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Question: find the value of 5 + 2 Γ’ β¬ Β’ ( 8 Γ’ β¬ β 3 )
A.25.
B.13.
C.17.
D.24.
e ) 15E.
5 + 2 Γ’ β¬ Β’ ( 8 Γ’ β¬ β 3 ) = 5 + 2 ( 5 ) = 5 + 2 * 5 = 5 + 10 = 15 correct answer e | null |
Question: the mass of 1 cubic meter of a substance is 500 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
A.0.8.
B.1.25.
C.2.0.
D.2.5.
e ) 80.0C.
"density is mass divided by volume . so density of the given substance will be mass / volume = 500 kg / 1 m ^ 3 = 800 kg / m ^ 3 or 1 g / 1.5 cm ^ 3 = 0.5 g / cm ^ 3 . next , ask yourself if 500,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 500,000 = 10 / 5 = 2.0 cubic centimeters . answer is c" | null |
Question: what least number should be added to 1057 , so that the sum is completely divisible by 23
A.A.4.
B.B.1.
C.C.2.
D.D.3.
e ) e ) 5B.
"explanation : ( 1057 / 23 ) gives remainder 22 22 + 1 = 23 , so we need to add 1 answer : option b" | null |
Question: he ratio between the sale price and the cost price of an article is 5 : 6 . what is the ratio between the profit and the cost price of that article ?
A.2 : 6.
B.1 : 8.
C.1 : 6.
D.2 : 1.
e ) 2 : 5C.
"let c . p . = rs . 6 x and s . p . = rs . 5 x . then , gain = rs . x required ratio = x : 6 x = 1 : 6 . answer : c" | null |
Question: . in digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be ?
A.3323.
B.1000.
C.2877.
D.2992.
e ) 7111B.
20 * 10 * 5 = 1000 answer : b | null |
Question: when 1 / 20 % of 8,000 is subtracted from 1 / 10 of 8,000 , the difference is
A.50.
B.200.
C.380.
D.798.
e ) 400D.
1 / 20 % of 8000 = 4 1 / 10 of 8000 = 800 800 - 2 = 798 ans : d | null |
Question: 35 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
A.4 %.
B.10 %.
C.96 %.
D.90.12 %.
e ) 70.77 %E.
no of employees = 100 ( say ) men = 35 women = 65 men speaking french = 0.6 * 35 = 21 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 21 = 19 and women not speaking french = 65 - 19 = 46 % of women speaking french = 46 / 65 * 100 = 70.77 % answer e | null |
Question: how many integers k greater than 100 and less than 700 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
A.50.
B.60.
C.70.
D.80.
e ) 90A.
"not sure if this is the shortest . . but this is how i did this there are 5 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . 506 | 607 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 5 sets with 10 such number in each set will give 5 x 10 = 50 integers . a" | null |
Question: a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 45 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
A.40.
B.45.
C.50.
D.55.
e ) 60E.
"a - b = 120 miles b - c = 60 miles avg speed = 45 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 45 = 180 / 4 t t = 60 b - c = 60 mph answer e" | null |
Question: which greatest possible length can be used to measure exactly 15 meter 20 cm , 12 meter 20 cm and 14 meter 20 cm
A.20 cm.
B.25 cm.
C.24 cm.
D.55 cm.
e ) 30 cmA.
"explanation : convert first all terms into cm . i . e . 1520 cm , 1220 cm , 1420 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 20 . option a" | null |
Question: dick and jane each saved $ 5,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 10,000 . approximately what percent less did jane save in 1990 than in 1989 ?
A.10 %.
B.15 %.
C.20 %.
D.25 %.
e ) 30 %A.
"1990 dick saved = $ 5500 jane saved = $ 4500 ( jane saved $ 500 less than she did the prior year ) jane saved approximately $ 500 / 5000 $ ( 10 % ) less in 1990 answer : a" | null |
Question: robert ate 7 chocolates , nickel ate 5 chocolates . how many more chocolates did robert ate than nickel ?
A.A.4.
B.B.7.
C.C.9.
D.D.5.
e ) e ) 2E.
7 - 5 = 2 . answer is e | null |
Question: a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 600 feet . what is its area , in square feet ?
