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on dividing 136 by a number, the quotient is 9 and the remainder is 1. find the divisor? | "d = ( d - r ) / q = ( 136 - 1 ) / 9 = 135 / 9 = 15 b )" |
a 72 gallon solution of salt and water is 10 % salt. how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume? | "amount of salt = 7.2 assume x gallons of water are added. 7.2 / 72 + x = 8 / 100 720 = 8 x + 576 8 x = 144 x = 18 correct |
the radius of a cylindrical vessel is 9 cm and height is 3 cm. find the whole surface of the cylinder? | "r = 9 h = 3 2 π r ( h + r ) = 2 * 22 / 7 * 9 ( 12 ) = 678.8 |
the simple interest on a sum of money will be rs. 600 after 10 years. if the principal is trebled after 5 years what will be the total interest at the end of the tenth year? | "p - - - 10 - - - - 600 p - - - 5 - - - - - 300 3 p - - - 5 - - - - - 900 - - - - - - = > 1200 |
a rectangular floor that measures 24 meters by 64 meters is to be covered with carpet squares that each measure 8 meters by 8 meters. if the carpet squares cost $ 24 apiece, what is the total cost for the number of carpet squares needed to cover the floor? | the width of the rectangular floor ( 24 m ) is a multiple of one side of the square ( 8 m ), and the length of the floor ( 64 m ) is also a multiple of the side of the square. so the number of carpets to cover the floor is ( 24 / 8 ) * ( 64 / 8 ) = 24. the total cost is 24 * 24 = $ 576. the answer is, therefore, b. |
what least number must be subtracted from 427751 so that remaining no. is divisible by 10 | "explanation: on dividing 427751 by 10 we get the remainder 1, so 1 should be subtracted option b" |
jim is able to sell a hand - carved statue for $ 660 which was a 20 % profit over his cost. how much did the statue originally cost him? | "cost price = 660 / 120 * 100 = 550 |
the minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. how much does the clock gain or lose in 12 hours? | after 60 minute rotation the minute hand will make an angle of 30 degree with hour hand. after that let the time required to make an overtake is t minute in this time angle covered by minute hand = ( 360 / 60 ) t = 6 t similarly angle covered by hour hand = ( 30 / 60 ) t = t / 2 so for overtake 6 t = 30 + t / 2 or t = 60 / 11 min = 5 min and 5 / 11 min = 5 min and 300 / 11 sec = 5 min and 27.273 sec so clock loses 27.273 seconds |
students at a school were on average 180 cm tall. the average female height was 170 cm, and the average male height was 184 cms. what was the ratio f of men to women? | ( a ) f = 184 x 5 + 170 x 2 = 1260. a |
average monthly income of a family of 3 earning members was rs. 735. one of the earning members died and therefore, the average income came down to rs 650. the income of the deceased was? | "answer income of the deceased = total income of 4 members - total income of remaining 3 members. = 735 x 3 - 650 x 2 rs. = 905 rs. correct |
a started a business with an investment of rs. 70000 and after 6 months b joined him investing rs. 120000. if the profit at the end of a year is rs. 52000, then the share of b is? | "ratio of investments of a and b is ( 70000 * 12 ): ( 120000 * 6 ) = 7: 6 total profit = rs. 52000 share of b = 6 / 13 ( 52000 ) = rs. 24000 |
a tank can supply water to a village for 20 days. if a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 15 days only. for how many days will the supply last if the leak drains out 20 liters per day? | "losing 10 liters per day results in a loss of 150 liters in 15 days. so, those 150 liters were for 5 days, making daily consumption of the village 30 liters per day. thus the capacity of the tank is 30 * 20 = 600 liters. losing 20 liters plus 30 liters gives 50 liters per day. at this rate the supply will last 600 / 50 = 12 days. the answer is d." |
31 of the scientists that attended a certain workshop were wolf prize laureates, and 14 of these 31 were also nobel prize laureates. of the scientists that attended that workshop and had not received the wolf prize, the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize. if 50 of the scientists attended that workshop, how many of them were nobel prize laureates? | "lets solve by creating equation.. w = 31.. total = 50.. not w = 50 - 31 = 19.. now let people who were neither be x, so out of 19 who won nobel = x + 3.. so x + x + 3 = 19 or x = 8.. so who won nobel but not wolf = x + 3 = 11.. but people who won both w and n = 13.. so total who won n = 11 + 14 = 25.. c" |
