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Question: find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 9 cm and 6 cm ?
A.210 cm 2.
B.150 cm 2.
C.168 cm 2.
D.198 cm 2.
e ) 987 cm 2A.
"1 / 2 * 28 ( 9 + 6 ) = 210 cm 2 answer : a" | null |
Question: the largest one digit number which is a perfect cube , is :
A.7.
B.8.
C.9.
D.1.
e ) 0B.
"explanation : 2 * 2 * 2 = 8 answer : b" | null |
Question: when the price of a product was decreased by 20 % , the number sold increased by 60 % . what was the effect on the total revenue ?
A.28 %.
B.32 %.
C.35 %.
D.45 %.
e ) 52 %A.
let the price of the product be $ 100 and let original sale be 100 pieces then , total revenue = 100 * 100 = $ 10000 new revenue = 80 * 160 = $ 12800 increase in revenue = 2800 * 100 / 10000 = 28 % answer is a | null |
Question: in a rare coin collection , all coins are either pure gold or pure silver , and there is initially one gold coin for every 3 silver coins . with the addition of 15 more gold coins to the collection , the ratio of gold coins to silver coins is 1 to 2 . based on this information , how many total coins are there now in this collection ( after the acquisition ) ?
A.124.
B.135.
C.146.
D.157.
e ) 168B.
initially the number of gold coins and silver coins is 2 k and 6 k . after adding gold coins , the number of coins is 3 k and 6 k . thus k = 15 and the total number of coins is 9 k = 135 . the answer is b . | null |
Question: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 100 . what is the value of y ?
A.50.
B.100.
C.200.
D.1,000.
e ) 2,000A.
"y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 100 y / 100 * 4 y = 100 y = 50 answer - a" | null |
Question: after giving a discount of rs . 45 the shopkeeper gets a loss of 10 % , if the cost price is rs . 180 . find the markup % ?
A.0.21.
B.0.2.
C.0.17.
D.0.21.
e ) 0.15E.
"cost price = 180 s . p = 180 * 90 / 100 = 162 disc = 45 so . . . mark price = 162 + 45 = 207 . . . . . . mark up % = 207 - 180 / 180 = 81 / 180 = . 15 or 15 % answer : e" | null |
Question: a student has to obtain 35 % of the total marks to pass . he got 100 marks and failed by 40 marks . the maximum marks are ?
A.280.
B.400.
C.420.
D.480.
e ) 520B.
"let the maximum marks be x then , 35 % of x = 100 + 40 35 x / 100 = 140 35 x = 140 * 100 = 14000 x = 400 answer is b" | null |
Question: if a : b = 3 : 4 , b : c = 7 : 9 , c : d = 5 : 7 , find a : d ?
A.5 / 12.
B.5 / 15.
C.5 / 10.
D.5 / 11.
e ) 5 / 13A.
"a / d = ( 3 / 4 ) * ( 7 / 9 ) * ( 5 / 7 ) = > 5 / 12 answer : a" | null |
Question: the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
A.8.
B.12.
C.15.
D.17.
e ) 18B.
"let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 β 40 y + 384 = 36 y + 432 β 4 y = 48 β΄ y = 12 b" | null |
Question: a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 12 days before the completion of the work . in how many days was the work completed ?
A.13 days.
B.16 days.
C.18 days.
D.11 days.
e ) 38 daysA.
"one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 12 days = 12 * ( 1 / 24 + 1 / 30 ) = 9 / 10 remaining work = 1 / 10 the number of days required for this initial work = 1 days . the total number of days required = 12 + 1 = 13 days . answer : a" | null |
Question: a parking garage rents parking spaces for $ 10 per week or $ 25 per month . how much does a person save in a year by renting by the month rather than by the week ?
A.$ 120.
B.$ 160.
C.$ 220.
D.$ 240.
e ) $ 260A.
"10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 25 = 300 $ 520 - 300 = 120 ans a" | null |
Question: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 630 , what is the least possible value of n ?
A.5.
B.6.
C.7.
D.8.
e ) 9C.
"630 = 2 * 3 * 3 * 5 * 7 , so n must be at least 7 . the answer is c ." | null |
Question: the total marks obtained by a student in mathematics and physics is 30 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
A.40.
B.30.
C.25.
D.data inadequate.
e ) none of these .C.
"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 30 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 30 + 20 ) / 2 = 25 . answer : c" | null |
Question: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1540 in all from both of them as interest . the rate of interest per annum is ?
A.7 %.
B.12 %.
