Nghengu123/Al_Challenge · Datasets at Hugging Face

id int64 14.8k 60.8k	category stringclasses 15 values	Problem stringlengths 5 4.31k	Rationale stringlengths 0 6.77k	options stringlengths 0 943	correct stringclasses 915 values
14,782	general	a man whose bowling average is 12.4 , takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?	"12.4 x + 26 / ( 5 + x ) = 12 12.4 x + 26 = 60 + 12 x x = 34 / 0.4 = 85 answer : d"	a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86	d
14,783	general	find the slope of the line perpendicular to the line y = x - 7	two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 . if m is the slope of the line perpendicular to the given line , then m × 1 = - 1 solve for m m = - 1 correct answer c ) - 1	a ) 1 , b ) 2 , c ) - 1 , d ) 4 , e ) 5	c
14,784	physics	a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be	"let the height of the building x metres . less lengthy shadow , less in the height ( direct proportion ) 40.25 : 28.75 : : 17.5 : x 40.25 * x = 28.75 * 17.5 x = ( 28.75 x 17.5 ) / 40.25 x = 12.5 answer is a ."	a ) 12.5 m , b ) 10 m , c ) 17.5 m , d ) 21.25 m , e ) 9.8 m	a
14,785	physics	the length of the bridge , which a train 160 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?	"speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 160 + x ) / 30 = 25 / 2 = = > 2 ( 160 + x ) = 750 = = > x = 215 m . answer : c"	a ) 766 m , b ) 156 m , c ) 215 m , d ) 156 m , e ) 156 m	c
14,786	gain	find the simple interest on $ 10000 at 8 % per annum for 12 months ?	"p = $ 10000 r = 8 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 8 * 1 / 100 = $ 800 answer is d"	a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 800 , e ) $ 1000	d
14,787	physics	a bus trip of 360 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?	"the time is the distance / speed . the time difference is 1 hour . 360 / v - 360 / ( v + 5 ) = 1 360 ( v + 5 ) - 360 v = ( v ) ( v + 5 ) 1800 = ( v ) ( v + 5 ) 40 * 45 = ( v ) ( v + 5 ) v = 40 mph the answer is b ."	a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55	b
14,788	probability	a bag contains 6 white marbles and 6 black marbles . if each of 6 girls and 6 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?	"first , total ways to select for all boys and girls , i . e 12 ! / ( 6 ! * 6 ! ) = 12 * 11 * 10 * 9 * 8 * 7 / 6 * 5 * 4 * 3 * 2 = 924 then there are one two way girls can have all same colors , either white or black . the number of ways in which 6 girls can select 6 white balls = 6 c 6 = 1 the number of ways in which 6 girls can select 6 black balls = 6 c 6 = 1 therefore , total favorable outcomes / total outcomes = 2 / 924 = 1 / 462 d"	a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 462 , e ) 1 / 252	d
14,789	general	john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 10 . what is the percent decrease ?	"the is always the difference between our starting and ending points . in this case , it ’ s 100 – 10 = 90 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 90 / 100 ) * 100 = ( 0.9 ) * 100 = 90 % . a"	a ) 90 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %	a
14,790	physics	if a train , travelling at a speed of 270 kmph , crosses a pole in 5 sec , then the length of train is ?	"d d = 270 * 5 / 18 * 5 = 375 m"	a ) 281 m , b ) 325 m , c ) 117 m , d ) 375 m , e ) 350 m	d
14,791	gain	an article with cost price of 280 is sold at 30 % profit . what is the selling price ?	"sp = 1.30 * 280 = 364 answer : b"	a ) 198 , b ) 364 , c ) 369 , d ) 207 , e ) 210	b
14,792	other	the ratio of three numbers is 1 : 2 : 3 and the sum of their squares is 2744 . the sum of the numbers is ?	"let the numbers be x , 2 x , 3 x then , x ^ 2 + 4 x ^ 2 + 9 x ^ 2 = 2744 14 x ^ 2 = 2744 x ^ 2 = 196 x = 14 answer is d"	a ) 10 , b ) 12 , c ) 15 , d ) 14 , e ) 9	d
14,793	general	the average of runs of a cricket player of 20 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?	"average = total runs / no . of innings = 36 so , total = average x no . of innings = 36 * 20 = 720 now increase in avg = 4 runs . so , new avg = 36 + 4 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 720 = 120 answer : e"	a ) 96 , b ) 106 , c ) 122 , d ) 116 , e ) 120	e
14,794	gain	what quantity of water should taken out to concentrate 18 liters of 40 % acidic liquid to 60 % acidic liquid ?	"required answer is = 18 ( 60 - 40 ) / 60 = 6 liters answer is e"	a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters	e
14,795	geometry	the monthly rent of a shop of dimension 20 feet × 18 feet is rs . 1440 . what is the annual rent per square foot of the shop ?	sol . monthly rent per square feet = 1440 / ( 20 * 18 ) = 4 & annual rent per square feet = 12 * 4 = 48 answer : a	['a ) 48', 'b ) 56', 'c ) 68', 'd ) 87', 'e ) 92']	a
14,796	general	a 100 - litre mixture of milk and water contains 36 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?	"in 100 l mixture we have 36 l milk and 64 l water . hence m and w are in the ratio of 9 : 16 . x l of solution has been removed . hence we have 36 - 9 / 25 x of milk and 64 - 16 / 25 x of water . for calculation simplicity multiply and divide 9 / 25 x by 4 we get 36 / 100 x since this procedure is repeated 2 times . this was my equation 25 = 36 * ( 36 - 36 / 100 x ) ^ 2 ) / ( 36 ) ^ 2 by solving it . we get x = 100 / 6 or 50 / 3 or 16.67 answer : b"	a ) 17.5 litres , b ) 16.67 litres , c ) 17.67 litres , d ) 16.5 litres , e ) 16 litres	b
14,797	physics	two pipes a and b can fill a tank in 10 hour and 15 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?	"part filled by a in 1 hour = 1 / 10 part filled by b in 1 hour = 1 / 15 part filled by a + b in 1 hour = 1 / 10 + 1 / 15 = 1 / 6 both the pipes will together will fill the tank in 6 hours . answer is b"	a ) 2 hrs , b ) 6 hrs , c ) 5 hrs , d ) 4 hrs , e ) 1 hr	b
14,798	gain	a milk man has 20 liters of milk . if he mixes 25 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :	"explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 45 % . answer : b"	a ) 20 % , b ) 45 % , c ) 33.33 % , d ) 18 % , e ) none of these	b
14,799	physics	a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 25 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?	"explanation : he covered 5 km in 1 hour , so he might cover 25 km in 5 hours . but he took 10 hours . he would have saved 10 â € “ 5 = 5 hours . answer : b"	a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7	b
14,800	physics	two trains running in opposite directions cross a pole placed on the platform in 47 seconds and 31 seconds respectively . if they cross each other in 33 seconds , what is the ratio of their speeds ?	explanation : let the speed of the trains be x and y respectively length of train 1 = 47 x length of train 2 = 31 y relative speed = x + y time taken to cross each other = 33 s = > = 33 = > ( 47 x + 31 y ) = 33 ( x + y ) = > 14 x = 2 y = > x / y = 2 / 14 = 1 / 7 = 1 : 7 answer : a	a ) 1 : 7 , b ) 8 : 7 , c ) 6 : 7 , d ) 6 : 5 , e ) 4 : 7	a
14,801	physics	jane makes toy bears . when she works with an assistant , she makes 44 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?	"let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 57.6 bears per 36 hours a week or 1.6 bears / hr ( [ 40 bears * 1.44 ] / [ 40 hrs * . 90 ] ) . [ ( 1.6 - 1 ) / 1 ] * 100 % = 60 % answer : b"	a ) 20 % , b ) 60 % , c ) 100 % , d ) 180 % , e ) 200 %	b
14,802	general	when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 6.12 , what is the value of y ?	"guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 6.12 and remainder is 6 so . 12 x y = 6 hence y = 50 ans c"	a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12	c
14,803	general	a large box contains 18 small boxes and each small box contains 28 chocolate bars . how many chocolate bars are in the large box ?	"the only thing you have to do is a simple multiply we have : 18 * 28 = 504 correct answer is : e ) 504"	a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 504	e
14,804	gain	the population of a town is 8000 . it decreases annually at the rate of 10 % p . a . what will be its population after 2 years ?	"formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 90 / 100 ã — 90 / 100 = 6480 answer : e"	a ) 5100 , b ) 5120 , c ) 5200 , d ) 5400 , e ) 6480	e