a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival. if the committee selects y / x % of the black - and - white films and all of the color films, what fraction x of the selected films are in color? | "it ' s y / xpercentnot y / x. if x = 20 and y = 10. then: 20 x = 400 black - and - white films; 6 y = 60 color films. y / x % = 10 / 20 % = 0.5 % of the black - and - white films, so 2 black - and - white films and all 60 color films, thus total of 62 films were selected. color films thus compose x = 60 / 62 = 30 / 31 of the selected films. |
if the average ( arithmetic mean ) of x + 1, x + 4, and x + 7 is 0, then x = | "( x + 1 + x + 4 + x + 7 ) / 3 = 0 = > 3 x + 12 = 0 = > x = - 4 answer a" |
for how many integers pair ( x, y ) satisfies the result ( 1 / x ) + ( ( 1 / y ) = 1 / 16 | it seems that the accepted answer is wrong, according to wolframalpha. the answer should be 31, which is n ' t even listed as a selectable answer. e |
of the female students at barkely university, 3 / 5 are on the honor roll. of the male students, 2 / 5 are on the honor roll. if 5 / 9 of the students are female, what fraction of all the students are on the honor roll? | "let the total students be 45 given 5 / 9 of the students are females = 25 then males = 4 / 9 = 20 3 / 5 of the females are on honor roll = 15 males on the honor roll = 2 / 5 = 8 total students on honor roll = 15 + 8 = 23 fraction = 23 / 45 c" |
abcd is a square. e and f are the midpoints of sides cd and bc, respectively. what is the ratio of the shaded region area to the unshaded region? | let ' s join the midpoints as shown in the figure then we ' ll get four small squares... aodx be 1 and similarly all squares.. and we can split the unit 1 into half and half as per the mid points... then shaded will be 1 + 1 / 2 + 1 / 2 + 1 / 2 = 5 / 2 and unshaded is 1 / 2 + 1 / 2 + 1 / 2 = 3 / 2.. shaded: unshaded is 5: 3.. ans option d. |
a certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. at 6: 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. at 7: 00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke? | "at 6 ' o clock, there would be 6 strikes. first strike, then a short interval, the second strike, then a short interval and so on till the 6 th strike. so there would be in all 5 intervals between 6 strikes. similarly, between 7 strikes, there would be 6 intervals. according to the question, the time spent in the strike and the interval is same. at 6 ' o clock, the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs. at 7 ' o clock, the 7 strikes and 6 intervals will take 2 * ( 7 + 6 ) = 26 secs a" |
a dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent? | "600 - - - 400 100 - - -? = > 66.7 % |
15 men can complete a piece of work in 25 days. in how many days can 20 men complete that piece of work? | "15 * 25 = 20 * x = > x = 18.75 days |
if n is a prime number greater than 5, what is the remainder when n ^ 2 is divided by 23? | "there are several algebraic ways to solve this question including the one under the spoiler. but the easiest way is as follows: since we can not have two correct answersjust pick a prime greater than 5, square it and see what would be the remainder upon division of it by 23. n = 5 - - > n ^ 2 = 49 - - > remainder upon division 49 by 23 is 3. |
the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 2 | + 5 is equal to: | "x ^ 2 - 8 x + 16 = | x - 2 | rhs can be - ve or + ve x ^ 2 - 9 x + 18 = 0 x ^ 2 - 7 x + 14 = 0 x = 7,6, 3,2 we test all 3 values in original equation, all ok. thus, sum = 7 + 6 + 3 + 2 = 18 ans ( e )" |
80 is what percent of 160? | 80 / 160 × 100 = 50 % |
the price of commodity x increases by 30 cents every year, while the price of commodity y increases by 20 cents every year. if in 2001, the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40, in which year will commodity x cost 40 cents more than the commodity y? | "the cost of commodity x increases by 10 cents per year relative to commodity y. the price of x must gain 20 + 40 = 60 cents on commodity y, which will take 6 years. the answer is a." |