C.74 %.
D.10 %.
e ) 45 %A.
"let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 1540 100 r + 120 r = 1540 r = 7 % answer : a" | null |
Question: solve for x and check : 25 x = 675
A.675.
B.725.
C.895.
D.1025.
e ) none of theseA.
"solution : dividing each side by 25 , we obtain ( 25 x / 675 ) = ( 675 / 25 ) therefore : x = 27 check : 25 x = 675 ( 25 * 27 ) = 675 675 = 675 answer : a" | null |
Question: given that x and y are events such that z ( x ) = 0.02 z ( y ) = 0.10 z ( xny ) = 0.10 z ( x | y ) = find z ( x | y ) and z ( x | y )
A.1 / 5.
B.1 / 6.
C.1 / 6.
D.1 / 4.
e ) 1 / 2A.
here , x and y are events z ( x | y ) = z ( xny ) / z ( y ) = 0.10 / 0.10 = 1 q ( g | h ) = z ( xny ) / z ( x ) = 0.4 / 0.02 = 1 / 5 answer is a | null |
Question: a jar contains a mixture of ab in the ratio 4 : 1 . when 40 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
A.12.
B.15.
C.16.
D.64.
e ) 25D.
40 litres of mixture that is replaced will contain 32 litres of a and 8 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 32 ] / [ k - 8 + 40 ] = 2 / 3 = > 12 k - 96 = 2 k - 16 + 80 = > 10 k = 160 solve for k which is k = 16 so initial volume of liquid a = 4 k = 64 litres answer : d | null |
Question: the length of a rectangle is 3 times its width . if the width of the rectangle is 6 inches , what is the rectangle ' s area , in square inches ?
A.30 square inches.
B.108 square inches.
C.68 square inches.
D.89 square inches.
e ) 92 square inchesB.
"if the width is 6 in and the length is 3 times the width , then the length is 3 * 6 = 18 in the area is given by 6 * 18 = 108 square inches correct answer b" | null |
Question: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 2500 . the difference between the profit shares of a and c is ?
A.621.
B.276.
C.236.
D.1000.
e ) 211D.
"explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 2500 = > 5 parts out of 15 parts is rs . 2500 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 2500 ) = rs . 1000 answer : d" | null |
Question: a truck drives 80 miles on local roads at 30 mph , and 50 miles on the highway at 60 mph , the truck also take a hour lunch break . what is the average speed of the entire trip ?
A.30 mph.
B.29 mph.
C.28 mph.
D.31 mph.
e ) 23 mphA.
so the answer is plainly a . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 80 miles , and v = 30 mph so we can obtain time : 30 * t = 80 or t = 80 / 30 = 2.6 hours the needed time to cover 80 miles in the same way we should divide 50 to 60 to find the needed time to cover 50 miles , so t = 0.8 hours so the total time for covering total distance would be 2.6 + 0.8 + 1 ( lunch time ) = 4.4 hours and total distance is 80 + 50 = 130 miles final stage : average speed is total distance divide to total time : 130 / 4.4 = 29.5 miles per hour rounding up to 30 . . . . | null |
Question: carrey rented a car for rs . 20 plus rs . 0.25 per kilometer driven . samuel rented a car for rs . 24 plus rs . 0.16 per kilometer driven . if each drove d km . and each was charged exactly the same amount for the rental , then d equals ?
A.44.4.
B.44.8.
C.1.
D.19.
e ) 44.11A.
explanation : 20 + 0.25 Γ d = 24 + 0.16 d solving we get d = 44.4 answer : a | null |
Question: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 24 ?
A.44.
B.46.
C.48.
D.50.
e ) 52C.
$ 24 = 4 * $ 6 the number of doughnuts is 4 * 12 = 48 the answer is c . | null |
Question: the speed of the boat in still water in 12 kmph . it can travel downstream through 48 kms in 3 hrs . in what time would it cover the same distance upstream ?
A.8 hours.
B.6 hours.
C.4 hours.
D.5 hours.
e ) 6 hoursE.
"still water = 12 km / hr downstream = 48 / 3 = 16 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 16 / 2 = 8 km / hr so time taken in upstream = 48 / 8 = 6 hrs answer : e" | null |
Question: on a sum of money , the simple interest for 2 years is rs . 326 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
A.15 %.
B.14.25 %.
C.8.58 %.
D.10.5 %.
e ) 11.5 %C.
"explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r Γ£ β si ) / ( 2 Γ£ β 100 ) difference between the compound interest and simple interest = 340 - 326 = 14 ( r Γ£ β si ) / ( 2 Γ£ β 100 ) = 14 ( r Γ£ β 326 ) / ( 2 Γ£ β 100 ) = 14 r = 8.58 % answer : option c" | null |
Question: in a certain supermarket , a triangular display of cans is arranged in 9 rows , numbered 1 through 9 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 120 cans in the entire display , how many cans are in the seventh row ?
A.13.
B.15.
C.17.
D.19.
e ) 21D.
"let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 24 ) = 9 x + 3 ( 1 + 2 + . . . + 8 ) = 9 x + 3 ( 8 ) ( 9 ) / 2 = 9 x + 108 since the total is less than 120 , x must equal 1 . the number of cans in the 7 th row is 1 + 3 ( 6 ) = 19 the answer is d ." | null |
Question: the length of a rectangle is 3 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?
A.30 square inches.
B.75 square inches.
C.68 square inches.
D.48 square inches.
e ) 92 square inchesD.
"if the width is 4 in and the length is 3 times the width , then the length is 3 * 4 = 12 in the area is given by 4 * 12 = 48 square inches correct answer d" | null |
Question: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.7 years . the ration of the number of boys to the number of girls in the class is ?
A.1 : 6.
B.2 : 3.
C.2 : 5.
D.2 : 1.
e ) 2 : 4A.
"let the ratio be k : 1 . then , k * 16.4 + 1 * 15.7 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.7 ) = k = 0.1 / 0.6 = 1 / 6 required ratio = 1 / 6 : 1 = 1 : 6 . answer : a" | null |
Question: a man walking at a rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge is ?
A.1250 m.
B.1310 m.
C.1500 m.
D.1000 m.
e ) 1195 mA.
"speed = 5 * 5 / 18 = 25 / 18 m / sec distance covered in 15 minutes = 25 / 18 * 15 * 60 = 1250 m answer is a" | null |
Question: a train traveling at 108 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
A.240 meters.
B.360 meters.
C.420 meters.
D.600 meters.
e ) can not be determinedB.
"answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 108 kmph * 12 seconds convert 108 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . β΄ 108 kmph = 5 / 18 β 108 = 30 m / sec therefore , length of the platform = 30 m / s * 12 sec = 360 meters . choice b" | null |
Question: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 11 . if p invested the money for 5 months , find for how much time did q invest the money ?
A.19.
B.17.
C.13.
D.11.
e ) 12D.
"7 * 5 : 5 * x = 7 : 11 x = 11 answer : d" | null |
Question: a fair price shopkeeper takes 10 % profit on his goods . he lost 30 % goods during theft . his loss percent is :
A.23 %.
B.42 %.
C.32 %.
D.12 %.
e ) 22 %A.
"explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 70 . s . p . of each item = rs . 1.10 total sale = 1.10 * 70 = rs . 77 hence , loss % = 23 / 100 * 100 = 23 % answer : a" | null |
Question: some people are standing square . from them 32 are removed and then form a small square and then 8 more removed . now we can not form the square . so how many people are there at the beginning ?
A.31.
B.32.
C.33.
D.34.
e ) ca n ' t be determinedE.
we should find the two square numbers whose difference is 32 . starting from 9,16 , 25,36 , 49,64 , 81,100 , . . . . we observe 81 - 49 = 32 & 49 - 8 = 41 which is not a square . answer : e | null |
Question: how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
A.22.
B.30.
C.88.
D.26.
e ) 12B.
"speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 500 * 3 / 50 = 30 sec . answer : b" | null |
Question: the ages of 2 persons differ by 32 years . if 12 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
A.30.
B.48.5.
C.50.4.
D.62.6.
e ) 47.9C.
"age of the younger person = x age of the elder person = x + 32 6 ( x - 12 ) = x + 32 - 12 x = 18.4 age of elder person = 18.4 + 32 = 50.4 answer is c" | null |
Question: on a certain date , pat invested $ 8,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 32,000 , in how many years total will the total value of the investment plus interest increase to $ 64,000 ?
A.15.
B.16.
C.18.
D.20.
e ) 24A.
"32,000 = 8,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 64,000 = 8,000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ." | null |
Question: the average age of 10 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
A.22.
B.30.
C.99.
D.38.
e ) 32E.
"total age increased = ( 10 * 2 ) years = 20 years . sum of ages of two new men = ( 21 + 23 + 20 ) years = 64 years average age of two new men = ( 64 / 2 ) years = 32 years . answer : e" | null |
Question: if 64 ( 8 ^ x ) = 1 then x =
A.2.