['A.172,800', 'B.19,600', 'C.20,000', 'D.20,400', 'e ) 20,800']A.
you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 600 , you can deduce the following a = 360 b = 480 360 x 480 = 172,800 a is the answer . | null |
Question: on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor
A.12.
B.14.
C.18.
D.22.
e ) 24A.
"d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 a )" | null |
Question: find compound interest on $ 10000 at 15 % per annum for 2 years 4 months , compounded annually .
A.3886.25.
B.3286.25.
C.3186.25.
D.3386.25.
e ) 3586.25A.
"time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 10000 x ( 1 + Β ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 10000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 13886.25 . : . c . i . = rs . ( 13886.25 - 10000 ) = $ 3886.25 answer a ." | null |
Question: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.28 at the candy store . what is john β s weekly allowance ?
A.$ 2.40.
B.$ 3.00.
C.$ 3.20.
D.$ 3.60.
e ) $ 4.80E.
"total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 1.28 therefore , x = $ 4.80 . answer e" | null |
Question: what is the range of all the roots of | x ^ 2 - 4 | = x ?
A.4.
B.3.
C.2.
D.1.
e ) 0B.
"we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 4 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 4 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 4 or x = 1 i guess range is 4 - 1 = 3 b" | null |
Question: sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 60 ps per meter is ?
A.287.
B.369.
C.150.
D.279.
e ) 361C.
"3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.60 = rs . 150 answer : c" | null |
Question: the cost price of a radio is rs . 1680 and it was sold for rs . 1450 , find the loss % ?
A.18.
B.13.
C.15.
D.18.
e ) 41B.
"1680 - - - - 230 100 - - - - ? = > 13 % answer : b" | null |
Question: when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 7 . when n is divided by ( p + 3 ) , the quotient is 15 and the remainder is 1 . what is the value of n ?
A.151.
B.331.
C.511.
D.691.
e ) 205E.
"n / p = 18 7 / p = 18 p + 7 n / ( p + 2 ) = 15 1 / ( p + 3 ) = 15 p + 45 + 1 solving these two equations we get p = 11 n = 205 answer is e ." | null |
Question: if a person walks at 25 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
A.50 km.
B.56 km.
C.13.3 km.
D.70 km.
e ) 80 kmC.
"let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 25 25 x = 10 x + 200 15 x = 200 x = 13.3 km . answer : c" | null |
Question: a big container is 30 % full with water . if 45 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
A.36 liters.
B.40 liters.
C.45 liters.
D.54 liters.
e ) 100 litersE.
"a big container is 30 % full with water and after 45 liters of water is added , the container becomes 75 % full . hence these 45 liters account for 45 % of the container , which means that the capacity of it is 45 / 0.45 = 100 liters . or : if the capacity of the container is x liters then : 0.3 x + 45 = 0.75 x - - > x = 100 liters . answer : e ." | null |
Question: 32 % of 1500 is
A.480.
B.440.
C.370.
D.415.
e ) 435A.
1 % of 1500 is = 15 32 % of 1500 is = 32 * 15 = 480 answer : a | null |
Question: find the smallest number that should be multiplied with 54000 to make it a perfect cube .
['A.4', 'B.5', 'C.6', 'D.3', 'e ) 7']A.
54000 = 2 ^ 1 * 3 ^ 3 * 10 ^ 3 to make it ps * 2 ^ 2 or 4 answer : a | null |
Question: a β palindromic integer β is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 500000 ?
A.160.
B.200.
C.240.
D.300.
e ) 480B.
the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b . | null |
Question: the average of 7 numbers is 25 . if each number be multiplied by 5 . find the average of new set of numbers ?
A.A.110.
B.B.122.
C.C.120.
D.D.125.
e ) e ) 145D.
"explanation : average of new numbers = 25 * 5 = 125 answer : option d" | null |
Question: a 90 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
A.25.
B.20.
C.47.
D.36.
e ) 30A.
"1 : 2 / 5 = 5 : 2 2 / 7 * 90 = 25 answer : a" | null |
Question: there are cats got together and decided to kill the mice of 999964 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
A.941,1009.
B.991,1001.
C.991,1009.
D.791,1009.
e ) 994,1006E.
"999964 can be written as 1000000 Γ’ β¬ β 36 = 10002 Γ’ β¬ β 62 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 6 ) * ( 1000 - 6 ) = ( 1006 ) * ( 994 ) given that number of cats is less than number if mice . so number of cats is 994 and number of mice were 1006 answer e" | null |
Question: what is the remainder when you divide 2 ^ 200 - 1 by 7 ?