a 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. what is the length of the platform? | explanation: length of the train = distance covered in crossing the post = speed × time = speed × 18 speed of the train = 300 / 18 m / s = 50 / 3 m / s time taken to cross the platform = 39 s ( 300 + x ) / ( 50 / 3 ) = 39 s where x is the length of the platform 300 + x = ( 39 × 50 ) / 3 = 650 meter x = 650 - 300 = 350 meter |
what is the remainder when 1034 * 1047 * 1050 * 1053 is divided by 33? | "take the remainder from each of 1034 / 33, 1047 / 33 and so on.. 1034 / 33 gives remainder = 11 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders. i. e = 11 * 24 * 27 * 30 break them into pairs 11 * 24 / 33 gives remainder 0 and 27 * 30 / 33 gives remainder 18 so 0 * 18 / 33 gives remainder 0. a" |
39 persons can repair a road in 24 days, working 5 hours a day. in how many days will 30 persons, working 6 hours a day, complete the work? | "let the required number of days be x. less persons, more days ( indirect proportion ) more working hours per day, less days ( indirect proportion ) persons 30: 39:: 12: x working hours / day 6: 5 30 x 6 x x = 39 x 5 x 24 x = ( 39 x 5 x 24 ) / ( 30 x 6 ) x = 26. |
two boats are heading towards each other at constant speeds of 4 miles / hr and 20 miles / hr respectively. they begin at a distance 20 miles from each other. how far are they ( in miles ) one minute before they collide? | "the question asks: how far apart will they be 1 minute = 1 / 60 hours before they collide? since the combined rate of the boats is 4 + 20 = 25 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 24 * 1 / 60 = 6 / 15 miles apart. |
1 / 0.04 is equal to | "explanation: 1 / 0.04 = ( 1 * 100 ) / 4 = 100 / 4 = 25 option c" |
a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200. if a store employee applied the 30 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder? | "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 30 emlpoyee paid =. 7 * 240 = 168 $ answer e" |
if an integer n is to be chosen at random from the integers 1 to 92, inclusive, what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8? | "n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8. thus when n is even, this whole expression will be divisible by 8. from 1 to 96, there are 46 even integers. now when ( n + 1 ) is multiple by 8, we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 46 + 12 ) / 92 = 58 / 96 = 29 / 46 ans is d" |
on dividing a number by 56, we get 27 as remainder. on dividing the same number by 8, what will be the remainder? | "number = 56 x + 27 ( ∵ since the number gives 27 as remainder on dividing by 56 ) = ( 7 × 8 × x ) + ( 3 × 8 ) + 3 hence, if the number is divided by 8, we will get 3 as remainder. |
what sum of money will produce rs. 90 as simple interest in 4 years at 3 1 / 2 percent? | "90 = ( p * 4 * 7 / 2 ) / 100 p = 642.9 |
a and b enter into a partnership. a contributed rs. 5000 for 8 months and b rs. 6000 for 5 months. find a ' s share in a total profit of rs. 8400. | explanation: ratio of capitals of a and b = ratio of their investments = 5000 × 8: 6000 × 5 = 40000: 30000 = 4: 3.: a ' s share = rs. [ ( 4 / 7 ) × 8400 ] = rs. 4800 |
two vessels a and b contain spirit and water in the ratio 5: 2 and 7: 6 respectively. find the ratio in which these mixtures be mixed to obtain a new mixture in vessel c containing spirit and water in the ratio 8: 5? | "explanation: let cost price ( cp ) of 1 litre spirit be rs. 1 quantity of spirit in 1 litre mixture from vessel a = 5 / 7 cost price ( cp ) of 1 litre mixture from vessel a = rs. = 5 / 7 quantity of spirit in 1 litre mixture from vessel b = 7 / 13 cost price ( cp ) of 1 litre mixture from vessel b = rs. = 7 / 13 quantity of spirit to be obtained in 1 litre mixture from vessel c = 8 / 13 cost price ( cp ) of 1 litre mixture from vessel c ( mean price ) = rs. = 8 / 13 = > mixture from vessel a: mixture from vessel b = 1 / 13: 9 / 91 = 7: 9 answer is d" |
