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Question: what is remainder of the division ( 1625 * 1627 * 1629 ) / 12 ?
A.3.
B.2.
C.1.
D.0.
e ) 4A.
remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : a | null |
Question: if henry were to add 8 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
A.25.
B.40.
C.64.
D.80.
e ) 96C.
"7 / 8 x - 3 / 4 x = 8 galls 1 / 8 * x = 8 gallons x = 64 gallons answer c" | null |
Question: find compound interest on $ 4000 at 15 % per annum for 2 years 4 months , compounded annually .
A.1554.5.
B.1509.5.
C.1108.5.
D.1107.5.
e ) 1100.5A.
"time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 4000 x ( 1 + Β ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 4000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 5554.50 . : . c . i . = rs . ( 5554.50 - 4000 ) = $ 1554.50 answer a ." | null |
Question: if x = 1 + β 2 , then what is the value of x 4 - 4 x 3 + 4 x 2 + 3 ?
A.- 1.
B.0.
C.4.
D.2.
e ) 3C.
"answer x = 1 + β 2 β΄ x 4 - 4 x 3 + 4 x 2 + 5 = x 2 ( x 2 - 4 x + 4 ) + 3 = x 2 ( x - 2 ) 2 + 3 = ( 1 + β 2 ) 2 ( 1 + β 2 - 2 ) 2 + 3 = ( β 2 + 1 ) 2 ( β 2 - 1 ) 2 + 3 = [ ( β 2 ) 2 - ( 1 ) 2 ] 2 + 3 = ( 2 - 1 ) 2 = 1 + 3 = 4 correct option : c" | null |
Question: a train is 485 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
A.20 seconds.
B.30 seconds.
C.40 seconds.
D.50 seconds.
e ) none of theseD.
"explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 485 + 140 = 625 meter time = distance / speed = 625 β 2 / 25 = 50 seconds option d" | null |
Question: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 1110 will be :
A.rs . 300.
B.rs . 200.
C.rs . 240.
D.rs . 350.
e ) none of theseA.
"z share = z , y = 1.2 z x = 1.25 Γ£ β 1.2 z , x + y + z = 111 ( 1.25 Γ£ β 1.2 + 1.2 + 1 ) z = 1110 3.7 z = 1110 , z = 300 answer : . a" | null |
Question: a train moves with a speed of 135 kmph . its speed in metres per second is
A.10.8.
B.37.5.
C.30.
D.38.8.
e ) noneB.
"solution speed = 135 kmph = ( 135 x 5 / 18 ) m / sec = 37.5 m / sec . answer b" | null |
Question: a 50 ml after - shave lotion at 30 % alcohol is mixed with 30 ml of pure water . what is the percentage of alcohol in the new solution ?
A.16.75 %.
B.17.75 %.
C.18.75 %.
D.19.75 %.
e ) none of theseC.
the amount of the final mixture is given by 50 ml + 30 ml = 80 ml the amount of alcohol is equal to the amount of alcohol in pure water ( which is 0 ) plus the amount of alcohol in the 30 % solution . let x be the percentage of alcohol in the final solution . hence 0 + 30 % 50 ml = x ( 80 ) solve for x x = 0.1817 = 18.75 % answer c | null |
Question: what is the remainder when 1201 Γ 1202 Γ 1205 Γ 1207 is divided by 6 ?
A.1.
B.2.
C.3.
D.4.
e ) 5D.
"the remainders when dividing each number by six are : 1 , 2 , 5 , and 1 . the product is 1 * 2 * 5 * 1 = 10 the remainder when dividing 10 by 6 is 4 . the answer is d ." | null |
Question: what is the value of 11 ^ x - 11 ^ ( x + 2 ) , where x is the largest integer such that 11 ^ x is a factor of 30030 ?
A.- 1331.
B.- 1320.
C.- 121.
D.- 120.
e ) - 1B.
the given expression is 11 x - 11 ( x ^ + 2 ) = 11 x ( 1 - x ) 1 x needs to be factor of 30030 and x needs to be the largest integer possible . this means 11 x needs to be the largest factor possible . the largest factor of a number is the number itself . the largest factor of 30030 is 30030 = ( 11 * 2730 ) x must be 2730 the value of 11 x ( 1 - x ) = β 1320 . answer : b | null |
Question: what percent of 7.2 kg is 18 gms ?
A.25.
B.66.
C.288.
D.19.
e ) 17A.
"explanation : required percentage = ( 18 / 7200 * 100 ) % = 1 / 4 % = 0.25 % answer : a ) . 25 %" | null |
Question: a β s speed is 17 / 14 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
A.1 / 14.
B.1 / 17.
C.3 / 14.
D.3 / 17.
e ) 1 / 31D.
"let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 17 v / 14 ) = xd / v ( 14 / 17 ) * d / v = x * d / v x = 14 / 17 b should have a head start of 3 / 17 of the full distance . the answer is d ." | null |
Question: a invested $ 100 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?