A.1.
B.2.
C.3.
D.4.
e ) 5C.
answer is c . this is very similar to the 32 ^ 32 ^ 32 - 1 divided by 7 question . | null |
Question: a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is :
A.16000.
B.18000.
C.20000.
D.22000.
e ) none of theseC.
"explanation : number of bricks = courtyard area / 1 brick area = ( 2500 Γ 1600 / 20 Γ 10 ) = 20000 option c" | null |
Question: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1008 ?
A.900.
B.2217.
C.2889.
D.2777.
e ) 2991A.
"1008 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 900 answer : a" | null |
Question: if a sum of money doubles itself in 20 years at simple interest , the ratepercent per annum is
A.12.
B.12.5.
C.13.
D.5.
e ) 14D.
"explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 20 ) = 5 option d" | null |
Question: what is the greatest integer m for which the number 50 ! / 10 ^ m is an integer ?
A.5.
B.8.
C.10.
D.11.
e ) 12E.
"as for 50 ! / 10 ^ m , the greatest value of m will be obtained by finding the maximum number of 5 s in 50 ! the quick process for that ( discussed in the link above ) is 50 / 5 = 10 10 / 5 = 2 total number of 5 s is 12 . so maximum value of m will also be 12 . answer ( e )" | null |
Question: at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 7.50 per hour , how much less than a manager does a chef earn each hour ?
A.$ 1.40.
B.$ 3.
C.$ 3.40.
D.$ 4.40.
e ) $ 5.40B.
"manager wages per hour = $ 7.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 7.50 ) = = > $ 3.75 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 3.75 = ( 20 * ( $ 3.75 ) ) / 100 - - > ( $ 75 ) / 100 - - > $ 0.75 therefore , chef wages per hour = $ 3.75 + $ 0.75 = = > $ 4.5 difference of wages between manager and chef = $ 7.50 - $ 4.5 = = > $ 3 answer : b" | 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 ) none of theseC.
"explanation : let the new s . p . be x , then . ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) = > ( 95 / 1140 = 105 / x ) = > x = 1260 option c" | null |
Question: a train is 400 meter long is running at a speed of 60 km / hour . in what time will it pass a signal post ?
A.28 seconds.
B.30 seconds.
C.40 seconds.
D.24 seconds.
e ) 18 secondsD.
speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 150 / 9 m / sec total distance = 400 meter time = distance / speed = 400 * ( 9 / 150 ) = 24 seconds answer : d | null |
Question: the average of first 10 natural numbers is ?
A.5.6.
B.5.5.
C.5.1.
D.5.8.
e ) 5.2B.
"sum of 10 natural no . = 110 / 2 = 55 average = 55 / 10 = 5.5 answer : b" | null |
Question: if a / b = 4 / 5 , then ( 5 a - 3 b ) / ( 5 a + 3 b ) = ?
A.4.
B.2 / 3.
C.3.
D.1.
e ) 1 / 7E.
"answer dividing numerator as well as denominator by b , we get given exp . = ( 5 a - 3 b ) / ( 5 a + 3 b ) = ( 5 a / b - 3 ) / ( 5 a / b + 3 ) since a / b = 4 / 5 this implies that = [ ( 5 * 4 ) / 5 - 3 ] / [ ( 5 * 4 ) / 5 + 3 ) ] = ( 4 - 3 ) / ( 4 + 3 ) = 1 / 7 option : e" | null |
Question: how long does a train 105 m long running at the speed of 68 km / hr takes to cross a bridge 90 m length ?
A.13.9 sec.
B.10.7 sec.
C.17.9 sec.
D.61.9 sec.
e ) 47.98 secB.
"speed = 68 * 5 / 18 = 19 m / sec total distance covered = 105 + 90 = 205 m . required time = 205 / 19 = 10.7 sec . answer : b" | null |
Question: there are 6 people in the elevator . their average weight is 152 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
A.145.
B.168.
C.189.
D.190.
e ) 200A.
"solution average of 7 people after the last one enters = 151 . Γ’ Λ Β΄ required weight = ( 7 x 151 ) - ( 6 x 152 ) = 1057 - 912 = 145 . answer a" | null |
Question: ms . lopez deposits $ 150 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?