company a imported 10,000 widgets made of either brass or aluminum. the widgets are painted blue, red or green. if 20 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported? | "answer a. we are told that 10 % of all imported widgets are made of brass and of those, 20 % are green and 40 % are red. since we know that there are only three colors, the remaining 40 % must be blue. 40 % blue of 20 % brass widgets leads to 8 % blue brass widgets out of the total 10,550 widgets. 10,000 / 100 * 8 = 800. answer c." |
a honey bee flies for 10 seconds, from a daisy to a rose. it immediately continues to a poppy, flying for 6 additional seconds. the distance the bee passed, flying from the daisy to the rose is 6 meters longer than the distance it passed flying from the rose to the poppy. the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. the bee flies how many meters per second from the daisy to the rose? | "let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to: rose to poppy: s + 3 = x / 6 - - - - - - - 1 daisy to rose: s = ( x + 6 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 3 m / s a" |
a rectangular lawn of dimensions 80 m * 40 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. what is the cost of traveling the two roads at rs. 3 per sq m? | "area = ( l + b â € “ d ) d ( 80 + 40 â € “ 10 ) 10 = > 1100 m 2 1100 * 3 = rs. 3300 |
there is enough provisions for 1200 girls in a hostel for 50 days. if there were 600 girls less, how long will the provision last? | "we have, m 1 d 1 = m 2 d 2 1200 * 50 = 600 * d 2 d 2 = 1200 * 50 / 600 = 100 days. |
a 50 kg metal bar made of alloy of tin and silver lost 5 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. what is the ratio of tin to silver in the bar? | "you can simply use this formula to avoid confusion: w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2. we have an overall loss ( average loss ). the average loss is 5 kg when 50 kg alloy is immersed. this is a loss of ( 5 / 50 ) * 100 = 10 %. this is aavg the loss of tin is 1.375 kg for every 10 kg. this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water. this is a 1. the loss of silver is. 375 kg for every 5 kg. this means it loses (. 375 / 5 ) * 100 = 7.5 % of its weight in water. this is a 2. weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e" |
a, b and c have rs. 300 between them, a and c together have rs. 200 and b and c rs. 350. how much does c have? | "a + b + c = 300 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 300 - - - - - - - - - - - - - - - - c = 250 |
united telephone charges a base rate of $ 7.00 for service, plus an additional charge of $ 0.25 per minute. atlantic call charges a base rate of $ 12.00 for service, plus an additional charge of $ 0.20 per minute. for what number of minutes would the bills for each telephone company be the same? | "lets take number of minutesx. given that, 7 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 100 minutes ans b" |
there are 50 students in a class. if 12 % are absent on a particular day, find the number of students present in the class. | "number of students absent on a particular day = 12 % of 50 i. e., 12 / 100 × 50 = 6 therefore, the number of students present = 50 - 6 = 44 students. |
how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 50 percent butterfat to obtain milk that is 20 percent butterfat? | "equate the fat: 0.1 x + 0.5 * 8 = 0.2 ( x + 8 ) - - > x = 24. |
can c and can в are both right circular cylinders. the radius of can c is twice the radius of can b, while the height of can c is half the height of can b. if it costs $ 4.00 to fill half of can b with a certain brand of gasoline, how much would it cost to completely fill can c with the same brand of gasoline? | let x be the radius of b and 2 h be the height of b. therefore, radius of c = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e |
a certain family has 3 sons: richard is 6 years older than david, and david is 8 years older than scott. if in 8 years, richard will be twice as old as scott, then how old was david 3 years ago? | "let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david, i. e. r = d + 6 david is 8 years older than scott i. e. d = s + 8 if in 8 years, richard will be twice as old as scott i. e. r + 8 = 2 x ( s + 8 ) i. e. r + 8 = 2 s + 16 i. e. r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore, 2 s + 8 = s + 14 i. e. s = 6 i. e. r = 20 i. e. d = 14 now, how old was david 3 years ago? i. e. d - 4 = 14 - 3 = 11 years |
