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Question: when 1 / 20 % of 6,000 is subtracted from 1 / 10 of 6,000 , the difference is
A.50.
B.200.
C.380.
D.598.
e ) 400D.
"1 / 20 % of 6000 = 3 1 / 10 of 6000 = 600 600 - 3 = 598 ans : d" | null |
Question: a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 620 in all . for how many days was he absent ?
A.8.
B.10.
C.15.
D.7.
e ) 4E.
"30 * 25 = 750 620 - - - - - - - - - - - 130 25 + 7.50 = 32.5 130 / 32.5 = 4 e" | null |
Question: in 1982 and 1983 , company b β s operating expenses were $ 13.0 million and $ 15.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b β s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
A.3 %.
B.46 1 / 6 %.
C.25 %.
D.33 1 / 3 %.
e ) 60 %B.
"profit in 1982 = 15.6 - 13 = 2.6 million $ profit in 1983 = 18.8 - 15 = 3.8 million $ percentage increase in profit = ( 3.8 - 2.6 ) / 2.6 * 100 % = 46 1 / 6 % answer b" | null |
Question: the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 80 respectively . the sum is :
A.rs . 1800.
B.rs . 1450.
C.rs . 1360.
D.rs . 6800.
e ) noneC.
"solution sum = s . i xt . d / ( s . i ) - ( t . d ) = 85 x 80 / 85 - 80 = rs . 1360 . answer c" | null |
Question: a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 75 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
A.69.55 $.
B.50.63 $.
C.60.95 $.
D.52.15 $.
e ) 53.15 $C.
"let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 75 x = 60.95 hence , the correct option is c" | null |
Question: the age of father 5 years ago was 4 times the age of his son . 5 years hence , father ' s age will be twice that of his son . the ratio of their present ages is :
A.5 : 4.
B.7 : 4.
C.5 : 2.
D.5 : 3.
e ) 7 : 5C.
let the ages of father and son 5 years ago be 4 x and x years respectively . then , ( 4 x + 5 ) + 5 = 2 [ ( x + 5 ) + 5 ] 4 x + 10 = 2 x + 20 x = 5 . required ratio = ( 4 x + 5 ) : ( x + 5 ) = 25 : 10 = 5 : 2 . answer : option c | null |
Question: the average of 11 numbers is 50 . out of 11 numbers the average of first 6 no . is 58 , and last 6 numbers is 65 then find 6 th number ?
A.A.188.
B.B.65.
C.C.58.
D.D.62.
e ) e ) 48A.
"6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 58 + 6 * 65 - 11 * 50 = 188 answer is a" | null |
Question: in a urban village of india named ` ` owlna ' ' , 70 % people have refrigerator , 75 % people have television , 80 % people got computers and 80 % got air - conditionor . how many people ( minimum ) got all these luxury .
A.23 %.
B.17 %.
C.11 %.
D.10 %.
e ) 15 %D.
"d 10 % 100 - [ ( 100 - 85 ) + ( 100 - 80 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 15 + 20 + 25 + 30 ) = 100 - 90" | null |
Question: the population of a town is 20000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
A.4300.
B.4500.
C.5120.
D.5230.
e ) 12800E.
"20000 Γ 80 / 100 Γ 80 / 100 = 12800 answer : e" | null |
Question: two spherical balls lie on the ground touching . if one of the balls has a radius of 6 cm , and the point of contact is 8 cm above the ground , what is the radius of the other ball ?
A.12 cm.
B.16 cm.
C.18 cm.
D.20 cm.
e ) none of the theseA.
"similar triangle properties . . 2 / r + 6 = 6 / r - 6 giving r = 12 . answer : a" | null |
Question: the population of a village is 15540 . it increases annually at the rate of 28 % p . a . what will be its population after 2 years ?
A.10000.
B.25460.
C.26709.
D.14000.
e ) 14400B.
"formula : ( after = 100 denominator ago = 100 numerator ) 15540 Γ 128 / 100 Γ 128 / 100 = 25460 b" | null |
Question: if x / 4 + 24 / x = 5 , what are the values of 2 x - 7 ?
A.8 and 9.
B.8 and 24.
C.17 and 21.
D.12 and 29.
e ) 17 and 9E.
i got the same thing e is the answer 9 or 17 | null |
Question: which greatest possible length can be used to measure exactly 12 meter 15 cm , 10 meter 15 cm and 10 meter 65 cm
A.45 cm.
B.25 cm.
C.4 cm.
D.5 cm.
e ) 50 cmD.