A.$ 118.00.
B.$ 120.00.
C.$ 181.15.
D.$ 122.00.
e ) $ 140.00C.
"using formula - a = p ( 1 + r / n ) ^ nt given p = 150 n = 2 t = 1 r = 0.2 substituting value in formula a = 150 ( 1 + 0.2 / 2 ) ^ 2 a = 181.15 $ = c" | null |
Question: a , b , c can complete a piece of work in 25 , 5,10 days . working together , they complete the same work in how many days ?
A.2.
B.4 / 5.
C.50 / 17.
D.10.
e ) 24 / 7C.
"a + b + c 1 day work = 1 / 25 + 1 / 5 + 1 / 10 = 17 / 50 a , b , c together will complete the job in 50 / 17 days answer is c" | null |
Question: how much is 70 % of 40 is greater than 4 / 5 of 25 ?
A.22.
B.67.
C.88.
D.12.
e ) 8E.
"( 70 / 100 ) * 40 β ( 4 / 5 ) * 25 = 8 answer : e" | null |
Question: one man adds 3 liters of water to 12 liters of milk and another 4 liters of water to 10 liters of milk . what is the ratio of the strengths of milk in 2 mixtures ?
A.11 : 21.
B.15 : 33.
C.28 : 25.
D.3 : 2.
e ) 31 : 33C.
"strength of milk in the mixture = quantity of milk / total quantity of mixture strength of milk in the 1 st mixture = 12 / 15 strength of the milk 2 nd mixture = 10 / 14 the ratio of their strengths = 12 / 15 : 10 / 14 = 28 : 25 answer is c" | null |
Question: 27 is a perfect cube . when x is added to the prime factor of 27 , the result is a prime number . what is x ?
A.1.
B.3.
C.5.
D.8.
e ) 11D.
27 is 3 * 3 * 3 then a 3 + 1 = 4 b 3 + 3 = 6 c 3 + 5 = 8 d 3 + 8 = 11 e 3 + 11 = 14 here d is the only addition that gives a prime number . | null |
Question: a part - time employee β s hourly wage was increased by 10 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
A.9 %.
B.15 %.
C.25 %.
D.50 %.
e ) 100 %A.
"let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 10 % wage increase , the employee makes $ 1.10 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.10 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.10 to get : new # of hours = 100 / 1.10 β 90 hours so , the number of hours decreases from 100 hours to ( approximately ) 90 hours . this represents a 10 % decrease ( approximately ) . answer choice a is the closest answer ." | null |
Question: the price of stock decreased by 5 % last year and rose by 10 % this year . what is the net percentage change in the price of the stock ?
A.0.2 %.
B.0.8 %.
C.1.2 %.
D.1.6 %.
e ) 4.5 %E.
"( 100 % - 5 % ) * ( 100 % + 10 % ) = 0.95 * 1.10 = 1.045 = 104.5 % . the net percentage change in the price of the stock is ( + ) 4.5 % the answer is e" | null |
Question: the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 β€ s β€ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 7 seconds than it was moving after 5 seconds ?
A.4.
B.28.
C.15.
D.48.
e ) 63B.
"given : z = s ^ 2 + 2 s for 0 β€ s β€ 7 z ( 5 ) = 5 ^ 2 + 2 * 5 = 35 z ( 7 ) = 7 ^ 2 + 2 * 7 = 63 therefore z ( 7 ) - z ( 3 ) = 63 - 35 = 28 km / hr option b" | null |
Question: a soccer team played 280 games and won 65 percent of them . how many games did it win ?
A.182.
B.100.
C.104.
D.150.
e ) 124A.
"65 % of 280 = x 0.65 * 280 = x 182 = x answer : a" | null |
Question: the difference between two numbers is 2395 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is
A.120.
B.239.
C.476.
D.523.
e ) 526C.
let the smaller number be x . then , larger number = ( 2395 + x ) therefore 2395 + x = ( 6 x + 15 ) βΉ = βΊ 5 x = 2380 βΉ = βΊ x = 476 . answer : c | null |
Question: right triangle xyzs the base of the prism in the figure above . if xy = xz = Γ’ Λ Ε‘ 9 and the height of the prism is 6 , what is the volume of the prism ?