14,805	general	in a race where 18 cars are running , the chance that car x will win is 1 / 8 , that y will win is 1 / 12 and that z will win is 1 / 6 . assuming that a dead heat is impossible , find the chance that one of them will win .	"required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 8 + 1 / 12 + 1 / 6 = 3 / 8 answer : d"	a ) 1 / 140 , b ) 1 / 180 , c ) 3 / 12 , d ) 3 / 8 , e ) 57 / 120	d
14,806	general	5301 x 13 = ?	"append 0 before and after : 053010 calculation : 1 x 3 + 0 = 3 ( take 3 as ones digit of the product ) 0 x 3 + 1 = 1 ( take 1 tens digit of the product ) 3 x 3 + 0 = 9 ( take 9 hundreds digit of the product ) 5 x 3 + 3 = 18 ( take 8 as thousands digit of the product , carry over 1 ) 0 x 3 + 5 = 5 ; 5 + 1 = 6 ( take 6 as ten thousands digits of the product ) so , 5301 x 13 = 68913 answer is e ."	a ) 89136 , b ) 31986 , c ) 68910 , d ) 53113 , e ) 68913	e
14,807	general	a man is 32 years older than his son . in six years , his age will be twice the age of his son . the present age of this son is	"explanation : let ' s son age is x , then father age is x + 32 . = > 2 ( x + 6 ) = ( x + 32 + 6 ) = > 2 x + 12 = x + 38 = > x = 26 years answer : option a"	a ) 26 years , b ) 27 years , c ) 28 years , d ) 29 years , e ) 30 years	a
14,808	general	the average weight of 8 person ' s increases by 2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?	"total weight increased = ( 8 x 2 ) kg = 16 kg . weight of new person = ( 65 + 16 ) kg = 81 kg . c )"	a ) 70 kg , b ) 80 kg , c ) 81 kg , d ) 90 kg , e ) 91 kg	c
14,809	general	on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price r per glass on the second day ?	"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."	a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45	d
14,810	general	469157 * 9999	"explanation : 469157 * ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 option c"	a ) 1691100843 , b ) 4591100843 , c ) 4691100843 , d ) 3691100843 , e ) none of these	c
14,811	general	how many positive integers between 1 and 300 are there such that they are multiples of 21 ?	"multiples of 21 = 21 , 42,63 , - - - - - 294 number of multiples of 21 = > 21 * 14 = 294 answer is a"	a ) 14 , b ) 16 , c ) 17 , d ) 13 , e ) 15	a
14,812	gain	a man took loan from a bank at the rate of 4 % p . a . s . i . after 10 years he had to pay rs . 2000 interest only for the period . the principal amount borrowed by him was ?	"principal = ( 100 * 2000 ) / ( 4 * 10 ) = rs . 5000 answer : a"	a ) 5000 , b ) 4500 , c ) 3200 , d ) 6000 , e ) 1592	a
14,813	general	on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with 5 times the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.80 per glass on the first day , what was the price per glass on the second day ?	on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 5 units of water was used to make 6 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 6 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 6 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 6 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.8 = 6 * x - - > x = $ 0.27 . answer : b .	a ) $ 015 , b ) $ 0.27 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45	b
14,814	gain	boy sells a book for rs . 720 he gets a loss of 10 % , to gain 10 % , what should be the sp ?	"cost price = 720 / 90 x 100 = 800 to gain 10 % = 800 x 10 / 100 = 80 sp = cp + gain = 800 + 80 = 880 answer : b"	a ) 430 , b ) 880 , c ) 550 , d ) 590 , e ) 600	b
14,815	general	10 ^ 222 ÷ 10 ^ 220 = ?	10 ^ 222 ÷ 10 ^ 220 = 10 ^ ( 222 - 220 ) = 10 ^ 2 = 100 answer is c	a ) 10 , b ) 1000 , c ) 100 , d ) 10000 , e ) 100000	c
14,816	physics	a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec . what is the length of the platform ?	"speed = 300 / 24 = 25 / 2 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 25 / 2 = > x = 187.5 m . answer : c"	a ) 389 m , b ) 350 m , c ) 187.5 m , d ) 299 m , e ) 219.5 m	c
14,817	gain	a watch was sold at a loss of 16 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?	"84 % 104 % - - - - - - - - 20 % - - - - 140 100 % - - - - ? = > rs . 700 answer : a"	a ) 700 , b ) 882 , c ) 799 , d ) 778 , e ) 901	a
14,818	general	the price of a consumer good increased by pp % during 20122012 and decreased by 1212 % during 20132013 . if no other change took place in the price of the good and the price of the good at the end of 20132013 was 1010 % higher than the price at the beginning of 20122012 , what was the value of pp ?	as per question = > price was simple 10 percent greater hence x [ 1 + 10 / 100 ] must be the final price . equating the two we get = > x [ 110 / 100 ] = x [ 1 + p / 100 ] [ 88 / 100 ] = > 44 p + 4400 = 5500 = > 44 p = 1100 = > p = 1100 / 44 = > 100 / 4 = > 25 . so p must be 25 answer : d	a ) − 2 % , b ) 2 % , c ) 22 % , d ) 25 % , e ) can not be determined	d
14,819	other	two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 7 : 5 and 1 : 2 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?	"mixture a has a total of 7 + 5 = 12 parts . if in the final mixture this represents 6 parts , then the total number of parts in mixture b should be ( 12 / 6 ) * 3 = 6 . so , we should take of mixture b a quantity with 3 and 6 parts , respectively . this will give us in the final mixture ( 7 + 3 ) : ( 5 + 6 ) , which means 10 : 11 answer d ."	a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 10 : 11 , e ) 7 : 9	d
14,820	general	when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 5 . what is the value of 7 y – x ?	"( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 5 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y + 1 = x 7 y - x = - 1 the answer is d ."	a ) 2 , b ) 1 , c ) 0 , d ) - 1 , e ) - 2	d
14,821	general	a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 25 % impurities to the product . find the net profit percentage of the dealer ?	"the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 25 % impurities to the product . it means that he is selling $ 5 worth of product for $ 6.25 . so his profit is $ 6.25 - $ 4 = $ 2.25 and his profit percent is ( 2.25 / 4 ) * 100 = 56.25 % answer : - d"	a ) 44 % , b ) 40 % , c ) 50 % , d ) 56.25 % , e ) 36.25 %	d
14,822	physics	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 answer : c"	a ) 227 , b ) 299 , c ) 330 , d ) 161 , e ) 212	c
14,823	general	what is the next number 12 13 15 17 111 113 117 119 123 129 ?	131 . these are the first 10 prime numbers ( 2 , 3 , 5 . . . ) prefixed with a 1 answer : d	a ) 154 , b ) 220 , c ) 129 , d ) 131 , e ) 224	d
14,824	gain	paul has to secure 50 % marks to clear his exam of class 7 th . he got 50 marks and failed by 10 marks . what is the maximum marks ?	c 120 to pass the exam ravish needs 50 + 10 = 60 marks . = > ( 60 / 50 ) * 100 = 120	a ) 100 , b ) 110 , c ) 120 , d ) 210 , e ) 200	c
14,825	physics	in a kilometer race , a beats b by 54 meters or 12 seconds . what time does a take to complete the race ?	"time taken by b run 1000 meters = ( 1000 * 12 ) / 54 = 222 sec . time taken by a = 224 - 12 = 212 sec . answer : a"	a ) 212 , b ) 190 , c ) 277 , d ) 181 , e ) 122	a
14,826	gain	in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 42 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 42 , so 0.14 * { total } = 42 - - > { total } = 300 . answer : d ."	a ) 70 , b ) 245 , c ) 150 , d ) 300 , e ) 350	d
14,827	gain	. in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 70 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?	registered voters = 100 d = 60 r = 40 70 % of d ( 60 ) = 42 20 % of r ( 40 ) = 8 total voter % of registered voters = 50 / 100 50 % ans a	a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %	a
14,828	general	in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 200 bricks in the wall , how many bricks does the bottom row contain ?	"the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 200 5 x - 10 = 200 5 x = 190 x = 38 answer : e"	a ) 42 , b ) 35 , c ) 40 , d ) 33 , e ) 38	e
14,829	gain	find the simple interest on rs . 520 for 7 months at 8 paisa per month ?	"i = ( 520 * 7 * 8 ) / 100 = 291 answer : c"	a ) 277 , b ) 270 , c ) 291 , d ) 266 , e ) 121	c
14,830	general	a teacher grades students ’ 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 70 , how many questions did student a answer correctly ?	"let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 70 ( subtracting twice of incorrect from correct ) 3 x = 270 x = 90 answer : b"	a ) 55 , b ) 90 , c ) 73 , d ) 82 , e ) 91	b
14,831	general	an exam consists of 2 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 70 % is a passing grade , what is the probability that brian passes ?	"if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 1 / 16 . a"	a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16	a
