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a certain company β s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 35 percent greater than its profit in 1996. the company β s profit in 1997 was what percent greater than its profit in 1995? | "profit in 1995 - 100 profit in 1996 - 115 % increae profit in 1997 in comparison to 1995 = 15 + 115 * 35 % = 55.25 correct |
a, b and c started a partnership business by investing rs. 12000, rs. 16000, rs. 20000 respectively. at the end of the year, the profit were distributed among them. if c ' s share of profit is 36000, what is the total profit? | "a: b: c = 12000: 16000: 20000 = 3: 4: 5 let total profit = p then p Γ£ β 5 / 12 = 36000 p = ( 36000 Γ£ β 12 ) / 5 = 86400 answer is c." |
two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively. if they cross each other in 24 seconds, what is the ratio of their speeds? | "let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 24 s = ( 27 x + 17 y ) / ( x + y ) = 24 = ( 27 x + 17 y ) / = 24 ( x + y ) = 3 x = 7 y = x / y = 7 / 3 |
sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 450 dollars. on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. each cup she sold had a total cost of 75 cents and sarah did not incur any other costs. if every day she sold exactly 32 cups and 3 of the days were hot, then what was the price of 1 cup on a hot day? | 7 regular days - - > sales = 7 * 32 * x = 224 x; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x; total sales = 224 x + 120 x = 344 x. total cost = 10 * 32 * 0.75 = 240. profit = 344 x - 240 = 450 - - > x = 2. 1.25 x = ~ 2.50. |
at sandi β s pet shop, 25 cups of bird seed are used every 5 days to feed 15 parakeets. how many cups of bird seed would be required to feed 14 parakeets for 7 days? | let ' s go step - by - step. 25 cups are used over a 5 day period, which means 5 cups a day. this feeds 15 parakeets, which means each parakeet needs 1 / 3 of a cup every day. for 14 parakeets, we need 14 * 1 / 3 cups = 4.62 cups a day. over 7 days, we need 32.34 cups. choice b. |
there are 2 available positions and 50 candidates, one half of whom are democrats and another half are republicans. if it was decided that the positions would be filled at random, then what is the probability e that the both positions will be taken by members of just one party? | e probability of one party having both spots: ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot. ( 24 / 49 ) because after one person from a particular party is chosen, there are 24 members of the same party left out of 49 total candidates. since this result can happen for both parties, ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) |
a car travels from point a to point b. the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 80 km / hr. what is the speed of the car in the second half of the trip? | "let d be the distance and let v be the speed in the second half. the total time = t 1 + t 2 d / 60 = d / 160 + ( d / 2 ) / v 8 d / 480 - 3 d / 480 = ( d / 2 ) / v d / 96 = d / 2 v and so v = 48 km / hr the answer is d." |
sonika deposited rs. 8000 which amounted to rs. 11200 after 3 years at simple interest. had the interest been 2 % more. she would get how much? | "( 8000 * 3 * 2 ) / 100 = 480 11200 - - - - - - - - 11680 |
a manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18 %. the wholesaler sells the same to retailer at a profit of 20 %. the retailer in turn sells them to a customer for rs. 30.09, there by earning a profit of 25 %. the cost price for the manufacturer is: | let the cost price for the manufacturer be rs. x. then, 125 % of 120 % of 118 % of x = 30.09. 125 / 100 * 120 / 100 * 118 / 100 * x = 3009 / 100 177 / 100 x = 3009 / 100 = > x = 17 |
how long will a boy take to run round a square field of side 40 meters, if he runs at the rate of 12 km / hr? | speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 40 * 4 = 160 m time taken = 160 * 3 / 10 = 48 sec answer is b |
the sum of the first 50 positive even integers is 2550. what is the sum of the even integers from 602 to 700 inclusive? | "2 + 4 + 6 + 8 +... + 100 = 2550 602 + 604 +... + 700 = 50 ( 600 ) + ( 2 + 4 +... + 100 ) = 30,000 + 2550 = 32,550 the answer is c." |