A.$ 100.
B.$ 75.
C.$ 20.
D.$ 120.
e ) $ 50E.
"a : b = 100 * 12 : 200 * 6 a : b = 1 : 1 a ' s share = 100 / 2 = $ 50 answer is e" | null |
Question: in a family 13 people eat only vegetarian , 8 people eat only non veg . , 6 people eat both veg and non veg . . how many people eat veg in the family ?
A.20.
B.11.
C.19.
D.31.
e ) 21C.
"total people eat veg = only veg + both veg and non veg total = 13 + 6 = 19 answer = c" | null |
Question: a shopkeeper labeled the price of his articles so as to earn a profit of 40 % on the cost price . he then sold the articles by offering a discount of 5 % on the labeled price . what is the actual percent profit earned in the deal ?
A.18 %.
B.20 %.
C.17 %.
D.33 %.
e ) none of theseD.
"explanation : let the cp of the article = rs . 100 . then labeled price = rs . 140 . sp = rs . 140 - 5 % of 140 = rs . 140 - 7 = rs . 133 . gain = rs . 133 Γ’ β¬ β rs . 100 = rs . 33 therefore , gain / profit percent = 33 % . answer : option d" | null |
Question: the total of 336 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is
A.238.
B.277.
C.278.
D.260.
e ) 288D.
"explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 336 - x ) . 0.20 * ( x ) + 0.25 ( 336 - x ) = 71 = > x = 260 . . answer : d ) 260" | null |
Question: a factory produces 6400 toys per week . if the workers at this factory work 3 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
A.1375 toys.
B.2133 toys.
C.3375 toys.
D.4375 toys.
e ) 5375 toysB.
"to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 3 days ) by 3 . 6400 / 3 = 2133 toys correct answer b" | null |
Question: walking at 5 / 6 th of its usual speed a cab is 15 mnts late . find its usual time to cover the journey ?
A.25 m.
B.45 m.
C.32 m.
D.75 m.
e ) 62 mD.
new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 15 m ut / 5 = 15 m ut = 75 m answer is d | null |
Question: a part - time employee whose hourly wage was increased by 20 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
A.11.
B.15.
C.16.66.
D.17.
e ) 18C.
"let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.2 x now we need to find number of hours worked so that x * y = 1.2 x * z i . e z = 1 / 1.2 y % decrease = ( y - 1 / 1.2 y ) / y * 100 = 16.66 thus my answer is c ." | null |
Question: a person purchased a tv set for rs . 16000 and a dvd player for rs . 6250 . he sold both the items together for rs . 35600 . what percentage of profit did he make ?
A.80 %.
B.49 %.
C.40 %.
D.60 %.
e ) 90 %D.
the total cp = rs . 16000 + rs . 6250 = rs . 22250 and sp = rs . 35600 profit ( % ) = ( 35600 - 22250 ) / 22250 * 100 = 60 % answer : d | null |
Question: two trains each 180 m in length are running on the same parallel lines in opposite directions with the speed of each 80 kmph . in what time will they cross each other completely ?
A.7.8 sec.
B.8.1 sec.
C.8.3 sec.
D.8.2 sec.
e ) 8.4 secB.
d = 180 m + 180 m = 360 m * 1 / 1000 = 0.36 kms rs = 80 + 80 = 160 kmph t = ( 0.36 / 160 ) * 3600 = 8.1 sec answer : b | null |
Question: 20 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?
A.30.
B.32.
C.60.
D.data inadequate.
e ) none of theseA.
"capacity of the tank = 20 Γ 13.5 = 270 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 270 β 9 = 30 answer a" | null |
Question: the number of the members of a club is more than 50 and less than 80 . when 4 people sit at a table , other people exactly divided to 8 - people groups ( 8 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 9 - people groups , how many people will be left ?
A.0.
B.2.
C.4.
D.6.
e ) 8D.
"the number of members is 7 k + 4 = 8 j + 4 the only number in this range which satisfies this is 60 . 60 / 9 = 6 ( 9 ) + 6 the answer is d ." | null |
Question: a train running at the speed of 72 km / hr crosses a pole in 9 seconds . find the length of the train .
A.150 meter.
B.286 meter.
C.180 meter.
D.288 meter.
e ) 265 meterC.
"speed = 72 * ( 5 / 18 ) m / sec = 20 m / sec length of train ( distance ) = speed * time ( 20 ) * 9 = 180 meter answer : c" | null |
Question: two clocks are set correctly at 1 0 ' clock in the afternoon . one keeps correct time . the other gains 5 seconds per minute . that evening , when the fast clock shows 6 : 20 , what does the correct clock show ?
A.4.0.
B.5.0.
C.6.0.