['A.3', 'B.27', 'C.13', 'D.12', 'e ) 15']B.
volume of prism = area of base * height = 1 / 2 * ( square root of 9 ) * ( square root of 9 ) * 6 = 27 answer : b | null |
Question: on dividing 22 by a number , the quotient is 7 and the remainder is 1 . find the divisor .
A.1.
B.2.
C.3.
D.6.
e ) 7C.
"d = ( d - r ) / q = ( 22 - 1 ) / 7 = 21 / 7 = 3 c" | null |
Question: the smallest number which when diminished by 5 , is divisible by 12 , 16 , 18 , 21 and 28 is
A.1008.
B.1013.
C.1022.
D.1032.
e ) 1043B.
"required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 5 = 1008 + 5 = 1013 answer : b" | null |
Question: the ratio between x and y is 7 / 5 ; x is multiplied by y and y is multiplied by x , what is the ratio between the new values of x and y ?
A.7 / 5.
B.5 / 7.
C.1.
D.49 / 25.
e ) it can not be determinedC.
ratio = 7 k / 5 k = 7 / 5 , 14 / 10 , etc . x is multiplied by y and y is multiplied by x - - > ( 7 k * 9 k ) / ( 9 k * 7 k ) = 1 answer : c | null |
Question: when x is multiplied by 3 , the result is 14 more than the result of subtracting x from 26 . what is the value of x ?
A.10.
B.- 2.
C.11.
D.13.
e ) 22A.
the equation that can be formed is : 3 x - 14 = 26 - x or , 4 x = 40 or , x = 10 . a answer . | null |
Question: raman , lakshmi and muthu enter into partnership . raman invests some money at the beginning , lakshmi invests double the amount after 6 months , and muthu invests thrice the amount after 8 months . if the annual gain be rs . 36000 . lakshmi ' s share is ?
A.12000.
B.14000.
C.8000.
D.5000.
e ) 3000A.
x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 36000 = 12000 answer : a | null |
Question: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 10 per square m ?
A.s . 9500.
B.s . 50000.
C.s . 57000.
D.s . 60000.
e ) s . 62000A.
length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 10 * 950 = rs . 9500 a | null |
Question: how many multiples of 4 are less than 6540 , and also multiples of 7 ?
A.234.
B.208.
C.340.
D.237.
e ) 267A.
"lcm of 4 & 7 = 28 tried dividing 6540 by 28 got quotient 233.5 ' so a is answer" | null |
Question: 31 of the scientists that attended a certain workshop were wolf prize laureates , and 18 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?
A.A.11.
B.B.18.
C.C.24.
D.D.29.
e ) D.36D.
"lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 13 . . so total who won n = 11 + 18 = 29 . . d" | null |
Question: if 4 men can colour 48 m long cloth in 2 days , then 2 men can colour 36 m long cloth in
A.1 day.
B.2 days.
C.3 days.
D.4 days.
e ) 5 daysC.
"the length of cloth painted by one man in one day = 48 / 4 Γ 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 Γ 2 = 3 day . c" | null |
Question: how many integers between 324,700 and 458,600 have tens digit 1 and units digit 3 ?
A.10,300.
B.10,030.
C.1,353.
D.1,352.
e ) 1,339E.
"there is one number in hundred with 1 in th tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 324,700 and 458,600 is 458,600 - 324,700 = 133,900 - one number per each hundred gives 133,900 / 100 = 1,339 numbers . answer : e" | null |
Question: a library has an average of 540 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
A.300.
B.276.
C.290.
D.285.
e ) noneC.
"since the month begins with sunday , to there will be five sundays in the month average required = ( 540 x 5 + 240 x 25 ) / 30 ) = 290 answer : option c" | null |
Question: on the number line , the number p is twice as many units from - 2 as - 2 is from 5 . if p is less than β 2 , what is the value of p ?
A.β 16.
B.β 10.
C.β 6.
D.10.
e ) 14A.
"distance between - 2 and 5 = 7 since number p is twice as many units from - 2 as - 2 is from 5 , therefore p can be - 16 since , p is less than - 2 , the value of p = - 16 answer a" | null |
Question: when sold at a 70 % discount , a sweater nets the merchant a 40 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
A.20 %.
B.40 %.
C.50 %.
D.60 %.
e ) 78.58 %E.