the average runs scored by a batsman in 10 matches is 40. in the next 10 matches the batsman scored an average of 30 runs. find his average in all the 20 matches? | "total score of the batsman in 10 matches = 400. total score of the batsman in the next 10 matches = 300. total score of the batsman in the 20 matches = 700. average score of the batsman = 700 / 20 = 35. |
there are 300 giraffes at a large zoo. the number of giraffes is 3 times the number of all the other animals combined. how many more giraffes are there than non giraffes animals at the zoo? | answer is d. total giraffes = 300 = 3 * other animals ( x ) or x = 10. so, difference in giraffes and x = 300 - 10 = 290. |
bucket a is 1 / 4 full of sand, and bucket b, which has one - half the capacity of bucket a, is 3 / 8 full of sand. jana pours the contents of bucket b into bucket a. bucket a is now filled to what fraction of its capacity? | let capapcity of a = x sand = x / 4 capacity of b = x / 2 sand = 3 x / 16 a total = x / 4 + 3 x / 16 = 7 x / 16 |
if n is an integer, f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 15. what is the value of f ( 6 )? | since f ( n ) = f ( n - 1 ) - n then: f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5. as given that f ( 4 ) = 15 then f ( 5 ) = 15 - 5 = 10 - - > substitute the value of f ( 5 ) back into the first equation: f ( 6 ) = f ( 5 ) - 6 = 10 - 6 = 4. |
a salesman β s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs. 1100 plus 2.5 % commission on all sales exceeding rs. 4,000. if his remuneration as per new scheme was rs. 600 more than that by the previous schema, his sales were worth? | "[ 1100 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 14000 |
andy solves problems 78 to 125 inclusive in a math exercise. how many problems does he solve? | "125 - 78 + 1 = 48 ' e ' is the answer" |
a fair 2 sided coin is flipped 3 times. what is the probability that tails will be the result at least twice, but not more than 3 times? | "at least twice, but not more than 3 timesmeans exactly 2 times, 3 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 3 c 2 / 2 ^ 3 = 3 / 8 |
a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1. what is the addition of the maximum and minimum possible values of ' a + b '? | "possible values of a and b can be 5,4; 4,5 ( which are same for a + b ) and 1,20; 20,1 ( same result for a + b ) so 21 + 9 = 30 ans c" |
3 / 5 of all married couples have more than one child. 2 / 5 of all married couples have more than 3 children. what fraction of all married couples have 2 or 3 children? | plug in simple numbers. take 100 couples for example. 3 / 5 of 100 couples have more than one child = 60 couples. 2 / 5 of 100 couples have more than 3 kids = 40 couples. this implies that 40 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples, which equals 20 couples have either one or no kids at all. we need to find couples that have 2 or 3 kids, so essentially, it is 60 - 40 = 20. fraction will be 20 / 100 = 1 / 5. option a |
one pump drains one - half of a pond in 2 hours, and then a second pump starts draining the pond. the two pumps working together finish emptying the pond in one - half hour. how long would it take the second pump to drain the pond if it had to do the job alone? | "the tricky part here, i believed is one half hour = 1 / 2. then everything would be easy. we have the 1 st pump working rate / hour = 1 / 2: 2 = 1 / 4 working rate of 2 pumps: 1 / 2: 1 / 2 = 1. working rate of 2 nd pump: 1 - 1 / 4 = 3 / 4 - - > time taken for the 2 nd pump to finish: 1: 3 / 4 = 4 / 3 = 1.3 hours. a" |
if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 18, then n = | "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 18 = > 4 x 2 ^ 2 n = 4 ^ 24 = 2 ^ 36 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 36 = > 2 ^ ( 2 n + 2 ) = 2 ^ 36 = > 2 n + 2 = 36 = > n = 17 so. answer will be c." |
a fair price shopkeeper takes 10 % profit on his goods. he lost 40 % goods during theft. his loss percent is: | explanation: suppose he has 100 items. let c. p. of each item be re. 1. total cost = rs. 100. number of items left after theft = 60. s. p. of each item = rs. 1.10 total sale = 1.10 * 60 = rs. 66 hence, loss % = 34 / 100 * 100 = 34 % |