"explanation : convert first all terms into cm . i . e . 1215 cm , 1015 cm , 1065 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 5 . option d" | null |
Question: the sum of money will be double itself in 10 years and simple interest find rate of interest ?
A.10 %.
B.15 %.
C.20 %.
D.25 %.
e ) 30 %A.
t = 10 years p = principle amount = x a = total amount = 2 x si = simple interest = a - p = 2 x - x = x r = 100 si / pt = 100 x / 10 x = 10 % answer is a | 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 11 hours longer than the first half , how many hours did it take the runner to run the second half ?
A.14.
B.15.
C.18.
D.22.
e ) 33D.
"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 + 11 t 1 = 11 and so t 2 = 22 . the answer is d ." | null |
Question: a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 6 km on foot . his total journey is
A.16 km.
B.10 km.
C.12 km.
D.24 km.
e ) 36 kmE.
"explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 6 = x 5 x + 36 = 6 x x = 36 km answer : option e" | null |
Question: the cost price of a radio is rs . 4500 and it was sold for rs . 3200 , find the loss % ?
A.28.9 %.
B.22 %.
C.28 %.
D.45 %.
e ) 32 %A.
"4500 - - - - 1300 100 - - - - ? = > 28.9 % answer : a" | null |
Question: the ratio of three numbers is 4 : 2 : 5 and their sum is 121 . the second number of the three numbers is ?
A.22.
B.26.
C.27.
D.29.
e ) 30A.
"4 : 2 : 5 total parts = 11 11 parts - - > 121 1 part - - - - > 11 the second number of the three numbers is = 2 * 11 = 22 answer : a" | null |
Question: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 197 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
A.9801.
B.10,000.
C.14,400.
D.12,696.
e ) can not be determinedA.
"let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 197 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 197 ( x + y ) ( x - y ) = 197 197 is a prime number and thus it will be ( 99 + 98 ) * ( 99 - 98 ) . thus x = 99 and y = 98 x ^ 2 = 99 ^ 2 = 9801 the answer is a ." | null |
Question: a special municipal payroll tax charges not tax on a payroll less than $ 200000 and only 0.2 % on a company β s payroll above $ 200000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ?
A.$ 180,000.
B.$ 202,000.
C.$ 220,000.
D.$ 300,000.
e ) $ 2.
200,000D.
answer : d , ( with different approach ) : the 200 paid is 0.2 % of the additional amount above 200,000 . let it be x now 0.2 % of x = 200 therefore x = 100,000 total = 200,000 + x = 300,000 | null |
Question: when positive integer n is divided by positive integer p , the quotient is 20 , with a remainder of 7 . when n is divided by ( p + 2 ) , the quotient is 15 and the remainder is 2 . what is the value of n ?
A.107.
B.331.
C.511.
D.691.
e ) 871A.
"n / p = 10 7 / p = 20 p + 7 n / ( p + 2 ) = 15 2 / ( p + 2 ) = 15 p + 30 + 2 solving these two equations we get p = 5 n = 107 answer is a ." | null |
Question: a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 4 less , he would have made a profit of 10 % . the c . p . of the article was
A.344.
B.600.
C.200.
D.800.
e ) 700D.
explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 4 = > x = 800 answer : d ) rs 800 | null |
Question: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 40 people were made to stand in a column , how many columns could be formed ?
A.12.
B.14.
C.16.
D.18.
e ) 20A.
"16 * 30 = 40 * n n = 12 the answer is a ." | null |
Question: find large number from below question the difference of two numbers is 1200 . on dividing the larger number by the smaller , we get 5 as quotient and the 4 as remainder
A.1234.
B.1345.
C.1456.
D.1567.
e ) 1499E.
"let the smaller number be x . then larger number = ( x + 1200 ) . x + 1200 = 5 x + 4 4 x = 1196 x = 299 large number = 299 + 1200 = 1499 e" | null |
Question: the area of a rectangular field is equal to 50 square meters . its perimeter is equal to 30 meters . find the width of this rectangle .
A.5.
B.10.
C.15.
D.20.
e ) 25A.
"l * w = 50 : area , l is the length and w is the width . 2 l + 2 w = 30 : perimeter l = 15 - w : solve for l ( 15 - w ) * w = 30 : substitute in the area equation w = 5 and l = 10 correct answer a" | null |
Question: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 35 % ?
A.600.
B.887.
C.256.
D.654.
e ) 675E.
"cost price = rs . 500 profit = 35 % of 500 = rs . 175 selling price = cost price + profit = 500 + 175 = 675 answer : e" | null |
Question: jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 3000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
A.13,000.
B.11,600.
C.12,000.
D.14,000.
e ) 16,400A.