14,832	general	on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.48 per glass on the first day , what was the price per glass on the second day ?	"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.48 = 3 * x - - > x = $ 0.32 . answer : d ."	a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.32 , e ) $ 0.45	d
14,833	general	an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 44.5 meters . how many times did the ball bounce ?	"division of total diatance travelled will be 16 + 16 + 8 + 4 + 0.5 ans : 4"	a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9	a
14,834	gain	sheela deposits rs . 3400 in bank savings account . if this is 15 % of her monthly income . what is her monthly income in ?	"explanation : 15 % of income = rs . 3400 100 % of income = 3400 x 100 / 15 = rs . 22666 answer : a"	a ) 22666 , b ) 20000 , c ) 25000 , d ) 22235 , e ) none of these	a
14,835	general	if x is an integer such that 0 < x < 7 , 0 < x < 15 , 5 > x > – 1 , 3 > x > 0 , and x + 2 < 4 , then x is	"0 < x < 7 , 0 < x < 15 , 5 > x > – 1 3 > x > 0 x < 2 from above : 0 < x < 2 - - > x = 1 . answer : a ."	a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5	a
14,836	general	a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes john can make using this recipe ?	"less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"	a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9	a
14,837	general	in digging a pond 20 m * 15 m * 5 m the volumes of the soil extracted will be ?	"20 * 15 * 5 = 1500 answer : d"	a ) 3387 , b ) 1000 , c ) 2866 , d ) 1500 , e ) 1121	d
14,838	geometry	the area of sector of a circle whose radius is 18 metro and whose angle at the center is 42 â ° is ?	"42 / 360 * 22 / 7 * 18 * 18 = 118.8 m 2 answer : d"	a ) 52.6 , b ) 52.9 , c ) 52.8 , d ) 118.8 , e ) 52.2	d
14,839	general	a number of 44 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?	"to maximize # of boxes we should minimize marbles per box : 13 * 3 + 1 * 5 = 44 - - > 13 + 1 = 14 . answer b"	a ) 10 , b ) 14 , c ) 15 , d ) 16 , e ) 17	b
14,840	physics	a train 110 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .	explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 110 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 1980 < = > x = 61 speed of the train is 61 kmph . answer : option d	a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 61 kmph , e ) 70 kmph	d
14,841	gain	if the simple interest on a certain sum of money for 5 years is one – fifth of the sum , then the rate of interest per annum is	"explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 5 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 5 ) = 20 / 5 = 4 % answer : option d"	a ) 4 % , b ) 7 % , c ) 6 % , d ) 4 % , e ) 3 %	d
14,842	general	a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 210 , then how much amount should c pay as his share of rent ?	"a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 210 × 9 / 35 = 6 × 9 = 54 answer is a"	a ) 54 , b ) 45 , c ) 25 , d ) 15 , e ) 55	a
14,843	general	mary and mike enter into a partnership by investing $ 900 and $ 100 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1600 more than mike did , what was the profit made by their business in that year ?	"explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 9 : 1 . i . e . , 90 % of 2 x would go to mary and 10 % of 2 x would go to mike . hence , mary would get ( 90 - 10 ) % of 2 x more than mike or 80 % of 2 x = $ 1600 i . e . , ( 60 / 100 ) * 2 x = 1600 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : e"	a ) $ 3500 , b ) $ 3400 , c ) $ 3300 , d ) $ 3200 , e ) $ 3000	e
14,844	other	three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 180 . what is their h . c . f . ?	"let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 180 x = 15 hcf of 2 x , 3 x and 4 x = x = 15 the answer is a ."	a ) 15 , b ) 20 , c ) 40 , d ) 60 , e ) 70	a
14,845	general	the sum of the average ( arithmetic mean ) of the even integers from 0 to 100 inclusive and the average ( arithmetic mean ) of the even integers from 0 to 50 inclusive ?	so , according to a mean of a set of even numbers from 0 to 100 = ( 0 + 100 ) / 2 = 50 and mean of a set of even numbers from 0 to 50 = ( 0 + 50 ) / 2 = 25 sum = 50 + 25 = 75 answer : d .	a ) 15 , b ) 125 , c ) 25 , d ) 75 , e ) 50	d
14,846	general	dick and jane each saved $ 1000 in 1989 . in 1990 dick saved 15 percent more than in 1989 , and together he and jane saved a total of $ 2000 . approximately what percent less did jane save in 1990 than in 1989 ?	1990 dick saved = $ 1150 jane saved = $ 850 ( jane saved $ 150 less than she did the prior year ) jane saved approximately $ 150 / 1000 $ ( 15 % ) less in 1990 answer : d	a ) 3 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 18 %	d
14,847	general	what is the unit digit in 8 ^ 100 ?	unit digit in 8 ^ 100 = unit digit in [ ( 8 ^ 4 ) ^ 25 ] but unit digit in 8 ^ 4 = 6 unit digit 8 ^ 100 = 6 answer is c	a ) 0 , b ) 1 , c ) 6 , d ) 3 , e ) 5	c
14,848	general	the product z of two prime numbers is between 20 and 56 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 14 but less than 30 then what is z ?	"the smallest possible product is 51 which is 3 * 17 . all other products are too big . the answer is d ."	a ) 26 , b ) 35 , c ) 39 , d ) 51 , e ) 55	d
14,849	geometry	10 business executives and 3 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?	"there are 10 business exec and in each handshake 2 business execs are involved . hence 10 c 2 = 45 also , each of 10 exec will shake hand with every 3 other chairmen for total of 30 handshake . total = 45 + 30 = 75 ans : e"	a ) 144 , b ) 131 , c ) 115 , d ) 90 , e ) 75	e
14,850	physics	at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 4 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?	"i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 4 ) = $ 160 total revenue : 1000 + 160 = $ 1160 the answer is b ."	a ) $ 1220 , b ) $ 1160 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880	b
14,851	gain	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 % answer : b"	a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 45 %	b
14,852	general	difference between two numbers is 5 , 6 times of the smaller lacks by 8 from the 4 times of the greater . find the numbers ?	explanation : x – y = 5 4 x – 6 y = 8 x = 11 y = 6 d )	a ) 5,1 , b ) 7,3 , c ) 9,8 , d ) 11,6 , e ) 13,7	d
14,853	general	at the beginning of 1992 , maria ' s stock portfolio was worth $ 600000 . during 1992 , the portfolio ' s value increased by 95 % . during the next year , the portfolio increased its worth by only 5 % . what was maria ' s portfolio worth , in dollars , by the end of 1993 ?	by the end of 1992 , the port folio worth is 1.95 * ( $ 600 k ) by 1993 , the portfolio is 1.05 * ( 1.95 * $ 600 k ) = $ 1 , 228,500 answer : d	a ) 1 , 180000 , b ) 1 , 200000 , c ) 1 , 200300 , d ) 1 , 228500 , e ) 1 , 330,000	d
14,854	general	how many positive integers , from 2 to 100 , inclusive , are not divisible by even integers greater than 1 ?	"the no will be of the form 2 ^ n to achieve this . since any other form will have odd no in the prime factorization . hence we need to find solution of n for equation - 1 < 2 ^ n < 101 . 2 ^ 6 = 64 , 2 ^ 7 - 128 hence n can take values from 1 to 6 . hence ans - ( b ) 6"	a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 50	b
14,855	general	jen has a jar of jam , and she ate 1 / 3 of the jam for lunch . if jen ate 1 / 7 of the remaining jam for dinner , what fraction of the jam was left after dinner ?	let x be the amount of jam at the beginning . after lunch , the remaining jam was ( 2 / 3 ) x . after dinner , the remaining jam was ( 6 / 7 ) ( 2 / 3 ) x = ( 4 / 7 ) x . the answer is c .	a ) 2 / 7 , b ) 3 / 7 , c ) 4 / 7 , d ) 9 / 14 , e ) 11 / 14	c
14,856	general	if r is the least positive integer that is divisible by every integer from 12 to 16 inclusive , then r / 13 is =	the integer should be divisible by : 12 , 13 , 14 , 15 and 16 , that is 3 * 2 ^ 2 , 13 , 2 * 7 , 3 * 5 and 2 ^ 4 . the least common multiple of these integers is the product of 13 , 7 , 5 , 3 and 2 ^ 4 . then , r / 13 is ( 13 * 7 * 5 * 3 * 2 ^ 4 ) / 13 = 7 * 5 * 3 * 16 = 1680 . answer : c .	a ) 40320 , b ) 21840 , c ) 1680 , d ) 840 , e ) 240	c