a and b go around a circular track of length 300 m on a cycle at speeds of 34 kmph and 50 kmph. after how much time will they meet for the first time at the starting point? | "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a, length of the track / speed of b } = lcm { 300 / ( 36 * 5 / 18 ), 300 / ( 54 * 5 / 18 ) } = lcm ( 30, 20 ) = 60 sec. |
in cliff β s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. of the igneous rocks, 3 / 4 are shiny and the rest are matte, while 1 / 5 of the sedimentary rocks are shiny. if there are 30 shiny igneous rocks, how many total rocks does cliff have? | "we can start with the known quantity and then go on to find the others. shiny igneous ricks are 30. these are ( 3 / 4 ) of total igneous rocks. ( 2 / 3 ) * total igneous rocks = 30 total igneous rocks = 30 * ( 4 / 3 ) = 40 total sedimentary rocks = 2 * total igneous rocks = 2 * 40 = 80 total number of rocks = 40 + 80 = 120 answer ( d )" |
two assembly line inspectors, smithy and glen, inspect widgets as they come off the assembly line. if smithy inspects every fifth widget, starting with the fifth, and glen inspects every third, starting with the third, how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector? | widgets inspected by smithy: ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by glen: ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both: ( ( 90 - 15 ) + 1 = 6 total: 19 + 32 - 6 = 45 hence, widgets not inspected: 98 - 45 = 53 option b |
what is the sum of the numbers between 1 and 12, inclusive? | "sol. add the numbers between 1 and 12. answer is d, 78." |
the speed of a car is 120 km in the first hour and 70 km in the second hour. what is the average speed of the car? | "s = ( 120 + 70 ) / 2 = 95 kmph |
in a class of 60 children, 30 % children can speak only english, 20 % hindi and english both and the rest of the children can speak only hindi. how many children can speak hindi? | number of students who speak only english = 30 % of 60 = 18 β΅ number of students who speak hindi and english = 20 % of 60 = 12 β΅ number of students who speak only hindi = ( 60 β 30 = ) 30 β΅ no. of students who speak hindi = 30 + 12 = 42 answer a |
25 % of a number is more than 20 % of 650 by 190. find the number? | "( 25 / 100 ) * x Γ’ β¬ β ( 20 / 100 ) * 650 = 190 1 / 4 x = 320 x = 1280 |
george ' s car calls for 8 ounces of oil for each cylinder used. his car ' s engine has 6 cylinders. if 16 ounces of oil has already been put into the engine used, then how many additional ounces of oil are needed? | number of ounces per cylinder 8 number of cylinders 6 ounces needed 48 ounces used 16 answer d |
a car traveled 35 % of the way from town x to town y at an average speed of 35 mph. the car traveled at an average speed of v mph for the remaining part of the trip. the average speed for the entire trip was 50 mph. what is v in mph? | "assume total distance = 100 miles time taken for 35 miles = 35 / 35 = 1 hour time taken for the rest of the 65 miles = 65 / v hours. average speed = 50 therefore the total time needed = 2 hours. 2 = 1 + 65 / v hence v = 65 mph |
if the compound interest on a certain sum of money for 2 years at 10 % per annum be rs. 993, what would be the simple interest? | "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p? p = 3000 / - now si @ 10 % on 3000 / - for 2 yrs = ( 3000 x 10 x 2 ) / 100 = 600 / - |
hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench. if the total weight of two hammers and two wrenches is one - third that of 8 hammers and 5 wrenches, then the total weight of one wrench is how many times that of one hammer? | x be the weight of a hammer and y be the weight of a wrench. ( 2 x + 2 y ) = 1 / 3 * ( 8 x + 5 y ) 3 ( 2 x + 2 y ) = ( 8 x + 5 y ) 6 x + 6 y = 8 x + 5 y y = 2 x ans - e |
tea worth rs. 126 per kg are mixed with a third variety in the ratio 1: 1: 2. if the mixture is worth rs. 163 per kg, the price of the third variety per kg will be | "solution since first 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. x - 163 / 22.50 = 1 = Γ’ β¬ ΒΊ x - 163 = 22.50 = Γ’ β¬ ΒΊ x = 185.50. hence, price of the third variety = rs. 175.50 per kg. answer c" |