D.7.2.
e ) 3.5C.
faster clock gains 5 seconds per minute or 5 * 60 = 300 seconds or 5 minutes per hour . both clocks are set at 1 : 00 at 2 : 00 correct clock is at 2 : 00 faster clock is at 2 : 05 : 00 ( 1 hour + gained 5 minutes ) at 3 : 00 - correct clock is at 3 : 00 faster clock is at 3 : 10 : 00 ( 2 hours + gained 10 minutes ) . in 5 hours , faster clock would gain 20 minutes . it will show 6 : 20 . at that point , the correct clock would show 6 : 00 . answer is c | null |
Question: the triplicate ratio of 1 : 3 is ?
A.1 : 27.
B.1 : 8.
C.1 : 3.
D.1 : 1.
e ) 1 : 2A.
"1 ^ 3 : 3 ^ 3 = 1 : 27 answer : a" | null |
Question: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 22.55 % . what would have been the percentage of profit earned if no discount was offered ?
A.60 %.
B.29 %.
C.39 %.
D.56 %.
e ) 73 %B.
"let c . p . be rs . 100 . then , s . p . = rs . 122.55 let marked price be rs . x . then , 95 / 100 x = 122.55 x = 12255 / 95 = rs . 129 now , s . p . = rs . 129 , c . p . = rs . 100 profit % = 29 % . answer : b" | null |
Question: 5 men are equal to as many women as are equal to 8 boys . all of them earn $ 90 only . men β s wages are ?
A.$ 4.
B.$ 6.
C.$ 7.
D.$ 9.
e ) $ 3B.
"b $ 6 5 m = xw = 8 b 5 m + xw + 8 b - - - - - $ 90 rs . 5 m + 5 m + 5 m - - - - - $ 90 rs . 15 m - - - - - - $ 90 = > 1 m = $ 6 ." | null |
Question: two trains of equal are running on parallel lines in the same direction at 48 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
A.60 m.
B.72 m.
C.80 m.
D.82 m.
e ) 84 mA.
"let the length of each train be x m . then , distance covered = 2 x m . relative speed = 48 - 36 = 12 km / hr . = 12 * 5 / 18 = 10 / 3 m / sec . 2 x / 36 = 10 / 3 = > x = 60 . answer : a" | null |
Question: how many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
A.14.
B.13.
C.12.
D.11.
e ) 10A.
"the numbers must be of the form 2 a + 3 b , 2 a + 3 b , where aa and bb are positive integers . the smallest number is 5 = 2 β 1 + 3 β 1.5 = 2 β 1 + 3 β 1 . starting with 55 , we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list . adding either 22 or 33 to 2 a + 3 b 2 a + 3 b will give another number of the same form . so , after 55 , we get 5 + 2 = 7,5 + 3 = 8,7 + 2 = 9,8 + 2 = 10 , . . . 5 + 2 = 7,5 + 3 = 8,7 + 2 = 9,8 + 2 = 10 , . . . we will get all the numbers up to 1919 inclusive , except 1,2 , 3,4 , 1,2 , 3,4 , and 6,6 , because once we have 77 and 8,8 , by adding 22 all the time we can get any odd or even number . we get a total of 19 β 5 = 1419 β 5 = 14 numbers . answer a" | null |
Question: a number is said to be prime saturated if the product of all the different positive prime factors of t is less than the square root of t . what is the greatest two digit prime saturated integer ?
A.99.
B.98.
C.97.
D.96.
e ) 95D.
"t = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ." | null |
Question: a cycle is bought for rs . 1500 and sold for rs . 1620 , find the gain percent ?
A.11.
B.8.
C.10.
D.20.
e ) 12B.
"1500 - - - - 120 100 - - - - ? = > 8 % answer : b" | null |
Question: a teacher grades students β tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 76 , how many questions did student a answer correctly ?
A.92.
B.60.
C.73.
D.82.
e ) 91A.
"let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 76 ( subtracting twice of incorrect from correct ) 3 x = 276 x = 92 answer : a" | null |
Question: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 11 percent . overall he make a .
A.228.
B.288.
C.27.
D.200.
e ) 280E.
"let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 11 / 100 ) = 8000 + 880 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 880 = rs . 280 as this is positive , an overall profit of rs . 280 was made . answer : e" | null |
Question: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 5 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
A.22 %.
B.23 %.
C.24 %.
D.25 %.
e ) 34 %B.
"since 5 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.95 = 0.22 ; { % of customers who sample candy } = 0.231 . answer : b ." | null |
Question: the average of first 22 natural numbers is ?
A.11.6.
B.11.5.
C.12.9.
D.15.4.
e ) 15.1B.
"sum of 22 natural no . = 506 / 2 = 253 average = 253 / 22 = 11.5 answer : b" | null |
Question: in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 10 and 400 , then the least and greatest integer on the card would be
A.3 and 15.
B.3 and 20.
C.4 and 13.
D.4 and 14.
e ) 5 and 14B.
"given : 10 < x ( x + 1 ) < 400 . now , it ' s better to test the answer choices here rather than to solve : if x = 3 then x ( x + 1 ) = 12 > 10 - - > so , the least value is 3 . test for the largest value : if x = 20 then x ( x + 1 ) = 20 * 21 = 420 > 400 answer : b ." | null |
Question: p , q and r have $ 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
A.2400.