14,857	geometry	a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 800 square feet , what is the total length of the fence , in feet ?	"two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 800 ie x ^ 2 = 400 ie x = 20 l = 40 w = 20 total length of fence = 2 * 20 + 40 = 80 my answer is b"	a ) 40 , b ) 80 , c ) 100 , d ) 120 , e ) 200	b
14,858	probability	jane and thomas are among the 7 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ?	"the total number of ways to choose 4 people from 7 is 7 c 4 = 35 . the number of committees without jane or thomas is 5 c 4 = 5 . there are 35 - 5 = 30 possible committees which include jane and / or thomas . the answer is a ."	a ) 30 , b ) 45 , c ) 55 , d ) 65 , e ) 70	a
14,859	general	the guests at a football banquet consumed a total of 327 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?	to minimize one quantity maximize other . 163 * 2 ( max possible amount of food a guest could consume ) = 326 pounds , so there must be more than 163 guests , next integer is 164 . answer : e .	a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164	e
14,860	general	at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 52 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 44 ¢ ?	if the average price is 52 , then mary has 6 oranges and 4 apples ( a ratio of 3 : 2 ) . for the average price to be 44 , the ratio should be 1 : 4 . mary must put back 5 oranges . the answer is e .	a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5	e
14,861	gain	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 answer : option c"	a ) a ) 600 , b ) b ) 700 , c ) c ) 800 , d ) d ) 900 , e ) e ) 1000	c
14,862	geometry	the volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is :	sol . required volume = volume of a sphere of radius 1 cm = [ 4 / 3 ∏ * 1 * 1 * 1 ] cm ³ = 4 / 3 ∏ cm ³ answer b	['a ) 3 / 4 ∏', 'b ) 4 / 3 ∏', 'c ) 5 ∏', 'd ) 5 / 9 ∏', 'e ) none']	b
14,863	physics	a train 240 m long passes a pole in 24 seconds . how long will it take to pass a platform 650 m long ?	speed = ( 240 / 24 ) m / sec = 10 m / sec . therefore , required time = ( 240 + 650 ) / 10 sec = 89 sec . answer is e .	a ) 65 , b ) 80 , c ) 85 , d ) 82 , e ) 89	e
14,864	gain	the cost of an article is decreased by 10 % . if the original cost is $ 100 , find the decrease cost .	"original cost = $ 100 decrease in it = 10 % of $ 100 = 10 / 100 ã — 100 = 1000 / 100 = $ 10 therefore , decrease cost = $ 100 - $ 10 = $ 90 answer : e"	a ) 33 , b ) 11 , c ) 68 , d ) 36 , e ) 90	e
14,865	general	what is the sum of all the multiples of 3 between 30 and 80 ?	"you first have to know all the multiples of 3 between 30 and 80 . they are 3 , 6,9 , 12,15 , 18,21 , 24,27 , 30,33 , 36,39 , 42,45 , 48,51 , 54,57 , 60,63 , 66,69 , 72,75 , and 78 . if you add all these numbers together , you get 1053 . final answer : c"	a ) 2103 , b ) 2106 , c ) 1053 , d ) 1252 , e ) 1535	c
14,866	geometry	in may , the grounds keeper at spring lake golf club built a circular green with an area of 81 π square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?	"area of circle 81 pi sq feet = pi r ^ 2 therefore r = 9 now green radi doubled i . e r = 18 area = 324 pi e"	a ) 100 pi , b ) 144 pi , c ) 196 pi , d ) 256 pi , e ) 324 pi	e
14,867	general	when the positive integer a is divided by 11 , the quotient is b and the remainder 3 . when a is divided by 19 , the remainder is also 3 . what is the remainder when b is divided by 19 ?	any number which when divided by divisor d 1 , d 2 , etc . leaving same remainderrtakes the form ofk + r where k = lcm ( d 1 , d 2 ) in this case the divisors are 1119 and remainder is 3 . so lcm ( 11,19 ) = 209 so n = 209 + 3 = 212 also a = d 1 q + 3 ; which means d 1 q = 209 d 1 = 11 therefore q = 19 and ( b divided by 19 ) 19 / 19 leaves remainder 0 . answer is e	a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0	e
14,868	general	i chose a number and divide it by 8 . then i subtracted 100 from the result and got 6 . what was the number i chose ?	"solution : let x be the number i chose , then x / 8 â ˆ ’ 100 = 6 x / 8 = 106 x = 848 answer e"	a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 848	e
14,869	general	( 4300231 ) - ? = 2535618	"let 4300231 - x = 2535618 then x = 4300231 - 2535618 = 1764613 answer is c"	a ) 1865113 , b ) 1775123 , c ) 1764613 , d ) 1675123 , e ) none of them	c
14,870	physics	the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 40 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?	"point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 40 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 15 . sub x = 15 either in ( x + 5 ) * 30 or in x * 40 to get the distance , which is 600 . so the correct choice is c ."	a ) 20 ft , b ) 25 ft , c ) 600 ft , d ) 900 ft , e ) 1000 ft	c
14,871	general	the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 40 percent of b , what is the value of m / x ?	a / b = 4 / 5 m / x = ( 3 / 5 ) * 5 / ( 5 / 4 ) * 4 = 3 / 5 the answer is e .	a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 5	e
14,872	general	evaluate : 434 - 12 * 3 * 2 = ?	"according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 434 - 12 * 3 * 2 = 434 - 8 = 426 correct answer a"	a ) 426 , b ) 526 , c ) 626 , d ) 726 , e ) 826	a
14,873	general	- 64 * 29 + 468 = ?	= > - 64 * ( 30 - 1 ) + 468 ; = > - ( 64 * 30 ) + 64 + 468 ; = > - 1920 + 532 = - 1388 . correct option : d	a ) 1430 , b ) 1302 , c ) - 2801 , d ) - 1388 , e ) none of these	d
14,874	general	a sum of money lent out at s . i . amounts to a total of $ 480 after 2 years and to $ 680 after a further period of 5 years . what was the initial sum of money that was invested ?	"s . i for 5 years = $ 680 - $ 480 = $ 200 the s . i . is $ 40 / year s . i . for 2 years = $ 80 principal = $ 480 - $ 80 = $ 400 the answer is c ."	a ) $ 360 , b ) $ 380 , c ) $ 400 , d ) $ 420 , e ) $ 440	c
14,875	general	the population of bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1000 to 500000 bacteria ?	2000 ^ 12000 ^ 22000 ^ 32000 ^ 4 . . . . . . . 2000 ^ 9 population increases in this sequence taking 9 * 2 = 18 answer : d	a ) 10 , b ) 12 , c ) 14 , d ) 18 , e ) 20	d
14,876	geometry	the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 972 sq m , then what is the breadth of the rectangular plot ?	"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 972 3 b 2 = 972 b 2 = 324 b = 18 m . answer : option c"	a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 14	c
14,877	gain	victor gets 80 % marks in examinations . if these are 240 marks , find the maximum marks .	"let the maximum marks be m then 80 % of m = 240 ⇒ 80 / 100 × m = 240 ⇒ m = ( 240 × 100 ) / 80 ⇒ m = 24000 / 80 ⇒ m = 300 therefore , maximum marks in the examinations are 300 answer : b"	a ) 334 , b ) 300 , c ) 376 , d ) 288 , e ) 271	b
14,878	general	4 car rental agencies a , b , c and d rented a plot for parking their cars during the night . a parked 15 cars for 12 days , b parked 12 cars for 20 days , c parked 18 cars for 18 days and d parked 16 cars for 15 days . if a paid rs . 1125 as rent for parking his cars , what is the total rent paid by all the 4 agencies ?	the ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15 = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60 let us consider the four amounts to be 45 k , 60 k , 81 k and 60 k respectively . the total rent paid by the four agencies = 45 k + 60 k + 81 k + 60 k = 246 k it is given that a paid rs . 1125 45 k = 1125 = > k = 25 246 k = 246 ( 25 ) = rs . 6150 thus the total rent paid by all the four agencies is rs . 6150 . answer : d	a ) rs . 6152 , b ) rs . 6159 , c ) rs . 6156 , d ) rs . 6150 , e ) rs . 6196	d
14,879	physics	a can finish a work in 18 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?	b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 18 * 1 / 3 ) = 6 days . correct option : c	a ) 5 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these	c
14,880	general	how many integers from 10 to 180 , inclusive , are divisible by 3 but not divisible by 7 ?	"we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 10 to 180 , inclusive is ( 168 - 21 ) / 21 + 1 = 8 ; 57 - 8 = 49 . answer : b ."	a ) 45 , b ) 49 , c ) 50 , d ) 52 , e ) 56	b
14,881	general	on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number r of races we need to conduct to get the top 3 fastest horses ?	"r = 7 is the correct answer . good solution buneul . b"	a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11	b