in an examination, 25 % of total students failed in hindi, 40 % failed in english and 35 % in both. the percentage of these who passed in both the subjects is: | "pass percentage = 100 - ( 25 + 40 - 35 ) = 100 - 70 = 30 |
the total circumference of two circles is 49. if the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii? | "let r = radius of smaller circle. let r = radius of larger circle therefore: 2 Ο r + 2 Ο r = 49 where 2 r = r thus: 2 Ο r + 4 Ο r = 49 6 Ο r = 49 r = approx 2.6 Ο r + 2 r Ο = 49 3 Ο r = 49 r = approx 5.2 r + r = approx 7.8 |
a certain pair of used shoes can be repaired for $ 10.50 and will last for 1 year. a pair of the same kind of shoes can be purchased new for $ 30.00 and will last for 2 years. the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes? | "1 ) cost of repairing = 10.5 ( for one year ), therefore for 2 years it would be $ 21. 2 ) cost of new pair which will last for 2 years is $ 30.00 percentage change formula = ( final value - initial value ) / ( initial value ) * 100. in this case the final value would be the price of new shoe initial value would be the cost of repairing the old shoe. i. e ( 30 - 21 ) / ( 21 ) * 100 = 42.85 %. ans is a" |
a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 6 hours. if both the taps are opened simultaneously, then after how much time will the cistern get filled? | "net part filled in 1 hour = ( 1 / 4 - 1 / 6 ) = 1 / 12 the cistern will be filled in 12 / 1 hrs i. e., 12 hrs. |
a and b invests rs. 8000 and rs. 9000 in a business. after 4 months, a withdraws half of his capital and 2 months later, b withdraws one - third of his capital. in what ratio should they share the profits at the end of the year? | "a: b ( 8000 * 4 ) + ( 4000 * 8 ): ( 9000 * 6 ) + ( 6000 * 6 ) 64000: 90000 32: 45. |
a runs twice as fast as b and gives b a start of 42 m. how long should the racecourse be so that a and b might reach in the same time? | "ratio of speeds of a and b is 2: 1 b is 42 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 42 m is 42 / 1 = 42 m so the total time taken by a and b to reach = 2 * 42 = 84 m |
in a certain town, the ratio of ny yankees fans to ny mets fans is 3: 2, and the ratio of ny mets fans to boston red sox fans is 4: 5. if there are 330 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many ny mets fans are there in this town? | "the ratio of yankees: mets: red sox = 6: 4: 5 the mets fans are 4 / 15 of the population. ( 4 / 15 ) * 330 = 88 the answer is b." |
what is the 26 th digit to the right of the decimal point in the decimal form of 6 / 11? | "6 / 11 = 0.54545454... the even numbered positions in the decimal expansion are all 4. the answer is b." |
what is the area of square field whose side of length 13 m? | "13 * 13 = 169 sq m |
a can complete a certain job in 9 days. b is 80 % more efficient than a. in how many days can b complete the same job? | "let, total work unit = 90 units a can finish in 9 days = 90 unit work i. e. a can finish in 1 days = 10 unit work i. e. b can finish in 1 days = 10 + ( 80 / 100 ) * 10 = 18 unit work days in which b will complete the work alone = 90 / 18 = 5 days |
a metallic sheet is of rectangular shape with dimensions 50 m x 30 m. from each of its corners, a square is cut off so as to make an open box. if the length of the square is 5 m, the volume of the box ( in m cube ) is: | "explanation: l = ( 50 - 10 ) m = 40 m, [ because 5 + 5 = 10 ] b = ( 30 - 10 ) m = 20 m, h = 5 m. volume of the box = ( 40 x 20 x 5 ) m cube = 4000 m cube. option e" |
in what time a sum of money double itself at 2 % per annum simple interest? | p = ( p * 2 * r ) / 100 r = 50 % |
a, b, c can complete a piece of work in 18, 6,12 days. working together, they complete the same work in how many days? | "a + b + c 1 day work = 1 / 18 + 1 / 6 + 1 / 12 = 11 / 36 a, b, c together will complete the job in 36 / 11 days answer is d" |
if the horse can run 10 miles / hour, how many days would it take for a horse to run from new york city to washington. d. c.? ( 240 miles from nyc to d. c. ) | the horse runs 10 miles / hour, thus it would take the horse 240 miles / 10 miles / hour to = 24 hours to run from nyc to d. c. there are 24 hours in a day, so days it take would be 24 hours / 24 hours / day = 1 day. correct |