"let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 3000 ) solving for x , we get the shares as 13000 . ans : ( option a )" | null |
Question: 65 boys can complete a work in 30 days . how many men need to complete twice the work in 20 days
A.160.
B.170.
C.180.
D.195.
e ) 200D.
"one man can complete the work in 30 * 65 = 1950 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1950 m = 195 workers answer : d" | null |
Question: in a recent election , james received 0.5 percent of the 2000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?
A.901.
B.989.
C.990.
D.991.
e ) 1,001D.
james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d | null |
Question: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 12000 , then find the annual income of a ?
A.rs . 420000.
B.rs . 403200.
C.rs . 201600.
D.rs . 504000.
e ) none of theseB.
"b ' s monthly income = 12000 * 112 / 100 = rs . 13440 b ' s monthly income = 2 parts - - - - > rs . 13440 a ' s monthly income = 5 parts = 5 / 2 * 13440 = rs . 33600 a ' s annual income = rs . 33600 * 12 = rs . 403200 answer : b" | null |
Question: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 42.5 % . what would have been the percentage of profit earned if no discount had been offered ?
A.28.5.
B.27.675.
C.30.
D.50.
e ) none of theseD.
"giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 Γ£ β ( 100 + 42.5 ) / ( 100 Γ’ Λ β 5 ) = 150 hence , required % profit = 150 Γ’ β¬ β 100 = 50 % answer d" | null |
Question: pants , shorts and shirts in a dresser are in the ratio of 7 : 7 : 10 . if there are 14 pants , the number of shirts in the dresser is :
A.14.
B.7.
C.20.
D.70.
e ) 35C.
explanation : let pants = 7 x , shorts = 7 x & shirts = 10 x . now , 7 x = 14 hence x = 2 . number of apples = 10 x = 20 . answer : c | null |
Question: if x / ( 11 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
A.22.
B.33.
C.44.
D.66.
e ) 99C.
"x / ( 11 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 11 * lowest value of p = 2 * 11 * 2 = 44 answer c" | null |
Question: list i : { y , 2 , 4 , 7 , 10 , 11 } list ii : { 3 , 3 , 4 , 6 , 7 , 10 } if the median r of list i is equal to the sum of the median of list ii and the mode of list ii , then y equals
A.5.
B.7.
C.8.
D.r = 9.
e ) 10D.
mode of list ii = 3 median r of list ii = 4 + 6 / 2 = 5 sum of mode + mean = 3 + 5 = 8 now to make 8 as the median we need to find a value of y such that if the no . of terms in list 1 are odd then y = 8 else if even then 7 + y / 2 = 8 here its even so 7 + y / 2 = 8 from this y = 9 ( d ) | null |
Question: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 4 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
A.$ 28.
B.$ 82.
C.$ 110.
D.$ 138.
e ) $ 194E.
"by the question , the equation would be 150 p - 84 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 194 . answer e for me ." | null |
Question: at a special sale , 9 tickets can be purchased for the price of 6 tickets . if 9 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 9 tickets ?
A.20 %.
B.33.3 %.
C.40 %.
D.60 %.
e ) 66.6 %B.
"let the price of a ticket be rs . 100 , so 6 tickets cost 600 & 9 tickets cost 900 9 tickets purchased at price of 6 tickets ie . , for 600 , so amount saved s rs . 300 , % of 9 tickets = ( 300 / 900 ) * 100 = 33.3 % answer : b" | null |
Question: how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat ?
A.6.
B.12.
C.14.
D.16.
e ) 28B.
"equate the fat : 0.1 x + 0.35 * 8 = 0.2 ( x + 8 ) - - > x = 12 . answer : b ." | null |
Question: a students was asked to find the arithmetic mean of the numbers 3 , 11 , 7 , 9 , 15 , 13 , 8 , 19 , 17 , 21 , 14 and x . he found the mean to be 12 . what should be the number in place of x ?
A.3.
B.7.
C.17.
D.31.
e ) 38B.
adding all the numbers we get 137 + x given - ( 137 + x ) / 12 = 12 137 + x = 12 * 12 x = 144 - 137 x = 7 answer : b | null |
Question: harkamal purchased 10 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
A.A.1190.
B.B.1065.
C.C.1070.
D.D.1075.
e ) e ) 1080A.
"cost of 10 kg grapes = 70 Γ 10 = 700 . cost of 9 kg of mangoes = 55 Γ 9 = 490 . total cost he has to pay = 700 + 490 = 1190 a" | null |
Question: a chemical supply company has 60 liters of a 40 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
A.12.
B.15.
C.20.
D.24.
e ) 30A.