6 years ago, the ratio of the ages of vimal and saroj was 6: 5. 4 years hence, the ratio of their ages will be 11: 10. what is saroj ' s age at present? | given that, six years ago, the ratio of the ages of vimal and saroj = 6: 5 hence we can assume that age of vimal six years ago = 6 x age of saroj six years ago = 5 x after 4 years, the ratio of their ages = 11: 10 ⇒ ( 6 x + 10 ): ( 5 x + 10 ) = 11: 10 ⇒ 10 ( 6 x + 10 ) = 11 ( 5 x + 10 ) ⇒ 5 x = 10 ⇒ x = 105 = 2 saroj ' s present age = ( 5 x + 6 ) = 5 × 2 + 6 = 16 answer is c. |
a boat can travel with a speed of 13 km / hr in still water. if the speed of the stream is 5 km / hr, find the time taken by the boat to go 70 km downstream. | "speed of boat in still water = 13 km / hr speed of the stream = 5 km / hr speed downstream = ( 13 + 5 ) = 18 km / hr time taken to travel 70 km downstream = 70 â „ 18 = 3.8 hours answer is b" |
if 60 % of ( x - y ) = 20 % of ( x + y ), then what percent of x is y? | "60 % of ( x - y ) = 20 % of ( x + y ) 60 / 100 ( x - y ) = 20 / 100 ( x + y ) 4 x = 8 y required percentage = y / x * 100 = 4 y / 8 y * 100 = 50 % answer is a" |
a and b undertake to do a piece of work for rs. 600. a alone can do it in 6 days while b alone can do it in 8 days. with the help of c, they finish it in 3 days.! find the share of each. | c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a: b: c = ratio of their 1 day ' s work = 1 / 6: 1 / 8: 1 / 24 = 4: 3: 1. a ’ s share = rs. ( 600 * 4 / 8 ) = rs. 300, b ' s share = rs. ( 600 * 3 / 8 ) = rs. 225. c ' s share = rs. [ 600 - ( 300 + 225 » ) = rs. 75. answer is c |
how many even integers n, such that 20 < = n < = 220 are of the form 3 k + 4, where k is any natural number? | "the first number is 22 = 16 + 6 ( 1 ). we can continue adding 6 to make a list: 22, 28, 34,... the last number is 220 = 16 + 6 ( 34 ) there are 34 numbers in the list. the answer is c." |
the edges of three metal cubes are 1 cm, 3 cm, and 4 cm respectively. a new cube is made by melting these three cubes together. what is the edge of the new cube ( in centimeters )? | the total volume is 1 ^ 3 + 3 ^ 3 + 4 ^ 3 = 92 the edge of the new cube is the cube root of 92 which is about 4.5 cm. the answer is c. |
an inspector rejects 10 % of the meters as defective. how many will he examine to reject 12? | "then, 10 % of x = 12 ( 10 / 100 ) x = 12 x = ( 12 * 100 * ) / 10 = 120 answer is b" |
a survey was sent to 60 customers, 7 of whom responded. then the survey was redesigned and sent to another 72 customers, 9 of whom responded. by approximately what percent did the response rate increase from the original survey to the redesigned survey? | "rate of first survey = 7 / 60 rate of second survey = 9 / 72 % response rate increase ( 9 / 72 - 7 / 60 ) / ( 7 / 60 ) = 7 % answer is b = 7 %" |
if the sides of a square are multiplied by 5, the area of the original square is how many times as large as the area of the resultant square? | "let x be the original length of one side. then the original area is x ^ 2. the new square has sides of length 5 x, so the area is 25 x ^ 2. the area of the original square is 1 / 25 = 4 % times the area of the new square. the answer is a." |
car a runs at the speed of 50 km / hr & reaches its destination in 6 hr. car b runs at the speed of 100 km / h & reaches its destination in 1 h. what is the respective ratio of distances covered by car a & car b? | "sol. distance travelled by car a = 50 × 6 = 300 km distance travelled by car b = 100 × 1 = 100 km ratio = 300 / 100 = 3: 1 |
a cubical block of metal weighs 8 pounds. how much will another cube of the same metal weigh if its sides are twice as long? | "for example our cube have a side 1 meter, so we have 1 cubical meter in this cube and this cubical meter weigth 6 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 8 pounds = 64 pounds so answer is e and similar but more theoretical approach: if we have sides a and b than they have equal ration with their areas: a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes: a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 8 * 8 = 64 so answer is e" |