solve below question 2 x + 1 = - 21 | "2 x + 1 = - 21 x = - 11 a" |
solution for 2.12 +. 004 +. 345 | 2.12 +. 004 +. 345 0 = 0 - 2.12 - 0.004 - 0.345 0 = - 2.469 |
in a throw of dice what is the probability of ge Γ¦ Β« ng number greater than 3 | "explanation: number greater than 3 is 4, 5, 6, so only 3 number total cases of dice = [ 1,2, 3,4, 5,6 ] so probability = 3 / 6 = 1 / 2 |
a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs. 1300, what is the reduced price for kg? | "1300 * ( 25 / 100 ) = 325 - - - - 5? - - - - 1 = > rs. 65 |
how many paying stones, each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1 / 2 m board? | "30 * 33 / 2 = 5 / 2 * 2 * x = > x = 99 answer b" |
20 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3: 2. how many liters of liquid q must be added to make the ratio 4: 3? | "let x be the amount of liquid q to be added. ( 2 / 5 ) * 20 + x = ( 3 / 7 ) * ( 20 + x ) 280 + 35 x = 300 + 15 x 20 x = 20 x = 1 the answer is a." |
a sum amounts to rs. 5292 in 2 years at the rate of 5 % p. a. if interest was compounded yearly then what was the principal? | "ci = 5292, r = 5, n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 5292 = p [ 21 / 20 ] ^ 2 5292 [ 20 / 21 ] ^ 2 4800 |
express a speed of 56 kmph in meters per second? | "56 * 5 / 18 = 15.56 mps |
in a fuel station the service costs $ 1.75 per car, every liter of fuel costs 0.65 $. assuming that a company owns 12 cars and that every fuel tank contains 45 liters and they are all empty, how much money total will it cost to fuel all cars? | "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 45 ) = 21 + 351 = > 372 hence answer will be ( b ) 372" |
a group of men decided to do a work in 12 days, but 6 of them became absent. if the rest of the group did the work in 14 days, find the original number of men? | "original number of men = 6 * 14 / ( 14 - 12 ) = 42 answer is b" |
a sells a cricket bat to b at a profit of 20 %. b sells it to c at a profit of 25 %. if c pays $ 234 for it, the cost price of the cricket bat for a is: | "125 % of 120 % of a = 234 125 / 100 * 120 / 100 * a = 234 a = 234 * 2 / 3 = 156. answer a" |
a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. if the poles of the fence are kept 5 metres apart, how many poles will be needed? | "solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m. β΄ number of poles = [ 280 / 5 ] = 56 m answer b" |
in town x, 64 percent of the population are employed, and 49 percent of the population are employed males. what percent of the employed people in town x are females? | "answer b male - employed - 64 % female - employed - 15 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 15 / 64 = 20 b" |
the hiker walking at a constant rate of 6 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 30 miles per hour. the motor - cyclist stops to wait for the hiker 12 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the motor - cyclist wait until the hiker catches up? | for the 12 minutes the motor - cyclist continues to overtake the hiker, she is going at 24 miles per hour faster than the hiker. once the motor - cyclist stops, the hiker is going at 6 miles per hour while the motor - cyclist is at rest so the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds. 24 / 6 * 12 or 48 minutes answer is ( d ) |
the speed at which a man can row a boat in still water is 15 kmph. if he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 90 metres? | "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 90 m = 90 / 5 = 18 seconds. |
a train consists of 12 boggies, each boggy 15 metres long. the train crosses a telegraph post in 9 seconds. due to some problem, one boggies were detached. the train now crosses a telegraph post in | "length of train = 12 Γ£ β 15 = 180 m. then, speed of train = 180 Γ’ Β β 9 = 20 m / s now, length of train = 11 Γ£ β 15 = 165 m Γ’ Λ Β΄ required time = 165 Γ’ Β β 20 = 8.25 sec. answer d" |
a lent rs. 5000 to b for 2 years and rs. 3000 to c for 4 years on simple interest at the same rate of interest and received rs. 2640 in all from both of them as interest. the rate of interest per annum is? | "let the rate be r % p. a. then, ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 2640 100 r + 120 r = 2640 r = 12 % |