"60 liters of a 40 % hno 3 solution means hno 3 = 24 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 24 + x = 50 % of ( 60 + x ) or x = 12 . hence , a" | null |
Question: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a Γ§ ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 36 litres of the mixed fruit juice . how many litres of the a Γ§ ai berry juice does he need to add ?
A.17 litres.
B.24 litres.
C.11 litres.
D.07 litres.
e ) 38 litresB.
"262.85 ( 36 ) + 3 , 104.35 x = 1 , 399.45 ( 36 + x ) solve the equation . 262.85 ( 36 ) + 3 , 104.35 x = 1 , 399.45 ( 36 + x ) 9 , 462.6 + 3 , 104.35 x = 50 , 380.2 + 1 , 399.45 x 9 , 462.6 + 1 , 704.9 x = 50 , 380.2 1 , 704.9 x = 40 , 917.6 x = 24 answer is b ." | null |
Question: a man spends 35 % of his income on food , 25 % on children education and 80 % of the remaining on house rent . what percent of his income he is left with ?
A.1 %.
B.8 %.
C.12 %.
D.5 %.
e ) 4 %B.
let the total income be x then , income left = ( 100 - 80 ) % of x - [ 100 - ( 35 + 25 ) ] % of x = 20 % of 40 % of x = 8 % of x answer is b | null |
Question: a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 261 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
A.408.
B.475.
C.550.
D.625.
e ) 700A.
"let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 261 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 561 a + b + c = 51 per hour so for eight hrs = 51 * 8 = 408 = answer = a" | null |
Question: a container contains 20 liters of milk , from this container 2 liters of milk was taken out and replaced by water . this process was repeated further 2 times . how much milk is now contained by the container ?
A.14.58 liters.
B.20.16 liters.
C.22.45 liters.
D.26.95 liters.
e ) 31.45 litersA.
"amount of milk left after 3 operations = 20 ( 1 - 2 / 20 ) ^ 3 = 20 * 9 / 10 * 9 / 10 * 9 / 10 = 14.58 liters answer is a" | null |
Question: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
A.140.
B.150.
C.160.
D.170.
e ) 180E.
"given that the area of the square = 2025 sq . units = > side of square = β 2025 = 45 units the radius of the circle = side of the square = 45 units length of the rectangle = 2 / 5 * 45 = 18 units given that breadth = 10 units area of the rectangle = lb = 18 * 10 = 180 sq . units answer : option e" | null |
Question: a train of length 250 m crosses a bridge of length 150 m in 25 seconds . what is the speed of train ?
A.57.6.
B.27.
C.25.
D.22.
e ) 72A.
sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 150 ) = 25 x speed speed = 400 / 25 = 16 m / s = 57.6 km / h answer = a | null |
Question: indu gave bindu rs . 500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
A.0.2.
B.1.2.
C.3.
D.4.
e ) 0.8E.
"500 = d ( 100 / 4 ) 2 d = 0.8 answer : e" | null |
Question: the product of the squares of two positive integers is 9 . how many pairs of positive integers satisfy this condition ?
A.0.
B.1.
C.2.
D.3.
e ) 4B.
"ans : b - 1 pairs ( x Λ 2 ) ( y Λ 2 ) = 9 [ square root both sides ] xy = 3 3 = 1 x 3 , 3 x 1 cancel the repeats this leaves us with exactly 1 options . hence , b" | null |
Question: with both inlets open , a water tank will be filled with water in 52 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
A.9,000.
B.10,500.
C.11,750.
D.17,500.
e ) 19,500E.
"the work done by inlet a and b together in 1 min = 1 / 52 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 52 ) - ( 1 / 120 ) = 1 / 92 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 92 ) - ( 1 / 120 ) = 50 cubic meter = 19,500 cubic meter answer : option e" | null |
Question: if each edge of a cube is increased by 50 % , find the percentage increase in its surface area
['A.125 %', 'B.129 %', 'C.185 %', 'D.725 %', 'e ) 145 %']A.
let the edge = a cm so increase by 50 % = = total surface area of original cube = tsa of new cube = = = increase in area = = increase % = = 125 % answer : a | null |
Question: 12 : 8 seconds : : ? : 4 minutes
A.10.
B.15.
C.6.
D.8.
e ) 7C.
"12 * 4 = 8 * x x = 6 answer : c" | null |
Question: in the xy - plane the point ( - 2 - 3 ) is the centre of a circle , the point ( - 2 , 0 ) lies inside the circle and the point ( 2 , - 3 ) lies outside the circle . if the radius r of the circle r is an integer then r =
A.6.