of the final grades received by the students in a certain math course, 1 / 5 are a ' s, 1 / 4 are b ' s, 1 / 2 are c ' s, and the remaining 20 grades are d ' s. what is the number of students in the course? | "we start by creating a variable for the total number of students in the math course. we can say: t = total number of students in the math course next, we can use variable t in an equation that we translate from the given information. we are given that, of the final grades received by the students in a certain math course, 1 / 5 are a ' s, 1 / 4 are b ' s, 1 / 2 are c ' s, and the remaining 20 grades are d ' s. since this represents all the grades in the class, it represents all the students in the class. thus we know: # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 20 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have: 4 t + 5 t + 10 t + 400 = 20 t 19 t + 400 = 20 t 400 = t there are a total of 400 students in the math class. answer is e." |
how many pieces of 0.85 meteres can be cut from a rod 42.5 meteres long | explanation: we need so simple divide 42.5 / 0.85, = ( 4250 / 85 ) = 50 option c |
ratio between rahul and deepak is 5: 2, after 6 years rahul age will be 26 years. what is deepak present age. | "explanation: present age is 5 x and 2 x, = > 5 x + 6 = 26 = > x = 4 so deepak age is = 2 ( 4 ) = 8 option c" |
in what time will a train 400 m long cross an electric pole, it its speed be 144 km / hr? | "speed = 144 * 5 / 18 = 40 m / sec time taken = 400 / 40 = 10.0 sec. |
set a consists of all the prime numbers between 62 and 85. what is the range of set a? | the range of a set of data is the difference between the highest and lowest values in the set in this set, highest number = 83 lowest number = 67 range = highest - lowest = 83 - 67 = 16 option d |
a fruit seller had some apples. he sells 60 % apples and still has 300 apples. originally, he had: | "a fruit seller had some apples. he sells 60 % apples and still has 300 apples. originally, he had: a. 656 apples b. 700 apples c. 750 apples d. 780 apples 800 apples |
s ( n ) is a n - digit number formed by attaching the first n perfect squares, in order, into one integer. for example, s ( 1 ) = 1, s ( 2 ) = 14, s ( 3 ) = 149, s ( 4 ) = 14916, s ( 5 ) = 1491625, etc. how many digits w are in s ( 99 )? | "focus on the points where the number of digits in squares change: 1, 2, 3 - single digit squares. first 2 digit number is 10. 4, 5,... 9 - two digit squares. to get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10 ^ 2. so 9 ^ 2 must be the last 2 digit square. 10, 11, 12,... 31 - three digit squares. to get 31, think of 1000 - the first 4 digit number. it is not a perfect square but 900 is 30 ^ 2. 32 ^ 2 = 2 ^ 10 = 1024, the first 4 digit square. 32 - 99 - four digit squares. to get 99, think of 10,000 - the first 5 digit number which is 100 ^ 2. so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353. b" |
a candidate got 35 % of the votes and lost to the rival by 1650 votes. how many votes were cast? | "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1650 10 % = 550 100 % of the votes = 5500 |
a certain car traveled twice as many miles from town a to town b as it did from town b to town c. from town a to town b, the car averaged 8 miles per gallon, and from town b to town c, the car averaged 18 miles per gallon. what is the average miles per gallon that the car achieved on its trip from town a through town b to town c? | "ans is b given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 8 ) + ( x / 18 ) ) = 15.5 ( formula avg speed = total distance / total time )" |
the total age of a and b is 10 years more than the total age of b and c. c is how many years younger than a.? | "( a + b ) - ( b - c ) = 10 a - c = 10 answer is c" |
if the area of a circle is 25 pi square feet, find its circumference. | "the area is given by pi * r * r. hence pi * r * r = 25 pi r * r = 25; hence r = 25 feet the circumference is given by 2 * pi * r = 2 * pi * 5 = 10 pi feet correct answer a" |