"we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 70 % of 100 = 30 . . profit = 40 % . . therefore the wholesale purchase cost = x . . . . 1.4 x = 30 or x = 21.42 . . . marked price was 100 so . . . so answer is 78.58 % . . e" | null |
Question: on a certain farm the ratio of horses to cows is 4 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 13 : 7 . after the transaction , how many more horses than cows would the farm own ?
A.30.
B.60.
C.75.
D.90.
e ) 105A.
"originally , there were 4 k horses and k cows . 7 ( 4 k - 15 ) = 13 ( k + 15 ) 28 k - 13 k = 195 + 105 15 k = 300 k = 20 the difference between horses and cows is ( 4 k - 15 ) - ( k + 15 ) = 3 k - 30 = 30 the answer is a ." | null |
Question: the total age of a and b is 12 years more than the total age of b and c . c is how many year younger than a
A.11.
B.12.
C.13.
D.14.
e ) 15B.
"explanation : given that a + b = 12 + b + c = > a β c = 12 + b β b = 12 = > c is younger than a by 12 years answer : option b" | null |
Question: if the diameter of circle r is 40 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
A.16 %.
B.18 %.
C.20 %.
D.22 %.
e ) 24 %A.
"let diameter of circle r , dr = 40 and diameter of circle s , ds = 100 radius of circle r , rr = 20 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 20 / 50 ) ^ 2 = ( 4 / 10 ) ^ 2 = 16 % answer : a" | null |
Question: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is ?
A.6.
B.12.
C.24.
D.36.
e ) 48B.
"q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b" | null |
Question: mary can do a piece of work in 26 days . rosy is 30 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
A.22.
B.20.
C.24.
D.26.
e ) 30B.
"ratio of times taken by mary and rosy = 130 : 100 = 13 : 10 suppose rosy takes x days to do the work . 13 : 10 : : 26 : x = > x = 20 days . hence , rosy takes 20 days to complete the work . answer : b" | null |
Question: if 2 ^ 4 , 3 ^ 3 , and 13 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?
A.198.
B.288.
C.363.
D.396.
e ) 468E.
i will go with e ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 13 ^ 1 = 468 | null |
Question: during a certain two - week period , 58 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
A.10 a.
B.9 a.
C.8 2 / 3 a.
D.11 a.
e ) 12 aC.
"total movies = 100 . comedies = 58 . action + drama = 42 . since there were 5 times as many dramas as action movies , then action + 5 * action = 42 - - > action = a = 7 . comedies = = 8 2 / 3 a answer : c ." | null |
Question: a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 56 marks . the maximum marks are ?
A.450.
B.300.
C.500.
D.610.
e ) 700E.
"let the maximum marks be x then , 33 % of x = 175 + 56 33 x / 100 = 231 x = 700 answer is e" | null |
Question: if s and t are both odd prime numbers ands < t , then how many different positive integer factors does 2 sthave ?
A.3.
B.4.
C.6.
D.8.
e ) 12D.
s and t are both odd prime numbers - it means either s or t is not 2 and since prime numbers have only two factors - 1 and the number itself s and t each will have ( 1 + 1 ) = 2 factors hence 2 st will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer | null |
Question: the maximum number of student amoung them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
A.91.
B.910.
C.1001.
D.1911.
e ) none of theseA.
"solution required number of student = h . c . f of 1001 and 910 = 91 . answer a" | null |
Question: a class of 20 students took a science test . 10 students had an average ( arithmetic mean ) score of 80 . the other students had an average score of 60 . what is the average score of the whole class ?
A.70.
B.60.
C.55.
D.65.
e ) 85A.
hear , 10 students had average score of 80 , so , 80 x 10 = 800 and 10 students had average score of 60 , so , 60 x 10 = 600 total no of student are 20 ( 800 + 600 ) / 20 = 70 correct ans is a | null |
Question: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 900 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 922.50 . what is the value of x ?
A.9000.
B.6000.
C.5000.
D.4000.
e ) 3000A.
simple way to solve this question is to use options . from si , we know that x * y = 45,000 . now , put the value of x = 9000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 9000 + 5 % of 9000 = 9450 . 2 nd year , amount = 9450 + 5 % of 9450 = 9922.50 . we can see after 2 years interest = 9922.50 - 9000 = 922.50 . hence , it satisfies the question . hence a is the correct answer | null |
Question: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 153 per kg , the price of the third variety per kg will be ?