B.5.
C.4.
D.3.
e ) 2C.
"can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 2 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 2 , - 3 ) - - - > lesser than 5 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,0 ) - - - - > greater than 3 units . thus the radius is > 3 but < 5 and as it is an integer , the only possible value of radius = 4 units . c is the correct answer ." | null |
Question: a hall 36 m long and 15 m broad is to be paved with stones , each measuring 4 dm by 5 dm . the number of stones required is :
A.180.
B.2700.
C.18.
D.18000.
e ) 1.8B.
"area of the hall = 3600 * 1500 area of each stone = ( 40 * 50 ) therefore , number of stones = ( 3600 * 1500 / 40 * 50 ) = 2700 answer : b" | null |
Question: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane β s output of toy bears per hour by what percent r ?
A.20 %.
B.80 %.
C.100 %.
D.180 %.
e ) 200 %C.
"c . let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 72 bears per 36 hours a week or 2 bears / hr ( [ 40 bears * 1.8 ] / [ 40 hrs * . 90 ] ) . r = [ ( 2 - 1 ) / 1 ] * 100 % = 100 % . c" | null |
Question: the cost to park a car in a certain parking garage is $ 15.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
A.$ 1.09.
B.$ 1.67.
C.$ 2.25.
D.$ 2.37.
e ) $ 3.03E.
total cost of parking for 9 hours = 15 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 15 + 7 * 1.75 = 27.25 thus the average parking price = 27.25 / 9 = 3.03 $ e is the correct answer . | null |
Question: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
A.2 : 9.
B.2 : 7.
C.1 : 6.
D.1 : 4.
e ) 1 : 3E.
"ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 4 - 2 ) / ( 10 - 4 ) = 2 / 6 = 1 / 3 so they should be mixed in the ratio 1 : 3 answer - e" | null |
Question: a trader sells 75 meters of cloth for rs . 4950 at the profit of rs . 15 per metre of cloth . what is the cost price of one metre of cloth ?
A.51.
B.88.
C.90.
D.42.
e ) 22A.
"sp of 1 m of cloth = 4950 / 75 = rs . 66 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 66 - rs . 15 = rs . 51 answer : a" | null |
Question: 587 x 999 = ?
A.586413.
B.587523.
C.614823.
D.615173.
e ) none of themA.
"= 587 x 999 = 587 x ( 1000 - 1 ) = 587 x 1000 - 587 - 1 = 587000 - 587 = 586413 answer is a" | null |
Question: the contents of a certain box consist of 14 apples and 12 oranges . how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?
A.3.
B.6.
C.14.
D.17.
e ) 20B.
"the objective here is that 70 % of the fruit in the box should be apples . now , there are 14 apples at start and there is no talk of removing any apples , so number of apples should remain 14 and they should constitute 70 % of total fruit , so total fruit = 14 / 0.7 = 20 so we should have 20 - 14 = 6 oranges . right now , there are 12 oranges , so to get to 6 oranges , we should remove 12 - 6 = 6 oranges . answer b" | null |
Question: he total marks obtained by a student in physics , chemistry and mathematics is 110 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
A.55.
B.65.
C.75.
D.85.
e ) 95A.
"let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 110 + p c + m = 110 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 110 / 2 = 55 . answer : a" | null |
Question: the diagonal of a square is 4 ? 2 cm . what will be the diameter of another square if their area is double that of the first square ?
['A.8 cm', 'B.9 cm', 'C.10 cm', 'D.11 cm', 'e ) 12 cm']A.
d 1 = 4 ? 2 = > area = 1 / 2 d 12 = 1 / 2 * ( 4 ? 2 ) 2 = 16 cm 2 area of new square = ( 2 * 16 ) cm 2 = 32 cm 2 therefore 1 / 2 * d 22 = 32 = > d 22 = 64 = > d 2 = 8 cm answer a | null |
Question: the sale price sarees listed for rs . 400 after successive discount is 10 % and 5 % is ?
A.166.
B.178.
C.342.
D.199.
e ) 112C.
"400 * ( 90 / 100 ) * ( 95 / 100 ) = 342 answer : c" | null |
Question: a volume of 10936 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
['A.2812', 'B.8231', 'C.2734', 'D.4222', 'e ) 4254']C.
a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 10936 l can be kept in ( 10936 / 4 ) hemispheres ans . 2734 answer : c | null |
Question: the average age of 31 students in a group is 16 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
A.31.
B.36.
C.48.
D.45.
e ) 57C.