excluding stoppages, the speed of a train is 67 kmph and including stoppages it is 51 kmph. of how many minutes does the train stop per hour? | "explanation: t = 16 / 67 * 60 = 14 |
the sides of a square region, measured to the nearest centimeter, are 9 centimeters long. the least possible value of the actual area of the square region is | "though there might be some technicalities concerning the termnearest ( as 7.5 is equidistant from both 7 and 8 ) the answer still should be: 7.5 ^ 2 = 56.25. |
the average runs of a cricket player of 8 innings was 24. how many runs must he make in his next innings so as to increase his average of runs by 8? | "explanation: average after 9 innings = 32 required number of runs = ( 32 * 9 ) – ( 24 * 8 ) = 288 – 192 = 96 answer d" |
if jack walked 4 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour? | distance walked in 1 hour and 15 mins = 4 miles speed per hour = distance / time = 4 / ( 5 / 4 ) = 3.2 miles per hour answer a |
yesterday it took robert 6 hours to drive from city a to city b. today it took robert 4.5 hours to drive back from city в to city a along the same route. if he had saved 30 minutes in both trips, the speed for the round trip would be 90 miles per hour. what is the distance between city a and city b? | 2 d / 90 = 9.5 ( because time = 6 + 4.5 - 1 hrs ) = > d = 430 answer - e |
a number consists of 3 digits whose sum is 10. the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. the number is: | "let the middle digit be x. then, 2 x = 10 or x = 5. so, the number is either 253 or 352. since the number increases on reversing the digits, so the hundred ' s digits is smaller than the unit ' s digit. hence, required number = 253. option b" |
how many seconds will a train 110 meters long take to cross a railway platform 165 meters long if the speed of the train is 132 kmph? | "d = 110 + 165 = 275 s = 132 * 5 / 18 = 110 / 3 mps t = 275 * 3 / 110 = 7.5 sec b ) 7.5 sec" |
2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. what is the ratio of their speeds | "explanation: we know total distance is 200 km if both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [ 110 + 90 = 200 km ] so ratio of their speed = 110: 90 = 11: 9 option a" |
50 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet. what is the area of her living room floor? | "50 % of area of the floor = 4 * 9 square feet = 36 square feet i. e. 100 % area of floor = ( 36 / 50 ) * 100 = 64.8 square feet |
a work can be finished in 13 days by ten women. the same work can be finished in fifteen days by ten men. the ratio between the capacity of a man and a woman is | work done by 10 women in 1 day = 1 / 13 work done by 1 woman in 1 day = 1 / ( 13 ã — 10 ) work done by 16 men in 1 day = 1 / 15 work done by 1 man in 1 day = 1 / ( 15 ã — 10 ) ratio of the capacity of a man and woman = 1 / ( 15 ã — 10 ): 1 / ( 13 ã — 10 ) = 1 / 15: 1 / 13 = 1 / 15: 1 / 13 = 13: 15 answer is b. |
if 213 × 16 = 3408, then 1.6 × 213.0 is equal to: | solution 1.6 × 21.3 = ( 16 / 10 x 213 ) = ( 16 x 213 / 10 ) = 3408 / 10 = 340.8. answer d |
a train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. its length is | "let the length of the train be x meters and its speed be y m / sec. they, x / y = 15 = > y = x / 15 x + 100 / 25 = x / 15 x = 150 m. |
the population of a bacteria colony doubles every day. if it was started 3 days ago with 3 bacteria and each bacteria lives for 12 days, how large is the colony today? | "9 days ago - 2 8 days ago - 4 7 days ago - 8 6 days ago - 16 5 days ago - 32 4 days ago - 64 3 days ago - 128 2 days ago - 256 yesterday - 512 today - 1024 |
the h. c. f of two numbers is 15 and their l. c. m is 3300. if one of the numbers is 225, then the other is? | "other number = ( 15 * 3300 ) / 225 = 220. |
a bag marked at $ 80 is sold for $ 68. the rate of discount is? | "rate of discount = 12 / 80 * 100 = 15 % answer is b" |