A.rs . 147.50.
B.rs . 785.50.
C.rs . 175.50.
D.rs . 258.50.
e ) none of theseC.
"explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 153 ) / \ x β 153 22.50 = > x β ( 153 / 22.50 ) = 1 . = > x β 153 = 22.50 . = > x = 175.50 rs . answer : c" | null |
Question: the number of boxes in a warehouse can be divided evenly into 7 equal shipments by boat or 28 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
A.28.
B.33.
C.54.
D.81.
e ) 162A.
"answer is the lcm of 7 and 28 = 28 answer a" | null |
Question: in what time will a railway train 50 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
A.5 sec.
B.4 sec.
C.3 sec.
D.6 sec.
e ) 1 secA.
"t = 50 / 36 * 18 / 5 = 5 sec answer : a" | null |
Question: the marks obtained by vijay and amith are in the ratio 8 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
A.12 : 5.
B.12 : 1.
C.6 : 5.
D.12 : 2.
e ) 6 : 3A.
8 : 5 3 : 2 - - - - - - - 24 : 15 : 10 24 : 10 12 : 5 answer : a | null |
Question: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 22 overs to reach the target of 282 runs ?
A.6.25.
B.11.36.
C.7.4.
D.5.
e ) 6B.
"explanation : runs scored in the first 10 overs = 10 Γ 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 22 run rate needed = 250 / 22 = 11.36 answer : option b" | null |
Question: x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 9 will be equal to :
A.3.
B.6.
C.1 / 9.
D.1 / 3.
e ) 9C.
"explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 9 ^ 2 = 1 / 9 answer : c" | null |
Question: a train running at the speed of 90 km / hr crosses a pole in 5 seconds . find the length of the train .
A.150 meter.
B.145 meter.
C.140 meter.
D.125 meter.
e ) none of theseD.
"explanation : speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time = 25 * 5 = 125 meter option d" | null |
Question: find the mean proportional between 64 & 81 ?
A.A.59.
B.B.61.
C.C.63.
D.D.72.
e ) e ) 67D.
"formula = β a Γ b a = 64 and b = 81 β 64 Γ 81 = 8 Γ 9 = 72 d" | null |
Question: if ( a + b ) = 12 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
A.16 ..
B.8 ..
C.7 ..
D.6 ..
e ) - 2 .D.
"given a + b = 12 = > a = 12 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 12 - b + 3 - c = > 15 - ( b + c ) = > 15 - 9 = 6 . option d . . ." | null |
Question: if the area of a circle is 64 pi square feet , find its circumference .
A.65 pi feet.
B.43 pi feet.
C.42 pi feet.
D.18 pi feet.
e ) 16 pi feetE.
"the area is given by pi * r * r . hence pi * r * r = 64 pi r * r = 64 ; hence r = 8 feet the circumference is given by 2 * pi * r = 2 * pi * 8 = 16 pi feet correct answer e" | null |
Question: what is the lowest positive integer that is divisible by each of the integers 1 through 8 inclusive ?
A.420.
B.840.
C.1260.
D.2520.
e ) 5020B.
"we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , and 2 ^ 3 . the lcm is 1 * 2 ^ 3 * 3 * 5 * 7 = 840 the answer is b ." | null |
Question: what is the perimeter of an isosceles right angled triangle . the area of the isosceles right angled triangle is 50 .
['A.25', 'B.36', 'C.25', 'D.30', 'e ) 34.14']E.
an isosceles right angled triangle has both the base and height same . the area of an isosceles triangle = 1 / 2 * base * height since height = base 1 / 2 * height * height = 1 / 2 * height ^ 2 = 50 height ^ 2 = 100 height = 10 = base since we know the base and height . we will calculate the hypotenuse using pythagoras base ^ 2 + height ^ 2 = hypotenuse ^ 2 10 ^ 2 + 10 ^ 2 = hypotenuse ^ 2 hypotenuse ^ 2 = 200 hypotenuse = 14.14 perimeter of the triangle = 10 + 10 + 14.14 = 34.14 ans : e | null |
Question: here 10 programmers , type 10 lines within 10 minutes then 60 lines can type within 60 minutes . how many programmers are needed ?
A.16.
B.10.
C.6.
D.60.
e ) 50D.