B.β 1.
C.0.
D.1.
e ) - 2E.
"8 ^ x = 1 / 64 8 ^ x = 1 / 8 ^ 2 8 ^ x = 8 ^ - 2 x = - 2 e" | null |
Question: a rectangle having length 105 cm and width 40 cm . if the length of the rectangle is increased by twenty five percent then how much percent the breadth should be decreased so as to maintain the same area .
A.25 %.
B.19.23 %.
C.40 %.
D.75 %.
e ) none of theseB.
"explanation : solution : ( 25 / ( 105 + 25 ) * 100 ) % = 19.23 % answer : b" | null |
Question: a tailor trims 6 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 80 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
A.16.
B.18.
C.20.
D.24.
e ) 32C.
"let the original side of the square be x . ( x - 12 ) * ( x - 10 ) = 80 = 8 * 10 x = 20 the answer is c ." | null |
Question: the base and height of a parallelogram are 12 m and 6 m respectively . then its area is = = = = = = ?
['A.27 sq . m', 'B.126 sq . m', 'C.84 sq . m', 'D.18 sq . m', 'e ) 72 sq . m']E.
a = b * h = > a = 12 * 6 = 72 sq . m . answer : ( e ) | null |
Question: how many prime numbers are between 76 / 8 and 124 / 5 ?
A.1.
B.2.
C.3.
D.4.
e ) 5E.
"76 / 8 = 38 / 4 = 19 / 2 = 10 - 124 / 5 = 25 - prime numbers between 10 and 29 are 11 , 13 , 17 , 19 , and 23 - sign signifies that the number is marginally less . answer e" | null |
Question: evaluate : 40 - 12 * 3 * 2 = ?
A.62.
B.52.
C.32.
D.12.
e ) 22C.
"according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 40 - 12 * 3 * 2 = 40 - 8 = 32 correct answer c" | null |
Question: pipe a can fill a tank in 6 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
A.18.
B.27.
C.96.
D.27.
e ) 21C.
"let the pipe b be closed after x minutes . 30 / 6 - x / 24 = 1 = > x / 24 = 30 / 6 - 1 = 4 = > x = 4 * 24 = 96 . answer : c" | null |
Question: what is the compound interest on rs : 40,000 for 4 months at the rate of 5 % per annum
A.670.85.
B.671.85.
C.672.85.
D.673.85.
e ) 674.85A.
"it is monthly compound rate = 5 / 12 % per month 40000 * ( 1 + 5 / 1200 ) ^ 4 - 40000 = 670.85 answer : a" | null |
Question: mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 6 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
A.1.
B.2.
C.3.
D.4.
e ) 5E.
"if n = 7 mark sold 1 box and ann sold 5 boxes total 6 < 7 answer : e" | null |
Question: the number of diagonals of a polygon of n sides is given by the formula q = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
A.3.
B.5.
C.6.
D.7.
e ) 8B.
"q = n ( n - 3 ) q = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b" | null |
Question: a fair price shopkeeper takes 10 % profit on his goods . he lost 70 % goods during theft . his loss percent is :
A.72 %.
B.42 %.
C.32 %.
D.67 %.
e ) 22 %D.
"explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 30 . s . p . of each item = rs . 1.10 total sale = 1.10 * 30 = rs . 33 hence , loss % = 67 / 100 * 100 = 67 % answer : d" | null |
Question: the age of somu is one - third his father ' s . 8 years back he was one - fifth of his father ' s age . what is his persent age ?
A.11.
B.13.
C.14.
D.16.
e ) 10D.
"explanation : let somu ' s age be x and that of his father be 3 x . so , x - 8 = 3 x - 8 / 5 = x = 16 answer : option d" | null |
Question: 13 buckets of water fill a tank when the capacity of each bucket is 42 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 6 litres ?
A.91.
B.80.
C.96.
D.98.
e ) 90A.
"capacity of the tank = ( 13 Γ£ β 42 ) litre number of buckets required of capacity of each bucket is 17 litre = 13 Γ£ β 42 / 6 = 13 Γ£ β 7 = 91 answer is a" | null |
Question: a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 4 tons ?
A.14.
B.20.
C.28.
D.32.
e ) 36C.
"the weight of one car and one truck is 4.75 tons . 70 / 4.75 = 14 plus a remainder the ferry could carry 14 cars and 14 trucks for a total of 28 vehicles . the answer is c ." | null |
Question: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 22 seconds . the ratio of their speeds is ?