14,782

general

a man whose bowling average is 12.4 , takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?

"12.4 x + 26 / ( 5 + x ) = 12 12.4 x + 26 = 60 + 12 x x = 34 / 0.4 = 85 answer : d"

a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86

d

14,783

general

find the slope of the line perpendicular to the line y = x - 7

two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 . if m is the slope of the line perpendicular to the given line , then m × 1 = - 1 solve for m m = - 1 correct answer c ) - 1

a ) 1 , b ) 2 , c ) - 1 , d ) 4 , e ) 5

c

14,784

physics

a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be

"let the height of the building x metres . less lengthy shadow , less in the height ( direct proportion ) 40.25 : 28.75 : : 17.5 : x 40.25 * x = 28.75 * 17.5 x = ( 28.75 x 17.5 ) / 40.25 x = 12.5 answer is a ."

a ) 12.5 m , b ) 10 m , c ) 17.5 m , d ) 21.25 m , e ) 9.8 m

a

14,785

physics

the length of the bridge , which a train 160 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?

"speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 160 + x ) / 30 = 25 / 2 = = > 2 ( 160 + x ) = 750 = = > x = 215 m . answer : c"

a ) 766 m , b ) 156 m , c ) 215 m , d ) 156 m , e ) 156 m

c

14,786

gain

find the simple interest on $ 10000 at 8 % per annum for 12 months ?

"p = $ 10000 r = 8 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 8 * 1 / 100 = $ 800 answer is d"

a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 800 , e ) $ 1000

d

14,787

physics

a bus trip of 360 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?

"the time is the distance / speed . the time difference is 1 hour . 360 / v - 360 / ( v + 5 ) = 1 360 ( v + 5 ) - 360 v = ( v ) ( v + 5 ) 1800 = ( v ) ( v + 5 ) 40 * 45 = ( v ) ( v + 5 ) v = 40 mph the answer is b ."

a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55

b

14,788

probability

a bag contains 6 white marbles and 6 black marbles . if each of 6 girls and 6 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?

"first , total ways to select for all boys and girls , i . e 12 ! / ( 6 ! * 6 ! ) = 12 * 11 * 10 * 9 * 8 * 7 / 6 * 5 * 4 * 3 * 2 = 924 then there are one two way girls can have all same colors , either white or black . the number of ways in which 6 girls can select 6 white balls = 6 c 6 = 1 the number of ways in which 6 girls can select 6 black balls = 6 c 6 = 1 therefore , total favorable outcomes / total outcomes = 2 / 924 = 1 / 462 d"

a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 462 , e ) 1 / 252

d

14,789

general

john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 10 . what is the percent decrease ?

"the is always the difference between our starting and ending points . in this case , it ’ s 100 – 10 = 90 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 90 / 100 ) * 100 = ( 0.9 ) * 100 = 90 % . a"

a ) 90 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %

a

14,790

physics

if a train , travelling at a speed of 270 kmph , crosses a pole in 5 sec , then the length of train is ?

"d d = 270 * 5 / 18 * 5 = 375 m"

a ) 281 m , b ) 325 m , c ) 117 m , d ) 375 m , e ) 350 m

d

14,791

gain

an article with cost price of 280 is sold at 30 % profit . what is the selling price ?

"sp = 1.30 * 280 = 364 answer : b"

a ) 198 , b ) 364 , c ) 369 , d ) 207 , e ) 210

b

14,792

other

the ratio of three numbers is 1 : 2 : 3 and the sum of their squares is 2744 . the sum of the numbers is ?

"let the numbers be x , 2 x , 3 x then , x ^ 2 + 4 x ^ 2 + 9 x ^ 2 = 2744 14 x ^ 2 = 2744 x ^ 2 = 196 x = 14 answer is d"

a ) 10 , b ) 12 , c ) 15 , d ) 14 , e ) 9

d

14,793

general

the average of runs of a cricket player of 20 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?

"average = total runs / no . of innings = 36 so , total = average x no . of innings = 36 * 20 = 720 now increase in avg = 4 runs . so , new avg = 36 + 4 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 720 = 120 answer : e"

a ) 96 , b ) 106 , c ) 122 , d ) 116 , e ) 120

e

14,794

gain

what quantity of water should taken out to concentrate 18 liters of 40 % acidic liquid to 60 % acidic liquid ?

"required answer is = 18 ( 60 - 40 ) / 60 = 6 liters answer is e"

a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters

e

14,795

geometry

the monthly rent of a shop of dimension 20 feet × 18 feet is rs . 1440 . what is the annual rent per square foot of the shop ?

sol . monthly rent per square feet = 1440 / ( 20 * 18 ) = 4 & annual rent per square feet = 12 * 4 = 48 answer : a

['a ) 48', 'b ) 56', 'c ) 68', 'd ) 87', 'e ) 92']

a

14,796

general

a 100 - litre mixture of milk and water contains 36 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?

"in 100 l mixture we have 36 l milk and 64 l water . hence m and w are in the ratio of 9 : 16 . x l of solution has been removed . hence we have 36 - 9 / 25 x of milk and 64 - 16 / 25 x of water . for calculation simplicity multiply and divide 9 / 25 x by 4 we get 36 / 100 x since this procedure is repeated 2 times . this was my equation 25 = 36 * ( 36 - 36 / 100 x ) ^ 2 ) / ( 36 ) ^ 2 by solving it . we get x = 100 / 6 or 50 / 3 or 16.67 answer : b"

a ) 17.5 litres , b ) 16.67 litres , c ) 17.67 litres , d ) 16.5 litres , e ) 16 litres

b

14,797

physics

two pipes a and b can fill a tank in 10 hour and 15 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?

"part filled by a in 1 hour = 1 / 10 part filled by b in 1 hour = 1 / 15 part filled by a + b in 1 hour = 1 / 10 + 1 / 15 = 1 / 6 both the pipes will together will fill the tank in 6 hours . answer is b"

a ) 2 hrs , b ) 6 hrs , c ) 5 hrs , d ) 4 hrs , e ) 1 hr

b

14,798

gain

a milk man has 20 liters of milk . if he mixes 25 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :

"explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 45 % . answer : b"

a ) 20 % , b ) 45 % , c ) 33.33 % , d ) 18 % , e ) none of these

b

14,799

physics

a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 25 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?

"explanation : he covered 5 km in 1 hour , so he might cover 25 km in 5 hours . but he took 10 hours . he would have saved 10 â € “ 5 = 5 hours . answer : b"

a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7

b

14,800

physics

two trains running in opposite directions cross a pole placed on the platform in 47 seconds and 31 seconds respectively . if they cross each other in 33 seconds , what is the ratio of their speeds ?

explanation : let the speed of the trains be x and y respectively length of train 1 = 47 x length of train 2 = 31 y relative speed = x + y time taken to cross each other = 33 s = > = 33 = > ( 47 x + 31 y ) = 33 ( x + y ) = > 14 x = 2 y = > x / y = 2 / 14 = 1 / 7 = 1 : 7 answer : a

a ) 1 : 7 , b ) 8 : 7 , c ) 6 : 7 , d ) 6 : 5 , e ) 4 : 7

a

14,801

physics

jane makes toy bears . when she works with an assistant , she makes 44 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?

"let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 57.6 bears per 36 hours a week or 1.6 bears / hr ( [ 40 bears * 1.44 ] / [ 40 hrs * . 90 ] ) . [ ( 1.6 - 1 ) / 1 ] * 100 % = 60 % answer : b"

a ) 20 % , b ) 60 % , c ) 100 % , d ) 180 % , e ) 200 %

b

14,802

general

when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 6.12 , what is the value of y ?

"guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 6.12 and remainder is 6 so . 12 x y = 6 hence y = 50 ans c"

a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12

c

14,803

general

a large box contains 18 small boxes and each small box contains 28 chocolate bars . how many chocolate bars are in the large box ?

"the only thing you have to do is a simple multiply we have : 18 * 28 = 504 correct answer is : e ) 504"

a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 504

e

14,804

gain

the population of a town is 8000 . it decreases annually at the rate of 10 % p . a . what will be its population after 2 years ?

"formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 90 / 100 ã — 90 / 100 = 6480 answer : e"

a ) 5100 , b ) 5120 , c ) 5200 , d ) 5400 , e ) 6480

e

14,805

general

in a race where 18 cars are running , the chance that car x will win is 1 / 8 , that y will win is 1 / 12 and that z will win is 1 / 6 . assuming that a dead heat is impossible , find the chance that one of them will win .