tickets numbered from 1 to 26 are mixed and then a ticket is selected randomly. what is the probability that the selected ticket bears a number which is a multiple of 3? | "here, s = [ 1, 2, 3, 4, β¦., 19, 20, 21, 22, 23, 24, 25, 26 ] let e = event of getting a multiple of 3 = [ 3, 6, 9, 12, 15, 18, 21, 24 ] p ( e ) = n ( e ) / n ( s ) = 8 / 26 = 4 / 13 the answer is d." |
in a certain boys camp, 20 % of the total boys are from school a and 30 % of those study science. if there are 56 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp? | "since 30 % of the boys from school a study science, then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a, then 0.2 * 0.7 = 0.14, or 14 % of the boys in the camp are from school a and do not study science. we are told that this number equals to 56, so 0.14 * { total } = 56 - - > { total } = 400. |
the number 219 can be written as sum of the squares of 3 different positive integers. what is the sum of these 3 different integers? | "sum of the squares of 3 different positive integers = 219 13 ^ 2 + 7 ^ 2 + 1 ^ 2 = 219 now, sum of these 3 different integers = 13 + 7 + 1 = 21 ans - b" |
a certain list consists of 21 different numbers. if n is in the list and n is 7 times the average ( arithmetic mean ) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list? | "series: a 1, a 2.... a 20, n sum of a 1 + a 2 +... + a 20 = 20 * x ( x = average ) so, n = 7 * x hence, a 1 + a 2 +.. + a 20 + n = 27 x so, the fraction asked = 7 x / 27 x = 7 / 27 answer a" |
in a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man. what is weight of new comer? | solution: member in group * age increased = difference of replacement or, 8 * 1 = new comer - man going out or, new comer = 8 + 60; or, new comer = 68 years. |
the ratio of a and b is 5: 3. after 2 years their ratio is 3: 2. what is the age of b? | the ratio of a and b is 5 x and 3 x years. after 2 years, their ratio will be 3 and 2. ( i. e ) ( 5 x + 2 ) / ( 3 x + 2 ) = 3 / 2 10 x + 4 = 9 x + 6 x = 2 b ' s age = 3 x = 3 ( 2 ) = 6 years answer is option c |
a train leaves delhi at 7 a. m. at a speed of 30 kmph. another train leaves at 2 p. m. at a speed of 40 kmph on the same day and in the same direction. how far from delhi, will the two trains meet? | "d = 30 * 7 = 210 rs = 40 β 30 = 10 t = 210 / 10 = 21 d = 40 * 21 = 840 km |
if the probability of rain on any given day in chicago during the summer is 50 %, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from july 4 through july 7, inclusive? | one case is rainy - rainy - rainy - not rainy. the probability of this case is ( 1 / 2 ) ^ 4 = 1 / 16 the number of possible cases is 4 c 3 = 4. p ( exactly 3 rainy days ) = 4 * 1 / 16 = 1 / 4 the answer is a. |
eight cubes, each with a volume of 512 cm ^ 3, are joined to form one large cube. what is the surface area of the large cube? | volume = a x a x a = a ^ 3 volume of cube = 8 x 512 = 4096 cm ^ 3 4096 = a ^ 3 a = 16 surface area of cube = 6 a ^ 2 = 6 x 16 ^ 2 = 1536 answer is b |
the length of a rectangle is twice its breadth. if its lengthis decreased by 5 cm & breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. what is the length of the rectangle? | let breadth = x cm then, length = 2 x cm area = x Γ 2 x = 2 x 2 sq. cm. new length = ( 2 x β 5 ) cm new breadth = ( x + 5 ) cm new area = ( 2 x β 5 ) ( x + 5 ) sq. cm. given that, new area = initial area + 75 sq. cm. β ( 2 x β 5 ) ( x + 5 ) = 2 x 2 + 75 β 2 x 2 + 10 x β 5 x β 25 = 2 x 2 + 75 β 5 x β 25 = 75 β 5 x = 75 + 25 = 100 β x = 1005 = 20 cm length = 2 x = 2 Γ 20 = 40 cm c |
every year an amount increases by 1 / 8 th of itself. how much will it be after two years if its present value is rs. 51200? | 51200 * 9 / 8 * 9 / 8 = 64800. |
set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2. if one of the numbers in set s is increased by 4, while all other numbers remain the same, what is the new average of set s? | "old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 4 then total increased to 62 + 4 = 66 new avg - 66 / 10 = 6.6. hence answer is a." |