A.3 / 1.
B.3 / 1.
C.1 / 1.
D.3 / 5.
e ) 5 / 2C.
"let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 22 = = > 27 x + 17 y = 22 x + 22 y = = > 5 x = 5 y = = > x / y = 1 / 1 . answer : c" | null |
Question: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 9 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
A.27.
B.35.
C.39.
D.60.
e ) 65A.
"the total number of the people in the room must be a multiple of both 7 and 9 ( in order 3 / 7 and 5 / 9 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 9 , which is 63 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 91 people in the room . therefore there are 3 / 7 * 63 = 27 people in the room under the age of 21 . answer : a ." | null |
Question: 4 , 12 , 48 , 240 , 1440 , 10080 , ( . . . )
A.80640.
B.10080.
C.6200.
D.10020.
e ) 12500A.
"explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7,8 answer : option a" | null |
Question: the product of two successive numbers is 7832 . which is the smaller of the two numbers ?
A.78.
B.68.
C.88.
D.97.
e ) 37C.
"c 88 from the given alternatives , 88 Γ 89 = 7832 β΄ smaller number = 88" | null |
Question: the value of 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 is
A.80.
B.800.
C.8000.
D.80000.
e ) none of theseB.
"solution therefore = 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 = 36 x 48 x 250 / 12 x 9 x 5 = 800 answer b" | null |
Question: two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 30 hr . if all pipes are opened simultaneously , then the cistern will be filled in
A.6.67 hr.
B.8 hr.
C.8.5 hr.
D.10 hr.
e ) none of theseA.
"solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 β 1 / 30 = 3 / 20 hence , tank will be filled in 20 / 3 = 6.67 hour option ( a )" | null |
Question: if 1 / 8 of a pencil is black 1 / 2 of the remaining is white and the remaining 7 / 2 is blue find the total length of the pencil ?
A.7.33 cm.
B.6.33 cm.
C.5.33 cm.
D.9.33 cm.
e ) 8.33 cmD.
( 1 / 8 ) p + ( 1 / 2 ) p + ( 7 / 2 ) = p on solving the above for p we get 9.333 now checking for the answer : 9.333 / 8 = 1.166 cm 9.333 / 2 = 4.665 cm now 1.166 + 4.665 + ( 7 / 2 ) = 9.33 cm answer : d | null |
Question: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 42 degrees . find the temperature on friday ?
A.34.
B.55.
C.66.
D.81.
e ) 21A.
"m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 42 tu + w + th = 192 - 42 = 150 f = 184 β 150 = 34 . answer : a" | null |
Question: a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
A.15.6.
B.16.0.
C.17.7.
D.18.7.
e ) 19.1C.
"a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.10 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.1 + $ 15.6 = $ 17.7 . answer : c ." | null |
Question: two cyclist start from the same places in opposite directions . one is going towards north at 30 kmph and the other is going towards south 40 kmph . what time will they take to be 50 km apart ?
A.1.32 hr.
B.0.714 hrs.
C.3.231 hrs.
D.0.515 hrs.
e ) 6.214 hrsB.
"to be ( 30 + 40 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 70 * 50 = 0.714 hrs answer is b" | null |
Question: in x - y plane , there is a right triangle abc ( β b = 90 o ) . if the length of ac is 25 and the slope of line segment ac is 4 / 3 , what is the length of ab ?
A.12.
B.18.
C.24.
D.20.
e ) 40D.
"slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 25 ^ 2 16 x ^ 2 + 9 x ^ 2 = 625 25 x ^ 2 = 625 x ^ 2 = 25 x = 5 therefore ab = 5 * 4 = 20 answer : d" | null |
Question: the average of 5 consecutive odd numbers a , b , c , d and e is 13 . what percent of b is c ?
A.98.2.
B.102.8.
C.108.2.
D.118.2.
e ) 122.8D.
explanation : in such a case the middle number ( c ) is the average β΄ c = 13 and b = 11 required percentage = 13 / 11 x 100 = 118.2 answer : option d | null |
Question: a palindrome is a number that reads the same forward and backward , such as 343 . how many odd , 8 - digit numbers are palindromes ?
A.4000.
B.4500.
C.5055.
D.5000.
e ) 2500D.
"first recognize you only need to consider the first four digits ( because the second four are just the first four flipped ) there are 9000 possibilities for the first four digits of a 8 digit number , 1000 - 9999 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 9000 = 5000 answer : d" | null |
Question: a person borrows rs . 7000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
A.100 rs.