"required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 8 + 1 / 12 + 1 / 6 = 3 / 8 answer : d"

a ) 1 / 140 , b ) 1 / 180 , c ) 3 / 12 , d ) 3 / 8 , e ) 57 / 120

d

14,806

general

5301 x 13 = ?

"append 0 before and after : 053010 calculation : 1 x 3 + 0 = 3 ( take 3 as ones digit of the product ) 0 x 3 + 1 = 1 ( take 1 tens digit of the product ) 3 x 3 + 0 = 9 ( take 9 hundreds digit of the product ) 5 x 3 + 3 = 18 ( take 8 as thousands digit of the product , carry over 1 ) 0 x 3 + 5 = 5 ; 5 + 1 = 6 ( take 6 as ten thousands digits of the product ) so , 5301 x 13 = 68913 answer is e ."

a ) 89136 , b ) 31986 , c ) 68910 , d ) 53113 , e ) 68913

e

14,807

general

a man is 32 years older than his son . in six years , his age will be twice the age of his son . the present age of this son is

"explanation : let ' s son age is x , then father age is x + 32 . = > 2 ( x + 6 ) = ( x + 32 + 6 ) = > 2 x + 12 = x + 38 = > x = 26 years answer : option a"

a ) 26 years , b ) 27 years , c ) 28 years , d ) 29 years , e ) 30 years

a

14,808

general

the average weight of 8 person ' s increases by 2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?

"total weight increased = ( 8 x 2 ) kg = 16 kg . weight of new person = ( 65 + 16 ) kg = 81 kg . c )"

a ) 70 kg , b ) 80 kg , c ) 81 kg , d ) 90 kg , e ) 91 kg

c

14,809

general

on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price r per glass on the second day ?

"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."

a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45

d

14,810

general

469157 * 9999

"explanation : 469157 * ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 option c"

a ) 1691100843 , b ) 4591100843 , c ) 4691100843 , d ) 3691100843 , e ) none of these

c

14,811

general

how many positive integers between 1 and 300 are there such that they are multiples of 21 ?

"multiples of 21 = 21 , 42,63 , - - - - - 294 number of multiples of 21 = > 21 * 14 = 294 answer is a"

a ) 14 , b ) 16 , c ) 17 , d ) 13 , e ) 15

a

14,812

gain

a man took loan from a bank at the rate of 4 % p . a . s . i . after 10 years he had to pay rs . 2000 interest only for the period . the principal amount borrowed by him was ?

"principal = ( 100 * 2000 ) / ( 4 * 10 ) = rs . 5000 answer : a"

a ) 5000 , b ) 4500 , c ) 3200 , d ) 6000 , e ) 1592

a

14,813

general

on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with 5 times the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.80 per glass on the first day , what was the price per glass on the second day ?

on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 5 units of water was used to make 6 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 6 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 6 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 6 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.8 = 6 * x - - > x = $ 0.27 . answer : b .

a ) $ 015 , b ) $ 0.27 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45

b

14,814

gain

boy sells a book for rs . 720 he gets a loss of 10 % , to gain 10 % , what should be the sp ?

"cost price = 720 / 90 x 100 = 800 to gain 10 % = 800 x 10 / 100 = 80 sp = cp + gain = 800 + 80 = 880 answer : b"

a ) 430 , b ) 880 , c ) 550 , d ) 590 , e ) 600

b

14,815

general

10 ^ 222 ÷ 10 ^ 220 = ?

10 ^ 222 ÷ 10 ^ 220 = 10 ^ ( 222 - 220 ) = 10 ^ 2 = 100 answer is c

a ) 10 , b ) 1000 , c ) 100 , d ) 10000 , e ) 100000

c

14,816

physics

a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec . what is the length of the platform ?

"speed = 300 / 24 = 25 / 2 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 25 / 2 = > x = 187.5 m . answer : c"

a ) 389 m , b ) 350 m , c ) 187.5 m , d ) 299 m , e ) 219.5 m

c

14,817

gain

a watch was sold at a loss of 16 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?

"84 % 104 % - - - - - - - - 20 % - - - - 140 100 % - - - - ? = > rs . 700 answer : a"

a ) 700 , b ) 882 , c ) 799 , d ) 778 , e ) 901

a

14,818

general

the price of a consumer good increased by pp % during 20122012 and decreased by 1212 % during 20132013 . if no other change took place in the price of the good and the price of the good at the end of 20132013 was 1010 % higher than the price at the beginning of 20122012 , what was the value of pp ?

as per question = > price was simple 10 percent greater hence x [ 1 + 10 / 100 ] must be the final price . equating the two we get = > x [ 110 / 100 ] = x [ 1 + p / 100 ] [ 88 / 100 ] = > 44 p + 4400 = 5500 = > 44 p = 1100 = > p = 1100 / 44 = > 100 / 4 = > 25 . so p must be 25 answer : d

a ) − 2 % , b ) 2 % , c ) 22 % , d ) 25 % , e ) can not be determined

d

14,819

other

two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 7 : 5 and 1 : 2 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?

"mixture a has a total of 7 + 5 = 12 parts . if in the final mixture this represents 6 parts , then the total number of parts in mixture b should be ( 12 / 6 ) * 3 = 6 . so , we should take of mixture b a quantity with 3 and 6 parts , respectively . this will give us in the final mixture ( 7 + 3 ) : ( 5 + 6 ) , which means 10 : 11 answer d ."

a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 10 : 11 , e ) 7 : 9

d

14,820

general

when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 5 . what is the value of 7 y – x ?

"( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 5 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y + 1 = x 7 y - x = - 1 the answer is d ."

a ) 2 , b ) 1 , c ) 0 , d ) - 1 , e ) - 2

d

14,821

general

a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 25 % impurities to the product . find the net profit percentage of the dealer ?

"the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 25 % impurities to the product . it means that he is selling $ 5 worth of product for $ 6.25 . so his profit is $ 6.25 - $ 4 = $ 2.25 and his profit percent is ( 2.25 / 4 ) * 100 = 56.25 % answer : - d"

a ) 44 % , b ) 40 % , c ) 50 % , d ) 56.25 % , e ) 36.25 %

d

14,822

physics

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 answer : c"

a ) 227 , b ) 299 , c ) 330 , d ) 161 , e ) 212

c

14,823

general

what is the next number 12 13 15 17 111 113 117 119 123 129 ?

131 . these are the first 10 prime numbers ( 2 , 3 , 5 . . . ) prefixed with a 1 answer : d

a ) 154 , b ) 220 , c ) 129 , d ) 131 , e ) 224

d

14,824

gain

paul has to secure 50 % marks to clear his exam of class 7 th . he got 50 marks and failed by 10 marks . what is the maximum marks ?

c 120 to pass the exam ravish needs 50 + 10 = 60 marks . = > ( 60 / 50 ) * 100 = 120

a ) 100 , b ) 110 , c ) 120 , d ) 210 , e ) 200

c

14,825

physics

in a kilometer race , a beats b by 54 meters or 12 seconds . what time does a take to complete the race ?

"time taken by b run 1000 meters = ( 1000 * 12 ) / 54 = 222 sec . time taken by a = 224 - 12 = 212 sec . answer : a"

a ) 212 , b ) 190 , c ) 277 , d ) 181 , e ) 122

a

14,826

gain

in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 42 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 42 , so 0.14 * { total } = 42 - - > { total } = 300 . answer : d ."

a ) 70 , b ) 245 , c ) 150 , d ) 300 , e ) 350

d

14,827

gain

. in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 70 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?

registered voters = 100 d = 60 r = 40 70 % of d ( 60 ) = 42 20 % of r ( 40 ) = 8 total voter % of registered voters = 50 / 100 50 % ans a

a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %

a

14,828

general

in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 5 rows in all and a total of 200 bricks in the wall , how many bricks does the bottom row contain ?

"the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 = 200 5 x - 10 = 200 5 x = 190 x = 38 answer : e"

a ) 42 , b ) 35 , c ) 40 , d ) 33 , e ) 38

e

14,829

gain

find the simple interest on rs . 520 for 7 months at 8 paisa per month ?

"i = ( 520 * 7 * 8 ) / 100 = 291 answer : c"

a ) 277 , b ) 270 , c ) 291 , d ) 266 , e ) 121

c

14,830

general

a teacher grades students ’ 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 70 , how many questions did student a answer correctly ?

"let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 70 ( subtracting twice of incorrect from correct ) 3 x = 270 x = 90 answer : b"

a ) 55 , b ) 90 , c ) 73 , d ) 82 , e ) 91

b

14,831

general

an exam consists of 2 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 70 % is a passing grade , what is the probability that brian passes ?