during a sale of 20 % on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies. the store still makes a profit of 18 % on this sale. what is the mark up percentage on each candy? | "hi akhil, i can share the way i solved it.. let ' s say marked price = m so, there ' s a discount of 20 % on m so, new s. p. = 80 % of m now, the child convinces the owner to sell 20 candies for the price of 14 candies. let ' s say each candy after discount is 1 $. so, s. p. of 20 candies = 20 $. the child bought it for 14 $ so, he got a discount of 6 / 20 * 100 = 30 % so, the latest s. p. = 70 % of 80 % of m = 0.7 * 0.8 m now, we are given that the shopkeeper still makes a profit of 12 %. so we have, 0.7 * 0.8 * m = 1.12 c. p so, we get, m = 2 c. p. i. e. marked price was kept 100 % above c. p. d" |
how many numbers are divisible by 4 between 1 and 100. | "numbers divisible by 4 till 100 = ( 100 / 4 ) = 25 but we should not consider 100 as we are asked to find the number between 1 to 100 which are divisible by 4. so answer is 24 numbers. |
if a person walks at 14 km / hr instead of 10 km / hr, he would have walked 20 km more. what is the actual distance travelled by him? | "assume that the person would have covered x km if travelled at 10 km / hr β speed = distancetime = x 10..... ( equation 1 ) give that the person would have covered ( x + 20 ) km if travelled at 14 km / hr β speed = distancetime = ( x + 20 ) 14..... ( equation 2 ) from equations 1 and 2, x 10 = ( x + 20 ) 1414 x = 10 x + 2004 x = 200 x = 2004 = 50 |
arjun started a business with rs. 40,000 and is joined afterwards by anoop with rs. 80, 000. after how many months did anoop join if the profits at the end of the year are divided equally? | "suppose anoop joined after 3 months. then, 40000 * 12 = 80000 * ( 12 β x ) = > x = 6. |
5555 Γ 9999 =? | "e 55544445 5555 Γ 9999 = 5555 ( 10000 - 1 ) = 5555 Γ 10000 - 5555 Γ 1 = 55550000 - 5555 = 55544445" |
1397 x 1397 =? | "1397 x 1397 = ( 1397 ) 2 = ( 1400 - 3 ) 2 = ( 1400 ) 2 + ( 3 ) 2 - ( 2 x 1400 x 3 ) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. b )" |
if 5 < x < 11 and y = x + 6, what is the greatest possible integer value of x + y? | "x + y = x + x + 6 = 2 x + 6 we need to maximize this value and it needs to be an integer. 2 x is an integer when the decimal of x is. 0 or. 5 the largest such value is 10.5 then x + y = 10.5 + 16.5 = 27. the answer is c." |
pipe p can fill a tank in 8 hours, pipe q in 12 hours and pipe r in 20 hours. if all the pipes are open, in how many hours will the tank be filled? | explanation: part filled by ( p + q + r ) in 1 hour = ( 1 / 8 + 1 / 12 + 1 / 20 ) = 31 / 120 all the three pipes together will fill the tank = 120 / 31 = 3.8 hours answer c |
a worker ' s take - home pay last year was the same each month, and she saved the same fraction of her take - home pay each month. the total amount of money that she had saved at the end of the year was 5 times the amount of that portion of her monthly take - home pay that she did not save. if all the money that she saved last year was from her take - home pay, what fraction of her take - home pay did she save each month? | "let x be the fraction of her take - home pay that the worker saved. let p be the monthly pay. 12 xp = 5 ( 1 - x ) p 12 xp = 5 p - 5 xp 17 xp = 5 p x = 5 / 17 the answer is c." |
a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. in order to earn a profit of 35 %, what should be the sale price of the mixed tea? | "c. p. of mixture = 80 Γ 15 + 20 Γ 20 / 80 + 20 = 16 β΄ s. p. = ( 100 + 35 ) / 100 Γ 16 = 21.6 answer b" |
if the sum of two numbers is 55 and the h. c. f and l. c. m of these numbers are 5 and 120 respectively, then the sum of the reciprocal of the numbers is equal to: | "let the numbers be a and b. then, a + b = 55 and ab = 5 * 120 = 600. required sum = 1 / a + 1 / b = ( a + b ) / ab = 55 / 600 = 11 / 120. |
a person bought 129 glass bowls at a rate of rs. 11 per bowl. he sold 118 of them at rs. 15 and the remaining broke. what is the percentage gain for a? | "cp = 129 * 11 = 1419 and sp = 118 * 15 = 1770 gain % = 100 * ( 1770 - 1419 ) / 1419 = 2900 / 129 |
a cube of edge 12 cm is immersed completely in a rectangular vessel containing water. if the dimensions of the base of vessel are 20 cm * 15 cm, find the rise in water level? | "increase in volume = volume of the cube = 12 * 12 * 12 cm ^ 3 rise in water level = volume / area = 12 * 12 * 12 / 20 * 15 = 5.76 cm answer is a" |