B.150 rs.
C.140 rs.
D.180 rs.
e ) 200 rsC.
"gain in 2 years = [ ( 7000 * 6 * 2 ) / 100 ] - [ ( 7000 * 4 * 2 ) / 100 ] 840 - 560 = 280 gain in 1 year = ( 280 / 2 ) = 140 rs answer : c" | null |
Question: two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 240 marks in the second test and failed by 57 marks in that test . find the pass mark in the first test ?
A.768.
B.243.
C.246.
D.264.
e ) 224D.
"let the maximum mark in each test be m . the candidate failed by 57 marks in the second test . pass mark in the second test = 240 + 57 = 297 45 / 100 m = 297 pass mark in the first test = 40 / 100 m = 40 / 45 * 297 = 264 . answer : d" | null |
Question: if the side of the regular hexagon above is 2 , what is the circumference of the inscribed circle ?
['A.2 β β 3', 'B.3 β', 'C.4 β / β 3', 'D.2 β / β 3', 'e ) β β 3']A.
now ac will be 1 because circle is touching the midpoints of the circle . then we get kite acbo . we have ac = 1 and cb = 1 , now we need to find bo which is radius from triplets we get 30 : 60 : 90 = 1 : β 3 : 2 now cbo is right angled triangle , then we get bo as β 3 . r = β 3 . . . circumference is 2 β r is 2 β β 3 . answer : option a . | null |
Question: what is the difference between the local value of 1 and 2 in the number 2124 ?
A.70.
B.75.
C.20.
D.80.
e ) 60D.
explanation : 100 Γ’ β¬ β 20 = 80 answer : d | null |
Question: in 10 years , a will be twice as old as b was 10 years ago . if a is now 7 years older than b the present age of b is
A.37.
B.38.
C.39.
D.40.
e ) 41A.
"let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 7 = > 2 b - b - 7 = 30 b = 37 so the present age of b is 37 years answer : a" | null |
Question: the ratio of the present age of sandy to that of molly is 9 : 2 . eight years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
A.18.
B.21.
C.24.
D.27.
e ) 30B.
"let the present age of sandy be 9 x years and that of molly be 2 x years . ( 9 x + 8 ) / ( 2 x + 8 ) = 5 / 2 8 x = 24 x = 3 six years ago , sandy ' s age was 9 ( 3 ) - 6 = 21 the answer is b ." | null |
Question: rebecca ' s annual income is $ 15 , and jimmy ' s annual income is $ 18 . by how much must rebecca ' s annual income increase so that it constitutes 50 % of rebecca and jimmy ' s combined income ?
A.7.
B.8.
C.9.
D.3.
e ) 10D.
"total rebecca = x + 15 ; total = x + 20 + 18 x + 15 / x + 33 = 50 / 100 therefore x = 3 d" | null |
Question: you buy a piece of land with an area of Γ’ Λ Ε‘ 1600 , how long is one side of the land plot ?
A.28.
B.40.
C.30.
D.31.
e ) 32B.
"try filling the numbers into the answer y x y = find the closest to 900 . answer b" | null |
Question: a can do a work in 15 days b in 14 days and c in 16 days . if they work on it together then in how many days required to complete the work ?
A.3360 / 210.
B.3360 / 21.
C.3360 / 674.
D.3360 / 240.
e ) 3360 / 224C.
person ( a ) ( b ) ( c ) ( a + b + c ) time - ( 15 ) ( 14 ) ( 16 ) rate - ( 224 ) ( 240 ) ( 210 ) ( 674 ) work - ( 3360 ) ( 3360 ) ( 3360 ) ( 3360 ) therefore a + b + c requires ( 3360 / 674 ) days to complete entire work = 3360 / 674 answer is c | null |
Question: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 9 meters , and the interior of tank b has a height of 9 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
A.75 %.
B.90 %.
C.100 %.
D.120 %.
e ) 125 %B.
"the radius of tank a is 9 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 81 / ( 4 * pi ^ 2 ) = 405 / ( 2 * pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 9 * pi * 100 / ( 4 * pi ^ 2 ) = 450 / ( 2 * pi ) tank a / tank b = 405 / 450 = 9 / 10 = 90 % the answer is b ." | null |
Question: what is the smallest positive integer x such that 66 - x is the cube of a positive integer
A.5.
B.7.
C.47.
D.9.
e ) 2E.
