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the population of a town increases 22 % and 25 % respectively in two consecutive years. after the growth the present population of the town is 1220. then what is the population of the town 2 years ago? | "explanation: formula: ( after = 100 denominator ago = 100 numerator ) 1220 * 100 / 122 * 100 / 125 = 800 |
in how many v ways can a 4 - letter password be chosen, using the letters a, b, c, d, e, and / or f, such that at least one letter is repeated within the password? | total number of four letter passwords = 6 * 6 * 6 * 6 = 1296 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 6 c 4 * 4! = 15 * 24 = 360 - - - - - - ( 2 ) therefore required value v = ( 1 ) - ( 2 ) = 1296 - 360 = 936. d |
the average expenditure of a labourer for 6 months was 85 and he fell into debt. in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. his monthly income is | "income of 6 months = ( 6 × 85 ) – debt = 510 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 780 average monthly income = 780 ÷ 10 = 78 answer d" |
what is the greatest positive integer x such that 7 ^ x is a factor of 343 ^ 10? | "343 ^ 10 = ( 7 ^ 3 ) ^ 10 = 7 ^ 30 |
in the xy - coordinate system, what is the slope of the line that goes through the point ( 4, 4 ) and is equidistant from the two points p = ( 0, 2 ) and q = ( 12, 8 )? | "first, get the middle coordinate between ( 0,2 ) and ( 12,8 )... x = 0 + ( 12 - 0 ) / 2 = 6 y = 2 + ( 8 - 2 ) / 2 = 5 second, get the slope of ( 6,5 ) and ( 4,4 ). m = 5 - 4 / 6 - 4 = 1 / 2 = 0.5 |
a sum of money is sufficient to pay b ' s wages for 12 days and c ' s wages for 24 days. the same money is sufficient to pay the wages of both for? | let the total money be $ x b ' s 1 day work = $ x / 12 c ' s 1 day work = $ x / 24 a + b 1 day work = $ x / 8 money is sufficient to pay the wages of both for 8 days answer is c |
jonathan, matthew and zac are picking strawberries from their yard. together they have picked a total of 550 strawberries. jonathan and matthew have picked 350 strawberries together. matthew and zac have picked 250 strawberries together. how many strawberries has zac picked by himself? | jonathan = matthew + zac = 550 strawberries j + m = 350 m + z = 250 use j + m = 350 to plug into the original formula ( j + m ) + z = 550 350 + z = 550 subtract 350 from each side z = 200 |
in a certain parallelogram the degree measure of one angle exceeds that of the other by 70 what is the degree measure of the smaller angle? | in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ). given: x + ( x + 70 ) = 180 - - > x = 55. |
a candidate got 35 % of the votes and lost to the rival by 1350 votes. how many votes were cast? | "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1350 10 % = 450 100 % of the votes = 4500 |
the product of two numbers is 2028 and their h. c. f. is 13. the number of such pairs is: | "explanation: let the numbers be 13 a and 13 b. then, 13 a * 13 b = 2028 = > ab = 12. now, co - primes with product 12 are ( 1, 12 ) and ( 3, 4 ). so, the required numbers are ( 13 * 1, 13 * 12 ) and ( 13 * 3, 13 * 4 ). clearly, there are 2 such pairs. answer is b" |
a train 140 m long crosses a platform 160 m long in 16 sec; find the speed of the train? | "d = 140 + 160 = 300 t = 16 s = 300 / 16 * 18 / 5 = 67.5 kmph |
a zeebra chases a tiger 5 hours after the tiger runs. zeebra takes 6 hours to reach the tiger. if the average speed of the zeebra is 55 kmph, what s the average speed of the tiger? | tiger take 11 hours and zeebra take 6 hours... then distance chased by them is 55 * 6. so speed of tiger is ( 55 * 6 ) / 11 = 30 kmph. answer is c |