two cars are driving toward each other. the first car is traveling at a speed of 100 km / h, which is 20 % slower than the second car ' s speed. if the distance between the cars is 1125 km, how many hours will it take until the two cars meet? | "the speed of the first car is 100 km / h. the speed of the second car is 100 / 0.8 = 125 km / h. the two cars complete a total of 225 km each hour. the time it takes the cars to meet is 1125 / 225 = 5 hours. the answer is d." |
a train 140 m long running at 84 kmph crosses a platform in 16 sec. what is the length of the platform? | "d = 84 * 5 / 18 = 16 = 373 Γ’ β¬ β 140 = 233 |
by travelling at 70 kmph, a person reaches his destination on time. he covered two - third the total distance in one - third of the total time. what speed should he maintain for the remaining distance to reach his destination on time? | let the time taken to reach the destination be 3 x hours. total distance = 70 * 3 x = 210 x km he covered 2 / 3 * 210 x = 140 x km in 1 / 3 * 3 x = x hours so, the remaining 70 x km, he has to cover in 2 x hours. required speed = 70 x / 2 x = 35 kmph. |
the cost of registration at a professional association meeting was $ 50 per person; a lunch for registrants only was available for an additional $ 22 per person. if the number of registrants who paid for lunch was 50 more than the number who did not, and if receipts for registration and lunch totaled $ 82,900, how many people paid just for registration at the meeting? | "hope this might be useful to you. let the number of people who have opted only to register = x now since the registration cost is 50 $ per person, the total amount sums to = 50 x $ as per the information given in the question, the number of registrants who paid for lunch was 50 more than the number who did not. that means, total number of people who registered and paid for lunch = 50 + x. for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $. total amount in this case sums to = 72 ( 50 + x ) = 3600 + 72 x now, total amount received was 82900. thus, from the above data, 50 x + 3600 + 72 x = 82900 122 x = 82900 - 3600 122 x = 79300 x = 650 hence the correct ans is b" |
the unit digit in the product ( 594 * 897 * 929 * 462 ) is: | "explanation: unit digit in the given product = unit digit in ( 4 * 7 * 9 * 2 ) = 4 |
how many times will the digit 8 be written when listing the integers from 1 to 1000? | "many approaches are possible. for example: consider numbers from 0 to 999 written as follows: 1. 000 2. 001 3. 002 4. 003......... 1000. 999 we have 1000 numbers. we used 3 digits per number, hence used total of 3 * 1000 = 3000 digits. now, why should any digit have preferences over another? we used each of 10 digits equal # of times, thus we used each digit ( including 8 ) 3000 / 10 = 300 times. |
a train passes a station platform in 36 sec and a man standing on the platform in 20 sec. if the speed of the train is 63 km / hr. what is the length of the platform? | "speed = 63 * 5 / 18 = 17.5 m / sec. length of the train = 17.5 * 20 = 350 m. let the length of the platform be x m. then, ( x + 350 ) / 36 = 17.5 = > x = 280 m. |
machine a and machine b are each used to manufacture 330 sprockets. it takes machine a 10 hours longer to produce 330 sprockets than machine b. machine b produces 10 percent more sprockets per hour than machine a. how many sprockets per hour does machine a produces? | "machine b: takes x hours to produce 330 sprockets machine a: takes ( x + 10 ) hours to produce 330 sprockets machine b: in 1 hour, b makes 330 / x sprockets machine a: in 1 hour, a makes 330 / ( x + 10 ) sprockets equating: 1.1 ( 330 / ( x + 10 ) ) = 330 / x 484 / ( x + 10 ) = 330 / x 363 x = 330 x + 3300 33 x = 3300 x = 100 a makes 330 / ( 110 ) = 3 sprockets per hour |
if the ratio of the sum of the first 6 terms of a g. p. to the sum of the first 3 terms of the g. p. is 217, what is the common ratio of the g. p? | "217 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 217 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2......... 217 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 216 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 216 = r ^ 3 r = 6 d" |