"given 66 - x is a perfect cube so we will take 64 = 4 * 4 * 4 66 - x = 64 x = 66 - 64 = 2 correct option is e" | null |
Question: a cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 12 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
A.5.2 hrs.
B.2.9 hrs.
C.12 hrs.
D.7.2 hrs.
e ) 1.4 hrsC.
"net part filled in 1 hour = ( 1 / 6 - 1 / 12 ) = 1 / 12 the cistern will be filled in 12 / 1 hrs i . e . , 12 hrs . answer : c" | null |
Question: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 40 percent ryegrass , what percent of the weight of this mixture is x ?
A.100 %.
B.33.33 %.
C.40 %.
D.50 %.
e ) 66.66 %A.
"- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 40 % 0.4 x + ( m - x ) 0.25 = 0.4 m 0.15 x = 0.15 m x = 1 m x = 100 % of m a" | null |
Question: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 125 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
A.50.
B.100.
C.150.
D.200.
e ) 250E.
it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 125 total = 125 + 125 = 250 answer ( e ) | null |
Question: the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if y 12 = 110 , what is the value of y ?
A.11.
B.12.
C.13.
D.15.
e ) 18A.
ab = ( a - 1 ) ( b - 1 ) y 12 = ( y - 1 ) ( 12 - 1 ) = 110 - - > y - 1 = 10 - - > y = 11 answer : a | null |
Question: each month a retailer sells 100 identical items . on each item he makes a profit of $ 60 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
A.191.
B.213.
C.221.
D.223.
e ) 226D.
"for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 60 sell price = $ 600 + $ 60 thus , the sell price is $ 660 for each item . selling all 100 items gives the retailer . . . 100 ( $ 60 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 660 ) = $ 33 discount $ 627 = $ 600 + $ 27 now , the retailer makes a profit of just $ 27 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 27 ( x ) = $ 2,000 x = 2,000 / 27 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d" | null |
Question: a and b go around a circular track of length 200 m on a cycle at speeds of 36 kmph and 72 kmph . after how much time will they meet for the first time at the starting point ?
A.120 sec.
B.198 sec.
C.178 sec.
D.20 sec.
e ) 276 secD.
"time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 200 / ( 36 * 5 / 18 ) , 200 / ( 72 * 5 / 18 ) } = lcm ( 20 , 10 ) = 20 sec . answer : d" | null |
Question: if x and y are both odd prime numbers and x < y , how many distinct positive r integer factors does 2 xy have ?
A.3.
B.4.
C.6.
D.8.
e ) 12D.
since 2 xy prime r factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer . | null |
Question: a man can row 8 kmph in still water . when the river is running at 3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
A.5.75.
B.5.7.
C.5.76.
D.5.74.
e ) 6.8E.
"m = 8 s = 3 ds = 11 us = 5 x / 11 + x / 5 = 1 x = 3.4 d = 3.4 * 2 = 6.8 answer : e" | null |
Question: the length of a train and that of a platform are equal . if with a speed of 36 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
A.752.
B.799.
C.300.
D.750.
e ) 712C.
"speed = [ 36 * 5 / 18 ] m / sec = 10 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 10 Γ£ Β¨ x = 10 * 60 / 2 = 300 answer : c" | null |
Question: the overall age of x and y is 19 year greater than the overall age of y and z . z is how many decades younger that x ?
A.11.
B.15.
C.12.
D.19.
e ) 20D.
"d 19 ( x + y ) Γ’ β¬ β ( y + z ) = 19 x Γ’ β¬ β z = 19" | null |
Question: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 16 , then v =
A.30.
B.33.
C.36.
D.39.
e ) 42C.
"( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 16 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 36 the answer is c ." | null |
Question: find the perimeter and area of the rectangle of length 11 cm and breadth 9 cm .
A.71 cm 2.
B.99 cm 2.
C.141 cm 2.
D.171 cm 2.
e ) 221 cm 2B.
"length = 11 cm , breadth = 9 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 11 + 9 ) cm = 2 Γ 20 cm = 40 cm we know that the area of rectangle = length Γ breadth = ( 11 Γ 9 ) cm 22 = 99 cm 2 answer : b" | null |
Question: a group of men decided to do a work in 55 days , but 15 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?
A.180.
B.150.
C.140.
D.100.
e ) 25A.
"original number of men = 15 * 60 / ( 60 - 55 ) = 180 answer is a" | null |
Question: two trains are moving in the same direction at 108 kmph and 54 kmph . the faster train crosses a man in the slower train in 24 seconds . find the length of the faster train ?