{ 5, 6, 3, 8, 4 } if we want to get the median value of the set to be 10 which value should be inserted in the set of 5 values? | median is the middle number of a sorted distribution. in case of even number of items, median will be the average of middle two values. the question asks fora new number that will cause the median of new set at 10. mentionable that given set is already sorted and number of items of new set will be 5 + 1 = 6. to get median 10, the sum of 3 th 4 th term should be 20 i. e. 3 + 7. so to keep the median 10, the new item should be > = 7 answer is b |
the area of a rhombus is equal to the area of a square whose side length is 8 cm. if one of the diagonals is 16 cm what is the length of other diagonal? | area of the square = 8 x 8 = 64 let ' l ' be the unknown diagonal 0.5 x 16 x ' l ' = 64 which gives ' l ' = 8 cm |
the cost price of 7 articles is equal to the selling price of 5 articles. what is the profit percent? | "5 * sp = 7 * cp sp = 1.4 * cp the profit percent is 40 %. the answer is d." |
in a kilometer race, a beats b by 20 meters or 10 seconds. what time does a take to complete the race? | "time taken by b run 1000 meters = ( 1000 * 10 ) / 20 = 500 sec. time taken by a = 500 - 10 = 490 sec. |
a positive number when decreased by 4 is equal to 21 times the reciprocal of the number. the number is | "sol. let the numbers be x. then, x - 4 = 21 / x ⇔ x 2 - 4 x - 21 = 0 ⇔ ( x - 7 ) ( x + 3 ) = 0 ⇔ x = 7. answer c" |
at what price must an book costing $ 47.50 be marked in order that after deducting 5 % from the list price. it may be sold at a profit of 25 % on the cost price? | "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 95 / 100 ) = 59.375 mp = 62.5" |
a car consumes 210 liters of petrol weekly. for how many days will 1470 liters of petrol be sufficient? | explanation: no explanation is available for this question! |
one type of liquid contains 20 % of water and the second type of liquid contains 35 % of water. a glass is filled with 10 parts of 1 st liquid and 4 parts of 2 nd liquid. the percentage of water in the new mixture in the glass is? | required percentage = ( 20 % of 10 + 35 % of 4 ) / 10 + 4 * 100 = 3.4 / 14 * 100 = 24.3 % answer is c |
the sum of two consecutive integers is 61. find the numbers. | "n + ( n + 1 ) = 61 2 n + 1 = 61 2 n = 60 n = 30 |
cuboid volume and base area are 144 m ^ 3 and 18 m ^ 3 respectively. find the height of a cuboid? | height of the cuboid = volume * base area = 144 / 18 = 8 metre answer is option d |
how many positive even integers less than 100 contain digits 7 or 9? | "two digit numbers: 7 at tens place: 70, 72,74, 76,78 9 at tens place: 90, 92,94, 96,98 if 7 and 9 is at units place, the number cant be even total: 5 + 5 = 10 answer e" |
in a group of 650 readers who read science fiction or literacy works or both, 250 read science fiction and 550 read literacy works. how many read both science fiction and literacy works? | "consider total number of reader n ( s u l ) = 650 people who read science fiction n ( s ) = 250 people who read literacy works n ( l ) = 550 both science fiction and literacy n ( s â ˆ © l ) =? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 650 = 250 + 550 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 800 - 650 n ( s â ˆ © l ) = 150 so people read both science fiction and literacy works are 150 |
if anangletis defined as 1 percent of 1 degree, then how many anglets are there in one half circle? | "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 180 degrees = 18,000 anglets answer - d" |
the speed of a car is 80 km in the first hour and 40 km in the second hour. what is the average speed of the car? | "s = ( 80 + 40 ) / 2 = 60 kmph |
two trains 200 m and 250 m long run at the speed of 72 kmph and 18 kmph in opposite directions in parallel tracks. the time which they take to cross each other is? | "relative speed = 72 + 18 = 90 kmph * 5 / 18 = 25 m / s distance covered in crossing each other = 200 + 250 = 450 m required time = 450 * 1 / 25 = 18 sec answer is e" |
the “ length of integer x ” refers to the number of prime factors, not necessarily distinct, that x has. ( if x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5. ) what is the greatest possible length of integer z if z < 3000? | "to maximize the length of z, we should minimize its prime base. the smallest prime is 2 and since 2 ^ 11 = 2048 < 3000, then the greatest possible length of integer z is 11. the answer is c." |