B.2403.
C.3998.
D.2539.
e ) 1600E.
"e 1600 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 ." | null |
Question: rahul and sham together can complete a task in 35 days , but rahul alone can complete same work in 60 days . calculate in how many days sham can complete this work ?
A.84 days.
B.82 days.
C.76 days.
D.68 days.
e ) 60 daysA.
explanation : as rahul and sham together can finish work in 35 days . 1 days work of rahul and sham is 1 / 35 rahul can alone complete this work in 60 days , so , rahul one day work is 1 / 60 clearly , sham one day work will be = ( rahul and sham one day work ) - ( rahul one day work ) = 1 / 35 - 1 / 60 = 1 / 84 hence sham will complete the given work in 84 days . answer is a | null |
Question: a train running at the speed of 60 km / hr crosses a pole in 6 sec . what is the length of the train ?
A.356.
B.278.
C.127.
D.100.
e ) 150D.
"speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 6 = 100 m answer : d" | null |
Question: lucy bought a 1 - year , 10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually . what was the total amount of interest paid on this certificate at maturity ?
A.10464.
B.864.
C.816.
D.800.
e ) 480D.
solution : it says , 8 percent per annum per compounded semi annually . therefore r = 8 / 2 = 4 % . so , p = 10000 r = 4 n = 2 net amount a = 10816 , i = 800 . answer : d | null |
Question: if x ^ 2 + ( 1 / x ^ 2 ) = 6 , x ^ 4 + ( 1 / x ^ 4 ) = ?
A.10.
B.11.
C.12.
D.34.
e ) 15D.
"- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 6 ^ 2 - 2 = 34 . thus , the answer is d ." | null |
Question: a bag marked at $ 125 is sold for $ 120 . the rate of discount is ?
A.10 %.
B.25 %.
C.20 %.
D.50 %.
e ) 4 %E.
rate of discount = 5 / 125 * 100 = 4 % answer is e | null |
Question: the radius of a cylindrical vessel is 8 cm and height is 3 cm . find the whole surface of the cylinder ?
A.308 sq cm.
B.220 sq cm.
C.440 sq cm.
D.553.1 sq cm.
e ) 138 sq cmD.
"r = 8 h = 3 2 Ο r ( h + r ) = 2 * 22 / 7 * 8 ( 11 ) = 553.1 answer : d" | null |
Question: the marks obtained by vijay and amith are in the ratio 6 : 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.1 : 5.
B.4 : 5.
C.9 : 5.
D.9 : 8.
e ) 9 : 7C.
"6 : 5 3 : 2 - - - - - - - 18 : 15 : 10 18 : 10 9 : 5 answer : c" | null |
Question: for what value of x , is | x β 3 | + | x + 1 | + | x | = 10 ?
A.0.
B.3.
C.- 3.
D.4.
e ) - 2D.
"there are 3 transition points : - 1 , 0 , 3 when x > 3 , | x β 3 | + | x + 1 | + | x | = 10 | x β 3 + x + 1 + x = 10 x = 4 satisfies when 0 < x < 3 | x β 3 | + | x + 1 | + | x | = 10 β ( x β 3 ) + ( x + 1 ) + x = 10 x = 6 ( not possible since 0 < x < 3 ) when - 1 < x < 0 | x β 3 | + | x + 1 | + | x | = 10 β ( x β 3 ) + β ( x + 1 ) + x = 10 x = - 8 ( not possible since - 1 < x < 0 ) when x < - 1 | x β 3 | + | x + 1 | + | x | = 10 - ( x - 3 ) - ( x + 1 ) - x = 10 x = - 8 / 3 satisfies answer : d" | null |
Question: when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 3 ) ^ 2 is divided by 5 ?
A.0.
B.1.
C.2.
D.3.
e ) 4B.
"n = 5 x + 3 , for some integer x ( n + 3 ) ^ 2 = ( 5 x + 6 ) ^ 2 = 5 y + 36 , for some integer y when we divide this by 5 , the remainder is 1 . the answer is b ." | null |
Question: right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy β s age will be 66 years . what is molly ' s age right now ?
A.15 years.
B.35 years.
C.25 years.
D.45 years.
e ) 55 yearsD.
"now , sandy is 66 - 6 = 60 molly ' s age is ( 3 / 4 ) * 60 = 45 the answer is d ." | null |
Question: a and b can do a work in 5 days and 10 days respectively . a starts the work and b joins him after 4 days . in how many days can they complete the remaining work ?
A.6 days.
B.2 / 3 days.
C.8 days.
D.3 days.
e ) 9 daysB.
"work done by a in 4 days = 4 / 5 remaining work = 1 / 5 work done by both a and b in one day = 1 / 5 + 1 / 10 = 3 / 10 remaining work = 1 / 5 * 10 / 3 = 2 / 3 days . answer : b" | null |
Question: ( 935421 x 625 ) = ?