"age of the teacher = ( 32 * 17 - 31 * 16 ) = 48 years . answer : c" | null |
Question: venki takes a trip and drives 5 hours from town x to town z at a rate of 80 miles per hour . on her way back , venki drives 45 miles per hour and stops in town y which is midway between town x and town z . how many hours does it take venki to drive from town z to town y ?
A.1.01.
B.4.44.
C.11.5.
D.1.75.
e ) 2.14B.
distance from x to z = 5 hr * 80 mph = 400 miles hence distance from y to z = 1 / 2 * 400 = 200 time = 200 / 45 = 4.44 hrs imo : b | null |
Question: if a rectangle have length 16 cm and diagonal 20 cm . calculate its area .
['A.185', 'B.132', 'C.165', 'D.192', 'e ) 212']D.
breadth = β 20 ^ 2 - 16 ^ 2 = β 144 = 12 cm area = 16 * 12 = 192 sq . cm answer d | null |
Question: a qualified worker digs a well in 5 hours . he invites 2 apprentices , both capable of working 3 / 5 as fast and 2 trainees both working 1 / 5 as fast as he . if the 5 - person team digs the same well , how much time does the team need to finish the job ?
A.1 : 42.
B.1 : 34.
C.1 : 44.
D.1 : 54.
e ) 2 : 14A.
and answer is correct as you have calculated : 100 / 59 hrs that is 1.71 hrs - 1 hr and 42 minutes , so 1 : 42 , hence , a . | null |
Question: find the cost of fencing around a circular field of diameter 28 m at the rate of rs . 1.50 a meter ?
['A.rs . 150', 'B.rs . 132', 'C.rs . 100', 'D.rs . 125', 'e ) rs . 225']B.
2 * 22 / 7 * 14 = 88 88 * 1 1 / 2 = rs . 132 answer : b | null |
Question: truck x is 14 miles ahead of truck y , which is traveling the same direction along the same route as truck x . if truck x is traveling at an average speed of 57 miles per hour and truck y is traveling at an average speed of 63 miles per hour , how long will it take truck y to overtake and drive 4 miles ahead of truck x ?
A.5 hours.
B.3 hours 20 minutes.
C.3 hours.
D.2 hours 45 minutes.
e ) 8 hoursC.
"relative speed = 63 - 57 = 6 miles per hour dist required = 14 + 4 = 18 miles time taken to overtake = 18 / 6 = 3 hours . c is the answer ." | null |
Question: a and b β s salaries together amount to rs . 2,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is a β s salary ?
A.rs . 500.
B.rs . 750.
C.rs . 1250.
D.rs . 1500.
e ) rs . 1520D.
"explanation : ( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 2000 4 b = 2000 = > b = 500 a = 1500 answer is d" | null |
Question: last year , for every 100 million vehicles that traveled on a certain highway , 80 vehicles were involved in accidents . if 4 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
A.1600.
B.3200.
C.800.
D.400.
e ) 200B.
"to solve we will set up a proportion . we know that β 100 million vehicles is to 80 accidents as 4 billion vehicles is to x accidents β . to express everything in terms of β millions β , we can use 4,000 million rather than 4 billion . creating a proportion we have : 100 / 80 = 4,000 / x cross multiplying gives us : 100 x = 4,000 * 80 x = 40 * 80 = 3200 answer : b" | null |
Question: on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 20 miles on saturday and sunday , how many miles did bill run on sunday ?
A.5.
B.6.
C.7.
D.8.
e ) 9B.
let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 20 . . 4 x + 12 = 20 . . x = 2 . . ans = x + 4 = 2 + 4 = 6 answer b | null |
Question: log root ( 8 ) / log 8 is equal to
A.1 / 2.
B.1 / 3.
C.1 / 4.
D.1 / 5.
e ) 1 / 6A.
= > log ( 8 ) ^ 1 / 2 / log 8 = 1 / 2 log 8 / log 8 = 1 / 2 answer a | null |
Question: one - third less than 40 % of 180 is equal to :
A.15.
B.30.
C.35.
D.40.
e ) 48E.
"lots of ways to tackle this . 40 % of 180 = 72 1 / 3 of 72 = 24 so , 1 / 3 less than 72 is equal to 72 - 24 = 48 answer : e" | null |
Question: alan buys 4 tvs , a 26 inch , a 28 inch , a 30 inch , and a 32 inch , for his new house . each tv costs $ 200 more than the size below it . alan spends a total of $ 4,600 . how much would he have spent if he had bought only the 28 inch and 30 inch tvs ?
A.850.
B.1,100.
C.1,700.
D.2,550.
e ) 2,300E.
