . 2490 = 12 ( 2490 / 60 ) = rs . 498 . answer : b" | null |
Question: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 20 % . what was its profit on the items sold in february ?
A.20 %.
B.30 %.
C.35 %.
D.37.5 %.
e ) 40 %A.
"assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.8 * 150 x = 120 x hence total profit = 20 % option a" | null |
Question: if the cost price of 50 articles is equal to the selling price of 20 articles , then the gain or loss percent is ?
A.16.
B.127.
C.12.
D.18.
e ) 150E.
"percentage of profit = 30 / 20 * 100 = 150 % answer : e" | null |
Question: what is rate of interest if principal . amount be 400 , simple interest 160 and time 2 year .
A.10.
B.12.5.
C.20.
D.12.
e ) 14.5C.
s . i = ( p * r * t ) / 100 160 = 800 r / 100 r = 160 / 8 = 20 % answer c | null |
Question: on her annual road trip to visit her family in seal beach , california , traci stopped to rest after she traveled 1 ⁄ 2 of the total distance and again after she traveled 1 ⁄ 4 of the distance remaining between her first stop and her destination . she then drove the remaining 200 miles and arrived safely at her destination . what was the total distance , in miles , from traci ’ s starting point to seal beach ?
A.250.
B.300.
C.800.
D.400.
e ) 550C.
"let d = total distance traci traveled 1 / 2 = d / 2 i . e . remaining distance = d / 2 she traveled 1 / 4 th of d / 2 = d / 8 thus : d = ( d / 2 ) + ( d / 8 ) + 200 d = 800 answer : c" | null |
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