"if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 1 / 16 . a"

a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16

a

14,832

general

on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.48 per glass on the first day , what was the price per glass on the second day ?

"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.48 = 3 * x - - > x = $ 0.32 . answer : d ."

a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.32 , e ) $ 0.45

d

14,833

general

an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 44.5 meters . how many times did the ball bounce ?

"division of total diatance travelled will be 16 + 16 + 8 + 4 + 0.5 ans : 4"

a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9

a

14,834

gain

sheela deposits rs . 3400 in bank savings account . if this is 15 % of her monthly income . what is her monthly income in ?

"explanation : 15 % of income = rs . 3400 100 % of income = 3400 x 100 / 15 = rs . 22666 answer : a"

a ) 22666 , b ) 20000 , c ) 25000 , d ) 22235 , e ) none of these

a

14,835

general

if x is an integer such that 0 < x < 7 , 0 < x < 15 , 5 > x > – 1 , 3 > x > 0 , and x + 2 < 4 , then x is

"0 < x < 7 , 0 < x < 15 , 5 > x > – 1 3 > x > 0 x < 2 from above : 0 < x < 2 - - > x = 1 . answer : a ."

a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5

a

14,836

general

a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes john can make using this recipe ?

"less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"

a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9

a

14,837

general

in digging a pond 20 m * 15 m * 5 m the volumes of the soil extracted will be ?

"20 * 15 * 5 = 1500 answer : d"

a ) 3387 , b ) 1000 , c ) 2866 , d ) 1500 , e ) 1121

d

14,838

geometry

the area of sector of a circle whose radius is 18 metro and whose angle at the center is 42 â ° is ?

"42 / 360 * 22 / 7 * 18 * 18 = 118.8 m 2 answer : d"

a ) 52.6 , b ) 52.9 , c ) 52.8 , d ) 118.8 , e ) 52.2

d

14,839

general

a number of 44 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?

"to maximize # of boxes we should minimize marbles per box : 13 * 3 + 1 * 5 = 44 - - > 13 + 1 = 14 . answer b"

a ) 10 , b ) 14 , c ) 15 , d ) 16 , e ) 17

b

14,840

physics

a train 110 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .

explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 110 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 1980 < = > x = 61 speed of the train is 61 kmph . answer : option d

a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 61 kmph , e ) 70 kmph

d

14,841

gain

if the simple interest on a certain sum of money for 5 years is one – fifth of the sum , then the rate of interest per annum is

"explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 5 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 5 ) = 20 / 5 = 4 % answer : option d"

a ) 4 % , b ) 7 % , c ) 6 % , d ) 4 % , e ) 3 %

d

14,842

general

a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 210 , then how much amount should c pay as his share of rent ?

"a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 210 × 9 / 35 = 6 × 9 = 54 answer is a"

a ) 54 , b ) 45 , c ) 25 , d ) 15 , e ) 55

a

14,843

general

mary and mike enter into a partnership by investing $ 900 and $ 100 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1600 more than mike did , what was the profit made by their business in that year ?

"explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 9 : 1 . i . e . , 90 % of 2 x would go to mary and 10 % of 2 x would go to mike . hence , mary would get ( 90 - 10 ) % of 2 x more than mike or 80 % of 2 x = $ 1600 i . e . , ( 60 / 100 ) * 2 x = 1600 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : e"

a ) $ 3500 , b ) $ 3400 , c ) $ 3300 , d ) $ 3200 , e ) $ 3000

e

14,844

other

three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 180 . what is their h . c . f . ?

"let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 180 x = 15 hcf of 2 x , 3 x and 4 x = x = 15 the answer is a ."

a ) 15 , b ) 20 , c ) 40 , d ) 60 , e ) 70

a

14,845

general

the sum of the average ( arithmetic mean ) of the even integers from 0 to 100 inclusive and the average ( arithmetic mean ) of the even integers from 0 to 50 inclusive ?

so , according to a mean of a set of even numbers from 0 to 100 = ( 0 + 100 ) / 2 = 50 and mean of a set of even numbers from 0 to 50 = ( 0 + 50 ) / 2 = 25 sum = 50 + 25 = 75 answer : d .

a ) 15 , b ) 125 , c ) 25 , d ) 75 , e ) 50

d

14,846

general

dick and jane each saved $ 1000 in 1989 . in 1990 dick saved 15 percent more than in 1989 , and together he and jane saved a total of $ 2000 . approximately what percent less did jane save in 1990 than in 1989 ?

1990 dick saved = $ 1150 jane saved = $ 850 ( jane saved $ 150 less than she did the prior year ) jane saved approximately $ 150 / 1000 $ ( 15 % ) less in 1990 answer : d

a ) 3 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 18 %

d

14,847

general

what is the unit digit in 8 ^ 100 ?

unit digit in 8 ^ 100 = unit digit in [ ( 8 ^ 4 ) ^ 25 ] but unit digit in 8 ^ 4 = 6 unit digit 8 ^ 100 = 6 answer is c

a ) 0 , b ) 1 , c ) 6 , d ) 3 , e ) 5

c

14,848

general

the product z of two prime numbers is between 20 and 56 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 14 but less than 30 then what is z ?

"the smallest possible product is 51 which is 3 * 17 . all other products are too big . the answer is d ."

a ) 26 , b ) 35 , c ) 39 , d ) 51 , e ) 55

d

14,849

geometry

10 business executives and 3 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?

"there are 10 business exec and in each handshake 2 business execs are involved . hence 10 c 2 = 45 also , each of 10 exec will shake hand with every 3 other chairmen for total of 30 handshake . total = 45 + 30 = 75 ans : e"

a ) 144 , b ) 131 , c ) 115 , d ) 90 , e ) 75

e

14,850

physics

at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 4 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?

"i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 4 ) = $ 160 total revenue : 1000 + 160 = $ 1160 the answer is b ."

a ) $ 1220 , b ) $ 1160 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880

b

14,851

gain

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 % answer : b"

a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 45 %

b

14,852

general

difference between two numbers is 5 , 6 times of the smaller lacks by 8 from the 4 times of the greater . find the numbers ?

explanation : x – y = 5 4 x – 6 y = 8 x = 11 y = 6 d )

a ) 5,1 , b ) 7,3 , c ) 9,8 , d ) 11,6 , e ) 13,7

d

14,853

general

at the beginning of 1992 , maria ' s stock portfolio was worth $ 600000 . during 1992 , the portfolio ' s value increased by 95 % . during the next year , the portfolio increased its worth by only 5 % . what was maria ' s portfolio worth , in dollars , by the end of 1993 ?

by the end of 1992 , the port folio worth is 1.95 * ( $ 600 k ) by 1993 , the portfolio is 1.05 * ( 1.95 * $ 600 k ) = $ 1 , 228,500 answer : d

a ) 1 , 180000 , b ) 1 , 200000 , c ) 1 , 200300 , d ) 1 , 228500 , e ) 1 , 330,000

d

14,854

general

how many positive integers , from 2 to 100 , inclusive , are not divisible by even integers greater than 1 ?

"the no will be of the form 2 ^ n to achieve this . since any other form will have odd no in the prime factorization . hence we need to find solution of n for equation - 1 < 2 ^ n < 101 . 2 ^ 6 = 64 , 2 ^ 7 - 128 hence n can take values from 1 to 6 . hence ans - ( b ) 6"

a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 50

b

14,855

general

jen has a jar of jam , and she ate 1 / 3 of the jam for lunch . if jen ate 1 / 7 of the remaining jam for dinner , what fraction of the jam was left after dinner ?

let x be the amount of jam at the beginning . after lunch , the remaining jam was ( 2 / 3 ) x . after dinner , the remaining jam was ( 6 / 7 ) ( 2 / 3 ) x = ( 4 / 7 ) x . the answer is c .

a ) 2 / 7 , b ) 3 / 7 , c ) 4 / 7 , d ) 9 / 14 , e ) 11 / 14

c

14,856

general

if r is the least positive integer that is divisible by every integer from 12 to 16 inclusive , then r / 13 is =

the integer should be divisible by : 12 , 13 , 14 , 15 and 16 , that is 3 * 2 ^ 2 , 13 , 2 * 7 , 3 * 5 and 2 ^ 4 . the least common multiple of these integers is the product of 13 , 7 , 5 , 3 and 2 ^ 4 . then , r / 13 is ( 13 * 7 * 5 * 3 * 2 ^ 4 ) / 13 = 7 * 5 * 3 * 16 = 1680 . answer : c .

a ) 40320 , b ) 21840 , c ) 1680 , d ) 840 , e ) 240

c

14,857

geometry

a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 800 square feet , what is the total length of the fence , in feet ?