if a certain coin is flipped, the probability that the coin will land heads is 1 / 2. if the coin is flipped 5 times, what is the probability that it will land heads up on the first 4 flips but not on the last flip? | p ( hhhht ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 the answer is e. |
a fruit seller had some apples. he sells 40 % and still has 420 apples. originally, he had? | "answer ∵ 60 % of n = 420 ∴ n = ( 420 x 100 ) / 60 = 700 correct |
the average age of students of a class is 15.8 years. the average age of boys in the class is 16.2 years and that of the girls is 15.4 years. the ration of the number of boys to the number of girls in the class is: | "let the ratio be k: 1. then, k * 16.2 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.2 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.4 = 1 / 1 required ratio = 1 / 1: 1 = 1: 1. |
a number is doubled and 9 is added. if resultant is trebled, it becomes 75. what is that number | "explanation: = > 3 ( 2 x + 9 ) = 75 = > 2 x + 9 = 25 = > x = 8 |
a batsman scored 210 runs which included 3 boundaries and 8 sixes. what % of his total score did he make by running between the wickets | "number of runs made by running = 210 - ( 3 x 4 + 8 x 6 ) = 210 - ( 60 ) = 150 now, we need to calculate 60 is what percent of 120. = > 150 / 210 * 100 = 71.4 % d" |
( 112 x 5 ^ 4 ) =? | "( 112 x 54 ) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 a )" |
x + ( 1 / x ) = 2 find x ^ 2 + ( 1 / x ^ 2 ) | "squaring on both sides ( x + 1 / x ) ^ 2 = 2 ^ 2 x ^ 2 + 1 / x ^ 2 = 4 - 2 x ^ 2 + 1 / x ^ 2 = 2 |
what least no. must be subtracted from 427398 so that remaining no. is divisible by 15? | "explanation: on dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted option b" |
in a box of 12 pens, a total of 3 are defective. if a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? | "# defective pens = 3 # good pens = 9 probability of the 1 st pen being good = # of favorable outcomes / # of total outcomes = 9 / 12 probability of the 2 nd pen being good = # of remaining favorable outcomes / # of total remaining outcomes = 8 / 11 total probability = 9 / 12 * 8 / 11 = 6 / 11 answer will be c" |
if a sum of money doubles itself in 15 years at simple interest, the ratepercent per annum is | "explanation: let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 15 ) = 6.67 option c" |
alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice - cream cups. the cost of each chapati is rs. 6, that of each plate of rice is rs. 45 and that of mixed vegetable is rs. 70. the amount that alok paid the cashier was rs. 883. find the cost of each ice - cream cup? | "explanation: let the cost of each ice - cream cup be rs. x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 883 96 + 225 + 490 + 6 x = 883 6 x = 72 = > x = 12. |
if a person walks at 16 km / hr instead of 8 km / hr, he would have walked 20 km more. the distance traveled by him if he walked at 16 km / hr? | "let the actual distance traveled be x km. then, x / 8 = ( x + 20 ) / 16 2 x - x = 20 = > x = 20 km. the required distance is = ( 20 + 20 ) km = 40 km |
drum x is 1 / 2 full of oil and drum y, which has twice the capacity of drum x, is 1 / 3 full of oil. if all of the oil in drum x is poured into drum y, then drum y will be filled to what capacity? | "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 3 ) y = ( 7 / 12 ) y the answer is c." |
find the area of trapezium whose parallel sides are 26 cm and 18 cm long, and the distance between them is 15 cm. | "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 26 + 18 ) * ( 15 ) = 330 cm 2 |
a train 160 m long passes a man, running at 6 kmph in the direction opposite to that of the train, in 6 seconds. the speed of the train is | "speed of train relative to man: 160 / 6 * 18 / 5 km / hr = 96 km / hr let speed of train = x therefore x + 6 = 96 x = 96 - 6 x = 90 km / hr |