"assume the cost of the least sized ( 26 inch ) tv = x cost of 28 inches tv = x + 200 cost of 30 inches tv = x + 400 cost of 32 inches tv = x + 600 total cost = 4 x + 1200 = 4600 therefore x = 3400 / 4 = 850 price of 28 inch + 30 inch = 1050 + 1250 = 2300 option e" | null |
Question: a can finish a piece of work in 4 days . b can do it in 12 days . they work together for two days and then a goes away . in how many days will b finish the work ?
A.4 days.
B.5 days.
C.6 days.
D.7 days.
e ) 8 daysA.
"2 / 4 + ( 2 + x ) / 12 = 1 = > x = 4 days answer : a" | null |
Question: when positive integer x is divided by 9 , the quotient is y and the remainder is 4 . when 2 x is divided by 7 , the quotient is 2 y and the remainder is 1 . what is the value of 5 y β x ?
A.- 3.
B.3.
C.- 4.
D.4.
e ) - 5B.
"( 1 ) x = 9 y + 4 ( 2 ) 2 x = 14 y + 1 ( 2 ) - ( 1 ) : x = 5 y - 3 5 y - x = 3 the answer is b ." | null |
Question: a school has 4 maths 3 physics and 3 chemistry teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
A.4.
B.5.
C.6.
D.7.
e ) 8B.
"total subjects = 4 + 3 + 3 = 10 max subjects by 1 teacher = 2 so , min of teachers required = 10 / 2 = 5 answer : b" | null |
Question: two stations a and b are 245 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
A.9.
B.10.
C.11.
D.12.
e ) 1E.
"suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 245 45 x = 270 x = 6 . so , they meet at 1 p . m . answer : option e" | null |
Question: for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 6 + 3 and * 6 + 6 , inclusive ?
A.one.
B.none.
C.two.
D.three.
e ) fourB.
"generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 6 would be divisible by all numbers from 1 to 6 . = > * 6 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 6 is divisible by 3 ) in fact adding anyprimenumber between 1 to 6 to * 6 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 6 + 3 and * 6 + 11 then the answer would be 1 . for * 6 + 3 and * 6 + 13 , it is 2 and so on . . . b" | null |
Question: the tax on a commodity is diminished by 35 % but its consumption is increased by 15 % . find the decrease percent in the revenue derived from it ?
A.18 %.
B.72 %.
C.32 %.
D.25.25 %.
e ) 52.25 %D.
"100 * 100 = 10000 65 * 115 = 7475 10000 - - - - - - - 2525 100 - - - - - - - ? = 25.25 % answer : d" | null |
Question: a university cafeteria offers 4 flavors of pizza - pepperoni , chicken , hawaiian and vegetarian . if a customer has an option ( but not the obligation ) to add extra cheese , mushrooms or both to any kind of pizza , how many different pizza varieties are available ?
A.4.
B.8.
C.12.
D.16.
e ) 32D.
there are 4 flavors of pizza and each can be : 1 . without cheese and mushrooms ; 2 . with cheese ; 3 . with mushrooms ; 4 . with cheese and mushrooms . so , the total number of pizza varieties is 4 * 4 = 16 . answer : d . | null |
Question: find the least number of five digits which is exactly divisible by 12 , 15 and 18 ?
A.1080.
B.10080.
C.10025.
D.11080.
e ) 12080B.
"lcm = 180 180 ) 10000 ( 55 9900 - - - - - - - - - 100 10000 + 180 - 100 = 10080 answer : b" | null |
Question: a tank can be filled by pipe a in 5 hours and by pipe b in 8 hours , each pump working on its own . when the tank is full and a drainage hole is open , the water is drained in 20 hours . if initially the tank was empty and someone started the two pumps together but left the drainage hole open , how long does it take for the tank to be filled ?
A.2.6 hours.
B.3.6 hours.
C.4.6 hours.
D.5.6 hours.
e ) none of theseB.
let ' s first find the rates of the pumps and the drainage hole pump a : 1 / 5 , pump b : 1 / 8 , drainage hole : 1 / 20 let t be the time for the pumps to fill the tank . the pumps , add water into the tank however the drainage hole drains water out of the tank , hence t ( 1 / 5 + 1 / 8 - 1 / 20 ) = 1 solve for t t = 3.6 hours answer b | null |
Question: a and b invests rs . 3000 and rs . 5000 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.8 : 8.
B.9 : 8.
C.9 : 7.
D.9 : 5.
e ) 9 : 10E.
( 3 * 6 + 6 * 6 ) : ( 5 * 12 ) 54 : 60 = > 9 : 10 answer : e | null |
Question: express a speed of 720 kmph in meters per second ?
A.120 mps.