A.542622125.
B.584632125.
C.544638125.
D.584638125.
e ) none of theseD.
"explanation : 935421 Γ 625 = 935421 Γ 54 = 935421 Γ ( 10 / 2 ) 4 = ( 935421 Γ 10000 ) / 16 = 584638125 . answer : option d" | null |
Question: a certain fraction is equivalent to 3 / 5 . if the numerator of the fraction is increased by 4 and the denominator is doubled , the new fraction is equivalent to 1 / 3 . what is the sum of the numerator and denominator of the original fraction ?
A.49.
B.35.
C.28.
D.56.
e ) 21D.
"x / y = 3 / 5 - > 1 ( x + 4 ) / 2 y = 1 / 3 - > 2 divide 1 by 2 : = > 2 x / ( x + 4 ) = 9 / 5 = > 10 x = 9 x + 36 = > x = 36 = > y = 5 / 3 * 12 = 20 so x + y = 56 the answer is d ." | null |
Question: a survey was sent to 65 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
A.2 %.
B.4 %.
C.14 %.
D.28 %.
e ) 63 %B.
"case 1 : ( 7 / 65 ) = x / 100 x = 10 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 10 ) % = 4 % answer is b" | null |
Question: bert and rebecca were looking at the price of a condominium . the price of the condominium was 100 % more than bert had in savings , and separately , the same price was also 60 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
A.1 : 5.
B.2 : 5.
C.3 : 5.
D.4 : 5.
e ) 1 : 1D.
"suppose bert had 100 so price becomes 200 , this 200 = 1.6 times r ' s saving . . so r ' s saving becomes 125 so required ratio is 100 : 125 = 4 : 5 answer : d" | null |
Question: a man swims downstream 30 km and upstream 20 km taking 5 hours each time , what is the speed of the man in still water ?
A.7.
B.8.
C.2.
D.5.
e ) 4D.
"30 - - - 5 ds = 6 ? - - - - 1 20 - - - - 5 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : d" | null |
Question: andrew purchased 8 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.1000.
B.1055.
C.1060.
D.1075.
e ) 1080B.
"cost of 8 kg grapes = 70 Γ 8 = 560 . cost of 9 kg of mangoes = 55 Γ 9 = 490 . total cost he has to pay = 560 + 490 = 1055 b" | null |
Question: how many integers v are prime numbers in the range 200 < v < 220 ?
A.1.
B.2.
C.3.
D.4.
e ) 5A.
my friend , every single odd number greater than can be written either as 4 v + 1 or as 4 v + 3 . if you divide any odd number by 4 , you will get a remainder of either 1 or 3 . that ' s not a rule unique to prime numbers at all . the 6 v + 1 or 6 v - 1 rule is basically every odd number that is not divisible by three , so it narrows the search a little . here ' s how i thought about the problem . first , eliminate all the even numbers and the odd multiples of 5 in that range . that leaves us with : { 201 , 203 , 207 , 209 , 211 , 213 , 217 , 219 } eliminate the four multiples of 3 . notice that 21 is a multiple of 3 , so 210 is also a multiple of 3 . if we add or subtract 3 or 9 , we get more multiples of three . when we eliminate those , we are left with . { 203 , 209 , 211 , 217 } now , notice that a cool thing about this range is that 210 is also a multiple 7 ( again , because 21 is a multiple of 7 ) . this means that 210 - 7 = 203 210 + 7 = 217 those two numbers are also multiples of 7 , so eliminate them from the list . now , we are left with { 209 , 211 } . we ' ve already checked all the prime numbers less than 10 , so we know that neither of these numbers is divisible by anything less than 10 . we have to check 11 now . we know that 22 is a multiple of 11 , so 220 is also a multiple of 11 . this means that 220 - 11 = 209 is also a multiple of 11 . we can eliminate this from the list also . that leaves us with just 211 . there ' s no zero option in the question , so this must be a prime number . answer = ( a ) | null |
Question: if the average of 20 digits is 500 and the average of 14 of them is 390 , calculate the average of the remaining 6 numbers ?
A.756.7.
B.751.7.
C.753.7.
D.752.7.
e ) 722.7A.
"explanation : total of the 20 digits - 20 * 500 = 10000 total of the 14 digits - 14 * 390 = 5460 total of the remaining 6 digits - 10000 - 5460 = 4540 average of the remaining 6 numbers = 4540 / 6 = 756.7 answer : a" | null |
Question: two bullet train s 140 m and 180 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
A.15.8 sec ..
B.11.52 sec ..
C.11.8 sec ..
D.10.8 sec ..
e ) 08.8 sec .B.
"relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 180 ) m = 320 m . required time = 320 x 9 / 250 = 11.52 sec . answer b" | null |
Question: a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 25 per kg , then his gain percent is
A.12 %.
B.33 %.
C.14 %.