A.320.
B.330.
C.340.
D.350.
e ) 360E.
"relative speed = ( 108 - 54 ) * 5 / 18 = 3 * 5 = 15 mps . distance covered in 27 sec = 24 * 15 = 360 m . the length of the faster train = 360 m . answer : e" | null |
Question: a student travels from his house to school at 10 km / hr and reaches school 2 hours late . the next day he travels 15 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?
A.60.
B.70.
C.80.
D.90.
e ) 100D.
"let x be the distance from his house to the school . x / 10 = x / 15 + 3 6 x = 4 x + 180 2 x = 180 x = 90 km the answer is d ." | null |
Question: a train 250 m long , running with a speed of 50 km / hr will pass a tree in ?
A.18 sec.
B.20 sec.
C.25 sec.
D.30 sec.
e ) 1 minA.
"speed = 50 * 5 / 18 = 125 / 9 m / sec time taken = 250 * 9 / 125 = 18 sec answer : a" | null |
Question: the length of minute hand of a clock is 5.4 cm . what is the area covered by this in 20 minutes
A.15.27.
B.16.27.
C.17.27.
D.30.54.
e ) 30.27D.
"area of circle is pi * r ^ 2 but in 20 minutes area covered is ( 20 / 60 ) * 360 = 120 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.4 ^ 2 ) * ( 120 / 360 ) = 30.54 cm ^ 2 answer : d" | null |
Question: country x imposes a two - tiered tax on imported cars : the first tier imposes a tax of 25 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 15 % . if ron imported a $ 30000 imported car and ended up paying $ 5500 in taxes , what is the first tier ' s price level ?
A.$ 10000.
B.$ 11000.
C.$ 12000.
D.$ 10500.
e ) $ 11500A.
let t be the tier price , p be total price = 30000 per the given conditions : 0.25 t + 0.15 ( p - t ) = 5500 0.25 t + 0.15 * 30000 - 0.15 t = 5500 0.10 t + 4500 = 5500 0.10 t = 5500 - 4500 = 1000 t = 1000 / 0.10 = 10000 answer a | null |
Question: in the faculty of reverse - engineering , 230 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
A.515 ..
B.545 ..
C.618 ..
D.649 ..
e ) 666 .D.
"answer is d : 649 solution : total number of students studying both are 423 + 230 - 134 = 519 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 519 , so 100 % is approx . 649 ." | null |
Question: the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 48 . what is a possible value for the mean of the distribution ?
A.46.
B.47.
C.48.
D.55.
e ) 50D.
"the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 48 : { mean } - 3 * { sd } > 48 ; { mean } - 6 > 48 ; { mean } > 54 . answer : d ." | null |
Question: a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 9 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
A.3.
B.9.
C.15.
D.21.
e ) 30A.
"let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 9 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 9 ) = 0.08 t - - > 60 + 6 ( t - 9 ) = 8 t - - > t = 3 . answer : a ." | 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 9 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 9 questions did zachary answer correctly ?
A.6.
B.7.
C.8.
D.9.
e ) 10C.
"i got two equations : 3 x - 2 y = 25 x + y = 9 3 x - 2 ( 9 - x ) = 25 3 x - 18 + 2 x = 25 5 x = 43 x = 8.6 or between 8 and 9 . ( ans c )" | null |
Question: if the average of 5 positive integers is 60 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
A.50.
B.52.
C.49.
D.68.
e ) 74D.
"sum of 5 integer ( a , b , c , d , e ) = 5 * 60 = 300 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 300 i . e . 5 a = 290 i . e . a = 58 i . e . largest e = 58 + 10 = 68 answer : option d" | null |
Question: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 160 of the workers of that company are men , how many of the workers are women ?
A.80.
B.95.
C.105.
D.120.
e ) 140E.
"set up equation : x = total number of workers 160 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 160 = 16 / 30 x x = 300 300 - 160 = 140 answer e" | null |
Question: the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 180,000 . what was the percent increase in the cost of the home ?
A.60 %.
B.50 %.
C.55 %.
D.40 %.
e ) 33.3 %B.
"percentage increase = increase in price / original price * 100 = ( 180000 - 120000 ) / 120000 * 100 = 50 % answer : b" | null |
Question: sum of 53 odd numbers is ?
A.2709.
B.2809.
C.2909.
D.3009.
e ) 3109B.
"sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 53 odd numbers = 53 ^ 2 = 2809 answer : b" | null |
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