B.200 mps.
C.181 mps.
D.190 mps.
e ) 125 mpsB.
"720 * 5 / 18 = 200 mps answer : b" | null |
Question: 84 / 12 / 0.8 = ?
A.8.17.
B.7.14.
C.6.23.
D.4.35.
e ) 8.75E.
"e 8.75 ? = 84 / ( 12 * 0.8 ) = 8.75" | null |
Question: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a king ?
A.2 / 13.
B.1 / 26.
C.5 / 26.
D.1 / 52.
e ) 17 / 52D.
"p ( club ) = 1 / 4 p ( king ) = 1 / 13 p ( club then a king ) = 1 / 4 * 1 / 13 = 1 / 52 the answer is d ." | null |
Question: the length of a rectangular plot is 20 mtr more than its breadth . if the cost of fencingthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
['A.50 m', 'B.60 m', 'C.65 m', 'D.75 m', 'e ) 80 m']B.
let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m b | null |
Question: define r * by the equation r * = Ο - r . then ( ( β Ο ) * ) * =
A.β 2 Ο.
B.- 1.
C.β Ο.
D.2 Ο.
e ) 4 ΟC.
for r * f ( f ( β Ο ) ) = f ( Ο β ( β Ο ) ) = f ( Ο + Ο ) = f ( 2 Ο ) = Ο β 2 Ο = β Ο = c | null |
Question: how many multiples of 5 are there between 5 to 100 ?
A.9.
B.18.
C.17.
D.none of these.
e ) can not be determinedB.
"explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 , 90 , 95 . answer : b" | null |
Question: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase r in sales ?
A.2 %.
B.17 %.
C.20 %.
D.65 %.
e ) 83 %C.
last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase r = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c . | null |
Question: a person travels equal distances with speeds of 3 km / hr , 6 km / hr , 9 km / hr . and takes a total time of 11 minutes . find the total distance ?
A.1 km.
B.500 mts.
C.900 mts.
D.2 km.
e ) 250 mtsC.
"let the each distance be x km total distance = 3 x then total time , ( x / 3 ) + ( x / 6 ) + ( x / 9 ) = 11 / 60 x = 0.3 total distance = 3 * 0.3 = 0.9 km = 900 meters correct option is c" | null |
Question: a bag of potatoes weighs 28 lbs divided by half of its weight . how much does the bag of potatoes weight ?
A.20 lb.
B.14 lb.
C.10 lb.
D.15 lb.
e ) 5 lbB.
"sol . 28 Γ· 2 = 14 . answer : b" | null |
Question: pipe a can fill a tank in 2 hours . due to a leak at the bottom , it takes 4 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
A.2.
B.5.
C.6.
D.4.
e ) 1D.
"let the leak can empty the full tank in x hours 1 / 2 - 1 / x = 1 / 4 = > 1 / x = 1 / 2 - 1 / 4 = 1 / 4 = > x = 4 . answer : d" | null |
Question: the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than a
A.11.
B.12.
C.13.
D.14.
e ) 15E.
"explanation : given that a + b = 15 + b + c = > a ? c = 15 + b ? b = 15 = > c is younger than a by 15 years answer : option e" | null |
Question: 306 Γ£ Β· ? Γ£ β 15 + 270 = 405
A.24.
B.25.
C.34.
D.39.
e ) 43C.
explanation : 306 Γ£ Β· ? Γ£ β 15 = 405 - 270 = 135 ( 306 Γ£ β 15 ) / ? = 135 ? = ( 306 Γ£ β 15 ) / 135 = 34 answer : option c | null |
Question: two trains of equal length , running with the speeds of 60 and 40 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
A.10 sec.
B.11 sec.
C.77 sec.
D.99 sec.
e ) 67 secA.
"rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2500 / 9 * 18 / 500 = 10 sec answer : a" | null |
Question: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 540 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
A.8 / 3.
B.3 / 8.
C.8 / 5.
D.12 / 5.
e ) 5 / 3D.
"distance traveled by eddy = 540 km time taken by eddy = 3 hours average speed of eddy = 540 / 3 = 180 km / hour distance traveled by freddy = 300 km time taken by freddy = 4 hours average speed of freddy = 300 / 4 = 75 km / hour ratio of average speed of eddy to freddy = 180 / 75 = 12 / 5 answer d" | null |
Question: in the first 10 overs of a cricket game , the run rate was only 3.4 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
A.4.25.
B.5.
C.6.2.
D.7.
e ) 7.5C.
"required run rate = 282 - ( 3.4 x 10 ) = 248 248 / 40 = 6.2 c )" | null |
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