"two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 800 ie x ^ 2 = 400 ie x = 20 l = 40 w = 20 total length of fence = 2 * 20 + 40 = 80 my answer is b"

a ) 40 , b ) 80 , c ) 100 , d ) 120 , e ) 200

b

14,858

probability

jane and thomas are among the 7 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ?

"the total number of ways to choose 4 people from 7 is 7 c 4 = 35 . the number of committees without jane or thomas is 5 c 4 = 5 . there are 35 - 5 = 30 possible committees which include jane and / or thomas . the answer is a ."

a ) 30 , b ) 45 , c ) 55 , d ) 65 , e ) 70

a

14,859

general

the guests at a football banquet consumed a total of 327 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?

to minimize one quantity maximize other . 163 * 2 ( max possible amount of food a guest could consume ) = 326 pounds , so there must be more than 163 guests , next integer is 164 . answer : e .

a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164

e

14,860

general

at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 52 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 44 ¢ ?

if the average price is 52 , then mary has 6 oranges and 4 apples ( a ratio of 3 : 2 ) . for the average price to be 44 , the ratio should be 1 : 4 . mary must put back 5 oranges . the answer is e .

a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5

e

14,861

gain

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 answer : option c"

a ) a ) 600 , b ) b ) 700 , c ) c ) 800 , d ) d ) 900 , e ) e ) 1000

c

14,862

geometry

the volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is :

sol . required volume = volume of a sphere of radius 1 cm = [ 4 / 3 ∏ * 1 * 1 * 1 ] cm ³ = 4 / 3 ∏ cm ³ answer b

['a ) 3 / 4 ∏', 'b ) 4 / 3 ∏', 'c ) 5 ∏', 'd ) 5 / 9 ∏', 'e ) none']

b

14,863

physics

a train 240 m long passes a pole in 24 seconds . how long will it take to pass a platform 650 m long ?

speed = ( 240 / 24 ) m / sec = 10 m / sec . therefore , required time = ( 240 + 650 ) / 10 sec = 89 sec . answer is e .

a ) 65 , b ) 80 , c ) 85 , d ) 82 , e ) 89

e

14,864

gain

the cost of an article is decreased by 10 % . if the original cost is $ 100 , find the decrease cost .

"original cost = $ 100 decrease in it = 10 % of $ 100 = 10 / 100 ã — 100 = 1000 / 100 = $ 10 therefore , decrease cost = $ 100 - $ 10 = $ 90 answer : e"

a ) 33 , b ) 11 , c ) 68 , d ) 36 , e ) 90

e

14,865

general

what is the sum of all the multiples of 3 between 30 and 80 ?

"you first have to know all the multiples of 3 between 30 and 80 . they are 3 , 6,9 , 12,15 , 18,21 , 24,27 , 30,33 , 36,39 , 42,45 , 48,51 , 54,57 , 60,63 , 66,69 , 72,75 , and 78 . if you add all these numbers together , you get 1053 . final answer : c"

a ) 2103 , b ) 2106 , c ) 1053 , d ) 1252 , e ) 1535

c

14,866

geometry

in may , the grounds keeper at spring lake golf club built a circular green with an area of 81 π square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?

"area of circle 81 pi sq feet = pi r ^ 2 therefore r = 9 now green radi doubled i . e r = 18 area = 324 pi e"

a ) 100 pi , b ) 144 pi , c ) 196 pi , d ) 256 pi , e ) 324 pi

e

14,867

general

when the positive integer a is divided by 11 , the quotient is b and the remainder 3 . when a is divided by 19 , the remainder is also 3 . what is the remainder when b is divided by 19 ?

any number which when divided by divisor d 1 , d 2 , etc . leaving same remainderrtakes the form ofk + r where k = lcm ( d 1 , d 2 ) in this case the divisors are 1119 and remainder is 3 . so lcm ( 11,19 ) = 209 so n = 209 + 3 = 212 also a = d 1 q + 3 ; which means d 1 q = 209 d 1 = 11 therefore q = 19 and ( b divided by 19 ) 19 / 19 leaves remainder 0 . answer is e

a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0

e

14,868

general

i chose a number and divide it by 8 . then i subtracted 100 from the result and got 6 . what was the number i chose ?

"solution : let x be the number i chose , then x / 8 â ˆ ’ 100 = 6 x / 8 = 106 x = 848 answer e"

a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 848

e

14,869

general

( 4300231 ) - ? = 2535618

"let 4300231 - x = 2535618 then x = 4300231 - 2535618 = 1764613 answer is c"

a ) 1865113 , b ) 1775123 , c ) 1764613 , d ) 1675123 , e ) none of them

c

14,870

physics

the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 40 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?

"point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 40 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 15 . sub x = 15 either in ( x + 5 ) * 30 or in x * 40 to get the distance , which is 600 . so the correct choice is c ."

a ) 20 ft , b ) 25 ft , c ) 600 ft , d ) 900 ft , e ) 1000 ft

c

14,871

general

the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 40 percent of b , what is the value of m / x ?

a / b = 4 / 5 m / x = ( 3 / 5 ) * 5 / ( 5 / 4 ) * 4 = 3 / 5 the answer is e .

a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 5

e

14,872

general

evaluate : 434 - 12 * 3 * 2 = ?

"according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 434 - 12 * 3 * 2 = 434 - 8 = 426 correct answer a"

a ) 426 , b ) 526 , c ) 626 , d ) 726 , e ) 826

a

14,873

general

- 64 * 29 + 468 = ?

= > - 64 * ( 30 - 1 ) + 468 ; = > - ( 64 * 30 ) + 64 + 468 ; = > - 1920 + 532 = - 1388 . correct option : d

a ) 1430 , b ) 1302 , c ) - 2801 , d ) - 1388 , e ) none of these

d

14,874

general

a sum of money lent out at s . i . amounts to a total of $ 480 after 2 years and to $ 680 after a further period of 5 years . what was the initial sum of money that was invested ?

"s . i for 5 years = $ 680 - $ 480 = $ 200 the s . i . is $ 40 / year s . i . for 2 years = $ 80 principal = $ 480 - $ 80 = $ 400 the answer is c ."

a ) $ 360 , b ) $ 380 , c ) $ 400 , d ) $ 420 , e ) $ 440

c

14,875

general

the population of bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1000 to 500000 bacteria ?

2000 ^ 12000 ^ 22000 ^ 32000 ^ 4 . . . . . . . 2000 ^ 9 population increases in this sequence taking 9 * 2 = 18 answer : d

a ) 10 , b ) 12 , c ) 14 , d ) 18 , e ) 20

d

14,876

geometry

the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 972 sq m , then what is the breadth of the rectangular plot ?

"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 972 3 b 2 = 972 b 2 = 324 b = 18 m . answer : option c"

a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 14

c

14,877

gain

victor gets 80 % marks in examinations . if these are 240 marks , find the maximum marks .

"let the maximum marks be m then 80 % of m = 240 ⇒ 80 / 100 × m = 240 ⇒ m = ( 240 × 100 ) / 80 ⇒ m = 24000 / 80 ⇒ m = 300 therefore , maximum marks in the examinations are 300 answer : b"

a ) 334 , b ) 300 , c ) 376 , d ) 288 , e ) 271

b

14,878

general

4 car rental agencies a , b , c and d rented a plot for parking their cars during the night . a parked 15 cars for 12 days , b parked 12 cars for 20 days , c parked 18 cars for 18 days and d parked 16 cars for 15 days . if a paid rs . 1125 as rent for parking his cars , what is the total rent paid by all the 4 agencies ?

the ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15 = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60 let us consider the four amounts to be 45 k , 60 k , 81 k and 60 k respectively . the total rent paid by the four agencies = 45 k + 60 k + 81 k + 60 k = 246 k it is given that a paid rs . 1125 45 k = 1125 = > k = 25 246 k = 246 ( 25 ) = rs . 6150 thus the total rent paid by all the four agencies is rs . 6150 . answer : d

a ) rs . 6152 , b ) rs . 6159 , c ) rs . 6156 , d ) rs . 6150 , e ) rs . 6196

d

14,879

physics

a can finish a work in 18 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?

b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 18 * 1 / 3 ) = 6 days . correct option : c

a ) 5 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these

c

14,880

general

how many integers from 10 to 180 , inclusive , are divisible by 3 but not divisible by 7 ?

"we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 10 to 180 , inclusive is ( 168 - 21 ) / 21 + 1 = 8 ; 57 - 8 = 49 . answer : b ."

a ) 45 , b ) 49 , c ) 50 , d ) 52 , e ) 56

b

14,881

general

on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number r of races we need to conduct to get the top 3 fastest horses ?

"r = 7 is the correct answer . good solution buneul . b"

a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11

b