D.15 %.
e ) 16 %B.
"explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 25 ) = rs . 200 . profit = 200 - 150 = 50 so , profit % = ( 50 / 150 ) * 100 = 33 % option b" | null |
Question: the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 768 sq meters , then what is the width ( in meters ) of the rectangular plot ?
A.24 m.
B.16 m.
C.35 m.
D.54 m.
e ) 43 mB.
"area = l * w = 3 w ^ 2 = 768 w ^ 2 = 256 w = 16 the answer is b ." | null |
Question: a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 500 that is both a prime and a palindrome . what is the sum of the digits of p ?
A.3.
B.4.
C.5.
D.6.
e ) 7B.
"given that p is smallest integer greater than 200 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 b" | null |
Question: if p / q = 4 / 5 , then the value of 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
A.4.
B.34.
C.1.
D.2.
e ) 3A.
"answer given exp . = 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 25 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 25 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 25 / 7 + 6 / 14 = 25 / 7 + 3 / 7 = 28 / 7 = 4 correct option : a" | null |
Question: a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price r of the machine ?
A.81.
B.100.
C.120.
D.135.
e ) 160C.
"since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price r = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c" | null |
Question: bottle r contains 350 capsules and costs $ 6.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
A.$ 0.25.
B.$ 0.12.
C.$ 0.0052.
D.$ 0.003.
e ) $ 0.002C.
"cost per capsule in r is 6.25 / 350 = 0.0178 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.0052 the answer is c" | null |
Question: the milk level in a rectangular box measuring 58 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
A.100.
B.250.
C.750.
D.5437.5.
e ) 5635.5D.
"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 58 * 25 * 1 / 2 = 725 feet ^ 3 of milk must be removed , which equals to 725 * 7.5 = 5437.5 gallons . answer : d ." | null |
Question: on a certain date , pat invested $ 7,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 28,000 , in how many years total will the total value of the investment plus interest increase to $ 56,000 ?
A.15.
B.16.
C.18.
D.20.
e ) 24A.
"28,000 = 7,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 56,000 = 7,000 ( 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: on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 160,000 ?
A.15.
B.16.
C.18.
D.20.
e ) 24E.
"if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 80 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years total 24 years . answer e" | null |
Question: a rectangular block 15 cm by 30 cm by 75 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
['A.6', 'B.40', 'C.15', 'D.10', 'e ) 22']D.
volume of the block = 15 * 30 * 75 = 33750 cm ^ 3 side of the largest cube = h . c . f of 15 , 30,75 = 15 cm volume of the cube = 15 * 15 * 15 = 3375 cm ^ 3 number of cubes = 33750 / 3375 = 10 answer is d | null |
Question: after replacing an old member by a new member , it was found that the average age of 5 members of a club is the same as it was 3 years ago . what is the difference between the ages of the replaced and the new member ?
A.12.
B.13.
C.14.
D.15.
e ) 16D.
explanation : i ) let the ages of the five members at present be a , b , c , d & e years . and the age of the new member be f years . ii ) so the new average of five members ' age = ( a + b + c + d + f ) / 5 - - - - - - - ( 1 ) iii ) their corresponding ages 3 years ago = ( a - 3 ) , ( b - 3 ) , ( c - 3 ) , ( d - 3 ) & ( e - 3 ) years so their average age 3 years ago = ( a + b + c + d + e - 15 ) / 5 = x - - - - - ( 2 ) = = > a + b + c + d + e = 5 x + 15 = = > a + b + c + d = 5 x + 15 - e - - - - - - ( 3 ) iv ) substituting this value of a + b + c + d = 5 x + 15 - e in ( 1 ) above , the new average is : ( 5 x + 15 - e + f ) / 5 equating this to the average age of x years , 3 yrs , ago as in ( 2 ) above , ( 5 x + 15 - e + f ) / 5 = x = = > ( 5 x + 15 - e + f ) = 5 x solving e - f = 15 years . thus the difference of ages between replaced and new member = 15 years . answer : d | null |
Question: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 26.1 kg of zinc has been consumed in it ?
A.58 kg.
B.60 kg.
C.64 kg.
D.70 kg.
e ) noneA.
"sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 26.1 kg zinc , mixture , melted = [ 20 / 9 x 26.1 ] kg = 58 kg . answer a" | null |
Question: the ratio of boys to girls is 6 : 4.60 % of the boys and 40 % of girls take lunch in the canteen . what % of class takes lunch ?
A.51 %.
B.52 %.
C.53 %.
D.54 %.
e ) 55 %B.
let total no of students 100 , boy 60 and girl 40 , so lunch taken by boy and girl respectively 60 * 60 / 100 = 36 and 40 * 40 / 100 = 16 so total 52 students takes lunch out of 100 students . . so required % is 52 % answer : b | null |
Question: a person x started at 3 hours earlier at 40 km / h from a place p , then another person y followed him at 60 km / h . started his journey at 3 o ' clock , afternoon . what is the diference in time when x was 30 km ahead of y and when y was 30 km ahead of x ?