10 10 programmer 10 line 10 mins . 10 programmer 20 line 20 mins . . . . . 10 programmer 60 line 60 mins . answer : d | null |
Question: in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are strategy majors ?
A.3.
B.5.
C.8.
D.11.
e ) 13E.
"pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are strategy majors is s = 13 . the answer is e ." | null |
Question: in a store , the total price for 25 shirts is $ 400 and the total price for 75 sweaters is $ 1500 . by how much does the average ( arithmetic mean ) price of a sweater exceed that of a shirt in this store ?
A.$ 1.
B.$ 2.
C.$ 3.
D.$ 4.
e ) $ 5D.
the average price of a shirt is : $ 400 / 25 = $ 16 . the average price of a sweater is : $ 1500 / 75 = $ 20 . the difference in price is : $ 20 - $ 16 = $ 4 . the answer is d . | null |
Question: jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 6 hours . how long would it take taimour to paint the fence alone ?
A.6 hours.
B.8 hours.
C.18 hours.
D.24 hours.
e ) 32 hoursC.
"i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 6 = > 1 / 18 working alone taimour can do the job in 1 = 1 / 18 * hours = > 18 answer c" | null |
Question: if the least common multiple of two prime numbers x and y is 10 , where x < y , then the value of 3 x + y is
A.7.
B.9.
C.11.
D.12.
e ) 21C.
"lcm ( x , y ) = 10 and both x an y are prime . the only values of x and y can be 2 and 5 ( x = 2 and y = 5 ) 3 x + y = 3 * 2 + 5 = 11 correct option : c" | null |
Question: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 800 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 820 . what is the value of x ?
A.8000.
B.6000.
C.5000.
D.4000.
e ) 3000A.
"simple way to solve this question is to use options . from si , we know that x * y = 40,000 . now , put the value of x = 8000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 8000 + 5 % of 8000 = 8400 . 2 nd year , amount = 8400 + 5 % of 8400 = 8820 . we can see after 2 years interest = 8820 - 8000 = 820 . hence , it satisfies the question . hence a is the correct answer" | null |
Question: i had 30 donuts when i left home this morning but only 9 when i came back home . what percentage of the donuts are missing ?
A.70.
B.65.
C.55.
D.75.
e ) 60A.
30 - 9 = 21 21 / 30 or 7 / 10 7 / 10 = 70 / 100 = 70 % answer is a | null |
Question: a semicircle has a radius of 10 . what is the approximate perimeter of the semicircle ?
A.27.
B.33.
C.39.
D.45.
e ) 51E.
"the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 10 + 2 * 10 which is about 51 . the answer is e ." | null |
Question: find the average of the first 19 natural numbers ?
A.8.
B.9.
C.10.
D.11.
e ) 12C.
average of the first ' n ' natural numbers = ( n + 1 ) / 2 we get ( 19 + 1 ) / 2 = 10 answer : c | null |
Question: if the remainder is 11 when positive integer n is divided by 18 , what is the remainder when n is divided by 9 ?
A.0.
B.2.
C.1.
D.3.
e ) 4B.
"assume x is quotient here , n = 18 x + 11 - - - - - - - - - - ( 1 ) and n = 9 x + ? we can also write equation ( 1 ) as : n = ( 18 x + 9 ) + 2 . ie 9 ( 2 x + 1 ) + 2 ie the first term is perfectly divisible by 6 . so , the remainder left is 2 . so , answer ( b ) is right choice ." | null |
Question: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 88,000 , how many purple chips were selected ?
A.1.
B.2.
C.3.
D.4.
e ) 5B.
"b - > 1 g - > 5 p - > x ; 5 < x < 11 r - > 11 now , 88000 = 11 * 8 ^ 2 * 5 ^ 4 * 1 ^ n hence no of balls drawn , b = cant be determined g = 4 p = 2 ( only possible value is 8 ) r = 1 hence b" | null |
Question: if n = 16 Γ 10 ^ ( - p ) and β 4 < p < 4 , how many different integer values of p will make n a perfect square ?
A.0.
B.2.
C.3.
D.5.
e ) 7C.
i think the answer should be c . thoose are p - values that satisfy given restriction : - 2 , 0 , 2 ( note , a fraction can be also a perfect square ) - - > 16 * 100 , 16 * 1 , 16 / 100 | null |
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