an aeroplane covers a certain distance at a speed of 240 kmph in 6 hours. to cover the same distance in 1 2 / 3 hours, it must travel at a speed of: | "distance = ( 240 x 6 ) = 1440 km. speed = distance / time speed = 1440 / ( 5 / 3 ) km / hr. [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 1440 x 3 / 5 ) km / hr = 864 km / hr answer e ) 864 km / hr" |
if 9 engines consume 24 metric tonnes of coal, when each is working 8 hoursday, bow much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type? | let 3 engines of former type consume 1 unit in 1 hour. then, 4 engines of latter type consume 1 unit in 1 hour. therefore 1 engine of former type consumes ( 1 / 3 ) unit in 1 hour. 1 engine of latter type consumes ( 1 / 4 ) unit in 1 hour. let the required consumption of coal be x units. less engines, less coal consumed ( direct proportion ) more working hours, more coal consumed ( direct proportion ) less rate of consumption, less coal consumed ( direct prportion ) number of engines 9: 8 working hours 8: 13 }:: 24: x rate of consumption ( 1 / 3 ): ( 1 / 4 ) [ 9 x 8 x ( 1 / 3 ) x x ) = ( 8 x 13 x ( 1 / 4 ) x 24 ) = 24 x = 624 = x = 26. hence, the required consumption of coal = 26 metric tonnes. answer is c. |
the value of log 2 ( log 5625 ) is | solution let log 5625 = x. then, 5 x = 625 = 54 ‹ = › x = 4. let log 2 ( log 5625 ) = y. then, log 24 = y ‹ = › 2 y = 4 y; 2. answer a |
if 16 percent of the students at a certain school went to a camping trip and took more than $ 100, and 75 percent of the students who went to the camping trip did not take more than $ 100, what percentage of the students at the school went to the camping trip? | "let x be the number of students in the school. 0.16 x students went to the trip and took more than 100 $. they compose ( 100 - 75 ) = 25 % of all students who went to the trip. therefore the toal of 0.16 x / 0.25 = 0.64 x students went to the camping which is 64 %. the answer is e" |
a man sitting in a train which is traveling at 55 kmph observes that a goods train, traveling in opposite direction, takes 10 seconds to pass him. if the goods train is 320 m long, find its speed | "explanation: relative speed = 320 / 10 m / sec = ( ( 320 / 10 ) × ( 18 / 5 ) ) kmph = 115 kmph. speed of goods train = ( 115 - 55 ) kmph = 60 kmph |
a man invests some money partly in 10 % stock at 90 and partly in 5 % stock at 90. to obtain equal dividends from both, he must invest the money in the ratio: | "solution for an income of rs. 1 in 10 % stock at 90, investment = rs. ( 90 / 10 ) = rs. 9. for an income of rs. 1 in 5 % stock at 90, investment = rs. ( 90 / 5 ) = rs. 18. ∴ ratio of investments = 9: 18 = 1: 2 answer a" |
average of 10 matches is 32, how many runs one should should score to increase his average by 6 runs. | "explanation: average after 11 innings should be 38 so, required score = ( 11 * 38 ) - ( 10 * 32 ) = 418 - 320 = 98 |
solve below question 2 x + 1 = - 23 | 1. subtract 1 from both sides: 2 x + 1 - 1 = - 23 - 1 2. simplify both sides: 2 x = - 24 3. divide both sides by 2: 4. simplify both sides: x = - 12 c |
calculate 85184 ÷? = 352 | "answer let 85184 ÷ x = 242 then x = 85184 / 242 = 352. |
7.51 8.22 7.86 8.36 8.09 7.83 8.30 8.01 7.73 8.25 7.96 8.53 a vending machine is designed to dispense 8 ounces of coffee into a cup. after a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. if the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.4 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean? | mean = 8.1 standard deviation = 0.4 within 1.5 standard deviation of the mean i. e. 1.5 standard deviation above the mean = 8.1 + 1.5 * 0.4 = 8.7 and 1.5 standard deviation below the mean = 8.1 - 1.5 * 0.4 = 7.5 all values are within the range hence, 12 values fall within 1.5 sd from mean |