A.8 h.
B.3 h.
C.6 h.
D.3 h.
e ) 1 hB.
explanation : time ( when x was 30 km ahead of y ) = ( 120 - 30 ) / 20 = 4.5 h time ( when y was 30 km ahead of x ) = ( 120 + 30 ) / 20 = 7.5 h thus , required difference in time = 3 h answer : b | null |
Question: a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with squre tiles . find the least number of squre tiles required to cover the floor ?
A.178.
B.128.
C.127.
D.176.
e ) 171D.
"area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d" | null |
Question: if i walk at 6 km / h , i miss the bus by 12 minutes . if i walk at 5 km / h , i reach 14 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
A.13 km.
B.12 km.
C.11 km.
D.6.5 km.
e ) 5.5 kmA.
"d = product of speed difference of time / difference of speed [ here , Γ’ β¬ β ve sign indicates before the schedule time ] d = 6 Γ£ β 5 / 60 [ 12 Γ’ Λ β ( Γ’ Λ β 14 ) / 6 - 5 ] Γ’ β‘ β d = 13 km answer a" | null |
Question: if 35 % of a number is 24 less than 50 % of that number , then the number is ?
A.180.
B.450.
C.160.
D.170.
e ) 185C.
explanation : let the number be n . then , 50 % of n - 35 % of n = 24 50 / 100 n - 35 / 100 n = 24 n = ( 24 x 100 ) / 15 = 160 . answer c | null |
Question: tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4500 . they earned a profit of rs . 5400 after completion of one year . what will be jose ' s share of profit ?
A.3000.
B.2200.
C.2309.
D.2400.
e ) 3200A.
"sol = ~ s - so anju β s share = [ 5 / 9 ] x 5400 = 3000 a" | null |
Question: if the selling price of 60 articles is equal to the cost price of 30 articles , then the loss or gain percent is :
A.55 %.
B.35 %.
C.66 %.
D.45 %.
e ) 50 %E.
"let c . p . of each article be re . 1 . then , c . p . of 60 articles = rs . 60 ; s . p . of 60 articles = rs . 30 . loss % = 30 / 60 * 100 = 50 % answer : e" | null |
Question: there are 5 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
A.90.
B.120.
C.150.
D.180.
e ) 200C.
number of ways of selecting 2 fiction books = 5 c 2 number of ways of selecting 2 non fiction books = 6 c 2 5 c 2 * 6 c 2 = 10 * 15 = 150 answer : c | 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 = 1,155 , and if 1 < p < q < r < s , how many students in the class are accounting majors ?
A.3.
B.5.
C.8.
D.11.
e ) 17A.
"prime factorization of the product pqrs = 1155 = 3 * 5 * 7 * 11 since 1 < p < q < r < s number of students who are accounting majors , p = 3 answer a" | null |
Question: the area of a triangle is with base 4 m and height 6 m ?
A.11 m 2.
B.10 m 2.
C.18 m 2.
D.19 m 2.
e ) 12 m 2E.
"1 / 2 * 4 * 6 = 12 m 2 answer : e" | null |
Question: if 40 sheep eat 40 bags of grass in 40 days . in how many days one sheep will eat one bag of grass ?
A.1.
B.20.
C.40.
D.80.
e ) 70C.
explanation : let the required number of days be x . less sheep , more days ( indirect proportion ) less bags , less days ( direct proportion ) sheep 1 : 40 : : 40 : x bags 40 : 1 1 x 40 x x = 40 x 1 x 40 x = 40 . answer : c | null |
Question: increasing the original price of an article by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by
A.40 %.
B.41 %.
C.42 %.
D.43 %.
e ) 44 %E.
"1.2 * 1.2 * x = 1.44 * x the answer is e ." | null |
Question: the age of somu is one - third his father ' s . 6 years back he was one - fifth of his father ' s age . what is his persent age ?
A.11.
B.13.
C.14.
D.12.
e ) 10D.
"explanation : let somu ' s age be x and that of his father be 3 x . so , x - 6 = 3 x - 6 / 5 = x = 12 answer : option d" | null |
Question: john builds a square with a side of 12 cm from some wire . if from the same wire , he builds a rectangle with a width of 6 cm , what will be the length of the rectangle ?
['A.18 cm', 'B.19 cm', 'C.20 cm', 'D.21 cm', 'e ) none']A.
solution : if the side of the square is 12 cm , then its perimetre will be 48 cm . we build the rectangle from the same wire , so it will have the same perimetre . its width is 6 cm , so its length will be ( 48 - 12 ) Γ· 2 = 36 Γ· 2 = 18 cm answer a | null |
Question: a train 560 m long , running with a speed of 63 km / hr will pass a tree in ?
A.15.
B.16.
C.17.
D.28.
e ) 32E.
"speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 560 * 2 / 35 = 32 sec answer : option e" | null |
Question: the banker Γ’ β¬ β’ s gain on a sum due 3 years hence at 12 % per annum is rs . 180 . the banker Γ’ β¬ β’ s discount is
A.rs . 960.
B.rs . 840.
C.rs . 1020.
D.rs . 680.
e ) noneD.
solution t . d = ( b . g x 100 / r x t ) = rs . ( 180 x 100 / 12 x 3 ) = rs . 500 . b . d = rs ( 500 + 180 ) = rs . 680 . answer d | null |
Question: 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 10 .
A.150.
B.152.
C.154.
D.163.
e ) 144D.
"d = d * q + r d = 17 * 9 + 10 d = 153 + 10 d = 163 answer d" | null |
Question: a lady builds 8 cm length , 15 cm width , and 5 cm height box using 10 cubic cm cubes . what is the minimum number of cubes required to build the box ?
A.107.
B.60.
C.70.
D.89.
e ) 78B.
"number of cubes required = volume of box / volume of cube = 8 * 15 * 5 / 10 = 60 cubes answer : b" | null |
Question: a furniture dealer purchased a desk for $ 100 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
A.40 %.
B.45 %.
C.50 %.
D.55 %.
e ) 60 %A.
"anyway , in this question , there is no discount but the mark up is given as 40 % of the selling price . so it is not 40 % of $ 100 but instead , 40 % of selling price which is obtained by adding mark up to $ 100 . so if selling price is s , 100 + 40 % of s = s or 100 = 0.6 s therefore s = 100 / 0.6 = s = profit = 100 / 0.6 - 100 which is calculated on cost price in % terms . so 40 / 100 * 100 = 40 % is profit . a" | null |
Question: there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total w of the book ?
A.3003.
B.3027.
C.3024.
D.3021.
e ) 3018A.
"first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) w 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ." | null |
Question: the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 33 kmph ?
A.210.
B.220.
C.125.
D.240.
e ) 250C.
"distance covered in 1 min = ( 33 * 1000 ) / 60 = 550 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 550 / 4.4 = 125 answer : c" | null |
Question: the population of a bacteria colony doubles every day . if it was started 8 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
A.512.
B.768.
C.1024.
D.2048.
e ) 4096A.
"8 days ago - 2 7 days ago - 4 6 days ago - 8 5 days ago - 16 4 days ago - 32 3 days ago - 64 2 days ago - 128 yesterday - 256 today - 512 ans : a" | null |
Question: how many quarters are equal to 7 dollars ?
A.1.
B.28.
C.12.
D.9.
e ) 7B.
"7 * 4 = 28 quarters answer : b" | null |
Question: what is 0.1 percent of 12,356 ?
A.0.12356.
B.1.2356.
C.12.356.
D.0.012356.
e ) 0.0012356C.
since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.1 ( 1 / 100 ) 12,356 . the answer is 12.356 . hence , the correct answer is c . | null |
Question: the difference between the value of a number increased by 25 % and the value of the original number decreased by 30 % is 22 . what is the original number ?
A.40.
B.50.
C.65.
D.70.
e ) 90A.
"let the original # be x then 1.25 x β 0.7 x = 22 - - > x = 40 answer : a ." | null |
Question: if a - b = 3 and a ^ 2 + b ^ 2 = 33 , find the value of ab .
A.12.
B.15.
C.10.
D.18.
e ) 13A.
"2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 33 - 9 = 24 ab = 12 . answer is a ." | null |
Question: 1 : 3 = 1 2 / 3 : x . the value of x is ?
A.1.
B.6.
C.7.
D.5.
e ) 8D.
x * 1 = 3 * 5 / 3 x = 5 answer : d | null |
Question: how many figures are required to number the pages the pages of a book containing 709 pages ?
A.2020.
B.2019.
C.1019.
D.2029.
e ) 2039B.
"1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 709 = 610 * 3 = 1830 - - - - - - - - - - - 2019 answer : b" | null |
Question: a cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm . the percentage of the wood wasted is :
['A.45 %', 'B.56 %', 'C.67 %', 'D.75 %', 'e ) none of these']D.
explanation : we will first subtract the cone volume from wood volume to get the wood wasted . then we can calculate its percentage . sphere volume = 4 / 3 Ο r 3 cone volume = 1 / 3 Ο r 2 h volume of wood wasted = ( 4 / 3 Ο β 9 β 9 β 9 ) β ( 1 / 3 Ο β 9 β 9 β 9 ) = Ο β 9 β 9 β 9 cm 3 required percentage = Ο β 9 β 9 β 9 / 4 / 3 Ο β 9 β 9 β 9 β 100 % = 3 / 4 β 100 % = 75 % option d | null |
Question: of the votes cast on a certain proposal , 66 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
A.290.
B.310.
C.330.
D.350.
e ) 370C.
"let x be the total number of votes cast . 0.6 x = 0.4 x + 66 0.2 x = 66 x = 330 the answer is c ." | null |
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